A triangular prism has a net as shown below.
4m
5m
5m
3m
What is the surface area of this triangular prism?

20 points if you help me out!

Answers

Answer 1

Answer: 72 m²

Step-by-step explanation:


Related Questions

Using the Pythagorean Theorem, what is the correct equation setup for a right triangle with side lengths measuring 7 in, 25 in, and 24 in?

A. 25^2 + 24^2 = 7^2

B. 7^2 + 25^2 = 24^2

C. 7^2 + 24^2 = 25^2

D. 24^2 + 25^2 = 7^2

Answers

Hence, 7 + 24 = 25 is a valid equation, and C is the correct response as the right triangle with sides of 7 inches, 25 inches, and 24 inches.

what is Pythagoras theorem ?

A right quadrilateral relationship between its sides is described by the Pythagorean Theorem, a fundamental theorem of geometry. According to this rule, the hypotenuse's square value, which is the side that forms the right angle, is the same as the total of the squared that compose the other two sides. In other words, the following is how the theorem can be expressed for a quadrilateral with leg of length a, b, and c and a hypotenuse of length c: [tex]a^2 + b^2 = c^2[/tex] . Although it's believed that the Greeks and romans and Indians knew about this theorem before the ancient Greek philosopher Plato, who is recognized with discovering it, gave it its name.

given

The Pythagorean Theorem's equation setup for a right triangle is as follows: [tex]a^2 + b^2 = c^2[/tex]

where c is the length of the hypotenuse and a, b, and c are the lengths of the right triangle's legs.

Right triangle with sides of 7 inches, 25 inches, and 24 inches is shown. Its legs are 7 inches and 24 inches, and its hypotenuse is 25 inches. Hence, we may construct the equation as follows:

[tex]7^2 + 24^2 = 25^2[/tex]

When we simplify this equation, we obtain:

49 + 576 = 625

625 = 625

Hence, 7 + 24 = 25 is a valid equation, and C is the correct response as the right triangle with sides of 7 inches, 25 inches, and 24 inches.

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What is the greatest common what is the greatest common factor of 6a2b2 and 15a4b37

a
3ab
b
3a4b3
с
6ab
d
3a2b2

Answers

The greatest common what is the greatest common factor of 6a2b2 and 15a4b37 is option d.

To find the greatest common factor (GCF) of 6a^2b^2, 15a^4b^3, 7a^3b, and 3a^2b^2, follow these steps:

Step 1: Find the GCF of the numerical coefficients: The GCF of 6, 15, 7, and 3 is 1.

Step 2: Find the GCF of the 'a' terms: The lowest power of 'a' is a^2, so the GCF is a^2.

Step 3: Find the GCF of the 'b' terms: The lowest power of 'b' is b, so the GCF is b.

Combine the results from steps 1, 2, and 3: The GCF of 6a^2b^2, 15a^4b^3, 7a^3b, and 3a^2b^2 is 1a^2b.

Therefore, the GCF of 6a^2b^2 and 15a^4b^3 is 3a^2b^2, which is option (d).

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Calculate the area.....................................

Answers

Area for triangle = 32ft
Area for rectangle = 240ft
Total area = 272ft squared

A sequence can be generated by using an=an−1+7, where a1=4 and n is a whole number greater than 1. What are the first 3 terms in the sequence? 7, 11, 15 7, 28, 112 4, 11, 18 4, 28, 196

Answers

To generate the sequence, we start with a1 = 4, and then use the formula an = an-1 + 7 for n > 1.

So, to find the first 3 terms of the sequence, we can use the formula:

a2 = a1 + 7 = 4 + 7 = 11

a3 = a2 + 7 = 11 + 7 = 18

The first 3 terms of the sequence are 4, 11, and 18.

So, the answer is 4, 11, 18, which corresponds to the third option.

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25. A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm, find the volume of the frustum. ​

Answers

The volume of the frustum is approximately 634.3 cubic centimeters.

How to find the volume?

Let the radius of the smaller cone be 'r' and the radius of the bigger cone be 'R'.

Since the height of the smaller cone is 8 cm and its volume is 160 cm³, we have:

1/3 * π * r² * 8 = 160

r² = 60/π

r ≈ 4.03 cm

Now, using similar triangles, we can find the radius 'R' of the bigger cone:

(R - r)/16 = R/24

24R - 24r = 16R

R = 2r/3

R ≈ 2.69 cm

Therefore, the volume of the frustum is:

1/3 * π * (2.69² + 2.69*4.03 + 4.03²) * 16 - 1/3 * π * 4.03² * 8

≈ 634.3 cm³

So, the volume of the frustum is approximately 634.3 cubic centimeters.

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What is the domain of the rational function f of x is equal to the quantity x squared plus x minus 6 end quantity over the quantity x cubed minus 3 times x squared minus 16 times x plus 48 end quantity question mark {x ∈ ℝ| x ≠ –4, –2, 3, 4} {x ∈ ℝ| x ≠ –4, 3, 4} {x ∈ ℝ| x ≠ –4, 4} {x ∈ ℝ| x ≠ –2, 3}

Answers

The domain of the rational function is: option (2)  {x ∈ ℝ | x ≠ -4, 3, 4}

What is Rational number ?

A rational number is any number that can be expressed as the ratio or fraction of two integers, where the denominator is not zero. In other words, a rational number is a number that can be written in the form of p/q, where p and q are integers, and q is not equal to zero.

The domain of a rational function is the set of all real numbers for which the function is defined, and the denominator is not equal to zero. So, we need to find the values of x for which the denominator of the given rational function is not zero.

The denominator of the given rational function is:

x³ - 3x² - 16x + 48

We can factor this polynomial using synthetic division or polynomial long division:

x³- 3x² - 16x + 48 = (x - 4)(x - 3)(x + 4)

So, the denominator of the rational function is not defined when:

x - 4 = 0 or x - 3 = 0 or x + 4 = 0

Solving these equations, we get:

x = 4 or x = 3 or x = -4

Therefore, the domain of the given rational function is:

{x ∈ ℝ| x ≠ –4, 3, 4}

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The potters want to buy a small cottage costing $118,000 with annual insurance and taxes of $710. 00 and $2800. 0. They have saved $14,000. 00 for a down payment, and they can get a 5%, 15 year mortgage from a bank. They are qualified for a home loan as long as the total monthly payment does not exceed $1000. 0. Are they qualified?

Answers

The potters are qualified for the home loan as their total monthly payment is $831.02, which is less than $1000.00.

The total cost of the cottage along with the annual insurance and taxes is $118,000 + $710 + $2800 = $121,510.

The down payment made by the potters is $14,000. Therefore, the amount to be financed through a mortgage is $121,510 - $14,000 = $107,510.

Using the formula for the monthly payment of a mortgage, which is given by:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where P is the principal (amount to be financed), i is the monthly interest rate, and n is the total number of monthly payments.

For a 5%, 15-year mortgage, the monthly interest rate is 0.05/12 = 0.0041667, and the total number of monthly payments is 15 x 12 = 180.

Plugging in the values, we get:

M = $107,510 [ 0.0041667 (1 + 0.0041667)^180 ] / [ (1 + 0.0041667)^180 - 1 ]

M = $831.02

Therefore, the total monthly payment for the mortgage and the annual insurance and taxes is $831.02 + $59.17 + $233.33 = $1123.52, which is more than the maximum allowed payment of $1000.00. Hence, the potters are qualified for the home loan.

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1)calculate the mean and standard deviation of the sampling distribution of
for srss of size 15.
2)interpret the standard deviation from part (1).
3)find the probability that the sample mean weight is greater than 3.55 kilograms.

Answers

It should be noted that to calculate the mean and standard deviation of the sampling distribution, you need to know the population mean (μ) and standard deviation (σ) and the sample size (n) of the distribution.

How to explain the mean

The mean (μx) of the sampling distribution of the sample mean (x) is equal to the population mean (μ):

μx = μ

The standard deviation (σx) of the sampling distribution of the sample mean (x is equal to the population standard deviation (σ) divided by the square root of the sample size (n):

σx = σ / √n

Therefore, in order to calculate the mean and standard deviation of the sampling distribution, you just need to plug in the values of μ, σ, and n into these formulas.

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How does one calculate mean and standard deviation of the sampling distribution.

How to interpret the standard deviation from part (1).

The diagram below shows the radius of the circular opening of a Ice cream cone.
Which of the following Is closest to the circumference of the opening in inches.

Answers

Circumference = 2 пr
r = 1.25 in
C = 2*1.25*п
C = 7.85 in

Answer: 7.85 in

Pls
provide correct answer. Will upvote if correct
Find the surface area of revolution about the x-axis of y 4 sin(3.c) over the interval 0

Answers

The surface area of revolution about the x-axis of y = 4 sin(3x) over the interval 0 <= x <= pi/6 is approximately 0.9402 units^2.

How to find the surface area of revolution of a curve?

To find the surface area of revolution about the x-axis of the curve y = 4 sin(3x) over the interval 0 <= x <= pi/6, we can use the formula:

Surface area = 2π∫[a,b] y √(1+(dy/dx)^2) dx

where a = 0, b = pi/6, and y = 4 sin(3x).

First, we need to find dy/dx:

dy/dx = 12 cos(3x)

Next, we need to find √(1+(dy/dx)^2):

√(1+(dy/dx)^2) = √(1+144 cos^2(3x))

Now, we can substitute y and √(1+(dy/dx)^2) into the formula and integrate:

Surface area = 2π∫[0,pi/6] 4 sin(3x) √(1+144 cos^2(3x)) dx

This integral is difficult to solve analytically, so we can use a numerical method to approximate the value. One possible method is to use Simpson's rule:

Surface area ≈ (π/3)[f(0) + 4f(h) + 2f(2h) + 4f(3h) + ... + 4f(b-h) + f(b)]

where h = (pi/6)/n, n is an even integer, and f(x) = 4 sin(3x) √(1+144 cos^2(3x)).

Using n = 10, we get:

h = (pi/6)/10 = pi/60

Surface area ≈ (π/3)[f(0) + 4f(pi/60) + 2f(pi/30) + 4f(3pi/60) + ... + 4f(9pi/60) + f(pi/6)]

where f(x) = 4 sin(3x) √(1+144 cos^2(3x)).

Evaluating each term:

f(0) = 0

f(pi/60) ≈ 0.3025

f(pi/30) ≈ 0.3069

f(3pi/60) ≈ 0.3192

f(4pi/60) ≈ 0.3227

f(5pi/60) ≈ 0.3227

f(6pi/60) ≈ 0.3192

f(7pi/60) ≈ 0.3069

f(9pi/60) ≈ 0.3025

f(pi/6) ≈ 0

Therefore, the surface area of revolution about the x-axis of y = 4 sin(3x) over the interval 0 <= x <= pi/6 is approximately:

[tex]\begin{equation}\begin{aligned}& \text { Surface area } \approx(\pi / 3)[f(0)+4 f(p i / 60)+2 f(\text { pi/30) }+4 f(3 \text { pi/60) }+\ldots+ \\& 4 f(9 \text { pi/60) }+f(\text { pi/6) }] \\& \approx(\pi / 3)[0+4(0.3025)+2(0.3069)+4(0.3192)+\ldots+4(0.3025)+0] \\& \approx 0.9402 \text { units }^{\wedge} 2 \text { (rounded to four decimal places) }\end{aligned}\end{equation}[/tex]

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15. sound waves can be modeled by the equations of the form y1 = 20 sin (3x + (). a wave traveling in the oppos

direction can be modeled by y2 = 20 sin (3x - 0). show that yı + y2 = 40 sin 3x cos 0.

Answers

The equation required to modelled sound waves is given by y₁ + y₂ = 40 sin 3x cos θ.

Equations used to modelled sound waves are,

y₁= 20 sin (3x + θ)

A waves travelling in the opposite direction are,

y₂ = 20 sin (3x - θ)

To show that y₁ + y₂ = 40 sin 3x cos θ,

Simply substitute the given expressions for y₁ and y₂ and simplify using trigonometric identities.

sin A + sinB = 2 sin  [(A + B)/2] cos [(A - B)/2].

y₁ + y₂ = 20 sin (3x + θ) + 20 sin (3x - θ)

⇒y₁ + y₂ = 20 ( sin (3x + θ) + sin (3x - θ) )

Using the identity for the sum of two sines, simplify this expression,

⇒y₁ + y₂ = 2 ×20 × sin (3x + θ + 3x -  θ)/2 cos (3x + θ - 3x + θ)/2

⇒ y₁ + y₂ = 2 ×20 × sin (3x) cos (θ)

⇒ y₁ + y₂ = 40 sin (3x) cos (θ)

Therefore, for the sound waves y₁ + y₂ = 40 sin 3x cos θ, as required.

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The above question is incomplete, the complete question is:

Sound waves can be modeled by the equations of the form y₁= 20 sin (3x + θ). a wave traveling in the opposite direction can be modeled by y₂ = 20 sin (3x - θ). show that y₁ + y₂ = 40 sin 3x cos θ.

Here is the income statement for Teal Mountain Inc.



TEAL MOUNTAIN INC.


Income Statement


For the Year Ended December 31, 2022


Sales revenue


$431,600


Cost of goods sold


234,300


Gross profit


197,300


Expenses (including $16,200 interest and $22,500 income taxes)


75,200


Net income


$ 122,100



Additional information:



1. Common stock outstanding January 1, 2022, was 26,700 shares, and 36,000 shares were outstanding at December 31, 2022.


2. The market price of Teal Mountain stock was $13 in 2022.


3. Cash dividends of $24,200 were paid, $6,600 of which were to preferred stockholders.



Compute the following measures for 2022. (Round all answers to 2 decimal places, e. G. 1. 83 or 2. 51%)



(a) Earnings per share


$enter earnings per share in dollars


(b) Price-earnings ratio


enter price-earnings ratio in times


times


(c) Payout ratio


enter payout ratio in percentages


%


(d) Times interest earned


enter times interest earned


times

Answers

Using the given information we can compute several financial ratios that help us evaluate the company's financial performance.

To calculate these ratios, we need to use information from the income statement and the additional information provided.

One important financial ratio is earnings per share (EPS), To compute EPS, we divide net income by the average number of common shares outstanding during the year. To find the average number of shares outstanding, we add the beginning and ending shares and divide by 2.

Net income = $122,100

Average number of common shares outstanding = (26,700 + 36,000) / 2 = 31,350

EPS = $122,100 / 31,350 = $3.89

Another important financial ratio is the price-earnings (P/E) ratio, To compute the P/E ratio, we divide the market price per share by the EPS.

Market price per share = $13

EPS = $3.89

P/E ratio = $13 / $3.89 = 3.34 times

The payout ratio measures the proportion of earnings that is paid out as dividends. To compute the payout ratio, we divide total dividends by net income. However, we need to adjust for the fact that some of the dividends were paid to preferred stockholders. To do this, we subtract the preferred dividends from the total dividends before dividing by net income.

Total dividends = $24,200

Preferred dividends = $6,600

Common dividends = $24,200 - $6,600 = $17,600

Net income = $122,100

Payout ratio = $17,600 / $115,500 = 15.24%

The times interest earned (TIE) ratio, To compute the TIE ratio, we divide earnings before interest and taxes (EBIT) by interest expense.

Interest expense = $16,200

EBIT = Gross profit - Expenses + Interest expense = $197,300 - $75,200 + $16,200 = $138,300

TIE ratio = $138,300 / $16,200 = 8.54 times

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Let f(x) = x^1/2(x-4). Find all values of x for which r*(x) - 0 or P(x) is undefined. As your answer please input the sum of all values of satisfying "(x) = 0 or () is undefined

Answers


x^(1/2) = 0

This equation has no real solutions, since no real number raised to any power can equal 0.

Therefore, the sum of all values of x satisfying r*(x) = 0 or P(x) is undefined is just 2, the only value of x for which r*(x) - 0.

To find the values of x for which r*(x) - 0 or P(x) is undefined, we first need to determine what r*(x) and P(x) are.

r*(x) is the derivative of f(x), which we can find using the product rule:

r*(x) = (1/2)x^(-1/2)(x-4) + x^1/2(1)

Simplifying this expression, we get:

r*(x) = (x-2)/sqrt(x)

To find the values of x for which r*(x) - 0, we can set r*(x) equal to 0 and solve for x:

(x-2)/sqrt(x) = 0

x - 2 = 0

x = 2

So the only value of x for which r*(x) - 0 is x = 2.

Next, we need to find the values of x for which P(x) is undefined. P(x) is undefined when the denominator of the expression for f(x) is equal to 0, since division by 0 is undefined. The denominator of f(x) is x^(1/2), so we need to solve the equation x^(1/2) = 0:

x^(1/2) = 0

This equation has no real solutions, since no real number raised to any power can equal 0.

Therefore, the sum of all values of x satisfying r*(x) = 0 or P(x) is undefined is just 2, the only value of x for which r*(x) - 0.

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Which shapes contain at least one obtuse angle?

Select each correct answer.

Responses are the pictures

Answers

Answer:

Shape 1 and Shape 3

Step-by-step explanation:

An obtuse angle is an angle that is greater than 90° but less than 180°.

We can see that the first shape has 2 angles that are greater than 90°, making this a correct choice.
The second shape has 4 boxes, meaning the angles are exactly 90°, making this incorrect.

The third shape has 6 angles that are greater than 90°, making this another correct choice.

The last shape has all 3 angles under 90°, making this also incorrect.

So, the 1st and 3rd shapes are correct.

Hope this helps! :)

Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximun and minimum. Select all that apply A. f(x)=x2 over(-5,0] B. g(x) over [-5,0] C. h(x)=1x-1 lover [-5.0] D. k( x) = Vx + 1 over [- 5,0] E. None of the above.

Answers

The extreme value theorem states that if a function f(x) is continuous on a closed interval [a, b], then there exists at least one point c in [a, b] where f(c) is the absolute maximum value and at least one point d in [a, b] where f(d) is the absolute minimum value.


A. f(x)=x2 over(-5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.

B. g(x) over [-5,0] - We do not have information about the function g(x), so we cannot determine whether it is continuous on the closed interval [-5,0]. Therefore, we cannot determine whether the extreme value theorem applies.

C. h(x)=1x-1 lover [-5.0] - This function is not continuous at x=0 because it has a vertical asymptote there. Therefore, the extreme value theorem does not apply.

D. k( x) = Vx + 1 over [- 5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.

E. None of the above - Only options A and D satisfy the conditions for the extreme value theorem, so the correct answer is none of the above.

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Can someone please help me ASAP? It’s due tomorrow

Answers

Applying the concept of combination, the number of different sandwiches that can be created is determined as: D. 6.

How to Apply the Concept of Combination to Determine How May Sandwiches to be Created?

To determine the number of different sandwiches that can be created with two different meats, we can use the concept of combinations.

In this case, we need to choose 2 meats out of 4 options. The number of combinations of 2 items that can be chosen from a set of 4 items is given by the formula:

nCr = n! / r!(n-r)!

where n is the total number of items, r is the number of items to be chosen, and the exclamation mark (!) denotes the factorial function.

In this case, we have:

n = 4 (since there are 4 meat options)

r = 2 (since Regan wants to choose 2 meats)

Therefore, the number of different sandwiches that can be created is:

4C2 = 4! / 2!(4-2)! = 6

This means there are 6 different ways to choose 2 meats out of 4, and hence 6 different sandwich options.

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i
need help with this question please help
Verify that the function f(x) = -4x2 + 12x - 4 In x attains an absolute maximum and absolute minimum on [1,2] Find the absolute maximum and minimum values. Hint: In 2 – 0.7, Inį -0.7. Verify that

Answers

The absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.

To find the absolute maximum and minimum values of the function f(x) = -4x^2 + 12x - 4 on the interval [1, 2], we need to check the critical points and the endpoints of the interval.

First, let's find the critical points by taking the derivative of the function:

f'(x) = -8x + 12

To find the critical points, set f'(x) to 0 and solve for x:

-8x + 12 = 0
x = 3/2

Now, we have 3 points to check: x = 1, x = 3/2, and x = 2.

Evaluate the function at each point:

f(1) = -4(1)^2 + 12(1) - 4 = -4 + 12 - 4 = 4
f(3/2) = -4(3/2)^2 + 12(3/2) - 4 = -9 + 18 - 4 = 5
f(2) = -4(2)^2 + 12(2) - 4 = -16 + 24 - 4 = 4

Comparing the function values at these points, we find that the absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.

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Answer:

The absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.

To find the absolute maximum and minimum values of the function f(x) = -4x^2 + 12x - 4 on the interval [1, 2], we need to check the critical points and the endpoints of the interval.

First, let's find the critical points by taking the derivative of the function:

f'(x) = -8x + 12

To find the critical points, set f'(x) to 0 and solve for x:

-8x + 12 = 0

x = 3/2

Now, we have 3 points to check: x = 1, x = 3/2, and x = 2.

Evaluate the function at each point:

f(1) = -4(1)^2 + 12(1) - 4 = -4 + 12 - 4 = 4

f(3/2) = -4(3/2)^2 + 12(3/2) - 4 = -9 + 18 - 4 = 5

f(2) = -4(2)^2 + 12(2) - 4 = -16 + 24 - 4 = 4

Comparing the function values at these points, we find that the absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.

Step-by-step explanation:

Jessica's cookie recipe calls for 1 1/2
cups of flour. She only has enough
flour to make 1/3 of a batch. How much
flour does she have?
A 1/3 cup
B 1/2 cup
C 1 cup
D 2 cups

Answers

Answer:

B

Step-by-step explanation:

1 1/2 x 1/3

=1/2

So therefore the answer is B (1/2 cup)

Answer:

The answer is B ( 1/2 cup)

x+2y=6
-7x+3y=-8 (using substitution)

Answers

Answer:

point form - (2,2)

x=2 y=2

7*. All lengths are in cm. Find the area of the right angled
triangle.
x-14( shortest side)
2x+5( hypotenuse)
2x+3( remaining side)

Answers

Answer:

504 cm^2.

Step-by-step explanation:

By Pythagoras:

(2x + 5)^2 = (2x + 3)^2 + (x - 14)^2

4x^2 + 20x + 25 = 4x^2 + 12x + 9 + x^2 - 28x + 196

20x - 12x + 28x + 25 - 9 - 196 = x^2

x^2 - 36x + 180 = 0

(x - 6)(x - 30) = 0

x = 6, 30.

As one of the sides is x - 14, x mst be 30 as its length has to be positive.

So the area of the triangle

= 1/2 * (x - 14) 8 (2x + 3)

= 1/2 * (30-14)(60 + 3)

= 1/2 * 16 * 63

= 504 cm^2.

find the first derivative x cos(14x + 13y) = y sin x

Answers

To find the first derivative of the equation x cos(14x + 13y) = y sin x, we will need to use the chain rule and product rule.

First, we will differentiate each term separately:

d/dx(x) = 1

d/dx(cos(14x + 13y)) = -sin(14x + 13y) * d/dx(14x + 13y)
= -sin(14x + 13y) * 14

d/dx(y) = 0 (since y is a constant)

d/dx(sin(x)) = cos(x)

Next, we will apply the product rule to differentiate the left-hand side of the equation:

d/dx(x cos(14x + 13y)) = cos(14x + 13y) + x * (-sin(14x + 13y) * 14)

Now, we can set this expression equal to the derivative of the right-hand side of the equation and solve for the first derivative:

cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)

Our final answer for the first derivative is:

cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)

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I NEED HELP this is grade 9 math

Answers

The measure of angles ADC is 30⁰.

The measure of angles DCA is 120⁰.

The measure of angles DCB is 180⁰.

The measure of angles AEB is 30⁰.

What is angle ADC?

The measure of each of the angles is calculated as follows;

if length AB = length CD, then AC = AB

Also triangle ACB = equilateral triangle, and each angle = 60⁰.

Angle DAB = 90 (since line DB is the diameter)

Angle DAC = angle ADC

DAC = 90 - 60 = 30 = ADC

DCA = 180 - (30 + 30) (sum of angles in a triangle)

DCA = 120⁰.

The value of angle DCB is calculated as follows;

DCB = 180 (sum of angles on straight line)

angle AEB = angle ADC (vertical opposite angles )

angle AEB = 30⁰

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Estimate to find the correct answer for each expression.



A. 270 349. 6 - 112. 8



B. 220 173. 3 + 78. 4



C. 240 817. 2 - 597. 1



D. 250 108. 8 + 159. 3

Answers

The correct answer of estimation for each expression is 269,900, 220,251.7, 240,220.1 and 250,268.1.

270,349.6 - 112.8 = 270,236.8

To estimate, we can round 270,349.6 to 270,000 and round 112.8 to 100. Subtracting 100 from 270,000 gives us 269,900. Therefore, the estimated answer is 269,900.

220,173.3 + 78.4 = 220,251.7

To estimate, we can round 220,173.3 to 220,000 and round 78.4 to 80. Adding 80 to 220,000 gives us 220,080. Therefore, the estimated answer is 220,080.

240,817.2 - 597.1 = 240,220.1

To estimate, we can round 240,817.2 to 240,000 and round 597.1 to 600. Subtracting 600 from 240,000 gives us 239,400. Therefore, the estimated answer is 239,400.

250,108.8 + 159.3 = 250,268.1

To estimate, we can round 250,108.8 to 250,000 and round 159.3 to 160. Adding 160 to 250,000 gives us 250,160. Therefore, the estimated answer is 250,160.

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14


5. Betty will spend $375. 00 on a new lawnmower. She will use her credit card to


withdraw $400 cash to pay for the lawnmower. The credit card company charges a $6. 00


cash-withdrawal fee and 3% interest on the borrowed amount, but not including the cash-


withdrawal fee. How much will Betty owe after one month ?

Answers

After one month, Betty will owe $407.02 on her credit card.

The amount Betty will owe after one month depends on how much of the stability she will pay off in the course of that point.

Assuming she does not make any payments in the course of the first month, here is how to calculate her balance:

The cash-withdrawal price is a one-time fee, so it does no longer affect the stability after one month.

Betty withdrew $400, so her starting balance is $406 ($400 for the lawnmower plus $6 cash-withdrawal price).

The interest rate is 3%, that's an annual price. To calculate the monthly charge, divide with the aid of 12: three% / 12 = 0.25%.

To calculate the interest charged for the first month, multiply the stability through the monthly interest rate: $406 * 0.25% = $1.02.

Add the interest to the balance: $406 + $1.02 = $407.02. that is Betty's balance after one month.

Consequently, after one month, Betty will owe $407.02 on her credit card.

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In ∆DEF, DG−→− bisects ∠EDF. Is ∆FDG similar to ∆EDG? Explain.


A. Yes; ∆FDG ≅ ∆EDG by ASA.


B. Yes; ∆FDG and ∆EDG may not be congruent, but they are similar by the ASA Similarity Postulate.


C. No; ∆FDG and ∆EDG are not similar unless DE = DF.


D. No; ∆FDG and ∆EDG are not similar unless DE = EG and DF = FG

Answers

In ∆DEF, DG−→− bisects ∠EDF. ∆FDG is similar to ∆EDG; ∆FDG and ∆EDG may not be congruent, but they are similar by the ASA Similarity Postulate. Therefore, the correct option is B.

Consider the following reasoning:

1. Since DG bisects ∠EDF, it means that ∠EDG = ∠FDG. This is the Angle Bisector Theorem.

2. In triangles FDG and EDG, we know that ∠FDG = ∠EDG (from step 1) and ∠DFG = ∠DEG (both are vertical angles and therefore congruent).

3. Now we have two pairs of congruent angles: ∠FDG = ∠EDG and ∠DFG = ∠DEG.

4. According to the (Angle-Side-Angle) or  ASA Similarity Postulate, if two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar. Therefore, ∆FDG is similar to ∆EDG.

Hence, the correct answer is option B: Yes; ∆FDG and ∆EDG may not be congruent, but they are similar by the ASA Similarity Postulate.

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If f(x) = 3(5") + x and g(x) = 3cos(x), what is (f9)'()? O (3(5*) In(5) + 1)(3cos(x)) + (3(5") + x)(sin(x)) O (3(5") In(5) + 1)(3sin(x)) O (3(5") In(5) + 1)(-3sin(x)) O (3(5) In(5) + 1)(3cos(x)) + (3(5") + x)(-3sin(x))

Answers

The derivative of (f∘g)(x) can be found using the chain rule, which states that the derivative of (f∘g)(x) is (f'(g(x)))(g'(x)).

In this case, (f∘g)(x) = f(g(x)) = 3(5^x) + 3cos(x), so we need to find f'(g(x)) and g'(x) and then multiply them together. The derivative of f(x) is f'(x) = 15^x * ln(5) + 1, so the derivative of f(g(x)) with respect to g(x) is f'(g(x)) = 15^(g(x)) * ln(5) + 1. The derivative of g(x) is g'(x) = -3sin(x). Therefore, using the chain rule, we have:(f∘g)'(x) = f'(g(x)) * g'(x) = (15^(g(x)) * ln(5) + 1) * (-3sin(x))Substituting g(x) = 3cos(x), we get:(f∘g)'(x) = (15^(3cos(x)) * ln(5) + 1) * (-3sin(x))So the correct answer is: (3(5^3cos(x)) ln(5) + 1) * (-3sin(x))

For more similar questions on topic a) The intervals for which f(x) = -5.5sin(x) + 5.5cos(x) is concave up and concave down on [0,2π] can be found by analyzing the second derivative of the function. Taking the second derivative of f(x), we get:

f''(x) = -5.5cos(x) - 5.5sin(x)

To find the intervals of concavity, we need to determine where f''(x) is positive and negative.

When f''(x) > 0, the function is concave up. When f''(x) < 0, the function is concave down.

Setting f''(x) = 0, we get:

-5.5cos(x) - 5.5sin(x) = 0

Simplifying, we get:

cos(x) + sin(x) = 0

Solving for x, we get:

x = 3π/4, 7π/4

These are the possible points of inflection for the function.

Using test intervals, we can determine the intervals of concavity:

When 0 ≤ x < 3π/4 or 7π/4 < x ≤ 2π, f''(x) < 0, so f(x) is concave down.

When 3π/4 < x < 7π/4, f''(x) > 0, so f(x) is concave up.

b) The possible points of inflection for f(x) on [0,2π] are x = 3π/4 and x = 7π/4. To find the coordinates of these points, we can substitute each value of x into the original function f(x):

f(3π/4) = -5.5sin(3π/4) + 5.5cos(3π/4) = 5.5√2 - 5.5√2/2 = 5.5√2/2

So the coordinates of the point of inflection at x = 3π/4 are (3π/4, 5.5√2/2).

Similarly, we can find the coordinates of the point of inflection at x = 7π/4:

f(7π/4) = -5.5sin(7π/4) + 5.5cos(7π/4) = -5.5√2 - 5.5√2/2 = -5.5(3/2)√2

So the coordinates of the point of inflection at x = 7π/4 are (7π/4, -5.5(3/2)√2).

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Prove by cases that 25k^2 + 15k is an even integer whenever 5k- 3 is an integer. ​

Answers

We can prove that 25k² + 15k is an even integer whenever 5k - 3 is an integer by considering two cases: when k is even and when k is odd.

Let's assume that 5k - 3 is an integer. Then, we can write k as k = (5k - 3 + 3)/5 = (5k - 3)/5 + 3/5. Since (5k - 3)/5 is an integer, we can write it as (5k - 3)/5 = n, where n is an integer. Thus, we have k = n + 3/5.

Now, we can substitute this expression for k into 25k² + 15k as follows:

25k² + 15k = 25(n + 3/5)² + 15(n + 3/5)

Expanding the square, we get:

25(n² + 6n/5 + 9/25) + 15n + 9 = 25n² + 45n/5 + 34/5

Simplifying, we get:

25k² + 15k = 5(5n² + 9n) + 34/5

Since 5n² + 9n is an integer, we can write it as m, where m is an integer. Thus, we have:

25k² + 15k = 5m + 34/5

Now, we can consider two cases:

Case 1: k is even. In this case, k can be written as k = 2p, where p is an integer. Substituting this expression into 5k - 3, we get:

5k - 3 = 5(2p) - 3 = 10p - 3

Since 10p is even, we can conclude that 10p - 3 is odd. Therefore, m must be odd, since 5m + 34/5 is even. Thus, 25k² + 15k is even, since it can be written as 5m + 34/5, where 5m is even and 34/5 is even.

Case 2: k is odd. In this case, k can be written as k = 2p + 1, where p is an integer. Substituting this expression into 5k - 3, we get:

5k - 3 = 5(2p + 1) - 3 = 10p + 2

Since 10p is even, we can conclude that 10p + 2 is even. Therefore, m must be even, since 5m + 34/5 is even. Thus, 25k² + 15k is even, since it can be written as 5m + 34/5, where 5m is even and 34/5 is even.

In both cases, we have shown that 25k² + 15k is an even integer whenever 5k - 3 is an integer. Therefore, the statement is proved.

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Factorize completely the expression (m+n)(2x-y)-x(m+n)

Answers

The complete factorization of the expression is  (m+n)(x-y).

What is the complete factorization of the expression?

The complete factorization of the expression is determined as follows;

To factorize the expression (m+n)(2x-y)-x(m+n), we can first factor out the common factor (m+n):

(m+n)(2x-y)-x(m+n) = (m+n)(2x-y-x)

Next, we will factorize completely as follows;

2x - x - y = x - y

(m+n)(2x-y-x)  = (m+n)(x-y)

Therefore, the fully factorized form of the expression is (m+n)(x-y).

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How many dollars worth of food is wasted in America each day?


How many additional people could survive eating the food that is thrown away?

Answers

Around $441 million worth of food is wasted in the US each day.

How much food is wasted in the USA each day?

According to the United States Department of Agriculture (USDA), about 30-40 percent of the food supply in the United States goes to waste. In terms of dollars, that translates to approximately $161 billion worth of food being wasted each year in the United States.

Dividing that number by 365, we can estimate that around $441 million worth of food is wasted in the US each day.

It's difficult to estimate how many people could be fed with the food that is thrown away, as food waste can take many forms, such as uneaten meals at restaurants, spoiled produce at grocery stores, and expired food in households. However, according to Feeding America, a national food bank network, approximately 42 million Americans, including 13 million children, are food insecure, which means they lack reliable access to affordable, nutritious food.

If we assume that all the food that is currently being wasted in the US could be redistributed to those who are food insecure, it could potentially feed a significant number of people. However, in reality, the logistics of collecting, storing, and distributing food waste can be complex, and some food waste may not be safe or nutritious to eat. Additionally, addressing food waste is just one piece of the puzzle in addressing food insecurity, which is a complex issue with many underlying factors.

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solve the following simple equations 6m=
12

Answers

Answer:

m = 2

Step-by-step explanation:

6m = 12

6 × m = 12

m = 12 ÷ 6

m = 2

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Answer:

m = 2

Step-by-step explanation:

6m = 12

6m = 6^2

• get rid of common element which is 6. Devide both side by six.

6m ÷ 6 = 6^2 ÷ 6

m = 2

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