distribute 5x(3x+7)
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Answer:

3 cakes

Step-by-step explanation:

just flow by the formula then ignore the remainder and take the whole number which is 3 then that becomes your answer good day.

[tex]A \cup B[/tex] represents the set that contains all the elements that are in at least one of the sets, so [tex]A \cup B=\{1, 2, 5, 6, 7, 8, 9, 10, 12, 16, 18, 19, 20, 21, 22, 23, 25\}[/tex].

We want the complement of this set (in other words, the set with all the elements in the universal set but not in the given set).

This set is {3, 4, 11, 13, 14, 15, 17, 24}

Answer:

  (a)  y = 5/12x and y = -5/12x

Step-by-step explanation:

Given the equation of a hyperbola 25x² – 144y² + 3,600 = 0, you want the equations of the asymptotes.

Dividing by 3600 and doing a little rearrangement, we have ...

  (y/5)² -(x/12)² = 1 . . . . . standard form equation of a hyperbola

The equation of the asymptotes is ...

  (y/5)² -(x/12)² = 0

Solving for y gives ...

  (y/5)² = (x/12)²

  y/5 = ±x/12 . . . . . . take the square root

  y = ±5/12·x . . . . . . . matches the first choice

__

Additional comment

The equation of a hyperbola with vertices on the y-axis is often written as ...

  y²/a² -x²/b² = 1

We have written it in the above form to better show the scale factors applied to x and y.

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It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.

This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]

The pressure by the statue exerted on the floor will be 1200 N per square meter.

The term pressure is defined as the force per unit area.

The formula is igven below.

P = F /A

A bronze statue weighs 2400 N and has a base that is 4 m by ½ m.

Then the base area will be

A = 4 x 1/2

A = 2 square meters

Then the pressure will be

P = 2400 / 2

P = 1200 N per square meter.

more about the pressure link is given below.

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Based on the altitudes of both the airplane and the helicopter, the number of minutes until they are at the same altitude is 20 minutes.

Assuming the minute both will be on the same altitude is x, the altitude that the airplane would be at that point is:

= 30,000 - 1,000x

The helicopter's altitude would be:

= 0 + 500x

Putting them together gives:

30,000 - 1,000x = 500x

30,000 = 1,500x

x = 30,000 / 1,500

= 20 minutes

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Answer:

Step-by-step explanation:

Find the area of a circle with a diameter of 10 ft.

Area of a Circle  

A = π × r²

r = diameter : 2

10 : 2 = 5 ft (radius)

A = π × 5²

A = 3.14 * 25

A = 78.5 ft²

Answer:

y = 4x - 5

Step-by-step explanation:

y = mx + b

By putting above values in equation (i)

-1 = 4 (1) + b

-1 = 4 + b

-5 = b

b = -5

y = 4x - 5

Answer:

C

Step-by-step explanation:

A and B are wrong because 37 is prime. 31 is prime and 33 is divisible by 11 and 3 so C

Answer:

64%

Step-by-step explanation:

Convert 16/25 to Percentage by Converting to Decimal

With this method, we first need to divide the numerator by the denominator:

16 ÷ 25 = 0.64

Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:

0.64 × 100 = 64%

We can see that this gives us the exact same answer as the first method: 16/25 as a percentage is 64%.

Note, the final percentage is rounded to 2 decimal places to make the answer simple to read and understand.

[tex]1) \text{ } f(-2)=8(-2)^{2}-3(-2)+2=\boxed{40}\\\\2) \text{ } f(-1)=8(-1)^{2}-3(-1)+2=\boxed{13}\\\\3) \text{ } f(0)=8(0)^{2}-3(0)+2=\boxed{2}\\\\4) \text{ } f(1)=8(1)^{2}-3(1)+2=\boxed{7}\\\\5) \text{ } f(2)=8(2)^{2}-3(2)+2=\boxed{28}[/tex]

The total surface area of the cone is 3π + 10 cm².

A cone is a three-dimensional object that consists of a circular base and a vertex.

Total surface area = πr (r + l)

Where:

π x 3 + (3 + 7)

3π + 10 cm²

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Answer:

16 x^14 / y^16

Step-by-step explanation:

Remember   ' PEDMAS '

Parentheses

Exponents

Division

Multiplication

Addition

Subtraction

 so do the stuff inside the parentheses to get

  y^8     ^-2

  4x^7  

Now do the exponents  ( the -2  one)

y^-16

4^-2 x^-14       then simplify

16 x^14 / y^16

Answer:

The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!

Answer:

d. 60°

Step-by-step explanation:

Since the clock is a full circle, it has a degree span of 360°.

∴ every 5-min interval on the clock

= 360° ÷ 12 five min intervals

= 30°

∴ acute angle formed by clock in figure

= two 5-min intervals

= 60°

Answer:

CI = $182.25

Step-by-step explanation:

Compound interest formula:

[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex]  ,

where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).

Using formula:

CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]

CI = $182.25

Answer:

Angle 1: 55 degrees
Angle 2: 55 degrees
Angle 3: 70 degrees

Step-by-step explanation:

Finding angle 1: We know that in a triangle, all three angles must add up to 180 degrees. In the triangle on the left, 2 of the angle measures are already given to us. Therefore, we can simply do 180 - 40 - 85, thus the measure of angle 1 is 55 degrees.
Finding angle 2: We know that opposite angles are congruent. Therefore, angle 2 and angle 1 have the same measure.
Finding angle 3: Using the same thought process as we used when finding the measure of angle 1, we can subtract the other 2 angles. 180 - 55 - 55 is equal to 70.

Answer:

first, we take the first triangle( the right one), since a triangle is equal to 180 we add 85 and 40 which gives us 125, we then subtract 125 with 180 getting 55 so (1) =55

to find (2) we put 55 the same number as no. (1) because of the property VERTICALLY OPPOSITE ANGLES.

then to find (3) we do the same steps as (1), we add 55 and 55 and subtract by 180. 55+55=110

             =110 - 180

             =70

There u go, please mark me as brainless

Answer: 1, -2, 1

Step-by-step explanation:

[tex]f(g(x))=f(x-1)=(x-1)^{2}=x^{2}-2x+1[/tex]

Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:

1.053x = 30.8.

x = 30.8/1.053

x = 29.2.

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Answer:

4 kg

Step-by-step explanation:

so 1.6 * 4 is 6.4 so you just double check if you want

4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)

4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)

there is another way by setting up an equation. let me know in comments if you want to see it that way

If  tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg

Two or more expressions with an Equal sign is called as Equation.

Given,

A tank weighs 5.6kg when it 1/4 filled with water

Tank weighs 10.4kg when it is full

We need to find the weight when it is empty.​

Let weight of the tank “x” and the weight of the water in the full tank “y”.

From the problem statements, we deduce the following equations:

x + y/4 = 5.6kg => x = 5.6kg - y/4

x + y = 10.4kg => y = 10.5kg - x

y = 10.5kg - (5.6kg - y/4)

3y/4 = 4.9

Thus y = 6.53kg; x = 0.93kg

Hence, weight of the tank when it is empty is 0.93kg.

To learn more on Equation:

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Step-by-step explanation:

1/2 represents every fraction, where the denominator (bottom part) is twice the numerator (top part).

like 4/8 or 6/12 or 128/256 or ...

what do we need in the denominator to calculate with 15/16 ?

the same : 16.

and what is half of 16 ? 8.

so, we need the 1/2 based on 16th = 8/16.

so, the dog ate 8/16 (1/2) of the original 15/16.

what was left was

15/16 - 8/16 = 7/16 pound

(a) If [tex]\alpha[/tex] and [tex]\beta[/tex] are roots of [tex]f(x)[/tex], then we can factorize [tex]f[/tex] as

[tex]f(x) = x^2 + (k - 6) x + 9 = (x - \alpha) (x - \beta)[/tex]

Expand the right side and match up coefficients:

[tex]x^2 + (k-6) x + 9 = x^2 - (\alpha + \beta) x + \alpha \beta \implies \begin{cases} \alpha + \beta = -(k-6) \\ \alpha \beta = 9 \end{cases}[/tex]

Now, recall that [tex](x+y)^2 = x^2 + 2xy + y^2[/tex]. It follows that

[tex]\boxed{\alpha^2 + \beta^2} = (\alpha + \beta)^2 - 2\alpha\beta = (-(k-6))^2 - 2\times9 = \boxed{k^2 - 12k + 18}[/tex]

and

[tex]\boxed{\alpha^2\beta^2} = 9^2 = \boxed{81}[/tex]

(b) If [tex]9(\alpha^2+\beta^2) = 2\alpha^2\beta^2[/tex], then

[tex]9 (k^2 - 12k + 18) = 2\times81 \implies 9k^2 - 108k = 0 \implies 9k (k - 12) = 0[/tex]

Since [tex]k\neq0[/tex], it follows that [tex]\boxed{k=12}[/tex].

(c) The simplest quadratic expression with roots [tex]\frac1{\alpha^2}[/tex] and [tex]\frac1{\beta^2}[/tex] is

[tex]\left(x - \dfrac1{\alpha^2}\right) \left(x - \dfrac1{\beta^2}\right)[/tex]

which expands to

[tex]x^2 - \left(\dfrac1{\alpha^2} + \dfrac1{\beta^2}\right) x + \dfrac1{\alpha^2\beta^2}[/tex]

Reusing the identity from (a-i) and the result from part (b), we have

[tex]\left(\dfrac1\alpha + \dfrac1\beta\right)^2 = \dfrac1{\alpha^2} + \dfrac2{\alpha\beta} + \dfrac1{\beta^2} \\\\ \implies \dfrac1{\alpha^2} + \dfrac1{\beta^2} = \left(\dfrac{\alpha + \beta}{\alpha\beta}\right)^2 - \dfrac2{\alpha\beta} = \left(\dfrac{-(k-6)}9\right)^2 - \dfrac29 = \dfrac29[/tex]

We also know from part (a-ii) that [tex]\alpha^2\beta^2=81[/tex].

So, the simplest quadratic that fits the description is

[tex]x^2 - \dfrac29 x + \dfrac1{81}[/tex]

To get one with integer coefficients, we multiply the whole expression by 81 to get [tex]\boxed{81x^2 - 18x + 1}[/tex].

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

[tex]\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;[/tex]

it is clear, the required constant is 12 (12 per hour).

Answer:

[tex]3 \frac{7}{8}[/tex]

Step-by-step explanation:

Answer:

[tex]\sf 1. \quad \tan(B)=\dfrac{4}{3}[/tex]

[tex]\sf 2. \quad \tan(A)=\dfrac{7}{2}[/tex]

[tex]\sf 3. \quad \angle A[/tex]

Step-by-step explanation:

Acute angle: an angle less than 90°

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Question 1

Refer to the first attached diagram.

If tan(A) = 3/4 then the side opposite ∠A is 3 units, and the side adjacent ∠A is 4 units.

Therefore:

[tex]\implies \sf \tan(B)=\dfrac{4}{3}[/tex]

Question 2

Refer to the second attached diagram.

If tan(B) = 2/7 then the side opposite ∠B is ,and the side adjacent ∠B is 7.

Therefore:

[tex]\implies \sf \tan(A)=\dfrac{7}{2}[/tex]

Angle A would be bigger (see second attachment).

Answer:

20x + 8

Step-by-step explanation:

5*4x + 5*5 -17

20x +25 -17

20x + 8

To find the point of intersection for two lines, we can use substitution to solve for the coordinates.

We're given:

With these two equations, we can:

Isolate x in the second equation:

[tex]x+2y=7\\x =7-2y[/tex]

Substitute the second equation into the first:

[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]

Solve for y:

[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]

Solve for x:

[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]

The point of intersection of the lines is (3,2).

Answer:

5 lbs 1 oz

Step-by-step explanation:

This year Lucille weighs 106 lb 13 oz. A

year ago she weighed 101 lb 12 oz. How

much has she gained in the year?

16oz = 1 lb

13 oz = 13/16 = .8125

12 oz = 12/16 = 3/4 = .75

106.8125 - 101.75

106.8125

-101.7500

---------------

   5.0625 =

5.0625 = 5 1/16

1/16 of a pound is 1oz

5 lbs 1 oz

Answer:

$41269.983

rounded:

$41,269.98

Step-by-step explanation:

well you begin with the equation a=p(1+r/n)[tex]^{nt}[/tex]

so 30,000(1+0.08/12)to the power of 4 times 12

when you plug all of that in a calculator your receive $41269.983

Answer:

C

Step-by-step explanation:

The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)

The y intercept is 2.