Elaina is trying to fit the longest stick she can into her pet lizard’s tank. She knows running it diagonally from the front corner to the back will give her the most room but she is uncertain what size she should buy. What is the biggest length stick that will fit into her 12 by 8 by 8 tank?

The resulting matrix after row 1 is multiplied by 2 is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

The first row is given as follows:

7, -4 and 8.

Multiplying the first row by two, we have that:

(when we multiply a matrix by a constant, each element of the matrix is multiplied by the constant).

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{ccc}14&-8&16\\-12&7&-13\end{array}\right][/tex]

(the second row was kept constant, while the first row was multiplied by 2).

The matrix is:

[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]

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Step-by-step explanation:

The 'x's '   ( the domain)  are mapped into two values of 'y' (the range)

Range =   1,6

Answer:

x²+14x+49

Step-by-step explanation:

(a+b)²=a²+2ab+b²

(x+7)²=x²+2×7×x+7²=x²+14x+49

Answer:

Set your calculator to degree mode.

2) tan(43°) = x/8.2

x = 8.2tan(43°) = 7.6

3) sin(29°) = 3.5/x

x sin(29°) = 3.5

x = 3.5/sin(29°) = 7.2

Answer:

B. Y= 5x - 2

Step-by-step explanation:

The Y is negative, you can see the number -5 below the point, if you go to the top, that is, to 0 and count down, the lines are two and the X is positive 5, you can see where the number 5 is and the point is above.

Answer:

it's an easy one

Step-by-step explanation:

1. combine those -->4v+4=16

2. subtract the like terms--> 4v=16-4--> 4v=12

3. divide--> v=12/4-->3

4. Answer--> v=3

Answer:

the average amount Mrs. Gordon pays in interest each month, we need to determine the total interest paid over the six-month period and divide it by the number of months.

The total interest paid can be found by subtracting the cost of the stove from the total amount paid over six months:

Total interest paid = Total amount paid - Cost of the stove

The total amount paid over six months is calculated by adding the monthly payments:

Total amount paid = $160/month * 6 months

Let's perform the calculations:

Total amount paid = $160/month * 6 months = $960

Total interest paid = Total amount paid - Cost of the stove

= $960 - $850

= $110

Now, to find the average amount Mrs. Gordon pays in interest each month, we divide the total interest paid by the number of months:

The average amount paid in interest each month = Total interest paid / Number of months

= $110 / 6 months

≈ $18.33

Therefore, Mrs. Gordon pays an average of approximately $18.33 in interest each month.

The probability that a single randomly selected value is greater than 31.9 is 0.511.

The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.

Probability that a single randomly selected value is greater than 31.9:

z = (31.9 - 32) / 3.9 = -0.026

We can find the probability:

P(X > 31.9) = P(Z > -0.026) = 0.511

Also, μ = 32, σ = 3.9, n = 66

z = (31.9 - 32) / (3.9 / √66) = -0.363

Using a standard normal distribution table or calculator, we can find the probability:

P(M > 31.9) = P(Z > -0.363) = 0.641

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The correct equation for the following sentence is 24 = 31.4n + (–8.4) . Option C

Algebraic expressions are simply described as those expressions that are made up of factors, coefficients, constants, terms and variables.

Additionally, algebraic expressions are made up of arithmetic or mathematical operations, such as;

From the information given, we have that;

24 is the constant

Let the number be represented as n

Then, the expression is given as;

24 = 31.4(n) - 8.4

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The cubic polynomial is given as y = 0.25(x³ - 12x + 16). Then the value of y when x = 6 will be 40.

Therefore the option  C is correct.

A polynomial expression is described as an algebraic expression with variables and coefficients.

If the zeroes of the polynomial are negative 4, 2, and 2.

Then the factors will be (x + 4), (x - 2), and (x - 2).

Then the cubic polynomial will be

we can write the polynomial equation as:

y = C(x³ - 12x + 16)

Then the polynomial is maximum at (-2, 8) then the value of C will be 0.25.

y = 0.25 (x³ - 12x + 16)

y = 0.25 (6³ - 12 × 6 + 16)

y = 0.25 (216 - 72 + 16)

y = 0.25 (160)

y = 40

Note that there was no  diagram provides, i solved a similar question

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The side length x of the given right angle triangle is: 14.97

When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.

According to the Pythagoras Theorem, the following equation can be written as:

x² = 18² - 10²

x = √224

x = 14.97

Thus, that is the missing length of the given right triangle

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Answer: Let's start by using algebra to represent the problem.

Let X be the amount of money that Kyle started with.

Then we can create the following equations:

And we know that he's out of money, so:

Substitute the first equation into the second equation to get:

Substitute the first two equations into the third equation to get:

Substitute all three equations into the fourth equation to get:

(0.5X + 36.50) + (0.25X + 9.25) + (0.25X + 4.75) = X

Simplify and solve for X:

Therefore, Kyle started with $101.

Step-by-step explanation:

Standard form of circle with    center  (h.k) and radius r :

( x-h)^2 + (y-k)^2 = r^2

FOr the data given:

(x + 4)^2  + ( y-3)^2 = 81             (81 is the radius, 9, squared)

The coordinates of the resulting point, R', are (1,-4).

A translation is a type of transformation in geometry that moves a point or an object from one place to another without changing its size, shape, or orientation.

To translate a point, you need to specify the direction and distance of the movement.

Given that:

The point R(1,-2) is being translated 2 units down, which means that it will move vertically downwards by a distance of 2 units.

The x-coordinate will remain the same, as the movement is only in the y-direction.

So, to find the coordinates of the resulting point, R', we subtract 2 from the y-coordinate of the original point R:

R' = (1, -2 - 2)

R' = (1, -4)

Therefore, resulting coordinates of R' are (1,-4).

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Answer:

[tex]A_{\text{red}} = 1766.25 \text{ in}^2[/tex]

Step-by-step explanation:

We can see that there are four bands total on the target, two of which are red bands. With this information, we can solve for the radius of the circle within each band, since we know that each band is the same width:

[tex]r_1 = \dfrac{1}{4} \cdot 30 = 7.5\\[/tex]

[tex]r_2 = \dfrac{2}{4} \cdot 30 = 15\\[/tex]

[tex]r_3 = \dfrac{3}{4} \cdot 30 = 22.5\\[/tex]

[tex]r_4 = 30[/tex]

We can now find the area of each red band by subtracting:

the area of the circle within the white band just inward of the red band

-- from --

the area of the circle within the red band.

Finding the area of the outer red band:

[tex]A_{\text{outer red}} = A(\text{circle within outer red}) - A(\text{circle within outer white})[/tex]

[tex]A_{\text{outer red}} = A(\odot \text{ with radius }r_4) - A(\odot \text{ with radius } r_3)[/tex]

↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])

[tex]A_{\text{outer red}} = (\pi \cdot 30^2) - (\pi \cdot 22.5^2)[/tex]

↓ using 3.14 for [tex]\pi[/tex]

[tex]A_{\text{outer red}} = (3.14 \cdot 30^2) - (3.14 \cdot 22.5^2)[/tex]

↓ evaluating the right side

[tex]A_{\text{outer red}} = 2826 - 1589.625[/tex]

[tex]A_{\text{outer red}} = 1236.375 \text{ in}^2[/tex]

Finding the area of the inner red band:

[tex]A_{\text{inner red}} = A(\text{circle within inner red}) - A(\text{circle within inner white})[/tex]

[tex]A_{\text{inner red}} = A(\odot \text{ with radius }r_2) - A(\odot \text{ with radius } r_1)[/tex]

↓ substituting the radius values into the circle area formula ([tex]\pi r^2[/tex])

[tex]A_{\text{inner red}} = (\pi \cdot 15^2) - (\pi \cdot 7.5^2)[/tex]

↓ using 3.14 for π

[tex]A_{\text{inner red}} = (3.14 \cdot 15^2) - (3.14 \cdot 7.5^2)[/tex]

↓ evaluating the right side

[tex]A_{\text{inner red}} = 706.5 - 176.625[/tex]

[tex]A_{\text{inner red}} = 529.875 \text{ in}^2[/tex]

Finally, we can find the area of all of the red on the target by adding the area of the outer and inner red bands.

[tex]A_{\text{red}} = A_{\text{outer red}} + A_{\text{inner red}}[/tex]

[tex]A_{\text{red}} = 1236.375 \text{ in}^2 + 529.875 \text{ in}^2[/tex]

[tex]\boxed{A_{\text{red}} = 1766.25 \text{ in}^2}[/tex]

Answer:

I can tell

Step-by-step explanation:

Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)

The baker should use 24kg amount of flour when making the biscuits. The correct answer is (b) 24kg.

To determine the amount of flour the baker should use when making biscuits, we can use the given ratio of flour to sugar, which is 4:1.

Since the ratio is 4:1, for every 4 parts of flour, there is 1 part of sugar. Therefore, the ratio of flour to sugar can be expressed as 4/1.

If the baker uses 6kg of sugar, we can set up a proportion to find the corresponding amount of flour:

4/1 = x/6

Cross-multiplying, we get:

4 * 6 = 1 * x

24 = x

Therefore, the baker should use 24kg of flour when making the biscuits.

In summary, the correct answer is (b) 24kg.

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Answer:

V ≈ 1809 ft^3

Step-by-step explanation:

Given:

r (radius) = 6ft

h (height) = 16ft

π = 3,14

Find: V (volume) - ?

[tex]v = \pi {r }^{2} \times h[/tex]

[tex]v = 3.14 \times {6}^{2} \times 16 ≈1809 \: {ft}^{3} [/tex]

The equation that can be used to determine the cost of each admission ticket is 4x + $25.00 = $175.00.

The cost in dollars of the admission ticket is $ 37.50.

Let x be the cost, in dollars, of each admission ticket, including tax.

The total cost of 4 admission tickets can be expressed as 4x, since the cost of each ticket is the same.

The total cost of 4 admission tickets and parking is given as $175.00, so we can write:

4x + $25.00 = $175.00

Simplifying the equation, we can solve for x:

4x = $175.00 - $25.00

4x = $150.00

x = $37.50

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Answer:

Step-by-step explanation:

Answer:    x=a/3      x=a/5

Step-by-step explanation:

15x²-2ax = a²          subtract a² from both sides

15x²- 2ax - a² = 0

You would solve this like you would any quadratic.  Factor.

Start my multiplying the first and last coefficients

15(-a²)  = -15a²    =>find 2 numbers that multiply to this but add to middle

                                term (-2a)

-5a   and   +3a     multiply to -15a² and adds to -2a

Substitute the middle term with the numbers we just found, keeping the x

15x²- 2ax - a² = 0

15x²- 5ax+3ax - a² = 0         > group the first 2 terms and last 2

(15x²- 5ax)(+3ax - a²)= 0      > this is not your factors, you need to take

                                                 GCF out of each grouping

5x(3x-a)+a(3x-a)=0              >if the parenthesis is same, you did good

                                                now the parenthesis is your GCF and one of

                                                your factors, whatever is left is your other

                                                factor

(3x-a)(5x-a)=0                        > set each factor = 0 and solve for x

(3x-a)=0         and             (5x-a)=0  

x=a/3                                    x=a/5

Answer:

1. $990

2. Sn = Sn-1 + (r/100) * Sn-1

3. $27,037.44

Step-by-step explanation:

1. The interest earned each year can be calculated using the simple interest formula:

Simple Interest = (Principal * Rate * Time) / 100

Here, Principal = $22,000, Rate = 4.5%, and Time = 1 year

So, the interest earned each year would be:

= (22,000 * 4.5 * 1) / 100

= $990

Therefore, the interest earned each year would be $990.

2. The recurrence relation to model the value of investment from year to year is:

Sn = Sn-1 + (r/100) * Sn-1

where Sn represents the value of the investment after n years, Sn-1 represents the value after n-1 years, and r represents the annual interest rate.

Using this recurrence relation, we can calculate the value of the investment for different years:

- S1 = 22,000 + 990 = 22,990

- S2 = 22,990 + (4.5/100) * 22,990 = 24,026.55

- S3 = 24,026.55 + (4.5/100) * 24,026.55 = 25,103.46

And so on...

3. To determine the value of the investment after 5 years, we can simply substitute n = 5 in the recurrence relation:

S5 = S4 + (r/100) * S4

= S3 + (r/100) * S3 + (r/100) * S3

= S2 + (r/100) * S2 + (r/100) * S2 + (r/100) * S2

= S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1 + (r/100) * S1

Substituting values from previous calculations:

S1 = 22,000 + 990 = 22,990

So,

S5 = 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990 + (4.5/100) * 22,990

= $27,037.44

Therefore, the value of the investment after 5 years would be $27,037.44.

The amount it would cost to paint the wall, given the cost of paint and the area covered is $ 56 .

The surface area of the circular wall would be :

A = 2 x π x r x h

The area is therefore:

= 2 x π x r x h

= 2 x 3. 14 x 15 x 4

= 376. 8 square feet

The number of gallons needed is therefore:

= 376. 8 / 225

= 1. 674

= 2 gallons

The cost of two gallons is:

= 2 x 28

= $ 56

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Answer: According to the problem, N Heracio used the computer for 40 hours last week. We are asked to find the difference between the time spent on shopping online and doing homework.

To do this, we first need to find the amount of time spent on each activity. We can do this by multiplying the total computer time by the percentage of time spent on each activity:

Time spent on videos = 10% of 40 hours = 4 hours

Time spent on homework = 15% of 40 hours = 6 hours

Time spent on games = 20% of 40 hours = 8 hours

Time spent on social media = 25% of 40 hours = 10 hours

Time spent on shopping online = 20% of 40 hours = 8 hours

Therefore, Heracio spent 6 hours on homework and 8 hours on shopping online.

The difference between these two amounts is:

6 hours - 8 hours = -2 hours

This means that Heracio spent 2 hours more on shopping online than on doing homework.

Step-by-step explanation:

Answer:

Step-by-step explanation:

C (Wait for another defendant, check with him and write this answer)

The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

We have to given that;

The set is,

⇒ {4, 5, 6, 7, 8}

Thus, We can write correct Set-builder form as,

⇒ {4, 5, 6, 7, 8}

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

So, The value of correct Set-builder form is,

⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }

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The statement that "if you took a true "if-then' statement and reversed the clauses, the new statement would also be true" is False.

By reversing the clauses within an accurate "if-then", one will manifest a new statement known as the "converse" of the initial formula. Though, it is not inevidably true.

For instance, if the original expression was "If it rains, then the ground gets wet", its converse is "If the ground gets wet, then it rains". Unfortunately, that specific converse has the potential to be incorrect since there are several other methodologies from which the land can gain moisture beside rain (e.g. sprinkler system, someone unintentionally pouring water, etc.).

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