–2x + 3y = 21

3x – 2y = 21

–2x – 3y = 21

–2x + 3y = 7

Final answer:

To express 112 as a product of prime numbers in index form, we perform prime factorization to get 2⁴ x 7.

Explanation:

To express 112 as a product of prime numbers in index form, we start by performing prime factorization, which is breaking down a composite number into the prime numbers that, when multiplied together, give the original number.

Let's find the prime factors of 112:

So, we can express 112 as a product of prime factors as 2⁴ × 7¹ or simply 2⁴ × 7, since any number to the power of 1 is the number itself.

Answer:

If Veronica gave $35 to Bill, she spent $70 to buy books and she has $70 left.

Step-by-step explanation:

The graph represents the function y = (x - 1), as per linear equation.

A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.

The given equation is:

y - 3 = x - 4

⇒ y = x - 1

Therefore, for x = 0, y = - 1

for x = 1, y = 0

for x = - 1, y = - 2

Therefore, the graph will pass through points (0, - 1), (1, 0), (- 1, - 2).

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Answer:

its A

Step-by-step explanation:

Answer:

Volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]

Step-by-step explanation:

Formula to find the volume of a cone is V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here r is the radius of the cone and h is the height of the cone.

Since radius of cone = [tex]\frac{1}{2}(\text{Radius of cylinder})[/tex]

                                  = [tex]\frac{r}{2}[/tex]

Height of the cone = radius of the cylinder = r

Now we put the values of radius and height of cone in the formula

Volume of cone = [tex]\frac{1}{3}\pi (\frac{r}{2})^{2}(r)[/tex]

= [tex]\frac{1}{3}\pi(\frac{r^{2}}{4})(r)[/tex]

= [tex]\frac{1}{12}\pi r^{3}[/tex]

Therefore, volume of the cone is [tex]\frac{1}{12}\pi r^{3}[/tex]

Answer:

The coefficient of x is  [tex]\frac{1}{3}[/tex]

7 is a constant

Step-by-step explanation:

[tex]\frac{x}{3} +7[/tex]

We need to find the coefficient of each term in the given expression

x/3 can be written as 1/3 times x

The coefficient is the number with the variable x

The coefficient of x is [tex]\frac{1}{3}[/tex]

7 is a constant

we know that

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

where

r is the radius of the circle

In this problem we have

[tex]A=64\pi \ ft^{2}[/tex]

substitute in the formula and solve for r

[tex]64\pi=\pi r^{2}[/tex]

Simplify

[tex]64=r^{2}[/tex]

Square root both sides

[tex]r=8\ ft[/tex]

therefore

the answer is

The value of r is [tex]8\ ft[/tex]

The following is not a properly formed syllogism.

Option A is the answer.

A syllogism is a form of argument where the conclusion follows from the truth of two or more given statements.

We have,

Statements:

If you drink tea, you always add sugar.

If sugar is added, then the tea is sweeter.

Conclusion:

If it is sweet, then you’re drinking tea.

This is not a conclusion from the truth of the given statements.

There is nowhere mention of tea in the statements.

Thus,

It is not a properly formed syllogism.

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Answer:

[tex]6x^2-31x+35[/tex]

Step-by-step explanation:

Given expression,

[tex](3x-5)(2x-7)[/tex]

By using distributive property,

[tex](3x-5)(2x) - (3x - 5)(7)[/tex]

Again by distributive property,

[tex]3x(2x) - 5(2x) - 3x(7) + 5(7)[/tex]

[tex]6x^2 - 10x - 21x + 35[/tex]

[tex]6x^2-31x+35[/tex]

Hence, FIRST option is correct.

Answer:

x = 7

Step-by-step explanation:

Figure ABCD is a parallelogram

So sides AD and BC will be parallel and their length will be same.

[Since opposite sides of parallelogram are equal in length]

So mAD = mBC

(5x + 3) = 38

5x = 38 - 3 = 35

x = [tex]\frac{35}{5}[/tex]

x = 7

Therefore, x = 7 will be the answer.

Answer:

The original price of socks was $8.

Step-by-step explanation:

James buys a shirt and a pair of socks on sale for 25% off.

The price of the shirt before the sale was $24 that means after discount the price was:

[tex]24-(0.25\times24)[/tex] = $18

And James paid a total of $24.

That means the price of socks after discount is = [tex]24-18[/tex] = $6

Let the original price of socks be x. And after 25% discount, it was for $6.

So, [tex]x-0.25x=6[/tex]

=> [tex]0.75x=6[/tex]

x = 8.

Hence, the original price of socks was $8.

Answer:

the answer is 7x on edg... i just took the pretest

Step-by-step explanation:

Answer:

22 secs.

Step-by-step explanation:

h(t) = -16t^2 + 704t

The maximum will happen where the first derivative is equal to 0.

h’(t) = -32t + 704

-32t + 704 = 0 => -32t = -704 After subtracting 704 from both sides of the equation

Now divide both sides of the equation by -32

t = 22 secs.

Double Check: recalculated/reasonable ✅ ✅

Answer: 22 secs.

Just an interesting aside. After 22 secs, the projectile will be -16(22)^2 + 704(22) = -7744 + 15,488 = 7744 units up as its maximum height.

The length of each side of the tablecloth is 13 inches.

To find the length of each side of the tablecloth, we need to take the square root of the area. Since the area is given as 169 square inches, we can take the square root of 169. The square root of 169 is 13, so each side of the tablecloth is 13 inches long.

Answer:

Dependent. When the first balloon is taken, it affects the ratio of red to blue balloons.

Step-by-step explanation:

Whatever color the sister choses is irrelevant, eliminating answers A and B, but it does change the odds. If there are 5 red balloons and 4 blue balloons, if the sister is given a blue balloon, the odds of the brother receiving a red balloon increases (vis versa).

we know that

the rule of the translation A is

[tex](x,y)-----> (x-9,y-2)[/tex]

that means

the translation is [tex]9[/tex] units to the left and [tex]2[/tex] units down

the rule of the translation B is

[tex](x,y)-----> (x+1,y-2)[/tex]

that means

the translation is [tex]1[/tex] unit to the right and [tex]2[/tex] units down

therefore

the rule of the composition A+B is

[tex](x,y)-----> (x-9+1,y-2-2)[/tex]

[tex](x,y)-----> (x-8,y-4)[/tex]

that means

the translation is [tex]8[/tex] units to the left and [tex]4[/tex] units down

so

the answer is

[tex](x,y)-----> (x-8,y-4)[/tex]

The translation rule that describes the result of the composition of the transformations (x, y) --> (x - 9, y - 2) and (x, y) --> (x + 1, y - 2) is (x, y) --> (x - 8, y - 4). This rule is obtained by sequentially applying each transformation to (x, y).

When we talk about compositions of translations in geometry, what we are doing is carrying out one translation after the other. So, if we have two translations: (x, y) --> (x - 9, y - 2) and (x, y) --> (x + 1, y - 2), we perform these operations sequentially.

First, we apply the transformation (x,y) --> (x - 9, y - 2). Then we take these new coordinates and apply the second transformation (x,y) --> (x + 1, y - 2). The result of this composition is (x - 9 + 1, y - 2 - 2) = (x - 8, y - 4), as you add (or subtract) the changes introduced by each translation.

So, the translation rule that can be used to describe the result of the composition of these transformations is: (x, y) --> (x - 8, y - 4).

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Rewrite the given equation in slope intercept form:

5 y = 10 – 2 x

y = - 0.4 x + 2

Since the two lines are parallel, therefore they have similar slope which is – 0.4, so the equation is:

y = - 0.4 x + b

Given that x = 5, y = -4, find for b:

-4 = - 0.4 (5) + b

b = -2

So the answer is:

y = - 0.4 x – 2

or

2 x + 5 y = - 10

Final answer:

To find the cost of each slice of white chocolate torte, divide the total cost to produce two tortes ($11.90) by the total number of slices (16), resulting in approximately 74 cents per slice.

Explanation:

Cost of Each Slice of White Chocolate Torte

To calculate the cost of each slice of white chocolate torte, we start by determining the total cost of producing the tortes. The restaurant's cost is $11.90 for 2 tortes, and each torte is cut into 8 slices. This means there's a total of 2 tortes × 8 slices/torte = 16 slices. Dividing the total cost by the number of slices gives us the cost per slice:

Total cost for 2 tortes: $11.90

Number of slices per torte: 8

Total number of slices: 2 tortes × 8 slices/torte = 16 slices

Cost per slice: $11.90 / 16 slices = $0.74375 per slice

Therefore, each slice costs approximately 74 cents to make.