The function h(x) is quadratic and h(3) = h(–10) = 0. Which could represent h(x)?

h(x) = x2 – 13x – 30
h(x) = x2 – 7x – 30
h(x) = 2x2 + 26x – 60
h(x) = 2x2 + 14x – 60

Equivalent equations can be created by multiplying or dividing the original equation by any nonzero constant. Lifting the coefficients of the given equations accordingly can create multiple equivalent equations.

To create two equations that are equivalent to the given equation 1.5x + 10y = 15, we can multiply the entire equation by a nonzero constant.  By multiplying by 2, we obtain 3x + 20y = 30. Conversely, dividing the original equation by 3 gives us 0.5x + 3.3333y = 5.

Applying the same concept to the second equation -9x - 12y = 6, multiplying by 2 gives us -18x - 24y = 12, and dividing by 3 gives us -3x - 4y = 2.

For the third equation -2x + 4y = -5, multiplying by any nonzero constant yields an equivalent equation. Multiplying by 2, we get -4x + 8y = -10, and dividing by 2 gives us -1x + 2y = -2.5.

Answer:

Step-by-step explanation:

6/8

Answer:

2

Step-by-step explanation:

Answer: 4 sqrt 7

Step-by-step explanation:

He is correct, the answer is the one above.

Option (D) To simplify the expression 5√7 + √7 - 2√7, combine like radicals by adding their coefficients to get the simplified form, which is 4√7.

The student is asked to simplify the expression 5√7 + √7 - 2√7. To simplify an expression that involves like radicals, combine them by adding or subtracting their coefficients, just as you would combine like terms in algebra.

The expression simplifies as follows:

Combine the terms with like radicals: (5 + 1 - 2)√7

Simplify the coefficients: 4√7

Therefore, the simplified form of the expression is 4√7.

the answer is A my good sir/madam

Area is determined by using the formula A=lw  Area= Length x  Width

A= 1 1/4 x 3   convert to an improper fraction

A= 5/4 x 3/1  multiply

A=15/4   divide

A=3 3/4 square feet

Answer: [tex]A=3\dfrac{3}{4}\ ft^2[/tex]

Step-by-step explanation:

Given: The dimensions of the wrapping paper :

[tex]1\text{ and}\dfrac{1}{4}\text{ feet }\text{ by 3 feet}\\\\\text{i.e }1+\dfrac{1}{4}\text{ feet }\text{ by 3 feet}\\\\\text{i.e }\dfrac{5}{4}\text{ feet }\text{ by 3 feet}[/tex]

Now, we know that the area of a rectangle is given by :-

[tex]A=length*width[/tex]

Now, the area of the wrapping paper is given by :-

[tex]A=\dfrac{5}{4}\times3=\dfrac{15}{4}=3\dfrac{3}{4}\ ft^2[/tex]

Answer with Step-by-step explanation:

The volume of cone is given by:

V=[tex]\dfrac{1}{3}\times \pi r^2h[/tex]

Where r is the radius of cone and h is height

r=d/2 where d is the diameter

Hence, here r=5 in.

height is twice its radius ⇒ h=10 in.

V=[tex]\dfrac{1}{3}\times 3.14\times 5^2\times 10[/tex]

V=261.66 in³

Hence, Volume of cone is:

261.66 in³

Answer:

Its really false!!!!!

Step-by-step explanation:

Answer:

  x ≈ 4.1 cm

Step-by-step explanation:

The side (z) opposite the 42° triangle can be found from the relation ...

  z/(3.6 cm) = tan(42°)

  z = (3.6 cm)·tan(42°) ≈ 3.2415 cm

The relationship between z and x is ...

  z/x = cos(38°)

  x = z/cos(38°) ≈ 4.1135 cm

  x ≈ 4.1 cm

Answer:

D isn't the correct answer. It's "It shrinks the graph vertically to 1/2 its original height."

Step-by-step explanation:

I'm not sure why though this is right because I graphed it, and I don't see how that could be the right answer.

Answer:

Option A - It shrinks the graph vertically to 1/2 its original height.

Step-by-step explanation:

Given : In the function [tex]y=\frac{1}{2} x^2[/tex]

To find : What effect does the number [tex]\frac{1}{2}[/tex] have on the graph, as compared to the graph of the function [tex]y=x^2[/tex] ?

Solution :

The parent function is [tex]y=x^2[/tex]

We have given that  [tex]\frac{1}{2}[/tex] number is multiply to the parent function.

When the unit is multiply to the function gives you vertical stretch or compression

i.e, f(x)→ bf(x), o<b<1 then the function is vertically compressed.

[tex]y=\frac{1}{2} x^2[/tex] As  [tex]0<\frac{1}{2}<1[/tex] means there is vertical compression or shrinks.

Therefore, Option A is correct.

It shrinks the graph vertically to 1/2 its original height.

There were about 1194 students at Marita's school last year.

To find the number of students last year when the current number is 1170 and represents 98% of last year's number, you can set up a simple equation.

Let "x" represent the number of students last year.

According to the given information, the current number of students is 98% of last year's number, which can be expressed as:

1170 = 0.98x.

To find the value of "x," you need to divide 1170 by 0.98:

[tex]\(x = \frac{1170}{0.98} = 1193.877\).[/tex]

Rounding to the nearest whole number, last year's number of students was approximately 1194.

So, there were about 1194 students at Marita's school last year.

To solve systems of equations, select a method based on the system's setup; using substitution, we solve the given system and find the solution to be (2, 0).

When solving systems of equations, one must choose the method that best fits the problem's constraints. Methods include substitution, elimination, and graphing. The method selected often depends on how the equations are presented and which method allows for the most straightforward calculation.

Choosing the system –y + 3x = 6 and y = –6x + 12, we can solve it using substitution since the second equation is already solved for y:

Our solution is (x, y) = (2, 0).

The statement is true for linear functions, but not in general for all functions.

The statement is true if f(x) is a linear function.

However, it is not true in general for all functions, so the statement is false.

An example of a linear function where the statement is true would be f(x) = 2x.

If we substitute s + t into the function, we get f(s + t) = 2(s + t) = 2s + 2t.

On the other hand, if we substitute f(s) + f(t) into the function, we get f(s) + f(t) = 2s + 2t.

Therefore, the equality holds and the statement is true for linear functions.

Answer

A

Step-by-step explanation:

Answer:

The baker made 36 batches of muffins.

Step-by-step explanation:

Let the total amount of flour be x

We know he used 2/5 of the flour for bread, we also know he used 16 pounds for bread.

We can write this as :

[tex]\frac{2}{5}\times x=16[/tex]

Solving this we get;

[tex]2x=80[/tex]

So, x = 40

Means total amount of flour was 40 pounds and he used 16 pounds for bread, so the remaining is for batches of muffins, which is [tex]40-16=24[/tex] pounds

As each batch of muffin uses 2/3 pounds, so 24 pounds of flour will be used to bake :

[tex]\frac{24}{\frac{2}{3} }[/tex]

= [tex]\frac{24\times3}{2} =36[/tex]

Hence, the baker made 36 batches of muffins.

Final answer:

To solve the word problem, we define three variables representing the number of first-, second-, and third-place finishers, respectively. We set up three linear equations based on the information provided, and by solving the system, we determined that 10 swimmers finished in first place, 8 in second, and 6 in third.

Explanation:

Setting Up the Equations

Let's denote the number of first-place finishers as x, second-place finishers as y, and third-place finishers as z. According to the information provided:

Total number of individuals placed: x + y + z = 24

Total points earned: 3x + 2y + z = 53

The number of first-place finishers equals the number of second and third-place finishers combined: x = y + z

This is our system of three equations.

Solving the System of Equations

To solve for the number of swimmers in each place, use the substitution or elimination method:

Since x = y + z, substitute x in the first two equations.

You'll get two equations with two variables (y and z).

Solve these equations to find the values of y and z.

Finally, substitute the found y and z back into x = y + z to get the value of x.

By solving this system, we find that 10 swimmers finished in first place, 8 swimmers finished in second, and 6 swimmers finished in third.