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2 years ago

Given a quadratic function in vertex form:

Mathematics

1 answer:

Alja [10]2 years ago

7 0

Answer:

See below

Step-by-step explanation:

Part A

A vertical stretch takes place when $a\cdot f(x)$ given that $|a| > 1$

Part B

A vertical compression takes place when $a\cdot f(x)$ given that $0 < |a| < 1$

Part C

A vertical stretch is different than a horizontal compression:

In a vertical stretch, the input stays the same, but the output is multiplied by the scale factor
In a horizontal compression, the output stays the same, but the input is multiplied by the scale factor

Part D

A reflection across the x-axis means that the output, our y-variable, is the opposite sign. This means that all values of $a$ must be negative such that $a\cdot f(x)$ as mentioned in parts A and B. Also, in part C, since our scale factor is negative, the output is the only one being multiplied by the scale factor.

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A firm produces 16,200 units at a total cost of $37,585.60. Find the cost per unit to the nearest cent.

Julli [10]

There are a total of 16 200 units with a total costs of 37 585.60 dollars. Now, Given with the choices for the answer, let's find out which one is correct. To be able to get the answer, simply divide the total costs, with the total number of units. => 37 585.60 dollars / 16 200 units => 2.3201 dollars per unit.Next, we need to round this cents to the nearest given options.Since the number next to hundredths is less than 5 , the let's round it to : => 2.32. - this is the correct answer.

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3 years ago

Show work and Factor 4x^2+xy-18y^2

grigory [225]

Answer:

$4x^2+xy-18y^2=(4x+9y)\,(x-2y)$

Step-by-step explanation:

Let's examine the following general product of two binomials with variables x and y in different terms:

$(ax+by)\,(cx+dy)= ac\,x^2+adxy+bcxy+bdy^2$

so we want the following to happen:

$a\,c = 4\\ad+bc=1\\bd--18$

Notice as well that $ad+bc =1$ means that those two products must differ in just one unit so, one of them has to be negative, or three of them negative. Given that the product $bd=-18$ , then we can consider the case in which one of this (b or d) is the negative factor. So let's then assume that $a\,\,and \,\,c$ are positive.

We can then try combinations for $a\,\,and \,\,c$ such as:

$a = 4;\,\,c=1\\a=2;\,\,c=2\\a=1;\,\,c=4$

Just by selecting the first one $(a=4;\,\,c=1)$

we get that $4d_b=1\\b=-4d-1$

and since

$bd=-18\\(-4d-1)\,d=-18\\-4d^2-d=-18\\4d^2+d-18=0$

This quadratic equation give as one of its solutions the integer: d = -2, and consequently,

$d=-18/(-2)\\d=9$

Now we have a good combination of parameters to render the factoring form of the original trinomial:

$a=4; \,\,b=9;\,\,c=1;\,\,d=-2$

which makes our factorization:

$(4x+9y)\,(x-2y)=4x^2+xy-18y^2$

6 0

3 years ago

Megan charges %5.00 for each hour, (h), she babysits. Last week, the total amount she earned by babysitting was $65.00.

mel-nik [20]

Answer:

Step-by-step explanation:

To find how many hours she worked you must divide $65 by $5 and B is the only equation where you can do that.

8 0

3 years ago

Haii guys I need help ASAP pleasee

Evgen [1.6K]

Answer: 100

Step-by-step explanation: Part B is 100, you get that answer because you have ten put out the 1 and then the two is telling you to put 2 zeros .

3 0

3 years ago

12) A radio transmission tower is 170 feet tall. How long should a guy wire be if it is to be attached 15 feet from the top and

ser-zykov [4K]

The length of guy wire needed to make an angle of 30° with the ground is 310 feet. The angle between the end of the shadow and the vertical side of the building is 23°

<h3>What is trigonometric ratio?</h3>

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

a) Let l represent the length of the guy wire.

sin(30) = (170 - 15) / l

l = 310 feet

b) Let Ф represent the angle, hence:

tanФ = 100/230

Ф = 23°

The length of guy wire needed to make an angle of 30° with the ground is 310 feet. The angle between the end of the shadow and the vertical side of the building is 23°

Find out more on trigonometric ratio at: brainly.com/question/24349828

6 0

2 years ago