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3 years ago

The sum of two consecutive integers is at most 45. What is the larger integer?

Mathematics

1 answer:

alina1380 [7]3 years ago

4 0

22 + 23 = 45
Largest would be 23

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What is the answer

Mrac [35]

Answer:

The coordinates of H′ are (-2,0).

Step-by-step explanation:

It is given that square EFGH stretches vertically by a factor of 2.5 with respect to the x-axis to create rectangle E′F′G′H′.

If a figure stretches vertically by a factor of 2.5 with respect to the x-axis, then the x-coordinates remains same and the points which lie on the axis are also remains the same after stretch.

It is given that the coordinates of H are (-2,0). This point lie on the x-axis, therefore it will remains the same after stretch.

Therefore the coordinates of H′ are (-2,0).

3 0

3 years ago

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Evaluate the function for the given values to determine if the value is a root. p(−2) = p(2) = The value is a root of p(x).

bija089 [108]

Note: Since you missed to mention the the expression of the function $p(x)$ . After a little research, I was able to find the complete question. So, I am assuming the expression as $p(x)=x^4-9x^2-4x+12$ and will solve the question based on this assumption expression of $p(x)$ , which anyways would solve your query.

Answer:

$p\left(-2\right)=0$

Therefore, $x=-2$ is a root of the polynomial $p(x)=x^4-9x^2-4x+12$

$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial $p(x)=x^4-9x^2-4x+12$

Step-by-step explanation:

As we know that for any polynomial let say $p(x)$ , $c$ is the root of the polynomial if $p(c)=0$ .

In order to find which of the given values will be a root of the polynomial, $p(x)=x^4-9x^2-4x+12$ , we must have to evaluate $p(x)$ for each of these values to determine if the output of the function gets zero.

So,

Solving for $p\left(-2\right)$

$p(x)=x^4-9x^2-4x+12$

$p\left(-2\right)=\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Simplify\:}\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12:\quad 0$

$\left(-2\right)^4-9\left(-2\right)^2-4\left(-2\right)+12$

$\mathrm{Apply\:rule}\:-\left(-a\right)=a$

$=\left(-2\right)^4-9\left(-2\right)^2+4\cdot \:2+12$

$\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}$

$=2^4-2^2\cdot \:9+8+12$

$=2^4+20-2^2\cdot \:9$

$=16+20-36$

$=0$

Thus,

$p\left(-2\right)=0$

Therefore, $x=-2$ is a root of the polynomial $p(x)=x^4-9x^2-4x+12$ .

Now, solving for $p\left(2\right)$

$p(x)=x^4-9x^2-4x+12$

$p\left(2\right)=\left(2\right)^4-9\left(2\right)^2-4\left(2\right)+12$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$p\left(2\right)=2^4-9\cdot \:2^2-4\cdot \:2+12$

$p\left(2\right)=2^4-2^2\cdot \:9-8+12$

$p\left(2\right)=2^4+4-2^2\cdot \:9$

$p\left(2\right)=16+4-36$

$p\left(2\right)=-16$

Thus,

$p\left(2\right)=-16$

Therefore, $x=2$ is not a root of the polynomial $p(x)=x^4-9x^2-4x+12$ .

Keywords: polynomial, root

Learn more about polynomial and root from brainly.com/question/8777476

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7 0

3 years ago

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Jermaine has just painted a large mural. It's 8 1/2 feet wide the wall he wants to place it on is 11 3/4 feet wide.Ahout how far

Fittoniya [83]

About 1.63 ft.
First subtract 8.5 from 11.75 which is 3.25
then divide 3.25 by 2 which is 1.625
Therefore about 1.63 ft. away from each side.

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3 years ago

Picking a month of the year in the day of the week (fundamental counting principle)

inysia [295]

Since you mentioned the fundamental counting principle, I assume you are looking for the total number of possibilities.

If you are picking a month, there are 12 options.
If you are selecting a day of the week, there are 7 options.

If you are doing both, you multiply the two numbers together.
12 x 7 = 84

8 0

3 years ago

A positive integer from one to six is to be chosen by casting a die. Thus the elements c of the sample space C are 1, 2, 3, 4, 5

Alex_Xolod [135]

Answer with Step-by-step explanation:

We are given that six integers 1,2,3,4,5 and 6.

We are given that sample space

C={1,2,3,4,5,6}

Probability of each element= $\frac{1}{6}$