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3 years ago

5

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. Which

of the following describes the domain of

1 answer:

Dmitrij [34]3 years ago

8 0

Answer: All the real values except x ≠ 7 and the x for which f(x)≠-3

Step-by-step explanation:

Since, For function f , the domain is R - {7}

That is, If x is any element of the domain of the function f,

Then, x ≠ 7

(gof)(x) = g(f(x))

Since, For the function g, the domain is R - {-3}

Thus, If f(x) is any element of the domain of the function g,

Then f(x)≠ -3

Hence, Fourth Option is correct.

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A rectangular school banner has a length of 36 inches and a width of 52 inches. A sign is made that is similar to the school ban

zalisa [80]

Answer:

<u>4212 : 1573</u> is the ratio.

Step-by-step explanation:

Given:

Length of rectangular school banner is 36 inches and width is 52 inches.

And, the sign made is similar to banner.

The sign's length is 22 inches.

Now, we have to find the ratio of the area of the banner to the area of the sign.

So, we have dimensions of rectangular school banner:

Length = 36 inches.

Width = 52 inches.

But, we have only length of sign:

Length = 22 inches.

Now, we have to find the width of sign by using cross multiplication method:

Let the width of sign be $x.$

<em>As, sign is similar to banner.</em>

So, if 36 inches is equivalent to 52 inches.

Then, 22 inches is equivalent to $x.$

$\frac{36}{52} =\frac{22}{x}$

<em>By cross multiplying we get:</em>

<em /> $36x=1144$ <em />

<em>Dividing both sides by 36 we get:</em>

$x=31\frac{7}{9} .$

<em>Hence, the width of sign is </em> $31\frac{7}{9}$ <em> inches.</em>

Now, we find the area of banner and the area of sign by putting formula:

Area of banner = length × width.

$Area\ of\ banner=36\times 52$

$Area\ of\ banner=1872\ square\ inches.$

Now, area of sign:

$Area\ of\ sign=length\times width\\\\Area\ of\ sign=22\times 31\frac{7}{9} \\\\Area\ of\ sign=22\times \frac{286}{9} \\\\Area\ of\ sign=\frac{6292}{9} \ square\ inches.$

Now, to get the ratio of the area of the school banner to the area of the sign:

$1872:\frac{6292}{9}$

$=\frac{1872}{\frac{6292}{9} } \\\\=\frac{16848}{6292}$

<em>On simplifying we get:</em>

$=\frac{4212}{1573}$

$=4212:1573.$

Therefore, the ratio of the area of the school banner to the area of the sign is 4212:1573.

8 0

3 years ago

Solve with a system of equations: Two angles are supplementary if the sum of their measures are 180 degrees. If one is 90 degree

julsineya [31]

Answer:

The measures of the angles are 150° and 30°.

Step-by-step explanation:

Let x and y represent the measures of the angles, with x representing the larger angle.

x + y = 180 . . . . . . the two angles are supplementary

x = 90 + 2y . . . . . one is 90° more than twice the other

___

Substituting the expression given by the second equation into the first, we have ...

(90 +2y) +y = 180

3y = 90 . . . . . . . . . . collect terms, subtract 90

y = 30 . . . . . . . . . . . divide by the coefficient of y

x = 180 -y = 150

The measures of the angles are 150° and 30°.

6 0

3 years ago

On a coordinate plane, rhombus W X Y Z is shown. Point W is at (7, 2), point X is at (5, negative 1), point Y is at (3, 2), and

Otrada [13]

Answer:

$P = 4\sqrt{13}$

Step-by-step explanation:

Given

$W = (7, 2)$

$X = (5, -1)$

$Y = (3, 2)$

$Z =(5, 5)$

Required

The perimeter

To do this, we first calculate the side lengths using distance formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2$

So, we have:

$WX = \sqrt{(5- 7)^2 + (-1 - 2)^2$

$WX = \sqrt{13}$

$XY = \sqrt{(3-5)^2 + (2--1)^2}$

$XY = \sqrt{13}$

$YZ = \sqrt{(5-3)^2 + (5-2)^2}$

$YZ = \sqrt{13}$

$ZW = \sqrt{(7 - 5)^2 + (2 - 5)^2}$

$ZW = \sqrt{13}$

The perimeter is:

$P = WX + XY + YZ + ZW$

$P = \sqrt{13}+\sqrt{13}+\sqrt{13}+\sqrt{13}$

$P = 4\sqrt{13}$

5 0

3 years ago

Read 2 more answers

ASAP AND BRAINLIEST please please help guys im in a hurry

Vera_Pavlovna [14]

Answer:

(2, 1.5)

Step-by-step explanation:

Outlier Definition: An outlier is defined as a data point that emanates from a different model than do the rest of the data.

The only one that stands out is (2, 1.5)

Answer: (2, 1.5)

8 0

3 years ago

Yes, a binary tree can be a maxheap. Consider a binary search tree with two values 3 and 5, where 5 is at the root. The tree is

Alchen [17]

Answer:

3 and 5

Step-by-step explanation:

factor tree is more appropriate.

4 0

3 years ago