The composition of a function and its inverse is always __________.

Answer:

D for both

Step-by-step explanation:

Exercise is the condition and healthier is the outcome. So if you exercise then you will be healthier.

All cardinals are red. But not all red birds are cardinals. So d is the only one that is always true

1. if you exercise, then you will be healthier.

2. if a bird is a cardinal, it is red

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences.

Given:

Exercise makes you healthier.

So, we have to write in the form of if- then statement

Thus, the statement is if you exercise, then you will be healthier..

Now, for the second statement "Cardinals are red birds."

The conditional statement is  if a bird is a cardinal, it is red.

Learn more about Conditional Statement here:

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Answer:

2x10 + 8x6 + 4x2 - x + 3

Step-by-step explanation:

it has the same numbers and variables. it is descending because it's starting from the the highest value or biggest variable then goes from greatest to least from there.

Answer:

[tex]2x^{10}+8 x^{6} +4x^{2} -x+3[/tex]

Step-by-step explanation:

The given polynomial is

[tex]4x^{2} -x+8x^{6}+3+2x^{10}[/tex]

A descending order refers to the position of terms, where the "higher term" has the greatest exponent (greatest grade), and we order from greatest to least to have a descending order, as follows

[tex]2x^{10}+8 x^{6} +4x^{2} -x+3[/tex]

Notice that the temrs are placed from greatest expoenent to least.

Therefore, the answer is [tex]2x^{10}+8 x^{6} +4x^{2} -x+3[/tex]

Answer:

Step-by-step explanation:

y=5/2x+2

2y=5x+4

y=5/2x+2

y=5/2x+2

they are the same line/equation so infinite number of solutions

Answer:

Step-by-step explanation:

Look at the picture.

If polygons ABCD and EFGH are similar, then corresponding sides are in proportion.

[tex]\dfrac{GH}{CD}=\dfrac{FG}{BC}[/tex]

We have

[tex]GH=z,\ CD=10,\ FG=6,\ BC=8[/tex]

Substitute:

[tex]\dfrac{z}{10}=\dfrac{6}{8}[/tex]          croaa multiply

[tex]8z=(10)(6)[/tex]

[tex]8z=60[/tex]           divide both sides by 8

[tex]z=\dfrac{60}{8}\\\\z=7.5[/tex]

92 boxes

1379/15=91.93 but u need a full box so 92

Answer:

92

Step-by-step explanation:

Given:

Number of Paperweights = 1,379

Number of Paperweights that each box can hold = 15

Number of boxes needed = 1379 ÷ 15 = 91.933 boxes

Because 0.933 of a box is of no use to anyone, we simply round this number up to the next whole box and just have the last box partially full.

This gives us 92 boxes.

[tex]\dfrac{x-3}{x}[/tex] - initial fraction

[tex]\dfrac{x-3+1}{x+1}=\dfrac{2}{3}\\\\\dfrac{x-2}{x+1}=\dfrac{2}{3}\\\\2(x+1)=3(x-2)\\2x+2=3x-6\\x=8\\\\\dfrac{8-3}{8}=\dfrac{5}{8}[/tex]

It's [tex]\dfrac{5}{8}[/tex]

The value of  [tex]f(g(x))=-6x-5[/tex]

Given functions are, [tex]f(x)=-2x-3,g(x)=3x+1[/tex]

We have to find composite function [tex]f(g(x))[/tex].

         [tex]f(g(x))=f(3x+1)\\\\f(g(x))=-2(3x+1)-3\\\\f(g(x))=-6x-2-3\\\\f(g(x))=-6x-5[/tex]

Learn more about the composite function here:

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To find (fxg)(X), you need to multiply the two given functions, apply the distributive property, and then combine like terms. The result for (fxg)(X) is -6x² - 11x - 3.

Step-by-step Explanation:

Therefore, (fxg)(X) = -6x² - 11x - 3.

Answer:

I believe it's 22/15

Step-by-step explanation:

17x -6 + 3x - 5 = 1x + 11 + 4x first you add the 17x and 3x and 1x and the 4x

which it would be: 20x - 6 -5 = 5x + 11;

20x - 11 = 5x + 11,

 -5            -5

15x - 11 = 11

      +11   +11

15x = 22

15       15     Divide

x = 22/15

Hope my answer has helped you if not i'm sorry.

Answer:

the y-intercept is -6

Step-by-step explanation:

3x+5y=30

    -5y -5y

(30-)3x=30-5y(-30)

3x-30=5y/y

3/5x-6=y

Answer:

(-2,0.2)

Step-by-step explanation:  

we have

[tex]f(x)=2(3)^{x}[/tex]

[tex]g(x)=10log(x+3)[/tex]  

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The intersection points are (-1.9,0.2) and (1,6)

see the attached figure

therefore

The solution of the system of equations are the points (-1.9,0.2) and (1,6)

Answer:

Δ = 60

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0

Then the discriminant

Δ = b² - 4ac

Given

3x² + 6x = 2 ( subtract 2 from both sides )

3x² + 6x - 2 = 0 ← in standard form

with a = 3, b = 6 and c = - 2

b² - 4ac = 6² - (4 × 3 × - 2) = 36 - (- 24) = 36 + 24 = 60

Answer: The general equation for the lateral area of a pyramid is LSA=(1/2)pl

P is the perimeter

L is the slant

Answer:

Option c. 30,000

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

Let

y ----> safe load in pounds

x ----> length in feet of a horizontal beam

we have

For [tex]x=15\ feet, y=2,000\ pounds[/tex]

Remember that

[tex]k=y*x[/tex]

substitute

[tex]k=2,000*15=30,000[/tex]

Answer:

199

Step-by-step explanation:

For this problem, you have to write an formula.

a(n)=a(1)+(n-1)d

n is the term you are trying to find (in this case it's 50).

a(1) is the first term in the sequence (in this case it's 3).

d is the common difference (in this case it's 4).

Plug those in, and you get:

a(50)=3+(50-1)4

And you can easily solve that and get a(50)=199.

Answer:

199

Step-by-step explanation:

Answer: 2(10y+3x)(10y-3x)

Step-by-step explanation:

2(100y²- 9x²)

2[ (10y+3x)(10y-3x) ]

Answer:

Green: 5/9 Red:2/9

Step-by-step explanation:

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

 can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

 must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle

Answer:

The coordinates of vertex A" is (3 , 1)

Step-by-step explanation:

* Lets revise The translation of a point

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

∵ Δ ABC has a vertex A = (-4 , 2)

∵ The Δ ABC is translated 2 units right and 5 units down to form

   triangle A′B′C′

- From the rule above the x coordinate id added by 2 and the

 y-coordinate is subtracted by 5

∴ A' = (-4 + 2 , 2 - 5) = (-2 , -3)

∴ The image of vertex A is A' = (-2 , -3)

∵ Δ A'B'C' is then translated 5 units right and 4 units up to form

   triangle A″B″C″

- From the rule above the x coordinate is added by 5 and the

 y-coordinate is add by 4

∴ A" = (-2 + 5 , -3 + 4) = (3 , 1)

* The coordinates of vertex A" is (3 , 1)

Answer:

it is a

Step-by-step explanation:

Answer:

Girls: 9; Boys: 11

Step-by-step explanation:

16-7=9

14-3=11

Answer:

20

Step-by-step explanation:

If the three numbers are x, x+1, and x+2, then:

x (x+1) (x+2) = 990

x (x² + 3x + 2) = 990

x³ + 3x² + 2x - 990 = 0

(x - 9) (x² + 12x + 110) = 0

Since x must be a whole number, x = 9.  You can also use simple trial and error to find that the three numbers are 9, 10, 11.

The sum is:

9 + 10 + 11 = 20

Answer:

d) Isoceles triangle

Step-by-step explanation:

you can only split it down the middle

Answer:

D. Isosceles Triangle

Step-by-step explanation:

Answer is:

37 nickels

Answer:

it takes 97 nickels

Step-by-step explanation:

4.85÷0.05=97

Hello There!

X=2

To solve this, we first need to understand that when we see an X in parentheses, we multiply the number before it in this case 4 by X.

The answer is 2 because we multiply 4 by 2 which is the x value so 4*2 is equal to 8 and they we add 9 to it because the sum of 6 and 3 is 9.

Finally, our answer we get is 17 so our X value is 2.

Have A Great Day!

Area of a triangle is 1/2 x base x height.

The base is 6 units long and the height is 4 units.

Area = 1/2 x 6 x 4 = 12 square units.

Answer:

86

Step-by-step explanation:

Since something minus a negative is just adding, we get 37-(-8)=37+8 or 45. We can do the same with 11-(-30) which is 11+30 or 41. So 45+41=86

Answer:

86.

Step-by-step explanation:

Work out the 'inner' parentheses first:

(37 - (-8)] + [11 - (-30)]

= (37 + 8) + (11 + 30)

Now the outer parentheses:

= 45 + 41

= 86.

0.001, 0.014, 0.1, 9.41

Answer:

"It is translated 1 unit left and stretched vertically by a factor of 3"

Step-by-step explanation:

The parent function here is y = x^2

Let's give out some general rules of transformation:

If y = f(x) is a parent function, then

1. If we have y = a * f(x)

| a | > 1 is a stretch;  

0 < | a | <1 is a compression, vertically for both

and

2. If we have y = f(x-c), this means horizontal translation to right c units and y = f(x+c) means horizontal translation c units left

Looking at y = 3(x+1)^2, we can say that "it is vertical stretch by a factor 3 and horizontal translation 1 units left"

Step-by-step explanation:

We know any line that is parallel to other line has same slope.

Here, m1=m2

So, slope will be -1/2.

For this case we have by definition, that if two lines are parallel then their slopes are equal. That is to say:

[tex]m_ {1} = m_ {2}[/tex]

If we have a line of the form:

[tex]y_ {1} = - \frac {1} {2} x_ {1} + b_ {1}[/tex]

Then a parallel line will be given by:

[tex]y_ {2} = - \frac {1} {2} x_ {2} + b_ {2}[/tex]

That is, the slopes are the same!

Answer:

Option C

Answer:

n=+ -0.0321563225311

Hello There!

To find out if these lengths make a triangle, you have to add up any two sizes and they must be greater than the third side for it to form a triangle.

Let's Test It!

"9+12=21" 21 is greater than 15

"9+15=24" 24 is greater than 12

Yes This Does Form A Triangle!

Answer:

Yes, the triangle lengths 9, 12, and 15 are lengths of the sides of a right triangle.

Step-by-step explanation:

There are multiple different ways to prove that this answer is correct.

To begin, we could recognize that these side lengths are a Pythagorean triple, or multiples of side lengths that satisfy the Pythagorean theorem, and thus prove that the lengths constitute a right triangle. In this case, 9, 12, and 15 represent the 3, 4, 5 Pythagorean triple where each side length is multiplied by a factor of three.

3x3=9

4x3=12

5x3=15

Therefore, these side lengths do make a right triangle because they represent a multiple of a Pythagorean triple.

If we didn’t recognize this, we could always plug the side lengths into the Pythagorean theorem, a^2 + b^2 = c^2.

In this case, we get

9^2 + 12*2 = 15^2

If we simplify, we get:

81+144 = 225

And if simplified further, we get:

225=225,

Which is a true statement, proving that these side lengths do make up a right triangle.

Hope this helps!