Perform the required operationson the following functions.
Given: f(x) = 3 - x; g(x) = -2x
Find g[f(x)]
2x-6
2x+3
-x-6

Answer:

The rhombus ABCD has an area of 22 square units.

Step-by-step explanation:

The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:

[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]

[tex]AC = 15.620[/tex]

[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]

[tex]BD \approx 2.828[/tex]

The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])

[tex]A = \frac{AC\cdot BD}{2}[/tex]

[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]

[tex]A = 22.087[/tex]

The rhombus ABCD has an area of 22 square units.

Answer:

22 units

Step-by-step explanation:

Answer:

[tex]x=\frac{7}{8}[/tex]

Step-by-step explanation:

[tex]10x-3-2x=4[/tex]

First, collect and rearrange the like terms.

[tex]10x-3-2x=4[/tex]

[tex]8x-3=4[/tex]

[tex]8x=4+3[/tex]

Then, solve the equation:

[tex]8x=4+3[/tex]

[tex]8x=7[/tex]

[tex]x=\frac{7}{8}[/tex]

So, the answer is [tex]x=\frac{7}{8}[/tex]. Hope my solution and explanation can help you. Thank you!

If you still cannot get the point, you can ask me anytime.

Answer:

x=7/8

Step-by-step explanation:

10x-3-2x=4

collect like term

8x-3=4

move constant to the right-hand side and change its sign

8x-3=4 into 8x=4+3

add up the number : 8x=4+3

8x=7 divide both sides of the equation by 8

x = 7/8

Answer:

220=48+h or 220=48h

Step-by-step explanation:

the word more can refer to a greater degree or extent.  possibly referring

to addition or multiplication.

Answer:

220=48+h

Step-by-step explanation:

We know that 220 is the sum of 48 and h so you just represent it in an equation/equality statement.

Answer:

The second option (see attached image)

Step-by-step explanation:

You are looking for a box diagram that represents 9 units, and from those, clearly marked sections that contain 3/2 = 1.5 units.The idea is to count how many 1.5 units you have in 9 units.

The in the second diagram you see 9 boxes subdivided in half. Then outlined in red other smaller boxes of length 1.5 units. We can clearly see from the diagram that there are exactly 6 of these smaller 1.5 units red boxes to produce the total 9 unit object.

Answer:what!?

Step-by-step explanation:

Answer:

x<-5 is the correct answer

Answer:

x<-5 is the answer

Step-by-step explanation:

Answer:

The second choice

Step-by-step explanation:

So first we would plug in the first term which is 2 so we would get [tex]an=2[/tex] times [tex]rn-1[/tex] so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be [tex]an= 2[/tex] times [tex]-3n-1[/tex]. Now we would just find the choice that matches and it would be the second choice.

Answer:

option 2

Step-by-step explanation:

First term [tex]a_{1} = 2\\[/tex]

common ratio = r = second term ÷ first term

                            = -6 ÷2 = -4

Plug in the values of  [tex]a_{1}[/tex] & r in the formula

[tex]a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}[/tex]

Answer:

c. (x-3) is not a factor.

Step-by-step explanation:

Answer:

  8 servings

Step-by-step explanation:

At the ratio of 15:1, the 75 grams of rice in one serving will require 75/15 = 5 g of spice. David's inventory of 40 g of spice is enough for ...

  40 g/(5 g/serving) = 8 servings

Only 8 servings can be made with the available spice.

Rice to spice ratio = 15 : 1

Number of grams per serving = 75 grams

Grams of spice available = 40 grams

Grams of rice, r required for available spice :

15 grams of rice = 1 gram of spice

r grams of rice = 40 grams of spice

Cross multiply :

r = (40 × 15)

r = 600 grams

The grams of rice which can go with the available spice :

Number of servings = grams of rice / grams per serving

Number of serving = 600 grams / 75 grams

Number of grams per serving = 8

Hence, The number of servings which can be made with the available spice is 8 servings

Learn more : https://brainly.com/question/18796573

Answer:

According to the graph, f(−3)=3 and f(9)=-7

-7-3/9-(-3)= −10/12

Therefore the answer is -5/6

From Khan

The average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.

        [tex]b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]

        where : [m] → is slope of line and [c] → is the y - intercept

We have the following function -

f(x) = x³ - 9

The average rate of change would be -

r = {720 - (- 36)}/{9 - (- 3)}

r = 756/12

r = 63

Therefore, the average rate of change over the interval [-3,9] will be 63 units per one unit change in y - value.

To solve more questions on exponents, visit the link below-

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[ Complete question -

what is the average rate of change of f(x) = x³ - 9 over the interval [-3,9] ]

Answer:

for every 3 tomato plants there will be 1 squash plants

Step-by-step explanation:

9 divided by 3 = 3. That will find the tomatoes

then you have to divide all the other plants by 3. Squash will be the only one with 1 plant per 3 tomato plants.

The answer is B

Answer:

B. Squash

Step-by-step explanation:

There are 9 tomato plants and there are 3 squash plants.

9 ÷ 3 = 3

3 tomato plants = 1 squash plants

3 × 3 = 1 × 3

9 = 3

9 tomato plants = 3 squash plants

Answer:

A and C

Step-by-step explanation:

The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The quadratic function f(q) = q² - 125 can be factored as (q - 5)(q + 5).

Now,

To find the roots, we set the function equal to zero and solve for q:

So,

q² - 125 = 0

(q - 5)(q + 5) = 0

q - 5 = 0 or q + 5 = 0

q = 5 or q = -5

Therefore,

The roots of the quadratic function f(q) = q² - 125 are q = 5 and q = -5.

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Answer:

62.5°

Hope this helps :)

Answer:

(-6,6), (0,12), (4,8)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 2 --> 2(x, y)

Before-> After dilation

2(-3,3) = (-6,6)

2(0,6) = (0,12)

2(2,4) = (4,8)

Please leave a 'thanks' if this helps!

Answer:

50 mph

Step-by-step explanation:

225 in 4.5 Hours

1 Hour - 50 miles

(225 ÷ 4.5 = 50)

Hope this helps.

Answer:

50mph

Step-by-step explanation:

To figure this out you would just have to divide the number of miles which is 255 by the number of hours which is 4.5 and you would get 50mph.

Answer:

arccsc(x)=1/cos(x)

Step-by-step explanation:

Answer:

the answer to your question is D

Step-by-step explanation:

Answer:

y = 3x

Step-by-step explanation:

Assume a slope of 3

The y intercept is 0

The slope intercept form of the equation is

y= mx+b where m is the slope and b is the y intercept

y =3x+0

y = 3x

The correct theorems which verifies that, WVU = RST is,

⇒ HL

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To find correct theorems which verifies that, WVU = RST

Now, We know that;

The Hypotenuse-Leg Theorem is the only viable way to determine congruency between 2 right triangles.

Here, By both triangles;

⇒ ∠VUW = 90°

⇒ ∠STR = 90°

Thus, The correct theorems which verifies that, WVU = RST is,

⇒ HL

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Answer:

c. x ≤ 6

Step-by-step explanation:

Well we can tell the line is solid so we can cross out answers,

b.

And it is 6 units to the right where x is less than or equal to 6.

Thus,

the answer is c. x ≤ 6.

Hope this helps :)

Answer:

C

Step-by-step explanation:

x less than or equal to 6

If there had been a dashed vertical line at 6, it would have just been less than

Answer:

[tex]|7\cdot m -56| = -7\cdot m + 56[/tex] if [tex]m< 8[/tex]

Step-by-step explanation:

According to the definition of absolute value:

[tex]f(x)[/tex] if [tex]f(x) \geq 0[/tex]

[tex]-f(x)[/tex] if [tex]f(x) <0[/tex]

If [tex]m < 8[/tex], then:

[tex]y_{max} = 7\cdot (8) - 56[/tex]

[tex]y_{max} = 0[/tex]

[tex]y[/tex] becomes negative as [tex]m[/tex] diverges to [tex]-\infty[/tex].

Then, the absolute value can be rewritten as follows:

[tex]|7\cdot m - 56| = -(7\cdot m -56)[/tex] if [tex]m <8[/tex]

[tex]|7\cdot m -56| = -7\cdot m + 56[/tex] if [tex]m< 8[/tex]

Answer:

Jordan weighs 120 pounds, Sam weighs 60 pounds

Step-by-step explanation:

We can create an equation 2s=J. Our second equation is S+J=180. We can substitute J for 2s and our new equation will be 3s=180. We can divide 3 from both sides and we get s= 60. And we know that Jordan weighs two times as sam, then Jordan weighs 120 pounds.

Answer: Jordan=120. Sam=60

Step-by-step explanation: Together they weigh 180 pounds Jordan weighs twice as much as sam. We can write their values as Sam=x and Jordan=2x then we can make a equation

2x+x=180

3x=180

x=60

Then we can substitute x in Jordan and sams values to get our final answe;

Jordan=120. Sam=60

Answer:

Tina

Step-by-step explanation:

Since Amy owns the dog, she doesn't have the ferret and we know that Jewel doesn't have the ferret so the answer is Tina.

Answer:

a) [tex]\boxed{-4}[/tex]

b) [tex]\boxed{26}[/tex]

c) [tex]\boxed{-12}[/tex]

d) [tex]\boxed{-9}[/tex]

e) [tex]\boxed{10}[/tex]

f) [tex]\boxed{-12}[/tex]

Step-by-step explanation:

1) [tex]\frac{41 - 3^2}{\sqrt{36}* 3-26 }[/tex]

=> [tex]\frac{41-9}{6*3-26}[/tex]

=> [tex]\frac{32}{18-26}[/tex]

=> [tex]\frac{32}{-8}[/tex]

=> -4

2) [tex]12+\sqrt[3]{8} * (9-2)[/tex]             ∴ [tex]\sqrt[3]{8} = 2[/tex]

=> [tex]12+2*(7)[/tex]

=> 12 + 14

=> 26

3) [tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]

=> [tex]\frac{28-(49+3)}{-13+15}[/tex]

=> [tex]\frac{28-52}{2}[/tex]

=> [tex]\frac{-24}{2}[/tex]

=> -12

4) [tex]\frac{28}{4} - \sqrt[3]{8} * 2^3[/tex]

=> 7 - 2 * 8

=> 7 - 16

=> -9

5) [tex]7^2-5*8+1[/tex]

=> 49 - 40 + 1

=> 9 + 1

=> 10

6) [tex](2 * \sqrt{16} ) - (\sqrt[3]{27} * \sqrt{81} ) + 7[/tex]

∴  [tex]\sqrt{16} = 4, \sqrt[3]{27} = 3 , \sqrt{81} = 9[/tex]

=> (2 * 4) - (3 * 9) + 7

=> 8 - 27 + 7

=> -19 + 7

=> -12

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

Apply order of operations to solve each expression.

[tex]\frac{41-9}{6 \times 3-26}[/tex]

[tex]\frac{41-9}{18-26}[/tex]

[tex]\frac{32}{-8}=-4[/tex]

[tex]12+2\times 7[/tex]

[tex]12+14=26[/tex]

[tex]\frac{28-(49+3)}{-13+15}[/tex]

[tex]\frac{28-52}{2}[/tex]

[tex]\frac{-24}{2} =-12[/tex]

[tex]7-2 \times 8[/tex]

[tex]7-16=-9[/tex]

[tex]49-40+1[/tex]

[tex]=10[/tex]

[tex](2 \times 4)-(3 \times 9) +7[/tex]

[tex]8-27+7[/tex]

[tex]=-12[/tex]

Answer:

[tex]$\frac{3\pi }{2}$[/tex]

Step-by-step explanation:

Solve for the interval: [tex][0, 2\pi)[/tex]

[tex]4 \csc(\theta)+1=-3[/tex]

[tex]4 \csc(\theta)=-4[/tex]

[tex]\csc(\theta)=-1[/tex]

[tex]$\frac{1}{\sin(\theta)} =-1 \Rightarrow \sin(\theta)=-1$[/tex]

We have [tex]\sin(\theta)=-1[/tex] for coterminal angles [tex]$\frac{3\pi }{2}+2\pi n$[/tex]

Once we just want the interval [tex][0, 2\pi)[/tex]

The solution is [tex]$\frac{3\pi }{2}$[/tex]

Answer:

Any negative number and 0 works for the expression.

Step-by-step explanation:

Looking at this type of equation, we know that either EVERY negative number and 0 or EVERY positive number and 0 will work for this equation, since nothing is being added and we're just working with absolutes/negatives.

Let's try a random positive number in the expression

[tex]|6| = -(6)\\6 \neq -6[/tex]

So this positive number doesn't work, let's just test with another one.

[tex]|9| = -(9)\\9 \neq -9[/tex]

So we know that positive numbers won't work with this expression.

Let's test 0 quickly, just to make sure.

[tex]|0| = -0\\0 = 0[/tex]

So 0 works.

Let's try a few negative numbers now.

[tex]|-5| = -(-5)\\5 = 5[/tex]

So yes, this does work. Let's try one more negative number.

[tex]|-120| = -(-120)\\120 = 120[/tex]

This works. So, every negative number and 0 work with this equation.

Hope this helped!

Answer:

|a|=−a is true only if a is negative or zero

Step-by-step explanation:

Recall that absolute values are always 0 or positive.  

|a|=−a is true only if a is negative or zero.

Answer:

Hello There. ☆~\《`°---_●£●__---`°》\~☆

An exponential growth function is represented by

f(x)=a(b)^{x},a>0,b>1.

The given functions can be written as,

A)f(x)=.001(1.77)^x,0.001>0,1.77>1

B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1

C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1

D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.

So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), (C).

Hope It Helps!~ ♡

ItsNobody~ ☆

The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.

Exponential growth is the process of gradual increase of quantity over time.

An exponential growth function is represented by

[tex]\rm f(x)=a(b)^{x}[/tex],  a>0,b>1

The given functions can be written as,

A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1

B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex]   2>0,  [tex]\sqrt{1.5}[/tex] >1

C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex],    5>0, 2>1

D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex],        5>0,  1/e.

So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), and (C).

Learn more about exponential growth;

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Answer:

Option A.

Step-by-step explanation:

there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents.

Let x and y be the number of stamps of 40 cents and 55 cents respectively.

Total number of stamps is 45. So

[tex]x+y=45[/tex]

Total cost of stamps is $18.75. So

[tex]0.40x+0.55y=18.75[/tex]

But Krista wrote the system of equations as

[tex]0.40x+y=45[/tex]

[tex]x+0.55y=18.75[/tex]

Krista put 0.40 in the first equation meant for the number of stamps.

Krista did not write 0.40 in the second equation meant for the value of stamps.

Therefore, the correct option is A.

Answer:

The answer is A

Step-by-step explanation:

TOOK THE TEST!

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

[tex]\angle AED = \angel BEC[/tex] ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

[tex]\angle ABC = 90^{\circ}[/tex]

In ΔDBC

BC=DC (Given)

So,[tex]\angle CDB=\angle DBC[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle CDB=\angle DBC=x[/tex]

So,[tex]\angle CDB+\angle DBC+\angle BCD = 180^{\circ}[/tex] (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So,[tex]\angle CDB=\angle DBC=x = 65^{\circ}[/tex]

Now,

[tex]\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90[/tex]

So,[tex]\angle ABD=90-x=90-65=25^{\circ}[/tex]

In ΔABD

AB = BD (Given)

So,[tex]\angle BAD=\angle BDA[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle BAD=\angle BDA=y[/tex]

So,[tex]\angle BAD+\angle BDA+\angle ABD = 180^{\circ}[/tex](Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively