Let F(x) = x^2 – 15 and
G(x)= 4 - x
Find (F/G)(–7) =

Answers

Answer 1

Answer:

[tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

FunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

F(x) = x² - 15

G(x) = 4 - x

Step 2: Find

Substitute in functions:                                                                                     [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(x) = \frac{x^2 - 15}{4 - x}[/tex]

Step 3: Evaluate

Substitute in x [Function (F/G)(x)]:                                                                    [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{(-7)^2 - 15}{4 - (-7)}[/tex]Exponents:                                                                                                         [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{49 - 15}{4 - (-7)}[/tex]Subtract:                                                                                                            [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]

Related Questions

15 times a certain number plus 5 times the same number is 80 what is the number​

Answers

x = 4

Every step shown. Once you become used to doing this you will almost be able to do the basic one's in your head without writing much down.

Explanation:

Let the unknown value be  

x

Converting the words into numbers:

First part: "15 times a certain number"  → 15 x

Second part: "plus 5 times the same number" → 15 x + 5 x

The last part: " is 80" ->  15x + 5 x = 80

We are counting  x ' s . 15 of them plus another 5 of them gives a total of 20.

So 15 x + 5 x = 20 x = 80

Divide both sides by 20

20 x ÷ 20 = 80÷ 20

20/20x=80/20

x=4

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 15x+5x=80[/tex]

[tex]\\ \sf\longmapsto (15+5)x=80[/tex]

[tex]\\ \sf\longmapsto 20x=80[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{80}{20}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

​There are two types of fish in a lake. These are carp and pike.
In a netted area of the lake 120 carp and 16 pike were caught
In the whole lake it is estimated there are 34 000 fish.How​ many pike are there?​​

Answers

Answer:pike are 250 ; from 120+16=136 and 34000/136 is 250

Step-by-step explanation:

The ratio of men to women working for a company is 5 to 3. If there are 200 employees total, how many women work for the company?​

Answers

Answer:

There are 200 employees, and the ratio is 5:3.

5+3 = 8

200/8 = 25

So, there are 5(25) = 125 men and 3(25) = 75 women.

There are 75 women who work for the company.

Let me know if this helps!

The central angle in a circle of radius 6 meters has an intercepted arc length of 10 meters. Find the measure of the angle in radians and in degrees

Answers

Answer:

The central angle is 5/3 radians or approximately 95.4930°.

Step-by-step explanation:

Recall that arc-length is given by the formula:

[tex]\displaystyle s = r\theta[/tex]

Where s is the arc-length, r is the radius of the circle, and θ is the measure of the central angle, in radians.

Since the intercepted arc-length is 10 meters and the radius is 6 meters:

[tex]\displaystyle (10) = (6)\theta[/tex]

Solve for θ:

[tex]\displaystyle \theta = \frac{5}{3}\text{ rad}[/tex]

The central angle measures 5/3 radians.

Recall that to convert from radians to degrees, we can multiply by 180°/π. Hence:

[tex]\displaystyle \frac{5\text{ rad}}{3} \cdot \frac{180^\circ}{\pi \text{ rad}} = \frac{300}{\pi}^\circ\approx 95.4930^\circ[/tex]

So, the central angle is approximately 95.4930°

A rectangular prism has volume 1,088 ft3 and height 8 ft. What is the area of the base of the prism?
a. 146 ft2
c. 136 ft2
b. 1,080 ft2
d. 1,096 ft2​

Answers

Height=8ftVolume=1083ft^3

We know

[tex]\boxed{\sf Volume=Area\:of\:Base\times Height}[/tex]

[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{Volume}{Height}[/tex]

[tex]\\ \sf\longmapsto Area\:of\:Base=\dfrac{1088}{8}[/tex]

[tex]\\ \sf\longmapsto Area\;of\:base=136ft^2[/tex]

Twice the difference of a number and 9 equals 5.

Answers

Answer:

7

Step-by-step explanation:

if the number is x then you know 2x-9=5

2x=14

x=7

so the number is 7

Carlos is an administrative assistant at an insurance agency. He wants to gather feedback from customers on their service. He doesn't have a lot of time, and he wants to have some data to share with his supervisor. What is the best way for Carlos to gather feedback? O a) Individual interviews O b) Survey O c) Focus group d) Phone calls

Answers

When a person does not have enough time he must should take the faster and effective route in this case carlos does not have time for individual interviews or phone calls. Focus group will not work i guess because discussion takes time so i guess it should be survey. I am not sure but it should be Survey or Focus Group

Must click thanks and mark brainliest

$26,876 is invested, part at 9% and the rest at 5%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 5% by $720.78, how much is invested at each rate? (Round to two decimal places if necessary.)

Answers

9514 1404 393

Answer:

$14,747 at 9%$12,129 at 5%

Step-by-step explanation:

Let x represent the amount invested at 9%. Then the difference in interest amounts is ...

  (9%)x -(5%)(26876 -x) = 720.78 . . . . . assuming a 1-year investment

  0.14x -1343.80 = 720.78 . . . . . . . . . simplify

  0.14x = 2064.58 . . . . . . . . . . . . . . add 1343.80

  x = 14,747 . . . . . . . . . . . . . . . . divide by 0.14

$14,747 is invested at 9%; $12,129 is invested at 5%.

What is the length of the arc of a circle of diameter 8 meters subtended by a central angle of
3pi/4 radians?

Answers

Answer:

9.42 meters

Step-by-step explanation:

diameter = 8 m

radius = 4 m

Length of arc = radius * central angle in radians

= 4 * 3[tex]\pi[/tex] / 4

= 12[tex]\pi[/tex] / 4

= 3[tex]\pi[/tex]

= 66 / 7

= 9.42 m

The length of the arc of a circle of diameter 8 meters subtended by a central angle of 3pi/4 radians is 9.42 meters.

What is the arc of the circle?

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

expalination:

⇒angle= arc/radius

= 3pi/4 radians

diameter = 8 m

radius = 4 m

Length of arc = radius * central angle in radians

⇒4 * 3 / 4

⇒12 / 4 = 3

⇒66 / 7

⇒9.42 m

Hence the arc of a circle is 9.42 m.

Learn more about arc of a circle here:-https://brainly.com/question/2005046

#SPJ2

A rhombus has an area of 5 square meters and a side length of 3 meters. In another similar rhombus, the length of a side is 9 meters. What is the area of the second rhombus?
(A) 30 square meters
(B) 45 square meters
(C) 60 square meters
(D) 75 square meters

Answers

Hence the area of the second rhombus is 45 square meters

The area of a rhombus is expressed as

A = base * height

For the rhombus with an area of 5 square meters and a side length of 3 meters

Height = Area/length

Height = 5/3 metres

Since the length of a similar rhombus is 9meters, the scale factor will be expressed as;

k = ratio of the lengths = 9/3

k = 3

Height of the second rhombus = 3 * height of the first rhombus

Height of the second rhombus = 3 * 5/3

Height of the second rhombus = 5 meters

Area of the second rhombus = length * height

Area of the second rhombus = 5 * 9

Area of the second rhombus = 45 square meters

Hence the area of the second rhombus is 45 square meters

Learn more here: brainly.com/question/20247331

The correct option is option B;

(B) 45 square meters

The known parameters in the question are;

The area of the rhombus, A₁ = 5 m²

The length of one of the sides of the rhombus, a = 3 m

The length of a side in a similar rhombus, b = 9 m

The unknown parameter;

The area of the second rhombus

Strategy or method;

We have that two shapes are similar if their corresponding sides are proportional

From the above statement we get that the ratio of the areas of the two shapes is equal to the square of the ratio of the lengths of the corresponding sides of the two shapes of follows;

[tex]\begin{array}{ccc}Length \ Ratio&&Area \ Ratio\\\dfrac{a}{b} &&\left (\dfrac{a}{b} \right)^2 \\&&\end{array}[/tex]

Let the area of the second rhombus be A₂, we get;

[tex]Area \ ratio = \dfrac{A_1}{A_2} = \left( \dfrac{a}{b} \right)^2[/tex]

Where;

a = 3 m, b = 9 m, and A₁ = 5 m², we get;

[tex]Area \ ratio = \dfrac{5 \ m^2}{A_2} = \left( \dfrac{3 \, m}{9 \, m} \right)^2 = \dfrac{1}{9}[/tex]

Therefore;

9 × 5 m² = A₂ × 1

A₂ = 45 m²

The area of the second rhombus, A₂ = 5 m².

Learn more about scale factors here;

https://brainly.com/question/20247331

find the missing side round to the nearest tenth

Answers

Answer:

[tex]cos49 = \frac{26}{x} \\ x = 39.6305[/tex]

There is 60% chance of making $12,000, 10% chance of breaking even and 30% chance of losing $6,200. What is the expected value of the purchase?

Answers

Answer:

$5,340

Step-by-step explanation:

Given :

Making a probability distribution :

X : ___12000 ____0 _____-6200

P(X) __ 0.6 _____ 0.1 _____ 0.3

Tge expected value of the purchase si equal to the expected value or average, E(X) :

E(X) = ΣX*p(X)

E(X) = (12000 * 0.6) + (0 * 0.1) + (-6200 * 0.3)

E(X) = 7200 + 0 - 1860

E(X) = $5,340

For f(x) = 4x2 + 13x + 10, find all values of a for which f(a) = 7.

the solution set is ???

Answers

Answer:

f(7)=109

Step-by-step explanation:

Since f(a)=7 then you just imput 7 on each x like this f(7)=8+13(7)+10= 109

Solve the equation for x 11x=110

Answers

Answer:

x = 10

Step-by-step explanation:

11x = 110

Divide both sides by 11

11x/11 = 110/11

x = 10

Tìm thể tích của khối bao bởi mặt z=5+(x−4)^2+2y và mặt x=3,y=4 và mặt phẳng tọa độ.

Answers

Step-by-step explanation:

ccxiddidificifificici i i ivi i i i i i i i iivvii iix9difi

Please help quicklyyy!!!

Answers

Answer:

Its the 3 one

Step-by-step explanation:

What is the measure of x?

Answers

Answer:

22

Step-by-step explanation:

This is a right angle so the sum of those would be equal to 90 degrees

x + 7 + 3x - 5 = 90 add like terms

4x + 2 = 90 subtract 2 from both sides

4x = 88 divide both sides by 4

x = 22

the line parallel to 2x – 3y = 6 and containing (2,6)
what is the equation of the line ?

Answers

First, write out the equation in slope intercept form.

-3y= -2x+6

y= 2/3x -2

The slope of the equation is 2/3, m.

Substitute the slope and coordinate into y=mx+b. Since it’s parallel, the slope remains the same.

6= 2/3(2)+b

6= 4/3+b

14/3=b

y= 2/3x + 14/3

f(x) = - 2x
g(x) = 8x^2 - 5x + 7
Find (f • g)(x).

Answers

9514 1404 393

Answer:

  (f•g)(x) = -16x^3 +10x^2 -14x

Step-by-step explanation:

  (f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)

Use the distributive property:

  (f•g)(x) = -16x^3 +10x^2 -14x

Which of the following is a polynomial?
A. X4- 2
B. 1/x+ 2
c. x-2-1
D.(x - 4)/(x + 1)

Answers

Answer:

ok um last person was rude but your answer is A

Step-by-step explanation:

14 over 17 as a decimal rounded to the nearest tenth

Answers

Step-by-step explanation:

14/17 is 0.82352941176

To the nearest tenth is 0.8

15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7cm B. 154cm C. 14cm D. 64cm​

Answers

Step-by-step explanation:

Given that,

Height of cylinder = 4 cmVolume of cylinder = 616 cm³

To find,

Diameter of the base = ?

Firstly we'll find the base radius of the cylinder.

[tex]\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\[/tex]

According to the question,

[tex]\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\[/tex]

[tex]\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\[/tex]

[tex]\longmapsto\rm{4312 = 88 \times r^2 }\\[/tex]

[tex]\longmapsto\rm{\cancel{\dfrac{4312}{88}} = r^2 }\\[/tex]

[tex]\longmapsto\rm{49 = r^2 }\\[/tex]

[tex]\longmapsto\rm{\sqrt{49} = r }\\[/tex]

[tex]\longmapsto\rm{7 \; cm = r }\\[/tex]

Now,

[tex]\longmapsto\rm{Diameter = 2r }\\[/tex]

[tex]\longmapsto\rm{Diameter = 2(7 \; cm) }\\[/tex]

[tex]\longmapsto\bf{Diameter = 14 \; cm}\\[/tex]

The required answer is 14 cm.

Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. SAS Postulate

Answers

Answer:

HJ = FG

Step-by-step explanation:

SAS means side - (included) angle - side.

we have one angle confirmed (at H and at G).

we have actually one side confirmed (HG), because the graphic shows that this side is shared between the triangles. so, implicitly it is not only congruent but really identical.

so, we need the confirmation of the second side enclosing the confirmed angle.

WILL GIVE BRAINLIEST
Combine like terms.
2x – 3 – 5x + 8 = [ ? ]x + [ ]

Answers

Answer:

-3x + 5

Step-by-step explanation:

like terms are the ones that have x and the ones that don't.

hope this makes sense

Answer:

-3x + 5

Step-by-step explanation:

2x - 3 - 5x + 8 can also be written as 2x - 5x - 3 + 8

→ Using the rewritten method collect the x terms

-3x - 3 + 8

→ Now collect the integers

-3x + 5

Cho X có phân phối nhị thức với n= 20 và p=0,4. Kỳ vọng của X là:
A.4
B.6
C.8
D.10

Answers

Step-by-step explanation:

[tex]10 \: is \: the \: answer[/tex]

PLEASE help me solve this!!!!
1. log2^64
2. log11^121
3. log8^512
4. log4^1/16

Answers

Here are all of the answers to these four questions:

1. log2^64=6, or 2 to the power of 6=64.

2. log11^121=2, or 11²=121.

3. log8^512=3, or 8³=512.

4. log4^1/16=-2, or 4 to the negative second (-2) power.

I hope that this answered your question.

Yeah, so the answer is 6, 2, 3, and -2.

The graph shows the distribution of lengths of songs (in seconds). The distribution is approximately Normal, with a mean of 227 seconds and a standard deviation of 31 seconds.

A graph titled Song length has length (seconds) on the x-axis, going from 103 to 351 in increments of 31. The highest point of the curve is at 227.

What percentage of songs have lengths that are within 31 seconds of the mean?

34%
68%
95%
99.7%

Answers

its everything between 196 and 258 seconds (at max 31secs away from the mean). imagine straight upward lines separating this area from the rest.

34% would be way too low, 95 and above way too much.

only 68% is remotely plausible.

Please help 20 points

Answers

it’s c since u would multiply 2 twice and it’s on a graph

0.06 + 2 =
0.03 + 0.4 =
0.5 + 0.02 =
0.06 + 5 =
0.01 + 0.5 =
0.2 + 4 =
0.02 + 2 =
0.6 + 0.1 =
0.5 + 0.1 =
0.05 + 3 =
00.3 + 1 =
0.0 + 0.2 =
0.4 + 00.1 =
0.1 + 0.3 =
0.02 + 0.00 =
0.02 + 0.05 =
0.01 + 6 =
0.2 + 3 =
0.03 + 0.5 =
0.2 + 1 =

Answers

Answer:

1.) 2.06

2.) 0.43

3.) 0.52

4.) 5.06

5.) 0.51

6.) 4.2

7.) 2.02

8.) 0.7

9.) 0.6

10.) 3.05

11.) 1.3

12.) 0.2

13.) 0.5

14.) 0.4

15.) 0.02

16.) 0.07

17.) 6.01

18.) 3.2

19.) 0.53

20.) 1.2

Step-by-step explanation:

Simple addition with decimals. If you have a whole number like 5, with a decimal like 0.07, 5+0.07 would be 5.07. 5 would take the spot of 0 in the ones place and .07 would remain. If you have 0.10+0.8, it would be 0.9 as your answer since we make 0.8 to 0.80 or 0.10 to 0.1 and add the two together. Hope this helped!

Leanne is planning a bridal shower for her best friend. At the party, she wants to serve 33 beverages, 33 appetizers, and 22 desserts, but she does not have time to cook. She can choose from 1313 bottled drinks, 77 frozen appetizers, and 1313 prepared desserts at the supermarket. How many different ways can Leanne pick the food and drinks to serve at the bridal shower

Answers

Answer:

She can pick the food and drinks in 780,780 different ways.

Step-by-step explanation:

The drinks, appetizers and desserts are independent of each other, so the fundamental counting principle is used.

Also, the order in which the beverages, the appetizers and the desserts are chosen is not important, which means that the combinations formula is used to solve this question.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Beverages:

3 from a set of 13. So

[tex]C_{13,3} = \frac{13!}{3!10!} = 286[/tex]

Appetizers:

3 from a set of 7, so:

[tex]C_{7,3} = \frac{7!}{3!4!} = 35[/tex]

Desserts:

2 from a set of 13, so:

[tex]C_{13,2} = \frac{13!}{2!11!} = 78[/tex]

How many different ways can Leanne pick the food and drinks to serve at the bridal shower?

286*35*78 = 780,780

She can pick the food and drinks in 780,780 different ways.

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