Mathematics College

Given the definitions of f(x) and g(x) below, find the value of g(f(-3)). f(x) = 5x + 11 g(x) = x2 + 4x – 11 ​

Answers

Answer 1

Answer:

g(f(-3)) = -11

Step-by-step explanation:

First, we evaluate f(-3) and then plug that value into g(x) for x:

f(x) = 5x + 11

f(-3) = 5(-3) + 11 = -15 + 11 = -4

Therefore:

g(f(-3)) = (-4)^2 + 4(-4) - 11 = 16 - 16 - 11 = 0 - 11 = -11

Answer 2

Answer: -11

Step-by-step explanation:

Find the value of g(f(-3)) given the two equations:

f(x) = 5x + 11

g(x) = x² + 4x - 11

Plug -3 into equation f(x).

f(-3) = 5(-3) + 11

Solve for f(x).

-4 = f(-3)

Plug -4 into the equation of g(x).

g(-4) = (-4)² + 4(-4) - 11

Solve for g(x).

g(-4) = (16) + (-16) - 11

g(-4) = -11

The value of g(f(-3)) is -11.

Related Questions

Which inequality represents this sentence?
A number is no less than 48.
n < 48
n > 48
n < 48
n>48

Answers

The inequality that can be used to represent the information that a number is no less than 48 will be n > 48.

Inequality simply means a mathematical expression that is used in which the sides aren't equal to each other.

It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.

Read related link on:

https://brainly.com/question/25701252

Answer: The correct answer is n≥48

Step-by-step explanation: Give me the brainiest

Ln(x)+ln(x+7)=1
solve this log equation

Answers

7n-1/1+n this should be it

What do you measure the amount of water in a vase

Answers

Liquid volumeis the amount of liquid in a container.

SUBTRACT the given polynomials : (x + 2) - (8x + 4)

A}7x + 2
B}7x - 2
C}-7x - 2
D}-7x + 2

WELP ;-;​

Answers

The equivalent expression for the subtraction (x + 2) - (8x + 4) is -7x - 2

Option C is correct

The given polynomial expression is:

(x + 2) - (8x + 4)

Expand the expression by removing the parenthesis

x + 2 - 8x - 4

Collect like terms

x - 8x + 2 - 4

-7x - 2

Therefore, the equivalent expression for the subtraction (x + 2) - (8x + 4) is -7x - 2

Learn more on polynomials here:

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I will give Brainliesttttt :D!

A car's gas mileage is the distance it can go using 1 gallon of gas (measured in miles per gallon).

Based on the graph, what is this car's gas mileage? Explain.​

Answers

Answer:

20 mpg

Step-by-step explanation:

Answer:

The car is traveling 20 miles per gallon.

Step-by-step explanation:

There are two ways you can solve this.

1) Since this is a graph of the car's gas mileage, all you have to do is look to find the miles for one gallon, which is plotted in this case. As you can see, for one, it is plotted halfway between 0 and 40, so that means the mile number would be 20. Looking at this, the car travels 20 miles per gallon.

2) You can also look at the point at the top that is clearly defined, and the point is (12, 240), 12 gallons used for 240 miles. To get the exact number of miles for one mile, you would divide 12 and 240 both by 12, which results in (1, 20). Since it is miles per gallon, the car gas mileage is 20 miles per gallon.

Hope this helped and have a great day!

Alyssa is baking a cake the recipe calls for 8 cups of flour she already put in 2 cups how many more cups does she need to add

Answers

You need 6 cups hope that helps

is this linear or not and why

Answers

Answer:

Yes

Step-by-step explanation:

Both equations of this system are of degree one.

They are both linear as the graph of both is a line.

Answer:

yes

Step-by-step explanation:

The highest power of variable is 1 . So it is a linear equation of two variables .

HELP ME PLEASE ASAP ASAP

Answers

The answer to this question is £155

What is 34÷18? Explain or show your reasoning.

Answers

Answer:

1.8889

Step-by-step explanation:

The owner of a bookstore buys used books from customers for one dollar and 50 Cent each owner then resells the used books for 400% of the amount he paid for them what is the price of a used book in the bookstore?

Answers

seeing as $1.50 would be 100% of the price a 400% mark up would cause you to multiply 100% of the cost($1.50) by 4 giving you $6
1.50 x 4 = 6

How much is f(x) = 3(4)x

Answers

Answer:

f ( x ) = 12 x

Step-by-step explanation: 3x4=12 so that makes it f(x)=12x

A substance with a half life is decaying exponentially. If there are initially 12 grams of the substance and after 2 hours there are 7 grams, how many grams will remain after 3 hours? Round your answer to the nearest hundredth, and do not include units.

Answers

If there initially 12 grams of the substance, 5.35 grams will remain after 3 hours

The initial amount, a = 12 grams

The amount after 2 hours, y = 7 grams

Time taken, x = 2 hours

First, let us calculate the decay constant, b

The formula for the final value of an exponential decay is:

[tex]y=a(1-b)^x[/tex]

Substitute y = 12, a = 7, and x = 2 into the equation to solve for b

[tex]7=12(1-b)^2\\\\\frac{7}{12} = (1-b)^2\\\\0.583=(1-b)^2\\\\\sqrt{0.583} = 1 - b\\\\0.764=1-b\\\\b=1-0.764\\\\b=0.236[/tex]

The decay constant, b = 0.236

After 3 hours:

Substitute x = 3, a = 12, and b = 0.236 to solve for y

[tex]y=a(1-b)^x\\\\y=12(1-0.236)^3\\\\y = 5.35[/tex]

Therefore, 5.35 grams will remain after 3 hours

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Given f(x) and g(x) are inverse functions. If f(-2)=1 then g(1)=-2

True

False

Answers

True.

The y-axis of the f(x) must equal to the x-axis of g(x)

The x-axis of the f(x) must equal to the y-axis of g(x)

quick mafs ill mark brainliest​

Answers

Answer:

LJ< JK<LK

Step-by-step explanation:

for a theorem, the order of the side of the triangle is the same as the order of the opposite angles since for the angles it's K<L<J, you replace each with the opposite side (quick trick, it's the one not containing the letter!)

20 feel from the ground i need a ladder placed 15 feet from the house what is the length

Answers

Answer:

helooo

Step-by-p explanation:

pls pls pls help!!!!
Determine the simple interest earned when $6, 100 is invested at a rate of 5% for 4 years.
$1,220
$305
$610
$1,525

Answers

Answer: I think A 1,220 (I'm not sure)

Step-by-step explanation:

the aswer is A.1,220 si think si correct.

tammy has soccer practice every 12 days, basketball 18 days, band practice 20 days, and music class every 24 days. If she has all these practices on the same day today, then how many days will it be until she has all four practices.

Answers

Answer:

360 days

Step-by-step explanation:

It would be a whole year until the classes line up on the same day again, because it would only be the exact same date of the next year that they line up.

Hope this helps!

Abcd is a parallelogram determine the length of BE
A)51 units
B)102 units
C)96 units
D) -11 units

Answers

Answer:

  B)  102 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. This means ...

  BE = ED

  3 -9x = -8x +14

  -11 = x . . . . . . . . . . . . add 9x -14

  BE = 3 -9x = 3 -9(-11) = 3 +99

  BE = 102 units

what has a fraction in numerator, denominator or both???

Answers

a fraction that has a numerator and a denominator, is called a Complex fraction, i’m not sure if this is what you were asking for though.

What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.

Answers

Factoring x2-6x+5

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5

Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization

Equation at the end of step
1
:

(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-1 = 0

Add 1 to both sides of the equation :
x = 1

Solving a Single Variable Equation:

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :
x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-6x+5

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000

Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}

please help me with -6 - (1 - 2 x) in Distributive Property this question

Answers

Answer:

-7 + 2x

Step-by-step explanation:


Emily is on a Ferris wheel and her height is modeled by the equation
27
y = 30.48 cos2pi/4.25 (x - 2) + 34.27 where x = the number of minutes since the
ride began and y = the height in feet of Emily.
a) What is the radius of the Ferris wheel?
b) How long does it take Emily to make one rotation?
The radius is______
feet and it takes Emily_____
minutes for one rotation.

Answers

The given function for the height of the Ferris wheel is a sinusoidal equation.

a) The radius is 30.48 feet and it takes Emily 4.25 minutes for one rotation

Reasons:

The function that gives the height of the Ferris wheel is presented as follows;

[tex]\displaystyle y = 30.48 \cdot cos \frac{2\cdot \pi }{4.25} \cdot \left(x - 2 \right) + 34.27[/tex]

Where;

x = The number of minutes since the ride began

y = The height in feet of Emily

a) Required:

The radius of the Ferris wheel

Solution:

Comparing the given equation with the general equation of a Ferris wheel, we have;

[tex]\displaystyle f(t) = \mathbf{A \cdot trig\left(B \cdot \left(t + C\right) \right) + D}[/tex]

The amplitude of the Ferris wheel = A = 30.48

The amplitude, A = The largest distance from the center = The radius, r

A = r

Therefore;

The radius of the Ferris wheel, r = A = 30.48 feet

b) The time it takes the Emily to make one rotation is given by the period, T, of the motion of the Ferris wheel as follows;

[tex]\displaystyle T = \mathbf{\frac{2 \cdot \pi}{B}}[/tex]

By comparison, we have;

[tex]\displaystyle B = \frac{2 \cdot \pi}{4.25}[/tex]

Therefore;

[tex]\displaystyle The \ period, \, T = \frac{2 \cdot \pi}{\left(\frac{2 \cdot \pi}{4.25} \right)} = 4.25[/tex]

The time it takes Emily to make one rotation, T = 4.25 minutes

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Lamis purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Lamis paid.

Answers

N x 5 = c hope this helps!
n5=c

n=number of notebooks
c=total cost

Lin's family has completed 30% of a trip, they have travelled 45 miles. How far is the trip?

Answers

Answer:

2 hours

Step-by-step explanation:

Answer:

150 miles

Step-by-step explanation:

45/3=15

15*7=105      15*3=45

105+45=150

15*10=150

:)

if in a game of glass stepping stones. there are 18 tiles of glass. two in each row. one is tempered and will be fine if you jump on it. and the other will break. if 1 player was to play what are his/her chances of getting across?
(NO links)​

Answers

There chance for just getting across each row would be 50% but there chance of getting across completely is 1 in 18

Scores on a recent exam followed a normal distribution and letter grades will be assigned with 15% A, 35% B, 30% C, 15% D, and 5% F. Suppose that Sue took the exam and had a standardized score of 0.85. What letter grade will Sue get?

Answers

Using the normal distribution, it is found that Sue will get a letter grade of B.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, Sue got a grade of 0.85, hence [tex]z = 0.85[/tex].

Looking at the z-table, z = 0.85 has a p-value of 0.8023, hence she is approximately in the top 20%, which is below the top 15% but above the top 50%, hence she got a letter grade of B.

A similar problem is given at https://brainly.com/question/25745464

6=4x^3-10x^2 please hurry it's a test

Answers

Answer:

x = about 2.705

Step-by-step explanation:

Does this help? Are you supposed to find x? That's what I did but you don't state what exactly you need.... So.....?

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⎪
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⎪
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​

y=−2x−5
y=2x−2
​

Answers

Answer:

This doesn't make since.

Step-by-step explanation:

Students are running in a relay race. Each team will run a total of 3 miles. Each member of a team will run 1/3 mile
How many students will a team need to complete the race? Circle the correct number below

Answers

Answer:

9 students

Step-by-step explanation:

If 1 student runs a 3rd we need 3 students to run 1 mile.

Since we need 3 times that amount of miles we multiply the amount of students it takes to run 1 mile so that we find out how many we need to run 3 miles.

3 x 3 = 9

They will need 9 students I hope this helps have a great day :)

Find positive numbers x and y satisfying the equation xy=20 such that the sum 4x+y is as small as possible.

Answers

The answer is 4 and 5.

They are 2 positive numbers that satisfy the equation, (5)(4)=20.

If that doesn’t work try 2 and 10.

Hope this works!! :)
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