Consider the functions f(x) = (5x +4)/(X+9) and g(x) = (9x – 4)/(5-x) (a) Find f(g(x)) (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other

Answer:

g(x) = |4x+3|

Step-by-step explanation:

g(x) = f(x) - 2

=|4x+3|

Answer:

Inequality 1: x + y ≤ 1.50

Inequality 2: 4x + 6.5y ≥ 780

So, the possible solution can be x = 20, y = 1.20

(1) The inequalities can be written as:-

Inequality 1: x + y ≤ 1.50

Inequality 2: 4x + 6.5y ≥ 780

(2) The possible solution for the value of x and y can be x = 0.30, y = 1.20.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Abigail owns a food truck that sells tacos and burritos. She only has enough supplies to make 130 tacos or burritos. She sells each taco for $3 and each burrito for $6. Abigail must sell no less than $600 worth of tacos and burritos each day.

The inequalities can be written as:-

Inequality 1: x + y ≤ 1.50

Inequality 2: 4x + 6.5y ≥ 780

The two inequalities can be solved as:-

x + y = 1.50 or x= 1.50 - y

4x + 6.5y = 780

4( 1.5 - y ) + 6.5y = 780

6 - 4y + 6.5y = 780

y = 1.20

The value of x will be,

x= 1.50 - y

x= 1.50 - 1.2

x = 0.30

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Answer:

The easiest way to convert a fraction to a decimal is to divide the numerator (the top of the fraction) by the denominator (the bottom of the fraction) by using a calculator. The resulting answer will be the value of the fraction expressed as a decimal number.

Step-by-step explanation:

Answer: The simplest method is to use a calculator.

Just divide the top of the fraction by the bottom, and read off the answer. Hope this helps! If not, I’ll come up with another explanation! :)

Answer:

Check the explanation

Step-by-step explanation:

Present predicted

Revenue - per test 10000 8000

Variable cost - per test 7000 7000

Contribution – per test 3000 1000

Net income (10,000 test – 11,500 tests) 30,000,000 11,500,000

Taking into account the definition of y-intercept,  the y-intercept of function g is (0,3) (option C).

To find the y-intercept of a function, simply replace x with 0; and then solve the equation.

That is, to find the intersection point with the ordinate axis, f(0) is calculated by making x = 0.

In this case, you know that:

f(x) = eˣ

g(x) = 2f(x)+1

Then, substituting the expression of the function f(x) in the function g(x), you obtain g(x)=2×eˣ + 1

The y-intercept of function g is g(0). So, g(0)=2×e⁰ + 1

Solving:

g(0)=2×1 + 1

g(0)= 2+1

g(0)= 3

Finally, the y-intercept of function g is (0,3) (option C).

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Answer:

x = -6 and y = -3

Step-by-step explanation:

x- 4y =6

x =4y +6......(i)

5x -4y =-18

20y +30 - 4y = -18

16y = -48

y = -3

x = -12+6

x = -6

Step-by-step explanation:

the nth root of something can be expressed as 1/n as exponent.

e.g. sqrt(2) = 2^(1/2).

so, the 5th root of 3⁴ = 3^(4/5)

for f(x) = 3^x

that means that x = 4/5 = 0.8.

so, I go on the x-axis to the right to 0.8, and from there straight up to the actual curve.

that is the desired point.

Work Shown:

(85 grams)/(3 ounces) = (200 grams)/(x ounces)

85/3 = 200/x

85x = 200*3

85x = 600

x = 600/85

x = 7.0588 approximately

This rounds to 7 ounces when rounding to the nearest whole number.

The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.

Explanation

On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).

To find the probability, you can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case:

Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)

Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%

So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.

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Answer:

Step-by-step explanation:

Answer:

2.694*10¹⁴

hops this helps

Answer:

mark me barinlest

Step-by-step explanation:

supplement angles have sum = 180, complement angles have sum = 90

180-x = 4(90-x)

180-x = 360 -4x

3x = 180

x = 180/3

x = 60

answer measure of the angle = 60

Answer:

Step-by-step explanation:

Supplementary angles sum to 180°.

Let the angle be x then the other angle is 4x.

Their sum is:

The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.

To define the supremum and infimum of the set A, we first need to determine the properties of the set.

The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.

To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.

Let's analyze the elements of A:

For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.

As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.

Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.

Again, analyzing the elements of A:

As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.

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To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

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Answer:it’s the third answer choice

Step-by-step explanation:

Answer:

To find the area of a square, multiply the 2 sides by each other (all sides are equal)

S=14×14=196

196m^2

When solving this system of equations by elimination, the resulting equation when the variable y has been eliminated is, 3x = -3.

Hence the correct option is (A).

The given system of linear equations is

9x + 3y = 12 ............... (i)

2x + y = 5 ................. (ii)

We have to solve the system using elimination method by eliminating the variable y first.

Coefficients of y in both equations are 3 and 1 respectively.

So, LCM(3, 1) = 3.

Multiplying the equation (ii) by 3 we get,

3(2x + y) = 3*5

6x + 3y = 15 ............. (iii)

Subtracting the equation (i) from the equation (iii) we get,

6x + 3y - 9x - 3y = 15 - 12

-3x = 3

3x = -3

so the resulting equation when the variable y has been eliminated is, 3x = -3.

Hence the correct option is (A).

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For this first one it's:

A. ---x = 13

B. ---x = 1

Second one:

C. ---x=1+5 root 2

D. ---x=1-5 root 2

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

D.

Step-by-step explanation:

{-1,0,1}

pls mrk me brainliest i need to get the next rank

Answer:17

Step-by-step explanation:

Answer: Look for like terms and then leave the equation as it is :)

Step-by-step explanation: Hope this helps :)

Answer: 26 minutes

Step-by-step explanation:

Assume that the total time spent in the morning which includes getting dressed, eating breakfast, making her bed, and driving to work is x.

Time getting dressed = ¹/₃x

Eating breakfast = 10 mins

Making bed = 5 mins

¹/₃x + 10 + 5 = 35 ½

¹/₃x + 15 = 35 ½

¹/₃x = 35 ½ - 15

¹/₃x = 20 ½

x = 20 ½ / ¹/₃

= 61.5 minutes

Total morning routine is is 61.5 mins

Time taken to drive to work is;

= 61.5 - 35 ½

= 26 minutes

Answer:

An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10

Step-by-step explanation:

How to determine an equation that satisfies all three pairs of a and b values listed in the table?

In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;

a - 3b = 10

0 - 3(-10) = 30 (False).

3a + b = 10

3(0) - 10 = -10 (False).

3a - b = 10

3(0) - (-10)

0 + 10 = 10 (True).

3a - b = 10

3(1) - (-7)

3 + 7 = 10 (True).

3a - b = 10

3(2) - (-4)

6 + 4 = 10 (True)

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Complete Question:

Which equation satisfies all three pairs of a and b values listed in the table?

a b

0 -10

1 -7

2 -4

The equation is?

A.) a-3b=10

B.) 3a+b=10

C.) 3a-b=10

D.) a+3b=10

Answer:

this answer is not available at the moment

Step-by-step explanation:

Answer:

p=m*9+9

So 45/4=9

9*4=36

36+9=45

Check with table

5*9=45

45+9=54

6+9=54

63+9=63

7+9=63

63+9=72

So as you can se the equation is p=9*m+9

Hopes this helps!

Answer:

B.

Step-by-step explanation:

Well we know that

\(224=2^{5} *7\)

so we can get the 2 outside of the radical

\(x^{11} =(x^{5} )^{2} *x\)

and we can get the x^2 outside too.

\(y^8=y^5*y^3\)

and we also can get y outside.

so we have:

\(2x^{2}y\sqrt[5]{7xy^3}\)

The probability of getting even and vowel is 1/6 if the number pyramid with faces 1-4 is tossed and a spinner a-f is spun option (b) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

As we know:

When events are independent with and statement:

P(A and B) = P(A)×P(B)

Let's suppose P(A) = probability of getting even number

Which is P(A) = 2/4 = 1/2

P(B) = Probability of getting vowel

Which is P(B) = 2/6 = 1/3

P(A and B) = (1/2)(1/3) = 1/6

Thus, the probability of getting even and vowel is 1/6 if the number pyramid with faces 1-4 is tossed and a spinner a-f is spun.

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