Given f(x) = x − 7 and g(x) = x2 Find f(g(4)). f(g(4)) =

Answer:

i) let x be the amount of money worth of drinks that Kevin sold.

ii) Kevin sells at most $60 worth of drinks.

iii) therefore the inequality can be written as

   x ≤ $60

Step-by-step explanation:

i) let x be the amount of money worth of drinks that Kevin sold.

ii) Kevin sells at most $60 worth of drinks.

iii) therefore the inequality can be written as

   x ≤ $60

Answer:

Carlos is 8

Step-by-step explanation:

I solved this by subtracting 9 from her age, which gets rid of that. 57-9=48

Carlos is 48/6 years old, or 8

Answer:

The answer is 8

Step-by-step explanation:

Answer:

Since the two angles are across from each other that tells us that they are equal in length, so we want to set them equal to each other

3x+50=6x-10, Now we want to solve it like a normal equation, get x by itself

First add 10 to each side

3x+50+10=6x-10+10

3x+60=6x

Now we want to subtract 3x from each side

3x-3x+60=6x-3x

60=3x

Now divide both sides by 3

60/3=3x/3

20=x

x=20

Hope this helps ;)

Step-by-step explanation:

answer:

im not sure. what is ur question

step-by-step explanation:

Answer:

Domain: -1 ≤ x ≤ 4

Range: -20 ≤ 5f(2x) ≤ 30

Step-by-step explanation:

Inputs of f are between -2 and 8

Input is now 2x, so

-2 ≤ 2x ≤ 8

-1 ≤ x ≤ 4

(Horizontal stretch, factor 1/2)

Range of f is -4 ≤ y ≤ 6

So,

-20 ≤ 5y ≤ 30

(Vertical stretch, factor 5)

The domain of g(x) is [-1, 4].

The  range of g(x) is [-20, 30].

A function is a relationship between inputs where each input is related to exactly one 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,

Domain of f(x) = [-2, 8]

Range of f(x) = [-4, 6]

g(x) = 5 f(2x)

Since -2 ≤ x ≤ 8 and -2 ≤ 2x ≤ 8 = -1 ≤ x ≤ 4.

The domain of g(x) = [-1, 4]

Now,

The range of g(x) = [-20, 30]

Since -4 ≤ y ≤ 6,

5 x (-4) ≤ 5y ≤ 5 x 6

-20 ≤ 5y ≤ 30

Thus,

The domain and range of g(x) are

[-1, 4] and  [-20, 30].

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Answer:

8

Step-by-step explanation:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

[tex]\frac{x}{80} = \frac{10}{100}[/tex]

80x10 = 800

800 = 100x

800 divide 100 = 8

answer = 8

Hope this helped!! :)

x = 11 (or) x = –13

Solution:

Theorem:

If three or more parallel lines are cut by a transversal then they divide the transversals proportionally.

Given lines l, m, n are parallel lines cut by a two transversal lines.

Therefore, they are in proportion by the above theorem.

[tex]$\Rightarrow\frac{x+5}{10}=\frac{12.8}{x-3}[/tex]

Do cross multiplication.

[tex]$\Rightarrow(x+5)\times(x-3)=12.8\times10[/tex]

[tex]$\Rightarrow x^2+5x-3x-15=128[/tex]

[tex]$\Rightarrow x^2+2x-15=128[/tex]

Arrange all terms in one side.

[tex]$\Rightarrow x^2+2x-15-128=0[/tex]

[tex]$\Rightarrow x^2+2x-143=0[/tex]

[tex]$\Rightarrow x^2-11x+13x-143=0[/tex]

Take common terms outside

[tex]$\Rightarrow x(x-11)+13(x-11)=0[/tex]

[tex]$\Rightarrow (x-11)(x+13)=0[/tex]

[tex]$\Rightarrow (x-11)=0\ \text{(or)}\ (x+13)=0[/tex]

⇒ x = 11 (or) x = –13

Hence x = 11 (or) x = –13.

Answer:

70,000

Step-by-step explanation:

In the population number 1,274,589 for Birmingham, the 7 is in the ten thousands place. Therefore, its value is 70,000.

This problem revolves around understanding of place values in Mathematics. Specifically, we are asked

what is the value of 7

in the population number 1,274,589 for Birmingham. A critical observation is that each position of a digit in a number has a different value. Counting from right (or the ones position) to left, we find that the number 7 is in the ten thousands place. Therefore, the value of 7 in this number is actually 70,000.

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The answer is gonna be 15

Answer:

a=2

Step-by-step explanation:

Given:                 5a-12=-2

Isolate Variable: 5a=10

Divide:                 a=2

Answer:

5a - 12= -2

5 x 2= 10 so,

5(2) - 12= -2

 ^

10-12= -2

The temperature increased by 15°C.

Temperature is a physical quantity that expresses the perceptions of hotness and coldness

Given that at midnight the temperature is -6°C. At midday the temperature is 9°C. Therefore, the difference in the temperature can be written as,

The difference in temperature

= Temperature in Midday - Temperature at midnight

= 9°C - (-6° C)

= 15° C

Therefore, The difference in the temperature is 15°C.

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There are three terms in polynomial

Solution:

Given polynomial is:

[tex]5x^2+3x-4[/tex]

We have to find the number of terms in polynomial

A term can be a signed number, a variable, or a constant multiplied by a variable or variables

When a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient.

Therefore, terms in polynomial are:

[tex]5x^2+3x-4\\\\Terms: 5x^2 \text{ and 3x and -4 }[/tex]

Thus there are three terms in polynomial

Answer:

Step-by-step explanation:

hello :

(7-2i)/(4 +3i)

=(7-2i)×(4-3i)/(4 +3i)×(4-3i)

but : (7-2i)×(4-3i) =28-21i-8i+6i²

(7-2i)×(4-3i) = 22-29i   ....i² = -1

(4 +3i)×(4-3i) = 4²-(3i)²...(identity)

                   = 16+9 =25

so :

(7-2i)×(4-3i)/(4 +3i)×(4-3i)

=(22-29i)/25

(7-2i)/(4 +3i) = 22/25 -29/25i

(form : a+ib)

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator.

To divide complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 4 + 3i is 4 - 3i. So, we have ((7 - 2i) * (4 - 3i)) / ((4 + 3i) * (4 - 3i)).

Multiplying the numerators and the denominators, we get (28 - 21i - 8i + 6i^2) / (16 - 12i + 12i - 9i^2).

This simplifies to (28 - 29i - 6) / (16 + 9).

Finally, dividing the real parts and the imaginary parts separately, the quotient is:

Quotient = (22 - 29i) / 25

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Answer:

[tex]t \geqslant 49[/tex]

Step-by-step explanation:

If Thomas earned $49 OR more, therefore he could have earned either $49 or greater. Please mark brainliest! : )

The inequality that describes the situation is t >= 49. This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.

The inequality that describes the situation is t >= 49.

This means that the amount Thomas earned, represented by the variable t, is greater than or equal to $49.

For example, if Thomas earned $49, the inequality is true. If Thomas earned more than $49, the inequality is also true.

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Answer: you will be able to buy 13.20224719101124 bananas.

Answer:

105/96

Step-by-step explanation:

Answer:

In dividing fractions, you do the inverse. (Also called the reciprocal.)

So take that attachment you attached as a example.

21           3            21               5

----    ÷   ----  =     ------     ÷    ------

32          5           32               3

Another reminder, when you find the reciprocal, you now multiply instead of divide. (Do not question the math world. I questioned it, and I paid the price. TnT)

So 21/32 multiplied by 5/3 would be....

21              5             105

-----    ×   -----    =      -------

32             3              96

You could leave it that way, or simplify it.

Simplest form is-

1 3/32

Non-simplified form is-

105/96

Good night and have a good day~

(Well at least, I'm going to sleep)

Answer:

They show as intersections with the x-axis

Step-by-step explanation:

For example, the quadratic y = x² - 1 has roots x = -1 and x = 1.

They show on the graph as intersections of the parabola with the x axis at x = -1 and x = 1.

Answer:

1548

Step-by-step explanation:

Their are 36 inches in a yard multiply by 43 it’s 1548

Answer:

The greatest area possible is 729[tex]inch^{2}[/tex]

Step-by-step explanation:

i) If a = [tex]-w^{2} + 54w[/tex] where w is the width of the picture frame

  differentiating on both sides we get

  [tex]\frac{da}{dw} = -2w + 54[/tex]

Differentiating the above again on both sides we get   [tex]\frac{d^2a}{dw^2}[/tex]  = -2

 Since the second order derivative is negative then we can get the solution for the maximum area by equating the fist order derivative equation to 0.

 Therefore -2w + 54 = 0     therefore w  = 27.

ii) If we substitute w = 27 into the equation in ii) we get

   a  = [tex]-(27)^2 +(54\times 27)[/tex] = (54 - 27) [tex]\times[/tex](27)  = [tex]27^{2}[/tex] = 729

Answer:

15

Step-by-step explanation:

Because if you draw a line straight just like the one below the x, it will connect to the 15.

Answer:

18

Step-by-step explanation:

Because you add 9 more angles to the smaller triangle

Answer:

1 - 3/10 = 7/10 of the distance left

(3/7)(7/10) = 3/10 of the total distance

Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.

To find the fraction of the total distance traveled to Zachary's aunt's house, we need to combine the distances traveled and express it as a fraction of the total distance.

Given:

1. Zachary's family traveled [tex]\( \frac{3}{10} \)[/tex] of the total distance to his aunt's house.

2. Then, they traveled [tex]\( \frac{3}{7} \)[/tex] of the remaining distance.

Step 1: Calculate the total distance traveled by combining the two distances.

[tex]\[ \text{Total distance traveled} = \frac{3}{10} + \frac{3}{7} \][/tex]

Step 2: Find a common denominator for [tex]\( \frac{3}{10} \) and \( \frac{3}{7} \).[/tex] The least common multiple (LCM) of 10 and 7 is 70.

Step 3: Rewrite the fractions with the common denominator of 70.

[tex]\[ \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \][/tex]

[tex]\[ \frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70} \][/tex]

Step 4: Add the fractions:

[tex]\[ \frac{21}{70} + \frac{30}{70} = \frac{21 + 30}{70} = \frac{51}{70} \][/tex]

Therefore, Zachary's family traveled [tex]\( \frac{51}{70} \)[/tex] of the total distance to his aunt's house.

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

[tex]\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

In this case,

[tex]\text{longest side}^2 = 17^2 = 289[/tex].

[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}[/tex].

In other words, indeed [tex]\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2[/tex]. Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor [tex]2[/tex] to simplify the calculations.

[tex]\text{longest side}^2 = 20^2 = 400[/tex]

[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}[/tex].

[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

[tex]\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121[/tex].

[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}[/tex].

[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

[tex]\text{longest side}^2 = 11^2 = 121[/tex].

[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

The cost of old computer is $ 357

Solution:

Let "x" be the cost of old computer

From given,

Cost of new computer = $ 709

Blairs new computer cost 5$ less than twice the cost of her old computer

Therefore,

Cost of new computer = twice the cost of old computer - 5

Cost of new computer = 2x - 5

709 = 2x - 5

2x = 709 + 5

2x = 714

Divide both sides by 2

x = 357

Thus the cost of old computer is $ 357

Answer:

$357

Step-by-step explanation:

709=2x-5      

+5           +5

cross the right column out

709+5 = 714

714=2x

divide 714 by 2 and get 357

HOPE THIS HELPS!!!

Answer:

2/3

Step-by-step explanation:

Option c: [tex]-\frac{\pi}{5}[/tex] is the correct answer.

Explanation:

The given degree is –36°

Since, [tex]1^{\circ}=\frac{\pi}{180}[/tex]

The radian of –36° can be determined by multiplying it with [tex]\frac{\pi}{180}[/tex]

Thus, the degree can be converted into radians, by multiplying the degree with [tex]\frac{\pi}{180}[/tex]

Hence, it can be written as

[tex]-36^{\circ} \times \frac{\pi}{180}[/tex]

Multiplying, we get,

[tex]\frac{-36^{\circ} \pi}{180}[/tex]

Dividing, we have,

[tex]-\frac{\pi}{5}[/tex]

Thus, the radian of -36° is [tex]-\frac{\pi}{5}[/tex]

Answer:

the answer is c

Step-by-step explanation:

Answer:

[tex] - 5 \frac{3}{4} \times \frac{8}{23} = - \frac{23}{4} \times \frac{8}{23} = - 2[/tex]

Answer:

8+2x=50

happy to help!!

Answer:

Step-by-step explanation:

Since the rectangle sits within the larger circle, let's look at it this way:

Area of Shaded Region = Area of Circle - Area of Rectangle

OR

(X) =( pi * r^2 ) - (rectangle length * rectangle width)

Now we fill in the numbers where we know the numbers:

(X) = (pi * (12 cm)^2) - (3cm * 10cm)

(X) = (pi * 144cm^2) - (30 cm^2)

(X) = 144pi - 30

(X) = 452.39 - 30

(X) = 422.39 cm^2

Take the area of the circle and subtract that with the area of the rectangle.

Area of circle= pi*r^2

Area of circle= pi*12^2

Area of circle=144pi

Area of circle= 452.16 cm^2

Area of rectangle: b*h

Area of rectangle: 10*3

Area of rectangle: 30 cm^3

452.16-30=422.16

So the area of the shaded region is 422.16 cm^2

Hope this helped!

To find the variance of the weights from the given standard deviation of 11.6118 kg, you square the value of the standard deviation, resulting in a variance of 134.9143 kg^2.

The question pertains to finding the variance of the weights from a given standard deviation. The standard deviation provided is 11.6118 kg. Variance is calculated as the square of the standard deviation, which helps in understanding the dispersion of a dataset relative to its mean. To calculate the variance, you square the value of the standard deviation.

Variance = Standard Deviation2

Thus, Variance = (11.6118 kg)2 = 134.9143 kg2. Therefore, the variance of their weights is 134.9143 square kilograms, rounded to four decimal places as required.

Answer:

Geometric with common ration of 4/3

Step-by-step explanation:

12/9=4/3

16/12=4/3