If the function is:

What is f(-4)?

Answers

Answer 1

Answer:

D. -11

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}2x-3 & \textsf{if }x \leq -4\\x^2 & \textsf{if }-4 < x < 0\\x+5 & \textsf{if }x \geq 0\end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=2x-3 \quad \textsf{ when x is equal to or less than -4}[/tex]

[tex]f(x)=x^2 \quad \textsf{ when x is greater than -4 or less than zero}[/tex]

[tex]f(x)=x+5 \quad \textsf{ when x is greater than zero}[/tex]

f(-4) means to substitute x = -4 into the function.

As x = -4 satisfies the interval of the first piece of the function, substitute x = -4 into f(x) = 2x - 3:

[tex]\begin{aligned}\implies f(-4) & =2(-4)-3\\& = -8 -3\\& = -11\end{aligned}[/tex]

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Answer 2

Answer is D. -11

Answer:

Solution Given:

f(-4) depends on the condition x≤-4,

f(-4)=2*-4-3=-8-3=-11

Related Questions

In science class, the average score on a lab report is 87 points, with all students scoring within 1.8 points of the average. If x represents a student's score, write an equation that represents the
minimum and maximum scores.

Answers

The equations which represents the minimum and maximum scores of the students is; x = 87 ± 1.8.

Which equations represents the minimum and maximum possible scores of each student?

According to the task content, the

Average score of the students in the science class is; 87 points

All students are within 1.8 points of the average,

it therefore follows from the task content that the

minimum score is;

= 87 -1.8

= 85.2

maximum score is;

= 87+1.8

= 88.8 points.

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Answer:

Step-by-step explanation:

A. |x − 87| = 1.8

-hope this helps.

What is the area of an equilateral triangle having side 'a' units?

Answers

Answer:

[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]

Step-by-step explanation:

Since an equilateral has all of the sides equal, we can find the height of triangle using: [tex]a^2+b^2=c^2[/tex]. I attached a diagram which should explain how I got the dimensions of the three sides. Using the information from the diagram we get the equation:

[tex]h^2+(\frac{a}{2})^2=a^2[/tex]

Subtract a^2 from both sides

[tex]h^2=a^2-(\frac{a}{2})^2[/tex]

Take the square root of both sides

[tex]h = \sqrt{a^2-(\frac{a}{2})^2}[/tex]

If you know the area of a triangle, it's: [tex]\frac{1}{2}bh[/tex]. In this case the base=a, and the height is what we defined above. Using this we get:

[tex]A = \frac{a}{2}*\sqrt{a^2-(\frac{a}{2})^2}[/tex]

We can distribute the exponent over the division to get:
[tex]A = \frac{a}{2}*\sqrt{a^2-(\frac{a^2}{4})[/tex]

Now we can rewrite a^2 as 4a^2/4

[tex]A = \frac{a}{2}*\sqrt{\frac{4a^2}{4}-(\frac{a^2}{4})[/tex]

Now add the two fractions:

[tex]A = \frac{a}{2}*\sqrt{\frac{3a^2}{4}[/tex]

We can distribute the square root the division just like how we distributed the exponent 2, since the square root can be expressed as an exponent (1/2)

[tex]A = \frac{a}{2}*\frac{\sqrt{3a^2}}{\sqrt{4}}[/tex]

There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{a*b}[/tex]. We can use this to rewrite one radical as multiple radicals to simplify it:

[tex]A = \frac{a}{2}*\frac{\sqrt{a^2}*\sqrt{3}}{2}[/tex]

Simplify:

[tex]A = \frac{a}{2}*\frac{a*\sqrt{3}}{2}[/tex]

Now multiply the two fractions

[tex]A = \frac{a^2*\sqrt{3}}{4}[/tex]

This is the formula for the area of an equilateral triangle, but it is also often written as:
[tex]A=\frac{\sqrt{3}}{4}a^2[/tex]

please help asap
thank you very much

Answers

Answer:

x=30 , y=165 & z=10

happy to help { bts army girl }

Answer:

Step-by-step explanation:

Comment

You must solve x and then y in that order. The reason for that is there are 2 x values and they can be equated to each other. The you can go after the y value, since they are supplement with the value you get from the first operation.

Equations

x + 45 = 2x+ 8

<3 + y + 30 = 180

Solution

<1 and <3 are equal Two vertically opposite angles are always =.

x + 45 = 2x + 8 Subtract x from both sides

x-x + 45 = 2x - x + 8 Combine

45 = x + 8 Subtract 8 from both sides

45 - 8 = x + 8 - 8 Combine

37 = x

<1 + <2 = 180 These two angles sit on the same straight line and have a side in common

x + 45 + y + 30 = 180 Substitute for x

37 + 45 + y + 30 = 180 Combine

112 + y = 180 Subtract 112 from both sides

112-112 + y = 180 - 112 Combine

y = 68

The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inches.

Suppose the area of this rectangle is less than 12 square inches. Which of the following numbers could be the value of the unknown number? Select all that apply.

Answers

Answer:

6,4

Step-by-step explanation:

I'm not sure if 4 is correct but 6 definitely is. I hope this helps

23 gram put into milligrams

Answers

Answer:

Step-by-step explanation: 23000 milligrams

23000 milligrams. just multiply by 1000

Find the slope of the line passing through the points (-4, -9) and (5, -9).

Answers

The slope of the line passing through the points (-4, -9) and (5, -9) is 0

How to determine the slope?

The points are (-4, -9) and (5, -9).

The slope is calculated using:

Slope = (y2 - y1)/(x2 - x1)

So, we have:

Slope = (-9 + 9)/(5 + 4)

Evaluate

Slope = 0

Hence, the slope of the line passing through the points (-4, -9) and (5, -9) is 0

Answers

Answer:

Step-by-step explanation:

[tex]x = \frac{141 - 25}{2} = 58[/tex]

what is the ration between 28000 and 14?

Answers

The ratio between 28,000 and 14 is 2000 : 1

How to determine the ratio?

The numbers are given as:

28,000 and 14

Express as ratio

Ratio = 28000 : 14

Divide each number by 14

Ratio = 2000 : 1

Hence, the ratio between 28,000 and 14 is 2000 : 1

Answers

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Translation is the movement of a point either up, left, right or down in the coordinate plane.

The algebraic description that maps the image ΔABC onto ΔA′B′C′ is (x, y) ⇒ (x + 7, y - 4)

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Which of the following equations is an example of inverse variation between
the variables x and y?

Answers

Answer:

we need a whole example not just the variables.

Step-by-step explanation:

Suppose f′(6)=5 and g′(6)=7.
Find h′(6) where h(x)=4f(x)+5g(x)+1.

Answers

The value of the derivative of functions h'(6) as requested in the task content is; 55.

What is the value of h'(6)?

Since it follows from the task content that the function h(x)=4f(x)+5g(x)+1.

Hence, the derivative of h(x) can be evaluated as;

h'(x)=4f'(x)+5g'(x)

On this note, by substitution, it follows that;

h'(6)=4(5)+5(7)

h'(6) = 55.

Answers

Answer:

f(n)={n/2 = if n is even= n={2/2

{3n+1 {3(2)+1 =7

Step-by-step explanation:

if n is even u can put any even no in that place and u can get odd no or even no.(i think)

1. Determine the measure of angle B.
B
30
A
64
51

Answers

Answer: 51.4°

Step-by-step explanation:

Use law of cosines:

(because you are trying to find angle B, you need to use Cos B)

Cos B = c² + a²-b²/ 2ca

Then, plug in your numbers:

Cos B = 30²+64²-51²/ 2(30)(64)

Simplify:

Cos B = 0.6237

Next, to get rid of Cos B, so that we have just B, you need to do the Arccosine or 0.6237:

B = arccosine (0.6237)

Which gets you: 51.4°

The measure of angle B is 51.41 degrees after applying the cos law of the triangle.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have given a triangle in the figure:

To find the measure of the angle B

We can apply cos law:

c² = a² + b² - 2ab cosB

The a, b, and c represents the side lengths of the triangle and the measures are:

a = 30

b = 64

c = 51

51² = 30² + 64² - 2(30)(64) cosB

3840CosB = 4996 - 2601

3840CosB = 2395

CosB = 2395/3840

CosB = 0.623

B = Cos⁻¹(0.623)

B = 51.41 degrees

Thus, the measure of angle B is 51.41 degrees after applying the cos law of the triangle.

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A company determines that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200), where x is the price of each lamp. At which of the following prices will the company’s revenue be $10,000?

Answers

The price that will maximize company’s revenue of $10,000 is $50.

How to calculate the price?

From the information, the company determines 50that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200),

Therefore, this will be:

R(x) = -20x² + 1200x

10000 = -20x² + 1200x

-20x² + 1200x - 10000 = 0

x² - 60x + 500

x² - 50x - 10x + 500

x(x - 50) - 10(x - 50)

(x - 50)(x - 10)

Therefore, x - 50 = 0

x = 0 + 50 = 50

The price is 50.

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Which of the following inequalities matches the graph?
-8 -0
O x>4
O x<4
O y> 4
O y<4
1

Answers

Answer:

it matches with equation c

Write the positive or negative number that best
represents the given information.
12 ft above sea level

Answers

Answer:

Step-by-step explanation:

Usually, above sea level is represented by a positive number and below sea level by a negative number.

12 ft above sea level = 12

Which of the following is the largest Y value from the solution set of the giving system round your answer to the nearest hundredth

Answers

The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)

What is the solution of a non-linear system

In this question we have a system of non-linear equation formed by a radical equation and a quadratic equation, which can be solved both analytically and graphically. By equalizing the two formulas we have the following equation:

√(2 · x + 4) = x² - 5 · x + 3

√(2 · x + 4) + 13 / 4 = x² - 2 · (5 / 2) · x + 25 / 4

√(2 · x + 4) + 13 / 4 = (x - 5 / 2) ²

√(2 · x + 4) = (x - 5 / 2) ² - 13 / 4

Then, we square both sides to eliminate the radical sign:

2 · x + 4 = (x - 5 / 2)⁴ - (13 / 2) · (x - 5 / 2)² + 169 / 16

2 · x + 4 = x⁴ + 4 · x³ · (- 5 / 2) + 6 · x² · (- 5 / 2)² + 4 · x · (- 5 / 2)³ + (- 5 / 2)⁴ - (13 / 2) · [x² + 2 · (- 5 / 2) · x + ( - 5 / 2)²] + 169 / 16

2 · x + 4 = x⁴ - 10 · x³ + (75 / 2) · x² - (125 / 2) · x + 625 /16 - (13 / 2) · x² + (65 / 2) · x - 325 / 8 + 169 / 16

2 · x + 4 = x⁴ - 10 · x³ + 31 · x² - 30 · x + 9

x⁴ - 10 · x³ + 31 · x² - 32 · x + 5 = 0

The real roots of this polynomial are:

x₁ ≈ 5.152, x₂ ≈ 2.862, x₃ ≈ 1.797, x₄ ≈ 0.189

Now we evaluate f(x) at each root:

y₁ ≈ 3.782, y₂ ≈ 3.118, y₃ ≈ 2.756, y₄ ≈ 2.092

The largest y-value from the solution set of the nonlinear system is 3.78. (Correct choice: C)

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The function f(X) =7^x + 1 is transformed to function g through a horizontal compression by a factor of 1/3

Answers

The equation of the function g(x) is g(x) = 7^(3x) + 1

How to determine the function g(x)

The function f(x) is given as:

f(x) = 7^x 1

When compressed horizontally by a factor of 1/3.

We have:

g(x) = f(3x)

This implies that:

g(x) = 7^(3x) + 1

Hence, the equation of the function g(x) is g(x) = 7^(3x) + 1

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Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem.

2. Use the distributive property to expand 0.05(50 + 40). (2 points)

Answers

Answer:

$4.50

Step-by-step explanation:

We can use the distributive property to solve this problem. 0.05(50+40) is the total sales tax. 0.05 being the percentage and 50 and 40 being the things we need to distribute 0.05 to. This becomes 2.5+2. This is 4.5.

Answer:

$0.45

Step-by-step explanation:

0.05(50 + 40) = 50 x 0.05 + 40 x 0.05 = 0.25 + 0.20 = 0.45

Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).

Answers

the expression simplified is:

[tex]12x^3 - 25x^2 + 9[/tex]

How to simplify the given expression?

Here we have the expression:

[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]

We just need to distribute the product, we will get:

[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]

Now we just need to group terms with the same exponent of x:

[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]

That is the expression simplified

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find x and y

plssss help

Answers

90 + 6x = 180

-90

6x = 90

÷6

x = 15

5y + 4y + 90 + (6x15) =360

9y + 90 + 90 = 360

9y + 180 = 360

- 180

9y = 180

÷9

y = 20

Hope this helps!

To graph the inequality t>3, you would put an open circle on 3 and shade to the left

Answers

Answer:

It is an open circle and you would shade to the right on a number line.

Step-by-step explanation:

The circle is open because you are not including 3. Put numbers in for t and you will see that the numbers greater than 3 are all on the right side of the number line.

A cube with an edge of 10cm is filled with water.How much can it contain?

Answers

The cube can contain 1000 cm^3 of water

How to determine the amount of water?

The side length is given as:

L = 10 cm

The amount of water it can contain is calculated as;

V =L^3

So, we have:

V = 10^3

Evaluate

V = 1000

Hence, the cube can contain 1000 cm^3 of water

Answers

Question 1 of 10
If f(x)=x-1, which of the following is the inverse of f(x)?

Correct Options is A

Match each function with the corresponding function formula when h(x) = 5 - 3x and g(x) = -3x + 5.

Answers

Answer: -5=x

Step-by-step explanation:

kmbtvonpvnp4tnv

a two digit number has twice as many ones as tens twice the original number is 9 more than the reversed number find the original number

Answers

Answer: 36

Step-by-step explanation:

As this is a two-digit number, it will have a digit in its 10's place and a digit in its 1's place. We can represent the 10's digit using x and the 1's digit using y.

Since the ones is twice the number of tens, this means that y is equal to 2*x. Let's put this into an equation.

[tex]y=2x[/tex]

If the 10's digit is x and the 1's digit is y, the original number would be [tex]10x + y[/tex], as x must be multiplied by 10 to get it to the 10's place. Similarly, the reversed number would be [tex]10y + x[/tex], as y must be multiplied by 10 to get it to the 10's place.

Twice the original number (10x+y) is equal to 9 more than (i.e. 9 plus) the reversed number. We can put this into an equation to help us answer the question.

[tex]2(10x+y)=9+10y+x\\20x+2y=9+10y+x\\19x+2y=9+10y\\19x=9+8y[/tex]

Now we have a system of two equations.

[tex]y=2x\\19x=9+8y[/tex]

We can solve this system by substituting y for 2x in the second equation. Then, we can isolate and get the value of x.

[tex]19x=9+8(2x)\\19x=9+16x\\3x=9\\x=3[/tex]

Now that we have the value of x, let's put it back into the first equation and solve for y.

[tex]y=2(3)\\y=6[/tex]

Remember that x is the 10's digit and y is the one's digit of our answer. Since x is 3 and y is 6, our answer is 36.

Checking

We can quickly check if our answer is right by making sure both conditions in the question are met.

6 (the one's digit) is twice the value of 3 (the ten's digit), making the first condition true. Twice of 36 is 72, which is 9 more than the reversed number, which is 63.

will give brainliest

Answers

ax² + bx + c = 0

discriminant = b² - 4ac

----> x² + 7x + 12

---> Discriminant of this equation = 7² - 12.1.4 = 49 - 48 = 1 (Positive discriminant)

x = (-7 + 1)/(2.1) = -6/2 = -3

x = (-7 - 1)/(2.1) = -8/2 = -4

Therefore, this equation has two real solutions and has a positive discriminant.

The correct answer is B

if sinA=4/5 solve sin2A, cos2A and tan2A

Answers

Step-by-step explanation:

1) if m(∠A)∈[0;90°), then

[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]

[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]

[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]

[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]

2) if m∠A∈[90°;180°), then

cos(A)=-0.6;

sin2A=-0.96;

cos2A=-0.28;

tan2A=-24/7.

Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.

Answers

Using the simple interest formula, it is found that the APR for the loan is of 4.472%.

What is the simple interest formula and when it is used?

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

A(0) is the initial amount.r is the interest rate, as a decimal.

The parameters for this problem are:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

We solve the equation for r to find the APR.

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark

{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}

Answers

The domain of the rational function is:

{x ∈ ℝ| x ≠ –2, 2}

What is the domain of the rational function?

Here we have the rational function:

[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]

We want to get the domain of that function. First, we can rewrite the numerator and denominator as:

[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]

[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]

Then we can rewrite the rational function as:

[tex]f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}[/tex]

This can be simplified to:

[tex]f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}[/tex]

Now, the domain will be the set of all real numbers, minus the values of x that generate problems.

In this case, the values:

x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so we conclue that the domain is:

{x ∈ ℝ| x ≠ –2, 2}

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If the function is: What is f(-4)?

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If the function is:

What is f(-4)?