Find f(g(x)) and g(f(x)) of f(x)=x^2-8, g(x)=2x-5

That triangle has a horizontal base with y=2.  The length of that base is RS=1-(-4)=1+4=5.  The height of the triangle is the vertical distance  from line y=2 to T(-5,-4).  That height is  2-(-4)=2+4=6.  The area of the triangle is  base * height/2 = 5*6/2= 15

The answer is 15 units ^2

Answer:

The answer is 15 units².

Step-by-step explanation:

I am a hundred percent sure. I did the math and got it right on my test.

∠C and ​ ∠D ​ are vertical angles

so <C = <D because vertical angles are equal

Substitute

−3x + 58  = x−2

Solve for x

Subtract x from both sides

-4x + 58 = - 2

Subtract 58 from both sides

-4x = - 60

Divide both sides by -4

x = 15

<D = x−2  = 15 - 2 = 13

Answer

<D = 13°

Answer:

The measure of angle D is 13°

Step-by-step explanation:

-3x+58=x-2

+3x to each side

58=4x-2

Add 2 to each side

60=4x

Divide each side by 4

X=15

Now substitute that in:

-3(15)+58=13

(15)-2=13

The measure of angle D is 13°

answer=2X8+3X5=16+15=31

40 mins is the answer

10 mins-4

20mins-8

30mins-12

40mins-16

Answer:

A) x + 0

Step-by-step explanation:

In triangle ABC, the coordinates are: A(1, -1), B(1, -5) and C(4, -5)

In triangle A'B'C', the coordinates are: A(1, -5), B(1, 1) and C(4, 1)

Look at the x-coordinates in both the triangles remains the same because the triangles are reflected over x-axis, therefore, only the y-coordinate changes.

Therefore, the rule for x-coordinates = x + 0

Answer: A) x + 0

Hope this will helpful.

Thank you.

Answer:a

Step-by-step explanation:

I know that i had it on a test its -2.11 Hope you ace it!

-2.11 hope this helps

Answer:

The correct option is A.

Step-by-step explanation:

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]          ..... (1)

Where, (h,k) is vertex and a is a constant.

From the given graph it is clear that the vertex of the graph is (3,-7) and y-intercept is (0,2).

Substitute h=3 and k=-7 in equation (1).

[tex]y=a(x-3)^2-7[/tex]

The y-intercept is (0,2). So, substitute c=0 and y=2 in the above equation to find the value of a.

[tex]2=a(0-3)^2-7[/tex]

[tex]2+7=a(3)^2[/tex]

[tex]9=9a[/tex]

Divide both sides by 9.

[tex]1=a[/tex]

The value of a is 1.

Substitute a=1, h=3 and k=-7 in equation (1).

[tex]y=1(x-3)^2-7[/tex]

[tex]y=x^2-6x+9-7[/tex]

[tex]y=x^2-6x+2[/tex]

The equation of the parabola is [tex]y=x^2-6x+2[/tex].

Therefore the correct option is A.

B. is the graph that fills the requirements

Graph2 with slope of 25 is the graph that shows the relationship on the table.

To find the equation of the line passing through points A(3, 75) and B(12, 300) follow these steps:

1. Calculate the slope m:

m = (y₂ - y₁)/x₂ - x₁)

m = (300 - 75)/(12 - 3)

m = 225/9

m = 25.

Graph2 with same slope as the calculated slope is the graph that shows the relationship on the table.

2. Use the point-slope form with one of the points (e.g., A(3, 75)

y - y₁ = m(x - x₁)

y - 75 = 25(x - 3)

3. Simplify the equation:

y - 75 = 25x - 75.

4. Isolate y

y = 25x.

So, the equation of the line passing through points A(3, 75) and B(12, 300) is y = 25x

learn more about graph here

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If you distribute the multiplication, your function is written as

[tex] y=f(x)=3x-6 [/tex]

Like every function in the form [tex] y = mx+q [/tex], this function represents a line. A line has no vertex and no axis of symmetry (actually, it is symmetric with respect to every perpendicular line).

2x+50=7x

50 = 5x

x = 10

2(10) + 50

20 + 50

= 70 degrees

Isolate the x. Note the equal sign. What you do to one side, you do to the other. First, add 1/3y to both sides

8x - 1/3y (+1/3y) = 15 (+1/3y)

8x = 15 + 1/3y

Divide 8 from both sides

(8x)/8 = (15 + 1/3y)/8

x = 15/8 + 1/24y

x = 1/24y + 1.875

x = 1/24y + 1.875 is your answer

hope this helps

x^2 - 3(x^2 + 3x - 1)

Distributive property.

x^4 + 3x^3 - x^2 - 3x^2 - 9x + 3

Combine like terms.

x^4 + 3x^3 - 4x^2 - 9x + 3

Answer:

The answer is 72.578 :))

Step-by-step explanation:

I got it right in my exam

1.  2a=9b  first we will divide the both sides with parameter b and get

2(a/b)=9 now we will divide both sides with number 2 and get

a/b=9/2 => a : b = 9 : 2

2. 6a-3b=5b first we will add to both sides number (+3) and get

6a=5b+3b => 6a=8b then divide the both sides with parameter b and get

6(a/b)=8 now we will divide the both sides with number 6 and get

a/b=8/6 if we simplify the fraction we get  

a/b=4/3 => a : b = 4 : 3

3.  a+b=3b we will add to the both sides parameter (-b) and get

a=3b-b => a=2b then divide the both sides with parameter b and get

a/b=2 => a/b=2/1 => a : b = 2 : 1

4.  a/5=b/7 first we will divide the both sides with paremeter b and get

a/(5b)=1/7 now we will multiply the both sides with number 5 and get

a/b=5/7 => a : b = 5 : 7

Good luck!!!

The ratio a:b in the four problems given are 9:2, 4:3, 2:1, and 5:7 respectively. This is achieved by isolating 'a' in each equation and simplifying the resulting expression.

Let's find the ratio between a:b for each of the problems you've provided:

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Given that Bart and Melinda are grand children and Bart lives

6 blocks from his grand parents.

Also given that Melinda lives 8 blocks farther from her grandparents as Bart does .

This means Melinda lives 6+8 = 14 blocks from her grand father house

This question involves addition because farther as Bart does means , Melinda lives 8 +6 hence we get 14

Answer is: Melinda lives 14 blocks from her grandfathers

ANSWERS

Find out the how many weeks will it take for Mary and Joe to have the same amount saved.

To proof

Let us assume that the number of week take for Mary and Joe to have the same amount saved be x.

As given

Mary start with $10 and earns $10 each week mowing lawn.

Joe already has $20 from birthday gifts and earns five dollars a week pulling weeds.

than the equation

10 + 10x = 20 +5x

5x = 10

x = 2 weeks

therefore 2 weeks will it take for Mary and Joe to have the same amount saved.

Hence proved

D

a direct linear variation equation has the form f(x) = kx

f(x) = x - 12 is not in this form thus does not show a direct linear variation

The number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

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.

We have:

A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number.

Total letters = 26

Total numbers = 10

As the repetitions are allowed.

Number of ways = 26×26×26×10×10×(26+10)

N=63,273,600 Ways

P(abc123 or 123abc) = P(abc123)+P(123abc) - P(abc123 and 123abc)

The intersection of abc123 and 123abc is zero because both license plates are not possible at a time

P(ABC123 or 123ABC)=P(ABC123)+P(123ABC)

[tex]\rm P=\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}\dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8} + \dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8}\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}[/tex]

P= 2/5616000

or

P = 1/2,808,000

Thus, the number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.

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Algebraically, you have to factor the square root of 7 to see why you're wrong:

[tex] 3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7} [/tex]

Conceptually, think that any object - say an apple - represents the square root of seven.

So, you have three apples, and you take away one apple. You have two apples remaining, i.e. [tex] 2\sqrt{7} [/tex]

[tex]3\sqrt{7} - \sqrt{7}[/tex]

Let x represent [tex]\sqrt{7}[/tex], then you can rewrite the expression as 3x - x.

3x - x = 2x.  Now replace "x" with  [tex]\sqrt{7}[/tex] and you get 2[tex]\sqrt{7}[/tex].

The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.

Answer:

Given equation is:

x/4 = 16

Multiply both side of equation by 4

4* x/4 = 16*4

x= 64

Step-by-step explanation:

This is called Multiplication property of Equality.

If you multiply equation by a number on both sides, it remain same or balance.

The equation x/4 =16 is solved by multiplying both sides by 4, resulting in x = 64. This action is justified by the Multiplication Property of Equality.

To solve the equation x/4 =16, the action one would use is to multiply both sides of the equation by 4. This operation will isolate the variable 'x'.

Your equation would thus be transformed as: 4 * (x/4) = 16 * 4. This simplifies to x = 64.

The property that justifies this action is the Multiplication Property of Equality, which states that multiplying both sides of an equation by the same non-zero number does not change the equality.

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Using complex numbers, you can have negative squares, since [tex] i^2=-1 [/tex]

So, you can find the solutions to

[tex] x^2+20=0 \iff x^2 = -20 \iff x=\pm\sqrt{-20}=\pm i \sqrt{20}=\pm 4i\sqrt{5} [/tex]

So, using the factorization [tex] (x-x_1)(x-x_2) [/tex] where [tex] x_{1,2} [/tex] are the roots of the quadratic equation, you have

[tex] x^2+20 = (x-4i\sqrt{5})(x+4i\sqrt{5})[/tex]

This expression can't be further factorized, because all terms have degree 1.

To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.

To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.

Using the quadratic formula, we start by finding the values of x that satisfy the equation x^2 + 20 = 0.

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = 0, and c = 20. Substituting these values into the quadratic formula, we get: x = ± √-20.

Since we are factoring over the complex numbers, we can express the solution as: x = ± √20i.

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Answer:

6:8, 9:12

Step-by-step explanation:

Answer:

6:8 9:12

Step-by-step explanation:

Answer: C

Step-by-step explanation:

A) not completely factored because 2 can be factored out of 2x + 4

B)  not completely factored because 3 can be factored out of 3x - 9

C) CORRECT

D) not factors because the terms are added instead of multiplied

Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.

It is a polynomial of maximum power 2. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

A.  (2x + 4)(x - 3)

On multiplying

2x² - 2x -12

B.  (x - 1)(3x - 9)

On multiplying

3x² -12x + 9

C.  (x + 4)(x - 3)

On multiplying

x² + x - 12

D.  (x - 2) + (x + 3)

On multiplying

2x + 1

Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.

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Answer:

4606.48 $

Step-by-step explanation:

Amount invested P = 3500 $

Rate of interest r = 6.12%

Compounding monthly

Monthly rate of interest = 6.12/12 =0.51%

Time = 4.5 years = 4.5 (12) = 54 months

Hence final amount would be

P(1+0.01r)^t

Here r = 0.51 and t = no of months = 54

Hence final amount

= 3500(1.0051)^54

= 3500(1.31613)

=4606.48 $

Thus 3500 if invested now will become 4606.48 in 4.5 years at the rate of interest of 6.12% compounding monthly.

The tax on a $9.95 purchase with a 6.8% tax rate, rounded to the nearest hundredth, is approximately $0.68.

To calculate the tax on a purchase, you can multiply the purchase amount by the tax rate. In this case, $9.95 is being multiplied by 6.8% (or by 0.068 as a decimal). So, the calculation would look like this: $9.95 * 0.068 = $0.6766. However, the question asks to round to the nearest hundredth. So, the final tax would be approximately $0.68.

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The original price of the computer was $411. This was found by adding the reduction amount to the final price, i.e., $355 + $56.

This question is concerned with a simple arithmetic operation. It's provided that the price of the computer was reduced by $56 to $355. The original price should thus be the markdown plus the final price.

Performing this calculation:
Add the amount of reduction ($56) to the current price ($355).

The solution is:
$355 (final price) + $56 (reduction) = $411 (original price)

Therefore, the original price of the computer was $411

So, option D is ($411) correct .

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