Which side lengths form a right triangle 30 POINTS!!

[tex]\frac{f(x)}{g(x)} =?[/tex]

Since you know f(x) = 2x and g(x) = 3x^3, you can substitute that into the function

[tex]\frac{f(x)}{g(x)} =?[/tex]

[tex]\frac{2x}{3x^3} =?[/tex]

When a variable(x or y) with an exponent is divided by another variable with an exponent, you subtract the exponents, only if the variables are the same.

For example:

[tex]\frac{x}{y}[/tex]   Since the variables on the top and bottom are not the same, you can't simplify it (or its already simplified)

[tex]\frac{x^3}{x^2} =x^{3-2} =x^1[/tex]

[tex]\frac{y^5}{y^7}=y^{5-7}=y^{-2} = \frac{1}{y^2}[/tex] (when an exponent is negative, you move it to the other side of the fraction to make the exponent positive)

[tex]\frac{2x}{3x^3} =?[/tex]

[tex]\frac{2x}{3x^3}= (\frac{2}{3})x^{1-3}= (\frac{2}{3})x^{-2} = (\frac{2}{3})\frac{1}{x^2}[/tex]  Since you can't simplify 2/3, you get:

(not sure if this is how it should look ---> (2/3)x^(1-3) but i'm assuming it is)

[tex]\frac{2}{3x^2}[/tex]

Answer:

[tex]\boxed{\frac{1}{8}}[/tex]

Step-by-step explanation:

You are starting with ½ pie. Then you cut it into four pieces.

You want to evaluate ½ ÷ 4

Step 1. Treat the integer as a fraction

[tex]\frac{1}{2}\div{\frac{4}{1}}[/tex]

Step 2. Invert the divisor and change divide to multiply

[tex]\frac{1}{2}\times{\frac{1}{4}}[/tex]

Step 3. Multiply numerators and denominators

[tex]\frac{1}{2}\times{\frac{1}{4}} = \mathbf{\frac{1}{8}}\\\\\text{Each piece is } \boxed{\mathbf{\frac{1}{8}}} \text{ of a whole pie.}[/tex]

Answer:

1/8

Step-by-step explanation:

Answer:

£ 1.96

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

1 kg = £ 4.90

( ÷ 10 )

100 g = £ 0.49

( × 4 )

400 g = £ 1.96

Answer:

£1.96

Step-by-step explanation:

1kg = 1000g

1 kg = £4.90

1000g = £4.90

1000g = £4.90

100 g = 4.90 ÷ 10 = £0.49

100g = £0.49

400g = 0.49 x 4 = £1.96

Final answer:

The amount deducted weekly for Social Security taxes from Tomas Gomez's gross weekly pay of $750 at a tax rate of 6.2% is $46.50.

Explanation:

The question relates to calculating deductions for Social Security taxes from Tomas Gomez's weekly pay. To calculate the amount deducted weekly for Social Security taxes at a tax rate of 6.2%, you multiply the gross weekly pay by the tax rate.

Gross Weekly Pay: $750
Social Security Tax Rate: 6.2%

Calculation: $750 * 6.2% = $750 * 0.062 = $46.50

Thus, the amount deducted weekly for Social Security taxes from Tomas Gomez's gross pay is $46.50.

Area of each cookie is approximately 28.3 cm2.

The area of a circle can be calculated using the formula A = πr2. Given that the diameter of each cookie is 6 centimeters, the radius would be half of the diameter, which is 3 centimeters. Plugging in the values, we get: A = 3.14 x (3 cm)2 = 3.14 x 9 = 28.26 cm2. Rounded to the nearest tenth, the area of each cookie is approximately 28.3 cm2.

answer:

-1/2

explanation

1-2 / 4-2 = -1/2

Slope between two points

 [tex](x_{1},y_{1}) \text{and},(x_{2},y_{2}) \text{is equal to}\\\\\text{and}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-2}{4-2}\\\\=\frac{-1}{2}[/tex]

Option D                                

  [tex]\frac{-1}{2}[/tex]

the answer is:

Area =518

Volume =735

hope this helps you good luck!!

Answer:

x = 4

Step-by-step explanation:

a = i-2j

b = 2i-xj

1 = k•2

-2 = k•(-x)

=> 1/2 = k

=> (-2)/(-x) = k

=> 1/2 = (-2)/(-x) => 1/2 = 2/x => x = 4

Answer:

[tex]\large\boxed{m=\dfrac{3w-2u-z}{u+w-z}}[/tex]

Step-by-step explanation:

Use the distributive property: a(b + c) = ab + ac

[tex]u(m+2)+w(m-3)=z(m-1)\\\\um+2u+wm-3w=zm-z\qquad\text{subtract}\ 2u\ \text{from both sides}\\\\um+wm-3w=zm-z-2u\qquad\text{add}\ 3w\ \text{to both sides}\\\\um+wm=zm+3w-2u-z\qquad\text{subtract}\ zm\ \text{from both sides}\\\\um+wm-zm=3w-2u-z\qquad\text{distributive}\\\\(u+w-z)m=3w-2u-z\qquad\text{divide both sides by}\ (u+w-z)\neq0\\\\m=\dfrac{3w-2u-z}{u+w-z}[/tex]

Answer:

y = -|x| +3

Step-by-step explanation:

Answer:

-/x/-3

Step-by-step explanation:

Answer:

Stay friends. Make him think you are over him.

Step-by-step explanation:

This will make him question if maybe you have found someone else. An opportunity to get back together might pop up out of it.

Answer:

Honestly as a boy I think that you should start talking to him again.

Step-by-step explanation:

Like we cant read minds. If you miss him then maybe if he sees that u have feelings for him then maybe yall can work things out. Also it depends on the boy. What type is he. and it depends on you. what type of girl are you. If you like can I please get brainliest

Answer:

hello :  x=1

Step-by-step explanation:

look this solution  :

Answer:

[tex]x=630[/tex]

Step-by-step explanation:

The Exponential Product rule tells us that...

[tex]x^m*x^n=x^{m+n}[/tex]

Therefore, [tex]x=1+2+3...+35[/tex].

Therefore, [tex]x=630[/tex]

Answer:

$9.75 per hour

Step-by-step explanation:

243.75/25= 9.75

Hope this helps you out!

Answer:

Jeff is paid $9.75 for one hour of work.

Step-by-step explanation:

Jeff made last week = $243.75

He worked 25 hours for a week.

We have to calculate his pay per hour, so we divide his total pay by the time he worked.

total pay ÷ time he worked ( in hours)

pay per hour = 243.75 ÷ 25 = $9.75/hour

Jeff is paid $9.75 for one hour of work.

Answer:

(-1,4)(1,4)

2

Step-by-step explanation:

Answer:

No, the area will not be doubled. Instead, it will be quadrupled

Step-by-step explanation:

Let the length of the base be b and the height be h.

Original area = b x h

= 3 x 5

= 15 square feet

New area = b x h

= (2 x 3) x (2 x 5)

= 6 x 10

= 60 square feet

Therefore, the area is quadrupled when both the base and the height are doubled.

Answer:

Sample response: No, the area will be multiplied by 4. The original area is 3 × 5 = 15 square feet. If the base and the height are both doubled, then the new area will be 6 × 10 = 60. 60 is 4 times 15.

Answer:

B is the greatest being 5.

Step-by-step explanation:

A.

[tex]-2-(-3)\\-2+3\\1[/tex]

B.

[tex]2-(-3)\\2+3\\5[/tex]

C.

[tex]-2-3\\-5[/tex]

D.

[tex]2+(-3)\\-1[/tex]

The expression 2-(-3) is determined to have the greatest value.

To determine which expression has the greatest value:

A: -2-(-3) = -2 + 3 = 1

B: 2-(-3) = 2 + 3 = 5

C: -2-3 = -5

D: 2+(-3) = 2 - 3 = -1

Answer:

[tex]y=B(2+0.1x)[/tex]

Step-by-step explanation:

B = number of sponsors

x = number of pins

Equation :

[tex]y=B(2+0.1x)[/tex]

Answer:

Y=-2.9x+120

Step-by-step explanation:

The most simple way to solve is plug any x value into each equation and see if it works

Answer:

2nd option choice or third

Answer:

153.86

Step-by-step explanation:

To find the area the equation is pi* radius squared

so it's 3.14*7 squared it's

3.14*49

The answer is 153.86

Answer:

t(ties) = $8,50 and s(shirts) = $19,50

Linda's purchase total price $36,50

Step-by-step explanation:

In mathematics, a system of linear equations is a set of two or more linear equations with more than one unknown that make up a mathematical problem that consists of finding the values ​​of the unknowns that satisfy those operations.  the unknowns are usually represented with letters of the alphabet

For this example, we can represent as a system of linear equations as follows:

For Ted

[tex]4s+2t=95[/tex] where s are shirts, t are ties, and 95 the total price of both products in $.

For Stephen

[tex]3s+3t=84[/tex] where s are shirts, t are ties, and 84 the total price of both products in $.

Each shirt and each tie were buying in the same clothing store which means that it has the same price and we can and we can relate both equations with a system of equations as follows:

[tex]\left \{ {{4s+2t=95} \atop {3s+3t=84}} \right.[/tex]

Using the reduction method, which is to clear in one of the equations with any unknown.

In this case the system has two unknowns, the selected one must be replaced by its equivalent value in the other equation.

Let's clear s in the second equation

[tex]3s+3t=84\\3s=84-3t\\s=\frac{84-3t}{3} \\s=28-t[/tex]

Substituting the value of [tex]s=28-t[/tex] in the first equation

[tex]4s+2t=95[/tex] with [tex]s=28-t[/tex]

[tex]4(28-t)+2t=95\\112-4t+2t=95\\-2t=95-112\\t=\frac{-17}{-2}=8.50[/tex]

We got that the price of a tie is t = $8,50

Substituting the value of t in the first equation in order to obtain the value of s

[tex]3s+3t=84\\3s+3(8.50)=84\\3s+25.50=84\\s=\frac{84-25.50}{3} = 19.50[/tex]

We got that the price of a shirt is s = $19,50

Checking if the result satisfies the equations

With t = 8.50 and s = 19.50

[tex]\left \{ {{4s+2t=95} \atop {3s+3t=2}} \right.\\\left \{ {{4(19.50)+2(8.50)=95} \atop {3(19.50)+3(8.50)=84}} \right.\\\left \{ {{78+17=95} \atop {58.50+25.50=84}} \right.[/tex]

Linda bought 1 shirt and 2 ties at the same store. What's the total price in dollars and cents of Linda's purchase?

If a shirt value is s = $19,50 and a tie value is t = $8,50

Then s + 2t = ?

$19,50 + 2($8,50) = $36,50

The system of equations can be used to find s, the cost of each shirt in dollars and t the cost of each tie in dollars is

4s + 2t = 95

4s + 2t = 953s + 3t = 84

Given:

Cost of shirt = s

Cost of tie = t

4s + 2t = 95 (1)

4s + 2t = 95 (1)3s + 3t = 84 (2)

Multiply (1) by 3 and (2) by 2

12s + 6t = 285 (3)

6s + 6t = 168 (4)

subtract (4) from (3)

12s - 6s = 285 - 168

6s = 117

s = 117/6

s = 19.5

substitute s = 19.5 into (1)

4s + 2t = 95 (1)

4(19.5) + 2t = 95

78 + 2t = 95

2t = 95 - 78

2t = 17

t = 17/2

t = 8.5

Therefore, the cost of each shirt is $19.5 and the cost of each tie is $8.5

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Answer:

I'm going to assume that this is compound interest, as simple interest in this case would not make sense.

Let A be the final amount ( in this case, after 4 years). A = 20,000(1+0.042/12)^12*4. In this formula, I am assuming that the interest compounds 12 times a year, or every month. I am also assuming that he pays it off once he hits the 4-year mark.

If the assumptions are correct, he would be paying $23651.79 at the 4-year mark.

Step-by-step explanation:

Final answer:

Marco will owe approximately $23,521.93 on his unsubsidized student loan after graduation, calculated using the future value formula for a loan with compounded interest.

Explanation:

To calculate the amount Marco will owe after he graduates, we need to apply the formula for the future value of a loan when interest is compounded annually and no payments are made until after a certain period. Since Marco's unsubsidized student loan does not require payments while he is in school, the interest will be capitalized and added to the principal amount of the loan.

The formula for future value FV of a present value PV after n periods at an interest rate r is:

FV = PV * (1 + r)ⁿ

Where:

PV is the initial loan amount ($20,000)

r is the annual interest rate (4.2% or 0.042 as a decimal)

n is the number of periods (years in this case) before he starts repaying the loan (4 years)

Using the formula, we get:

FV = $20,000 * (1 + 0.042)⁴

FV = $20,000 * (1.042)⁴

F = $20,000 * 1.1760965435

FV = $23,521.93

Thus, Marco will owe approximately $23,521.93 once he graduates, before he starts making any payments on the loan.

Answer:

The height of the prism is [tex]24\ in[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

In this problem we have

[tex]V=5,376\ in^{3}[/tex]

[tex]L=14\ in[/tex]

[tex]W=16\ in[/tex]

substitute in the formula and solve for H

[tex]5,376=(14)(16)H[/tex]

[tex]H=5,376/[(14)(16)][/tex]

[tex]H=24\ in[/tex]

Answer:

PR = 20

Step-by-step explanation:

The perimeter is the sum of the 3 sides, thus

4z + z + 3 + 3z + 2 = 45 ← simplify left side

8z + 5 = 45 ( subtract 5 from both sides )

8z = 40 ( divide both sides by 8 )

z = 5

PR = 4z = 4 × 5 = 20

Answer:

40

Step-by-step explanation:

Using the triangle perimeter formula [P=2(l) + 2(w) / 2]:

45 = 2 (z + 3) + 2 (3z + 2) / 2

45 = 2z + 6 + 6z + 4 / 2

45 = 8z + 10 / 2

45 = 4z + 5

40 = 4z

z = 10

PR

4z

4 (10)

40

Answer:

20

Step-by-step explanation:

The question tells us that line a is parallel to line b (even if they don't seem to be in the image).

∠8 = ∠4 and ∠5 = ∠1 since line t crosses the parallel lines.

We are given ∠4 = 3x and ∠5 = 6x.

Since we know ∠8 = ∠4 , we can then say

∠8 = 3x and ∠5 = 6x

Since ∠8 and ∠5 are complementary and combined they form a flat angle of 180 degrees, we can say:

3x + 6x = 180

9x = 180

x = 20

Answer:

(7,2)

y= -47 or (0,-47)

Step-by-step explanation:

You can use a graphing calculator to find the vertex and y intercept

The coordinates of the vertex are - V(7, 2) and the y - intercept will have coordinates - Y(0, - 47).

Given is the following equation -

- x² + 14x - 47

We can write the vertex as -

[tex]{\displaystyle V=\left(-{\frac {b}{2a}},{\frac {4ac-b^{2}}{4a}}\right)}[/tex]

So, we can write -

V = (-14/-2, {4 x -1 x -47 - 196}/{-4})

V = (7, 2)

and the point of the parabola intersecting the y - axis has coordinates -

(0, c)

(0, - 47)

Therefore, the coordinates of the vertex are - V(7, 2) and the y - intercept will have coordinates - Y(0, - 47).

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Answer:

correct answer is option b.

Step-by-step explanation:

so Ashley has markdown one item by 15%

and mark up other items by 10% to get $3.77

assuming she marked ceiling fan mark down by 15%

if each  item is sold

  =  0.85 ×  $64.79 +1.1 × $51.49 +1.1 ×  $45.99 + 1.1 × $37.39

  = $203.4285

profit

= $203.4285 - $64.79 -$51.49 - $45.99 -$37.39

=$3.7685   ≅$3.77

hence ceiling fan price will be draw down by 15%

hence correct answer is option b.

The item that was marked down was the b. ceiling fan, from $64.79 to $55.07.

A markdown reduces the cost or price of an item by the percentage markdown.

A markup, on the other hand, increases the cost of the item.

Markdown = 15%

Markup = 10%

Items                   Prices

Power drill          $51.49

Ceiling fan           64.79

Circular saw        45.99

Screwdriver set   37.39

Total price       $199.66

Increase in the price = $3.77

New price = $203.43 ($199.66 + $3.77)

Most likely, Ashley will mark down the Ceiling fan to attract customers to purchase other items.

Therefore, the new prices after applying the changes will be:

Items                   Prices    Markup/down

Power drill          $51.49      $56.64 ($51.49 x 1.1)

Ceiling fan           64.79        55.07 ($64.79 x 0.85)

Circular saw        45.99       50.59 ($45.99 x 1.1)

Screwdriver set   37.39         41.13 ($37.39 x 1.1)

Total price       $199.66  $203.43

New total price = $203.43

Old total price = $199.66

Increase in cost = $3.77 ($203.43 - $199.66)

Thus, the item that was marked down was the b. ceiling fan.

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To find the measure of Angle B, solve the equation 5x - 15 = 2x + 21, which gives x = 12. Then, substitute x back into the expression for Angle B to get 2(12) + 21 = 45°. Thus, Angle B measures 45°.

Solve for x and find the measure of Angle B

To solve for x and find the measure of Angle B, follow these steps:

Now, substitute x back into the expression for Angle B:

Angle B = 2x + 21
= 2(12) + 21
= 24 + 21
= 45°

Therefore, the measure of Angle B is 45°.

Answer:

Step-by-step explanation:

Look at the picture.

We have the triangles 45° - 45° - 90° and 30° - 60° - 90°.

The sides of those triangles are in ratio:

1 : 1 : √2 and 1 : √3 : 2

Therefore

If AC = 6√2 then AB = BC = 6

If BC = 6 then x = 6 : 2 = 3

Answer:$2700

Step-by-step explanation: Really depends on the kind of interest, but you would take the initial amount, and multiply it by the APR for the amount of interest, then add the interest to the initial amount.

To repay the full principle and interest in the first year of the loan with an interest rate of 8%, David borrowed $2500 from his local bank, would need to pay a total of $2700 to the bank.

To answer your question, we first need to calculate the interest David needs to pay. The formula used to calculate the interest on a loan is: Principal sum x Annual interest rate. David's principal sum is $2500 and the annual interest rate is 8%.

Here's the calculation step-by-step:

So, if David pays the full principle and interest in the first year of the loan, he will pay a total of $2700 to the bank.

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