Gigi makes a scale drawing of a patio. The drawing below shows the two scales use she used to plan two patios of different sizes. Which shows the correct dimensions of the rectangle in both scales?

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:$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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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°.

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.

Answer:

She applied the exponent -2 to 4(-2) instead of applying the exponent to just -2

Step-by-step explanation:

we have the expression

[tex]\frac{4m^{-3}n^{-2}}{m^{-1} n}[/tex]

Simplify

[tex]\frac{4m^{-3}n^{-2}}{m^{-1} n}=4m^{(-3+1)}n^{(-2-1)}= 4m^{(-2)}n^{(-3)}[/tex]

Substitute the values of m and n in the expression

For[tex]m=-2, n=4[/tex]

[tex]4(-2)^{(-2)}(4)^{(-3)}=4(\frac{1}{4})* (\frac{1}{64})=\frac{1}{64}[/tex]

She applied the exponent -2 to 4(-2) instead of applying the exponent to just -2

Answer: It’s C

Step-by-step explanation:

Juss took a test

Answer:

1. x>4

2.y>-3

the assumption here, being that it's a square pyramid, thus its base is a square, namely a 6x6, Check the picture below.

notice, the pyramid has four triangular faces with a height of 9 and a base of 6, and the squarish base, so we can simply get the area of each of those figures and sum them up.

[tex]\bf \stackrel{\textit{area of four triangles}}{4\left[\cfrac{1}{2}(6)(9) \right]}+\stackrel{\textit{area of base}}{(6\cdot 6)}\implies 108+36\implies 144[/tex]

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:

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:

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:260

53×5=260

Step-by-step explanation:

265 paving stones will be needed if it is 53 for each project

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:

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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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:

[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:

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:

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:

(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:

£ 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

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:

[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:

hello :  x=1

Step-by-step explanation:

look this solution  :

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

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:

(-1,4)(1,4)

2

Step-by-step explanation:

Answer:

Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are angles that are opposite of the transversal line, but are found outside or the external side of the of the line that intersects them.

If the lines that intersect them happen to be parallel, then their measures would be congruent.

ANSWER

<1 and <8 are alternate exterior angles.

EXPLANATION

From the diagram we can trace a Z shape between the two parallel lines.

When we trace the shape, <1 and <8 will be on the exterior corners of the z-shape.

z-angles are called alternate angles.

These two angles are alternate to each other.

Hence <1 and <8 are alternate exterior angles.

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]

Answer:

[tex]2*10^{-1}[/tex]

Step-by-step explanation:

From 0 to 1, there are 5 units, so each of the lines are 1/5.

Hence, it is  0, 1/5, 2/5, 3/5, 4/5, 1

The point P is the first line, so that is 1/5, or in decimal, 0.2

Now we check all the options:

First Choice:  2 ^ -1 = 1/2^1 = 1/2  NO

Second Choice:  2 ^ 0 = 1  (anything to the power 0 is 1)  (NO)

Third Choice:  2 ^ 1 = 2 (NO)

Fourth Choice:  2 * 10 ^ -1 = 2 * 1/10 = 1/5 or 0.2 (RIGHT)

So, last choice is correct.

Answer:

y = -|x| +3

Step-by-step explanation:

Answer:

-/x/-3

Step-by-step explanation:

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