Clare’s aunt used a credit card to pay $42 for an outfit. Six weeks later, the credit card company charged her 2% interest.
a. How much is the 2% interest?
b. How much will Clare’s aunt have to pay in total?

Answer:

okay so the is 140 degrees right and d and e are on a straight line so extend every line in that diagram so to get a it will be 180 degrees - 140 and e is equals to 40 degrees k will be 180 degrees because of angle y and d Angle c is equals to 100 degrees because it falls on a straight line with 80 degrees and angles in a straight line add up to 180° uncle g is equals to 100 degrees because it alternate angles c

The measure of angle g from the given figure is 80°.Therefore, option C is the correct answer.

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

Given that, angle d is 140°.

We know that, sum of interior angles of a quadrilateral is 360°.

From the given figure,

c°+80°=180°

c°=100°

Now, 40°+d°+g°+c°=360°

40°+140°+g°+100°=360°

g°+280°=360°

g°=80°

Therefore, option C is the correct answer.

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d)

[tex] \frac{2 {x}^{2} - xy + 2xy - {y}^{2} }{6xy - 3 {y}^{2} } = \frac{x(2x - y) + y(2x - y)}{3y(2x - y)} = \\ [/tex]

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

_________________________________

e)

I think -6 should be +6

or +3x should be -3x

[tex] \frac{ {x}^{2} + 2x + x + 2 }{ {x}^{2} + 2x + 3x + 6 } = \frac{x(x + 2) + (x + 2)}{x(x + 2) + 3(x + 2)} = \\ [/tex]

[tex] \frac{(x + 1)(x + 2)}{(x + 3)(x + 2)} = \frac{x + 1}{x + 3} \\ [/tex]

Or

[tex] \frac{x(x + 2) + (x + 2)}{x(x + 2) - 3(x + 2)} = \frac{(x + 1)(x + 2)}{(x - 3)(x + 2)} = \\ [/tex]

[tex] \frac{x + 1}{x - 3} \\ [/tex]

_________________________________

f)

[tex] \frac{ {a}^{2} - 5a - 4a + 20 }{ {a}^{2} - 5a + 2a - 10 } = \frac{a(a - 5) - 4(a - 5)}{a(a - 5) + 2(a - 5)} = \\ [/tex]

[tex] \frac{(a - 4)(a - 5)}{(a + 2)(a - 5)} = \frac{a - 4}{a + 2} \\ [/tex]

And we're done.

Thanks for watching buddy good luck.

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Answer:

3,1

Step-by-step explanation:

Answer:

(3,1)

Step-by-step explanation:

To dilate of the small triangle to get the large triangle the center of dilation is required

The description of the dilation is as follows;

Location of the center of dilation;

The coordinate of the center of dilation is given as follows;

[tex]\left( x_0 = \dfrac{k \cdot x_1 - x_2}{k - 1}, \ y_0 = \dfrac{k \cdot y_1 - y_2}{k - 1} \right)[/tex]

Where;

k = The scale factor of dilation

(x₁, y₁) = A coordinate point on the preimage

(x₂, y₂) = A coordinate point on the image

From the given drawing, we have;

Two vertices on the preimage are; (2, 0), and (5, 1)

Two corresponding vertices on the image are; (0, 0), and (9, 3)

Using the formula for length, l, we have;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

[tex]l_{small} = \sqrt{\left (1 -0 \right )^{2}+\left (5-2 \right )^{2}} = \sqrt{10}[/tex]

[tex]l_{large} = \sqrt{\left (9 -0 \right )^{2}+\left (3-0 \right )^{2}} = \sqrt{90} = 3 \cdot \sqrt{10}[/tex]

[tex]\left( x_0 = \dfrac{3 \times 2 -0}{3 - 1}, \ y_0 = \dfrac{3 \times 0 - 0}{3 - 1} \right)[/tex]

[tex]\left( x_0 = 3, \ y_0 = 0\right)[/tex]

The steps to create the larger triangle from the center of dilation are as follows;

Alternatively larger triangle can also be created using the vertices as follows;

The coordinates of the third vertex of the small triangle are; (4, -2)

To obtain the coordinates of the large triangle, the coordinates of

the small triangle are multiplied by the scale factor, followed by adding the

coordinates of the center of dilation, we have that the coordinates of the

image are;  

[tex](k \times x_{ai} + x_0, \ k \times y_{ai} + y_0)[/tex]

Where;

[tex](x_{ai}, \ y_{ai})[/tex] = The difference between the coordinate values of the vertices of

the small triangle and the center of dilation, we have;

(2 - 3, 0 - 0) = (-1, 0)

(5 - 3, 1 - 0) = (2, 1)

(4 - 3, -2 - 0) = (1, -2)

We have [tex](k \times x_{ai} + x_0, \ k \times y_{ai} + y_0)[/tex] are;

(3 ×(-1) + 3, 3× 0 + 3) = (-3 + 3, 0) = (0, 0)

(3 × 2 + 3, 3 × 1 + 0) = (6 + 3, 3) = (9, 3)

(3 × 1, 3 × (-2) + 0) = (3 + 3, -6) = (6, -6)  

The vertices of the larger triangle are found as (0, 0), (9, 3), (6, -6)

By drawing lines joining derived vertices the larger triangle can be created

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Answer:

x = 6°

Step-by-step explanation:

We know that all the interior angles of a triangle sum up to 180°.

(7x+3)°+(80°)+(55°) = 180°

(7x+3)°+(135°) = 180°

(7x+3)°= 45°

7x = 42°

x = 6°

Answer:

A.1/10

you provided the answer... you said one tenth which is 1/10

Step-by-step explanation:

Answer:

A 1/10

Step-by-step explanation:

your welcome

Answer:

Step-by-step explanation:

START

=> Alternate Interior Angles (Slanted Downwards Right)

=> Vertical Angles (Up)

=> Linear Pair (Right)

=> Corresponding Angles (Down)

=> Alternate Exterior Angles (Down)

=> Interior Angles on the Same Side (Left)

=> Alternate Interior Angles (Left)

=> Corresponding Angles (Slanted Downwards Right)

=> Exterior Angles on the Same Side (Right)

FINISH

Answer:

Point of Intersection = (2/3, -16/3)

Step-by-step explanation:

Equation of line AB

=> y + 18 / -15 + 18 = x + 3 / -2 + 3

=> y + 18 = 3x + 9

=> y = 3x - 9

Equation of Line CD

=> y + 13 / -7 + 13 = x + 7 / -1 + 7

=> y + 13 = x + 7

=> y = x - 6

Intersection

=> 3x - 9 = x - 6

=> 2x = 3

=> x = 2/3

y = 2/3 - 6

y = -16/3

Point of Intersection = (2/3, -16/3)

A) The experimental probabilities are:

R = 0.45, B = 0.4, and Y = 0.15

From this, we can expect to get a red ball on the next draw.

B) This can happen because the experimental probabilities are bad estimations, or because the balls on the machine are not replaced.

A) The probability of getting each color will be given by the quotient of the number of balls of that color and the total number of balls.

For example, we know that 100 people buy gumballs, and 45 of them got red ones, so the experimental probability of getting a red gumball is:

R = 45/100 = 0.45

40 got a blue ball, so the probability of getting a blue ball is:

B = 40/100 = 0.4

15 got a yellow gumball, so the probability here is:

Y = 15/100 = 0.15

As you can see, the experimental probability of getting a red gumball is 3 times the probability of getting a yellow one. based on that, we can expect that the next gumball out from that machine will be red.

B) So now 10 more people go to the machine, and they get:

7 yellow, 1 red, and 2 blue gumballs.

This clearly does not follow the experimental probability we got above, why this may happen?

There are two main reasons.

First, to get a valuable experimental probability an experiment must be performed a lot of times, 100 is a ratter a small number. So the experimental probability that we got on point A may be a really bad estimation.

On another hand, there is a possibility that the gumballs in the machine are not being replaced. So initially, there is a fixed number of red, yellow, and blue balls.

This would mean that if we remove one red ball on the first try. Then for the next try, the probability of getting a red ball will be smaller (because now the machine has fewer red balls).

Then, because out of the 100 first balls most were red or blue, we can assume that most of the remaining balls on the machine are now yellow, and then the probability of getting a yellow ball is increased.

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It will take 8 weeks to Tom to achieve his goal.

The amount earned by him is given by multipliy number or hours and eaning in a hour.

Given

Tom has a goal of saving enough money to buy a new set of rims for his car.

Tom makes $7. 50 an hour take home pay at his job working 15 hours per week.

The earning of Tom in an hour = $7.5

If tom worked 15 hours in a week, then the amount earned by him in one week is;

[tex]=15\times 7.5\\\\=112.5[/tex]

The required amount to achieve his goal = $900

The number of week he need to work to achieve his target is;

[tex]= \dfrac{900}{112.5}\\\\= 8[/tex]

Hence, It will take 8 weeks to Tom to achieve his goal.

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(12, 5)

equations:

To solve with elimination, either the x or y coefficient should be similar.

Then,

[tex]\sf 3x-5y=11[/tex]

[tex]\sf 3x-12y=-24[/tex]

==============       [ subtract equation 2 from equation 1 ]

[tex]\sf 7y = 35[/tex]

[tex]\sf y = 5[/tex]

For x,

[tex]\sf 3x-5(5)=11[/tex]

[tex]\sf 3x-25=11[/tex]

[tex]\sf 3x=11+25[/tex]

[tex]\sf x=\dfrac{36}{3}[/tex]

[tex]\sf x=12[/tex]

In ordered pair: (x,y) → (12, 5)

Answer:

Height = 108.35 cm

Step-by-step explanation:

Given :-

Radius = 26 cm

Total Volume = 230,000 cm³

To Find :-

Height

Formula Required :-

Volume (cylinder) = π x (radius)² x height

=> height = volume / π x (radius)²

Solving :-

h = 230,000 / (3.14 x 676)

h = 230,000 / 2122.64

Solution :-

Height = 108.35 cm

Answer:

f =[tex]\frac{6}{5h}[/tex]+m

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

5h(−m+f)=6

Step 1: Add 5hm to both sides.

5fh−5hm+5hm=6+5hm

5fh=5hm+6

Step 2: Divide both sides by 5h.

5fh/5h=5hm+6/5h

f=5hm+6/5h

Answer:

See below.

Step-by-step explanation:

Solving :-

#1

#2

They both have the numerator in both solutions to be 5 and -3 respectively. I believe this is because both equations have the constant term, c, to be -15 and 5 and -3 are factors of -15.

Answer:

All you need to do is find the reciprocal and switch the exponent to a negative. The answer is 8^-6

Step-by-step explanation:

Answer: 8^-6

Step-by-step explanation:

got it right from the answer above

Answer:

[tex]\huge\boxed{\sf 22670.80 \ cm^3}[/tex]

Step-by-step explanation:

Height = h = 20 cm

Diameter = d = 38 cm

Radius = d / 2 = 38 / 2 = 19 cm

Volume of cylinder:

[tex]= \pi r^2 h\\\\= (3.14)(19)^2(20)\\\\= (3.14)(361)(20)\\\\= 22670.80 \ cm^3\\\\\rule[225]{225}{2}[/tex]

Solution:

Given:

First, let's find the radius of the cylinder as the radius of the cylinder is included in the formula.

[tex]\text{Diameter = 2(Radius)}[/tex]

[tex]\text{Radius} = \dfrac{\text{Diameter}}{2}[/tex]

[tex]\text{Radius} = \dfrac{38}{2}[/tex]

[tex]\text{Radius} = 19 \ \text{cm}[/tex]

Recall that the volume of a cylinder is πr²h. Now, let's use the formula to find the volume of the cylinder.

[tex]\pi r^{2} h = \text{Volume of cylinder}[/tex]

[tex](\pi)( r^{2})( h) = \text{Volume of cylinder}[/tex]

[tex](3.14)( 19^{2})( 20) = \text{Volume of cylinder}[/tex]

[tex]\boxed{22670.8 \ \text{cm}^{3} = \text{Volume of cylinder}}[/tex]

Answer:

The area of the original garden is x^2 square feet.

The lengths of the sides of the new garden are x + 2 feet and x + 7 feet.

The area of the new garden, in square feet, is

[tex](x + 2)(x + 7)[/tex]

[tex] {x}^{2} + 9x + 14[/tex]

1) the area of his garden is, x² feet²

2) the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

And, the area of the new garden is,

Area = x² + 9x + 14

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Farmer Bob has a small square garden that is x feet by x feet.

Now,

We know that;

Area of square = Side²

Here, Side = x feet

Hence, the area of his garden is,

Area = x × x

Area = x² feet²

Now, When He decides to add 2 feet to one side of the garden and 7 feet to the other side.

Then, the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

Hence, the area of the new garden is,

Area = (x + 2) (x + 7)

Area = x² + 2x + 7x + 14

Area = x² + 9x + 14

Thus, 1) the area of his garden is, x² feet²

2) the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

And, the area of the new garden is,

Area = x² + 9x + 14

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Answer:

-11/3, -2.25, -3/2, 0.5

Step-by-step explanation:

The amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

For the considered case, we're given that:

The final amount at the end of 4 years in the considered account of Laura is evaluated as:

[tex]A = 5500(1 + \dfrac{1.6}{100})^4 = 5500(1.016)^4 \approx 5860.53 \: \rm (in \: dollars)[/tex]

Thus, he amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)

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Answer:

See below

Step-by-step explanation:

15% of 120 is 18

120 plus 18 is 138

=138

I think the answer is 59.6

The length of BC to the nearest tenth will be 20.7 units

The steps are as follow:

AC=B=15

AB=C=13

BC=A=?

Cos95° = (b^2+c^2-a^2)/2bc

Cos95° = (15^2+13^2-a^2)/(2*15*13)

2*13*15*cos 95 =15^2+13^2-a^2

-34=225+169-a^2

A^2=394+34

A^2=428

A = 20.68 = 20.7 units

So the length of BC to the nearest tenth will be 20.7 units

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Answer:

Multiple of 4 = {4,8,12,16,20,24}

Step-by-step explanation:

Answer:

2400 candies

Step-by-step explanation:

2 hrs - 80 boxes w/ 10 candies each = 800 candies

2 x 3 = 6

800 x 3 = 2400

So:

In 6 hours, the candy maker can make 2400 candies.

Hope this helped!

Answer:

2400 candy thank me later

Answer:

x = 1 and

x = 3

Step-by-step explanation:

The solution is the x for each row where the f(x) and g(x) are the same. When x is 1, f(x) and g(x) are both 0.

When x is 3, f(x) and g(x) are both 6.

Answer:

slope: 5/1x (or just 5x)

y-int: -3

Step-by-step explanation:

The y-intercept is (0,-3)

The slope of the line is 4

         [tex]\frac{y2-y1}{x2-x1} =\frac{2--3}{1-0} =\frac{5}{1} =5[/tex]

Hope it helps!

Answer:

744

Step-by-step explanation:

solved on calcultor

Budget of a film = 1200

Money they spend on equipment :-

= 62% of total expense

= 62% of 1200

[tex]= \frac{62}{100} \times 1200[/tex]

[tex] = \frac{62 \times 1200}{100} [/tex]

[tex] = \frac{74400}{100} [/tex]

[tex]\color{purple}= 744[/tex]

Which means , the group of friends spent 744 on equipment .

Then , money they spent on costume :-

= 100 - 62 % of 1200

= 38% of 1200

[tex] = \frac{38}{100} \times 1200[/tex]

[tex] = \frac{38 \times 1200}{100} [/tex]

[tex] = \frac{45600}{100} [/tex]

[tex] \color{orange} = 456[/tex]

Which means the group of friends spent 456 on costumes .

Therefore , the group of friends spent 456 on costumes .

Answer: Si 3-3 \ 4 lb de dulces cuestan $ 20.25, ¿cuánto sería 1 lb de dulces

Step-by-step explanation: