A sweater that originally cost $40 is on sale for 10 percent off. What is the amount of the discount?
$2
$4
$30
$36

Answer:

a = 9    b = 9    c = 18

Step-by-step explanation:

a+b = c

a+ b + c = 36        but we know   a+b = c   sub that in

  c    + c = 36

       c = 18             now  a + b = c    and a and b are the same

                                   so  a and b are = 9

Answer:

a is 9

b is 9

c is 18

Step-by-step explanation:

Let's list the information provided

a + b =c

a + b + c = 36

a=b

Knowing that a=b we can replace b with a in the equations

a+a is the same as 2a since a is being doubled

2a=c

Knowing this we can replace c with 2a

2a+2a=36

Now solve for a

[tex]2a+2a=36\\4a=36\\\frac{4a}{4} =\frac{36}{4} \\a=9[/tex]

Now let's sub this value of a into the equations to see what the other values are

a=b

9=b

2a=c

2(9)=c

18=c

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

[tex]6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}[/tex]

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

[tex]L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet[/tex]

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

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Answer:

f(9.5) = 558.02.

Step-by-step explanation:

Because it is an exponential function, it can be written: y = (a)(b)^x

Now substitute in the two known points:

72 = (a)(b)^7.5 and

2 = (a)(b)^4 : => since 2 = (a)(b)^2 divide the left side by 2 and the right by (a)(b)^2

72/2 =[(a)(b)^7.5]/[(a)(b)^4]: => the (a) cancels out and b becomes b^(7.5–4)

36 = b^3.5: => To isolate b take the 3.5 root of both sides

{3.5 root}(36) = {3.5 root}(b^3.5)

2.783927 = b

Now to solve for a

2 = (a)(b)^4 => 2 = (a)(2.783927)^4 => 2 = (a)(60.066375) divide both sides by 60.066375 0.0332965 = a

Equation: y = (0.0332965)(2.783927)^x

Now plug in 9.5 for x

(0.0332965)(2.783927)^9.5 = 558.0178525 = 558.02

Answer:

Last option

Step-by-step explanation:

In order to manipulate a, you have to divide by 3 on both sides.

Answer:X = 13

Step-by-step explanation:

An exterior angle is equal to the sum of the two opposite interior angle

⇒95=4x+3 + 3x+ 1

95=4x + 3x + 3 + 1

95=7x + 4

95-4=7x

91=7x

91/7=x

13=x

This implies that X= 13

Answer:

7/6561

Step-by-step explanation:

nth term = a1 r^(n-1) so

9th term =  7* (1/3)^(9-1)

= 7*(1/3)^8

= 7/6561

Answer:

You must know all forms of additional payment and expenses, like medical bills and community expenses that can happen at any given time.

                                              ~Hope it helps~

                                                  ~Be great~

Answer:

  (b)  64 sq. in.

Step-by-step explanation:

The shaded area is the difference between the overall area and the areas of the cutout corners.

The overall area is 10 in by 10 in, so is ...

  A = s² = (10 in)² = 100 in²

The area of the cutout at each of the four corners is ...

  A = s² = (3 in)² = 9 in²

So, the total area of the four cutouts is ...

  cutout area = 4 × 9 in² = 36 in²

The remaining area is then ...

  100 in² -36 in² = 64 in²

The Volume of solid A that is similar to solid B is: 960 × 1.25 = 1,200 m³.

If two solids, A and B, are given and have corresponding dimensions as a and b respectively, we would have the following:

Surface area of solid A/Surface area of solid B = a²/b²

Volume of solid A/Volume of solid B = a³/b³

Given that solid A and solid B are similar, and:

Find their corresponding dimensions, a and b:

Surface area of solid A/Surface area of solid B = a²/b²

Substitute

675/432 = a²/b²

√(675/432) = a/b

1.25 = a/b

Scale factor of Solid A to Solid B is 1.25.

Multiply 1.25 by 960 to get the volume of solid A.

Volume of solid A = 960 × 1.25 = 1,200 m³.

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The semi-annual payment is $1662.47

Given : A 3 year loan of $8,561 at 9.1% compounded semi-annually.

We have to determine the semi annual payment.

We know,

[tex]P=\dfrac{PV.r}{1-(1+r)^{-n}}[/tex]

Where PV is present value of loan.

r is rate of interest

n is time period.

Given loan is calculated semi annually,

So PV = $ 8561

r=9.1 % =9.1/200

and time period is 3 years = 6 number of period as semi annually.

Thus, Substitute,

We get,

[tex]P=\dfrac{8561(\dfrac{9.1}{200})}{1-(1+\dfrac{9.1}{200})^{-6}}[/tex]

[tex]P=1662.47[/tex]

Hence the semi-annual payment is $1662.47

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Answer:549.81

Step-by-step explanation:because that is thhe answer you get

Answer:

$549.81

Step-by-step explanation:

Price

Money in hand

Money needed

Answer:

B. Subtract 2x

D. Add 6

Step-by-step explanation:

To solve this problem, isolate it by the term of x from one side of the equation.

First, add by 6 from both sides.

[tex]\sf{8x-6+6=2x+24+6}[/tex]

Solve.

Add.

24+6=30

Rewrite the problem down.

[tex]\sf{8x=2x+30}[/tex]

You have to subtract by 2x from both sides.

[tex]\sf{8x-2x=2x+30-2x}[/tex]

Solve.

8x-2x=6x

Rewrite the problem down.

6x=30

Then, you divide by 6 from both sides.

6x/6=30/6

Solve.

Divide the numbers goes from left to right.

30/6=5

x=5

Therefore, the solution is x=5, which is our answer.

In the correct answer is B and D.

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

Step-by-step explanation:

Let

The equations as per question are below

Crazy Curly's

Bill's Beauties

Solve the system by substitution

Answer:

10.7

Step-by-step explanation:

the tenth place is the first number that comes after the decimal so, that is the number you are rounding. We take a look following that number and it it is equal to or greater than 5, (which it is), we round up one number.

Answer:

10.7

Step-by-step explanation:

Any number between 1-4 rounds down and 5-9 rounds up, so here you will round up. I've included the decimal places as well below. The number after the decimal point is the tenth's place.

Good luck! Hope this helps

Answer:

6 6

---- ÷ ---

16 10

Step-by-step explanation:

equals 5/8

The division is one of the four fundamental arithmetic operations. The amount that is needed to be paid by each friend is $74.75.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

As it is given that the total cost of the computer is $299, it is needed to be split between four friends. Therefore, the price will be paid by the four friends equally which can be written as,

[tex]\text{Amount paid by each friend}=\dfrac{\text{Total cost of computer}}{\text{Number of friends}}\\\\\\\text{Amount paid by each friend}=\dfrac{\$299}{4} = \$74.75[/tex]

Thus, the amount that is needed to be paid by each friend is $74.75.

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Answer:

D. The trinomial is equivalent to (x+2)(x-1)

Step-by-step explanation:

1. Factor out the common term x:

= x(x^2+x-2)

2. Factor the equation:

= x(x - 1)(x + 2)

From this, we can see that because the equation was factorable, it is not prime. Option B is not completely factored, so it is incorrect. The final ordered pair shown in Option C is has (x + 1), when it should be (x - 1), so it is also incorrect. Option D is the true statement.

Answer: a6=70

Step-by-step explanation:

we know that

In the Arithmetic Sequence the formula is:

an= a1 + d(n−1)

where

a1 is the first term

d is the common difference

n is the number of terms

in this problem

a1=5

a2=18

a3=31

a4=44

a5=57

so

d=a2-a1 or a3-a2 or a4-a3 or a5-a4

d=57-44----> 13

find a6

a6= a1 + d(n−1)

n=6

d=13

a1=5

a6=5+13*(6-1)----> a6=5+13*5----> a6=70

Answer:

Let's see

[tex]\\ \bf\bull\rightarrowtail z^2-9[/tex]

[tex]\\ \bf\bull\rightarrowtail z^2-3^2[/tex]

[tex]\\ \bf\bull\rightarrowtail (z+3)(z-3)[/tex]

Answer:

(z+3)(z-3)

Step-by-step explanation:

a^2 - b^2 = (a+b)(a-b) where a = z and b= 3

Answer:

D. 201.1

Step-by-step explanation:

We see that the radius o the given circle is 16, so we do 16^2*pi

then we multiply that be 90/360

which rounds to 201.1

Answer: -0.383

Step-by-step explanation:

Since this is on the unit circle, the cosine is equal to the x coordinate and the sine is equal to the y coordinate.

Since cot = 1/tan = cos/sin, the approximate value is (-0.358)/(0.934), which is about -0.383.

Step-by-step explanation:

what number you need help with

25/100

Step-by-step explanation:

if he has a fraction of a bar graph it is 25% if that grah so in other words 25% as a fraction is 25/100

Answer:

A formula is a method that has been proven to work when solving specific types of problems.

Step-by-step explanation:

Answer:

1/3 probability

Step-by-step explanation:

The probability that you flip heads is 1/2, one heads out of two possible (heads and tails).

The probability that you draw a purple marble is 2/3, two purples and three total (2 p +1 w).

To find the probability of both happening, multiply the probabilities together:

(1/2) * (2/3) = (2/6) = (1/3)

Answer:

514 square feet

Step-by-step explanation:

2(7×4+4×5+5×7)+2(10×8+8×6+10×6)

=2*83 +2*188

=166+376

=542 square feet

7*4=28

542-28=514 square feet

Answer:

640ft

Step-by-step explanation:

7ft×4ft×5ft = 160

10ft×8ft×6ft=480

Add them together

480+160=640 so the answer is 640ft

Answer:

[tex]\fbox{Gradient of curve = -6}[/tex]

Step by step explanation:

Given:

Equation of curve ↦ xy = 6

Point ↦(1,6)

To find:

The gradient of curve = ?

Solution:

[tex]Using \: the \: equation, \\ xy = 6 \\ [/tex]

Taking log both the side,

[tex]log(xy) = log(6) \\ log(x) + log(y) = log(6) \\ Taking \: derivative \: both \: the \: side \\ \frac{1}{x} + \frac{1}{y} \cdot\frac{dy}{dx} = \: 0 \\ (Derivative \: of \: any \: constant =0) \\ \frac{1}{y} \cdot\frac{dy}{dx} = - \frac{1}{x} \\ \frac{dy}{dx} = - \frac{y}{x} \\ To \: find \: gradient \: at \: point (1,6) \\ \frac{dy}{dx} \mid_{(1,6)} = \frac{ - 6}{1} \\ \frac{dy}{dx} \mid_{(1,6)} = - 6 \\ \fbox{Gradient of curve = -6}[/tex]

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Answer:

[tex]\boxed{6}\times 10^{\boxed{26}}[/tex]

Step-by-step explanation:

[tex](3 \times {10}^{9} ) \times (2 \times {10}^{17} ) \\ \\ = (3 \times 2) \times ( {10}^{9} \times {10}^{17}) \\ \\ = 6 \times {10}^{9 + 17} \\ \\ = \huge \boxed{ 6} \times {10}^{ \boxed{26}} [/tex]