A dilation maps (6, 10) to (3,5). What are the coordinates of the image of (12, 4) under the same dilation?

Answer:

-6

Step-by-step explanation:

We use PEMDAS to solve this,

so P stands for parentheses, so that's where we start.

We first, square the innermost parentheses with the exponent which is the E in PEMDAS, then then the outer parentheses

-12/3*(-8+16-6)+2

-12/3*(2)+2

Now we divide as in Division in PEMDAS.

-4*2+2

Now we multiply as in Multiplication in PEMDAS.

-8+2

Now we add as in A for Addition

-6

In PEMDAS, Multiplication doesn't always come before division, and same for addition and subtraction.

Answer:

3q + 5

Step-by-step explanation:

Three times a number q is 3q, and 5 more than that is 3q + 5.

Answer:

7

Step-by-step explanation:

5×0.4 = 2

2 + 5 = 7

The number a would be 7 which is 40% more than five more than a number a.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given the number that is 40% more than five more than a number a.

We need to find the unknown number a.

So, 40 % = 0.4

Let find the first part that is; "the number that is 40% more than five"

5 × 0.4 = 2

Now, five more than a number a.

2 + 5 = a

a = 7

Therefore, the number a would be 7 which is 40% more than five more than a number a.

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Answer:

[tex]\Huge \boxed{m=0}[/tex]

Step-by-step explanation:

[tex]m +5=-m-2-5m+7[/tex]

Adding m and 5m to both sides of the equation.

[tex]m +5+m+5m= -m-2-5m+7+m+5m[/tex]

Subtracting 5 from both sides of the equation.

[tex]m +5+m+5m-5=-2+7-5[/tex]

Combining like terms and simplifying.

[tex]7m=0[/tex]

Dividing both sides of the equation by 7.

[tex]m=0[/tex]

Answer:

m = 0

Step-by-step explanation:

m + 5 = - m - 2 -5m + 7

m + 5 = -m - 5m - 2 + 7

m + 5 = -6m + 5  (combine like terms)

m = 0

Answer:

$ 3051

Step-by-step explanation:

Original cost = $ 1000

Marked up Price = Original cost + 170% of 1000

                            = 1000 + 1.7 * 1000

                            = 1000 + 1700

                            = $ 2700

Sales tax = 13% of 2700

               = 0.13 * 2700

               = 351

Total cost paid by Bernie = 2700 + 351 = $ 3051

Answer:

[tex]\huge\boxed{x=0}[/tex]

Step-by-step explanation:

[tex]x+1=1\\\\x+1-1=1-1\\\\\boxed{x=0}[/tex]

Answer:

Volume of a rectangular prism = x^3 - 4x^2

Step-by-step explanation:

V = L*W*H

Where,

V= Volume of a rectangular prism

L= Length

W= Width

H= height

Volume of a rectangular prism= Length × Width × Height

Let

length of the box = x

width = length

Width = x

Height= x - 4

Volume of a rectangular prism= Length × Width × Height

= x * x * (x - 4)

= x^2 * (x - 4)

= x^3 - 4x^2

Volume of a rectangular prism = x^3 - 4x^2

Answer:

Step-by-step explanation:

Using the sine rule

Airplane A has

6 / sin 44 =

6 / 0.6947 =

8.64

Airplane B has.

6 / sin 40 =

6 / 0.6428 =

9.33

therefore, the answer is airplane B, because it was 9.33 miles away

Answer:

See below.

Step-by-step explanation:

1)

For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:

[tex]f(x)=2(3)^x[/tex]

The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.

2)

Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:

[tex]f(x)=10(2)^x[/tex]

The 10 represents the initial amount while the 2 represents the rate.

3)

I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.

4)

To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:

For Amber:

Day 3:

[tex]f(3)=3(4)^3=192[/tex]

Day 10:

[tex]f(10)=3(4)^{10}=3,145,728[/tex]

For Ben:

Day 3:

[tex]f(3)=2(3)^3=54[/tex]

Day 10:

[tex]f(10)=2(3)^{10}=118,098[/tex]

And for Carter:

Day 3:

[tex]f(3)=10(2)^3=80[/tex]

Day 10:

[tex]f(10)=10(2)^{10}=10,240[/tex]

5)

Amber's new graph of:

[tex]f(x)=3(4)^x+45[/tex]

will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.

6)

On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.

7)

If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.

Answer:

Here is the slope:

[tex]y = zy + dsince m = 0c = 9[/tex]

Hope this helps

Answer: 4 or [tex]\sqrt{4 * 4}[/tex]

To find the square root of a number, remember that there will be two factors that are the same that will give you the product.

Lets start from 1:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

As you can see, 4 x 4 is 16. To make sure I'm correct, remember that a square roots consists two identical factors.

4 and 4 are the same numbers.

Therefore, [tex]\sqrt{16}[/tex] = 4

It can also be written as [tex]\sqrt{4 * 4}[/tex]

Answer:

the answer is 4

Step-by-step explanation:

I use a calulator but if you dont have one then the way to do square roots is find a number say 4 and put it to the 2 power and it equaks 16 (4^2)=16. I cant really explain much more

Answer:

[tex]x = 10[/tex]. In other words, there number of girls is [tex]10[/tex].

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

[tex]\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}[/tex].

Rewrite to obtain:

[tex]\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}[/tex].

For this question:

[tex]\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}[/tex].

[tex]\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}[/tex].

On the other hand, there are [tex](15 + x)[/tex] boys and girls in total. Using the formula for average:

[tex]\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}[/tex].

From the question, this average should be equal to [tex]123[/tex]. In other words:

[tex]\displaystyle \frac{1875 + 120\, x}{15 + x} = 123[/tex].

Solve this equation for [tex]x[/tex] to obtain:

[tex]1875 + 120\, x= 123\, (15 + x)[/tex].

[tex](123 - 120)\, x = 1875 - 123 \times 15[/tex].

[tex]x = 10[/tex].

In other words, the number of girls here is [tex]10[/tex].

Answer:

Rs 253.13

Step-by-step explanation:

The item cost him x.

Selling at a profit of 20% means he sold it for 1.2x.

Selling at a loss of 12% means that he sold it for 0.88x.

1.2x - 81 = 0.88x

1.2x - 0.88x = 81

0.32x = 81

x = 253.13

Answer:

Step-by-step explanation:

What's missing from the original condition.

1000

1001

1002

=====

3003

So the answer is y - 3003

Answer:

Step-by-step explanation:

[tex]a^{m}*a^{n}= a^{m+n}\\\\\\(-3)^{5}*(-3)^{2}=(-3)^{5+2}=(-3)^{7}[/tex]

Answer:

[tex]\Huge \boxed{\mathrm{(-3)^7}}[/tex]

Step-by-step explanation:

[tex](-3)^5 \times (-3)^2[/tex]

When bases are same for exponents in multiplication, the exponents are added.

[tex]a^b \times a^c=a^{b+c}[/tex]

[tex](-3)^{5+2}[/tex]

Add the exponents.

[tex](-3)^7[/tex]

Answer:

P=25 q= -31

Step-by-step explanati

The value of p and q​ are 32 and 24. The relationship will be as p/q = 8/6.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The cost of an electrical gadget and the cost of a plumbing material were in the ratio 8:6 last year ,this year each cost was reduced by GHÇ 4.00 and their ratio changed to 7:5.

Make p the subject

p = 8q/6 ........equation 1

The year the price was reduced by 4

p - 4/q - 4 = 7/5

Cross multiplication;

5(p-4) = 7(q-4)

5p-20 = 7q-28

5p - 7q = -8 .......equation 2

Subtract 8q/6 for p in equation 1

5(8q/6) - 7q = -8

Multiply through by 6

40q - 42q = -48

-2q = -48

q = 24

Subtract 24 for q in equation 1

p = 8(24)/6

p = 192/6

p = 32

Therefore, the value of p and q​ are 32 and 24. The relationship will be as p/q = 8/6.

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Answer:

answer is attached

Answer:

156

Step-by-step explanation:

n times the constant of proportionality = a

so n will always 156 times greater

Answer:

4.625

Step-by-step explanation:

5/8 = 0.625

To find 5/8, simply divide it.

So 4 and 5/8

= 4.625

Answer:

See below.

Step-by-step explanation:

1)

So we have the equation:

[tex]2x+3y=1470[/tex]

To change into the slope-intercept form, we need to isolate the y-variable. Thus, subtract 2x from both sides:

[tex](2x+3y)-2x=(1470)-2x[/tex]

The left side cancels:

[tex]3y=1470-2x[/tex]

Now, divide both sides by 3. The left side cancels:

[tex](3y)/3=(-2x+1470)/3\\y=-\frac{2}{3} x+490[/tex]

The slope-intercept form is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Thus, the slope is -2/3 and the y-intercept is 490.

2)

So, since we already know the y-intercept is 490, plot a point at (0,490).

The slope is too small to use. Thus, multiply the fraction by 100. It is now (-200/300). This means that we move down 200 for every 300 (recall that the slope means rise over run. Thus, we move down 200 for every 300 to the right). Thus, another possible point would be (0+300,490-200) or (300,290). Plot that. Then, connect them.

3)

To write in in function notation, simply substitute the y-variable for the function notation. Our independent variable here is x so we'll use that.

[tex]y=-\frac{2}{3}x+490\\ f(x)=-\frac{2}{3}x+490[/tex]

This means that for every x sandwiches made, there is f(x) wraps made for the total sum to be $1,470.

For example, if 105 sandwiches were made, then f(105)=-2/3(105)+490=420 wraps were made for the total profit to be $1,470.

4)

Please refer to the attached graph.

5)

First, since the total profit has now increased, the graph above and to the right of the old graph. This is because Sal needs to sell more sandwiches and wraps. Likewise, because of this, the x- and y-intercepts will also be different. Nevertheless, if converted into the slope-intercept equation, the slope will remain the same.

Answer:

Hey mate,these answers has been excluded from the NCERT syllabus.

Thank you

I've answered as fast as I can to answer your question.Hope you understood it.

Pls mark my answer as brainliest and follow me.

Answer:

6

Step-by-step explanation:

12/2=6/1=6

Answer:

6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

X times x is x squared then x times - 2 is - 2x but 4 times x is 4x. So 4x plus - 2x is 2x. Then 4 times - 2 is - 8 put that all together you'll get x^+ 2+2x-8

Answer to the 1st part: [tex]6x^2+12xh+6h^2-2x-2h+1[/tex]

Answer to the 2nd part: [tex]12x+6h-2[/tex]

==============================================

Work Shown:

Replace every x with (x+h). Expand and simplify

[tex]f(x) = 6x^2-2x+1\\\\f(x+h) = 6(x+h)^2-2(x+h)+1\\\\f(x+h) = 6(x^2+2xh+h^2)-2(x+h)+1\\\\f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\[/tex]

----------------------------

Subtract off f(x), then divide everything over h. Simplify.

[tex]f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-(6x^2-2x+1)\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-6x^2+2x-1\\\\f(x+h)-f(x) = 12xh+6h^2-2h\\\\\frac{f(x+h)-f(x)}{h} = \frac{12xh+6h^2-2h}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{h(12x+6h-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} = 12x+6h-2\\\\[/tex]

The value of Function,  [tex]f (x + h) = 6x^2 + 6 h^2 + 12 x h - 2x -2h + 1[/tex]

And, The value of  [tex]\frac{f (x + h)- f(x)}{h} = 12 x + 6h -2[/tex].

Here, the function is given as,

[tex]f (x) = 6x^{2} -2x + 1[/tex]

What is function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y.

Now,

Replace every x with (x + h) and expand it,

   [tex]f (x) = 6x^{2} -2x + 1\\f (x+h) = 6(x+h)^{2} -2(x+h) + 1\\f (x+h) = 6 (x^{2} +h^{2} + 2xh) - 2x -2h +1\\f (x+h) = 6x^{2} +6h^{2} +12xh -2x-2h+1\\[/tex]

And,

[tex]f (x+h) - f(x) = ( 6x^{2} +6h^{2} +12xh -2x-2h+1) - (6x^{2} -2x+1)\\\frac{f (x+h) -f (x)}{h} =\frac{ ( 6x^{2} +6h^{2} +12xh -2x-2h+1) - (6x^{2} -2x+1)\\}{h} \\\frac{f (x+h) -f (x)}{h} =\frac{ 6x^{2} +6h^{2} +12xh -2x-2h+1 -6x^{2} +2x-1\\}{h} \\\\\frac{f (x+h) -f (x)}{h} =\frac{12xh +6h^{2}-2h }{h} \\\frac{f (x+h) -f (x)}{h} = 12x + 6h -2[/tex]

Hence,

The value of function [tex]f (x + h) = 6x^2 + 6 h^2 + 12 x h - 2x -2h + 1[/tex]

And, The value of  [tex]\frac{f (x + h)- f(x)}{h} = 12 x + 6h -2[/tex].

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Step-by-step explanation:

Let the number to be found be x

68 is what percent of 80 is written as

[tex] \frac{x}{100} \times 80 = 68[/tex]

Multiply both sides by 100

We have

80x = 6800

Divide both sides by 80

we have the answer as

x = 85

Let the number be x

88.83 is 423% of what is written as

[tex] \frac{423}{100} x = 88.83[/tex]

Multiply through by 100

We have

423x = 8883

Divide both sides by 423

We have the answer as

x = 21

Let the number be x

36.8% of what number is 28.52 is written as

[tex] \frac{36.8}{100} x = 28.52[/tex]

Multiply through 100

We have

36.8x = 2852

Divide both sides by 36.8

We have the answer as

x = 77.5

What number is 95% of 40 is written as

[tex] \frac{95}{100} \times 40[/tex]

We have the final answer as

Hope this helps you

Answer:

There are two simple rules to remember: When you multiply a negative number by a positive number then the product is always negative.

Step-by-step explanation:

Answer:

A. 39

Step-by-step explanation:

( 2 + 6 ) / 4 + 12 × 3 + 1

first solve the bracket .

8 / 4 + 12 × 3 + 1

then do the division or multiplication.

2 + 36 + 1

finally do the addition or subtraction.

39

The order

{

1. B - Bracket

2. O - Or

3. D - Division

M - Multiplication

4. A - Addition

S - Subtraction }

Answer:

A) 2 miles

Step-by-step explanation:

2)   In the figure the solid path indicates the usual path of a taxi cab. Unfortunately, there was construction and the taxi cab had to take the dotted route. If each tick mark represents one mile, how much longer was the detour than the regular route?  

A) 2 miles  

B) 3 miles  

C) 5 miles  

D) 11 miles  

Answer:

Hello, thank you for your word problem. However, your word problem doesn't have a question to it. Please double check your answer. Thank you!

Step-by-step explanation:

Answer:

0.19 = 19/100

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

0.19=0.191

Multiply to remove 2 decimal placesy 102 = 100

0.19/1 × 100/100 = 19100

Conclusion

0.19=19100

Answer:

x = -5

Step-by-step explanation:

x + 4 = -1  (subtract -4 on each side)

(x + 4) + (-4) = -1 + (-4)

therefore,

x = -5

Answer:

  see below

Step-by-step explanation:

The four major arcs that include B will be the remainder of the circle after each minor arc is excluded.

Excluding minor arc AB, we have major arc BCA.

Excluding minor arc BC, we have major arc CDB.

Excluding minor arc CD, we have major arc DAC.

Excluding minor arc DA, we have major arc ABD.