Quadrilateral ABCD is dilated by a scale factor of 1 over 3 centered around (1, 2). Which statement is true about the dilation?
segment B prime D prime will run through (1, 2) and will be shorter than segment BD.
segment B prime D prime will run through (1, 2) and will be longer than segment BD.
segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.
segment B prime D prime will be parallel to segment BD and will be longer than segment BD.

Answer:

35/ 12

Step-by-step explanation:

5/6 divided by 2/7

= 5/6 x 7/2

= 35/ 12

Answer:

A) The increase population of town after 3 years is 1.2 times initial population

B) The increase population of town after 5 years is 1.4 times initial population .

Step-by-step explanation:

Given as :

The rate of growth of population of a town = r = 7.5%

Let The initial population of town = p

A ) Let The increase population of town after 3 years = P

The time period = n = 3 years

Now, According to question

The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, The increase population of town after 3 years  = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 3}[/tex]

Or, P = p × [tex](1.075)^{3}[/tex]

Or, P = p × 1.242

So, The increase population of town after 3 years = P = 1.2 times initial population

Hence,The increase population of town after 3 years is 1.2 times initial population .  Answer

B )  Let The increase population of town after 5 years = P'

The time period = n = 5 years

Now, According to question

The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The increase population of town after n years = initial population of town × [tex](1+\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or,  The increase population of town after 5 years = p × [tex](1+\dfrac{\textrm 7.5}{100})^{\textrm 5}[/tex]

Or, P' = p × [tex](1.075)^{5}[/tex]

Or, P' = p × 1.4356

So, The increase population of town after 5 years = P' = 1.4 times initial population

Hence,The increase population of town after 5 years is 1.4 times initial population . Answer

Answer:

The number of dimes is 14 and the number of quarters is 7.

Step-by-step explanation:

Given:

Emily has $3.15 worth of dimes and quarters.

She has twice as many dimes as quarters.

Now, to determine the number of dimes and the number of quarters.

Let the number of quarters be [tex]x.[/tex]

And the number of dimes be  [tex]2x.[/tex]

So, the total worth of dimes and quarters = $3.15.

Now, to get the number of dimes and quarters:

According to question:

[tex]0.10(2x)+0.25x=3.15[/tex]

[tex]0.20x+0.25x=3.15[/tex]

[tex]0.45x=3.15[/tex]

Dividing both sides by 0.45 we get:

[tex]x=7.[/tex]

Thus, the number of quarters = 7.

So, the number of dimes = [tex]2x=2\times 7=14.[/tex]

Therefore, the number of dimes is 14 and the number of quarters is 7.

Answer:

See explanation

Step-by-step explanation:

1. Lines l and k are parallel. These lines are cut be transversal n. Angles 2 and 7 are corresponding angles when parallel lines l and k are cut by transversal n. By Corresponding Angles Ttheorem, angles 2 and 7 are congruent.

2. Lines m and n are parallel. These lines are cut be transversal k. Angles 2 and 10 are alternate interior angles when parallel lines m and n are cut by transversal k. By Alternate Interior Angles Theorem, angles 2 and 10 are congruent.

3. Angles 2 and 7 are congruent (see 1)

   Angles 2 and 10 are congruent (see 2)

  Hence, angles 7 and 10 are congruent by transitive property.

7/19

bc 2 5/7 = 19/7. the reciprocal is a fraction reversed. or upside down that is. So, your answer is 7/19

Answer:

7/19

Step-by-step explanation:

2 5/7=19/7

Answer:

Mean= 59.8 and median = 59.5

Step-by-step explanation:

Mean  = Summation of values/ No. of Values

Mean of Girls' height= 61+58+63+57+58+59+62+64+60+56/10

Mean=  598/10= 59.8

Arranged Data = { 56, 57,58,58,59, 60, 61,62,63,64}

As the number of observations is even so the 5th and 6th value will be added and divided by 2

59+60/2= 59.5

Median = 59.5

Answer:

Step-by-step explanation:

an = 6n - 13

If n  = 10  ,  a10 = 6*10 - 13 = 60-13 = 47

If n  = 11 ,  a11 = 6*11 - 13 = 66-13 = 53

If n  = 12  ,  a12 = 6*12 - 13 = 72-13 =  59

The formula to find the nth term of the sequence an, is a(n) = -13 + 6n

From the question, we have the following parameters that can be used in our computation:

a(10) = 47

a(11) = 53

a(12) = 59

a(13) = 65

The nth term of an arithmetic sequence can be represented as

a(n) = a(1) + (n - 1) * d

Where,

common difference,

d = 6

So, we have

a(n) = a(1) + (n - 1) * 6

Using the 12th term, we have

a(1) + (12 - 1) * 6 = 59

a(1)  = 59 - 66

a(1)  = -7

So,, we have

a(n) = -7 + (n - 1) * 6

Expand

a(n) = -13 + 6n

Hence, the formula to find an is a(n) = -13 + 6n

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Answer:

[tex]\large\boxed{x=\dfrac{50y-585}{156}}[/tex]

Step-by-step explanation:

[tex]y=0.39(8x+30)\qquad\text{use the distributive propety}\\\\y=(0.39)(8x)+(0.39)(30)\\\\y=3.12x+11.7\qquad\text{multiply both sides by 100}\\\\100y=312x+1170\qquad\text{subtract 1170 from both sides}\\\\100y-1170=312x\qquad\text{divide both sides by 312}\\\\\dfrac{100y-1170}{312}=x\\\\x=\dfrac{100y:2-1170:2}{312:2}\\\\x=\dfrac{50y-585}{156}[/tex]

Note: As you missed to mention the graph for f(x) = x + 1 from where we had to check which option defines the accurate graph. But, after a little research, I was able to get the graph of this question, and hence attaching the graph. So, I am answering based on that graph which, anyways, would clear your concept about determining the domain of the function that shows in a graph.

Answer:

x > 1 is the domain of the f(x) = x + 1.

Step-by-step explanation:

A domain is the set of all x values that a function passes through. It means a domain is set of all input values where the function is defined, meaning whatever you input the x value, for every x-value there is only one y-value that corresponds to it.

So, now lets talk about the given function f(x) = x + 1 and its graph as shown in attached figure. Carefully observe the top right part of the graph of f(x) = x + 1. It is validating the condition of x > 1.

For example,

Just input some x values, greater than 1 i.e. x > 1, in f(x) = x + 1 to determine the output values.

For example, for x > 1

and so on.

So, the top right part of the graph of f(x) = x + 1 is validating the condition of x > 1 as it is passing through P(2, 3), P(3, 4) and P(4, 5) etc. and so on.

So, x > 1 is the domain of the f(x) = x + 1.

Keywords: domain, function

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Answer:

"D"  X > 1

Step-by-step explanation:

HOPE THIS HELPS!!!

Answer:5x+7y

Step-by-step explanation:

Your welcome

The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.

Step-by-step explanation:

Given,

Cost of one pound of Caramels = $10.28

Cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel = [tex]10.28*1\frac{3}{4}[/tex]

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99[/tex]

Cost of one pound of chocolate milk = $13.85

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]13.85*1\frac{3}{4}=13.85*\frac{7}{4}[/tex]

Cost of [tex]1\frac{3}{4}[/tex] pounds = [tex]\frac{96.95}{4}=\$24.24[/tex]

Difference = 24.24 - 17.99 = $6.25

The cost of [tex]1\frac{3}{4}[/tex] pounds chocolate milk is $6.25 more than the cost of [tex]1\frac{3}{4}[/tex] pounds of Caramel.

Keywords: difference, multiplication

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Final answer:

The cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels, after calculating the total cost of each based on their per pound price.

Explanation:

To find out how much more the cost for 1 3/4 pounds of milk chocolate is than the cost for 1 3/4 pounds of caramels, we first need to calculate the cost of 1 3/4 pounds of each type of candy. Since the cost per pound of caramels is $10.28 and the cost per pound of milk chocolate is $13.85, we can set up our calculations as follows:

Total cost of caramels = 1.75 (pounds) * $10.28 (per pound) = $17.99

Total cost of milk chocolate = 1.75 (pounds) * $13.85 (per pound) = $24.24

Now, we subtract the total cost of caramels from the total cost of milk chocolate to find the difference:

Cost difference = $24.24 - $17.99 = $6.25

So, the cost for 1 3/4 pounds of milk chocolate is $6.25 more than the cost for 1 3/4 pounds of caramels.

burned: 756 calories

hours: 3

same number of calories each hour

-> to find this, we must split the number of calories evenly among the hours

steps

756/3

= 252 calories per hour

Answer:

252

Step-by-step explanation: 756/3

Answer:

3.3 x - (3.3*8) - x = 1.2

2.3 x - (3.3*8) = 1.2

2.3 x - 26.4 = 1.2

2.3 x - 26.4 + 26.4 = 1.2 + 26.4

2.3 x = 27.6

2.3 x / 2.3 = 27.6 / 2.3

x = 12

Answer:

[tex]\frac{78}{25}[/tex]

Step-by-step explanation:

A rational number has the form

[tex]\frac{a}{b}[/tex] ← where a and b are integers

3.12 = [tex]\frac{312}{100}[/tex] ← divide numerator/denominator by 4, thus

3.12 = [tex]\frac{78}{25}[/tex] ← in simplest form

Answer:

200g of sugar, 600g of flour, 400g of butter

Step-by-step explanation:

50g sugar = 15 biscuits

3 x 50g = flour --) 150g = flour

2 x 50g = butter --) 100g = butter

60/15 = 4; 4 times as much

4 x 50g = 200g of sugar

4 x 150g = 600g of flour

4 x 100g = 400g of butter

The amount of flour she needed is 600g.

Given that,

Based on the above information, the calculation is as follows:

50g sugar = 15 biscuits

[tex]= 3 \times 50g\\\\ = 150g\ flour[/tex]

And.  

[tex]= 2 \times 50g \\\\= 100g \ butter[/tex]

Now  

[tex]= 60\div15[/tex]

= 4 times

Therefore, the amount of floor should be

[tex]= 150 \times 4[/tex]

= 600 grams.

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The y-intercept of [tex]\(12x + y^3 = 2\) is at \((0, \sqrt[3]{2})\).[/tex]

To find the y-intercept of the equation [tex]\(12x + y^3 = 2\)[/tex], we first need to understand what the y-intercept represents. The y-intercept is the point where the graph intersects the y-axis, which means the x-coordinate of this point is 0.

To find the y-intercept, we set [tex]\(x = 0\)[/tex] in the equation and solve for y:

[tex]\[12(0) + y^3 = 2\][/tex]

[tex]\[y^3 = 2\][/tex]

To solve for y, we take the cube root of both sides:

[tex]\[y = \sqrt[3]{2}\][/tex]

So, the y-intercept of the equation is [tex]\((0, \sqrt[3]{2})\).[/tex]

Answer:

24%

Step-by-step explanation:

Formula:

   x                 new price - old price

---------    =     ---------------------------------

100%                      old price

Answer:

[tex]4.624[/tex]

Step-by-step explanation:

[tex]y=0.043x+0.324\\given \ miles \ x=100\\y= 0.043\times100+0.324\\=4.3+0.324\\=4.624[/tex]

25% off means it would be selling for 75% of the original price ( 100% - 25% = 75%).

To find the sale price you would multiply the regular price by 75%:

The equation would be y = 0.75x

Answer:

12

Step-by-step explanation:

2/3 x + x = 20

2/3 x + 3/3x = 20

5/3 x = 20   ... times 3/5 both sides

x = 12

check: 2/3 x 12 + 12 = 8 + 12 = 20

Answer:

x =  28/5

Step-by-step explanation:

Step 1: Cross-multiply

x  / 28 = 2/10

x*(10)=(2)*(28)

10x=56

Step 2: Divide both sides by 10.

10x  / 10 = 56/10

x = 28/5

The given ratios can be solved to obtain x as 5.6.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given expression is x/28 = 2/10.

In order to find the equality of two ratios, the cross products of their numerators and denominators are equal which is given as,

10x = 2 × 28

⇒ x = 56/10

⇒ x = 5.6

Hence, the value of x is given as 5.6.

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Answer:

It would be (3,5)

Step-by-step explanation:

On a coordinate plane it would be changed in which the 2nd number becomes first & the + or - changes. Same for the first number.

Answer:

No.

Step-by-step explanation: Assuming you mean x^3*x-7, these two equations do not produce the same line.

Answer:

Step-by-step explanation:

[tex]x^3\cdot x^{-7}=x^{3+(-7)}=x^{-4}\\\\\text{used}\ a^n\cdot a^m=a^{n+m}\\\\\text{Other way}\\\\a^{-n}=\dfrac{1}{a^n}\\\\x^3\cdot x^{-7}=x^3\cdot\dfrac{1}{x^7}=\dfrac{x^3}{x^7}=\dfrac{x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1\cdot x\!\!\!\!\diagup^1}{x\!\!\!\!\diagup_1\cdot x\!\!\!\!\diagup_1 \cdot x\!\!\!\!\diagup_1 \cdot x\cdot x\cdot x\cdot x}=\dfrac{1}{x^4}=x^{-4}[/tex]

Answer:

18) If ∠1 = 124° , then ∠4 = 56°.

19) if ∠2 = 48°, then ∠3 = 132°.

20) if ∠4 = 55°, then ∠2 = 55°.

21) if ∠6 = 120° , then ∠8= 120°.

22) if ∠7 = 50.5 , then ∠6= 50.5°.

23) if ∠3 = 118.7°, then ∠2= 61.3°

Step-by-step explanation:

Given two parallel lines a and b.

And other line, which is called transversal line cuts these two parallel lines to make 8 angles.

Now,

18) Given, ∠1 = 124°

 Now, sum of consecutive interior angles made by transversal line with parallel lines = 180° .

⇒∠1 + ∠4 = 180°

⇒∠a = 180° - 124° = 56°.

19) ∠2 = 48°.

as sum of consecutive interior angles made by transversal line with parallel lines = 180° .

∠2 + ∠3 = 180°.

⇒ ∠3 = 180° - 48° = 132°.

20) ∠4 = 55°

Alternate angles made by transversal line with parallel lines are equal .

⇒∠2 = ∠4 = 55°.

21) ∠6 = 120°

As corresponding angles made by transversal line with parallel lines are equal. ∠6 = ∠3 = 120°.

now, also opposite angles are equal

⇒ ∠3 = ∠8 = 120°.

22) ∠7 = 50.5

As corresponding angles made by transversal line with parallel lines are equal. ∠7 = ∠2 = 50.5°.

now, also opposite angles are equal

⇒ ∠2 = ∠6 = 50.5°.

23) ∠3 = 118.7°

as sum of consecutive interior angles made by transversal line with parallel lines = 180° .

∠3 + ∠2 = 180°.

⇒ ∠2 = 180° - 118.7° = 61.3°

Answer:

see the explanation

Step-by-step explanation:

we know that

The y-intercept is the value of the function when the value of x is equal to zero. Also is called the initial value of the function

I will analyze two cases

Part 1) we have

[tex]f(x)=-3x[/tex]

so

For x=0

substitute

[tex]f(0)=-3(0)=0[/tex]

therefore

The y-intercept is the point (0,0)

Part 2) we have

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

so

For x=0

substitute

[tex]f(0)=-3^0=-1[/tex]

therefore

The y-intercept is the point (0,-1)

84 miles I would think

Explanation:

14 whales in all, each travelled 6 miles.

14x6=84

Hope I helped :)

For this case we must simplify the following expression:

[tex](2a ^ 3-5a) - (7a+ 3a ^ 2) =[/tex]

By definition of the law of multiplication signs we have to:

[tex]- * + = -[/tex]

Rewriting the expression we have:

[tex]2a ^ 3-5a-7a-3a ^ 2 =[/tex]

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

[tex]2a ^ 3-3a ^ 2-12a[/tex]

ANswer:

[tex]2a ^ 3-3a ^ 2-12a[/tex]

Answer:

x = -5

Step-by-step explanation:

let the number be x

"five times a number" : 5x

"Six more than five times a number" : 5x + 6

"twice the number" = 2x

"Six more than five times a number = 2x - 9

"Six more than five times a number" = "Six more than five times a number

5x + 6 = 2x - 9

5x - 2x = -9 -6

3x = -15

x = -15 / 3

x = -5