Mathematics High School

Eliza paints a circle on her bedroom wall as part of a mural. After she paints it, she decides that she wants a much bigger circle. So, she multiplies her original radius by four and repaints the circle. Which statement best describes Eliza's solution?

a.) The area of the new circle is two times larger.

b.) The area of the new circle is four times larger.

c.) The area of the new circle is eight times larger.

d.) The area of the new circle is 16 times larger.

Answers

Answer 1

D. the area of the new circle is 16 times larger

Hope this helps :)

Answer 2

Answer: d.) The area of the new circle is 16 times larger.

Step-by-step explanation:

Let the radius of the original circle be r.

Then the area of the original circle will be :-

[tex]\text{A}_1=\pi r^2[/tex]

When she multiplies her original radius by four and repaints the circle.

The new radius = [tex]R=4r[/tex]

Then the area of the new circle will be :-

[tex]\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1[/tex]

Hence, The area of the new circle is 16 times larger.

Related Questions

which definitions or properties would you use to simplify the expression
[tex]( {4}^{8} \times {4}^{ - 4} {)}^{ - 2} [/tex]
explain

Answers

Exponent multiplication and addition will simplify this expression.
Exponent Addition: a^b * a^c = a^(b + c)
Exponent Multiplication: (a^ d) ^ e = a ^ (d * e)

Multiplication of 4^8 * 4^(-4) is the same as adding exponents together:
4^(8 - 4)

Which makes the expression simplify to (4^4). This expression is now to another exponent which is equivalent to multiplying exponents together:

(4^4)^-2 = 4^ (4 * -2) = 4 ^ -8

The expression has been reduced to its simplest form.

**HELP!**

El Generico public high school got a new flag pole. But they completely forgot to buy a cord and NO ONE knows how tall the flagpole is! To find out, they decided to use similar figures! As the sun was setting, Bob the janoitor set up a 5-foot stick next to the flagpole and compared shadows. The 5 foot stick cast an 8-foot shadow. The shadow of the flagpole was 32-feet long.

Use rules of similar polygons to figure out how tall the flagpole is! HINT: this will involve proportions!

Answers

if two figures or lengths are similar, then the ratios of the corresponding lengths are equal.
Thus, 8/32 =5/x
8x = 160
x = 20 feet
Therefore, the length of the flag pole was 20 feet long

An antique car was purchased for $7400 and is not worth $10,600. What is the approximate percent of change

Answers

I assume you meant "is now worth," right?

% CHANGE FORMULA:
(New # - Original #) ÷ Original # x 100

%= ($10600 - $7400)/7400 x 100
%= $3200/$7400 x 100
%= 0.432 x 100
%= 43.2% increase

ANSWER: 43% increased change

Hope this helps! :)

The approximate percentage of change will be 43.24%.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

An antique car was purchased for $7400 and is not worth $10,600.

Then the approximate percent of change will be given as,

P = [(10600 - 7400) / 7400] x 100

P = (3200 / 7400) x 100

P = 0.4324 x 100

P = 43.24%

The approximate percentage of change will be 43.24%.

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In a hockey club there are 5% more boys than there are girls. If there is a total of
246 members in the club, what is the number of boys and the number of girls?
HOW WOULD I WORK THIS OUT

Answers

Determine the percentage of boys and the percentage of girls in the club.
For an instance, pb stands for percentage of boys, and pg stands for percentage of girls.
pb + pg = 100%

There are 5% more boys, pb = pg + 5%
Input to the previous equation to find the percentage of the girls
pb + pg = 100%
pg + 5% + pg = 100%
2pg + 5% = 100%
2pg = 100% - 5%
2pg = 95%
--------------- divide each side by 2
pg = 47.5%

Substitute the percentage of girls to either equations to find the percentage of the boys
pb = pg + 5%
pb = 47.5% + 5%
pb = 52.5%

Find the number of the boys and the girls
The boys
b = pb × total members
b = 52.5% × 246
b = 0.525 × 246
b = 129.15
Because the number of people couldn't be a fraction, round to the nearest whole number
b = 129

The girls
g = total - b
g = 246 - 129
g = 117

There are 129 of boys, and 117 of girls

The number of boys and the number of girls are 126 and 120 respectively.

What is percentage?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, there are 5% more boys than there are girls, there is a total of

246 members in the club,

We need to find the number of boys and the number of girls,

Here we will use the concept of percentage as well as equation solving,

Let the number of girls be x, so, the number of boys = 105% of x = 1.05x

According to the question,

x+1.05x = 246

2.05 x = 246

x = 120

1.05x = 126

Hence, the number of boys and the number of girls are 126 and 120 respectively.

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Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).

Write the equation of this cubic polynomial function.

Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
-5

The linear factors of the cubic are

Answers

Zeros are the x values which make the function equal to zero. Set it up as you would for a binomial with a constant multiplier "k" to account for the y-intercept (0, -5) given.

f(x) = k(x-2)(x-3)(x-5)

Use the y-intercept (0,-5) to solve for k.

-5 = k(0-2)(0-3)(0-5)
-5 = -30k
-5/-30 = k
1/6 = k

The cubic polynomial function is then ..

f(x) = (1/6)(x-2)(x-3)(x-5)

Linear factors are the linear (line) expressions you can factor out of the polynomial. They are (x-2), (x-3) and (x-5).

The cubic polynomial equation which passes through the coordinate (0,-5) and whose zeroes are (2 , 0), (3 , 0), and (5 , 0) is: [tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex] and it can be determine by arithmetic operations.

Given :

A cubic polynomial whose zeroes are (2 , 0), (3 , 0), and (5 , 0).Cubic polynomial equation passes through (0 , -5).

Arithmetic operations can be used to determine the cubic polynomial equation. The generalised cubic polynomial equation is given by:

[tex]y = K(x-a)(x-b)(x-c)[/tex]

Where, K is constant and a, b, and c are the zeroes of the cubic polynomial equation. Therefore, the value of a, b, and c are 2, 3, and 5 respectively.

[tex]y = K(x-2)(x-3)(x-5)[/tex] ----- (1)

It is given that cubic polynomial equation passes through (0 , -5). So, put x = 0 and y = -5 in equation (1) to evaluate the value of K.

[tex]-5=K(0-2)(0-3)(0-5)[/tex]

[tex]5=30K[/tex]

[tex]K = \dfrac{1}{6}[/tex]

Therefore the cubic polynomial equation is given by:

[tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex]

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The volume of a rectangular box is found by multiplying its length, width, and height: V = lwh. A certain box has a volume of b 3 + 3b 2 - 4b - 12. Factor the four-term polynomial to find the dimensions of the box. Hint: Use factoring by grouping to factor the four term polynomial first.

Answers

i think its (b+3) (b+2) (b-2) maybe wrong not sure

Answer:

The dimensions of the box are (b+3), (b-2) and (b+2).

Step-by-step explanation:

The volume of a rectangular box is

[tex]V=l\times w\times h[/tex]

The volume of a certain box is

[tex]V=b^3+3b^2-4b-12[/tex]

First of all find the factors of above expression by grouping method.

[tex]V=b^2(b+3)-4(b+3)[/tex]

[tex]V=(b+3)(b^2-4)[/tex]

[tex]V=(b+3)(b^2-2^2)[/tex]

[tex]V=(b+3)(b-2)(b+2)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]

Volume of a rectangle is the product of its dimensions, therefore the dimensions of the box are (b+3), (b-2) and (b+2).

i need to know the equations

Answers

Let l, t, b represent the numbers of lions, tigers, bears, respectively.

2l +3t +3b = 156 . . . . . . . 156 meals per day are supplied
l +t = 3b . . . . . . . . . . . . . . there are 3 times as many great cats as bears
l +t +b = 68 . . . . . . . . . . . there are a total of 68 animals

_____
The last 2 equations tell you
.. 4b = 68
.. b = 17
Subtracting 3 times the last equation from the first gives
.. -l = -48
There are 48 lions, 3 tigers, and 17 bears.

Let L = number of lions
Let T = number of tigers
Let B = number of bears

If one lion eats 2 meals per day, then L number of lions eat 2L meals per day.
Tigers eat 3T meals per day, and bears eat 3B meals per day.

In one day, all animals combined ate 156 meals.

That gives us our first equation.

2L + 3T + 3B = 156

The lions and tigers are considered great cats. The bears are not cats.
There are 3 times as many great cats as bears.
This gives us our second equation.

L + T = 3B

In all there are 68 animals in the zoo.
From here we get our third equation.

L + T + B = 68

Our system of equations is:

2L + 3T + 3B = 156
L + T = 3B
L + T + B = 68

Now we solve the system of equations.

Subtract the second equation from the third equation.

B = -3B + 68

4B = 68

B = 17

Substitute B = 17 into the first and second equations.

2L + 3T + 3B = 156

2L + 3T + 3(17) = 156

2L + 3T + 51 = 156

2L + 3T = 105      New Equation A

L + T = 3B

L + T = 3(17)

L + T = 51   Equation B

Equations A and B have only two variables, so we can solve them as a system of two equations in two unknowns.

2L + 3T = 105
L + T = 51

Rewrite equation A. Multiply Equation B by -2 and write underneath Equation A. Then add the equations.

       2L + 3T = 105
+    -2L - 2T = -102
-------------------------
                T = 3

Now use B = 17 and T = 3 in the original third equation to solve for L.

L + T + B = 68

L + 3 + 17 = 68

L + 20 = 68

L = 48

Answer: There are 48 lions, 3 tigers, and 17 bears

Check:
"Lions eat 2 meals per day, tigers and bears eat 3 meals each per day."
Number of meals:
2 * 48 + 3 * 3 + 3 * 17 = 96 + 9 + 51 = 156

"There are 3 times as many great cats in the zoo as bears."
48 + 3 = 51, and 51 is 3 times 17

"There are 68 animals in the zoo."
48 + 3 + 17 = 68

All statements are satisfied by our solution, so the answer above is correct.

A dad has two daughters – wendy and julia. wendy is twice as old as julia. the man is now five times as old as wendy, and in 4 years he will be six times as old as julia. find the present age of the father.

Answers

x = age of julia
2x = age of Wendy
10x = age of dad (because dad is five times as old as Wendy)
(x+4)*6=10x+4 (because in four years, that's why I added 4 to both sides, dad's age will be now 10x+4 and Julia's age x+4, now dad is 6 times as old and I multiplied Julia's age by six) ==> 6x+24=10x+4, now subtract 4 from both sides:
6x+20=10x, let's subtract 6x from both sides
20=4x ==> x=5
because age of father is 10x, we substitute x value and we get
10*5=50

Answer: 50

Step-by-step explanation:

If Chloe has $3,200 in weekly sales, she will earn more money with

Answers

the correct question in the attached figure

we know that
weekly sales------------> $3200
8% weekly sales--------> 0.08*3200=$256
Option 1---------> salary=$600 per week
Option 2---------> salary=$350+$256=$606 per week
Option 2> Option 1
then
she will earn more money with the option 2

the answer part A) is option 2

Part B)
If x represents Chloe’s weekly sales
equation option 1---------> 600
equation option 2---------> 350+0.08*x

the equation can be used to determine which option will benefit her the most is making the two options equal
600= 350+0.08*x

the answer Part B) is 600= 350+0.08*x

Part C)
she will earn more money with Option 1 when
600 > 350+0.08*x------------> (600-350) > 0.08*x-------> 250 > 0.08*x
250/0.08 > x------> 3125 > x---------> x < $3125

the answer Part C) is x < $3125

Determine whether each pair of angles is a pair of vertical angles, a linear pair of angles, or neither. Select the correct answer for each lettered part.

Answers

A)  ∠AFC and ∠CFD are neither. They share more than a vertex, so they are not vertical angles. Also, they do not form a straight line so they do not make a linear pair.
B)  ∠AFB and ∠CFD are neither. Vertical angles are also known as vertically opposite angles. While these two only share a vertex, they are not opposite each other. They also do not form a linear pair, as they do not form a straight line.
C)  ∠BFD and ∠AFE are vertical angles. They are opposite each other and share only a vertex.

Answer:

Linear Pair, Neither, Vertical.

Its also in the attached PNG just in case the question you have decides to put them out of order. You are all welcome! I hope this helps you people in the future

Then net folds into s cube. Which two letters appear on the opposite faces?

Answers

Out of the choices given, B and E will be opposite of each other when the folding occurs. You have to imagine what it would look like, once folded.

B and E i'm confident

The volume of the cylinder is 392 cm cubed work out the length

Answers

Well if you are given the radius, you can solve for it. As the volume of a cylinder is area of the base which is a circle times it height.

B • h = Pi r ^2 • h = 392 cm^3.

H = 392/Pi r^2.

This is the height or length.

Please help me Idk what I’m doing thanks

Answers

check the picture below.

What value of x makes the denominator of the function equal zero? y = 6/4x-40

Answers

As writtten, x is in the numerator and the denominator is 4. No value of x will make it be zero.

Perhaps you intend
.. y = 6/(4x -40)
Then x=10 will make the denominator zero.

Find the volume of this

Answers

V = 4 cm * 5 cm * 3 cm = 60 cm³

3cm * 4cm * 5cm = 60 cm^3
Answer is C

Jennifer wants to rent a car for 5 days, and she’s interested in a the loss damage waiver but not the collision damage wavier.If the daily rate is $39 and LDW is $65 for the rental period,what is her total cost?

Answers

T= total cost
n= number of days

Total cost equals the cost per day times the number of days plus the fee.

T= $39n + $65
substitute 5 for n
T= 39(5) + 65
T= 195 + 65
T= $260 total cost

Hope this helps! :)

APEX $260 is correct answer.

What is the equation of the line that is perpendicular to the line and passes through the point (6, 2)?

Answers

Hey there! :D

So, when you find something perpendicular, you are finding the opposite reciprocal.

The slope is 1/2 because:

y=mx+b <== it is in this form; m is equal to slope.

Flip the 2 and 1 and make it negative.

2/1= -2

We already know "C" and "D" aren't the options. Now, we can just plug in the points given to see if it works. Plug in the set of points (6,2)

y=-2x+14

2=-2(6)+14

2=-12+14

2=2 <== this works. This is our answer. Let's just make sure by checking the other one.

y=-2x-2

2=-2(6)-2

2=-12-2

2=-14 <== that is not true.

The first option is correct.

I hope this helps!
~kaikers

Step [tex]1[/tex]

Find the slope of the line perpendicular to the given line

we have

the equation of the given line is

[tex]y=\frac{1}{2}x+7[/tex]

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

[tex]m1*m2=-1[/tex]

in this problem the slope m1 of the given line is

[tex]m1=\frac{1}{2}[/tex]

[tex]m2=-\frac{1}{m1}[/tex]

[tex]m2=-2[/tex]

Step [tex]2[/tex]

Find the equation of the line with slope m2 and passes through the point [tex](6, 2)[/tex]

we know that

the equation of the line is

[tex]y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14[/tex]

therefore

the answer is the option A

the equation of the line is [tex]y=-2x+14[/tex]

see the attached figure to better understand the problem

Write a quadratic function f whose zeros are 3 and 8

Answers

The standard form of a quadratic equation is: ax²+bx+c=0, and it is represented with a polynomial of degree 2, that's why it is also called "Equation of degree 2".

1. So, if 3 and 8 are zeros of the quadratic function, then they are factors of it. Therefore, you have:

(x+3)(x+8)=0

2. When you write it in the standard form, you have:

x²+11x+24=0

a=1
b=11
c=24

solve the following question: |x|=3/4

Answers

Answer: "x = [tex] \frac{3}{4} [/tex]" or "x = - [tex] \frac{3}{4} [/tex]" .
____________________________________________________

Or, write as: " x = ± [tex] \frac{3}{4} [/tex] " .

____________________________________________________

Answer: x = ¾, -¾

Process:Remove the absolute value term. This create a _ On the right side of the equation because |x| = _x.
x = _ ¾

Set up the positive portion of the _ solution.
x = ¾

Set up the negative portion of the _ solution.
x = -¾

The solution to the equation includes both the positive and negative portions of the solution.
x = ¾, -¾

I hope this helps!
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My jar has 25 dimes and some quarters, nickels, and pennies. The number of quarters plus dimes equals the number of pennies. I have 4 nickels for every dime and 2 pennies for every nickel. How many quarters are there? A. 175 B. 150 C. 125 D. 75

Answers

d = dimes = 25
q = quarters
p = pennies
n = nickels
1. q + n = p
2. 4n = 1 d
3. 2p = 1n

1 d = 4n
25 d = x
x = 4 * 25 = 100 nickels

1 n = 2 p
100 n = x p
100 n = 200 p

q + n = p
There are 100 nickels. there are 200 pennies
q + 100 = 200
q = 200 - 100
q = 100

Answer
There are 100 quarters,<<<<======

Answer:

Quarters = 175

Step-by-step explanation:

Let the number of dimes in the jar = 25

number of Nickels = n

number of quarters = q

number of pennies = p

Now we will form the equation

Number of quarters plus dimes equal the number of pennies.

q + 25 = p --------(1)

You have 4 nickles for every dime

n = 4d

n = 4 × 25 = 100

and you have 2 pennies for every nickels

p = 2n

p = 2 × 100 = 200

Now we replace p = 200 in equation (1)

q + 25 = 200

q = 200 - 25

q = 175

Option A. 175 will be the answer.

The corners of a fence are at a (11,3), b (3,-11), c (-13,-9), and d (-5,9). let q be the midpoint of ????????⎯⎯⎯⎯⎯, r be the midpoint of ????????⎯⎯⎯⎯⎯, s be the midpoint of ????????⎯⎯⎯⎯⎯, and t be the midpoint of ????????⎯⎯⎯⎯⎯. what are the midpoints of the sides of this fence?

Answers

The midpoints and their coordinates are shown in the attached figure.

The midpoint between two points (a, b) and (c, d) can be found by averaging their coordinates:
.. midpoint = ((a+c)/2, (b+d)/2)

Between which 2 consecutive numbers is radical 46

Answers

[tex]\bf \sqrt{46}\approx 6.78239983 \\\\\\ \boxed{6}\text{\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash}6.78239983\text{\textemdash\textemdash\textemdash}\boxed{7}[/tex]

In the diagram, △ABC ≅ △WRS. What is the perimeter of △WRS?

10 units
11 units
12 units
13 units

Answers

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

△ABC ≅ △WRS

So, Perimeter of △ABC is given by

AB+BC+CA

here, AB = 3 units

BC = 4 units

AC = x

By pythagorus theorem, we get that

[tex]AC^2=AB^2+BC^2\\\\x^2=3^2+4^2\\\\x^2=9+16\\\\x^2=25\\\\x=\sqrt{25}\\\\x=5\ units[/tex]

So, perimeter of △ABC is

3+4+5=12 units

So, the perimeter of △WRS is also 12 units as they are similar triangles .

Hence, Third option is correct.

Answer:

The Answer Is 12

Step-by-step explanation:

Please help !! Thank you :)

Answers

If we presume north is along the positive y-axis, then Rachel's initial position is
.. (x, y) = (-√2, √2)
This does not match any of the offered choices.

If Rachel starts 2 mi NE of her house, then selection D is appropriate.

.help me please thank you.

Answers

it should be the second option which is the SAS postulate

it is the SAS postulate

Anna started a race at 9:30am. She ran for 3 hours and 47 minutes. What time did she finish her race?

Answers

so we know the time she start and hownp many time the race was so let's add them together to get the end time

9:03+3h47=12h50

so the race ends at 12h50 (noon)

The solution is, the race ends at 12h50 (noon)

What is addition?

It can be stated as, Addition is a way of combining things and counting them together as one large group.We know that, Addition in math is a process of combining two or more numbers.

here, we have,

Anna started a race at 9:30am. She ran for 3 hours and 47 minutes.

so we know the time she start and how many time the race was so let's add them together to get the end time

now,

9:03+3h47

=12h50

so the race ends at 12h50 (noon)

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Find the area of the following circle. (Round answer to the nearest hundredth.)
d = 15 in
area = _____ square inches
circumference = ______ inches

Answers

The area of the circle is 176.63 inches

The area of circle is,

⇒ 176.62 in²

And, ⇒ Circumference = 47.1 in.

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The diameter of circle is,

d = 15 in.

Hence, Radius of circle is.

r = 15 / 2

r = 7.5 in,

Thus, Area of circle is,

⇒ πr²

⇒ 3.14 × 7.5²

⇒ 176.62 in²

And, Circumference = 2πr

⇒ Circumference = 2 × 3.14 × 7.5

⇒ Circumference = 47.1 in.

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Nial is signing a lease for an apartment that rents for $1020/month. How much will he pay to move in if he must pay the first and last months' rent and a security deposit equal to 60% of his monthly rent?

2040

$2448

$2652

$2856

Answers

1020 + 1020 = 2040
%60 of 1020 is:612
2040+612=2652
so third one is true

Answer:

Option (c) is correct.

He pays $ 2652.

Step-by-step explanation:

Given : Nial is signing a lease for an apartment that rents for $1020/month.

We have to find the amount he pay to move in if he must pay the first and last months' rent and a security deposit equal to 60% of his monthly rent.

Since, given he must pay the first and last months' rent and a security deposit equal to 60% of his monthly rent.

Given monthly rent is $ 1020

That is 60% of his monthly rent = [tex]\frac{60}{100}\times 1020=612[/tex]

Thus, total amount he needs to pay is first month rent + last month rent + 60% of his monthly rent.

That is 1020 + 1020 + 612 = 2652.

Thus, He pays $ 2652.

Sabastian is driving 400 miles to meet his friend. He travels 100 miles in the first two hours of his trip. If he continues at the same rate, how long will it take to drive the remaining distance?

Answers

His rate so far is (100 mi)/(2 h), so 50 mi/h. The remaining 300 miles will take
.. (300 mi)/(50 mi/h) = 6 h

Describe how you would estimate the square root of a number that is not a perfect square without using a calculator. lets say n was the imperfect square number and the square root is w. the square root of n = n+w squared/ 2w.

Answers

To get the square root of imperfect square we can use the formula , which is usually accurate to about two decimal places,
√X =√S +(X-S)2√S
Where, X = the number you want the square roof of, and S is the closest square you know to x.
For example 75 is an imperfect square
Thus, X=75 and thus the nearest number S = 81, this ,means √81 =9.
Putting this into the formula;
√75= 9+(75-81)/2/2(9)
= 9 + -6/18
= 9-0.33333 = 8.667
= 8.667, thus the square root of 75 is 8.66

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