What happens to the surface area of a rectangular prism when each of the dimensions is doubled? (1 point) i?

Answers

Answer 1

The surface area will be 4 times the original size. Here is why: You are doubling each dimension, and area is a 2 dimensional measurement. Because of this whatever you are doing to the length of the side will happen 2 times. In this case it would be x2 x2 which equals 4. You can provide evident by using a cube. The surface area of a cube with side lengths of 1 would be 1 x 6=6 square inches. If you double the side length, it would be 4 x 6= 24 square inches.

Answer 2

Final answer:

The surface area of a rectangular prism increases by four times when each of the dimensions is doubled because surface area scales in proportion to the square of the linear dimensions.

Explanation:

When the dimensions of a rectangular prism are doubled, the surface area of the prism increases by a factor of four. This is because the surface area is proportional to the square of the linear dimensions. If the length, width, and height of the prism are doubled, the new surface area (A') compared to the original surface area (A) is calculated as follows:

A' = 2l × 2w + 2l × 2h + 2w × 2h

A' = 4(lw + lh + wh)

A' = 4A

Thus, if each dimension is doubled, the surface area increases by four times.

Related Questions

Please help if you know how to do this type of math! :)

Answers

It's just a tiny bit sloppy. The 10.2 cm should be designated with a right angle too. I'll answer it that way.

Area = (L1 + L2)*h/2
L1 = 10.2
L2 = 12.2
h = 12.6
all givens are in cm.

Area = (10.2 + 12.2)*12.6/2
Area = 22.4 * 6.3
Area = 78.12 cm^2

The sum of two numbers is 58 . the smaller number is 10 less than the larger number. what are the numbers?

Answers

X+Y=58
X-Y=18 ADD
----------------
2X=76
X=76/2

X=38 ANS. FOR THE LARGER NUMBER.
38+Y=58
Y=58-38
Y=20 ANS. FOR THE SMALLER NUMBER.
PROOF:
38-20=18
18=18

Andrew has a coupon for $2.80 puppy treats. One bag of treats usually costs $9.94 and contains 42 of the treats. If Andrew uses his coupon what will be the price per puppy treats

Answers

Here are the given facts of this question:

1. The regular price for a bag of treats $9.94
2. There are 42 treats in a box
3. The coupon worths $2.80

In order to find out how much it would be per puppy treats
You will have to do the following steps:

Step1 find out how much it would be after the discount:

Regular price 9.94 － The worth of the coupon 2.80 = $7.14
Now know how much it would be after the discount we'll have to find out how much it would be per puppy treat.

Step2 dividing the # of treats and the price after discount

The discount price 7.14 / The amount of treats per bag 42 = $0.17 per treat

So it would be $0.17 for each treat.

Hope this helps!

Andrew's price per puppy treat, after using a $2.80 coupon on a $9.94 bag that contains 42 treats, will be $0.17.

Andrew has a coupon that will reduce the price of puppy treats. Without the coupon, one bag of treats costs $9.94 and contains 42 treats. To find the price per treat after using the $2.80 coupon, we first subtract the coupon value from the original price of the bag. This gives us the discounted price of the bag:

Discounted Price = Original Price - Coupon Value = $9.94 - $2.80 = $7.14

Next, we find the price per treat by dividing the discounted price of the bag by the number of treats in the bag:

Price per Treat = Discounted Price ÷ Number of Treats = $7.14 ÷ 42 = $0.17 (rounded to two decimal places)

After using the coupon, the price per puppy treat will be $0.17.

**NEED HELP!!!

Bo’s gross annual income is $45,408. He is paid semimonthly and has 6% deducted from his paychecks for his 403(b). His employer matches his deduction, up to 3%.

How much is deposited into Bo’s 403(b) each payday?

Answers

Answer:

170.28

Step-by-step explanation:

I just took the test and am reviewing the correct answers.

A cube has a volume of 27 squared feet. What is the length of each side?

Answers

Hello!

The formula for volume of a cube is [tex]V= a^{3} [/tex]; you are given the volume, so plug it into the formula for [tex]V[/tex].

[tex]V= a^{3} [/tex]
[tex]27= a^{3} [/tex]

Take the cube root of each side:

[tex]27= a^{3} [/tex]
[tex] \sqrt[3]{27} = a^{3} [/tex]
[tex]3=a[/tex]

Answer:
The length of each side is 3 cubic feet.

using formula v=a^3
a=v^1/5=27^1/5=3
to checking your answer
v=a^3
3^3
27
the answer for your question is 3

Look Ray 0.45 hour to rake the leaves and 3/4 hour to mow the lawn how many minutes did it take him to do both tasks

Answers

0.45*60=27
0.75*60=45
27+45=72
The answer is 72 minutes

Help please on properties of exponents? will give a medal!

A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.

a. 3 to the 2 over 3 power inches squared

b. 3 to the 8 over 3 power inches squared

c. 9 inches squared

d.9 to the 2 over 3 power inches squared

2.)Explain how the Quotient of Powers was used to simplify this expression.

2 to the fifth power, over 8 = 2 to the 2nd power

a.By finding the quotient of the bases to be one fourth and cancelling common factors

b. By finding the quotient of the bases to be one fourth and simplifying the expression

c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents

d. By simplifying 8 to 23 to make both powers base two and adding the exponents

3.)the cube root of 2 to the seventh power

a. 2 to the 3 over 7 power

b. 2 to the 7 over 3 power

c. 2^21

d. 2^4,

Answers

Answer
1) c. 9 inches squared
2) c. By simplifying 8 to 23 to make both powers base two and subtracting the exponents
3) b. 2 to the 7 over 3 power

Explanation.
Question 1
The area of a rectangle is given by
area=l×w
=〖81〗^(1/3)×3^(2/3)
3^(4/3)×3^(2/3)=3^(4/3+2/3)
=3^(6/3)=3^2=9 inches squared

Question 2
Finding the 2^5/8=2^2
The steps for finding this is first to write 8 as 23. Then divide.
2^5/8=2^5/2^3
When dividing exponents with the same base you subtract the powers.
=2^(5-3)=2^2

Question 3
The question wants us to solve, ∛(3^7 ).the cube root of a number can be written as a power of a third.
So,
∛(3^7 )=3^(7×1/3 )
=3^(7/3)

Answer:

Ques 1)

Option: C is the correct answer.

c. 9 inches square.

Ques 2)

Option: c

c. By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.

Ques 3)

Option: b

b. 2 to the 7 over 3 power

Step-by-step explanation:

Ques 1)

A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches.

i.e. let 'l' and 'b' denote the length and width of the rectangle.

i.e.[tex]l=\sqrt[3]{81}\\\\l=(3^4)^{\dfrac{1}{3}}\\\\l=3^{\dfrac{4}{3}[/tex]

since,

[tex](a^m)^n=a^{mn}[/tex]

and

[tex]w=3^{\dfrac{2}{3}}[/tex]

Hence, the area of rectangle is given by:

[tex]Area=l\times w\\\\\\Area=3^{\dfrac{1}{3}}\times3^{\dfrac{4}{3}}\\\\\\Area=3^({\dfrac{1}{3}+\dfrac{4}{3}})\\\\\\Area=3^{\dfrac{6}{3}}\\\\\\Area=3^2\\\\\\Area=9\ square\ inches[/tex]

As we know that:

[tex]a^m\times a^n=a^{m+n}[/tex]

Hence, Area=9 square inches.

Ques 2)

2 to the fifth power, over 8 = 2 to the 2nd power

i.e. we need to prove that:

[tex]\dfrac{2^5}{8}=2^2[/tex]

As we know that:

[tex]\dfrac{2^5}{8}=\dfrac{2^5}{2^3}=2^{5-3}=2^2[/tex]

( since

[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex] )

Hence, the correct answer is: Option: c

Ques 3)

The cube root of 2 to the seventh power.

i.e.

[tex]\sqrt[3]{2^7}\\\\=(2^7)^{\dfrac{1}{3}}\\\\=2^{\dfrac{7}{3}}[/tex]

Since,

[tex]\sqrt[n]{x}=x^{\dfrac{1}{n}}[/tex]

and

[tex](a^m)^n=a^{mn}[/tex]

Hence, the correct answer is: option: b

In the previous problem, Ken predicted a drop in temperature. Explain why a drop in temperature would lead to adding a negative integer.

Answers

A drop in temperature means the temperature will decrease. That decrease is represented by a negative integer, which should be added to the previous temperature.

Answer:

Because a drop in temperature means decrease in temperature therefore, we take an integer with negative sign and added to previous temperature.

Step-by-step explanation:

Drop in temperature means decrease in the temperature .When the temperature decreases then we take decrease value of temperature in negative integer. Because decrease means the temperature fall down .Hence , the decrease in temperature measure with negative sign .

For example, if we take temperature T= 70°C.

If the temperature decreases by 5°c then the temperature

Decrease in temperature=-5°C

Hence, the temperature T= 70+(-5)=65°C.

Therefore , from example we can say that when temperature decreases by some value in integer . Then ,we get final temperature obtained by adding drop in temperature ( negative integer ) in previous value of the temperature.

SOMEONE HELP ASAPPPPPPP!!! PLEASE
1. A person at ground level measures the angle of elevation to the top of a building to be 74°. If at this point the person is 34 feet away from the base of the building, then how tall is the building?

Please round to the tenths place.
Please show work/steps and provide units with your answer.

2. In right triangle PQR, P and Q are complementary angles. The value of sin Q is
9/
. What is the value of cos P?

A.9/41
B.41/9
C.40/41
D/41/40

Answers

Part 1
The distance between the person and the building can be written as:
[tex]x=c\cdot \cos(\theta)[/tex]
C would be the line connecting the top of the building and the person(hypotenuse).
The height of the building is:
[tex]h=c\cdot \sin(\theta)[/tex]
If we get the c from the first equation and plug in the second one we get:
[tex]h=\frac{x}{\cos(\theta)}\cdot\sin(\theta)=x\cdot \tan(\theta)=32ft\cdot3.45=110.4$ft[/tex]
Part 2
If we P and Q are complementary that means that they sum is 90 degrees.
Because of this sin(Q) must be the same as cos(P).
Sum of the angles in any triangle is 180 if we have a right triangle and two complementary angles that means that those two angles have to be 45 degrees. Sin and cos are the same for the 45-degree angle.
I attached the diagram that would make this clear.

A water tank has the shape of an inverted right circular cone of altitude 12 ft and base radius 6 ft. if water is being pumped into the tank at a rate of 10 gal/min, approximate the rate at which the water level is rising when it is 3 ft deep

Answers

The radius of the water surface at that point is (3 ft)/(12 ft)*(6 ft) = 1.5 ft, so the surface area is
.. π(1.5 ft)^2 = 2.25π ft^2

The rate of rise is then
.. (10 gal/min)*(77/576 ft^3/gal)/(2.25π ft^2) ≈ 0.18911 ft/min

_____
The rate of change of depth is equal to the rate of change of volume divided by the surface area. Here's how you can get there from derivatives.

V = (1/3)Bh
V' = (1/3)(B'h +Bh')
Here we have B = π(h/2)^2 = (π/4)h^2, so B' = (π/2)h*h'
V' = (1/3)((π/2)*h^2*h' +(π/4)h^2*h')
V' = (π/4)h^2*h'
V' = B*h'

plz help me on this question

Answers

g(x) is f(x) shifted 2 down.

So the answer is:

g(x) = f(x) - 2
(B)

Which net matches the figure?

Answers

The first net because the figure shown is a square pyramid

The top choice to the left, is your answer. I hope this helps!

What are the zeros of the quadratic function f(x) = 8x2 – 16x – 15? x = –1 – and x = –1 + x = –1 – and x = –1 + x = 1 – and x = 1 + x = 1 – and x = 1 +

Answers

To find the zeros of the quadratic function [tex]$ f(x) = 8x^2 - 16x - 15 $[/tex], you need to solve for [tex]$ x $ when $ f(x) = 0 $[/tex].

So, you set $ f(x) $ equal to zero:

[tex]\[ 8x^2 - 16x - 15 = 0 \][/tex]

To solve this quadratic equation, you can use the quadratic formula:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]where $ a = 8 $, $ b = -16 $, and $ c = -15 $.[/tex]

Plugging these values into the quadratic formula:

[tex]\[ x = \frac{{-(-16) \pm \sqrt{{(-16)^2 - 4(8)(-15)}}}}{{2(8)}} \]\[ x = \frac{{16 \pm \sqrt{{256 + 480}}}}{{16}} \]\[ x = \frac{{16 \pm \sqrt{{736}}}}{{16}} \][/tex]

Now, you simplify the expression under the square root:

[tex]\[ \sqrt{736} = \sqrt{16 \times 46} = 4\sqrt{46} \][/tex]

So, the expression becomes:

[tex]\[ x = \frac{{16 \pm 4\sqrt{46}}}{{16}} \][/tex]

Now, you can simplify further:

[tex]\[ x = \frac{{4(4 \pm \sqrt{46})}}{{4 \times 4}} \]\[ x = \frac{{4 \pm \sqrt{46}}}{{4}} \][/tex]

This gives you two solutions:

[tex]\[ x = \frac{{4 + \sqrt{46}}}{{4}} \]\[ x = \frac{{4 - \sqrt{46}}}{{4}} \][/tex]

These are the zeros of the quadratic function [tex]$ f(x) = 8x^2 - 16x - 15 $.[/tex]

Complete question :

What are the zeros of the quadratic function f(x) = 8x2 - 16x - 15?

Order the group of quadratic functions from widest to narrowest graph. y = 6x2, y = −4.5x2, y = −x2

Answers

To solve this problem you must keep on mind the following information: By definition, a quadratic function has the following form:
[tex] y=ax^{2}+bx+c [/tex]
Where [tex]a [/tex] is the leading coefficient.
If the leading coeficient is closer to zero, the parabola is widest,if it has a larger positive or negative value, the parabola is narrowest.
Therefore, by knowing the information above, you have that the answer is:
[tex]y=- x^{2} \\ y=-4.5 x^{2} \\ y=6 x^{2} [/tex]

y = 6x2, y = −4.5x2, y = −x2

This should be correct answer:) He got it mixed up in his answer below when graphing.:)

If your credit score is 750, how much will you pay in interest by the end of 1 month if you owe $2,375.00?

$31.17
$24.74
$18.31
$11.38,

Answers

The answer is $18.31. The answer would be the third option.
The interest is 1/12
Then 9.25% multiplied by the $2,375 balance
(0.0925 * 2375) / 12 = 219.69
=219.69 / 12
= $18.31

Answer:

$18.31

Step-by-step explanation:

Credit score = 750

Period (n) = 1 month

Debt = $2375

Since the score is 750, from the table annual rate = 9.25%

Monthly rate (r) = 9.25/12 = 0.7708%

Interest =.PRT/100

P= principal amount

R= rate

T = time taken

Interest = (2375*0.7708*1)/100

= 18.6065

= $18.31 (approximately )

Use the equation and type the ordered-pairs.

y = 3^x

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

Answers

See the attachment for a table. Of course, the first ordered pair is (-1, 1/3).

Answer: [tex](-1,\frac{1}{3}),\ (0,1),\ (1,3),\ (2,9),\ (3,27),\ (4,81)[/tex]

Step-by-step explanation:

The given exponential function :

[tex]y=3^x[/tex]

At x = -1, we get

[tex]y=3^{-1}=\dfrac{1}{3}[/tex]

At x = 0, we get

[tex]y=3^{0}=1[/tex]

At x = 1, we get

[tex]y=3^{1}=3[/tex]

At x = 2, we get

[tex]y=3^{2}=9[/tex]

At x = 3, we get

[tex]y=3^{3}=27[/tex]

At x = 4, we get

[tex]y=3^{4}=81[/tex]

Hence, the completed ordered pairs are : [tex](-1,\frac{1}{3}),\ (0,1),\ (1,3),\ (2,9),\ (3,27),\ (4,81)[/tex]

A population has size 25 at time t = 0, with t measured in years. (a) if the population decreases by 4 people per year, find a function for the population size, p, at time t. enter your answer as an equation with p on the left side, and an expression involving t on the right

Answers

First we define the variables:
p = population
t: time in years
The equation that best fits this problem is a linear equation of the form:
p = -4t + 25
Note that for t = 0 the value of p is 25, which represents the initial population.
Answer:
a function for the population size, p, at time t is:
p = -4t + 25

Find two numbers that multiply to make the first number and add to make the second number. (I understand how to do it, I’m just having some issues. It’s not registering.)

Answers

Let
x-----------> the first number
y-----------> the second number

we know that
x*y=x-----------> y=x/x----------> y=1
and x+y=y------> x=y-y---------> x=0

the answer is
the first number is 0
the second number is 1

The student's question pertains to solving a system of equations to find two numbers that multiply to a given product and add to a given sum. The solution involves testing pairs of factors of the product until the pair that also sums to the required number is found, for example, finding that 3 and 8 multiply to 24 and add to 11.

The student is looking to solve a classic problem in algebra: finding two numbers that, when multiplied together, result in a given number (the product), and when added together, sum to another given number (the sum). This is often related to factoring a quadratic equation or finding the roots of a polynomial. The solution involves setting up a system of equations based on the given conditions and solving for the two unknown numbers. This process typically requires identifying the correct pair of numbers that satisfy both the multiplication and addition conditions. Let's take an example:

Suppose we need to find two numbers that multiply to make 24 and add to make 11. We can denote these numbers as x and y, leading to the following equations:

x . y = 24 (multiplication condition)x + y = 11 (addition condition)

By systematically testing pairs of factors of 24 (e.g., 1 and 24, 2 and 12, 3 and 8, 4 and 6), we find that 3 and 8 satisfy both conditions, because 3 . 8 = 24 and 3 + 8 = 11. Therefore, the two numbers are 3 and 8.

Will give BRAINLIEST!! I REALLY NEED HELP..What is -1/2(-3y+10) as a equivalent expression? pls help me

Answers

Any expression has many equivalents. For something like this, it is often convenient just to make use of the distributive property.

= (-1/2)*(-3y) +(-1/2)*(10)
= (3/2)y -5

Another equivalent has a common denominator
= (3y -10)/2

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so the height of the dam is meters. NextReset

Answers

the height of a dam:
h = x + 1.65 m,
where:
x = 90 m · tan 26°
x = 90 · 0.4877
x = 43.90
h = 43.90 m + 1.65 m = 45.55 m
Answer:
The height of the dam is 45.5 m.

Answer:

The height of dam =45.5 m.

Step-by-step explanation:

We are given that Scarlett stands 90 m away from the dam and records the angle of elevation to the top of the dam to be [tex]26^{\circ}p[/tex]

Scarelett's height is 1.65 meters.

We have to find the height of the dam.

Let h be the height of dam

AC=AB+BC

BC=x

h=1.65+x

CD=EB=90 m

In triangle ABE

[tex]\theta=26^{\circ}[/tex]

[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]

[tex]tan26^{\circ}=\frac{AB}{90}[/tex]

[tex]0.4877=\frac{x}{90}[/tex]

[tex]x=0.4877\times 90[/tex]

[tex]x=43.893 m[/tex]

Therefore, the height of dam=1.65+43.893=45.543 m

Answer: The height of dam =45.5 m

Someone please explain how the GCF of x^4 and x^3 equals x^3. This has me stumped.

Answers

GCF is the greatest common factor. its the value of the factors that are common to both the numbers being compared. In other words the product of the factors that are common to both numbers or the greatest factor common to both numbers.
factors of x⁴ = x * x * x * x = (x * x * x) * x
factors of x³ = x * x * x = (x * x * x)
factors common to both are (x * x * x) Therefore GCF is x³

1) when to use the median to describe the measure of center of a data set, 2) what measures of spread can we find when using box-plots, 3) what measure of spread is most appropriate to describe symmetrical data sets, 4) how does an outlier affect the mean of data set and give an example,

Answers

1. You should use the median to describe the measure of center of a data set when an outlier is present in a data set. Having an outlier will skew the mean of the data. This means it will adjust the average to be smaller or greater than what the actual numbers are showing. The median should be used as the measure of center in these circumstances.

2) Using a box plot, you can find the range and interquartile range. The range is the distance from the smallest number to the largest. The interquartile range is the distance from the first quartile to the third quartile. All these values are found on a box plot.

3)The best measure of spread to describe symmetrical data sets is the mean absolute deviation. This tells us how far on average the numbers are spread out from the mean.

4) See the answer given in #1 for the explanation. An example would be a student who scores 8, 9, 10, 9, 10, 2 on 6 quizzes. The mean would be an average of 8, which is not a good number to represent the score this student normally gets. The median of 9 is a better number to show how this student normally performs.

Answer:

what the dude above me put he wrong

Step-by-step explanation:

Moa finished 60% of her homework in 45 minutes how many minutes does it take her to do the whole thing

Answers

The percentage of homework completed in 45 min is 60%
The whole homework is 100%.
The total amount of time it will take Moa to finish the homework will be given by:
100/60×45
=75 min
=1 hour 15 min

The area of a rectangular swimming pool is
10x2 – 19x – 15. The length of the pool is 5x + 3.
What is the width of the pool?

Answers

width 2x-5 hope this helped

Suppose you are given the graph of y = f (x) . Explain how to obtain the graphs of
a. y = f (x / 2)
b. y = f (x - 2)
c. y = f (2 x - 1)

Answers

Suggest you make yourself a list of transformations and their associated rules. The ones you're concerned with here are
.. f(x) ⇒ f(kx) . . . . . . horizontal compression by a factor of k
.. f(x) ⇒ f(x -k) . . . . . right shift by k units

a) Each point (x, y) gets moved to (2x, y). The graph is expanded horizontally by a factor of 2.

b) Each point (x, y) gets moved to (x+2, y). The graph is translated horizontally 2 units to the right.

c) Each point (x, y) gets moved to ((x +1)/2, y). The graph is translated horizontally 1 unit to the right, then compressed horizontally by a factor of 2.

Figure ABCD is rotated 90°counterclockwise about the origin. Which of the following gives the correct measure of an image of one of its sides?

B'C' = √17
C'D' = √10
D'D' = 5
A'B' = √17

Answers

the length of a side is: A'B' = sqrt (17)

What is the simplified form of (3 / x^3) / (1 / x^2) ?

Answers

The simplified form of (3/x^3) / (1/x^2) is 3/x

Bill takes a loan of 9,000.00 at a 8% simple interrst rate for 6 years a.how much interest will he pay after 2 years? b. how much interest will he pay in total for the loan

help plz

Answers

Final answer:

Bill will pay an interest of $1440 after 2 years and a total interest of $4320 over 6 years.

Explanation:

The subject of your question is related to simple interest calculation. The formula to calculate the simple interest is I = P * R * T, where I is the interest, P is the principal amount (initial loan), R is the annual interest rate in decimal form and T is time in years.

So when you ask 'how much interest will Bill pay after 2 years?', you plug in your values as follows: I = $9000 * 0.08 * 2 which calculates to $1440.

For the total interest Bill will pay over the 6 years, we substitute the values into the formula again but this time T = 6. So, I = $9000 * 0.08 * 6 which calculates to $4320.

Learn more about simple interest calculation here:

https://brainly.com/question/19903178

#SPJ12

Bill will pay $1,440.00 in interest after 2 years and a total of $4,320.00 in interest for the entire loan period of 6 years.

Simple interest can be calculated using the formula Interest = Principal × Rate × Time (I = PRT).

Part A: Interest After 2 Years

The principal amount is $9,000.00, the interest rate is 8%, and the time is 2 years.

Interest = 9,000 × 0.08 × 2 = 1,440

Bill will pay interest of $1,440.00 after two years.

Part B: Total Interest for the Loan

Again, using the same formula but for 6 years:

Interest = 9,000 × 0.08 × 6 = 4,320

Bill will pay a total of $4,320.00 in interest over the entire loan period.

MATH HELP PLEASE WILL GIVE BRAINLIEST!!!
This figure shows circle A with inscribed ∠RSQ .

m∠RSQ=24°

What is the measure of RSQ?

Answers

the measure of RSQ is 24 degrees

For a better understanding of the solution and the explanation given here please go through the diagram in the file attached.

By definition, measure of an arc is the angle subtended by the arc at the centre of the circle. Thus, the measure of the arc [tex] \overarc {RSQ} [/tex] is the measure of the [tex] \angle RAQ [/tex] (in red) which the arc [tex] \overarc {RSQ} [/tex] subtends at the center.

Now, in order to find the measure of the [tex] \angle RAQ [/tex] (in red) we will have to use the information given in the question. We have been told that [tex] m\angle RSQ=24^{\circ} [/tex]. Now, we know that the double angle theorem says that, the angle subtended at the centre of a circle is double the size of the angle subtended at the circumference from the same two points. Therefore, applying this theorem we get:

[tex] \angle RAQ =2\times 24^{\circ}=48^{\circ} [/tex]

Thus if [tex] \angle RAQ [/tex] (in red)=[tex] 48^{\circ} [/tex], then [tex] \angle RAQ [/tex] (in green) will be equal to measure of the arc [tex] \overarc {RSQ} [/tex]. Now, [tex] \angle RAQ [/tex] (in green) will obviously be:

[tex] \angle RAQ [/tex] (in green)=[tex] 360^{\circ}-\angle RAQ [/tex] (in red)

[tex] \angle RAQ [/tex] (in green)=[tex] 360^{\circ}-48^{\circ} [/tex]

[tex] \angle RAQ [/tex] (in green)=[tex] 312^{\circ} [/tex]

Thus, the measure of arc [tex] \overarc {RSQ} [/tex]=[tex] 312^{\circ} [/tex]

Tyler is 9 years old his sister Olivia is 6 years less than twice his age writ a numerical expression for Olivia’s age

Answers

Hello there!

The following will show you

T = tyler

O = olivia

O = 2t - 6

when you include numbers, it is represented by:

O = (2 * 9) - 6

Now, let's solve this to find out just how old Olivia is.

2 * 9 = 18

18 - 6 = 12

Olivia is 12

This means that olivia is 3 years older than tyler

I hope I helped!

~ Fire

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