Mrs. Karabin wants to paint the inside of her brand new two-car garage. The garage is 20 feet wide, 24 feet long, and 12 feet tall. She wants to paint the walls and the ceiling (not the floor). What’s the surface area of the parts she wants to paint?

The correct option is C.

In an isosceles triangle ABC with base angles A and the sides b and c equal, you can use the Law of Cosines to find the length of the other side (a) in terms of b and c. The Law of Cosines is given by:

[tex]\[a^2 = b^2 + c^2 - 2bc \cos(A)\][/tex]

Given that A = π/4, b = c = 4, you can substitute these values into the equation:

[tex]\[a^2 = 4^2 + 4^2 - 2 \cdot 4 \cdot 4 \cos\left(\frac{\pi}{4}\right)\][/tex]

Simplify the expression:

[tex]\[a^2 = 16 + 16 - 32 \cos\left(\frac{\pi}{4}\right)\][/tex]

Now, you know that [tex]\(\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\)[/tex], so substitute that in:

[tex]\[a^2 = 16 + 16 - 32 \cdot \frac{\sqrt{2}}{2}\][/tex]

[tex]\[a^2 = 32 - 16\sqrt{2}\][/tex]

Now, factor out 16 from the expression:

[tex]\[a^2 = 16(2 - \sqrt{2})\][/tex]

So, the correct answer is:

[tex]\[a^2 = 4^2(2 - \sqrt{2})\][/tex]

Complete the question:

Suppose an isosceles triangle ABC has A= π /4 and b=c=4. What is the length of a^2 ？ A. 4^2sqrt(2) B. 4^2(sqrt(2)-2) C. 4^2(2-sqrt(2)) D. 4^2(2+sqrt(2))

Final answer:

By applying the Pythagorean theorem to the 45-45-90 isosceles triangle, we find that since both the sides a and b are 4, the square of side a is a² = 16.

Explanation:

In the context of an isosceles triangle with sides labeled a, b, and c, where side a is opposite angle A and side b equals side c, we can utilize the Pythagorean theorem to find the length of side a given that it's a right triangle. The Pythagorean theorem states:

a² + b² = c².

Given that angle A = π/4 radians (45 degrees), it implies that triangle ABC is a 45-45-90 right triangle, which tells us that sides a and b are equivalent in length. Under these conditions, the Pythagorean theorem simplifies to:

2a² = c².

We're given that b = 4, accordingly a would also be 4 (since a=b in an isosceles right triangle), and we're asked to find the length of a². Squaring side a, we get:

a² = 4² = 16.

Therefore, the length of a² is 16.

Answer:

2√3

Step-by-step explanation:

√2^2x3

√2^2 √3

2√3 (answer)

Answer:

[tex]\large\boxed{\sqrt{12}=2\sqrt3\approx3.46}[/tex]

Step-by-step explanation:

[tex]\sqrt{12}=\sqrt{4\cdot3}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt3=2\sqrt3\\\\\text{If you want to get an approximate value, use the calculator:}\\\\\sqrt{12}\approx3.46[/tex]

Answer:

60√5

Step-by-step explanation:

(5√5)(6√4)

= (5√5)(12)

= 60√5

The answer is the fourth choice , I think

The symbol for congruent in mathematics is ≅. It signals that two figures have the same shape and size, and is vital in ensuring dimensional consistency in equations, analogous to ensuring that measurements are directly comparable.

The mathematical symbol for congruent is ≅. This symbol is used to denote that two figures are of the same size and shape. When dealing with equations, it is important that both sides of the equation have the same dimensions, meaning they can be directly compared or equated. For instance, you cannot sensibly add two quantities of different dimensions, similar to the saying "You can't add apples and oranges". In geometry, congruent figures are identical in form and dimension, just as measurements must be commensurate within equations to maintain dimensional consistency.

Another important concept in mathematics and physics is dimensional analysis, where different physical quantities are expressed with respect to their basic unit dimensions, such as length (L), mass (M), and time (T). Comparing measurements of different units also falls under this analysis. To indicate two measurements are related but not necessarily the same, we can use inequality symbols or symbols like ≈ (approximately) when numbers are close in value but not exactly equal.

[tex]s = \frac{a + b}{2} \times h[/tex]

S = (19+23)/2×14

S = 42/2×14

S = 21×14

S = 294 cm^2

Answer294

Step-by-step explanation:

Answer:

x>-3 is the answer hope it helps

Answer:

4 or up

Step-by-step explanation:

Answer:

The series is 5 , 6 , 7 , 8 , 9 , 10 , 11

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between

 each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….  (constant difference is 3)

# 5  ,  10  ,  15  ,  20  ,  …………………………  (constant difference is 5)

# 12  ,  10  ,  8  ,  6  ,  ……………………………  (constant difference is -2)

* General term (nth term) of an Arithmetic series:

- If the first term is a and the common diffidence is d, then

 U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- So the nth term is Un = a + (n – 1)d, where n is the position of the

 number in the series

* Lets solve the problem

- Jeff wants to increase the number of miles he runs each day

∴ He will add the initial value by constant number each day

- He plans on increasing the number of miles he runs a day by 1

∴ The constant value is 1 mile

-  On the first day of training, Jeff runs 5 miles

∴ The first value is 5 miles

∴ The series is arithmetic

∵ a = 5 , d = 1

- He do that for the remainder of the week

∵ The week has 7 days

∴ The series has 7 terms

∵ The rule of the series is Un = a + (n - 1)d

∵ a = 5 and d = 1

∴ Un = 5 + (n - 1)(1)

∴ Un = 5 + n - 1

∴ Un = 4 + n ⇒ n is the position of the number

- Substitute n from 1 to 7 to find the series

∴ The series is 5 , 6 , 7 , 8 , 9 , 10 , 11

Answer:

the next answer is arithmetic, and then 56 miles

Step-by-step explanation:

I just did on edge :)

d ≅ 272ft. A car that is traveling at 70mph it will stop 272ft after the brakes are applied.

The key to solve this problem is using the equation d = k(r²), where d is the distance after the brakes are applied, k is the desaceleration constant and r is the speed of the car.

In order to maintain the consistency of the units, we have to convert mph to ft/s using the equation ft/s = mph x 1.467.

30mph x 1.467 ≅ 44ft/s

We know the speed of the car and the distance travelled after brakes are applied. The, clear k for the equation d = k(r²)

k = d/(r²)

Solving with d = 50ft and r = 44 ft/s

k = 50ft/(44ft/s)²= 0.0258 s²/ft

Then, is the same car now is traveling at 70mph, how many feet will it take to stop?

Convert 70mph to ft/s

70mph x 1.467 = 102.69ft/s

Using the equation d = k(r²), where k = 0.0258 s²/ft and r = 102.69ft/s

d = 0.0258s²/ft[(102.69ft/s)²] = 272.06ft

Answer:

It was first used as “centi” by the French, who introduced the measurement when they created the metric system. When used as centi, it is defined as one-hundredth of a unit. Thus, a meter is 100 cm, or a centimeter is one-hundredth of a meter.

Step-by-step explanation:

Answer:

c. 28 liters

Step-by-step explanation:

Given tha tJanet is mixing a 15% glucose solution with a 35% glucose solution. This mixture produces 35 liters of a 19% glucose solution. Now we need to find about how many liters of the 15% solution is Januet using in the mixture.

Let the number of liters of the 15% solution is Januet using in the mixture = x

Let the number of liters of the 35% solution is Januet using in the mixture = y

Then we get equations:

x+y=35...(i)

and

(15% of x) + (35% of y) = 19% of 35.

or

0.15x+0.35y=0.19(35)

15x+35y=19(35)

3x+7y=19(7)

3x+7y=133 ...(ii)

solve (i) for x

x+y=35

x=35-y...(iii)

Plug (iii) into (ii)

3x+7y=133

3(35-y)+7y=133

105-3y+7y=133

105+4y=133

4y=133-105

4y=28

y=28/4

y=7

plug y=7 into (iii)

x=35-y=35-7=28

Hence final answer is c. 28 liters

Answer: C on edge:)

Step-by-step explanation:

ANSWER

[tex]a = - 7[/tex]

[tex]b = 1[/tex]

[tex]c = 4[/tex]

EXPLANATION

The given quadratic equation is:

[tex]0 = 4 - 7 {x}^{2} + x[/tex]

We rewrite in the standard quadratic equation form to obtain,

[tex] - 7 {x}^{2} + x + 4 = 0[/tex]

Comparing this to the general standard quadratic equation.

[tex]a {x}^{2} + bx + c = 0[/tex]

We have my

[tex]a = - 7[/tex]

[tex]b = 1[/tex]

[tex]c = 4[/tex]

Quadratic equations can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

The coefficients are a = -7, b = 1 and constant term c = 4.

The given quadratic equation is;

[tex]\rm -7x^2+x+4=0[/tex]

Quadratic equations can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

The general form of the quadratic equation is;

[tex]\rm ax^2+ bx + c = 0[/tex]

Where x is an unknown variable and a, b, c are numerical coefficients.

On comparing the given equation with the quadratic equation the values of coefficient and constant terms are;

[tex]\rm ax^2+ bx + c = 0[/tex]

[tex]\rm -7x^2+x+4=0[/tex]

Here, a = -7, b = 1, c = 4

Hence, the coefficients are a = -7, b = 1 and constant term c = 4.

To know more about the Quadratic equation click the link given below.

https://brainly.com/question/11443935

Answer:

$101.99

Step-by-step explanation:

She doesn't go over her 200 free miles.

If she drives 155 miles, then the amount she need to pay for the rental is:

                          $ 101.99

She got a special weekend rental deal for $101.99, with 200 free miles.

and $0.32 per mile after.

This means that for any mile covered less than or equal to 200 she just need to pay $ 101.99.

If she drives 155 miles, which is less than 200 miles then the amount she need to pay as a rent is:

             $ 101.99

Answer:

Option D is correct.

Step-by-step explanation:

We are given [tex]\sqrt[5]{x^7}[/tex]

We know that[tex]\sqrt[5]{x} = x^\frac{1}{5}[/tex]

and we are given:

[tex]\sqrt[5]{x^7}\\ We\,\, can\,\, write\,\, as\,\,\\x^\frac{7}{5}[/tex]

So, Option D is correct.

Answer: There is 40% of team's win that Ryan score a goal.

Step-by-step explanation:

Since we have given that

                              Team Won   Team lost

Ryan scored               6                   4

Did not score             9                   11

(by Ryan)

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

Total                          15                    15

Percentage of team's win that Ryan score a goal is given by

[tex]\dfrac{6}{15}\times 100\\\\=40\%[/tex]

Hence, there is 40% of team's win that Ryan score a goal.

Answer:

40%

Step-by-step explanation:

because I said so.

Answer:

3 -1 > 1/4

Step-by-step explanation:

On the left hand side we have the expression;

3 - 1

3- 1 = 2

On the right hand side we have the value;

1/4

Therefore we are comparing 2 and 1/4

Since 2 is greater than 1/4 we have;

2 > 1/4

3 -1 > 1/4

The answers are:

Question 7:

154.29°

Question 8:

Yes, because the opposite sides are congruent.

For question 7:

We know that the sum of all interior angles of any polygon is determined by the following formula:

[tex]Angles=180*(sides-2)[/tex]

Therefore the sum of all interior angles of a 14-gon is equal to 2160°, so, the measure of each interior angle is given by the following calculation:

[tex]14-gon=(14-2)*180\°=2160\°[/tex]

Each interior angle is equal to:

[tex]\frac{2160\°}{12}=154.29\°[/tex]

For question 8:

We know that a quadrilateral is a parallelogram when the opposite sides are parallel or congruent.

From the statement we know that:

BE≅ED

and

AE≅EC

So, we can assume that the triangles formed by the sides BE and AE, and the sides EC and ED, are also congruent, meaning that the opposite sides BA and CD are congruent, so, the quadrilateral is a parallelogram.

Have a nice day!

-Hello There-

Great Question!

It is 20%. Assume Josh is 100000 and Jeff is 125000

The formula is  (Jeff-  Josh)/Jeff * 100 = (25000)/100000 *100 = 20%

Have A Great Day!

Hundred (100) means the 3rd number from the right, which is: 249,982 . So use the number before that (further to the right) to determine whether you will round up or stay the same, which is 249,982

The number before the hundreds spot (8) is greater then 5, therefore we will round the number in the hundreds spot up 1

Since the number above 9 is 10 you will have to round the number in the thousands spot up as well

249,982

And it looks like the number in the thousands spot is 9 and the next number up is 10. This means you will have to round the number in the ten thousands place up 1

249,982

so...

250,000

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

250000

Step-by-step explanation:

hundred thousand  ten thousand  thousand, hundred  ten one

 2                                  4                     9           , 9               8   2

We are rounding to the nearest hundred, so we look at the tens place

8 ≥5 so we round the hundreds place up

9 will round to 10 so the thousands place gets one bigger and the hundreds place is a zero

9 will become to 10 so the ten thousands place gets one bigger at 5 and the thousands place is a zero

249,982 becomes 250,000

Answer:

Step-by-step explanation:

die rolled and coin flipped

Jacob wins if tail and even number

Amanda wins if head

Outcomes,

1H 2H 3H 4H 5H 6H

1T 2T 3T 4T 5T 6T

12 outcomes.

b) Prob of Jacob winning (tail and even number)

2T 4T 6T

3/12 total outcomes

1/4 probability

c) prob of Amanda winning (head)

6/12

1/2

d) the game is not far because both people do not have equal chances of winning

e) Yes, Tail and odd is where the outcome is not decided.

There are 12 different outcomes. The probability that Jacob wins is 1/4, and the probability that Amanda wins is 1/2. The game is not fair. There are no outcomes where the game is not decided.

To find the number of different outcomes, we need to multiply the number of outcomes for flipping the coin and rolling the die. For flipping a coin, there are 2 possible outcomes (H or T), and for rolling a 6-sided die, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6). Therefore, the total number of different outcomes is 2 * 6 = 12.

To find the probability that Jacob wins, we need to find the number of favorable outcomes for Jacob (tail and even number) divided by the total number of outcomes. There are 3 favorable outcomes (T2, T4, T6) out of 12 total outcomes, so the probability is 3/12 = 1/4.

To find the probability that Amanda wins, we need to find the number of favorable outcomes for Amanda (head) divided by the total number of outcomes. There are 6 favorable outcomes (H1, H2, H3, H4, H5, H6) out of 12 total outcomes, so the probability is 6/12 = 1/2.

The game is fair if the probabilities of winning for Jacob and Amanda are equal. Since the probabilities are different (1/4 for Jacob and 1/2 for Amanda), the game is not fair.

There are no outcomes where the game is not decided since there is always a tail or a head flipped and a number rolled on the die, resulting in a win for one of the players.

Answer:

Step-by-step explanation:

5 sides of the top cube is exposed.

so we get 1*1*5 = 5 in ^2

the second cube has 4 sides exposed also, so 2^2 * 4 = 16 in ^2, but also it has one side with the cube on top, so we have 4-1 = 3 on that side, so the overall is 19 in ^2

Then we have for the 3rd cube 5 sides exposed, so we have 3^2 * 5 = 45. We also have the area of the 2 in cube on it, so we get 3^2 - 2^2 = 9-4 =5.

So the overall is 45+5+19+5 = 55+19 =74

I hope im right sorry if im not!

The surface area of the three cube tower is 71 square inches.

Calculating the Surface Area of a Three Cube Tower

To find the surface area of the three cube tower, we need to carefully consider how the cubes are stacked and which faces are exposed.

Calculate the surface area of each individual cube:

Each face is 3x3 = 9 sq. inches. Since a cube has six faces, the total surface area is 6 x 9 = 54 sq. inches.

    2. For the 2-inch cube:

       Each face is 2x2 = 4 sq. inches. The surface area is 6 x 4 = 24 sq. inches.

    3. For the 1-inch cube:

        Each face is 1x1 = 1 sq. inch. The surface area is 6 x 1 = 6 sq. inches.

Consider overlapping faces between stacked cubes:

Combine the visible surface areas:

Therefore, the surface area of the three cube tower is 71 square inches.

Answer:

[tex]-\frac{7}{3}[/tex]

Step-by-step explanation:

To solve this, we are using the average rate of change formula:

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

where

[tex]m[/tex] is the average rate of change

[tex]a[/tex] is the first point

[tex]b[/tex] is the second point

[tex]f(a)[/tex] is the function evaluated at the first point

[tex]f(b)[/tex] is the function evaluated at the second point

We want to know the average rate of change of the function [tex]f(x)=0.5^x-6[/tex] form x = -3 to x = 0, so our first point is -3 and our second point is 0. In other words, [tex]a=-3[/tex] and [tex]b=0[/tex].

Replacing values

[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]

[tex]m=\frac{0.5^0-6-(0.5^{-3}-6)}{0-(-3)}[/tex]

[tex]m=\frac{1-6-(8-6)}{3}[/tex]

[tex]m=\frac{-5-(2)}{3}[/tex]

[tex]m=\frac{-5-2}{3}[/tex]

[tex]m=\frac{-7}{3}[/tex]

[tex]m=-\frac{7}{3}[/tex]

We can conclude that the average rate of change of the exponential equation form x = -3 to x = 0 is [tex]-\frac{7}{3}[/tex]

Final answer:

Two congruent supplementary angles both measure 90 degrees each. The equation representing their measures is 2d = 180, where d stands for the degree measure of each angle.

Explanation:

If two supplementary angles are congruent, this means that they have the same measure. Supplementary angles add up to 180 degrees. Given that we have two congruent angles, let's name the measure of each angle as d. Therefore, the equation we are looking for will add the two angles together to equal 180 degrees.

The equation that gives the measure of each angle in degrees is:

d + d = 180

Since we have two of the same angles, we can simplify this to:

2d = 180

By dividing both sides of the equation by 2, we find that:

d = 90

Therefore, the measure of each congruent supplementary angle is 90 degrees.

Answer:

Step-by-step explanation:

From first piece -6 < x ≤ 0.

From second piece 0 < x ≤ 4.

Therefore -6 < x ≤ 4 → x ∈ (-6, 4]

-7 ∉ (-6, 4]

-6 ∉ (-6, 4]

4 ∈ (-6, 4]

5 ∉ (-6, 4]

Answer:

p = 80- 64 = 16

p = 16

Step-by-step explanation:

That's is the answer

Nandini needs to score at least 17 points to win.

To represent the number of points Nandini needs to win the game, we can use the inequality:

[tex]\( p > 80 - 64 \)[/tex]

Now, let's solve this:

[tex]\( p > 16 \)[/tex]

Therefore, Nandini needs more than 16 points to win the game.

Explanation:

1. Nandini needs more than 80 points to win the game, which means her total score should exceed 80 points.

2. She currently has 64 points, so to find out how many more points she needs, we subtract her current score from the total required points: \( 80 - 64 = 16 \).

3. Hence, the inequality representing the number of points she needs, denoted by \( p \), is \( p > 16 \), indicating that she needs more than 16 points to win the game.

This means Nandini needs to score at least 17 points to win.

Complete question:

Nandini needs more than 80 points to win a game. She has 64 points so far. which inequality represents p, the number of points she needs to win the game

Answer:

Step-by-step explanation:

[tex]|4r-2|>8\iff4r-2>8\ \vee\ 4r-2<-8\qquad\text{add 2 to both sides}\\\\4r>10\ \vee\ 4r<-6\qquad\text{divide both sides by 4}\\\\r>\dfrac{10}{4}\ \vee\ r<\dfrac{-6}{4}\\\\r>\dfrac{5}{2}\ \vee\ r<-\dfrac{3}{2}\\\\r>2.5\ \vee\ r<-1.5[/tex]

<, > - open circle

≤, ≥ - closed circle

<, ≤ - line to the left

>, ≥ - line to the right

Equation A is linear and equation B is nonlinear

Answer:

Equation A is linear and equaiton B is nonlinear

Step-by-step explanation:

Equation A respresents a straight line with a x-intercept of x=-3/2 and a y-intercept of y = -2. This equation is linear because it is a first degree polynomical equation with x^1 = x

Equation A is not a linear equation and is written as :

[tex]y=3/(x+5)[/tex]  

This is a rational function but it is not linear because x is in the denominator and not numerator.

Answer:

V-678.58

Step-by-step explanation:

it is volume so it is 678.58

For this case we have that by definition, the volume of a cone is given by:

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

We have by the statement of the problem that:

[tex]r = 9 \ units\\h = 8 \ units[/tex]

Substituting:

[tex]V = \frac {1} {3} \pi * r ^2 * h\\V = \frac {1} {3} \pi * 9 ^ 2 * 8\\V = \frac {1} {3} \pi * 81 * 8\\V = \frac {1} {3} \pi * 648\\V = 216 \pi[/tex]

Answer:

[tex]216 \pi \ units ^ 3[/tex]

Answer:

C. $199.84

Step-by-step explanation:

The price of an upholstery fabric is $ 12.49 per yard.

This means that 1 yard costs $ 12.49

Now we want to find the cost of 16 yards of the upholstery fabric.

We just have to multiply $12.49 by 16.

We multiply to obtain:

[tex]12.49\times 16=199.84[/tex]

Therefore 16 yards will cost $ 199.84

The correct answer is C.

Answer:

The sum is [tex]S=\frac{16}{5}=3.2[/tex]

Step-by-step explanation:

To find the sum of the infinite geometric series we must first find the common ratio r.

The series is:

4-1 + 1 / 4-1 / 16 +

[tex]r =\frac{a_{n+1}}{a_n}[/tex]

[tex]r=\frac{-1}{4}=-\frac{1}{4}\\\\r=\frac{\frac{1}{4}}{-1}=-\frac{1}{4}[/tex]

Then the common ratio r is

[tex]r=-\frac{1}{4}[/tex]

The first term is: [tex]a_1=4[/tex]

By definition when [tex]0 <| r | <1[/tex] then the sum of the infinite sequence is:

[tex]S=\frac{a_1}{1-r}\\\\S=\frac{4}{1-(-\frac{1}{4})}\\\\S=\frac{4}{\frac{5}{4}}\\\\S=\frac{16}{5}[/tex]

Answer:

12

Step-by-step explanation:

Hi

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