An art exhibit is made by stacking three identical prisms on top of each other end-to-end so their smallest faces overlap. One of the prisms is shown here.

Find the surface area of the total exhibit.​

Step-by-step explanation:

Let the required number be x.

Therefore, according to the given condition:

[tex] {x}^{2} - 10 = 3x \\ \therefore \: {x}^{2} - 3x - 10 = 0 \\ \therefore \: {x}^{2} - 5x + 2x - 10 = 0 \\ \therefore \: x(x - 5) + 2(x - 5) = 0 \\ \therefore \: (x - 5)(x + 2) = 0 \\ \therefore \: x - 5 = 0 \: \: or \: \: x + 2 = 0 \\ \therefore \: x = 5 \: \: or \: \: x = - 2 \\ [/tex]

Therefore, x = - 2 is the negative solution.

Good morning ☕️

Answer:

Step-by-step explanation:

First ,we need to model the situation by expressing it as an equation

so, let x represent the uncknown negative number :

We get

x² - 10 = 3x

then

x² - 3x - 10 = 0

now using the quadratic formula:

Let Δ be the discriminant

Δ = b² - 4ac = (-3)² - 4(1)(-10) = 9 + 40 = 49 → √∆ = 7

Therefore

[tex]x = \frac{3+7}{2}=5 \\or\\x= \frac{3-7}{2}=-2[/tex]

_______________________________________

:)

Answer:

5.14

Step-by-step explanation:

[tex]3.7\times2.7[/tex]

Multiply the second numbers in both decimals to each other:

[tex].7\times.7=.14[/tex]

Now multiply the first numbers to each other:

[tex]3\times2=5[/tex]

[tex]=5.14[/tex]

Area of the figure is 42 in²

Step-by-step explanation:

⇒ Area of the rectangle = length × width = 6 × 5 = 30 in²

⇒ Area of the triangle = 1/2 × base × height = 1/2 × 4 × 6 = 12 in²

∴ Area of the figure = 30 + 12 = 42 in²

Answer:

12

Step-by-step explanation

4 designes of necklaces

in 3 different stones

4x3= 12 DIFFERENT DESIGHNES

Answer:

$6.03

Step-by-step explanation:

Let the amout Travis spent on pizza be reapresented as A.

Travis bought a sticker for $2.53,

Belt = $5.68

Pizza = ?

Total amount of money spent = $14.24

To get the amount spent on pizza , add up amount of everything he bought and equate them to total amount spent

That’s

$2.53 + $5.68 + A = $14.24

$8.21 + A = $14.24

Subtract $8.21 from both sides

$8.21 - $8.21 + A = $14.24 - $8.21

A = $6.03

Travis spent $6.03 on the pizza

Step-by-step explanation:

Question 5

y = - 3x

Question 6

[tex]y = \frac{50}{x} \\ [/tex]

Answer:

The expression showing how many more meters Mathieu ran than Edgar ran during that time is  [tex]t(m-e)[/tex].

Step-by-step explanation:

Edgar ran 'e' meters per second, and Mathieu ran 'm' meters per second. The boys ran for 't' seconds.

The expression [tex]t(m-e)[/tex] describes how many more meters Mathieu ran than Edgar ran during that time.

We can also use the expression [tex]tm-te[/tex] represent the same quantity.

We know that,

[tex]\text{Distance} =\text{Speed}\times \text{Time}[/tex]

Distance covered by Edgar = te

Distance covered by Mathieu = tm

Difference in distance [tex]d= tm - te=t(m-e)[/tex]

The expression showing how many more meters Mathieu ran than Edgar ran during that time is  [tex]t(m-e)[/tex].

Answer:

X would have to equal 6. To work it out, you subtract 4 from each side to cancel out the 4. -x = -6. You have to make -x just x so you × each side by -1. You get x = 6.

Step-by-step explanation:

[tex]4 - x = - 2 \\ - x = - 2 - 4 \\ - x = - 6 \\ x = 6 [/tex]

Answer: Graph C

Step-by-step explanation:

Answer:

Option A -280 feet

Step-by-step explanation:

Let

x ----> the lowest elevation in Long Beach, California in feet

y ----> the approximate elevation of Death Valley in feet

Remember that

An elevation below the sea level is negative and above the sea level is positive (The sea level is the level zero)

we know that

The lowest elevation in Long Beach, California, is 7 feet below sea level

so

[tex]x=-7\ ft[/tex]

The elevation  of Death Valley is about 40 times lower than the elevation of Long Beach.

so

[tex]y=40x[/tex]

substitute the value of x

[tex]y=40(-7)=-280\ ft[/tex]

therefore

The approximate elevation of Death Valley is about 280 feet below the sea level

Answer:

1056.25 pi

Step-by-step explanation:

f the circumference of the circle is 65\pi, then the diameter is 65. If the diameter is 65, the radius is \frac{1}{2} * 65, and then you would do 32.5^2 * \pi, which would equal

Answer:

A =1056.25 pi

Step-by-step explanation:

The circumference is given by

C = 2*pi*r

65 pi = 2*pi*r

Divide each side by 2 pi

65 pi /2 pi = 2*pi*r/2pi

32.5 = r

To find the area

A = pi * r^2

A = pi *(32.5)^2

A =1056.25 pi

Answer:

The answer is 25

Step-by-step explanation:

you move the decimal back one place.

Hey there!

Our goal is to create the slope intercept equation for line W, which requires two things that we need to find out: the slope and the y-intercept.

We see that Line W is parallel to line V. Therefore, they have the same slope. So, the slope of Line W is 10/7.

Now, we need to find the y-intercept. To do this, we will plug the slope and the point we are given into the slope intercept equation and solve for b.

-3= 10/7(-3)+b

-3= -4 2/7+b

b=1 2/7

Now, we plug this into our final slope intercept form.

y=10/7x+1 2/7

I hope this helps! Have a great day!

The probability of not drawing an I is the number of non-I letters divided by the total number of letters, which is 7/11.

The word MISSISSIPPI has a total of 11 letters, with the following distribution: 4 I's, 4 S's, 2 P's, and 1 M. To find the theoretical probability of NOT drawing an I, we need to consider all the other letters that could be drawn instead. There are 11 - 4 = 7 letters that are not Is. Therefore, the probability of not drawing an I is the number of non-I letters divided by the total number of letters, which is 7/11.

Answer:

$2.5

Step-by-step explanation:

The amount saved is 10% of $25

That’s

10% /100% x $25

0.1 x $25

$2.5

Amount saved is $2.5

Answer: y = 3/2x+4 if you need to write it in slope intercept form and please give brainliest i will appreciate it.

Final answer:

The ratio of the surface areas of the two cubes with a linear scale factor of 4:1 is 16:1, because surface area is proportional to the square of the scale factor.

Explanation:

When working with scale factors in geometry, and specifically with cubes, the ratio of scale factors for linear dimensions affects the surface area and volume in specific ways. If two cubes have a scale factor of 4:1, the ratio of their surface areas is the square of the scale factor. Since the scale factor for the linear dimensions is 4, the ratio of the surface areas will be 42:12, or 16:1.

The surface area of a cube is calculated by multiplying the area of one face (length x width) by 6, as a cube has 6 faces. If one cube has a side four times as long as the other, each of its faces will be 42 times larger because area is a two-dimensional measurement. Thus, the surface area of the larger cube will be 16 times greater than that of the smaller cube, hence the ratio 16:1.

Step-by-step explanation:

Nicole starts with the budget:

$395

Now, she only expects to pay half the deposit;

$72 ÷ 2 = $36

Subtract this from the budget:

$395 - $36 = $359

Divide by cost per hour:

$359 ÷ $60 = 5.983333... (3 repeating)

This means, Nicole can rent a maximum of 5 hours with her budget. The inequality would be

[tex]x \leqslant 5[/tex]

Jessica's rate could be any rate greater than 0.1765 tiles per minute.

To determine Jessica's rate, we first find Meg's rate by dividing the number of tiles laid by the time taken: [tex]\(Rate_{\text{Meg}} = \frac{15 \, \text{tiles}}{50 \, \text{minutes}} = 0.3 \, \text{tiles per minute}\).[/tex] Since Jessica works at a faster rate per tile than Meg, her rate is greater than 0.3 tiles per minute. To calculate the minimum rate Jessica could have, we consider the case where she completes one tile in 85 minutes: [tex]\(Rate_{\text{Jessica}} = \frac{1 \, \text{tile}}{85 \, \text{minutes}} \approx 0.0118 \, \text{tiles per minute}\)[/tex]. Therefore, Jessica's rate could be any value greater than 0.0118tiles per minute.

The rate Jessica could have falls within the range of 0.0118 to 0.3 tiles per minute, as she is working at a faster rate than Meg. The provided answer, 0.1765 tiles per minute, is within this range. Jessica's rate per tile is not limited to any specific value, but it must be greater than Meg's rate of 0.3 tiles per minute. In summary, Jessica could work at any rate greater than 0.0118 tiles per minute, making 0.1765 tiles per minute a valid option.

Answer:

You are right! The answer is c.

Step-by-step explanation:

"Then I will need an average quality score of 3.28  to meet 85.28 goal."

Step-by-step explanation:

⇒ (4/100)[tex]\times[/tex]82

⇒ 82/25

⇒ 3.28

The improved average quality score = 82+3.28 = 85.28

The employee needs an average quality score of 3.28 to meet the goal of 85.28

Solution:

Given that,

Amanda answered all the questions on her math test but got 10 answers wrong

She received 4 points for every correct answer, and there were no points for wrong answers

Find the number of questions answered correctly:

Her final score was 76 points

4 points for every correct answer

Thus,

[tex]correct\ answers = \frac{76}{4} = 19[/tex]

From given.

Incorrect answers = 10

Let "x" be the total number of questions on his math test

Then,

x = correct answered questions + incorrect answered questions

x = 19 + 10

x = 29

Thus there are 29 total number of questions on his math test

Amanda's test had 29 questions in total.

Amanda answered all the questions on her math test but got 10 answers wrong. She received 4 points for every correct answer, with no points for wrong answers, and her final score was 76 points.

Step-by-Step Solution

1. Let q represent the total number of questions on the test.

2. The number of correct answers Amanda got is (q - 10).

3. Amanda's score for correct answers can be represented as 4 × (q - 10).

4. According to the problem, her score was 76 points, so we can set up the equation: 4 × (q - 10) = 76.

5. Simplify and solve for q:
4q - 40 = 76
4q = 116
q = 29

Therefore, the total number of questions on Amanda's math test is 29.

Answer:

Step-by-step explanation:

16.) 2/3

You add up the fractions and then reduce.

(5/12 + 3/12 = 8/12 = 2/3)

17.) No because if you add all the fractions together, you only get 7/8. This means the project is not complete yet.

x = 45°

Solution:

Given data:

Measure of larger arc = 152°

Measure of smaller arc = 62°

If a tangent and a secant intersect at the exterior of a circle then the measure of angle formed is one-half the positive difference of the measures of the intercepted arcs.

[tex]$\Rightarrow x = \frac{1}{2}(\text{ larger arc }- \text{smaller arc} )[/tex]

[tex]$\Rightarrow x = \frac{1}{2}(152^\circ-62^\circ)[/tex]

[tex]$\Rightarrow x = \frac{1}{2}(90^\circ)[/tex]

⇒ x = 45°

The value of x is 45°.

Answer:

45

Step-by-step explanation:

Answer:

187.2

Step-by-step explanation:

just multiply everything

Answer:

a b c d e f g the jgh hgghg

Step-by-step explanation:

Final answer:

Provides equations to find the area and width of a rectangular deck based on given information.

Explanation:

a. Let the width of the deck be w. The length is given as 6 feet more than 2 times the width, which translates to 2w + 6. The area of a rectangle is length multiplied by width, so for this case, the equation expressing the area in terms of the width is w(2w + 6) = 80.

b. By solving the equation w(2w + 6) = 80, we find the width of the deck to be 10 feet.

Answer:

4 mph

Step-by-step explanation:

Givens

Current = c = 2 mph

Alberta = r = ?

d = 2 mph upstream

d1 = 6 mph downstream

Formula

d = r * t

The time is the same so the formula becomes d/r = t

2/(r  - 2) = 6/(r + 2)    

Solution

Cross Multiply

2*(r + 2) = 6*(r - 2)

2r + 4 = 6r - 12                      Subtract 2r from both sides

4 = 6r - 2r - 12                       Combine the right.

4 = 4r - 12                             Add 12 to both sides.

4 + 12 = 4r

16 = 4r                                  Divide by 4

16/4 = 4r/4

r = 4

Answer:

13

Step-by-step explanation:

If you use the square root method, p^2 becomes p and 169 becomes 13.

Answer:

13

Step-by-step explanation:

The equation is basically

And 13x13 equals 169 so its 13

Answer:

The answer to 36 is -18

Step-by-step explanation:

x=-18 because 3×(-6)=(-6×-6) cancels

The surface area is the area of all the faces of the solid.

So, it is composed by the two triangles (front and rear) and the two lateral rectangles.

The triangles have base 12 and height 8 (both given), so their area is

[tex]A_t=\dfrac{12\cdot 8}{2}=12\cdot 4=48[/tex]

The rectangles have base 14 and height 10 (both given), so their area is

[tex]A_r=14\cdot 10=140[/tex]

Finally, there's a base rectangle with dimensions 14 and 12, which has area

[tex]A_b = 14\cdot 12 = 168[/tex]

The surface area is made of two lateral rectangles, one base rectangle and two triangles, so it is

[tex]S=2A_r+2A_t+A_b=96+280+168=544[/tex]

Answer: 544

Step-by-step explanation: