A triangular prism is 18 centimeters long and has a triangular face with a base of 12 centimeters and a height of 8 centimeters. The other two sides of the triangle are each 10 centimeters.
What is the surface area of the triangular prism?

186 cm³ will be the surface area of the given figure.

To calculate the surface area of the given figure, we need to add the surface area of two cubes and reduce the area of the hidden part.

Thus,

Total surface area = Surface area of bigger cube + surface area of the smaller cube - 2* surface area of the hidden part.

So,

Total surface area = 6*(5*5)+6*(3*3)-2*(3*3)

Total surface area = 150+54-18

Total surface area = 186

Therefore, the surface area of the given figure will be 186 cm³.

Learn more about the Surface area here:

https://brainly.com/question/29298005

#SPJ1

Few families can survive on a single salary is true statement

Many families rely on dual incomes to make ends meet, especially in areas with high living costs.

However, there are still many families that rely on a single salary to support themselves.

While it may be challenging to make ends meet on a single salary, it is still possible for families to survive and even thrive in these circumstances.

To learn more on Salary click:

https://brainly.com/question/14371457

#SPJ1

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

For more questions on trigonometric form

https://brainly.com/question/31744474

#SPJ8

Answer:

what do you mean by equation

Step-by-step explanation:

i was able to get you the slope form of it if thats okay

y=2x-2 in order to find the slope use the pdf i attached it should provide an example

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

Know more about numerator here:

https://brainly.com/question/1217611

#SPJ8

1. Hence, after 5 years, there are roughly 113,500 white-sided "jackrabbits" and 157,700 black-tailed "jackrabbits" living in North America.

2. Yard will be left over after the pool is built 29.48

A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and consists of variables (also known as indeterminates) and coefficients. Variables can be present in polynomials, which can be expressed in the following way: \(a 2x2 + a 1x + a 0 + a nxn + a n-1xn-1 +\)..  where x is the variable, and the coefficients are a n, a n-1,..., a 2, a 1, a 0. The highest exponent of the variable in an expression is the polynomial's degree. For instance, the polynomial \(3x2 + 2x - 1\)has a degree of 2 since the largest exponent of x is 2. Calculus, algebra, and geometry are just a few of the mathematical disciplines where polynomials are employed.

given,

We can enter x = 5 into the corresponding polynomials to determine the population of white-sided "jackrabbits" and black-tailed "jackrabbits" over a 5-year period.

Regarding white-sided "jackrabbits":

\(8.7(5) + 5.9 - 6.5(5)2 = 113.5\) thousand

For jackrabbits with black tails:

157.7 thousand is equal to \(6.5(5)2 + 9.2(5) + 1.2.\)

Hence, after 5 years, there are roughly 113,500 white-sided "jackrabbits" and 157,700 black-tailed "jackrabbits" living in North America.

The backyard's size is 8 x 7 x 56 x 2.

The pool's surface area is:

\(\pi (3x)^{2} =9\pi x^{2}\)

Following the construction of the pool, the remaining yard space is:

\(56x^{2} -9\pi x^{2}\)\(=14.74x^{2}\)

Consequently, 14.74x2 of the yard will remain after the pool is constructed.

To know more about "jackrabbits" visit:

brainly.com/question/28857051

#SPJ1

Answer:

= 4.32 × 10^6

(scientific notation)

= 4.32e6

(scientific e notation)

= 4.32 × 10^6

(engineering notation)

(million; prefix mega- (M))

= 4320000

(real number)

Hence number using scientific notation is 4.32*\(10^{6}\)

When a number between 1 and 10 is multiplied by a power of 10, it is written in scientific notation. 650,000,000, for example, can be expressed as 6.5 108 in scientific notation. Sal Khan and the CK-12 Foundation collaborated on this project.

Given   4,320,000 which can be broken in 432*10000

Which can be written as 432*\(10^{4}\)

432 can be written as 4.32*100*\(10^{4}\)=4.32*\(10^{6}\)

Hence number using scientific notation is 4.32*\(10^{6}\)

Learn more about scientific notationhttps://brainly.com/question/1767229

#SPJ2

Answer:

C

Step-by-step explanation:

x-3≠0

x≠3

so C

Answer:

it is C

Step-by-step explanation:

i just took the test

Answer:it might be 3

Step-by-step explanation:

due to someone getting 5sec wrong me getting 2 wrong another post with only three stars said 4 so did leave it to 4 or 3.

By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

For more such questions on graph

https://brainly.com/question/19040584

#SPJ8

The best description of range is (b) The y-values on a graph.

A graph is characterized by the following concepts:

The domain of a function is the set of input values of the graph

On the other hand, the range of a function is the set of output values of the graph

This in other word means that the range is the y-values on a graph.

Hence, the best description of range is (b) The y-values on a graph.

Read more about range at

https://brainly.com/question/2264373

#SPJ1

Answer:

its B

Step-by-step explanation:

the y values on the graph

i did the quiz and got a 100

Hello

Step-by-step explanation:

hello I'm Filipino people

I can only help you with the first one, because I'm new to geometry, but here it is:

Area: 91cm

Perimeter: 136cm You need to add all the side measures together.

Circumference: It isn't possible to find circumference unless it is a circular shape. So there is no circumference for this shape.

I hope this helps!

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

To learn more about polar coordinates click :

https://brainly.com/question/26193139

#SPJ1

Answer:

D

Step-by-step explanation:

3.083 when rounded up to 2 decimal places is equal to 3.08.

The formula for circumference is used to determine the diameter of the circle that the teeter totter creates as it spins, which is 232.12 inches.

The circumference of the circle that the teeter totter makes as it spins is given by the formula:

Circumference = 2 * pi * radius

where "pi" is the mathematical constant approximately equal to 3.14, and "radius" is the distance from the center of the circle to its outside edge.

In this problem, we are given that the distance from the center to the outside edge of the teeter totter is 37 inches, which means that the radius of the circle is also 37 inches. Therefore, we can use the formula for circumference to calculate the distance around the circle that the teeter totter makes as it spins.

In this case, the radius is 37 inches, so we can plug in these values to get:

Circumference = 2 * 3.14 * 37

Simplifying this expression gives:

Circumference = 232.12

Therefore, the circumference of the circle that the teeter totter makes as it spins is approximately 232.12 inches, rounded to the nearest hundredth of an inch.

To learn more about circumference please click on below link        

https://brainly.com/question/28757341

#SPJ1

The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

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

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

Read more about complex expressions at

https://brainly.com/question/10662770

#SPJ1

Answer:

The amount of weeks is your independent variable, or X variable, and the height is you dependents variable.

Step-by-step explanation:

I don't know what this question is about so I'm gonna use plants as an example. The amounts of weeks that you are growing a plant is not dependent on anything. Nothing can cause change to that variable, so it would be your X. The height that your plant has grown DOES depend on how long you've grown it, so the amount of weeks, making it your Y variable.

The equation of line passes through the point (x_1,y_1) and (x_2,y_2) is,

Substitute the coordinates of the points in the equation to obtain the equation of line.

The general equation of line with slope m and y-intercept b is,

On compare the general equation with y=5x+4, it can be observed that slope is m=5 and y intercept b is 4.

So answer is m=5 and b=4.

Answer:

Angle AFE = 102(degree symbol)

Step-by-step explanation:

supplementary means two angles that add up to 180

hope this helps! :)

Answer:

The angle supplementary to ∠AFB is ∠EFA.

The reason why this is, is because a supplementary angle consists of two angles that have a sum of 180°.

Supplementary angles combine to form a straight line.

In this case, ∠EFA is the supplement of ∠AFB because, ∠EFA is the other part of the angle, AFB, that creates a full straight line(180°).

And to find the value of m∠EFA you would need to arrange an equation.

Since we know that the given angle measure of AFB is 78°, ∠EFA would have to equal a different measure so that both measures will have a sum of 180°.

We will consider the value of m∠EFA to be 'x' in our equation, so;

x + 78 = 180°

Solve for x:-

-78        -78

x = 102°, therefore m∠EFA = 102°.

Answer:

  7 miles

Step-by-step explanation:

You want to know how far apart two skaters are after 3.5 hours when they start together and one is traveling 10 mph while the other is traveling 12 mph in the same direction.

The relation between time, speed, and distance is ...

  distance = speed × time

For this problem, the relevant speed is the speed of separation of the two skaters. That is the difference of their speeds: 12 mph -10 mph = 2 mph. Then their separation distance after 3.5 hours is ...

  distance apart = (2 mi/h) × (3.5 h) = 7 mi

Nell and Kristin will be 7 miles at the end of 3.5 hours.

Answer:

The angles are adjacent and x=100

Answer:

A

Step-by-step explanation:

The profit for selling x pairs of shoes is given by:

\(P(x)=-4x^2+32x-39\)

And we want to determine the number of pairs that needs to be sold in order to maximize profit.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex point. The x-coordinate of the vertex of a quadratic is given by:

\(\displaystyle x=-\frac{b}{2a}\)

In this case, a = -4, b = 32, and c = -39. Substitute and evaluate:

\(\displaystyle x=-\frac{(32)}{2(-4)}=\frac{32}{8}=4\)

So, in order to maximize profit, only four pairs of sohoes should be sold.

Our answer is A.

Answer:

A

Step-by-step explanation:

Answer: none of these

Step-by-step explanation:

He completed volunteering in 39 hours 40 minutes in 4 weeks

How to determine this

If Ken volunteers 1 hr 25 mins each day

i.e 1 hr 25 mins = 1 days

By converting 1 hr 25 mins to mins

When 60 mins = 1 hr

1 hr 25 mins = 60 + 25 = 85 mins

How many hours of volunteering is completed in 4 weeks

Let x represent the numbers of hours

i.e x = 4 weeks

By converting 4 weeks to days

When 7 days = 1 week

4 weeks = 4 * 7 days

= 28 days

So, when 85 mins = 1 day

x mins = 28 days

x = 28 days * 85 mins/1 day

x = 2380 mins

By converting it back to hour

When 60 mins = 1 hour

2380 mins = x

x = 2380/60 hour

x = 39 hours 40 mins

Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes

Read more about Word problem

https://brainly.com/question/23343509

#SPJ1

Answer: Read the solution

Step-by-step explanation:

A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.

B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.

we have the function

Applying the limit definition

substitute given values

simplify

therefore

simplify