Which equation can be used to calculate the surface area of the triangular prism net show below?

The net of a rectangular prism. The rectangular sides are 10 centimeters by 13 centimeters, 10 centimeters by 12 centimeters, and 10 centimeters by 5 centimeters. The triangular sides have a base of 5 centimeters and height of 12 centimeters.

[Not drawn to scale]

Surface Area = (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)
Surface Area = (one-half) (5) (13) + (one-half) (5) (13) + (13) (10) + (12) (10)
Surface Area = (2) (5) (13) + (5) (10) + (13) (10) + (12) (10)
Surface Area = (one-half) (5) (12) + (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)

The graph of the system of inequalities can be seen below.

Here we have the inequalities:

y < -(1/3)*x + 1

y ≤2x-3

To graph the first inequality, we need to graph the line -(1/3)*x + 1 with a dashed line (because the symbol < was used) and shade the region below that line.

For the second inequality we need to graph the line 2x-3 with a solid line this time, and again, shade the region below the line.

The graph of the system is shown in the image below.

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Answer:

x+10

Step-by-step explanation:

So they did a bet, and placed 5 cents each. George lost the bet that gives Joyce 5 points plus 5 more that make 10.

After the bet George has: x cents

Before the bet George had: x + 5 cents

Before the bet Joyce had also x + 5 cents

Since Joyce won 5 cents, after the bet she has x + 5 + 5 = x + 10 cents.

Answer:

-22

Step-by-step explanation:

-14+(-12）+4

=-14-12+4

=-26+4

=-22

Answer:

x^2-x-2=0

Step-by-step explanation:

x^2+3=x+5

x^2-x-2=0

Answer: the correct is x=1,

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

x=1

Answer:

1

Step-by-step explanation:

you can plug it in and it gives you 3-1 which results in 2 as the question asks for

Answer: $201.81

Step-by-step explanation:

The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.

Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]

Answer:

all are the properties of square

Step-by-step explanation:

all are correct

Tony will have 486 cookies if he bakes 10 batches more.

Take two points from table: (8, 234), (9, 252)

Find slope:

[tex]slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow slope \ (m) : \dfrac{252-234}{9-8} = 18[/tex]

This determines that one batch of cookies has 18 cookies.

So, if he bakes 10 more batches:

(10 × 18) = 180 cookies

Total cookies he then will have:

306 cookies + 180 cookies = 486 cookies.

The best description of the car's motion as shown in the graph is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

In a distance-time graph, an horizontal line implies no distance was covered within that time frame, meaning there was a stop.

Thus, in the graph given, the stop occurred 1 and 2, which is equivalent to an hour. From 2 to 5 on the x-axis means there was movement for up to 3 hours.

Therefore, the best description is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

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The integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

A demand function describes the mathematical relationship between the quantity demanded and one or more determinants of the demand, as the price of the good or service, the price of complementary and substitute goods, disposable income, etc.

Here, given differential equation;

R'(x) = 599 - 0.21[tex]\sqrt{x}[/tex]

we can also write this as;

[tex]\frac{d}{dx}R(x) = 599 - 0.21\sqrt{x}[/tex]

[tex]d R(x) = (599 - 0.21\sqrt{x} ) dx[/tex]

On integrating both sides, we get

[tex]\int\ d R(x) = \int\ (599 - 0.21\sqrt{x} ) dx[/tex]

R(x) = [tex]599x - 0.21 X \frac{2}{3}x^{3/2}[/tex] + C

R(x) = 599x - 0.14[tex]x^{3/2}[/tex] + C       ...........(i)

Also given, at x = 0, R(x) = 0, Put these values in equation (i), we get

0 = 0 - 0 + C

C = 0

Put the value of C in equation (i), we get

R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

Thus, the integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

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Answer:

[tex]y=-\frac{1}{3}x -8[/tex]

Step-by-step explanation:

1) Write down the standard form of an equation of a line and the formula to find m.

[tex]y=mx+b[/tex]

[tex]m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

2) Find m using the formula then substitute it into [tex]y=mx+b[/tex].

[tex]m=\frac{-5 - (-6) }{-9 - (-6)}\\m=\frac{-5 +6 }{-9 +6}\\m=\frac{1}{-3} \\m=-\frac{1}{3}[/tex]

So, [tex]y=-\frac{1}{3}x +b[/tex].

3) Find b by substituting a pair of coordinates the line goes through.

[tex]-6=-\frac{1}{3}(-6) +b\\-6=2+b\\-6 - 2=b\\-8=b[/tex]

4) Substitute b into [tex]y=-\frac{1}{3}x +b[/tex] to get your final answer.

[tex]y=-\frac{1}{3}x -8[/tex]

the largest length of the squares will be 120m.

The largest possible length will be equal to the greatest common factor between the dimensions of the rectangular plot, so we need to find the GCF between 600 and 720.

If we decompose both numbers, we get:

600 = 2*2*2*3*5*5

720 = 2*2*2*2*3*3*5

Then the greatest common factor is: (2*2*2*3*5) = 120

So the largest length of the squares will be 120m.

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The bisector of angle APQ passes through O and this is illustrated below.

From the information given, the center is O. and the circle passes through O and cuts at K.

In this case, it should be noted that the circles are equal according to the SAS test.

Here, AOB + APQ = 180° (Linear pair)

2AOB = 180

AOB = 90.

Therefore, the bisector of angle APQ passes through O.

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With the use of formula, the interest rate is 18.2%

The Interest is the product of the principal, time and the rate in percentage. That is, I = PTR / 100

Where

Substitute all the parameters into the formula

80 = (880 x 0.5R)/100

cross multiply

8000 = 440R

R = 8000/440

R = 18.2%

Therefore,  the (simple) interest rate is 18.2%

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Answer:

16

Step-by-step explanation:

he missed 25%

if 4 = 25% then 16 questions total

4*4=16 and 25% * 4 = 100%

Answer: 16 problems

Step-by-step explanation:

First find out how many John got wrong. 100%-75%=25%. Then do cross multiplication: 4*100=25x; 400=25x. Divide 25 on both sides and... BOOM! you get 16 problems.

Angles on straight line = 180

110 + 5x = 180 degrees

-110

5x. = 70

÷ 5

x. = 14

5 x 14 = 70

Angles in triangle = 180

70 + 40 = 110

So, the missing angle inside the triangle is 70

Now to find y, use angles on straight line = 180

2y + 70 = 180

- 70

2y = 110

÷2

y = 55 degrees

Hope this helps!

Rewriting the equation of the given line in slope-intercept form,

[tex]-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-\frac{1}{4}x-\frac{1}{4}[/tex]

From this, we know the slope of the given line is -1/4.

Since parallel lines have the same slope, we know the line whose equation we want to find has a slope of -1/4.

Substituting into point-slope form,

[tex]y=-\frac{1}{4}(x+4)\\\\\boxed{y=-\frac{1}{4}x-1}[/tex]

Answer:

x=4, y=-2, p=14

Step-by-step explanation:

First simplify the LHS:

[tex]LHS = (16p^8)^\frac{3}{2} \times (216p^{-3})^{-\frac{2}{3}}[/tex]

[tex]= 64 p^{12} \times \frac{1}{36} p^{2}[/tex]

[tex]=\frac{16}{9}p^{14}[/tex]

[tex]=\frac{2^4}{3^2}p^14\\=2^43^{-2}p^{14}[/tex]

Hence x=4, y=2, p=14

Answer: [tex]\frac{k(k+1)}{2}[/tex]

Step-by-step explanation:

This is a standard formula.

The numbers of runners that are 50 and above are 3000.

Using the pie chart,

If there are 1500 runners that are under 20, therefore,

1500 = 10 / 100 × x

where

x = total number of runners

10x = 150000

x = 15000

Therefore,

the number of runners that are 50 and above = 20 / 100 × 15000 = 3000

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Answer:

It is.

Step-by-step explanation:

(x, y, z) => (4, -5, -4)

substitute 4 in x, -5 in y & -4 in z for all the equations in the system.

4x + 2y + z = 2

4(4) + 2(-5) - 4 = 2

2 = 2

5x - 4y - z = 44

5(4) - 4(-5) - (-4) = 44

44 = 44

3x + y + 4z = -9

3(4) + (-5) + 4(-4) = -9

-9 = -9

All equations therefore agree with the ordered triple.

Hi! ⋇

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  All proportions have this form:

  [tex]\sf{\dfrac{a}{b}=\dfrac{c}{d}}[/tex], Where [tex]\sf{\dfrac{a}{b}}[/tex] is equal to [tex]\sf{\dfrac{c}{d}}[/tex].

 If [tex]\sf{\dfrac{a}{b}\neq\dfrac{c}{d}}[/tex], it's not a proportion.

_________________________

  Here we have two pairs of numbers:

40,10 and 32,8.

Written As a proportion, they look like :

[tex]\sf{\dfrac{40}{10}=\dfrac{32}{8}}[/tex]

Hope this made sense to you :)

[tex]\it{Calligrxphy}[/tex]

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Based on the function given, the year when the cost of mailing a first class letter would reach 60 cents is 2007.

If the cost of mailing a first-class letter is 41 cents, then the inflation rate has not stayed constant.

0.60 = 0.29 (1.046)^t

0.60 / 0.29 = (1.046)^t

log (2.07) = t x log (1.046)

t = 16 years

Added to 1991:

= 1991 + 16

= 2007

The cost of mailing a first-class ticket was 41 cents however which means that inflation was not constant.

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None solutions to the system exist.

Given statement: A system of three linear equations in three variables is inconsistent.

Concept: If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.

We know that if a system has no solution, then it is known as inconsistent.

[If there are one, two, or an infinite number of solutions to the system, then it is called consistent.]

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The diameter of a sphere is a chord that passes through the centre of the sphere.

We need to complete the given statement.

The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere. If is the radius of a circle or sphere, then. The ratio of the circumference of a circle or great circle of a sphere to the diameter.

A chord of a sphere is a segment whose endpoints are on the sphere. A diameter is a chord that contains the centre.

Therefore, the diameter of a sphere is a chord that passes through the centre of the sphere.

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The equation of the parabola is y = 2/25x^2 + 2

The complete question is in the image

The given parameters are:

Vertex, (h, k) = (0,2)

Point (x,y) = (-5, 4)

The parabola is represented as;

y = a(x - h)^2 + k

Substitute (h, k) = (0,2)

y = a(x - 0)^2 + 2

This gives

y = ax^2 + 2

Substitute (x, y) = (-5,4)

4 = a(-5)^2 + 2

This gives

4 = 25a + 2

Subtract 2 from both sides

25a = 2

Divide by 25

a = 2/25

Substitute a = 2/25 in y = ax^2 + 2

y = 2/25x^2 + 2

Hence, the equation of the parabola is y = 2/25x^2 + 2

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The distance between the start and end points is 28.3 miles.

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_2 -y_1)^2}[/tex]

Here the initial point is (0mi, 0mi).

If we define the north as positive y-axis and east as the positive x-axis, after that Thomas travels 24 miles north and 15 miles west his new position is:

(-15mi, 24mi).

The distance is then:

[tex]d = \sqrt{(-15mi - 0mi)^2 + (24mi - 0mi)^2} = 28.3mi[/tex]

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The  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

A transformation is a rule that is used to manipulate the position of a point of geometric figure.

And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.

Hence,  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

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Answer:

15

Step-by-step explanation:

Supplementary angles add to 180 degrees

Let the supplement be x

x+165 = 180

x +165-165= 180-165

x = 15

The supplement is 15

Answer:

Hello! The answer is 15°.

Step-by-step explanation:

Supplementary angles add up to 180°.

To find the measure of each angle, we can now set up an equation because we have the total that supplementary angles add up to:

x + 165 = 180

Now, we can subtract 165 from both sides to get x by itself:

x + 165 = 180

    -165  -165

This leaves us with:

x = 15