A triangular prism is 18 inches long and has a triangular face with a base of 16 inches and a height of 15 inches. The other two sides of the triangle are each 17 inches. What is the surface area of the triangular prism?

The age of Marissa and her younger brother.

We know that the older brother's age is 18 and he is twice older than the younger brother.

Let the unknown be "x"

[tex] x=\frac{18}{2} [/tex]

[tex]\large\boxed{\sf{x=9 \: years}}[/tex]

Now, we know that the younger brother's age is 9 and Marissa is 3 years older than him.

Let the unknown be "x"

[tex]x=9 + 3[/tex]

[tex]\large\boxed{\sf{x=12 \: years}}[/tex]

Therefore, Marissa is 12 and her younger brother is 9

Answer:

Marissa's age = 12

Younger brother's age = 9

Step-by-step explanation:

Let age of Marissa be x, and her younger brother's y.

Equations formed :

Finding age of younger brother using Equation 2 :

⇒ 2y = 18

⇒ 2y/2 = 18/2

⇒ y = 9 years old

Substituting y in Equation 1 :

⇒ x = y + 3

⇒ x = 9 + 3

⇒ x = 12 years old

Marissa's age = 12

Younger brother's age = 9

Answer:

b

Step-by-step explanation:

used graphing calculator

The equation most closely models the line of best fit for the scatter plot is y = 2.5x

A line is the defines as the minimum distance between two points. The equation of a line is given in the form y =mx + b

where:

In order to determine the required equation, we can use the coordinate  (3, 5000) and (9, 20000)

Determine the slope

Slope = 20000-5000/9-3
Slope = 15000/6 = 2500

Determine the y-intercept

5000 = 2500(3) + b

b = 5000 - 7500
b = -2500

Determine the equation

y = 2.5x - 2.5

Therefore the equation most closely models the line of best fit for the scatter plot is y = 2.5x

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The estimate that 2.8 million square feet of the building is used for office space is not reasonable

From the plan, the width of the building is:

Width = 230 feet

The building has a circular area, and it has four floors

So, the estimate of the building area is:

Area= 4πR²

So, we have:

Area= 4 * 3.14 * 230²

Evaluate

Area= 664424

The above value cannot be approximated to 2.8 million

Hence, the estimate used for office space is not reasonable

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The slope as evaluated from the given pair of points is; Slope, m = 5.

Slope of given Points

The slope of a line defined by two points simply refers to the rate of change of the function given by the line.

Hence, slope, m = (28 -18)/(4 -2)

Slope, m = 10/2

Slope, m = 5

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#1

Slope

#2

Slope

#3

Slope

#4

Slope

CODE IS

Answer: We minutes hand moves for 20minutes ,it makes 120° central angle

Length=x/360×2πr

=120/360×2×22/7×42

On simplyfing

Length=88cm

Step-by-step explanation:

The equation that the given graph of the system of equations solves is: 1/3x + 1 = 2x - 4.

Where m is the slope and b is the y-intercept, the equation of a line in slope-intercept form is expressed as y = mx + b.

Equation of the Blue Line:

Slope (m) = change in y / change in x = 2/1 = 2

y-intercept (b) = -4.

Equation: y = 2x - 4

Equation of the Red Line:

Slope (m) = change in y / change in x = 1/3

y-intercept (b) = 1

Equation: y = 1/3x + 1

The equation that the graph of the systems of equations solve would be: 1/3x + 1 = 2x - 4.

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Answer:

d=-21

Step-by-step explanation:

Answer:

Its 37ft

Step-by-step explanation:

Answer:

126.35cm

Step-by-step explanation:

quick use of a calculator

Answer:

26.6 cm

Step-by-step explanation:

height= 133/5

height of year= 26.6 cm

Answer:

(100,10)

Step-by-step explanation:

The exercise has to do with the Graphing of a Cosecant Function. From the graph, the completed statements have been indicated below.

The completed statements are:

It is to be noted that the graph is of the function 2Sec (3x) – 1.

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Answer:

2pi/3

corresponding cosine function is 2.

1 unit down.

graph 2sec(3x) – 1

Step-by-step explanation:

The surface area of the cone is the amount of space on it, the radius of the cone is about 13 feet

The given parameters are:

The surface area is calculated using:

[tex]A =\pi r(r + \sqrt{h^2 + r^2})[/tex]

So, we have:

[tex]A =\pi r(r + \sqrt{(3r)^2 + r^2})[/tex]

Substitute 2167 for A

[tex]2167 =\pi r(r + \sqrt{(3r)^2 + r^2})[/tex]

Evaluate the sum

[tex]2167 =\pi r(r + \sqrt{10r^2})[/tex]

Divide both sides by [tex]\pi[/tex]

[tex]689.78 =r(r + \sqrt{10r^2})[/tex]

Evaluate the exponent

[tex]689.78 =r(r + 3.16r)[/tex]

Evaluate the sum

689.78 =r(4.16r)

Open the bracket

689.78 = 4.16r²

Divide both sides by 4.15

r² =165.8125

Take the square root of both sides

r = 13 (approximated)

Hence, the radius of the cone is about 13 feet

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Answer:

10x8=80 not 800 the answer should be

Step-by-step explanation:

5x8=40

5x50=250

10x8=80 not 800

10x50=500

500+250=750

750+40=790

790+80=870

The amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Henry has a box in the shape of a square pyramid.

He wants to wrap the box with paper.

If the base has side lengths of 5 in. and the lateral height is 8 in.

Then the amount of the wrapping paper that he needs to cover the pyramid will be

[tex]\rm Area = 4 \times \dfrac{1}{2} \times 5 \times 8 + 5 \times 5\\\\\\Area = 80 + 25\\\\\\Area = 105 \ in^2[/tex]

Thus, the amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.

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Answer:

(a) 43%

(b) 49%

Step-by-step explanation:

Add a total column and a total row to the table:

[tex]\begin{tabular}{| c | c | c | c |}\cline{1-4} & Playing video games & Watching TV & Total\\\cline{1-4} Girls & 45 & 108 & 153\\\cline{1-4} Boys & 84 & 63 & 147\\\cline{1-4} Total & 129 & 171 & 300\\\cline{1-4}\end{tabular}[/tex]

Percentage of students who prefer video games:

[tex]=\dfrac{\textsf{total no. of students who play video games}}{\textsf{total no. of students}} \times \sf 100\%[/tex]

[tex]=\sf \dfrac{129}{300} \times 100 \%[/tex]

[tex]= \sf 43 \%[/tex]

Percentage of students who are boys:

[tex]=\dfrac{\textsf{total no. of students who are boys}}{\textsf{total no. of students}} \times \sf 100\%[/tex]

[tex]=\sf \dfrac{147}{300} \times 100 \%[/tex]

[tex]= \sf 49 \%[/tex]

Answer:

total num playing video games/total no of studen×100

a) 43%

b) 49%

Answer:

[tex]distance = \sqrt{(3 - 3) {}^{2} } + ( - 2 - 0) {}^{2} \\ = \sqrt{0 + 4} \\ = \sqrt{4 } \\ = 2unit[/tex]

Answer:

m<S = 68 degrees.

m<D = 112 degrees

Step-by-step explanation:

Opposite angles of a parallelogram are equal so:

4x - 4 = 3x + 14      

4x - 3x = 14 + 4

x = 18.

So m < S = 4(18) - 4

= 72-4

= 68 degrees.

Angles on the same side of a parallelogram are supplementary, so

m < D = 180 - 68

= 112 degrees.

[tex]\Large\textsf{\textbf{Answer\::}}[/tex]

-1, 260

[tex]\large\textsf{\textbf{Calculations\;:}}[/tex]

First , take a look at the signs of the numbers we're asked to multiply .

One of them is negative , and the other one is positive .

If we have a negative number times a positive number , the product is a positive number .

Multiply :

(-315) × 4

-1, 260 (Ans)

[tex]\footnotesize\text{hope\:helpful~}[/tex]

Answer:

[tex]\sqrt{54}[/tex] = 7.3484  , to the nearest 10th , then is  7.35

Step-by-step explanation:

The probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of students in classroom 101 = 13+7 = 20

Total number of students in classroom 103 = 8+12 = 20

The probability of choosing a boy from both classrooms:

= 19/20

Choosing a girl from Classroom 101 and a boy from Classroom 103:

Since both are independent event.

Probability of choosing a girl from Classroom 101 = 13/20

Probability of choosing a boy from Classroom 103 = 12/20

The probability of choosing a girl from Classroom 101 and a boy from Classroom 103:

= (13/20)(12/20)

= 156/400

= 39/100

Similarly, the probability of Choosing a boy from Classroom 101 and a girl from Classroom 103:

= (7/20)(8/20)

= 56/400

= 7/50

Similarly, we can find remaining probability.

Thus, the probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50

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Answer:

[tex]\sf Sin \ \theta = \dfrac{5}{13}\\\\Cos \ \theta =\dfrac{12}{13}[/tex]

Step-by-step explanation:

            [tex]\sf =\dfrac{BC}{AB}\\\\ =\dfrac{5}{13}[/tex]

[tex]\sf Cos \ \theta = \dfrac{adjacent \ side \ of \ angle \ A}{hypotenuse}\\[/tex]

       [tex]\sf =\dfrac{AC}{AB}\\\\= \dfrac{12}{13}[/tex]

Answer:

26

Step-by-step explanation:

1.) Step plug it in ---}  4*2 + 7 (4) - 10

2.) Step multiply what u have so

4 x 2= 8

7 x 4 = 28

3. )Put it back ---}  8+ 28 - 10

4.) Solve from there.

8+28=36

36 - 10 =26

Answer: 57

Step-by-step explanation: First have to put x=4 and do multiplication in brackets then do subtraction and add at the end to get final answern action pien r

Answer: 10x^2-8x+16

Step-by-step explanation:

Use the formula (b/2)^2

then plug in values:

(-8/2)^2 = -4^2 = 16

ans: 10x^2-8x+16

hope this helps

Answer:

x = -1

y = -3

Step-by-step explanation:

[tex]\begin{cases}2x+3=y+4\\ 2+y=3x+2\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}2x-y=1&\left( 1\right) \\ 3x-y=0&(2)\end{cases}[/tex]

(2) - (1) ⇒ (3x - y) - (2x - y) = 0 - 1 ⇒ x = -1

(1) ⇒ 2x - y = 1 ⇒ y = 2x - 1 = 2(-1) - 1 = -3

Answer:

1500 people.

Step-by-step explanation:

100% of the fans are not known,

So let the total number of fans or 100% of the fans be X

SINCE 10% ••••••••••• 150

100% ••••••••••••X

we're going to Cross multiply

= 10×X = 100 × 150

10X = 15000

dividing bothsides by 10

10X/10 = 15000/10

X = 1500 people.

Answer:

y = 1/3*x -3

Step-by-step explanation:

Method 1:

Grab two random points from the line.

(0,-3) and (3,-2)

Using the Point-Slope Form solve for m.

(-3 - (-2)) = m * (0 - (3))

-1 = m * (-3)

m = 1/3

Turning Point-Slope form into Slope intercept Form.

(y - (-3)) = 1/3 * (x - 0)

y + 3 = 1/3x

y = 1/3 - 3

Method 2:

Look at the y-intercept since y-int becomes our b. b = -3

From the y-int count rise/run as thats our Slope m. m = 1/3

Slope-intecept Form:

y = 1/3*x -3

Answer:

y=1/3x-3

rise/run= 1/3

y-int. is -3

Step-by-step explanation:

Answer:

( - 1, - 5)

Step-by-step explanation:

Elimination Method:

Multiply the second equation by -1, then add the equations together.

(3x−4y=17)

−1(7x−4y=13)

Becomes:

3x−4y=17

−7x+4y=−13

Add these equations to eliminate y:

−4x=4

Then solve−4x=4for x:

−4x=4

-4x / -4 = 4/-4 (Divide both sides by -4)

x= −1

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

3x−4y=17

Substitute−1forxin3x−4y=17:

(3)(−1)−4y=17

−4y−3=17(Simplify both sides of the equation)

−4y−3+3=17+3(Add 3 to both sides)

−4y=20

-4y/ -4 = 20/ -4 (Divide both sides by -4)

y=−5

Answer:

x=−1 and y=−5

Answer:

1728 units cubed

Step-by-step explanation:

V = LWH
V = 12x16x9
V = 1728