Question 11-(3 marks available)
Find the total surface area of this triangular prism.
13 cm
5 cm
12 cm
9 cm
20 cm

Answer:

  shifted down 4 units

Step-by-step explanation:

You want to know the effect on the graph of changing y=2x+2 to y=2x-2.

The constant in the equation y=2x+2 is the y-intercept. The line described by this equation crosses the y-axis at y=2.

When the equation is changed to y=2x-2, the y-intercept changes from +2 to -2, a shift down of 4 units. The shifted line has the same slope as the original, so is parallel to it.

The effect on the graph is to move it down 4 units.

Answer: x=43

Step-by-step explanation:

3x-19=110

3x-19+19=110+19

3x=129

3x/3=129/3

x=43

a. Using the Pythagorean Theorem, side c = 150 feet

b. Area = 5,400 ft²

c. Applying the converse of the Pythagorean Theorem, the triangle would be a right triangle if the sum of the squares of two sides equals the square of the other side.

The converse of the Pythagorean theorem states that if the sum of the squares of the two smaller sides of a triangle is equal to the square of the longer side, then the triangle is a right triangle.

a. Apply the Pythagorean theorem:

c = √(a² + b²)

c = ?

a = 90 feet

b = 120 feet

Substitute

c = √(90² + 120²)

c = 150 feet

b. Area = 1/2(a)(b) = 1/2(90)(120)

Area = 1/2(10,800)

Area = 5,400 ft²

c. Using the converse of the Pythagorean Theorem, we can check if the sum of the squares of two sides equals the square of the other side.

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By using the rate of change formula for linear equations, we will see that the statement is true.

Here we have the following statement:

"The student reads at a rate of 48 pages per hour."

Which relates to the linear equation represented on the table.

A general linear equation is written as:

y = a*x + b

Where a is the rate and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the rate is:

rate = (y2 - y1)/(x2 - x1)

Using the first two points (1,644) and (4, 500) we can get the rate:

R = (500 - 644)/(4 - 1) = -48

So the number of pages remaining decreases by 48 each hour of reading, then yes, the student reads at a rate of 48 pages per hour.

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Answer:

v>3

Step-by-step explanation:

2v>7-1

2v>6

v>6/2

v>3

Answer:

I'm pretty sure the answer would be >

Answer: |-8|>-2

Step-by-step explanation:

Because of the lines on both sides of the "-8" you don't pay attention to the "-" sign. That is because this is an absolute value sign. So instead you would read that as 8 ? -2 and which of course 8 is clearly greater

Hope this helps ;)

In order pair (4,9), 9 is the y- coordinate while 4 is the x-coordinate.

The coordinates are the pair of numbers that describe the position of some point in a plane using the horizontal x-axis and the vertical y-axis as the point of reference. The representation of this coordinate is usually done by (x,y) where x represents the point's reference with respect to the x-axis and y represents the point's reference with respect to the y-axis. There are four quadrants in the graph which are named quadrant 1, quadrant 2, quadrant 3, and quadrant 4. In quadrant 1 both the x and y-axis is positive, in quadrant 2 x-axis is negative and the y-axis is positive, in quadrant 3 both the x and y-axis are negative, and in quadrant 4 x-axis is positive while the y-axis is negative.

I hope this answer helps

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Answer:

9

Step-by-step explanation:

Remember that all points have the form, [tex](x,y)[/tex].

Soo in this problem,

                    [tex]\begin{cases}\text{4 is the x-coordinate}\\\text{9 is the y coordinate}\end{cases}[/tex]

Thus, The y-coordinate is 9!!

Answer:

x = 20

Step-by-step explanation:

We know that a straight line is 180 degrees. We also know that the line A and B is a supplementary angle.

We subtract 180 - 110 which will come out to 70 which is the value of angle B

We know that angles D and E are 90 degrees and since D and C is 180 degrees, that means C and E is equal to 90 degrees as well.

Since B is equal to 70 degrees, we subtract 90 - 70 to get 20 degrees which is the value of x

In the garden club there are 18 ladies and 2 gentlemen.

Given, In a garden club, 90% is ladies.

The number of ladies is 12 more than 3 times the number of gentlemen.

Let the total members be, x

the number of ladies be, l and the number of gentlemen be, g

according to the question,

l = 90x/100

l = 9x/10

also, l = 12 + 3g

g = (l - 12)/3

as, l + g = x

9x/10 + (9x/10 - 12)/3 = x

9x/10 + 9x/30 - 4 = x

36x/30 - 4 = x

6x/30 = 4

x = 20

so, ladies be, l = 9x/10 = 18

and gentlemen be, g = 20 - 18 = 2

Hence, in the garden club there are 18 ladies and 2 gentlemen.

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The price of the share 3 years later, given the increase in value, can be found to be $43.29

The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.

This means that the price of the share 3 years later would be:

= Share price currently x ( 1 + increase in value)

= 37 x ( 1 + 17 % )

= 37 x 1. 17

= $ 43. 29

The price is  $43.29

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Answer:

Step-by-step explanation:

Given a car's cost of operation is $485 for 500 miles, you want an equation relating cost for m miles, and solutions to that equation for 1200 miles, and for a cost of $820.

The cost per mile is found by dividing the cost by the associated number of miles:

  $485/(500 mi) = $0.97 /mi

The equation for the cost will show the cost as the cost per mile multiplied by the number of miles:

  C = 0.97m . . . . . where C is cost in dollars for m miles driven

The cost for driving $1200 miles will be ...

  C = 0.97(1200) = $1164

The cost of driving 1200 miles is $1164.

The number of miles that can be driven for a cost of $820 is ...

  820 = 0.97m

  m = 820/0.97 = 845.36

About 845 miles are driven for a cost of $820.

The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Answer:

Step-by-step explanation:

It would be D.

Answer: 81

Step-by-step explanation:

[tex]v=\sqrt{2gh}\\\\g=32, v=72\\\\\implies 72=\sqrt{2(32)h}\\\\5184=64h\\\\h=81[/tex]

The alternative to random sampling is called as systematic sampling which is accepted by a pollster to poll every 10th person that comes out of a store.

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).

This method will provide you with a representative sample that can be used to make generalizations about the population if the order of the population is random or random-appearing (for example, alphabetical).

Simple random sampling has numerous advantages over systematic sampling in terms of randomization, but systematic sampling is a little bit simpler to carry out.

Similar to basic random sampling, systematic sampling can be used with a list of the complete population. Contrary to basic random sampling, one can still utilize this technique if you don't have access to a list of the population beforehand.

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Parameter are values ​​that represents fixed characteristics of a population.

What is a parameter?

The parameter is an important component in statistical analysis because it describes fixed characteristics of the given population. The way to conclude the population characteristics is to perform statistical analysis on a sample of the population then calculate it with the parameter formula. The most commonly used parameters are mean, median, and mode. Data distribution of a ratio can be described by mean.  The Median is used to calculate the variables of data distribution which has a few data points that are different. Mode is used to know which number appears the most in a data distribution.

Based on statistical calculations from the existing population sample, conclusions can be drawn regarding the fixed characteristics of the entire population using parameters.

Hence, a parameter represents fixed characteristics of a population.

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Answer:

I believe the answer is Yes because there is a constant arithmetic sequence and I believe the common difference is 4.

Answer: No Solution

Explanation: 10 + r = 3 + r - 7

Combine like terms: 10 + r = -4 + r

Subtract R to both sides: 10 = 4

There is NO SOLUTION

Answer:

Step-by-step explanation:

a find the interpret the slope and the y-intercept of the graph

If 1/5 of Joanna's monthly savings is $55 the equation of her savings is

The solution to the equation is $275

information from the question include

Joanna saves $55 each month from her part-time job

She saves 1/5 of her earnings

let x represent the Joanna's earnings

The equation of Joanna savings is represented in the form

1/5 of x = 55

This equation deals with multiplication and the term 'of' as used in math represents multiplication

Hence 1/5 of x = 1 / 5 * x = x/5

x/5 = 55

multiplying both sides by 5

x = 275

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Answer:

b. y + 5 = -2(x + 3) or

    y = - 2x - 11

Step-by-step explanation:

Point-slope equation:

Convert this to slope-intercept form:

Correct choice is b.

41/5

Step-by-step explanation:

14/5=9+2+q

14/5=11+q

14=55+5q

14-55=5q

-41=5q

q=-41/5

The slope of the line that passes through (1, 1)  and (7, 5) is 2/3

From the question, the points are given as

a. (1, 1) and (7,5)

Rewrite the above points properly

So, we have the following ordered pairs

(1, 1) and (7,5)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (1, 1) and (7,5)

Substitute the known values in the above equation

So, we have the following equation

Slope = (5 - 1)/(7 - 1)

Evaluate

Slope = 2/3

Hence, the slope of the line is 2/3

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Possible question

Find the slope of the line that passes through a. (1, 1) and (7,5)

A 99% confidence interval of what the actual average mileage is for a car before it is junked is;  (153589, 174411)

The formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

s is standard deviation

n is sample size

z is critical value at confidence level

We are given;

x' = 164000

n = 48

s = 28000

CL = 99%

z-score at confidence level of 99% is 2.576

Thus;

CI = 164000 ± 2.576(28000/√48)

CI = 164000 ± 10410.78

CI = (164000 - 10410.78), (164000 + 10410.78)

CI = (153589, 174411)

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Answer:

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140 Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160

Step-by-step explanation:

The the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3

The quadratic function is given by

f(x) = [tex]-3(x+2)^2[/tex] + 1

The vertex form of the quadratic function is

f(x) = [tex]a(x-h)^2[/tex] + k

Where (h, k)  is the coordinates of the vertex

x =  h is the axis of symmetry

Compare the given function and the vertex form of the quadratic function and find the value of the each term

The value of h = -2

The value of k = 1

The coordinates of the vertex = (-2, 1)

The axis of symmetry is at x = h

h = -2

Draw the graph using the details

Hence, the the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3

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The equation of the line perpendicular to y = - (1 / 2) · x - 2 and that passes through the point (x, y) = (- 3, - 5) is y = 2 · x + 1.

In this problem we must determine the equation of a line perpendicular to another line, provided that the equation of a line and a point of intersection are given. According to analytical geometry, two lines are perpendicular if and only if the product of the two slopes equals - 1.

The equations of the line are defined by functions of the form:

y = m · x + b

Where:

And the slope relationship between two perpendicular line:

m · m' = - 1

Where:

First, derive the equation of the line in slope-intercept form:

x + 2 · y = - 4

2 · y = - x - 4

y = - (1 / 2) · x - 2

Second, calculate the slope of the perpendicular line by the slope relationship:

m' = - 1 / (- 1 / 2)

m' = 2

Third, find the y-intercept of the perpendicular line by the equation of line, the slope and the coordinates of the given point:

b = y - m · x

b = - 5 - 2 · (- 3)

b = - 5 + 6

b = 1

Then, obtain the equation of the line in slope-intercept form:

y = 2 · x + 1

The equation of the line is y = 2 · x + 1.

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Answer:

The measure of its supplementary angle is 18.6 degrees

Step-by-step explanation:

A Supplementary angle is any two angles that sum up to 180 degrees

With this in mind we can subtract 180 - 161.4 to get the measure of the other angle.

Since 161.4 + 18.6 = 180 this is correct

Answer: The supplementary angle to 161.4 degrees is 18.6 degrees.

Step-by-step explanation: the sum of two supplementary angles is always 180 degrees.

180-161.4 is equal to 18.6 degrees.

The value of x in the given figure is x = 22.56 m .

In the question ,

a figure is given where the measure of angle(C) = 70° and angle(A) = 30°

In the triangle ABC ,

By Angle Sum Property Of Triangle  

angleA + angleB + angleC = 180°

30° + angleB + 70° = 180°

angleB = 180° - 100°

angle(B) = 80°

By using Sine Law ,

a/Sin(A) = x/Sin(C)

From the figure ,

a = 12 m

we get ,

12/Sin(30°) = x/Sin(70°)

x = (Sin70° × 12)/Sin(30°)

x = 11.2763/0.5

x = 22.5526

x ≈ 22.56 m

Therefore , The value of x in the given figure is x = 22.56 m .

The given question is incomplete , the complete question is

Find the value of x in the given figure ?

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