The RSM geometry Principal test has 8 true-false questions. In how many ways can a student answer these questions?

Thank you :)

The correct equation is 45(x+3)=60x. Option A

We are told in the word problem that the contractor got 45 expensive wood and 60 cheap wood for the same total price and that  the 45 expensive wood cost $3.00 more than the 60 cheap wood.

If x =price of the 60 cheap wood then we have that 45(x + 3) + 60x = total cost of the wood.

45x + 135 + 60x = total cost of the wood

105x + 135 = total cost of the wood

45(x + 3) + 60x = 105x + 135

Simplifying;

45(x + 3) = 60x

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The solution is ,if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.

Here, we have,

given that.

if it takes three people 4 hours to clean a warehouse

now, we have to find that  how long will it take 4 people to clean the warehouse.

i.e. we have,

3 people take to clean = 4 hours

let, 4 people will take to do it x hours.

now, we have,

3 people take to clean = 4 hours

so, 1 people take to clean = 4*3 hours

so, 4 people take to clean = 4*3 / 4 hours

i.e. we get,

x = 4*3 / 4 hours

or, x = 12/4 hours

       = 3 hours

Hence, if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.

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Answer:

t = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

calculate the gradient (slope) of AB using the slope formula and equate to the slope of the perpendicular line.

given line with slope 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex]

calculate [tex]m_{AB}[/tex] using slope formula

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

with (x₁, y₁ ) = A (2, - 3 ) and (x₂, y₂ ) = B (- 2, t )

[tex]m_{AB}[/tex] = [tex]\frac{t-(-3)}{-2-2}[/tex] = [tex]\frac{t+3}{-4}[/tex]

equating corresponding slopes

[tex]\frac{t+3}{-4}[/tex] = - [tex]\frac{4}{5}[/tex] ( multiply both sides by - 4 to clear the fraction )

t + 3 = - [tex]\frac{4}{5}[/tex] × - 4 = [tex]\frac{16}{5}[/tex] ( subtract 3 from both sides )

t = [tex]\frac{16}{5}[/tex] - 3 = [tex]\frac{16}{5}[/tex] - [tex]\frac{15}{5}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

8 and -5

Step-by-step explanation:

8 - 5 = 3

(-5) (8)=-40

Answer:

-8,+5

Step-by-step explanation:

-8+5 = 3

-8×+5 = -40

The missing height of the triangle is h = 66 inches

Given data ,

Let's denote the missing height of the triangle as "h" inches.

The formula for the area of a triangle is given by:

Area = (1/2) * base * height

Given that the area of the triangle is 6,460 inches squared and the base is either 136 inches or 196 inches, we can set up two equations to solve for "h".

For the base of 136 inches:

Area = (1/2) * 136 * h

6460 = 68h

h = 6460 / 68

h ≈ 95 inches

For the base of 196 inches:

Area = (1/2) * 196 * h

6460 = 98h

h = 6460 / 98

h ≈ 66 inches

Hence , the height of the triangle is h = 66 inches or 95 inches

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The heart will pumps 31,536 litres in 1 year and pumps 2,207,520 liters in 70 years.

There are 72 heartbeats in a minute.

If heart pumps 7 × 10⁻² litre per heartbeat,

then in 1 min,

7 × 10⁻² x 72 = 5.04 litres/minute

In one year (365 days), the heart pumps:

5.04 x 60 x 24 x 365 = 31,536 litres/year

Hence in 1 year, heart pumps 31,536 litres

In 70 years, the heart would pump:

31,536 x 70 years = 2,207,520 litres

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For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = [tex]\pi* r^2 *h[/tex]

Part A

The total length of the assembled rocket will be the length of the cone and the cylinder.

The total length of the assembled rocket  = 25 + 3 = 28cm

Part B

The volume of the rocket is the combined volume of the cone and cylinder.

=  4/3 × 3.14 × 16 × 28

= 1875.62 cubic cm

To convert cm into pounds

1875.62 cubic cm = 4.135 pound

Part C

If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.

Then 1875.62 cubic cm × 0.006

= 11.253

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

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The person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

The above problem is asking how much farther a person will travel in one revolution of the Adventure Land ferris wheel compared to one revolution of the Kiddie Land ferris wheel.

The Adventure Land ferris wheel has a diameter of 30 meters, and the Kiddie Land ferris wheel has a diameter of 10 meters.

This means that the circumference of the Adventure Land ferris wheel (the distance traveled in one revolution) is

3.14×30= 94.2 meters

The circumference of the Kiddie Land ferris wheel is

3.14 ×10= 31.4 meters

Here, 94.2-31.4 =62.8 meters

Therefore, the person will travel 62.8 meters farther in one revolution of the Adventure Land ferris wheel than in one revolution of the Kiddie Land ferris wheel.

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The fraction of the game board that is orange is 1/6

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

Sections = 6

Orange = 1

using the above as a guide, we have the following:

Fraction = Orange /Total Number of sections

So, we have

Fraction = 1/6

Other forms of the fraction are

Fraction = 2/12 and 3/18

Hence, the fraction is 2/6

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The required, there were 644 premium seats and 646 regular seats sold.

Let x be the number of premium seats sold and y be the number of regular seats sold. Then we have two equations:

x + y = 1290 (total seats sold)

30x + 20y = 32240 (total revenue)

We can use the first equation to solve for y in terms of x:

y = 1290 - x

Substituting this into the second equation, we get:

30x + 20(1290 - x) = 32240

Simplifying and solving for x, we get:

x=644

So 644 premium seats were sold. Substituting this into the first equation, we get:

644+ y = 1290

y = 646

So 646 regular seats were sold.

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Answer:

x=144

Step-by-step explanation:

since they are similar their sides have a common ratio

24/x=42/7

7x=42*24

7x=1008

x=144

The roots of the quadratic equation y = 5 · x²  + 2 · x + 7 are contained by x = - 1 / 5 ± i √34 / 5.

In this problem we must solve a quadratic equation, whose roots must be found. This can be done by using algebra properties, by completing the square. First, write the entire quadratic equation:

y = 5 · x²  + 2 · x + 7

Second, use algebra properties to find all roots:

y = 5 · [x² + (2 / 5) · x + 7 / 5]

y = 5 · [x² + (2 / 5) · x + 1 / 25] + 5 · (34 / 25)

y = 5 · (x + 1 / 5)² + 34 / 5

Third, use y = 0:

5 · (x + 1 / 5)² + 34 / 5 = 0

5 · (x + 1 / 5)² = - 34 / 5

(x + 1 / 5)² = - 34 / 25

x + 1 / 5 = ± √(- 34) / 5

x = - 1 / 5 ± √(- 34) / 5

x = - 1 / 5 ± i √34 / 5

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There are 60 seconds in 1 minute, so 4 minutes would be:

4 minutes * 60 seconds/minute = 240 seconds

Therefore, it takes 240 seconds to complete the administrative task.

Answer:

∠ GJK = 102°

Step-by-step explanation:

(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so

2x + 92 + 3x + 63 = 180

5x + 155 = 180 ( subtract 155 from both sides )

5x = 25 ( divide both sides by 5 )

x = 5

Then

∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°

Answer:

3

Step-by-step explanation:

The graph of the table is attached accordingly. It examines the relationship betwen Hours and Height of the tides.

The graph shows that there is very wide variations between the height of the tides.

The relationship cannot said to be inverse or positive

Note, the following are three advantages of graphs: It makes data more attractive and understandable. It aids in the concise summarization of facts. It allows for more accurate data comparison.

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Alan paid  an amount $850 to the bank each month to repay his debt.

The total amount that Alan paid back to the bank is equal to the initial amount that he owed minus the remaining amount after 0.5 year(s):

Total amount paid = Initial amount - Remaining amount

= $11750 - $6650

= $5100

We know that Alan paid this amount back over a period of 0.5 year(s), which is equivalent to 6 months.

Let x be the fixed amount that Alan paid back to the bank each month. Therefore, we can set up the following equation:

Total amount paid = Monthly payment × Number of months

$5100 = x × 6

x = $5100 / 6

= $850

Therefore, Alan paid  an amount $850 to the bank each month to repay his debt.

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The value that lie above 25% of the data of the box plot is 31 and the lower quartile (Q1) = 14 upper quartile (Q3) = 31

Given data ,

The minimum value, which is 14

Now , the lower quartile, which is 16 (25% of the data is below this value)

And , the median, which is 24 (50% of the data is below this value)

Now , the upper Quartile, which is 31 (75% of the data is below this value)

And , the maximum value is 32.

The upper and lower quartiles of a box plot, also known as the 75th percentile (Q3) and 25th percentile (Q1) respectively, represent the range within which the middle 50% of the data falls.

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

Hence , 25% of the data lie above 31, which is the upper quartile.

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Answer:

your answer

Step-by-step explanation:

analogous colors

Answer:

-35.7 as a mixed number is -35 and 7/10.

Answer:

Your answer should be [tex]-35 \frac{7}{10}[/tex]

Step-by-step explanation:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

We have,

To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.

a) 1.241 km = 1.241 × 1000 m = 1241 m

b) 6.002 km = 6.002 × 1000 m = 6002 m

c) 5.168 km = 5.168 × 1000 m = 5168 m

d) 3.4 km = 3.4 × 1000 m = 3400 m

e) 21.32 km = 21.32 × 1000 m = 21320 m

f) 0.895 km = 0.895 × 1000 m = 895 m

Therefore,

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

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Johnson's pizza had a 120-degree angle when he ate it. The solution is choice C.

When a pizza is cut into 12 equal pieces, each piece has a central angle of:

360 degrees / 12 pieces = 30 degrees/piece

If Johnson ate 4 adjacent pieces, then he ate a total central angle of:

4 pieces * 30 degrees/piece = 120 degrees

Therefore, the measure of the angle of the pizza that Johnson ate is 120 degrees. The answer is option C).

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The simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

Given information:

f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)

h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)

Using the rules of logarithms, we can simplify g(x) as follows:

g(x) = log₂(x³) - 6

= 3 log₂(x) - 6.

Now we can substitute this into the expression for h(x):

h(x) = (log₂(x) + 2) + 3 log₂(x) - 6

= 4 log₂(x) - 4

Therefore, the simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

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Answer:

2 yards

Step-by-step explanation:

2 yards equals 6 feet because 2x3=6 or 72 inches because 6x12 equals 72. 1 yard is equal to 3 feet.

The solution of the equation 39=2x+1 is 19

The given equation is 39=2x+1

We have to find the solution of the equation

2x+1=39

Let us find the value of x

Subtract 1 from both sides

2x=38

Divide both sides by 2

x=19

Hence, the solution of the equation 39=2x+1 is 19

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There are a total of 4 + 3 + 2 + 1 = 10 marbles in the bag. The probability of picking a red marble is the number of red marbles divided by the total number of marbles:

Probability of picking a red marble = 4/10 = 2/5

Therefore, the probability Aisha picks a red marble is 2/5 or 0.4 when written as a decimal.

Answer:
y=2x3 - 3

Step-by-step explanation:

Here's the photo for the solution if needed.

The linear model for the given equation would be the model that has the points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).

To find the linear model that has the given equation, come up with values of x and then use the equation to solve for y. The linear model that has the points that you solve for, would be the right one.

Assuming values of x of -1, 0, 1, 2, 3

The y values would be:

x = - 1 :

y = - 2 x ( - 1 ) - 3

y = - 1

x = 0

y = - 3

x = 1

y = - 5

x = 2

y = - 7

x = 3
y = - 9

The linear model has points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).

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