MP Precision Three students measure the height of a bookshelf. Student A measures 72 units, Student B measures units, and Student C measures 6 units. The teacher says all three students are correct. What units did each student use? 15​

According to the given information, the correct answer is option b): (z+15)(z-15).

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent quantities or values that can vary, depending on the values assigned to the variables in the expression. Algebraic expressions can be simple or complex, and they can have one or more variables.

We can factorize the expression z² - 225 using the difference of squares formula, which states that a² - b² = (a + b)(a - b). In this case, a = z and b = 15, so we have:

z² - 225 = (z + 15)(z - 15)

Therefore, the correct answer is option b): (z+15)(z-15).

To know more about algebraic expressions visit:

brainly.com/question/17499155

#SPJ1

Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

For more questions Pythagorean theorem:

https://brainly.com/question/343682

#SPJ8

Answer:

21

Step-by-step explanation:

\(\frac{v}{7} = 3\)

multiple both sides by 7

v = 21

Check:

21/7 = 3

3 = 3

Answer:

b. 21

Step-by-step explanation:

Edge 2023

Answer:

9 is added by 4 times y is the correct answer.

The given option don't describe the expression 4y+9

The total number of workers if, In a​ company, 90​% of the workers are women, If 440 people work for the company who​ aren't women is 4400.

What is percentage?

As it is clear from the term per-cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

In a​ company, 90​% of the workers are women,

If 440 people work for the company who​ aren't women,

Calculate the percentage of people who aren't women as shown below,

The percentage of people who aren't women = 100% - the percentage of women

The percentage of people who aren't women = 100% - 90%

The percentage of people who aren't women = 10%

Assume that there are a total of x workers then according to the statement,

10% of x = 440

10 / 100 × x = 440

x = 440 × 100 / 10

x = 4400

Learn more about percentages at:

brainly.com/question/20818421

#SPJ1

Answer:

10+2x

the tree would be 40 feet tall in 15 years.

The total number of outcomes as obtained from the sample space is 30.

From the question, we have:

Sticks = 5

Word = SPRING

From the above, we have:

Popsicle sticks = 1, 2,3,4,5

Letters of "SPRING" = S, P, R, I, N, G

Creating the sample space (S), we have

S = {S1, S2, S3, S4, S5, P1, P2, P3, P4, P4, R1, R2, R3, R4, R5, I1, I2, I3, I4, I5, N1, N2, N3, N4, N5, G1, G2, G3, G4, G5}

The sample space is created by selecting a letter from the word and a number from the list

Counting the number of samples in the space, we have

Outcomes = 30

This means that the total number of possible outcomes is number of total occurrences in the sample space which is 30.

Hence, the number of outcomes is 30.

The tree diagram is attached

Learn more on sample space

https://brainly.com/question/29719992

#SPJ9

Answer:

A, D,

A.) He decides to give all male athletes Gatorade and the female athletes eitherPowerade or Vitaminwater.

D.) He has some of the athletes drink the sports drink two hours beforerunning,others one hour before running, and the rest 30 minutes beforerunning.

Step-by-step explanation:

Confounding variables could be described as variables which introduces elements that causes unwanted relationship between measured variables in data. Such that observed relationship is actually not as a result of the independent variable.

The confounding variables in the options chosen are gender and timing of the consumption and when the athletes eventually ran.

As for gender, male athletes are expected to put up a better running speed and energy than women and Hence would finish the rate faster based on these fact. Hence, it will be wrong to conclude that Gatorade has Better effect on performance.

As for timing, those who run shortly after taking an energy drink are more likely to be boosted that those who take much later and this the effect may not necessarily be in the type of energy drink consumed.

Confounding variables are the variables which are not related to the experiment.

Confounding variables are the variables which are not related to the experiment. Confounding variables provides the affects the useless results and affects the experiment.

Given information-

The total number of meters the athletes runs is 400 meters.

The sports drink given to athletes are Powerade, Gatorade and Vitamin water.

The given options are,

Hence,

learn more about the confounding variable here;

https://brainly.com/question/10458420

Answer:

x = 50

Step-by-step explanation:

By the definition of vertical angles you can set these two equations equal to each other.

2x+20=3(x-10)

then, just simplify to get the correct answer by using order of operations.

2x+20=3x-30

x=50

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

To know more about denominator, visit:

https://brainly.com/question/17153086

#SPJ1

Answer:

The answer is D. -9 and -3

Step-by-step explanation:

since the graph starts at 1 and goes backwards, it cant be 1. so that rules out A. and B. then it requires the numbers to be negative because if they are a whole number over 1, they don´t fit the inequality. I hope this helps :))

Answer:

x = 12

Step-by-step explanation:

We use the Alternate Interior Angles Theorem to help us solve for missing degree x.

Step 1: Set up equation

m∠2 = m∠3

35° = (4x - 13)°

Step 2: Solve for x

35 + 13 = 4x - 13 + 13

48 = 4x

48/4 = 4x/4

12 = x

x = 12

Answer:

They did not state exactly what the width or length is. So in this case, let's name the number of width to be x. And thus we can derive to the conclusion of,

Step-by-step explanation:

Width : x

Length : x-44 (from the 1st sentence of question)

So, We all know that a rectangle has 2 Lengths and 2 widths. So we can derive the conclusion that,

2(x)+2(x-44)=150150

2x+2x-88=150150

4x-88= 150150

4x= 150150+88=150238

4x=150238

x= 150238÷4

=37559.5

Answer:

The width is 8 meters and the length is 3(8)-2=22 meters. Hope this helps (owo)/ brainlist please.

Step-by-step explanation:

Let x= the width

then 3x-2= length (because the length is 2 meters less than 3 times the width)

P=2l+2w

60=2(lenght)+2(width)

60=2(3x-2)+2x      

60=6x-4+2x    Distribute

60=8x-4          Combine like terms

64=8x             Divide both sides by 8

8=x

Therefore, the number of students who study only one subject is n(H-only) + n(G-only) = 14 + 28 = 42.

In mathematics, a set is a collection of distinct objects, which are called its elements. These objects can be anything, such as numbers, letters, or even other sets. Sets are usually denoted by capital letters and the elements of a set are listed within braces, separated by.

Given by the question.

i. n (H ∩ G) can be found using the formula:

n(H ∩ G) = n(H) + n(G) - n(H U G)

where n (H U G) represents the number of students who study either History or Government or both.

We know that n(H) = 2x and n(G) = 3x. Also, n(U) = 54, which means the total number of students is 54. Therefore, we can write:

n (H U G) = n(H) + n(G) - n (H ∩ G)

54 = 2x + 3x - x

54 = 4x

x = 13.5

Since x must be a whole number, we can round it up to 14. Therefore, n (H ∩ G) = x = 14.

ii. The number of students who study only one subject can be found by subtracting n (H ∩ G) from n(H) and n(G) respectively, and then adding the number of students who study neither History nor Government.

n(H-only) = n(H) - n (H ∩ G) = 2x - x = x = 14

n(G-only) = n(G) - n (H ∩ G) = 3x - x = 2x = 28

n(Neither) = n(U) - n (H U G) = 54 - 14 = 40

To learn more about subtracting:

https://brainly.com/question/2346316

#SPJ1

Answer:

x= 7.5

Step-by-step explanation:

The 3rd answer, y = 2x + 3

The graph has a y-intercept of positive 3. The y-intercept is when x is equal to 0 on the line.

Answer: A

In looking for solutions in the graph of y=f(x) where f(x) = 0, you're looking for the x-intercepts.  The catch is that you only want the x-value of the intercepts.

The intercepts are (-4,0) and (7,0), so the solutions are -4 and 7.

Answer:

4.2 (nearest tenth)

Step-by-step explanation:

Draw a scatter plot using the given information.

Draw a line of best fit (regression line).

To find the Arm Span of a player with a height of 4.4, find y-value of the point of intersection of x = 4.4 and the line of best fit.

Therefore, based on the table, the Arm Span of a player with a height of 4.4 is:

Extrapolation

For this problem, we have used the line of best fit (regression line) to predict a value of that is outside the range of the original data.

When using values of x outside the range to predict corresponding values of y, this is called extrapolation.

These predictions can be unreliable because there is no evidence that the relationship described by the regression line is true for all values of x. Therefore, caution should be applied in these cases.

The other way to approach this question would be to enter the data from the table into a statistical calculator and calculate the regression line of y on x:  

After entering the data into a statistical calculator:

Therefore, the equation of the regression line is:

\(y=-\dfrac{1}{120}+\dfrac{23}{24}x\)

Substitute x = 4.4 into the equation:

\(\implies y=-\dfrac{1}{120}+\dfrac{23}{24}(4.4)\)

\(\implies y=\dfrac{101}{24}\)

\(\implies y=4.2\; \sf (nearest\;tenth)\)

Using the concept of ratio, the month of February had a better ratio in sales compared to January

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

This is the process of comparing two quantities against one another to determine their ratio against each other.

In the question given;

January = 10 minivans, 20 sedans

The ratio of minivans to sedan = 10 / 20 = 1/2

The ratio of minivans to sedan in January = 1/2

February = 15 minivans, 25 sedans

The ratio of minivans to sedans  = 15/25 = 3/5

The month of February has the highest ratio

Learn more on ratio here;

https://brainly.com/question/2328454

#SPJ1

Answer:

57.4

Step-by-step explanation:

82.4 - 25 is too easy, a calculator can solve this.

the answer is g(x)= (x+6).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

from the given , we get,

f(x)=x^4

and, f(g(x))= (x+6)^4

hence, the answer is g(x)= (x+6).

To learn more on function click:

brainly.com/question/21145944

#SPJ1

Answer:

Step-by-step explanation:

1. x is inversely proportional to y

x=k/y

k is the constant of proportionality

x =60/y

2. x=60/y

x=60/12

x=5

Answer:

10x^2 or 10x because you are adding x

Answer:

4

Step-by-step explanation:

move the constant to the right 3c+5=17

calcute 3c=17-5

divide both sides 3c=12

so the answer is 4

The vertical parabola that goes through \((x_{1}, y_{1}) = (-2, -3)\), \((x_{2}, y_{2}) = (3, 12)\) and \((x_{3}, y_{3}) = (5, 46)\) is \(x^{2} + \frac{1}{2}\cdot D -\frac{1}{2}\cdot y -\frac{9}{2} = 0\)

The general form of the equation for the vertical parabola is described below:

\(x^{2}+D\cdot x + E\cdot y + F = 0\) (1)

Where \(D\), \(E\) and \(F\) are coefficients of the parabola equation.

We need three distinct coplanar points to determine all coefficients.

If we know that \((x_{1}, y_{1}) = (-2, -3)\), \((x_{2}, y_{2}) = (3, 12)\) and \((x_{3}, y_{3}) = (5, 46)\), then we get the following system of equations:

\(-2\cdot D -3\cdot E + F = - 4\) (2)

\(3\cdot D + 12\cdot E + F = -9\) (3)

\(5\cdot D + 46\cdot y + F = -25\) (4)

The solution set of the system is: \(D = \frac{1}{2}\), \(E = -\frac{1}{2}\), \(F = - \frac{9}{2}\)

The vertical parabola that goes through \((x_{1}, y_{1}) = (-2, -3)\), \((x_{2}, y_{2}) = (3, 12)\) and \((x_{3}, y_{3}) = (5, 46)\) is \(x^{2} + \frac{1}{2}\cdot D -\frac{1}{2}\cdot y -\frac{9}{2} = 0\).

We kindly invite to check this question on parabolae: https://brainly.com/question/21685473

C 89.54 goes to A

D goes to B

A goes to C

B goes to D

F goes to E

Since the laptop is on sale, that would make it $206.99.

It should be noted that r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.

The radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given.

r = [(s - a)(s - b) (s - c)/s]1/2, where s = (a + b + c)/2.

a, b , c actual lengths of the sides,

s = average length of the sides

So that we can write

L = [(L - L)(L - L) (L - L)/L]^1/2

= [(L)(L) (L)/L]^1/2

= [L^2]^1/2

= L

Therefore r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.

Learn more about equations on:

https://brainly.com/question/2972832

#SPJ1