SAFF (Students against Fatty Food) is a group of students who are protesting the food in high school cafeterias. At a recent rally, the students covered the first 40 yards by 40 yards of the football field. There were 24 students in each 8 feet by 8 feet square. How many students were present at the rally?

The measure of the length MP is equal to 6.

Two triangles are similar triangles if they have the same corresponding angle measures and proportional side lengths.

Given is a triangle ΔOMN.

Now, ΔOMN and ΔOPQ are similar. This means that the side lengths are proportional to each other. We can write -

OP/OM = PQ/MN

12/OM = PQ/MN

12/(OP + PM) = PQ/MN

It is given that -

PQ = MP + 2

12/(OP + PM) = (MP + 2)/MN

12MN = (MP + 2)(OP + PM)

12 x 12 = (MP + 2)(MP + 12)

(MP)² + 12MP + 2MP + 24 = 144

(MP)² + 14(MP) - 120 = 0

Let MP = x, then we can write -

x² + 14x - 120 = 0

(x + 20)(x - 6) = 0

(x + 20) = 0   and    (x - 6) = 0

x = - 20   and   x = 6

x = 6      {Lengths cannot be negative}

Therefore, the measure of the length MP is equal to 6.

To solve more questions on similar triangles, visit the link below -

https://brainly.com/question/14926756

#SPJ1

Answer:

Approximately - 9.7%

Step-by-step explanation:

By using the percent change formula, you will be able to calculate the percent decrease.

(b-a)/a times 100 <-- (percent change formula)

(120-133)/133 times 100

-13/133 times 100

-9.7744%

Answer:

  9.8% decrease

Step-by-step explanation:

You want the percent decrease from 133 to 120.

The amount of change as a percent can be found using the formula ...

  percent change = ((new value)/(old value) -1) × 100%

Here, the new value is 120, and the old value was 133. The change is ...

  percent change = (120/133 -1) × 100% ≈ (0.90226 -1) × 100%

  = -0.09774 × 100% ≈ -9.8%

The change from 133 to 120 is a 9.8% decrease.

__

Additional comment

When the sign of the change is negative, as here, the change is a decrease. If the sign is positive, the change is an increase. That is, a change of -9.8% is a 9.8% decrease. (You can use either the minus sign or the word "decrease" to indicate the direction of the change. The acceptable form of the answer will depend on your grader.)

<95141404393>

A linear system has one solution if the slopes of the equation of lines are different.

The 3  possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

A linear equation is equal to the equation of a line, which has the form:

y = mx +b

where m = slope

If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.

Example:

2x + 5y = 34  .. .. (equation 1)

x + 5y = 32  .........(equation 2)

Change the equation 1 and equation 2 into slope-intercept form:

y = (-2/5) x + 34/5   ..... (equation 1a)

y =  (-1/5) x + 32/5   ..... (equation 2a)

The slope of equation is (-2/5) while equation 2 is (-1/5), which is different from equation 1.  Hence, the system of linear equation has one solution.

Learn more about linear system here:

https://brainly.com/question/25858757

#SPJ4

The proportion equation for c in terms of j is written as c = 0.9j

In order to find the proportional equation for c in terms of j that matches the context, what you would have to do would be to divide 9.90 dollars by 11 bottles of pineapple juice.

This would tell us the price that one of the bottles of juice is been sold for.

Hence we would have

9.90 / 11

= 0.9

Hence the equation would be: c = 0.9j

Read more on proportional equations here: https://brainly.com/question/24868934

#SPJ1

that usually means that word has a definition that will be given at the bottom of the page or in the glossary depending on what type of book or excerpt of text you have.

hope this helps!

Answer:

POKEMON YEAH!

Okay, so you first want to take 2485, and subtract it from 4500, because that is the amount of money he has already collected.

4500 - 2485 = 2015

Now you need to find out how many time you can multiply 155, to get 2015, or higher. In this case, I am just gonna divide:

2015/155 = 13

It will take him 13 more weeks to have enough for the Pokemon cards!

Step-by-step explanation:

Hope it helps! =D

The function of the scenario is f(x) = 18.5(1.06)^x

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

Initial value = $18.50

Rate = 6%

The function of the scenario is then represented as

f(x) = Initial value * (1  + rate)^x

Substitute the known values in the above equation, so, we have the following representation

f(x) = 18.5(1 + 6%)^x

Evaluate

f(x) = 18.5(1.06)^x

This means that

x = 10

So, we have

f(10) = 18.5(1.06)^10

Evaluate

f(10) = 33.13

This means that

x = -15

So, we have

f(-15) = 18.5(1.06)^(-15)

Evaluate

f(-15) = 7.72

Hence, the price is $7.72

Read more about exponential function at

https://brainly.com/question/2456547

#SPJ1

Therefore, as a result, the angles of the triangle m∠ABD and m∠DBC equal 37 et 58 degrees, accordingly.

You can link any key steps in a plane to form triangle, that have sides and three angles. They were among of the first geometric forms to be examined. Since triangles might well be divided into any polygon, regardless of whether it contains four, five, six, ... n sides, they are very significant.

Here,

Given that in this case mABC is 95 degrees

The meeting of two lines forms an angle, while a line cutting an angle in half equally divides it.

Looking at the example,

∠ABC is equal to ∠ABC + ∠ABCD.

with the following

95 degrees, ∠AB

∠ABD = 2x + 23

∠DBC = 9x - 5

Put the missing pieces of the equation in.

95 = 2x + 23 + 9x - 5

95 =11x +18

11x = 95 - 18

11x = 77

x = 77/11

x = 7

Recognize the angle AB

∠ABD = 2x + 23

∠ABD = 2(7) + 23

<ABD = 14 + 23

∠AB = 37°

Apply the ∠DBC angle.

95 - ADBD is ∠DBC.

∠DBC = 95 - 37

A DB of 58 degrees

The readings of m∠ABD and m∠DBC are therefore 37 and 58 °, respectively.

To know more about triangle, visit

brainly.com/question/2773823

#SPJ1

The minimum number of pizzas must they sell in order to have at least $300 is 44.

What is the profit?

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.

The student council needs to raise $300 - $235 = $65 to reach their goal.

They make a profit of $1.50 for each pizza they sell.

so they need to sell $65 / $1.50 = 43.333 pizzas to reach their goal.

As you cannot sell a fractional number of pizzas, they need to sell at least 44 pizzas to raise enough money for the field trip.

Hence, the minimum number of pizzas must they sell in order to have at least $300 is 44.

To learn more about the profit visit,

https://brainly.com/question/26483369

#SPJ4

Answer:

36

Step-by-step explanation:

let the number be 10x+y

x - y = 3 (eq 1)

given: y = 2x (eq 2)

putting 2 in 1

x - 2x = 3

-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)

y = 6

number is 36

The Two steps equation in mathematics are the equations that can be solved within exactly two steps.

What is a Two Step Equation ?

The Two Step Equation are the algebraic problems that  just take two steps to solve. It is a linear equation in one variable.

When solving the two step equation, we have to perform operation on both sides of the equation .

For Example : Solve [tex]2x+6=12[/tex] ;

Step1 : we Subtract -6 from both sides to isolate variable x.

⇒ [tex]2x + 6 - 6 = 12 - 6[/tex]

⇒ [tex]2x = 6[/tex]

Step2 : We Divide both the sides of equation by 2 and solve for x.

⇒ [tex]\frac{2x}{2} =\frac{6}{2}[/tex]

⇒ [tex]x = 3[/tex] ;

Therefore , the equation is solved in two steps .

The given question is incomplete , the complete question is

What is the two step equation in math ?

Learn more about Two Step Equations here

https://brainly.com/question/26119747

#SPJ4

Answer:

C. x=68 and y=112

Step-by-step explanation:

We can find that x=68 by adding 52 and 60 together which would get us 112. Then subtracting 112 from from 180 leaving us with our sum of 68, which means x=68. Then we find the value of y by adding the two interior angles on the opposite sides of the triangle. So 52+60=112. This makes y=112.

-Hope this helped

Answer:

x = 68

y = 112

Step-by-step explanation:

The interior angles of a triangle add to 180º.

Using this knowledge, we can solve for x:

52º + 60º + xº = 180º

↓ subtract 52º and 60º from both sides

xº = 180º - 52º - 60º

xº = 68º

x = 68

The interior and corresponding exterior angles of a triangle are supplementary (they add to 180º).

Using this knowledge, we can solve for y:

xº + yº = 180º

↓ substitute for solved x-value

68º + yº = 180º

↓ subtract 68º from both sides

yº = 112º

y = 112

If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

If p(x) is a polynomial function with p ( 3/4 ) = 0

Then we need to find which of the given statements are true.

A. The function has a factor of (4x + 3).

If x=3/4 then 4(3/4)+3 which is not equal to zero

B. The function has a factor of (4x – 3).

If x=3/4 then 4(3/4)-3 which is equal to zero

C. The function has a factor of (3x + 4).

If x=3/4 then 3(3/4)+4 which is not equal to zero

D. The function has a factor of (3x – 4).

If x=3/4 then 3(3/4)-4 which is not equal to zero

Hence, If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).

To learn more on Polynomials click:

https://brainly.com/question/11536910

#SPJ1

As a result, using the values provided, we can turn these data into a bar graph.

A graph is a type of non-linear data structure that consists of nodes, also called vertices, and edges. Any two edges can connect the nodes, which are also known as vertices in a graph. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 5, and 4, 50.

Here,

The gene contributes to the development of pigment.

Yes, factors such as temperature, light cycle, and the presence of mutagens can affect the color of the fur.

In the evolution chart, Mcl provided has ullets that it runs. In mature solutions, the dominating truit moderate is thus always present.

Therefore, using the supplied numbers, we may convert these data into a bar graph.

To know more about graph , visit

brainly.com/question/17267403

#SPJ1

Answer:

It will take approximately 14.2 years for April’s money to double.

Step-by-step explanation:

Answer:

y = 2x - 1

Step-by-step explanation:

Point 1: (0, -1); Point 2: (1, 1)

           (x₁, y₁)              (x₂, y₂)

y₂ - y₁      1 - (-1)       1 + 1       2

---------- = --------- = -------- = ------ = 2

x₂ - x₁      1 - 0           1          1

y - y₁ = m(x - x₁)

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

y + 1 = 2x - 0

   -1          -1

-----------------------

y = 2x - 1

I hope this helps!

A normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

Since all three of these variables are equal in a normal distribution, they serve as the center of the graph and can either be zero or not.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The distribution's mean is another name for the center of the range.

Therefore, a normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

Know more about normal distribution here:

https://brainly.com/question/4079902

#SPJ4

Answer:

x = 9

Step-by-step explanation:

The equation is y = mx + b

m = The slope

b = y-intercept

The slope here is undefined, and there is no y-intercept, so the equation is

x = 9

Bacteria are important in the nitrogen cycle because they convert gaseous nitrogen into ammonia.

The nitrogen cycle is a biogeochemical process through which nitrogen is changed into a variety of forms before returning to the atmosphere after first entering the soil and then organisms.

Given:

The cycle's most crucial component is bacteria.

The nitrogen is changed between states by bacteria so it can be utilised.

Different bacteria assist nitrogen change states when it is absorbed by the soil so that it may be absorbed by plants.

Then, the plants provide the nitrogen for the animals.

Hence, Bacteria convert gaseous nitrogen into ammonia.

Learn more about Nitrogen Cycle here:

https://brainly.com/question/1615727

#SPJ1

The required length of the curst on the edge of one piece of pizza 1.5 π. Option D is correct.

Perimeter is the measure of the figure on its circumference. The perimeter of a circle is given as 2πr, where r is the radius of the circle.

here,
A pizza has an 18-inch diameter
Circumference of pizza = 18π

The pizza is sliced into 12 pieces, and the length of the crust on the edge of one piece of pizza is given as,
= 18π/12
= 1.5π

Thus, the required length of the curst on the edge of one piece of pizza is 1.5 π.

Learn more about perimeter here:

brainly.com/question/6465134

#SPJ1

On solving the provided question, we can say that - the value of x in triangle ABD is = 60

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here, in triangle ABD

x = 60

as its acute angle

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:Subtract

8

from

−

16

.

−

24

≥

0

Step-by-step explanation:

In the graph, there is a strong positive relationship between the variables. Option D

We know that the term correlation has to do with how two or more variables are related. The way that the variables are related can be seen from the graph that is shown.

There is a strong positive correlation if we notice that the straight-line of the graph is moving in the positive direction. As we can see from the graph that we have, there is a positive correlation among the variables.

Learn more about correlation:https://brainly.com/question/30116167

#SPJ1

The two lines are neither parallel nor perpendicular to each other.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the two equations of the lines are y= -1/3x+2 and 5y+15x=-40.

y= -1/3x+2

5y+15x=-40.

5y = -15x - 40

y =-3x - 40/3

Here the slopes of the lines are,

m₁= -1 / 3

m₂ = -3

For the lines to be parallel the slopes should be equal and for the lines to be perpendicular the slopes should be inverse and reciprocal.

Here the slopes are neither equal nor have the inverse reciprocal.

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ1

By unitary method, you can get  joules by $1.

When given a percentage of an amount, the unitary method can be used to determine the full amount. For instance, if $23 represents 10% of a sum of money, then $10 times $23 equals $230. $6000 is equal to 8% of a sum of money.

Price of 1 Gallon= $3

Energy produced by 1 gallon =  joules

by $1 , you can get 1/3 gallon

energy produced by 1/3 gallon = = joules

To know more about unitary method visit:-

brainly.com/question/22056199

#SPJ4

Answer:

[tex]\text{Perimeter}=8x^2+14x-5[/tex]

Step-by-step explanation:

[tex]\text{Perimeter}=(7x-4)+(3x^2+7x-1)+(5x^2)\\\text{Perimeter}=7x-4+3x^2+7x-1+5x^2\\\text{Perimeter}=5x^2+3x^2+7x+7x-4-1\\\text{Perimeter}=8x^2+14x-5[/tex]

Check the picture below.

If the student perform one trial of scientific experiment , and the result of that trial do not support the prediction , then the student should repeat the experiment , modify the experiment and can use alternative Method .

If in the Scientific Experiment the result does not support the prediction of the student in one trial , then the student can :

(i) Modify the Experiment :

The students can modify scientific experiment in other way and try again. For Example, they student change variables being tested or methods used to collect data.

(ii) Use Alternative Explanations :

The students can use alternative explanations for  results. It may be possible that the prediction was correct, but there were other factors  that may influence outcome of experiment.

(iii) Repeat the Experiment :

The student can repeat the experiment by the same procedures to see if he gets same results and if results are consistent, it can concluded that the prediction was incorrect .

The given question is incomplete , the complete question is

Student perform one trial of a scientific experiment if the result of that trial do not support the prediction what should the student do next ?

Learn more about Scientific Experiment here

https://brainly.com/question/28531991

#SPJ4

Answer: 10.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

c