Question 20
A rectangular courtyard has a cement walkway around its perimeter. The area of the courtyard can be represented by the expression 24(5x - 1).
The area of the cement walkway can be represented by the expression 32(5x-1 + 8)- 24(5x-1). Write an equivalent expression that
represents the area of the cement walkway.square yards

Answer: y=-2x+36

Step-by-step explanation:

slope intercept form

Y=mx+b

m= slope

b= Y-intercept

to find the slope, use the slope formula

y2-y1=x2-x1

(4,28),(11,14)

14-28/11-4

-14/7

-2

Slope is -2

y=-2x+b

Substiute in (11,14) to find b

14=-2(11)+b

14=-22+b

b=36

y=-2x+36

Answer:

x< 5

Step-by-step explanation:

See the graph below

The equation y = 10x - 9 is rewritten in standard form as: -10x + y = -9.

A line's equation can be expressed in standard form as Ax + By = C. Here, A, B, and C are integers.

We are given the equation of a line as y = 10x - 9, which is expressed in slope-intercept form. We are asked to rewrite the equation in standard form. Follow the steps below:

y = 10x - 9 [given]

Subtract 10x from both sides of the equation:

y - 10x = 10x - 9 - 10x [subtraction property of equality]

y - 10x = -9

Rearrange the equation to fit the standard form:

-10x + y = -9

Therefore, in standard form, the equation, y = 10x - 9 is rewritten as -10x + y = -9.

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Answer:

(0,14)  This is the y intercept.

(28,0) This is the x intercept.

Step-by-step explanation:

Let x = 0

x + 2y = 28

0 + 2y = 28

2y = 28  Divide both sides by 2

x = 14

(0,14)  This is the y intercept.

Let y = 0

x + 2y = 28

x + 2(0) = 28

x + 28

(28,0) This is the x intercept.

Mr. Kenny can complete five projects without running out of clay.

The number of projects that can be completed will be calculated using division.

1/6 of a pound of clay is required for number of project = 1

7/8 pounds of clay will be required for number of project = 7/8 ÷ 1/6

Rewriting the fraction with numerator and denominator

Number of projects = (7×6)÷(8×1)

Performing multiplication in numerator and denominator

Number of projects = 42/8

Performing division

Number of projects = 5.25

Rounding off, we get number of projects = 5

Mr. Kenny can complete 5 projects.

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Answer: the slope of the line is 4

Step-by-step explanation:

We only need two ordered pairs to find the slope

(-2,-10), (-1,-6)

the slope formula is y2-y1/x2-x1

-6-(-10)/-1-(-2)

-6+10/-1+2

4/1

4

the slope of the line is 4

Answer:

4

Step-by-step explanation:

Knowledge Needed

The slope is the amount the y-value changes on a line when the x-value changes by 1.

Slope Formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Question:

We have the points:

(-2,-10)

(-1,-6)

(0,-2)

(1,2)

We only need 2 points to plug into the slope formula. I'll use the first 2.

(-2,-10) ; (-1,-6)

[tex]\frac{-6--10}{-1--2}[/tex]

[tex]\frac{4}{1}[/tex]

4

The new coordinates of each of the triangle coordinates are;

1) A'(-12, 6), B'(3, 9), C'(-9, 18)

2) A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)

3) X'(-8, 2), Y'(2, 14), Z'(8, 8)

4) X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)

5) A'(-8, 4), B'(2, 6), C'(-6, 12)

6) X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)

7) X'(-20, 5), Y'(5, 35), Z'(20, 20)

8) A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)

Dilation is a transformation whereby an image size could increase or even decrease but will retain the same shape as the original one. Therefore, we will simply multiply each coordinate by the scale factor;

The coordinates of both triangles are given as;

Triangle ABC = A(-4, 2), B(1, 3), C(-3, 6)

Triangle XYZ = X(-4, 1), Y(1, 7), Z(4, 4)

1) The dilation transformation of triangle ABC by a scale factor of 3 means we multiply each ABC coordinate by 3 to get;

A'(-12, 6), B'(3, 9), C'(-9, 18)

2) The dilation transformation of triangle ABC by a scale factor of 1/2 means we multiply each ABC coordinate by 1/2 to get;

A'(-2, 1), B'(1/2, 3/2), C'(-3/2, 3)

3) The dilation transformation of triangle XYZ by a scale factor of 2 means we multiply each XYZ coordinate by 2 to get;

X'(-8, 2), Y'(2, 14), Z'(8, 8)

4) The dilation transformation of triangle XYZ by a scale factor of 1/4 means we multiply each XYZ coordinate by 1/4 to get;

X'(-1, 1/4), Y'(1/4, 7/4), Z'(1, 1)

5) The dilation transformation of triangle ABC by a scale factor of 2 means we multiply each ABC coordinate by 2 to get;

A'(-8, 4), B'(2, 6), C'(-6, 12)

6) The dilation transformation of triangle XYZ by a scale factor of 1/3 means we multiply each XYZ coordinate by 1/3 to get;

X'(-4/3, 1/3), Y'(1/3, 7/3), Z'(4/3, 4/3)

7) The dilation transformation of triangle XYZ by a scale factor of 5 means we multiply each XYZ coordinate by 5 to get;

X'(-20, 5), Y'(5, 35), Z'(20, 20)

8) The dilation transformation of triangle ABC by a scale factor of 1/4 means we multiply each ABC coordinate by 1/4 to get;

A'(-1, 1/2), B'(1/4, 3/4), C'(-3/4, 3/2)

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Answer:

9, 13

Step-by-step explanation:

√81 = √9 x 9 = 9

√169 = √13 x 13 = 13

Franklin has 10 granola bars and 6 pieces of dried fruit. The greatest number of snack bags Franklin can make is 2 bags.

The factor shared by at least two numbers is known as the common factor. Each of the given numbers is divided exactly by two or more numbers.

Here given granola bar = 10 and dried fruit = 6.

Then, the common factors of 10 and 6 are

1, 2, 3, and 6 are used to represent factors of 6.

1, 2, 5, and 10 are used to represent factors of 10.

2 is discovered to be the biggest common factor between 6 and 10.

Then, the greatest number of snack bags Franklin can make is 2 bags.

The complete question -

Franklin wants to create a snack bag for a trip he is going on. He has 10 granola bars and 6 pieces of dried fruit. If the snack bag should be identical without any food left over, what is the greatest number of snack bags Franklin can make?

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The probability of a success gets closer to zero is 15.

What is behavior of the standard deviation ?

The average squared difference between data points and their mean value is called variance, and it is the variance's square root that is used to calculate standard deviation. The symbol for standard deviation can be seen below.

Both the standard deviation and the variance are indicators of dispersion, but the standard deviation is more explicitly the typical distance between a data point and the mean. The majority of the data will be within one standard deviation of the mean. While the variance is not measured in the same units as the actual data, the standard deviation is

If mean deviation is 12, what is its standard deviation?

Lets look the problem .

Given ,

Mean deviation (MD) =12

Here is the inequality to calculate the standard deviation.

6QD=5MD=4SD ,

Where ,QD stands for the Quartile deviation.

SD stands for the standard deviation.

So,

Standard deviation =(5/4)*MD

=(5/4)*12

=15

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The motion of the shape in each frame are:

Rigid transformation is a method in which the orientation, size or position of a given object is changed.

Rigid transformation implies either increasing, decreasing or changing the orientation of a given shape. Some types of rigid transformation are: reflection, rotation, translation, and dilation.

i. Reflection is a method in which a given object is flipped about a reference point or line.

ii. Rotation is the process in which a given object is turned about a certain angle in degrees.

iii. Translation involves moving a given object a definite units horizontally or vertically.

iv. Dilation is a process in which the dimensions of a given object is either increased or decreased as required.

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Answer:

Refer to the photo taken.

Step-by-step explanation:

The Question is based on concept of Simplification and answer to this question is -19√2

What is Simplification?

Simplification is the process of making a task, problem, or system easier to understand and manage. It involves breaking down a concept or problem into simpler parts in order to better understand the whole. Simplification can help streamline a process, making it more efficient and easier to complete. It can also help to make complex topics more accessible to a wider audience. Simplification can also be used to make a difficult problem more manageable, allowing for easier solutions.

Here we are given question 2√2 - 7√8 we can do some simplifications like:
but we know we can write √8 = 3√2
hence putting back in original eqn
2√2 - 7(3√2)
2√2 - 21√2
-19√2
Hence required answer is -19√2 by simplification

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The number of people who speaks neither of these languages is 8.

Set theory is a branch of mathematical logic that studies sets, which can be described informally as collections of objects. Although any object can be collected into a set, set theory as a branch of mathematics is primarily concerned with those that are relevant to mathematics as a whole.

Sets are well-defined collections that are entirely defined by their elements. In this case, in the group of 42 people, 30 people speak Spanish and 20 people speak French, those who speak neither of these languages will be:

= 20 + 30 - 42

= 8

Therefore, 8 people neither speaks the languages.

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Answer: x = 19

Step-by-step explanation:

Let's start with what we have, we'll let x = the number:

4x - 12 = 64

Then we add 12 to both sides:

4x = 76

Divide by 4 from both sides:

x = 19

Answer:

He has 171 colored pencils before drawing

53+118 = c

Step-by-step explanation:

To write the equation:

53+118 = c

171=c

Answer:

x = 53 + 118

Step-by-step explanation:

Now we have to,

→ find and write an equation.

Let's assume that,

→ Total pencils = x

Forming the equation,

→ x = Used pencils + Left pencils

Then the equation will be,

→ x = 53 + 118

→ [ x = 171 ]

Hence, total pencils are 171.

Answer:Y=10X-16

Step-by-step explanation:

y = x3- 2x 2,( 2, 4)( Given)

Find the first outgrowth, calculate the pitch and find the equation.

We should first know the pitch of the wind at(,4)

pitch at any point on the wind is written by its first outgrowth as

dy/ dx = 3x2- 2

pitch at x = 2

m = 3( 2) 2- 2 = 12- 2 = 10

Equation of a digression is given as

c mx = y

Where m is the pitch

Substituting the values

c 10 × 2 = 4

On farther computation

c 20 = 4

c = 16

The equation of the digression is y = 10 x- 16

Thus, the equation of the digression line to the wind is y = 10x-16

Answer:

ax+b=cx+d

Step-by-step explanation:

The length of each wooden plank will be 30.48 cm

Here given,

The total length of the wooden plank is 121.92 centimeters.

Also given that ,

A carpenter cuts the plank into 4 equal parts

=> 121.92 / 4

=> 30.48

Therefore the length of each piece will be 30.48 cm

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Answer: 22%

Step-by-step explanation:

The equations are 2r + b = 8.40 and 3r + b = 9.35. Then the cost of refill and egg breakfast will be $0.95 and $6.50, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The eatery charge you and your companion got was not organized. You requested 2 beverage tops off and the egg breakfast, for a sum of $8.40. Your companion requested 3 tops off and the egg breakfast for $9.35.

Let 'r' be the cost of refill and 'b' be the cost of egg breakfast. Then the equations are given as,

2r + b = 8.40            ...1

3r + b = 9.35            ...2

From equations 1 and 2, then we have

3r - 2r = 9.35 - 8.4

r = $0.95

Then the cost of the egg breakfast will be given as,

2 (0.95) + b = 8.40

b = $6.50

The equations are 2r + b = 8.40 and 3r + b = 9.35. Then the cost of refill and egg breakfast will be $0.95 and $6.50, respectively.

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Answer: y=4x-5     y=4x

Step-by-step explanation:

first we find the slope by using

(y2-y1)/(x2-x1)

(-1-3)/(3-2)

-4/1

-4

so we know the slope is -4

y=4x+b

now we can use either point but ill use (2,3)

we substitute to find b

3=4(2)+b

3=8+b

-5=b

so now we know that the y intercept is -5

so put it together

y=4x-5

if it passes through the origin

it would have the y-intercept of 0

so that equation just be

y=4x

and it keeps the same slope

because they are parallel

hope this helped

Answer: 11 feet

Step-by-step explanation:

The equation for area of square is

area = s^2

So we just need to take the square root of 121, and we will get the answer is 11 ft!

Answer:

11 ft

Step-by-step explanation:

Since the area of the square is 121 (and squares have all four sides the same length), the sides must be 11 feet. Because

11 × 11 = 121

You could show work by using an equation.

Area = s^2

121 = s^2

Square root both sides.

sqrt121 = sqrt(s^2)

11 = s

The side length is 11 feet.

A child of a parent with a mutation in collagen and displaying OI will have 50% probability of also having OI.

Osteogenesis imperfecta (OI) is an inherited or genetic bone disorder which is present at birth. It is also known as brittle bone disease. A child born with OI may have soft bones which fracture easily, bones which are not formed normally, and other problems. Signs and symptoms may range from mild to severe.

Life expectancy for OI babies vary greatly depending on OI type. Babies with Type II generally die soon after birth. Children with Type III may live longer, but mostly only until around age 10.

About 90% of OI cases are caused by autosomal dominant mutations in the type I collagen genes. Mutations in one or the other of these genes cause the body to make either abnormally formed collagen or too little collagen. Mutations in these genes cause OI Types I through IV.

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Answer:

It will take 4 Hours

Step-by-step explanation:

5 x 40 equals 200 (So 200 is the total distance needed to be made)

We can now divde the total distance by how fast the car is moving to get the time.

200 / 50 = 4

So the answer is 4 hours

Answer:

B. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are pairs of angles on the outer side of the two parallel lines but on the opposite side of the transversal. They also have the same degree. So, the answer is B.

Answer: Look in the attachment:

Step-by-step explanation: If it was random sampling, it would all be done randomly, barley without doing anything, and NOT doing anything particular, the 4 that are circled (in the attachment) are the ones that I am talking about; they ARE NOT examples of random sampling. If you look at the attachment, you might understand a little more :P

Answer:

6:5 or [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

[tex]\frac{90}{75}[/tex]  Divide by [tex]\frac{15}{15}[/tex]

[tex]\frac{6}{5}[/tex] or 6:5