Police stop every fifth car at a sobriety checkpoint.

The area of a triangle is 4 square units.

Given that, the coordinates of the triangle ABC are A(4, 3), B(5, 1) and C(1, 1).

We need to find the area of a triangle ABC.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

The base of the triangle = |5-1|=4

From vertices, A(4, 3) to the base the distance is 2 units at the vertice (4, 1)

So, the height of the triangle = 2 units

Now, the area of a triangle ABC = 1/2 × 4 × 2 = 4 square units.

In the given solution the height of a triangle is wrongly calculated.

Therefore, the area of a triangle is 4 square units.

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Answer:

Step-by-step explanation:

 a : b

 9 : 6

 2 : x

Cross multiply

6*2 = 9x

12 = 9x

12/9 = x

4/3 = x

The numbers as powers of 5 are 5^-1, 5^-2, 5^-3 and 5^0

The numbers are given as:

• 0.2

• 0.04

• 125^-1

• 15^0

Number 1: 0.2

Express as fraction

1/5

Apply the power rule of indices

5^-1

Number 2: 0.04

Express as fraction

1/25

Express 25 as 5^2

1/5^2

Apply the power rule of indices

5^-2

Number 3: 125^-1

Express as fraction

1/125

Express 125 as 5^3

1/5^3

Apply the power rule of indices

5^-3

Number 4: 15^0

Evaluate the exponent

15^0 = 1

Express 1 as 5^0

15^0 = 5^0

Hence, the numbers as a power of 5 are 5^-1, 5^-2, 5^-3 and 5^0

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Answer: 120km/hr

He went from A to B in 1 hour

Answer:

15. x = 4

17. AB = 9

Step-by-step explanation:

15.

Since B is in the middle of AC, AB + BC = AC

So,

x + 5 + 2x - 4 = 13

3x + 1 = 13

3x = 12

x = 4

17.

Since B is in the middle of AC, AB + BC = AC

So,

x + 16 + x + 17 = 19

2x + 33 = 19

2x = -14

x = -7

Going back to the question, it says to find the length of AB.

AB = x + 16 = -7 + 16 = 9

Answer:

In ascending order:8,12,16,18,20

Step-by-step explanation:

median=?

N=5

now

median =(N±1/2)th item

=(5±1/2)th item

(6/2)th item

=3rd item

so median quiz score is 16

Hope its helpful for you

Step-by-step explanation:

13 is the answer that is need

The hypothesis of both statements are false.

1) Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear,

Thus, if A, B, C, and D are collinear, then they cannot lie in the same plane.

Thus, the hypothesis is not true.

2) When we bisect an angle, it is possible that one of the endpoints of the line may be outside the interior of the bisected angle. Thus, the hypothesis is Not true.

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1. A. 2/3 of the volume of the rectangular prism crate = 5.7 ft³

B. Amount of space the dog will occupy is: 2.55 ft³. Josiah should buy the medium crate.

2. 21.05 ft²

The volume of a rectangular prism = (length)(width)(height).

1. Part A:

Length of the rectangular prism crate = 2.5 ft

Width = 1.7 ft

Height = 2 ft

Volume of the rectangular prism crate = (2.5)(1.7)(2)

Volume of the rectangular prism crate = 8.5 ft³

2/3 of the volume of the rectangular prism crate = 2/3(8.5) = 5.7 ft³

Part B:

Amount of space the dog will occupy = volume = (length)(width)(height).

Length = 2 ft

Height = 1 2/3 = 1.7 ft

Width = 3/4 = 0.75 ft

Amount of space the dog will occupy = volume = (2)(0.75)(1.7)

Amount of space the dog will occupy = volume = 2.55 ft³

The space the dog will occupy is less than 2/3 of the space of the crate, therefore, Josiah should buy the medium crate.

2. Amount of fabric needed to cover the crate = surface area of rectangular prism - (lw) = 2·(1.7·2.5+2·2.5+2·1.7) - (2.5)(1.7)

= 25.3 - 4.25

= 21.05 ft²

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Answer:  He can make 9 hamburgers.

Step-by-step explanation:

one  hamburger can be made by 1/3 of beef,

so according to ratio and proportions ,

1 beef can make 3  hamburgers,

hence 3 pound of beef can be used to make

=3*3

=9  hamburgers

hence,

He can make 9 hamburgers.

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Answer:1

Step-by-step explanation: firstly , divide 3 by 1\3  then 3÷1\3=1

The number added to the numerator and the denominator is 2/3.

It is given in the question that when the same number is added to the numerator and denominator of fraction 5/7, the result is 17/23.

We have to find the number added to the numerator and the denominator.

Let the number be x.

Hence, according to the data given in the question, we get,

(5 + x)/(7 + x) = 17/23

By cross - multiplication, we get

23(5 + x) = 17 (7 + x)

Opening the bracket according to the distributive property of addition and multiplication, we get,

115 + 23x = 119 + 17x

23x - 17x = 119 - 115

6x = 4

x = 4/6

x = 2/3

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======================================================

Explanation:

To find the inverse, we swap x and y, then solve for y.

y = 2x-3

x = 2y-3

x+3 = 2y

2y = x+3

y = (x+3)/2

y = x/2 + 3/2

y = (1/2)x + 3/2

This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.

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

Another approach:

Since we're given a list of multiple choice answers, we can rule out the non-answers.

Plug x = 0 into the first equation of choice A. It leads to y = 2

That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.

This allows us to rule out choice A. Choices B and C are similar stories.

Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.

Answer:

Step-by-step explanation:

Algorithm for deriving the formula of the inverse function

Step 1. In the formula for the original function, replace the notation of the argument and the value:

Step 2. From the resulting formula, express y(x).

Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.

[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]

[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]

3/8 pints of milk will fill an empty mug of the same size.

In this question, we have been given Pia poured 1/4 pint of milk into an empty mug.

The milk filled 2/3 of the mug.

We need to find the pints of milk that will fill an empty mug of the same size.

Let 'm' pints of milk will fill an empty mug of the same size.

From given data, we get proportion.

⇒ (1/4) / (2/3) = m / 1

We simplify above equation to find the value of m.

⇒ (2/3) m = 1/4

⇒ m = (1/4) × (3/2)

⇒ m = 3/8

Therefore, 3/8 pints of milk will fill an empty mug of the same size.

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The number of books taken by each student is 6.

Average is defined as the ratio of the sum of the number of the data sets to the total number of the data. The average actually determines the middle value of the data.

Given that the total number of books checked out of the library at your high school is 14,400 and the student population is about 2400.

The average is calculated by dividing the sum of the total number of items by the total counts of the items.

Average = 14400 / 2400

Average = 6

Therefore, the number of books taken by each student is 6.

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The equation that could be used to determine, m, the average number of miles she would have to ride to meet her goal is; m = (55.5 - 19)/5

Distance that she wants to ride this week = 55.5 miles

Distance she has already ridden so far = 19 miles

Now, we are told that she will ride 5 more days.

If m is the average number of miles she has to ride to meet her goal, then we can say that;

5m + 19 = 55.5

Making m the subject by, we have;

m = (55.5 - 19)/5

Thus, the equation that could be used to determine, m, the average number of miles she would have to ride to meet her goal is;

m = (55.5 - 19)/5

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when drawing a line use arrows to show that the line continues endlessly in both directions.

As a reminder, an arithmetic sequence or arithmetic progression (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the progression is constant.

Therefore, the expression for the nth term is

an = a₁ + (n − 1) d

and in general

an = am + (n - m) d.

where d is the difference.

For an arithmetic series with initial term a₁ and difference between terms of d

an = a₁ + (n − 1) d

We are told

d = -2 and

S8 = 240

So,

a1 = 240 = a1 + ( 30 - 1) * ( -2 ) = a1 - 58

a1 = 240+58 =298

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Answer: 2x+9>17 or  5x+10<10 compound inequalities is x<0

Step-by-step explanation:

What is Meant by Compound Inequality?

In Mathematics, a compound inequality is a sentence which has two statements connected using the word “and” or by the word “or”. If the statements are connected using the word “and”, then both the statements of the compound sentence are true at the same time. If the statements are connected using “or”, then the compound sentence is true if at least one statement is true.

2x+9>17 or  5x+10<10

Let take 2x+9>17

Subtract -9 on both sides

2x+9-9>17-9

2x+0>8

2x>8

Now we need to divide by 2 both sides

2x÷2>8÷2

x>4

Now we solve 5x+10<10

we need to subtract -10 on both side

5x+10-10<10-10

5x+0<0

5x<0

Now we need to divide  5 on both sides

5x÷5<0÷5

x<0

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0<x>4

the value of x lies between 0 and 4.

A compound inequality is an inequality that combines two simple inequalities. A compound inequality is made up of two inequalities connected by the word “and” or the word “or.” To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement.

lets take 2x+9>17

now lets subtract 9 from both sides.

2x + 9 > 17

     - 9 > -9

2x > 8

now divide both sides by 2

2x ÷ 2 > 8 ÷ 2

x > 4

lets take the second part i.e 5x +10 <10

substract 10 from both sides

5x + 10 < 10

     - 10 < -10

5x < 0

now divide both sides by 5

5x ÷ 5< 0 ÷ 5

x < 0

0<x>4

the value of x lies between 0 and 4.

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Part A: The student was supposed to divide before subtracting

Part B: The student was supposed to simplify the parentheses before finding the exponents

Part C: The simplification of the expression gives -16.

From the question, we are to simplify the given expression

The given expression is

(∛64 - 16 ÷ 2)(2 - 4)²

Part A:

The mistake the student made was not applying the PEMDAS rule

P - Parentheses

E - Exponent

M - Multiplication

D - Division

A - Addition

S - Subtraction

Since division comes before subtraction, the student was supposed to divide before subtracting

Part B:

The student mistake was trying to simplify the exponent before simplifying the parentheses. The student was supposed to simplify the parentheses before finding the exponents.

Part C:

Simplifying the expression

(∛64 - 16 ÷ 2)(2 - 4)²

Simplify the cube root

(4 - 16 ÷ 2)(2 - 4)²

Divide

(4 - 8)(2 - 4)²

Simplify the parenthesis

(-4)(-2)²

Simplify the exponent

(-4)(4)

Evaluating

-16

Hence, the simplification of the expression gives -16.

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The numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

It should be noted that even numbers can be divided by 2.

The multiple of 3 in the numbers are 12 and 18 that can be divided by 2 as well.

Therefore, the numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.

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From the question, the first table is not a function while the other two tables are functions.

A function is a correspondence or mapping from a first set of numbers, called the domain of the function, to a second set of numbers, called the range of the function, such that for each member of the domain there is exactly one member of the range.

A function is said to be one-to-one if every y value has exactly one x value mapped onto it, and many-to-one if there are y values that have more than one x value mapped onto them. This graph shows a many-to-one function.

4) We see that all the y-values are the same or equal. Thus, we can say that it is not a function because it doesn't match the definition above.

5) Yes the table describes a function because all input values produces a unique output y-value.

6) Yes, the table represents a function because all input values produces a unique output y-value.

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The area enclosed by the ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] is 60 square units.

The general form of the equation of ellipse is  [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

Given the equation of ellipse is,  [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex]

⇒ [tex]\frac{x^2}{2^2}+\frac{y^2}{9^2}=1[/tex]

That is, a = 2 and b = 9

Now,  [tex]\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}[/tex]

⇒ [tex]y=\frac{9}{2} \sqrt{4-x^2}[/tex]

Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant

Therefore, Area of ellipse in the first quadrant, A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx[/tex]

Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0

A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx[/tex]

  = [tex]\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx[/tex]

  = [tex]\int\limits^2_0{9 sin^2\theta} \, dx[/tex]

 = [tex]\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta[/tex]

  = [tex]\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta[/tex]

  = [tex]\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta[/tex]

  = [tex]\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta[/tex]

  = 27/2 x (-cosθ) - 9/6 x (-cos3θ) |  θ = 0 to  θ =  π/2

  = 15 square units.

Therefore, the area enclosed by ellipse  [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] = 4 x A = 4 x 15 = 60 square units.

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Answer:

8^3

Step-by-step explanation:

there are three 8s soo all u do is count the number and then how many of that same number you can put into an exponent

Answer:

19.56

Step-by-step explanation:

Number of pages x copies

164 x 16 = 2608

Divided by number of pages per ream

2608 ÷ 50 = 5.216

Total Reams by cost

5.216 x 3.75 = 19.56