y= 2x+4

Slope-intercept form

y=mx+b

Where:

m= slope

b= y-intercept

y=2x+4

Slope = m= 2

Perpendicular lines have negative reciprocal slopes.

So, the slope of the new line = -1/2

New equation:

y= -1/2x+b

Replace x,y by the point (4,2) and solve for b:

2 = -1/2(4)+b

2= -2 + b

2+2 = b

4 = b

New line equation:

**y= -1/2x+4**

One positive integer is 2 less than twice another. The sum of their squares is 745.

The numbers are 13 and 24

**What is Integers?**

The negative numbers are the additive inverses of the corresponding positive numbers.[2] In the language of mathematics, the set of **integers **is frequently denoted by the boldface Z or blackboard bold displaystyle mathbb Z mathbb Z.[3][4][5] An **integer **is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative **integer **with a minus sign

y=first number

x=2y-2 (second number)

y^2+(2y-2)^2=745

y^2+4y^2-8y+4=745

5y^2-8y+4-745=0

5y^2-8y-741=0

Now, from the equation we can solve

5y^2 -65y +57y - 741 = 0

5y(y - 13) + 57(y - 13) = 0

(5y + 57)(y - 13)= 0

now, since the Integers are positive so the value obtained from (5y + 57) = 0 can't hold true.

So, y-13 = 0

y = 13

The first number is : 13

The second number is :

x = 2(13) - 2

x = 26 - 2

x = 24

The second number is : 24

Hence, the numbers are 13 and 24

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Question 10(Multiple Choice Worth 1 points)

(08.01 LC)

Susan wants to conduct a survey to find how much time the students of her school spent eating in a local cafeteria. Which of the following is an appropriate statistical question for this survey?

Who eats at the cafeteria on weekends?

How many students eat in the cafeteria on Mondays?

How many students eat in the cafeteria once a week?

How many hours during the week do you eat in the cafeteria?

I would say D.

How many hours during the week do you eat in the cafeteria.

1st answer is too informal and the 2nd and 3rd answers aren’t focused on the TIME spent

How many hours during the week do you eat in the cafeteria.

1st answer is too informal and the 2nd and 3rd answers aren’t focused on the TIME spent

Create your own quadratic equation whilst explaining how to use the quadratic formula to solve it. Be specific, using a, b, and c of your equation and give solutions to theequation you chose.

Let the quadratic equation is

[tex]x^2-8x+16=0[/tex]Here, a is the coefficient of x^2, b is the coefficient of x and c is the constant.

For the equation we have a = 1, b = -8 and c = 16.

We know that the quadratic formula is given by:

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]So, the solution of the quadratic equation is:

[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(16)}}{2(1)} \\ x=\frac{8\pm\sqrt[]{64-64}}{2} \\ x=\frac{8\pm\sqrt[]{0}}{2} \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Thus, there are two real and equal solutions for the given quadratic equation that is x = 4 and x = 4.

please help me please

**It's a line that slopes down**

**The second choice is the answer because the slope is negative.**

Evaluate x^3 - 6y + 2 for x = 4 and y= 6.

The given expression is x^3 - 6y + 2

We are gven x = 4 and y = 6

Substituting the given values into the expression, it becomes

4^3 - 6*6 + 2

= 12 - 36 + 2

= - 22

estimate the difference of 1 1/5 - 9/10

estimate the difference of 1 1/5 - 9/10

we have

1 1/5=1+1/5=6/5

6/5=12/10

so

12/10-9/10=3/10=0.3

answer is 0.3

estimete

1 1/5 is about 1

9/10=0.9

so

1-0.9=0.10

the estimate is 0.10

steps

Rounded 1 1/5------> 1

we know that

9/10=0.9

so

substitute

1-0.9=0.10

Expressing the relationship between two quantities with a linear equation. A stationary store sells large and small packages of greeting cards. Each large package contains h greeting cards. Each small package contains k greeting cards., which is 4 less than the larger package. Express h in terms of k

large = h greeting cards

small = k greeting cards this is four less

** h = k + 4 This is the answer **

Solve the inequality and draw the solution |r|-3>2

We want to solve the following inequality

[tex]|r|\text{ -3 >2}[/tex]To solve this inequality, we first add 3 on both sides, so we get

[tex]|r|>2+3=5[/tex]So we have the inequality

[tex]|r|>5[/tex]Recall that the absolute value represents the distance from a number to 0. So this means that the number r is greater than 5 or it is less than -5. So we have the following two inequalities

[tex]r>5[/tex][tex]r<\text{ -5}[/tex]This could be drawn on the number line as follows. Greater than (>) means that the number 5 is on the left, and the less than (<) means that the number -5 is on the right side. So we get the following

I need help finding

The proeprty of rhombus is that

The diagnol of a rhombus VX bisect the angle WVY in two equal parts .

Therefore, the angle YVX = angle XVW.

[tex]\angle YVX=(9n+4)^{\circ}[/tex]The another property of rhombus is that the diagnol are perpendicular .

[tex]3n^2-0.75=90[/tex]Consider the following graph. Does a graph represent a function? Yes or no?

Concept

A technical definition of a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Next

The graph is a function because every input has unique output.

Final answer

**It is a function**

−8(2) +5(2 − 12)+ (−2)(5 −2) +(−3)(3)

**Answer:**

The answer is -81.

**Step-by-step explanation:**

Let me know if I got it wrong.

The length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. The perimeter of the piece of steel is 60 meters. Find the length of the pieceof steel. Find the width of the piece of steel.

Let "x" represent the width of the rectangular steel, then the length, which is 2meters less than triple the width, can be expressed as "3x-2".

The perimeter of the rectangular piece is 60meters.

The formula for the perimeter is the following:

[tex]P=2w+2l[/tex]Replace the formula with the expressions for the width and length and the given perimeter of the piece of steel:

w=x

l=3x-2

P=60

[tex]60=2x+2(3x-2)[/tex]From this expression, you can determine the value of x.

-First, distribute the multiplication on the parentheses term

[tex]\begin{gathered} 60=2x+2\cdot3x-2\cdot2 \\ 60=2x+6x-4 \end{gathered}[/tex]-Second, simplify the like terms and pass "-4" to the left side of the expression by applying the opposite operation "+4" to both sides of it

[tex]\begin{gathered} 60=8x-4 \\ 60+4=8x-4+4 \\ 64=8x \end{gathered}[/tex]-Third, divide both sides by 8 to determine the value of x

[tex]\begin{gathered} \frac{64}{8}=\frac{8x}{8} \\ 8=x \end{gathered}[/tex]The value of x is 8m, which means that the width of the piece of steel is 8m

To determine the length you just have to replace the expression by x=8

[tex]\begin{gathered} l=3x-2 \\ l=3\cdot8-2 \\ l=24-2 \\ l=22 \end{gathered}[/tex]The length is 22m

f(x) = (x-1.5)^2 find the vertex

The given function is

[tex]f(x)=(x-1.5)^2[/tex]It is important to know that the function is in vertex form

[tex]f(x)=a(x-h)^2+k[/tex]Where h and k are the coordinates of the vertex.

Having said that, we can deduct that the vertex of the given function is (1.5, 0) because those are the values for h and k.

Hence, the answer is V(1.5, 0).4. During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the care for 4 days at a rate of $36 per day. There was an additional charge of $0.20 per mile after the first 200 miles.

a. Write an expression to represent the amount Devon paid for additional mileage.

b. Write an expression to represent the number of miles over 200 miles that Devon drove.

c. How many miles overall did Devon drive overall if he paid $174 for the car rental? Show work.

**Answer:**

A)

c = 0.20m + 144

Where c is total cost and m is miles driven.

B)

c = (200 + 0.20m) + 144

C)

174 = 0.20m + 36x4

174 = 0.20m + 144

30 = 0.20m

30/0.20 = m

m = 150+200

m = 350miles

Hope that helps

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the same theorem. __________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.

The parallelogram can be redrawn as,

To Prove: The opposite side of the parallelogram are equal.

Given: In the given parallelogram AB is parallel to CD and BC is parallel to AD.

Construction: Diagonal AC is drawn.

Proof:

[tex]\begin{gathered} AC=AC\text{ (Common)} \\ \angle BAC=\angle DCA\text{ (Alternate angles)} \\ \angle BCA=\angle DAC\text{ (Alternate angles)} \\ \Delta ABC\cong\Delta CDA\text{ (ASA)} \\ AB=CD\text{ (CPCT)} \\ BC=DA\text{ (CPCT)} \end{gathered}[/tex]Thus, t**raingle ABC is congruent to triangle CDA by ASA congruency theorem** is the missing information from the paragraph.

6 hours into minute i want answer of this

**Answer: 6 hours into minutes is 360**

**Step-by-step explanation:**

a model of a skyscraper is made so that 1 inch represents 75 feet what is the height of the actual building if the height of the model is 20 1/4 inches

Given the proportional relationship:

1 in = 75 feet

To get feet, of 20 1/4th inches, we have to multiply the inches by 75:

[tex]\begin{gathered} 20\frac{1}{4}\times75 \\ =\frac{81}{4}\times75 \\ =\frac{6075}{4} \\ =1518\frac{3}{4}\text{ fe}et \end{gathered}[/tex]*Note: we converted 20 1/4th to improper fraction, then did the mulitplication.*

*The answer is:*

solve the equations and verify the answer

6.6 is value t in of **linear equation .**

**What is linear equation with example?**

2t + 3/3 = 3t - 8/2

2( 2t + 3 ) = 3( 3t - 8 )

4t + 6 = 9t - 24

9t - 4t = 9 + 24

5t = 33

t = 33/5

t = 6.6

Learn more about ** linear equation**

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Hello, I could use some help understanding this question please.

To determine the total number of employees, we need to determine first how many are men in the company.

To determine the number of men in the company, we can use the given ratio 7 men is to 5 women and apply direct proportion.

[tex]\frac{7men}{5women}=\frac{?}{135women}[/tex]To solve for the number of men (?), let's apply cross multiplication in the equation above.

[tex]\begin{gathered} \frac{7men\times135women\text{ }}{5women\text{ }}=? \\ \frac{945}{5}=\text{?} \\ 189men=? \end{gathered}[/tex]Hence, there are 189 men in the company.

**In total,** there are 189 men + 135 women =** 324 employees in the company. **

How many pairs of parallel edges are there in a rectangular prism

**Answer:**

*A rectangular prism has 3 pairs of congruent parallel faces.*

Determine the slope of any line perpendicular to the line illustrated in the graph below.

Points (2, -1) and (1,-4)

Finding slope

[tex]m=\frac{-4+1}{1-2}=\frac{-3}{-1}=3[/tex]For slope for the perpendicular line

[tex]m=\frac{-1}{3}[/tex]Robert has two more than three times the number of cards that Amanda has which expression represents the number of cards that Robert has

To state the equation that represents the given situation, we take x as the number of cards Amanda has. Three times the number of cards is 3x, two more is +2. It means that the expression that represents this situation is:

[tex]3x+2[/tex]Let d represent the number of $2 decreases i price. Let r be the company’s revenue. Write a quadratic function that reflects the company’s revenue.

**Answer:**

Let d be the number of $2 decreases, and r be the company´s revenue, then the company can sell:

[tex]800+40d[/tex]cellphones per week at a price of:

[tex]80-2d[/tex]dollars.

Therefore, the **quadratic equation** that represents the revenue is:

Now, **graphing** the above equation we get:

From the above graph, we can determine the vertex and the vertex gives us for which value of d the company gets the maximum revenue.

**The company should charge** $80-10($2)=$80-$20=$60.

the equation of line m is y =9/5x +9. line n is parallel to line m. what is the slope of line n?

the slope for the line n is 9/5

plss help me with this i need help

You cannot add denominators.

Therefore the denominator stays as 9 and the sum is 6/9

You can simplify by deviding 6 and 9 by 3

the final answer is 2/3

Therefore the denominator stays as 9 and the sum is 6/9

You can simplify by deviding 6 and 9 by 3

the final answer is 2/3

exercise after work, Albert (A) went running and Tanisha (T) walked for exercise. Their times and distances are showing in the graph below. How much as Albert running than Tanisha walking in miles per hour? Explain how you found your answer.

In the picture, there are two lines that graph distance versus time, so the slope of the line is teh rate or the speed of Albert or Tanisha.

We need to calculate the slope of each line. We can note that the two lines start in the origin point (0, 0), so:

[tex]\begin{gathered} \text{For Albert, we can s}ee\text{ that the point (10, 1) is in the line, so:} \\ slopeofAlbert=m_A=\frac{1}{10}=0.1\frac{miles}{\min ute} \\ \text{For Tanisha, we can se}e\text{ thet the point (}20,\text{ 1) is in the line. so:} \\ slopeofTanisha=m_T=\frac{1}{20}=0.05\frac{miles}{\min ute} \end{gathered}[/tex]The different between the slopes (speed) is:

[tex]\begin{gathered} m_A-m_T=0.1\frac{miles}{\min ute}-0.05\frac{miles}{\min ute}=0.05\frac{miles}{\min ute} \\ In\text{ miles/hours is:} \\ m_A-m_T=0.05\frac{miles}{\min ute}\cdot\frac{60\text{minutes}}{1\text{hour}}=3\frac{miles}{hour} \end{gathered}[/tex]**Albert goes 3 miles/hour faster than Tanisha**

Geometric properties of the section are

**Answer:**

The geometric properties of sections, which are indicators of the structural performance and load resistance capacity of sections, are characterized by the section shape and dimensions, regardless of material properties.

Jay had 60 tickets he could turn in at the end of the year for extra-credit points he had earned during the year. Some tickets were worth two points and others were worth five points. If he was entitled to a total of 231 extra-credit points, how many two-point tickets did he have?

**Answer:**

23 2-points + 37 5-points = 231

**Step-by-step explanation:**

**Answer:**

53 two-point tickets.

**Step-by-step explanation:**

This is a system of equations:

x + y = 60

2x + 5y = 231

Then..

-2x - 2y = -120

2x + 5y = 231

Then...

3y = 111

y=7

All you need to do now is plug it in:

x + 7 = 60

60-7 = x

x = 53

The scatterplot shows the average miles per gallon

versus the age, in years, of cars at a used car dealership.

Fuel Efficiency

Miles per Gallon

35

30

25

20

15

10

5

●

0 1 2 3 4 5 6 7 8 9 10

Age (Years)

Select the most likely value of r for this data set.

O-0.78

O-0.35

O 0.15

O 0.88

**Answer:**

-0.78

**Step-by-step explanation:**

The close to 1 or -1 it is the straight the line will be. 0 will be no correlation.

all you need is in the photo please answer all the 3 questions

**a) y =2^x **

**b) Exponential**

**c) **

a) According to that graph, we have point (1,2) and (2,4) since that exponential function is

[tex]\begin{gathered} y=a(b)^x \\ 1=a(b)^0\rightarrow a\text{ =1} \\ 4=ab^2\text{ }\rightarrow4\text{ =}b^2\rightarrow\text{ }b=2 \\ y=2^x \end{gathered}[/tex]Since the function is increasing, due to its direction, we can write **y =2^x**

**b)**The type of function is exponential, since x= 0, y = 1, and due to its shape.

3) As we can see the shape of the graph is curve,

What is an example of a type of communication that shows the difference between communication skills among humans and communication among animals?
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Most of the western United States, except the Pacific states, saw population growth during the mid-2000s. What is the best explanation for the lack of growth in the Pacific states?A.The Pacific states are a less attractive region to live in.B.The Pacific states have a higher cost of living than the states further inland.C.Many people disagree with the politics and beliefs of people living in these states.D.More people were moving to New England and the Northeast
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