Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation. Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line.


A. (–2, 4), one, three


B. (4, –2), one, three


C. (2, 4), one, three


D.(4, –2), three, one

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

20 km

Step-by-step explanation:

We can use ratios to solve

1 cm          4 cm

--------  = ------------

5 km          x km

Using cross products

1 * x = 4 * 5

x = 20

20 km

Answer:

1/5 = 4/x

Step-by-step explanation:

Each cm on the map represents 5 km. If it shows 4 cm apart of the map, you can use the proportion 1 cm : 5 km = 4 cm : x km.

The demand equation illustrates the price of an item and how it relates to the demand of the item.

From the question, we have:

[tex]Plates = 300[/tex]

[tex]Price = 20[/tex]

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{25-20}{290-300}[/tex]

[tex]m = \frac{5}{-10}[/tex]

[tex]m = -\frac{1}{2}[/tex]

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]

Open the brackets to calculate the maximum revenue

[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]

[tex]R(x) =6000 + 1300x - 50x^2[/tex]

Equate to 0

[tex]6000 + 1300x - 50x^2 =0[/tex]

Differentiate with respect to x

[tex]1300 - 100x =0[/tex]

Collect like terms

[tex]100x =1300[/tex]

Divide by 100

[tex]x =13[/tex]

So, the price at maximum revenue is:

[tex]Price= 20 + 5x[/tex]

[tex]Price= 20 + 5 * 13[/tex]

[tex]Price= 85[/tex]

In conclusion:

Read more about demand equations at:

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Answer:

The game's expected value is of -$1.5.

Step-by-step explanation:

Expected value:

Probability of each outcome multiplied by the outcome.

One out of 6 sides is 2:

1/6 probability of the player earning 45 - 9 = $36.

5/6 probability of the player losing $9. So

[tex]E = 36\frac{1}{6} - 9\frac{5}{6} = \frac{36 - 45}{6} = -\frac{9}{6} = -1.5[/tex]

The game's expected value is of -$1.5.

The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.

For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD

So, the perimeter is:

[tex]P_{\triangle ACD} = AC + AD + CD[/tex]

For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD

So, the perimeter is:

[tex]P_{\triangle ABD} = AB + AD + BD[/tex]

The difference in the perimeters is:

[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]

So, we have:

[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]

Open brackets

[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]

Evaluate like terms

[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]

Make BD the subject

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]

The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.

[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes

[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]

Open bracket

[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]

Evaluate like terms

[tex]BD = 2[/tex]

Base on the assumed values, the length of side BD is 2.

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Answer:

7

This question is tying to introduce an idea that

eventually becomes a calculus question ....

(4^2 + 3(4)) - (0^2+3(0))

             4 - 0

28 - 0       = 7

   4

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

1. Approach

The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.

Given function: [tex]f(x)=x^2+3x[/tex]

Intervale, [tex][0, 4][/tex]

This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane ([tex]x, y[/tex]). Finally, one can find the slope of the line that passes through the points by using the following slope formula,

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

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are coordinate points.

2. Find the points

With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,

[tex]f(x)=x^2+3x[/tex]

[ 0, 4 ]

[tex]f(0)=(0)^2+3(0)\\=0 + 0\\ =0[/tex]

Point: (0, 0)

[tex]f(4)=(4)^2+3(4)\\= 16 + 12\\ = 28[/tex]

Point: (4, 28)

3. Find the average rate of change,

Now substitute the points the formula to find the slope, then simplify to evaluate

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

(0, 0), (4, 28)

Substitute,

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{28-0}{4-0}\\\\=\frac{28}{4}\\\\= 7[/tex]

The average rate of change is 7.

Hi there!

[tex]\large\boxed{tanC = 40/9}[/tex]

tan = O / A, or the opposite side over the adjacent side.

From the diagram, we can see that the opposite side = 40 and the adjacent side = 9, so:

tan C = 40 / 9

Answer:

tan C = 40/9

Step-by-step explanation:

According to SOH - CAH - TOA, tan = opposite over adjacent.

In the picture, the opposite of tan C is 40 and the adjacent is 9.

So, tan C = 40/9

P.S. - Answer above is also correct.

Answer:

The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8

Step-by-step explanation:

√50 + √98​ ​= √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2

It's the third option.

Completing the square yields

x ² + 9x + 7 = 0

(x ² + 9x + 81/4) + 7 = 81/4

(x + 9/2)² + 7 = 81/4

Now solving for x gives

(x + 9/2)² = 53/4

x + 9/2 = ± √(53/4) = ± √53/2

x = (-9 ± √53)/2

.

.

..

.

.............

Answer:

[tex]13+19=n+25[/tex]

[tex]n+25=13+19[/tex]

Add 13+19= 32

[tex]n+25=32[/tex]

Now Subtract 25 from both sides

[tex]n+25-25=32-25[/tex]

[tex]n=7[/tex]

OAmalOHopeO

Answer:

should be 192

Step-by-step explanation:

Step-by-step explanation:

A = 12.25cm2

P perimeter 14cm

Answer:

A=12.25cm²

P=14

Answer:

24n^7/m^16

Step-by-step explanation:

Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.

One piece will be length x and the other piece will be 20 cm longer, so it will be x + 20 cm long.  

Added together the length of these two boards will equal 86 cm. So you can write an equation:  

x + (x + 20) = 86  

Remove the parentheses and add the two x's together to get:  

2x + 20 = 86

Subtract 20 from both sides:  

2x = 66  

Divide both sides by 2 and you have:  

x = 33  

The short piece is 33 cm and the other piece is 20 cm longer or 33 + 20 = 53 cm.

Answer:

2a^4c-2ac^2-15

Step-by-step explanation:

Sorry, I not sure if this is right or not cause I don't know if the exponent for -4a^4c is that or -4a^4c-15, but I'm just going to go with -4a^4c. However aside from that you just combine like terms.

Answer:

[tex]2a^4c-2ac^2-15[/tex]

Step-by-step explanation:

[tex]6a^4c+8ac^2-4a^4c-15-10ac^2[/tex]

We need to organize this expression into groups of like terms, so we can combine them easier. There are 2 groups of like terms,

[tex]6a^4c-4a^4c[/tex] and [tex]8ac^2-10ac^2[/tex]

[tex]6a^4c-4a^4c+8ac^2-10ac^2-15[/tex]

Add similar elements:

[tex]2a^4c+8ac^2-10ac^2-15[/tex]

Add, [tex]8ac^2-10ac^2=-2ac^2[/tex]

[tex]=2a^4c-2ac^2-15[/tex]

OAmalOHopeO

Answer:

26ft

Step-by-step explanation:

10^2 +24^2 =AB^2

AB=26

Answer: 26 ft

Step-by-step explanation:

a^2+b^2=c^2

10^2+24^2 = c^2

100+576=c^2

Sqrt 676 = c

C = 26

Answer:

4

Step-by-step explanation:

7+sqrt(7) is an irrational number

Answer:

p = 8 when b = 16 and p = -8 when

b = -16

Step-by-step explanation:

x² + bx + 64 = x² + 2px + p²

Cancel x² on both sides,

bx + 64 = 2px + p²

Now, by comparing both sides, you'll get the following equations,

1. b = 2p

2. p² = 64

From equation (2),

p = ±√64

= 8 or -8

Substitute p = 8 and p = -8 into equation (1),

b = 2(8) and b = 2(-8)

b = 2(8) and b = 2(-8) = 16 = -16

Therefore, p = 8 when b = 16 and p = -8 when

b = -16

Answer:

D. 75

Step-by-step explanation:

To find the possible number of teachers at the meeting, find which answer choice creates a whole number answer when calculating the 40% of teachers that are male and the 20% of them that teach math.

This number is answer choice D, 75.

40% of 75 is 30.

Of those 30 teachers, 20% of 30 is 6.

So, since each quantity is a whole number, this could be the possible number of teachers at the meeting.

The correct answer is D. 75

Answer:

D

Step-by-step explanation:

inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting

Answer:

the the 3rd one Is the one

Answer:

55.41 feet

Step-by-step explanation:

Let the width be x.

ATQ, (x+50)*x=300, x=5*srt(37)-25=5.41. Length is 55.41 feet

The process of copying an angle through construction involve ensuring

that the distance between the two rays forming the angle is the same or

equal in the original and copy of the angle at a given equal distance from

the vertex of both angles

The step where the error occur is step 4. She measured the incorrect length

The reason for the above selection is as follows:

The steps to copy an angle are as follows;

A critical step in the copying process involves the finding the distance

between the initial line and the terminal line EF at a given distance DG =

AE from the angle vertex

The step where the error occur is in step 4. by opening the compass

between points A and E which are points on the same line and placing the

compass at point G on line l to draw an arc intersecting the arc created

from point D at H, thereby making the radial distance between the two lines

forming the angle, in the copied angle at a distance E from the vertex,

equal to AE rather than EF

Therefore, the error occurred in step 4. She measured the incorrect length

Learn more about the steps to copy an angle here:

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Answer:

Hello,

Answer A

Step-by-step explanation:

if x=0 then sin(2*0)=sin(0)=0

if x= π/4 then sin(π/2)=1

if x= π/2 then sin(π)=0

The equation of the sinusoid will be y=Sin(2x)

It is defined as the relation between two variables, for a sinusoidal wave the equation will be in the form of Sin or Cos.

if x=0 then sin(2*0)=sin(0)=0

if x= π/4 then sin(π/2)=1

if x= π/2 then sin(π)=0

Hence the equation of the sinusoid will be y=Sin(2x)

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#SPJ2

Answer:

i think 1/58 is correct

i hope its help you

Answer:

8.5

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

Since MR=MR and XM=MY and angle XMR = angle RMY,

then triangle XMR is congruent to triangle RMY by SAS postulate

Therefore, XR has to be equal to RY.

Making 6x+2=17

subtracting both sides by 2 gives you 6x=15

then dividing both sides by 6 gives you x=15/6

simplifying this fraction gives you x=5/2

Hope this helps.

Answer:

x > -2

Step-by-step explanation:

14 <-7x

or, 14/-7=-7x/-7

or, -2 < x

Answer:

3

Step-by-step explanation:

2x-xy

2(x)-(x)(y)

2(-1/2)-(-1/2)(8)

-1 - (-4)

-1 + 4

3

Answer:

3

Step-by-step explanation:

2x-xy

Let x = -1/2 and y = 8

2(-1/2) - (-1/2)(8)

Multiply

-1 - (-4)

Subtracting a negative is like adding

-1+4

Add

3