Write an equation of the line passing through the given point and satisfying the given condition. Give the equation (a) in slope-intercept form and (b) in standard form.
(8,6); perpendicular to 2x - y = 4
(a) Write the equation of the line in slope-intercept form.

Answers

Answer 1

Answer:

y =  -[tex]\frac{1}{2}[/tex]x + 10

Step-by-step explanation:

To find the equation of a line that passes through the point (8,6) and perpendicular to the equation 2x - y = 4, we will follow the steps below:

first write the equation 2x - y = 4 in a standard form

we will find the slope of our equation using this equation

2x - y = 4

y = 2x -4

comparing the above with

y = mx  + c

m = 2

[tex]m_{1}[/tex][tex]m_{2}[/tex] = -1  ( slope of perpendicular equations)

2[tex]m_{2}[/tex] = -1

[tex]m_{2}[/tex]  = -1/2

our slope m = -1/2

We can now go ahead and form our equation

[tex]x_{1}[/tex] =8   [tex]y_{1}[/tex] =6

y-[tex]y_{1}[/tex] = m (x-[tex]x_{1}[/tex])

y-6 = -[tex]\frac{1}{2}[/tex](x-8)

y-6 =  -[tex]\frac{1}{2}[/tex]x + 4

y=  -[tex]\frac{1}{2}[/tex]x+4+6

y =  -[tex]\frac{1}{2}[/tex]x + 10


Related Questions

An airplane takes 5 hours to travel a distance of 3900 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is _____ (mph,hour,miles) and the speed of the wind is ____(mph,hour,miles)

Answers

Answer:

not quite sure what this is asking for but the average speed is 7800/11

It did 7800/11 ¯\(º_o)/¯

Help Help Help ! Math wiz

Answers

Answer:

This is not an exponential function because the variable is in the exponent position.

A prism has a volume of 238 cubic millimeters. Which is the correct substitution for finding the length of the prism?

Answers

Answer:

D. V = l w h. 238 = l times 8 and one-half times 3 and one-half

Step-by-step explanation:

A prism has a volume of 238 cubic millimeters.

A prism has a length of l millimeters, height of 3 and one-half millimeters, and width of 8 and one-half millimeters.

Which is the correct substitution for finding the length of the prism?

A. V = l w h. 238 = l + 8 and one-half + 3 and one-half

B. V = l w h. V = 238 times 8 and one-half times 3 and one-half

C. V = l w h. l times 8 and one-half times 3 and one-half

D. V = l w h. 238 = l times 8 and one-half times 3 and one-half

From the question

V=lwh

Volume of a prism=length)(width)(height)

Volume=238

l= l mm

w= 8 1/2

h= 3 1/2

Substituting all the values

V=lwh

238= l * 8 1/2 * 3 1/2

D. V = l w h. 238 = l times 8 and one-half times 3 and one-half

Answer:

D

Step-by-step explanation:

got it right on edge 2020

The height of the trunk is 26 inches the length of the trunk is 50 inches. The tv is 54 inches wide. And 96 inches in height. Assuming the trunk is at least 96 inches deep can the tv fit into the trunk? Explain

Answers

Answer:

It states that assuming the trunk is 96" long.  So with that information assuming the trunk is at least 96 inches deep and the tv is 96” long and the length of the trunk diagonal is 56.36” which is greater than the TV length 56”, so the TV will fit diagonally in the trunk.

Step-by-step explanation:

The length of the diagonal of the trunk is 56.356011 inches.

What is Pythagoras Theorem?

A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.

Given:

height of the trunk= 26 inches

length of the trunk= 50 inches

using Pythagorean theorem,

diagonal length of the trunk=√(height² +length²)

=√(26²+50²)

=√3176

=56.356011 inches

Hence, the length of the diagonal of the trunk is 56.356011 inches.

Learn more about this concept here:

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PLEASE HELP!!!
Which graph represents the solutions to the inequality |2x - 6| < 10? (5 points)

Answers

Answer:

3

Step-by-step explanation:

To do this you would take absolute value so you get [tex]2x+6\leq 10[/tex] then you would subtract 6 from both sides so you get [tex]2x\leq 10[/tex] then you would divide 2 from both sides so you would get [tex]x\leq 2[/tex] so graph 3 would be the write answer

Your answer would be 3

fleur wants to make tables and chairs. She has a total of 150 wooden boards and 330 nails. 17T + 6C ≤ 150 represents the number of tables T and chairs C she can make with 150 Wooden boards. 34T + 27C ≤ 330 represents the number of tables and chairs she can make with 330 nails. Does Fleur have enough boards and nails to make 3 tables and 9 chairs? Choose 1 answer: (Choice A) Fleur has enough boards and nails. (Choice B) Fleur has enough boards but not enough nails. (Choice C) Fleur has enough nails but not enough boards. (Choice D) Fleur has neither enough boards nor enough nails.

Answers

Answer::

Choice B : fleur has enough boards but not enough nails

Answer:

Fleur has enough boards but not enough nails.

Step-by-step explanation:

T = 3

C = 9

substitute

Write the function f(x) = x^2 + 8x + 12 in vertex form. Enter all work. Please help me.

Answers

Hello!

Answer:

f(x) = (x + 4)² - 4

Step-by-step explanation:

Write the equation f(x) = x² + 8x + 12 in vertex form by completing the square:

f(x) = (x² + 8x + (8/2)²) + 12 - (8/2)²

Simplify:

f(x) = (x² + 8x + 16) + 12 - 16

Subtract to find the 'k' value:

f(x) = (x + 4)² - 4. This is the equation in vertex form.

Please help will mark brainliest
the bearing from Canada to Atlanta is 040 degrees. Calculate the bearing from Atlanta to Canada

Answers

Answer:

The bearing from Atlanta to Canada is 220 degrees

Step-by-step explanation:

Given

Represent Canada with C and Atlanta with A

Bearing from C to A = 040

Required

Determine the bearing from A to C

This concept is referred to as Back Bearing and it's calculated as follows.

Because the front bearing is less 180 (040, to be precise), we have to add it to 180 to get the back bearing;

Hence,

[tex]A\ to\ C\ =\ 180\ + C\ to\ A[/tex]

Substitute 040 for C to A

[tex]A\ to\ C\ =\ 180\ + 040[/tex]

[tex]A\ to\ C\ =\ 220[/tex]

Hence, the bearing from Atlanta to Canada is 220 degrees

Which value makes the inequality x^2 ≥ x false?
A. -1/4
B. 0
C. 1/4
D. 1

Answers

Answer:

D

Step-by-step explanation:

cas if x =1

then 1^2>or=1

1is not >or=1

the answer is D. -1/4 because it would make 1=1 instead of greater than or equal to 1

Which statement is true about the polynomial 5s6t2 + 6st9 – 8s6t2 – 6t7 after it has been fully simplified? It has 3 terms and a degree of 9. It has 3 terms and a degree of 10. It has 4 terms and a degree of 9. It has 4 terms and a degree of 10.

Answers

Answer: The polynomial has 3 terms and a degree of 10.

Step-by-step explanation:

The given polynomial: [tex]5s^6t^2 + 6st^9 - 8s^6t^2 - 6t^7[/tex]

Here, two terms [tex]5s^6t^2[/tex] and [tex]8s^6t^2[/tex] have same power for s and t i.e. they are like terms.

Combine like terms , we get

[tex]6st^9 - 3s^6t^2 - 6t^7.[/tex] i.e. there are 3 terms.

Degree of [tex]6st^9[/tex]  is 1+9=10;

Degree of [tex]- 3s^6t^2[/tex] is 6+2=8;

Degree of  [tex]- 6t^7[/tex]  is 7.

Since degree of the polynomial = highest degree i.e. 10

Hence, the polynomial has 3 terms and a degree of 10.

The statement which is true about the polynomial 5s⁶t² + 6st⁹ – 8s⁶t² – 6t⁷ is; It has 4 terms and a degree of 10.

Discussion:

By counting the number of terms in the polynomial;

We can conclude that the polynomial has 4 terms and hence can be called a tetranomial.

Additionally, the degree of the polynomial is 10.

This is from the term with the highest degree which is; 6st⁹; where s has degree 1 and t has degree 9; total of which is; 10.

Read more on polynomial degree;

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Pls help with this question thank u all

Answers

Answer:

4 cm (A)

Step-by-step explanation:

triangle BAC is just a larger version of triangle EAD. given that ED is 5cm, and BC is 10cm, triangle BAC must be twice the size of EAD. since the ratio of AD to ED is 4:5, and BC is twice the size, all we need to do is multiply both sides by 2 to find length AC. 4*2 = 8. now we can subtract length AD from AC to get CD. 8 - 4 = 4.

sorry if what i wrote is a little confusing

Answer:

(A) 4cm


Explanation

Which expression is equivalent to ....

Answers

Answer:

Its the first answer 24

It’s equivalent to.... answer number one (24)

Mark decided to donate a lot of his shirts to two different organizations and keep
the rest. First he 1/10 donated of his shirts to his church, and then he donated 2/3 of

what was left to a consignment shop.
1) What fractional part of his shirts did he donate to the consignment shop?
2) What fractional part of his shirts did he keep?
3) If Mark kept 15 shirts, how many shirts did he donate?

(also please help me with drawing a picture that's a fraction to shade in for the problem)

Answers

Answer:

1.) 3/5

2.) 3/10

3.) 50

Step-by-step explanation:

i believe my answers are right, they might be wrong. I'm not that old so I can't solve most of these problems.

1.) to get this, you need to multiply the remaining shirts and 2/3

2.) subtract 1/10, and 3/5 from 1, which equals 3/10

3.) is 3/10 is equal to 15, then 1/10 is equal to 5, 5*10=50

Answer:

1) 3/5

2) 3/10

3) 35

Step-by-step explanation:

For majority of the questions, you just have to multiply the numbers together. I think all of them is right... T-T

sry if its wrong.. :|


Please help
calculate the coefficient of x^14y^4 in the expansion of (x+y)^18

Answers

..................(1x+14y)4

describe the y-intercept in terms of knots and rope length

Answers

Answer:

what is the y-intercept sorry i can't help there isn't enough information

Step-by-step explanation:

The taxi fare in Gotham City is $2.40 for the first ½ mile, and each additional mile costs $0.20. You plan to give the driver a $2.00 tip. How many miles can you ride for $10.00?

Answers

Answer:

He can ride for 28 miles

Step-by-step explanation:

Total cost of the ride = $ 10

Tips = $ 2

Cost of ride excluding tips = 10 - 2 = $ 8

Taxi fare for first 500 miles = $ 2.40

Taxi fare excluding first 500 miles =  8 - 2.40 = $ 5.60

distance traveled by him excluding first 500 miles = 5.60 ÷ cost of additional mile

 = 5.60 ÷ 0.20

=28 miles

Line 'L' is horizontal and passes through (-5,8). Line 'L is vertical and passes through $(4,-1)$. Find the point of intersection of $\ell_1$ and $\ell_2$.

Answers

The two lines intersect at (4,8)

Every y coordinate on the horizontal line is the same, so each point has a y coordinate of y = 8. This is to be able to pass through (-5,8)

Every x coordinate on the vertical line is the same, so each point has an x coordinate of x = 4. This is to be able to pass through (4,-1)

Put this together to get the answer (x,y) = (4,8)

Answer:

The two lines intersect at (4,8).

Write an expression of 4 less than twice a number

Answers

Answer:

2x-4

Step-by-step explanation:

you can't really explain this, is just have the meaning 4 less twice a number.

I wish this is the correct one and will help you!

Answer:

2x-4

Step-by-step explanation:

Can someone help me with the question please

Answers

Answer:

Purple line: 4

Red dashed line: 2

Blue line: 1/2

Step-by-step explanation:

The purple line is the steepest line, therefore it has the biggest constant of proportionality or slope. Since 4 is the biggest number among the others, we attribute it to the purple line (the one with the point C on it).

Think of it this way:

[tex]y = ax+b \\[/tex]

here [tex]b = 0[/tex] so [tex]y = ax[/tex]

The greater a is, the greater y is. So for any value of x, y will be become bigger and bigger if we increase the value of a.

Take for example this one:

[tex]y = 2x \\[/tex]

Take [tex]x=2\\[/tex] therefore [tex]y =4[/tex]

Now take [tex]y = 4x[/tex] and take [tex]x =2[/tex] therefore [tex]y = 8[/tex]

When we increased this constant of proportionality, as you can see from 2 to 4, the value of y increase from 4 to 8.

Hope this is helpful. Think of it really carefully, and I'm sure you'll grasp the concept.

Sam's total expenses last month were $1840. What was his total variable cost for last
month?
Expense
Amount
Rent
$100
Groceries and drinks
$1000
$10
Insurance premiums
Loan interest payment
Clothes
$30
$200
&
Utilities
$300
Home security fee
$200​

Answers

Answer:

$1500

Step-by-step explanation:

It is given that

Rent  = $100

Groceries and drinks = $1000

Insurance premiums   = $10

Loan interest payment  =$30

Clothes  = $200

Utilities  = $300

Home security fee  = $200​

Fixed cost are costs that does not vary and variable cost are costs that vary with goods and services.

In the given problem, rent , insurance premiums, loans interest payment ad home security fee are fixed cost.

Groceries and drinks, clothes and utilities are variable cost.

So, total variable cost for last month is

[tex]\text{Total variable cost}=\$1000+\$200+\$300=\$1500[/tex]

Therefore, total variable cost for last month is $1500.

Answer:

$1500

Step-by-step explanation:

I just took the test and got it right

The circle below has center C. Suppose angle EDF = 84º and DF is tangent to the circle at D.
Find the following. Type your numerical answers (without units) in each blank.

Answers

Answer: [tex]m\overbrace{ED}[/tex]=  168° and ∠ECD =  168°

Step-by-step explanation:

In the given , we have a circle centered at C , ED is a chord and DF is a tangent touching circle at D, ∠EDF = 84°.

Also, CE = CD = radius

⇒ ∠CED = ∠CDE  ---(i)  [angles opposite to equal sides of triangle are equal]

Since radius makes a right angle with tangent.

So, ∠CDF = 90°

⇒ ∠CDE =∠CDF - ∠EDF

⇒ ∠CDE=  90° - 84°

⇒ ∠CDE = 6°

From (i) ∠CED =∠CDE = 6°

In ΔCDE

⇒∠CED + ∠CDE + ∠ECD =  180°

⇒ 6°+6°+ ∠ECD =  180°

⇒ 12°+ ∠ECD =  180°

⇒∠ECD =  180° - 12°

⇒∠ECD =  168°

Since , Angle measure of the central angle is equal to the measure of the intercepted arc.

Therefore m∠ECD = [tex]m\overbrace{ED}[/tex]

⇒[tex]m\overbrace{ED}[/tex]=  168°

Hence,  [tex]m\overbrace{ED}[/tex]=  168° and ∠ECD =  168°

Estimate to the nearest hundredth: √48 A. 6.93 B. 7.12 C. 24.00 D. 6.55

Answers

Answer:

The answer is option A.

√48 = 6.93 to the nearest hundredth

Hope this helps you

Answer:

A

Step-by-step explanation:

Horatio wants to ship a batch of 8 machine parts. The packaging for each part weighs 2 pounds. If each part weighs x pounds, which expression represents the total weight of the parts and their packaging? And if each part weighs 6 pounds, what will the total weight of the shipment be? A. The expression is 2(x + 8), and the weight is 28 pounds. B. The expression is 8(x – 2), and the weight is 32 pounds. C. The expression is 8x – 2, and the weight is 46 pounds. D. The expression is 8x + 2, and the weight is 50 pounds. E. The expression is 8(x + 2), and the weight is 64 pounds. Reset Next

Answers

Answer: E. The expression is 8(x + 2), and the weight is 64 pounds.

Step-by-step explanation:

Given: Number of machine parts in a batch = 8

weight of packaging for each part = 2  pounds

Let  x be the weight of each part ( in pounds).

Weight of each part with packaging = x+2

Then, Total weight of the parts and their packaging =  (Number of machine parts) x (Weight of each part with packaging )

= 8(x+2)

If each part weighs 6 pounds, then put x= 6

Total weight of the parts and their packaging =  8(6+2)

= 8 x 8 = 64 pounds

Hence, If each part weighs 6 pounds, then the total weight of the shipment will be 64 pounds .

Here is what we know:

8 machine parts

each part = x pouunds

packaging for each part is 2 pounds so 16 pounds for packaging

If y=total weight wiith that information we can form this equation

y=8x + 16

If each part equals 6 pounds the total shipment will be

y=8x+16

y=8(6) + 16

y= 48 + 16

y=64

Please help with the questions on the picture, it's very urgent......Thank you✨​

Answers

Answer:

2. sinθ= cos 35°

sinθ= sin(90°-35)

θ= 55°

3. cos4θ= sin5θ

cos 4θ= cos (90-5θ)

4θ=90°-5θ

collect like terms

4θ+5θ=90°

9θ=90° (divide both sides by 9)

therefore θ=10°

Please help me on this question

Answers

Answer:

x = [tex]\frac{k(a+r)}{7}[/tex]

Step-by-step explanation:

Given

a = [tex]\frac{7x}{k}[/tex] - r ( add r to both sides )

a + r = [tex]\frac{7x}{k}[/tex] ( multiply both sides by k to clear the fraction )

k(a + r) = 7x ( divide both sides by 7 )

[tex]\frac{k(a+r)}{7}[/tex] = x

Answer:

        ak - kr                 k(a - r)

x = --------------  or  x = ------------

             7                          7

Step-by-step explanation:

1. Multiply all three terms by k to eliminate the fraction:

ak = 7x - kr

2.  Subtract kr from both sides:

7x = ak - kr

3.  Divide both sides by 7:

        ak - kr                 k(a - r)

x = --------------  or  x = ------------

             7                          7

Use the De Morgan law that states: ~(p ∧ q) is equivalent to ~ p ∨ ~ q to write an equivalent English statement for the statement. It is not the case that a gun and a nose are both weapons. A gun is not a weapon or a nose is not a weapon. guns are not noses. A gun is a weapon but a nose is not. A gun is not a weapon and a nose is not a weapon.

Answers

Answer:

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

Step-by-step explanation:

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

Write a 75-100 word essay on the topic "Should people keep animals as pets?" No copying from other websites, I will mark your answer brainiest If I Like It!

The equivalent statement for the given statement -  It is not the case that a gun and a nose are both weapons is A gun is not a weapon or a nose is not a weapon.

What is De Morgan's Law?

The De Morgan's law states that → ~(p ∧ q) is same as (~ p ∨ ~ q). Theoretically, we can write it as → Not (A and B) is the same as Not A or Not B.

Given is the following statement - It is not the case that a gun and a nose are both weapons.

Now, we know that the De Morgan's law states that → Not (A and B) is the same as Not A or Not B. In the statement given -

A = gun

B = nose

~(p ∧ q) = Not(A ∧ B)

So, we can write it as -

~(p ∧ q) =  Not(A ∧ B) = A gun is not a weapon or a nose is not a weapon.

where -

A gun is not a weapon → ~p

or →

a nose is not a weapon → ~q

Therefore, the equivalent statement for the given statement -  It is not the case that a gun and a nose are both weapons is A gun is not a weapon or a nose is not a weapon.

To solve more questions on De Morgan's Law, visit the link below-

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What is the distance, in units, between P=(−6,8) and Q=(9,8)?

Answers

Answer:

15 units

Step-by-step explanation:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(9 - (-6))² + (8 - 8)²]

d = √[(15²) + (0²)]

d = √15²

d = 15

Answer:

15 units

Step-by-step explanation:

9-(-6) = 15

What is the surface area of the rectangular pyramid below? 13,13,13

Answers

Answer:

1,014

Step-by-step explanation:

Assuming those 13’s represent the Length and Width of the sides of the prism, the equation would be

13x13x6 (6 sides)

=1014

Answer:

507

Step-by-step explanation:

apeex


9. Find the value of x. Using that value, what is the
measurement of ZUTQ?
thank you <3

Answers

Answer:

92°

Step-by-step explanation:

We know that [tex]\overline{QV}[/tex] is a straight line which means that we know that ∠QTU + ∠VTU = 180

11x+4+∠VTU = 180

∠VTU = 180-11x-4

∠VTU = 176-11x

Then, using the triangle inequality, we know that ∠VTU+∠TUV+∠UVT = 180

3x+14+54+176-11x=180

-8x+244=180

-8x = -64

x=8

Now we can substitute and solve for ∠UTQ

11(8)+4 = 88+4 = 92°

Answer: 92°

Step-by-step explanation:

If water flows 12 feet in 9 seconds through the turbine, how far will the water flow in 54 seconds? If the water continues to flow at this rate, how long will it take the water to travel 54 feet?

Answers

54/9 = 6
12 x 6 = 72
72 feet in 54 seconds
54/72 = 0.75
1 foot = 0.75 seconds
0.75 x 54 = 40.2 seconds to travel 54 feet

Answer:

40.5 sec

Step-by-step explanation:

The flow rate is (12 ft) / (9 sec), or 4/3 ft/ sec.

In 54 sec, the water will have moved

(4/3 ft/sec)(54 sec) = 72 ft.

If the flow rate is 4/3 ft/sec and the distance covered is 54 ft, we divide

54 ft by (4/3 ft/sec) to determine how long it takes the water to flow 54 ft:

   54 ft

---------------- = 40.5 sec

(4/3 ft/sec)

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