Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).

Answers

Answer 1

2x + 4y = 6
4y = -2x + 6
y = -1/2x + 3/2
slope = -1/2

y = mx + b
y = -1/2x + b

At point (6, 4)
4 = -1/2(6) + b
4 = -3 + b
b = 7

Equation : y = -1/2x + 7

Related Questions

Use addition to solve the linear system of equations. Include all of your work in your final answer.

x - y = 4
x+ 2y = 4

Answers

we have that
x - y = 4-------> multiply by -1-----> -x+y=-4-----> equation 1
x+ 2y = 4------> equation 2

add equation 1 and equation 2
-x+y=-4
x+2y=4
-----------------
0+3y=0-----> y=0
x+2y=4------> x+0=4------>x=4

the solution is the point (4,0)

A trapezoid with an area of 166.75 in has bases that measure 21 in and 8 in find the height of the trapezoid

Answers

The required height of the trapezoid is 11.5 inches.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,
The formula for the area of a trapezoid is:

A = (b₁ + b₂) * h / 2

where A is the area, b1 and b2 are the lengths of the two bases, and h is the height.

We are given that the area of the trapezoid is 166.75 in² and the lengths of the two bases are 21 in and 8 in. So we can plug these values into the formula and solve for h:

166.75 = (21 + 8) * h / 2

Simplifying the expression on the right side:

166.75 = 29 * h / 2

Multiplying both sides by 2:

333.5 = 29 * h

Dividing both sides by 29:

h = 11.5

So the height of the trapezoid is 11.5 inches.

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Final answer:

To find the height of a trapezoid given its area (166.75 sq in) and bases (21 in and 8 in), you use the formula-

[tex]A = \frac{1}{2} h(b_1 + b_2)[/tex]

By rearranging to solve for h, you find that the height is 11.5 inches.

Explanation:

The question asks to find the height of a trapezoid given its area and bases. The area of a trapezoid is calculated using the formula A = [tex]$\frac{1}{2}$h(b_1 + b_2)[/tex], where A represents the area, h the height, and [tex]b_1[/tex] and [tex]b_2[/tex] the lengths of the two bases. In this case, the area is 166.75 square inches, and the bases measure 21 inches and 8 inches.

To find the height, we can rearrange the formula to-

h = [tex]$\frac{2A}{b1 + b2}$[/tex]

Plugging in the given values gives us-

h = [tex]$\frac{2 \times 166.75}{21 + 8}$[/tex]

which simplifies to-

h = [tex]$\frac{333.5}{29}$[/tex]

Therefore, the height of the trapezoid is 11.5 inches.

trignometry help what's the answer?

Answers

You have the 175 on the wrong line, the problem says 175 feet from the base, this is the bottom of the tree.

See attached picture for solution:

|-x-2y| for x =-3 and y=3

Answers

[tex]|-x-2y|\ for\ x=-3\ and\ y=3.\\\\substitute:\\\\|-(-3)-2\cdot3|=|3-6|=|-3|=3[/tex]

Tom has been given 35 chores to complete today this morning he finished seven of them how many chores does he now have left to do

Answers

Simple equation: 35-7=28 chores left to do

He should only have 28 left to do.

Henry has a defined benefit plan that promises a 2.5% annual retirement benefit based on the average of his last five years of salary. At retirement Henry has 21 years of service and an average salary over the last five years of $95,000. What will his annual benefit be?

Answers

Henry's annual retirement benefit will be $2,375.

We have,

To calculate Henry's annual retirement benefit, we need to find 2.5% of his average salary over the last five years.

First, let's calculate 2.5% of $95,000:

2.5% = 2.5/100 = 0.025

Annual benefit = 0.025 * $95,000

Annual benefit = $2,375

Therefore,

Henry's annual retirement benefit will be $2,375.

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Algebra question ( Matrices and Determinants ) 20 points

Answers

For this case, what you must have is the following:
You must multiply each term of the matrix by the scalar 4.
Since it is a multiplication by a scalar, the dimension of the matrix must be the same.
Answer:
option B
See attached image.

A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. tables Which of the following correctly represents the given data in the problem?

Answers

We have that 48 students are in the band and that 24 out of them also play sport. Hence, in total 24 students are in the band but dont play sports. We have that there are 4 categories and we know the other 2 categories (do both, do none). There is a 4th category, only sports. We know that the sum of all those categories is 80 (since a student either does or does not a combination of those). Hence, 80=24+24+22+x. We have that x=10, hence 10 students play sports but are not in the band.

D) a = 24, c = 48, e = 22, i = 80

During a family vacation, Ms. Walker drove 918 miles on 3 tanks of gasoline. Her daughter, Amani, wants to create an equation in the form em equals square tee, to represent the total number of miles, m, her mom can drive on t tanks of gasoline. What number should Amani put in the square to complete her equation?

Answers

To complete the equation Amani needs the rate of the miles driven per tank, this will be given by:
Rate=(miles)/(number of tanks)
thus the rate will be:
miles=918 mile
tanks=3 tanks
thus
rate=918/3=306 miles/tank

You draw a single card from a standard deck of cards. what is the probability of drawing a diamond?

Answers

There are 13 diamond cards in a deck of 52.

13/52=25

25%

Which expression is equivalent to 4 sqrt 16x^11y^8/81x^7y^6

Answers

Final answer:

The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.

Explanation:

The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.

We start by simplifying the square root of each component:

Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.

Now, divide and simplify:

(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)

Therefore, we get:

(4/9) * x^2 * y

Need help with math thank u

Answers

5,-1
2,-4
These are two answers
It is infinitely many solutions

The line plot represents the heights of students in a second-grade classroom. Which statement is true?

A. The median is less than the mode.

B. The median height is 42 inches, and the mode height is 36 inches.

C. Most of the students in the class are shorter in height.

D. The mode is less than the median.

Answers

The correct answer is A

Answer:

B. The median is less than the mode

Step-by-step explanation:

what is the solution of the equation?
please help!!

Answers

The answer is 46, The solution is listed below:

[tex] \sqrt{2x+8}-6=4 \\ \\ \sqrt{2x+8}=10 \\ \\ 2x+8=(10)^{2} \\ \\ 2x+8=100 \\ \\ 2x=92 \\ \\ x= 46 [/tex]

This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.

Answers

Your choice is correct. The slope of the function on the interval is negative. The slope of the inverse function is the reciprocal of that, still negative.

It is NOT true that [tex]\dfrac{d}{dx} \left( f^{-1}(x) \right) \ge 0[/tex]

match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
A.

B.

C.

D.

Answers

The correct linear system for the student's question is D. x + 3y \<= 38, x + y \<= 12, which matches the conditions of Lewis's situation for acquiring baseball cards.

The student is looking to match a situation with a linear system. The situation is that Lewis wants at most 12 packages of baseball cards, some containing 4 rookie cards and others 3 rookie cards, with a total of 38 rookie cards at most.

To match the situation with the correct linear system, we must set up two inequalities: one for the number of packages and another for the number of rookie cards.

Let x represent the number of packages with 4 rookie cards and y represent the number of packages with 3 rookie cards.

The first condition is that Lewis can have at most 12 packages, which gives us the inequality x + y \<= 12. The second condition is that the total number of rookie cards is at most 38, which gives us the inequality 4x + 3y \<= 38.

Considering these conditions, the correct answer is: D. x + 3y \<= 38, x + y \<= 12.

The perimeter of the base of a pentagonal prism is 25 inches and one of its lateral edges is 4 inches. The lateral area of the prism is ________ square inches.

Answers

Answer:

Lateral area=100 square inches

Step-by-step explanation:

It is given that the perimeter of the base of a pentagonal prism is 25 inches, therefore each sides of the pentagon will be of 5 inches.

Also, one of its lateral edge is 4 inches, therefore each lateral face has area which will be equal to=[tex]5{\times}4[/tex]=[tex]20[/tex]square inches.

Since, there are 5 lateral faces of the pentagonal prism, therefore the lateral area of the prism will be: [tex]5{\times}20[/tex]

= [tex]100[/tex]square inches.

Which additional information is needed to solve this problem?

John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?

A.
total amount John can save in 1 week

B.
the cost of the game

C.
amount John earns per hour babysitting

Answers

Hi there!

The answer is B.
the cost of the game.

We need to know the cost of the game in order to find out how many weeks John has to save money. If we don't know this price, we'll never know whether John has saved enough money.

We can find out the total amount of money John can save in 1 week (so A. is not the answer). The amount of money John earns per hour doesn't matter to answer the question (so C. is wrong).

~ Hope this helps you!

the answer is B he won't know how much to save if he does not know the cost of the game

Ms.kellsons storage closet is 3ft long,3ft wide,and 7 ft high.can she fit 67 boxes that each have a volume of 1 cubic foot in her closet

Answers

Volume = 3 x 3 x 7 = 63 ft³

67 x 1 ft³ = 67 ft³

Answer: No, she does not have enough to fit 67 boxes of 1 ft³ each.

A poll was conducted in states A, B, and C to determine which candidate voters would most likely vote for. The results are displayed in the table below:
What is P(conservative | State B)?

State A State B State C Total
Liberal 17 20 12 49
Conservative 23 15 13 51
Total 40 35 25 100

Answers

Answer:

15/35 = 3/7 = 0.428571

Explanation:

We are asked to find the probability that a given voter is conservative given they are in State B.

Going to the State B column, we see that there are 15 conservatives. This is out of a total of 35 voters in state B; this makes the probability 15/35.

Probability helps us to know the chances of an event occurring. The probability that a voter from State B is supporting Conservative is 0.4285.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

We're supposed to figure out how likely it is that a specific voter in State B is a conservative.

There are 15 conservatives in State B, according to the column. This is based on a total of 35 voters in state B, resulting in a 15/35 probability. Therefore,

P(conservative | State B) = 15/35 = 3/7 = 0.4285

Hence, the probability that a voter from State B is supporting Conservative is 0.4285.

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simplify radical (1-cos0)(1+cos0)/ cos^2 0

HELP ME PLS!! ASAP

Answers

that would be tan

(1-cos)(1+cos)=1-cos² which equals to sin²

√sin²/cos²= sin/cos which equals to tan

Ajuda eu !!!!!!!!!!!!!!!!

Answers

please type the question

QS is the perpendicular bisector of PR solve for x

Answers

2x-20=70-x
3x=90
so the answer is x=30

2x - 20 = 70 - x

3x - 20 = 70

3x = 90

x = 30

How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?

A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h

Answers

we know that
[the volume of an oblique cylinder]=pi*r²*h
if the radius is reduced to 2/9 of its original size and the height is quadrupled
then
[the new volume of an oblique cylinder]=pi*[(2/9)*r]²*[4*h]---> (16/81)*pi*r²*h

the answer is
the option B. V=16/81pir^2h

Tell whether each set of ordered pairs representd a function. Justify your answers.
a. (0,0), (1,1), (2,2), (3,3), (4,4)
b. (0,8), (1,6), (2,4), (3,2), (4,0)
c. (3,0), (3,1), (3,2), (3,3), (3,4)

Answers

To be a function every x should have only one y-value.
a. (0,0), (1,1), (2,2), (3,3), (4,4) - We do not see repeating values of x, so it is a function

b. (0,8), (1,6), (2,4), (3,2), (4,0)- We do not see repeating values of x, so it is a function

c. (3,0), (3,1), (3,2), (3,3), (3,4) - We see repeating value of x, that means that one value of x corresponds many values of y , so it is not a function.

Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F

Answers

the correct question is
Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F'?

we know that
the transformation has the following rule
(x,y)--------> (x+6,y-6)
so
(-9,2)-----> (-9+6,2-6)------> (-3,-4)

the answer is
(-3,-4)

Answer:

-6,-6

Step-by-step explanation:

(-9,2) + (-8,3) = (-6,-6)

correct on the test :)

Cans of juice cost 25p each to produce
There are 6 cans in a pack.
12 packs are sold at £3.60 each.
What is the profit?

Answers

the profit is 1.60 beacuse at 25 cents times 6 is two dollars and since it is 3.60 the profit is 1.60 and 1.60 times twelve is 19.20 so the answer is 19 dollars and twenty cents

Consider the arithmetic series:

1 + 9 + 17 + 25 + ...

Write a formula for the sum of the first n terms in this series.
A) 4n2 - 3n
B) 6n2 - 7n
C) 8n2 - 5n

Answers

The sum of an Arithmetic Series is given as:

[tex] S_{n}= \frac{n}{2}(2a_{1}(n-1)*d) [/tex]

where,
d = Common Difference = Difference of any two consecutive terms.
So,
d = 8

a1 = First term = 1

Using the values, we get:

[tex] S_{n}= \frac{n}{2}(2*1+(n-1)*8) \\ \\ S_{n}= \frac{n}{2} (2+8n-8) \\ \\ S_{n}= \frac{n}{2}(8n-6) \\ \\ S_{n}=n(4n-3) \\ \\ S_{n}==4n^{2}-3n [/tex]

The above equation gives the formula for n terms of an Arithmetic Series.

So, option A is the correct answer

sin^{2} theta +cos theta = 2
Use the pythagorem identity sin^{2} theta +cos^{2} theta =1 to replace sin^{2} theta in the given equation

Answers

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\\\\ -------------------------------\\\\ \underline{sin^2(\theta )}+cos(\theta )=2\implies \underline{1-cos^2(\theta )}+cos(\theta )=2 \\\\\\ 0=cos^2(\theta )-cos(\theta )+1[/tex]

Final answer:

Applying Pythagorean Identity, the original equation sin² theta +cos theta = 2 can be altered by substituting sin² theta with 1 - cos² theta. This forms a quadratic equation: cos² theta - cos theta - 1 = 0, which can be solved using the quadratic formula to find the possible values of cos theta.

Explanation:

To solve the equation sin² theta +cos theta = 2 by using the Pythagorean identity sin² theta +cos² theta =1, we can substitute sin² theta in the original equation with 1 - cos² theta.

Step-by-step solution:

We start by replacing sin² theta in the equation with 1 - cos² theta. So, the equation becomes 1 - cos² theta + cos theta - 2 = 0.This can be rearranged to form a quadratic equation as cos² theta - cos theta - 1 = 0.We can solve this quadratic equation using the quadratic formula cos theta = [- (-1) ± √{(-1)²-4(1)(-1)} ] /2(1).Computing the values, we get the two possible values of cos theta.

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Vanessa is opening a clothing store. She plans to start by selling gym shorts. If it costs her $4 for each pair of shorts, $3 for the ink per pair of shorts, and $0.20 a bag, what is her unit cost per pair of shorts?

Answers

Unit cost=(total cost)/(number of units)
cost of shorts=$4
Number of pairs=1
thus
unit cost=4/1=4 dollars per pair

Answer: 4 dollars per pair

Answer:

its $7.20 on APEX

Step-by-step explanation:

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