If 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(5a, 2a), where a > 0, what is the value of a?

Answers

Answer 1

Answer:

The value of a is 80

Step-by-step explanation:

The distance of a point [tex](x_o,y_0)[/tex] from the y-axis can be written as [tex]d_y=|x_o|[/tex]  because the x-coordinate of the y-axis is zero.

Similarly, the distance of a point  from the x-axis can be written as [tex]d_x=|y_0|[/tex]

since the y-coordinate of the x-axis is zero.

In this problem:

- The distance of the point A (−30, −45) from the y-axis can be written as

[tex]d_A=|-30|=30[/tex]

- The distance of point B (5a,2a) from the x-axis can be written as

[tex]d_B=|2a|=2a[/tex]

Since [tex]a>0[/tex]

We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means

[tex]\frac{2}{3}d_A=\frac{1}{4}d_B[/tex]

Therefore,

[tex]\frac{2}{3}(30)=\frac{1}{4}(2a)[/tex]

And solving for a,

[tex]20=\frac{1}{2}a\\a=40[/tex]


Related Questions

Please help with this too!

Answers

Answer:

b>1

Step-by-step explanation:

[tex]3(3b-4)> 8b-11\\9b-12> 8b-11\\9b-8b> -11+12\\b> -11+12\\b>1[/tex]

A cyclist rides her bike at a speed of 10 kilometers per hour. What is this speed in miles per
computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers,
미픔
Speed:
Х
?
Distance traveled in 4 hours:

Answers

Dnene e hope this helps

0.8 rounded to nearest hundred

Answers

Answer:

1

Step-by-step explanation:

extending answer to be able to send

Answer:

0.9

Step-by-step explanation:

There is not even half of 10 hundredths to make another tenth. Therefore, 0.81 is closer to 0.8 than it is to 0.9. 0.81 becomes 0.8, rounded off to the nearest tenth.

Fast pls do this I need it really quick

Answers

Answer:

1 to 20 to 17 to 29

Step-by-step explanation:

Use the distributive property of operations and choose the correct equivalent expression for the given expression 2(3+6y)

Answers

The expanded or distributed form of the expression 2(3 + 6y) is 6 + 12y.

What are GCF and distributive property?

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given, An expression 2(3 + 6y).

Now, Expanding this expression of form a(b + c) to the form ab + ac we'll have,

2(3 + 6y).

= 6 + 12y Or 12y + 6.

There are also other properties for example commutative property of addition which states the order of adding numbers does not matter.

a + b = b + a.

2 + 3 = 3 + 5 is equal to 5.

learn more about the distributive property here :

https://brainly.com/question/29647107

#SPJ5

John has $200 in his savings account. He deposits $50 each week. What is the rate of change?

Answers

Answer:

50

Step-by-step explanation:

It would be plus 50

6 hats for $45 what was the cost per hat ​

Answers

Answer:

270

Step-by-step explanation:

you will times 6 by 45

Answer:

$7.50

Step-by-step explanation:

45÷6=7.50

7.50=$7.50

I hope this helps! Please give me brainliest!

Find the area of the rectangle in cm2
12 CM
5 CM

Answers

Answer:

56

Step-by-step explanation:

12CMx

5M

Select all of the statements that are true for the given parabola.
A. The minimum is (1,-2).
B. The line of symmetry is y=-2.
C. The maximum is (1,-2).
D. The x-intercepts are (3,0) and (-1,0).

Answers

Answer:

A & D

Step-by-step explanation:

The parabola opens up, so the minimum value of y is at the point (1, -2) and the graph passes thru the x-axis at 3 and -1, so those are the x-intercepts.

The axis  of symmetry is x = 1, not y = -2 and the graph never has a maximum value.  Parabolas that open up never have a maximum value.

PLEASE HELLP MEEE THIS IS THE LAST QUESTION

Answers

Answer:

40

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

it's going up by 3. jjjj

If m<13=m<15=m<7, what conclusions can you make about lines a, b, c, and d?

•Only lines a and b are parallel.
•Only lines c and d are parallel.
•Lines a and b are parallel, and lines c and d are parallel.
•No conclusions can be made.

Answers

Answer:

Lines a and b are parallel, and lines c and d are parallel.

Step-by-step explanation:

D. Describe why this statement is false.
"75% of the days had 20 or more parts per million of pollution."

Answers

Answer:

59%

Step-by-step explanation:

There are 7 days out of 14 that are 20 or more

That would be 59%

which is greater 1 2/4 or 1 3/4

Answers

Answer:

this is simple... 1 3/4

Step-by-step explanation:

Answer:

1 3/4 is greater

Step-by-step explanation:

1 2/4 = 1 1/2 = 150%

1 3/4 = 175%

Pls Help Asap (15 Points) Best Answer Gets Brainliest

Answers

Answer:

4 or D

Step-by-step explanation:

↓Energy Pyramid Provided Below↓

Answer:

the last one

Step-by-step explanation:

Please can someone help I’m crying myself out here please I don’t understand this I’m going to fail if I don’t do this please help for gods sake!

Answers

Answer:

Step-by-step explanation:

in right trigons with a 45 degree angle, a side length of x will mean the hypotenuse is [tex]x\sqrt{2}[/tex].

In right trigons with a 30 or 60 degree angle, if the shortest side is of length x, the longer side would be [tex]x\sqrt{3}[/tex] and the hypotenuse would be 2x.

Answer:

7√2

Step-by-step explanation:

*Note: this is only for the first question

So the picture at the bottom shows the ratio of the sides of a triangle with the angles of 45 degrees, 45 degrees, and 90 degrees.

In the image, they give you the side length that corresponds to a in the picture.

This means that to find the length of the hypotenuse, all you have to do is multiply 7 by the square root of 2

Rhombus ABCD has side lengths of (6x + 4) inches, (4y + 10) inches, (8x − 14) inches, and (7y − 26) inches. The diagonals are 80 inches and 84 inches and intersect forming an angle of (8z + 2)°.

Answers

Answer:

x = 9, y = 12, z = 11

Step-by-step explanation:

A rhombus is a quadrilateral (has four sides and four angles) with four equal sides. Opposite sides of a rhombus are parallel to each other and the diagonals bisect each other at right angles i.e. 90°.

Given the rhombus ABCD:

(6x + 4) = (4y + 10) = (8x − 14) = (7y − 26) [the sides of a rhombus are equal].

Hence; 6x + 4 = 8x - 14

8x - 6x = 14 + 4

2x = 18

x = 9

Therefore the side length = 6x + 4 = 6(9) + 4 = 58 inches

Also: 4y + 10 = 7y - 26

7y - 4y = 10 + 26

3y = 36

y = 12

(8z + 2) = 90° (diagonals of a rhombus bisect each other)

8z + 2 = 90

8z = 90 - 2

8z = 88

z = 11

Pls help
It due asap
Ydydbdbgdbs

Answers

Answer:

1 & 7

2 & 8

5 & 3

6 & 4

Step-by-step explanation:

Answer:

1 and 7

2 and 8

5 and 3

6 and 4

40=16-8r help me plzzzz

Answers

Answer:

r = - 3

Step-by-step explanation:

Given

40 = 16 - 8r ( subtract 16 from both sides )

24 = - 8r ( divide both sides by - 8 )

- 3 = r

Mr. Richards purchased 8 T-shirts for the volleyball team. The total cost of the T-shirts was $70.56. How much did each shirt cost?

Answers

Answer:

$8.82

Step-by-step explanation:

$70.56÷8 =$8.82 total

Answer:

$8.82

Step-by-step explanation:

The total cost of the T-shirts was 70.56. Each T-shirt is equal in money, so what you need to do is divide the total cost by the number of T-shirts.

70.56 / 8 = 8.82

Each T-shirt cost $8.82

The sum of three consecutive odd integers is 105. What is the value of the smallest integer?

Answers

Answer:

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

The sum is 105

n+n+2+n+4=105

3n+6=105

minus 6 both sideds

3n=99

divide both sides by 3

n=33

n+2=35

n+4=37

Factories (2u_7v)square+7v_2u

Answers

So when I told when where there was a solution to my grandmis a little thing and no

What is the length of line segment AB in the triangle shown below?

Answers

Answer: 15

Step-by-step explanation: Pythagorean theorem

8^2+b^2=17^2

64+b^2=289

b^2=225

b=15

Brainliest please

Answer:

15  inches.

Step-by-step explanation:

[tex]AB=\sqrt{AC^{2}-BC^{2} } =\sqrt{17^{2}-8^{2} } =\sqrt{289-64} =\sqrt{225}= 15 \: ( inches)[/tex]

HELP QUICK PLEASE!!!!

A scatter plot is shown:
What type of association does the graph show between x and y?

Linear positive association

Nonlinear positive association

Linear negative association

Nonlinear negative association

Answers

X y is the one for that


Which rule best describes the following pattern?
8, 4, 10, 6, 12, 8, 14, ...
HELP ASAP I WILL GIVE BRILLIANT OR SOMETHING PLZZZ

Answers

Answer:

Umm ok so each number you have you subtract for then add 6 and so on and so forth.

Step-by-step explanation:

8, 4, 10, 6, 12, 8, 14, 10, 16, 12, 18

or you can say this

8,10,12,14,16 and

4,6,8,10,12

are part of the same sequence but each part counts by two.


Are these figures similar?
yes or no

Answers

Answer:

Step-by-step explanation:

No

No they at least need to be the same sides

Plz help would mean a lot.....thanks ❤️

Answers

Answer:

7-s/3=2

6=7-s

-1=-s

s=1

Give brainlist

I need the answer and explanation pls

Answers

Answer:

67°

Step-by-step explanation:

A right angle = 90°

90° - 23° = x° =  67°

Answer:

67

Step-by-step explanation:

You can see that there is a square in the corner, that means this is a 90 degree angle.

So just subtract 90 to 23 and you'll get 67.

a home owner is building a fence around his backyard and needs to know how much material to buy. he would need to calculate _______________

a. area
b. perimeter
c. metric conversions

Answers

B.perimeter is the answer the perimeter is the outside of the house where the fence goes
b . perimeter as that is the area around which would be the fence


FIND THE VALUE OF X.Please

Answers

I think it’s 55 I think not to sure but ya it’s that

The difference of three times Faye’s age and four times Joshua’s age is 31. If Faye’s age is five more than twice Joshua’s age, how old is Faye?

Answers

Answer:

Faye is 21

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

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