The width, y, of a rectangle with a fixed area varies inversely with its length, x. The width is 3 inches when the length is 14 inches. Find the width when the length is 30 inches.

Answers

Answer 1

Answer:

[tex]y = 1.4[/tex]

Step-by-step explanation:

Given

[tex]y = width[/tex]

[tex]x = length[/tex]

[tex]y = 3;\ when\ x = 14[/tex]

Required

Find y when x = 30

Being an inverse variation, we have:

[tex]y\ \alpha\ \frac{1}{x}[/tex]

Convert the variation to an equation

[tex]y = \frac{k}{x}[/tex]

First, we solve for k

Make k the subject to solve for k

[tex]k = xy[/tex]

[tex]y = 3;\ when\ x = 14[/tex]

So, the value of k is:

[tex]k = 14 * 3[/tex]

[tex]k = 42[/tex]

To solve for y when x = 30

Substitute 30 for x and 42 for k in [tex]k = xy[/tex]

[tex]42 = 30 * y[/tex]

Make y the subject

[tex]y = \frac{42}{30}[/tex]

[tex]y = 1.4[/tex]

Answer 2

The width of the rectangle would be as follows:

[tex]1.4[/tex]  inches

Inverse Proportion

Inverse proportion occurs when one value increases and the other decreases.

The width, [tex]y[/tex], of a rectangle with a fixed area varies inversely with its length, [tex]x[/tex].

So, [tex]y=\frac{k}{x}[/tex] where [tex]k[/tex] is the constant.

The width is [tex]3[/tex] inches when the length is [tex]14[/tex] inches.

So,

[tex]3=\frac{k}{14} \\k=42y=\frac{42}{x}\\Put x=30[/tex]

Therefore, [tex]y=\frac{42}{30}=1.4[/tex] inches

Thus, Width is [tex]\boldsymbol{1.4}[/tex] inches when the length is [tex]30[/tex] inches.

Find out more information about inverse proportion here: https://brainly.com/question/2548537


Related Questions

Convert 10°C to Fahrenheit.
45°F
65°F
50°F
42°F

Answers

Answer:

C. 50°F

Step-by-step explanation:

(10°C × 9/5) + 32 = 50°F

What is 2896.9874 rounded to the nearest hundredth?

Answers

2896.99 because the hundredth is the second number after decimal point

any of them, please help

Answers

Answer:

this is

Step-by-step explanation:

number 9 hope it's right

Suppose we have a right triangle with legs of length a and b and hypotenuse of length c. Suppose b=3 and c=5. Then a= , For the opposing angles, we have sin(A)= , cos(A)= , and tan(A)= .

Answers

Answer:

Length of right-angle  triangle 'a' = 4

b)

[tex]sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}[/tex]

[tex]cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}[/tex]

[tex]tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}[/tex]

Step-by-step explanation:

Step(i):-

Given  b = 3 and hypotenuse c = 5

Given ΔABC  is a right angle triangle

By using pythagoras theorem

        c² = a² + b²

  ⇒ a² = c² - b²

 ⇒  a² = 5²-3²

          =25 - 9

      a² = 16

⇒   a = √16 = 4

The sides of right angle triangle  a = 4 ,b = 3 and c = 5

Step(ii):-

[tex]sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}[/tex]

[tex]cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}[/tex]

[tex]tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}[/tex]

which ordered pair represents a point in Quadrant IV?
A) (4, -4)
B) (3, 0)
C) (-1 -6)
D) (-4, 2)

Answers

Answer:

pretty sure it's A. (4, -4)

One side of each pentagon lies along a side of the octagon.
AB is a side of the octagon.
AC is a side of one of the pentagons.
BC is a side of the other pentagon.
Work out the size of angle y.
Show your working clearly.

Answers

Answer:

The size of angle y is 126°

Step-by-step explanation:

From the diagram of the regular polygons, we have;

One side of each pentagon lies along a side of the octagon

The interior angle of the octagon > The interior angle of the pentagon

Each interior angle of a regular pentagon = 108°

Each interior angle of a regular octagon = 135°

Therefore, ∠ABC = 135° - 108° = 27°

Similarly, ∠BAC = 135° - 108° = 27°

Therefore, by triangle the angle sum theorem, we have;

∠y = ∠ACB = 180° - ∠BAC - ∠ABC = 180° - 27° - 27° = 126°

The size of angle y, ∠y = 126°.

Using a pencil, pair of compasses and ruler, construct a triangle with sides 8cm, 9cm and 6cm
Measure the size of the angle between the 8cm and 9cm sides to the nearest degree.​

Answers

Answer:

The nearest degree of the angle between the 8cm and 9cm sides is:

41°

Step-by-step explanation:

To obtain the correct angle in a small triangle like the triangle formed with the measures in the exercise is a little bit hard, in a change of this, I used a triangle calculator, with this I obtained the right angle formed by the sides with 8 cm and 9 cm, which I'm gonna add like an attachment.

From this image, you can guide yourself to draw the triangle without mistakes and to identify the right angle, which is 40,8° but the compass is not so defined, by this reason you can take it like 41° or 40°.

is this triangle congruent? pls answer i will mark you brainlyist :)

Answers

Answer:

no

Step-by-step explanation:

PLZ HELP ME PLZZZZZZZZZZZZZZZZZZZZZZ

Answers

Answer and Step-by-step explanation:

Ok, so all we have to do is input the values into the equation.

We are told Adam bought 2 mechanical pencils and 8 spiral notebooks, which cost $13

and that

Kia bought 3 mechanical pencils and 5 spiral notebooks, which cost $12.50.

Adam: 2p + 8n = 13

Kia:     3p + 5n = 12.5

This is the answer.

#teamtrees #WAP (Water And Plant)

Answer: Adam: 2p + 8n = 13

Kia:     3p + 5n = 12.5

Step-by-step explanation:

F(x)=3x+1 and g(x) = square root of x-1 find (fog)(5)

Answers

Answer:

The answer is [15(√x - 1) + 5].

Step-by-step explanation:

(fog)(5) = [3(√x-1) + 1] (5)

= [3(√x - 1) +1] (5)

= 15(√x - 1) + 5

hi please help me out :)) theres a picture right here!!

Answers

Answer:

40%

Step-by-step explanation:

Percent is from 0% to 100%

If you multiply them all by 2 you get your answer. (My comments were wrong sorry-)

This is da right answer trust me

The lunch choices last Friday were mushroom or pepperoni pizza. The cafeteria made 20 mushroom pizzas and 80 pepperoni pizzas. What percentage of the pizzas were mushroom pizzas?

Answers

Answer:

20%

Step-by-step explanation:

in total there 100 pizzas each one is a percent and there are 20 mushroom so 20% is answer.

Solve the inequality. Graph the solution.

d+12<19

Answers

Answer:

Move all terms not containing d

to the right side of the inequality.

Inequality Form:

d<7

Step-by-step explanation:

Sorry no graph

Answer:

d < 7

Step-by-step explanation:

d + 12 < 19

1. Subtract 12 from both sides

d + 12 - 12 < 19 - 12

d < 7

What Is the volume of the pyramid in the diagram?

Answers

Answer:

I think is A

Step-by-step explanation:

I hope it help

WHAT ARE THESE ALSO EXPLAIN HOW YOU DID ITT DUE SOOOON

Answers

Answer:

down below

Step-by-step explanation:

4. 5/11 x 2/2 = 10/22: yes

5. 36/4 = 9 but 2x9 = 18 not 20: no

Which expression is equivalent to (144k2r14)1/2 for all positive values of k and r ?

A.144kr7

B.12kr7

C.12k2r4

D.72k2r14

Answers

Answer:

12kr⁷ is the equivalent expression.

Step-by-step explanation:

We need to find an expression that is equivalent to [tex](144k^2r^{14})^{1/2}[/tex]

We know that, 12² = 144

[tex](144k^2r^{14})^{1/2}=(12^2\times k^2\times r^{14})^{1/2}\\\\=12^{2\times \dfrac{1}{2}}\times k^{2\times \dfrac{1}{2}}\times r^{14\times \dfrac{1}{2}}\\\\=12\times k\times r^7\\\\=12kr^7[/tex]

So, the equivalent expression is [tex]12kr^7[/tex]. Hence, the correct option is (B).

.
The battery charge must be:
greater than 25% charged, but
1
• less than charged, and
. a multiple of 0.20

Answers

Answer:

40 percent

Step-by-step explanation:

(X^3-2x^2+5x+6)÷(X-3)
How do I solve this with long division?

Answers

Answer: X^2+3X+9+- 2x^2+33/X-3

Step-by-step explanation:

Please help me with this math question asap. I will mark brainliest. Thank you so much! Question 4/5

Answers

Answer:

list the givens

line SU ≅line UT⇒def of a midpoint

ΔSVU≅ΔTWU⇒SSS

∠SVU≅∠TWU ⇒CPCTC

Step-by-step explanation:

What is the midpoint of the segment whose endpoints are (0.4) and (-4,-6)

Answers

Answer:

The coordinates of the midpoint are (-2,-1)

Step-by-step explanation:

The Midpoint of a Segment

Given a segment defined by points (x1,y1) and (x2,y2), the coordinates of the midpoint (xm,ym) are calculated as follows:

[tex]\displaystyle x_m=\frac{x_1+x_2}{2}[/tex]

[tex]\displaystyle y_m=\frac{y_1+y_2}{2}[/tex]

We have the endpoints (0,4) and (-4,-6):

[tex]\displaystyle x_m=\frac{0-4}{2}[/tex]

[tex]\displaystyle x_m=\frac{-4}{2}=-2[/tex]

[tex]\displaystyle y_m=\frac{4-6}{2}[/tex]

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

The coordinates of the midpoint are (-2,-1)

Identify the inequality that represents the following problem. One less than twice a number is no less than five. What is the solution set?

2 n - 1 > 5
2 n - 1 ≥ 5
1 - 2 n ≥ 5
1 - 2 n > 5

Answers

Answer:

is the last one

1 - 2n > 5. The solution set is (-∞, -2)

Step-by-step explanation:

e are dealing here with two problems:

First, to determine which mathematical statement represents "One less than twice a number is no less than five".

Second, solve n, that is, the solution set for the numbers that solve the inequality.

First Part: Identifying the inequality

"One less than twice a number" can be written as  , where n is the unknown number.

If it is not less than five, thus it is greater (no less) than five. Then, the symbol here is  " > " (greater).

As a result: "One less than twice a number is no less than five" could be rewritten as "One less than twice a number is greater than five", or:

.

Second Part: Finding the solution set

The solution set for this inequality is as follows:

Subtract -1 from each member of the inequality:

⇒  ⇒  

Multiply each member of the inequality by  (or divide each member by -2). We have to remember here that when we multiply or divide an inequality by a negative number (-n), this inverts the inequality, that is:

The solution set is then , which is any value less than -2 (not including -2, because is < and not ≤), and we have infinite negative numbers with such a characteristic. We can write it mathematically as an interval notation:

Solution set for  is .

Answer:

1-2n>5

hope it help3d

twelve is what percent of 42

Answers

Answer:

28.57 percent

hope that helped

Answer:3.5 percent of 42 gives you 12

Step-by-step explanation:

what’s the answer i need help? Find slope using triangles and rise over run

Answers

Answer:

slope is 1/3

Step-by-step explanation:

notice the points on the line, from the first point go one square up and three to the right, thats how i got 1/3    

If i dont get this done ima get grounded for like a bazziin years so plaese HALP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The yes mean proportional and the no means not proportional and the unit rates were not the same

Does the point (-9, 18) satisfy the equation y = -2x?
yes
no

Answers

Answer:

Yes

Step-by-step explanation:

If you plug the numbers into the equation and solve it

18 = -2(-9)

18 = 18

I want to get as many bags of chips as possible to each cost $2 I also told my mom I would get her a carton of eggs eggs cost $5 I have $25 total create an equation to represent the scenerio and figure out how many chips I can buy

Answers

Answer:

y(total)=2x+5

Step-by-step explanation:

Answer:

2x+5=25 I think.......

What is the slope pf the line represented by 2x-3y=4?

Answers

Answer:

2/3

Step-by-step explanation:

Get it into slop-intercept form

2x - 3y = 4

3y = 2x - 4

y = 2/3x - 4/3

Answer:

Slope= 2/3

Step-by-step explanation:

-3y=-2x+4

y=2/3x-4/3

Factorise
x2 — 73 — 44

Answers

Answer:

Step-by-step explanation:

here you go mate

step 1

x^2-73-44  equation

step 2

x^2-73-44  (CLT)

step 3

(x^2)+(-73+-44)  simplify

answer

x^2-117

0.15 km converted to centimetres

Answers

Answer:

15000

Step-by-step explanation:

you times it by 100000

why is -3>1-1 not correct

Answers

Answer:

It is incorrect because -3 is less than 0

Step-by-step explanation:

Say we have a number line that is- uhm

-5 to five so he numbers would look somewhat like

-5 -4 -3 -2 -1 0 1 2 3 4 5

(lesser to greater)

if you take -3>1-1 and simplify 1-1

you would now have -3>0

this statement says -3 is greater than 0

if you look on our number line which goes from lesser to greater then you see that -3 is less than 0 therefore -3>1-1 is incorrect.

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