a rectangle has an area of 156 square inches and a perimeter of 50 in what are the width and the length of the rectangle

Answers

Answer 1

W = 13 inches

L = 12 inches

P = 2(l+w) and L=P/2 - w=50/2 - 13 = 12

Answer 2

Final answer:

To find the length and width of the rectangle with an area of 156 square inches and a perimeter of 50 inches, we can set up and solve a system of equations based on the area and perimeter formulas. After solving, we determine that the length is 13 inches and the width is 12 inches.

Explanation:

The student has asked to find the length and width of a rectangle given that it has an area of 156 square inches and a perimeter of 50 inches. To solve this problem, we need to use the formulas for the area and perimeter of a rectangle.

Area and Perimeter Formulas

Area formula: A = length × width

Perimeter formula: P = 2(length + width)

Let's denote the length as 'l' and the width as 'w'. The area of the rectangle is 156, so we can write:

l × w = 156

The perimeter of the rectangle is 50, so we can write the perimeter formula as:

2(l + w) = 50

This simplifies to:

l + w = 25

Now, we have two equations:

l × w = 156

l + w = 25

We can solve this system of equations by expressing one variable in terms of another. Let's express 'w' in terms of 'l' from the second equation:

w = 25 - l

Now, substitute 'w' in the area equation:

l × (25 - l) = 156

This is a quadratic equation that can be solved to find the values of 'l'. Once we have 'l', we can find 'w' using the second equation.

After solving, we find that the length is 13 inches and the width is 12 inches. Therefore, the rectangle's dimensions are 13 inches by 12 inches.

Related Questions

a motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.
please help slove and steps

Answers

Going upstream: 432 km / 6 hours = 72 km/h
Going downstream: 384 km / 4 hours = 96 km/h
Going upstream against the current means that the effective speed is:
r_boat - r_current = 72
Meanwhile, going downstream with the current means;
r_boat + r_current = 96
Adding both equations (to cancel out r_current) gives:
2r_boat = 72 + 96
r_boat = 84 km/h
Substituting back into one of the original equations: r_current = 12 km/h.

Distance between New York and San Francisco is 2539.79 MI a train travels at an average speed of 90 miles per hour what equation shows the relationship between distance traveled (Dl speed (s) and time taken (t)

Answers

D = s*t . . . . . . . distance is the product of speed and time

_____
If you want to know the time it takes to get from New York to San Francisco, you can substitute the given values and solve for t.
2539.79 = 90t
2539.79/90 = t ≈ 28.2199 . . . . hours

3 over 5 is 30% of what number?

Answers

3/5 = 0.3 * x
3/5 is 30% of x - This is how they match up from the word problem to a number sentence

So to solve it...
3/5 = 0.3x
x = 3/5 ÷ 0.3 = 2

translated 2 units left and 9 units down

Answers

Move 2 times to the left and go down 9 times i think....

The translation of the given expression is "[tex]\bold{y=(x+2)^2-9}[/tex]"

Translation of equation:

Given:

"translated 2 units left and 9 units down".

we assume the equation is "y" so, the translation of the above-given expression is equal to "[tex]\bold{y=(x+2)^2-9}[/tex]".

Please find the attached diagram for the translated expression.

Find out more information about the translation here:

brainly.com/question/24649944

Admission to the state fair costs $5 and each ride costs $0.75. If Ahmed wants to spend no more than $14 at the fair, how many rides can he ride?
-Show All Work Please-

Answers

14-5= 9

9 divided by .75 = 12

He can ride 12 rides.

Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) she can raise with 10 dark power crystals. How many zombie soldiers can Liliana raise with 10 power crystals?

Answers

4c = 14z.
1c = 3.5z.
10c = 35z.
So she can raise 35 with 10 power crystals. Hope it helps !:)

Answer:- Liliana can raise 35 zombie soldiers with 10 power crystals.

Explanation:-

Let the number of zombie soldiers raised by 10 dark power crystals be 'x'.

Zombie raised by 4 power crystals = 14

Since the number of zombie and power crystals are in direct proportion.

Therefore, we get

[tex]\frac{x}{10}=\frac{14}{4}[/tex]

Multiply 10 on both the sides, we get

[tex]\Rightarrow\ x=\frac{14}{4}\times10=35[/tex]

Liliana can raise 35 zombie soldiers with 10 power crystals.

Carlisle is testing different types of planting soil to determine which type is most effective in growing blueberry bushes. He purchases 2 different brands of planting soil from a local store. Carlisle applies Brand A to an area of the yard that receives full sunlight and Brand B to another area of the yard that is in partial shade. He waters both areas daily. At the end of the study, Carlisle concludes Brand A is more effective in growing blueberry bushes. Why is his conclusion not valid?

Answers

This conclusion is not valid because BOTH SOIL BRANDS WERE NOT SUBJECTED TO THE SAME CONDITIONS.
Carlisle applied brand A to the part of the yard that received full sunlight while brand B was applied to the area of the yard which received partial sunlight. This implies that the soils were subjected to different conditions and this ought not to be so, since sunlight is a very important factor, which the soils need.

His conclusion is not valid because his dependent variables weren't the same. When testing out an independent variable, which is the soil in this case, all the other factors of the experiment has to remain the same in order to provide a correct conclusion. Since Carlisle was testing out two different types of soils, he had to set all the other conditions of the plants exactly the same, including the amount of lights that the plants receive. Brand B received full sunlight whereas brand A received less. This could definitely have impaired the results of this experiment, therefore, making it invalid.

what do i do?? i just have to find what the the question marks show.

Answers

------------------------------------------------------
Given information
------------------------------------------------------
100% = $27.60

------------------------------------------------------
Rewriting it
------------------------------------------------------
[tex]\$27.60 = 100 \%[/tex]
[tex]\$1 = 100 \div 27.60 \%[/tex]
[tex]\$1 = \frac{250}{69} \%[/tex]

------------------------------------------------------
Find $4.14 in percentage
------------------------------------------------------
[tex]\$1 = \frac{250}{69} \%[/tex]
[tex]\$4.14 = \frac{250}{69} \times 4.14[/tex]
[tex]\$4.14 = 15%[/tex]

------------------------------------------------------
Answer: 15%
------------------------------------------------------

------------------------------------------------------
Find $31.74 in percentage
------------------------------------------------------
[tex]\$1 = \frac{250}{69} \%[/tex]
[tex]\$31.74 = \frac{250}{69} \times 31.74[/tex]
[tex]$31.74 = 115%[/tex]

------------------------------------------------------
Answer: 115%
------------------------------------------------------

Which is greater 320 fl oz of 18 pt

Answers

16 ounces = 1 pint
320/16 = 20 pints

320 fl oz is greater than 18 pt

5.1 times 10 to the fourth power

Answers

The answer is 6,765,201. I apologize if I got this wrong.

5.1*10=51
so, 51*51*51*51=6765201

when using fraction strips how do you know that two fractions are equivalent

Answers

The same strip area is covered by equivalent fractions. That's what makes them equivalent.

She is correct. The first person that answered

jack has 3 quarters, 2 dimes, and one penny. how much money does jack have in all? show your work.

Answers

75+20+1=96 cents

your welcome

how would you graph y=| x-2|-4

Answers

To graph ty function simply make a table of values, where you choose any value for x and substitute that value in the function.

Then take the absolute value of the expression in the square bracket.

It is always positive, the absolute value of -6 is 6 etc.

Then graph the resulting points.

Another way to do it is simply draw the graph of y = |x| then move it 2 spaces to the right and 4 spaces down, I believe.

How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3?

Answers

infinitely many solutions. Since your slope and Y axis values are the same on both sides no matter what you fill in for x your answer will be true.

What is the arc length of a circle (in meters) with a radius of 2 meters that has an arc angle of 90°? A 2π B π C 2 D 4π

Answers

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad de grees\\ ------\\ r=2\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (2)}{180}\implies s=\pi [/tex]

If the correlation between height and weight of a large group of people is 0.75, find the coefficient of determination (as a percent) and explain what it means. assume that height is the predictor and weight is the response, and assume that the association between height and weight is linear.

Answers

Independent variable is the predictor variable which is the height and dependent variable is the response variable which is weight in this scenario.

The square of correlation coefficient gives the coefficient of determination. It is denoted by R² (R squared).

We are given:
R = 0.75

So,
R² = 0.75²

R² = 0.5625

R² = 56.25 %
The coefficient of determination tells how much of the trend of dependent data can be explained by the independent data using the linear regression model. So in the given case, Height can explain 56.25% of the trend in the weight.

Answer:

Step-by-step explanation:

Given that the correlation between height and weight of a large group of people is 0.75

Coefficient of determination = [tex]R^2 =0.75^2 =0.5625=56.25%[/tex]

Coefficient of determination gives us the strength of association between two variables and how much the variability of the response variable i.e. weight is due to the variability of the predictor variable i.e. height

When there is a linear association correlation coefficient square gives us the reason for the variability and percentage due to the variability in predictor variable

Imagine a world in which only decimal,not fractions,are used.how would your life be different

Answers

This answer depends a bit on your age, the types of activities you partake in and the kind of work you do/are planning to do but here goes:

I am thinking of some uses of fractions where decimals are not typically used. One might be cooking. Often the ingredients (1/2 cup of four and so on) are measured using fractions. If you were in a world with decimals you might need to make (1/3) the servings of a recipe that calls for 1/4 of a cup of some ingredient and instead of 1/12 have to deal with a long repeating decimal that probably would need to be approximated so would not be precise.

While on the subject of food ordering pizza (1/2 with pepperoni, 1/4 mushrooms and 1/4 plain) would be doable after you got used to it but probably not as comfortable. Dividing up slices of pizza among friends (one slice is usually 1/8 of a pie) might be awkward though eventually doable.

Estimation - the biggest issue is exactitude versus estimation. When we use a fraction like 1/3 that is an exact value, but when we use .333 or .3333333 no matter how many 3s we use we are only estimating because the 3s go on forever and we can't write them forever. Yes, we can use .3 (with a bar over the 3, but now try to multiply that with .456565656 with a bar over the 56. This becomes practically impossible unless we estimate ... so the biggest issue would be that you would lose precision in many calculations and measurements and have to deal with answers that are good enough (but not exact).

Now say you work on some major car company or you design bridges or you are a scientist developing medicine that cures diseases, would not you want the ability to measure and compute precisely? If I split the pizza up wrong it is not a big deal. If I use a little more flour or a little less than I should in the recipe it might not make much of a difference in the end but if I am doing something that impacts the health, safety or well being of another human being, I would not want to live in a world where I have to estimate and can't count on having the exact, precise value.

At a certain time of day the angle of elevation of the sun is 30 a tree has a shadow that is 25 feet long find the tree to the nearest foot

Answers

If we draw out this scenario, we can see that it is a 30-60-90 right triangle, and the tree shadow is the leg opposite of the 60 degree angle. The problem asks for the length of the tree, which is the leg opposite of the 30 degree angle. In a 30-60-90 triangle, the leg opposite of the 30 degree angle has length “x”, and the leg opposite of the 60 degree angle has length “x times sqrt 3” (or “x rad 3”). We know the leg opposite of the 60 degree angle is 25 feet, so we can setup the equation “x rad 3 = 25”. We divide sqrt of 3 on both sides and end up with “x = 25/sqrt 3”. The problem asked for the leg opposite of the 30 degree angle, which we set as “x”. The problem asks for the length to the nearest foot. When put into a calculator, “25/sqrt 3” ends up being about 14 feet, which is our final answer.

Which of the following is the same as 5(2 − 1)?

a 5 − 2 − 1

b 5 × 2 × 1

c 10 − 1

d 10 − 5

e one of the above

Answers

I believe it would be D

Koji is installing a rectangular window in an office building. The window is 8/23 feet wide and 5/34 feet high. The formula for the area of a rectangle is A=bh. What is the area of the window? Enter your answer as a mixed number in simplest form in the box. $$ ft2

Answers

Here, We know, Area = Base * Height
We have: b = 823 Ft
h = 534 Ft

Substitute their values,
A = 823 * 534
A = 439482 Ft²

In short, Your Answer would be: 439482 Ft²

I really hope this helps!

Buying something in order to increase social status is known as _____ consumption.

1 Conspicuous
2 Emotional
3 Research
4 Wise

Answers

1) conspicuous consumption

1) Conspicous Consumption

Can you please explain this

Answers

1st triangle is isoceles triangle as one as two angles are equal due to the equal sides......
2nd triangle is equilateral triangle as all sides are same

The two triangles are not congruent because we do not know if the third sides of both triangles are congruent. We can see that the first and second sides are congruent to their corresponding sides in the 2nd triangle. However, if we do not know that the third side in the first triangle is congruent to its corresponding side in the second triangle, then we cannot conclude that the two sides are congruent.

Select three rations that are equivalent to 7: 6.

Answers

14:12
21:18
28:24
............

round 543,873 to nearest ten thousand

Answers

For this case we have the following number.
543,873

1) Remember that when rounding the number to the nearest tousand, the number must have the first three digits (from right to left) equal to zero.

2) The fourth digit of the number (from right to left) must be rounded to the next number only if the third digit (from right to left) is greater than or equal to 5.

3) Following steps 1) and 2) we have the number rounded to the nearest tousand is:544,000

Answer:
Round to the nearest tousand:
544,000

Final answer:

To round 543,873 to the nearest ten thousand, we assess the digit in the ten thousand's place (4) and the digit to its right (3). Since the latter is less than 5, we round down, resulting in 540,000.

Explanation:

The question asks to round the number 543,873 to the nearest ten thousand. To do this, we look at the digit in the ten thousand's place, which is 4, and then look at the digit to its right, which is 3. If the digit to the right is 5 or above, we would round up. However, since it's less than 5, we round down. Therefore, 543,873 rounded to the nearest ten thousand is 540,000.

A town has two fire engines, a and b, that operate independently. the probability that engine a is available when needed is 0.96. the probability that engine b is available when needed is also 0.96. 12. what is the probability that neither fire engine is available when needed?

Answers

P(both unavailable) = P(A unavailable)*P(B unavailable) = 0.04^2 = 0.0016

how do you graph y=2sin(2x)

Answers

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.

on the a axis, you set the x value at 0, π/4, π/2, 3π/4, π
2sin0=0, 2sin(π/2)=2, 2sinπ=0, 2sin(3π/2)=-2, 2sin(2π)=0
so the y values are 0, 2, 0, -2, 0 respectively
locate the points and connect
extend the pattern left and right if there is no limit for x. It should look like a wave

-4x-2y=-12 and 4x+8y=-24 using addition/eliminatin method

Answers

Use the elimination method:

-4x - 2y = -12
+4x + 8y = -12
--------------------
0 + 6y = -24

6y = -24
6y/6 = -24/6
y = -4

Plug in -4 for y in one of the equations
-4x - 2y = -12
-4x - 2(-4) = -12
-4x + 8 = -12
-4x + 8 (-8) = -12 (-8)
-4x = -20
-4x/-4 = -20/-4
x = 5

x = 5, y = -4

hope this helps

elimination method is best because one equation has 4x and the other has -4x. Add the two equations together.

-4x - 2y = -12
+4x + 8y = -24
----------------------
0 + 6y = - 36

divide by 6 both sides
y = -6

use this to find x in either equation.
4x + 8(-6) = -24
4x - 48 = -24
4x = -24 + 48
4x = 24
x = 6

A prism is comply filled with 3996 cubes that have edge lengths of 1/3 inches. What is the volume of the prism

Answers

The volume of a cube by definition is:
V = L ^ 3
Where:
L: side.
We have then that the volume of a cube is:
V = (1/3) ^ 3
V = 1/27
Then, the prism volume is:
Vtotal = 3996 * V
Vtotal = 3996 * (1/27)
Vtotal 148 inches ^ 3
Answer:
the volume of the prism is:
Vtotal 148 inches ^ 3

Can someone explain? Please help! 15 pts!!!!

Answers

Let
x--------------> the third stone measure

we know that
the recommended height for the bench is ------> 20 in
20=[4 3/8]+[4 1/2]+[5 1/4]+[x]
4 3/8---------> (4*8+3)/8=35/8
4 1/2---------> (4*2+1)/2=9/2
5 1/4---------> (5*4+1)/4=21/4

20=[35/8]+[9/2]+[21/4]+[x]

x=20-(35/8)-(9/2)-(21/4)

x=20-(35+4*9+2*21)/8-----> 20-113/8------- > (8*20-113)/8

x=47/8---------- > 5.875=5 7/8

the answer is 5 7/8 in

pete's dog weighed 30 pounds . then lost 16% of its weight , how much weight did the dog loose

Answers

The dog would now way 25.2 pounds, having lost 4.8 pounds.

the dog had lost 4.8

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