All categories

2 years ago

The area of a rectangle is 70 in 2 and the length of the rectangle is 3 in. Longer than the width

Mathematics

1 answer:

Snezhnost [94]2 years ago

6 0

Alright, lets get started.

I hope, the dimensions of rectange are asked in this question.

Suppose the width of rectangle = x in

Given that length of the rectangle is 3 in longer than the width.

It means length of the rectangle = (x+3) in

Now, the area of the rectangle = lenght * width

area of the rectangle = $x * (x+3)$

area of the rectangle = $x^2+3x$

The area of a rectangle is 70 in square (given in question)

Equalling both areas

$x^2 + 3x = 70$

Subtracting 70 in both sides

$x^2 + 3x - 70 = 70 - 70$

$x^2 + 3x - 70 = 0$

Factoring

$(x-7)(x+10) = 0$

It will give two values of x

x = -10 (which is not possible because length could not be negative)

x = 7

Means width $= 7 in$

length $= 7 + 3 = 10 in$

Means the dimensions of rectangle are 7 in and 10 in. : Answer

Hope it will help :)

You might be interested in

The diameter of a ball is 8 in.

Cerrena [4.2K]

267. 95cm^3

hope this helped

5 0

2 years ago

Ron has 2,500 pounds of horse feed to deliver. He wants to deliver an equal amount on each of 4 trips.

uysha [10]

4f=2500 because 4 trips from 2500 means $f= \frac{2500}{4}$ .

6 0

3 years ago

Cw 10.5 10.5 V. W<br> A great

Semmy [17]

Answer:

Refer to step-by-step.

Step-by-step explanation:

12. x = 28

BC = x

AB = 96

AC = 100

We use the Pythagorean theorem to find the value of x.

a² + b² = c²

x² + 96² = 100²

x² + 9216 = 10000

x² = 10000-9216

x² = 784

√x² = √784

x = 28

13. x = 64

a² + b² = c²

48² + x² = 80²

2304 + x² = 6400

x² = 6400 - 2304

x² = 4096

√x² = √4096

x = 64

14. YES and 25 = 25

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

So this means that AB is tangent to the circle.

15. NO and 45 ≠ 49

a² + b² = c²

3² + 6² = 7²

9 + 36 = 49

45 = 49

So this means the AB is not tangent to the circle.

16. x = 4.5 and P = 52

To find the value of x, we need to determine the value of our hypotenuse.

QU is congruent to QT, therefore, QT = 4

UR is congruent with SR, therefore, UR = 13

PS is congruent to AB, therefore:

2x = 9

Divide both sides by 2

x = 4.5

The perimeter of a triangle is:

P = a + b + c

a = 9 + 4 or 13

b = 2(4.5) + 13 or 22

c = 4 + 13 or 17

P = 13 + 22 + 17

P = 52

17. x = 13 and P = 72

TJ is congruent to UJ, therefore, TJ = 13

x = 13

The perimeter of a parallelogram is:

P = 2(a+b)

a = HR + RK

b = KU + UJ

a = 13 + 5 or 18

b = 5 + 13 or 18

P = 2(18 + 18)

P = 2(36)

P = 72

18. x = 8 and P = 80

We know that part of the whole of 26 is 18 because one side is congruent to 18.

to find the value of the other half, we simply subtract 18 from 26.

26 - 18 = 8

x is congruent to 8, therefore x = 8

The line segment 14 is congruent to the opposite segment of x, therefore making the value 14.

So then we have:

a = 8 + 14 or 22

b = 26

c = 18 + 14 or 32

P = a + b + c

P = 22 + 26 + 32

P = 80

19. x = 6 and P = 52

Now we have the case of x + 2 is congruent to 8.

x + 2 = 8

Combine like terms.

x = 8 - 2

x = 6

Now that we have the value of x, we can simply look for the value of the line segment attached to it.

4 is congruent to the line segment attached to x + 2, therefore the value is 4.

To find the perimeter we have to add all sides together.

P = (8+5)+(5+9)+(9+4)+(8+4)

P = 52

20. x = 5, y = 2, z =10, and P = 68

Let's take this one step at a time.

First we look for x.

2x + 2 = 3x - 3

Combine like terms.

2x - 3x = -3 - 2

-x = -5

Divide both sides by -1.

x = 5

Now let's get the value of y.

5y - 2 = 3y + 2

Combine like terms.

5y - 3y = 2 + 2

2y = 4

Divide both sides by 2.

y = 2

Now let's look for z.

34 - 2z = z + 4

Combine like terms.

-2z - z = 4 - 34

-3z = -30

Divide both sides by -3.

z = 10

Now that we have the values of x, y, and z. We can substitute them to find the values of our segments.

2x + 2

2(5) + 2 = 12

3x - 3

3(5)-3 = 12

5y - 2

5(2) - 2 = 8

3y + 2

3(2) + 2 = 8

z + 4

10 + 4 = 14

34 - 2z

34 - 2(10)

34 - 20 = 14

Now that we have our values let's look for our perimeter.

P = a + b + c

P = (12 + 8) + (12 + 14) + (14 + 8)

P = 20 + 26 + 22

P = 68

4 0

3 years ago

1.5 Determine the degree of the following algebraic expressions:

tatuchka [14]

By identifying the largest exponent in each expression, we see that the answers are:

a) D = 3.

b) D = 5.

c) D = 0.

<h3></h3><h3>How to determine the degree of an expression?</h3>

The degree is just the largest exponent of the variable in an expression.

First, we have:

a) √3xyz - 5

The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.

b) y² - 3y⁵ -y + 2y³ - 4

Here the largest exponent is on the second term, so we can see that the degree is 5.

c) -10³

Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:

-10³*x⁰

Where we use the fact that x⁰ = 1

If you want to learn more about degrees:

brainly.com/question/1600696

#SPJ1

6 0

2 years ago

A research team is testing a product that will minimize wrinkles among women. Volunteers in the age group of 40 to 45 are includ

artcher [175]

There are mistakes in the answer options attached. These are the correct ones.

a. The group that received the bottle of solution is the control group.

b. The group that received the bottle of solution that did not contain the ingredients that are meant to lessen wrinkles is the control group.

c. Both the groups are control groups.

d. Neither group is an control group.

Answer:

B. The group that received the bottle of solution that did not contain the ingredients that are meant to lessen wrinkles is the control group

Step-by-step explanation:

In an experiment of this type, the control group is the group that does not contain the treatment. So in this group The effect of the treatment unknown unlike the experimental group which gets the treatment that the researcher is trying to find it's effect.

I. Conclusion, the group that got bottles that did not contain Ingredients for wrinkles lessening is the control group.

4 0

3 years ago