Ruth decides to test the method of proportions and similar

Solve for x.<br> −x+8=−9<br> Enter your answer as a number, like this: 42

Ymorist [56]

Answer:

x=17

Hope it helps;)

Step-by-step explanation:

Subtract 8 from both sides of the equation

-x+8=9

-x+8-8=9-8

Simplify

Subtract the numbers

x= -17

Divide both sides of the equation by the same term

x= 17

-x/-1= -17/-1

Simplify

Cancel terms that are both in the numerator and denominator

Divide the numbers

x = 17

8 0

3 years ago

In studying the insurance preferences of homeowners the following conclusions are made: A homeowner is three times as likely to

Ede4ka [16]

Answer:

0.632

Step-by-step explanation:

Given that a homeowner is three times as likely to purchase additional jewelry coverage as additional electronics coverage

If probability of purchasing additional electronics coverage = p, then prob of purchasing jewelry coverage = 3p

The two events are independent hence joint probability is product of these two.

i.e. P(both) = $p(3p) =3p^2$

This is given as 0.2

$3p^2 =0.2\\p = 0.258$

the probability that a homeowner purchases exactly one coverage.

$=P(AUB)-P(A \bigcap B)$

= Prob he purchases I + prob he purchases II-2(prob he purchases both)

$= 0.258+3(0.258)-2(0.2)\\=0.632$

5 0

3 years ago

A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th

Nina [5.8K]

Answer:

The length of the diagonal = 3.6 feet

Step-by-step explanation:

* Lets change the story problem to equation to solve it

- Diagonal in a rectangle is the line which joining two

opposite vertices in it

- The diagonal , the length and the width formed together right

angle triangle where the diagonal is the hypotenuse of the

triangle and the length, the width are the two legs of the

right angle

- The length of the diagonal d is √(l² + w²) ⇒ Pythagoras theorem

∴ d² = l² + w²

- The diagonal is 2 feet more than the width

∴ d = w + 2

- The length is twice the width

∴ l = w

* Lets substitute the value of d and l in the equation of Pythagoras

∴ (w + 2)² = (2w)² + w² ⇒ solve the bracket

∴ w² + 4w + 4 = 4w² + w² ⇒ collect them in one side and add like term

∴ 4w² + w² - w² - 4w - 4 = 0 ⇒ add the like term

∴ 4w² - 4w - 4 = 0 ⇒ divide all term by 4

∴ w² - w - 1 = 0 ⇒ solve the quadratic using the formula

- In ax² + bx + c = 0

$x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

∵ a = 1 , b = -1 , c = -1

∴ $x=\frac{-(-1)+\sqrt{(-1)^{2}-4(1)(-1)}}{2(1)}=\frac{1+\sqrt{5}}{2}=1.6feet$

-The value of the width is 1.6 feet

∴ The length = 1.6 × 2 = 3.2 feet

∴ The length of the diagonal = 2 + 1.6 = 3.6 feet

8 0

4 years ago

Carpet is installed in the hallways of a building. The cost of carpet and installation is $32.50 per square yard. A total length

Aloiza [94]

Answer:

$Total = \$7800$

Step-by-step explanation:

Given

$Cost = \$32.50$ per square yard

$Length = 432.0ft$

$Width = 5.0ft$

Required

Determine the cost of carpet and installation

First, calculate the area of the carpet

$Area = Length * Width$

$Area = 432.0ft * 5.0ft$

$Area = 2160ft^2$

Convert to square yard

$Area = \frac{2160yd^2}{9}$

$Area = 240yd^2$

The cost is then calculated as:

$Total= Area * Unit\ Cost$

$Total = 240 * \$32.50$

$Total = \$7800$

6 0

3 years ago

A cook has 4 cups of raisins to make oatmeal cookies. The recipe requires 3 cup of raisins for each

Ierofanga [76]

Answer: 1⅓ batch of cookies

Step-by-step explanation:

From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.

Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:

= 4/3

= 1⅓ batch of cookies

7 0

3 years ago