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swat32
3 years ago
6

The width of a rectangle is the length minus 3 units. The area of the rectangle is 10

Mathematics
1 answer:
sergeinik [125]3 years ago
3 0

Answer:

w=2

Step-by-step explanation:

A=length times width (A=lw)

w= l-3

A=10

Substituting in, we get:

10= l(l-3)

Now, solve the equation.

10= l^{2}-3l

l^{2}-3l-10=0

(l+2) (l-5)=0 (factoring the equation)

Therefore, l= -2 or 5

Throw out the negative value because a length of rectangle will never be negative.

Now let's solve for width

Remember w=l-3

therefore

(5)-3=2

so, w=2

(honestly, this is easier to just do in your head. But here is the long form math if you happen to run into more complicated problems.)

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As you are walking down a path, you see a sign telling the path has a 2% grade (ie., a rise of 2 metres for a horizontal change
Leni [432]

Answer:

Option (A)

Step-by-step explanation:

It has been given in this question that sign telling path has a 2% grade.

2% grade means a rise of 2 meters for a horizontal change of 100 m (As given in the figure attached).

All the trigonometric ratios for the angle θ between the path and the horizontal are,

Sinθ = \frac{\text{Opposite side}}{\text{Hypotenuse}}

Cosθ = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

tanθ = \frac{\text{Opposite side}}{\text{Adjacent side}}

Since measures of the opposite side and adjacent sides are given

Therefore, tangent ratio will be applied to get the measure of the angle,

tanθ = \frac{2}{100}

θ = \text{tan}^{-1}(\frac{2}{100})

Option (A) will be the answer.

5 0
3 years ago
Find the missing side or angle.<br> Round to the nearest tenth.<br> C=5<br> b=4<br> a=2<br> B=[ ? ]°
Ipatiy [6.2K]

Answer:

for this one b=49.458

Step-by-step explanation:

8 0
3 years ago
Oliver plans to purchase a $1500 certificate of deposit (cd) at his bank. The CD will earn 2.3% interest, compounded semi-annual
vekshin1

Answer:

Step-by-step explanation:

Weren't there more instructions?  Please, share everything about each problem you post here.

Use the compound amount formula:  A = P(1 + r/n)^(nt).

Here we have

A = $1500(1 + 0.023/2)^(2t), where t is the number of years.

3 0
3 years ago
Factor and find the zeros. z^2-z+56
Inessa [10]

Answer:

Sry its long but if your to lazy to look thru it here is the answer=   z = {-7, 8}

Step-by-step explanation:

Simplifying

z2 + -1z + -56 = 0

Reorder the terms:

-56 + -1z + z2 = 0

Solving:

-56 + -1z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.

(-7 + -1z)(8 + -1z) = 0

Subproblem 1

Set the factor '(-7 + -1z)' equal to zero and attempt to solve:

Simplifying:

-7 + -1z = 0

Solving:

-7 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1z = 0 + 7

-1z = 0 + 7

Combine like terms: 0 + 7 = 7

-1z = 7

Divide each side by '-1'.

z = -7

Simplifying:

z = -7

Subproblem 2

Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying:

8 + -1z = 0

Solving:

8 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0

0 + -1z = 0 + -8

-1z = 0 + -8

Combine like terms: 0 + -8 = -8

-1z = -8

Divide each side by '-1'.

z = 8

Simplifying:

z = 8

Solution

z = {-7, 8}

4 0
3 years ago
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Pavlova-9 [17]

Answer:

Approximately Normal, with a mean of 950 and a standard error of 158.11

Step-by-step explanation:

To solve this question, we need to understand the Central Limit Theorem.

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error s = \frac{\sigma}{\sqrt{n}}.

In this problem, we have that:

\mu = 950, \sigma = 1000

The sampling distribution of the sample mean amount of money in a savings account is

By the Central Limit Theorem, approximately normal with mean \mu = 950 and standard error s = \frac{1000}{\sqrt{40}} = 158.11

So the correct answer is:

Approximately Normal, with a mean of 950 and a standard error of 158.11

8 0
3 years ago
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