Solve these equations. |x+8|=x+8

Can the sides of a triangle be in the given ratio? 3:4:5

RUDIKE [14]

Answer:

Yes

Step-by-step explanation:

In order to determine if a triple of values will form a triangle, we must apply the Triangle Inequality Theorem, which states that for a triangle with lengths a, b, and c:

a + b > c

a + c > b

b + c > a

Here, let's suppose that since the ratio of the sides is 3 : 4 : 5, then let the actual side lengths be 3x, 4x, and 5x, where x is simply a real value.

With loss of generality, set a = 3x, b = 4x, and c = 5x. Plug these into the Triangle Inequality to check:

a + b > c ⇒ 3x + 4x >? 5x ⇒ 7x > 5x ⇒ This is true

a + c > b ⇒ 3x + 5x >? 4x ⇒ 8x > 4x ⇒ This is also true

b + c > a ⇒ 4x + 5x >? 3x ⇒ 9x > 3x ⇒ This is true

Since all three conditions are satisfied, we know that a true triangle can be formed given that the ratio of their sides is 3 : 4 : 5.

<em>~ an aesthetics lover</em>

5 0

3 years ago

Read 2 more answers

Suppose you are testing the null hypothesis that a population mean is less than or equal to 46, against the alternative hypothes

PolarNik [594]

Answer:

Option A) 2.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 46

Sample mean, $\bar{x}$ = 50

Sample size, n = 25

Alpha, α = 0.05

Population standard deviation, σ = 8

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 46\\H_A: \mu > 46$

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{50 - 46}{\frac{8}{\sqrt{25}} } =2.5$

Option A) 2.5

6 0

4 years ago

Find the value of trigonometric ratio

Nana76 [90]

Answer:

We know that Sin,

$=\frac{perpendicular}{hypotenuse}$

$SinA=\frac{BC}{AC}$

$SinA=\frac{9}{41}$

<u>OAmalOHopeO</u>

7 0

3 years ago

2. Meryl spends a total of $68.82 for 2 pairs of 68.8

kupik [55]

Answer:

The cost of each pair of sneakers is $33.25.

Step-by-step explanation:

Consider the provided information.

Meryl spends a total $68.82 for 2 pairs of sneakers with the same cost.

If the sales tax is $5.32 and she also uses a coupon for $3.00 off her purchase.

First subtract the sales tax from the spend amount.

$\$68.82- \$5.32=\$63.5$

She use a coupon for $3.00 OFF.

$\$63.5+\$3=\$66.5$

$66.5 was the cost of 2 pairs of sneakers before using the coupon.

Now divide $66.5 by 2 so that we can find the cost of one pair of sneakers.

$\frac{\$66.5}{2} =\$33.25$

Hence, the cost of each pair of sneakers is $33.25.

5 0

3 years ago

Arnie skated 1 3/4 miles from home to the lake. He stated 1 1/3 miles around the lake and then skate it back home. How many mile

Flura [38]

Answer:

$4\frac{5}{6}=4.833$ miles.

Step-by-step explanation:

We have been given that Arnie skated 1 3/4 miles from home to the lake. He skated 1 1/3 miles around the lake and then skate it back home.

To find the total miles that Arnie skate in all we will add all distances covered by Arnie while skating.

$\text{The total number of miles skated by Arnie}=1\frac{3}{4} +1\frac{1}{3}+ 1\frac{3}{4}$

Upon converting our mixed fractions into improper fractions we will get,

$\text{The total number of miles skated by Arnie}=\frac{7}{4} +\frac{4}{3}+ \frac{7}{4}$

$\text{The total number of miles skated by Arnie}=\frac{14}{4} +\frac{4}{3}$

Now let us have a common denominator,

$\text{The total number of miles skated by Arnie}=\frac{3*14}{3*4} +\frac{4*4}{4*3}$

$\text{The total number of miles skated by Arnie}=\frac{42}{12} +\frac{16}{12}$

$\text{The total number of miles skated by Arnie}=\frac{42+16}{12}$

$\text{The total number of miles skated by Arnie}=\frac{58}{12}$

$\text{The total number of miles skated by Arnie}=4\frac{10}{12}$

$\text{The total number of miles skated by Arnie}=4\frac{5}{6}=4.833$

Therefore, Arnie skated $4\frac{5}{6}=4.833$ miles in all.

8 0

3 years ago