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3 years ago

A triangle has sides of lengths 9,7, and 12. Is it a right triangle? Explain.

1 answer:

8 0

Answer: No, it is not a right triangle.

Explanation:
9^2 + 7^2 (?) 12^2

81 + 49 (?) 144

130 = 144

Since 12^2 = 144, and the square root of 130 is 11.4^2, it is not a right triangle.

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Draw or write to explain why i hundred 4 ten and 14 tens name the same amount

butalik [34]

ten tens are one hundred and then they both have 4 tens or forty

8 0

3 years ago

Read 2 more answers

How many solutions does the equation |x + 6| − 4 = c have if c = 5? If c = −10? Complete the explanation

mixer [17]

Answer:

<h2>For c = 5 → two solutions</h2><h2>For c = -10 → no solutions</h2>

Step-by-step explanation:

We know

$|a|\geq0$

for any real value of a.

|a| = b > 0 - two solutions: a = b or a = -b

|a| = 0 - one solution: a = 0

|a| = b < 0 - no solution

|x + 6| - 4 = c

for c = 5:

|x + 6| - 4 = 5 add 4 to both sides

|x + 6| = 9 > 0 TWO SOLUTIONS

for c = -10

|x + 6| - 4 = -10 add 4 to both sides

|x + 6| = -6 < 0 NO SOLUTIONS

Calculate the solutions for c = 5:

|x + 6| = 9 ⇔ x + 6 = 9 or x + 6 = -9 subtract 6 from both sides

x = 3 or x = -15

5 0

3 years ago

The temperature at 12 am was 44 degrees. The temperature dropped steadily for the next 8 hours to reach the daytime low of 20 de

adelina 88 [10]

Answer:

62 degrees

Step-by-step explanation:

Points (12,440 and (20,20)

Slope = -3

Equation of line: y - 44 = -3(x - 12)

Plug in x = 6 to get y = 62.

6 0

3 years ago

Which is a factor of 144 - 49x²? O 12-7x² O 72-7x² O 12-7x O 72 + 7x

lisabon 2012 [21]

Answer: C: 12-7x

Step-by-step explanation:

This expression is a good example of the difference of two squares, as 144 is the square of 12, while 49x² is the square of 7x.

Any difference of two squares $a^2-b^2$ can be factored into the sum of their square roots times the difference of their square roots $(a+b)(a-b)$ .

Let's factor our expression.

$144-49x^2=(12+7x)(12-7x)$

Out of all the options given, only $12-7x$ is a factor. Hence, option C is correct.

4 0

2 years ago

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and

forsale [732]

Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

$\frac{x^2}{a^2}+\frac{y^2}{b^2}$

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

$a=\frac{38}{2}=19ft$

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

$\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}$

and we can simplify the equation, so we get:

$\frac{x^2}{361}+\frac{y^2}{144}$

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

$\frac{y^{2}}{144}=1-\frac{x^{2}}{361}$

$y^{2}=144(1-\frac{x^{2}}{361})$

we can add everything inside parenthesis so we get:

$y^{2}=144(\frac{361-x^{2}}{361})$

and take the square root on both sides, so we get:

$y=\sqrt{144(\frac{361-x^{2}}{361})}$

and we can simplify this so we get:

$y=\frac{12}{19}\sqrt{361-x^{2}}$

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

$y=\frac{12}{19}\sqrt{361-(8)^{2}}$

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

5 0

3 years ago