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Ronch [10]
3 years ago
15

Which table contains points that lie on a line with a slope of −2?

Mathematics
2 answers:
o-na [289]3 years ago
7 0
C, or the top right table. I don’t exactly feel like explaining unless you really want me to... in that case lmk.
Nutka1998 [239]3 years ago
6 0
The one on the top right, if you do delta y over delta x it gives you -2 for the slope
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In right ABC, AN is the altitude to the hypotenuse. FindBN, AN, and AC,if AB =2 5 in, and NC= 1 in.
Rama09 [41]

From the statement of the problem, we have:

• a right triangle △ABC,

,

• the altitude to the hypotenuse is denoted AN,

,

• AB = 2√5 in,

,

• NC = 1 in.

Using the data above, we draw the following diagram:

We must compute BN, AN and AC.

To solve this problem, we will use Pitagoras Theorem, which states that:

h^2=a^2+b^2\text{.}

Where h is the hypotenuse, a and b the sides of a right triangle.

(I) From the picture, we see that we have two sub right triangles:

1) △ANC with sides:

• h = AC,

,

• a = ,NC = 1,,

,

• b = NA.

2) △ANB with sides:

• h = ,AB = 2√5,,

,

• a = BN,

,

• b = NA,

Replacing the data of the triangles in Pitagoras, Theorem, we get the following equations:

\begin{cases}AC^2=1^2+NA^2, \\ (2\sqrt[]{5})^2=BN^2+NA^2\text{.}\end{cases}\Rightarrow\begin{cases}NA^2=AC^2-1, \\ NA^2=20-BN^2\text{.}\end{cases}

Equalling the last two equations, we have:

\begin{gathered} AC^2-1=20-BN^2.^{} \\ AC^2=21-BN^2\text{.} \end{gathered}

(II) To find the values of AC and BN we need another equation. We find that equation applying the Pigatoras Theorem to the sides of the bigger right triangle:

3) △ABC has sides:

• h = BC = ,BN + 1,,

,

• a = AC,

,

• b = ,AB = 2√5,,

Replacing these data in Pitagoras Theorem, we have:

\begin{gathered} \mleft(BN+1\mright)^2=(2\sqrt[]{5})^2+AC^2 \\ (BN+1)^2=20+AC^2, \\ AC^2=(BN+1)^2-20. \end{gathered}

Equalling the last equation to the one from (I), we have:

\begin{gathered} 21-BN^2=(BN+1)^2-20, \\ 21-BN^2=BN^2+2BN+1-20 \\ 2BN^2+2BN-40=0, \\ BN^2+BN-20=0. \end{gathered}

(III) Solving for BN the last quadratic equation, we get two values:

\begin{gathered} BN=4, \\ BN=-5. \end{gathered}

Because BN is a length, we must discard the negative value. So we have:

BN=4.

Replacing this value in the equation for AC, we get:

\begin{gathered} AC^2=21-4^2, \\ AC^2=5, \\ AC=\sqrt[]{5}. \end{gathered}

Finally, replacing the value of AC in the equation of NA, we get:

\begin{gathered} NA^2=(\sqrt[]{5})^2-1, \\ NA^2=5-1, \\ NA=\sqrt[]{4}, \\ AN=NA=2. \end{gathered}

Answers

The lengths of the sides are:

• BN = 4 in,

,

• AN = 2 in,

,

• AC = √5 in.

7 0
1 year ago
What is the answer to 18 - 3w = 4w
adelina 88 [10]

Answer:

Step-by-step explanation:

18 - 3w = 4w

Let's get all of the terms with the w on the right-hand side of the equation, and everything else on the left-hand side of the equation.

To do this, we should add 3w to both sides of the equation to remove the -3w from the left-hand side of the equation:

18 - 3w + 3w = 4w + 3w

18 = 7w

Finally, to get the w by itself, we can divide both sides by 7:

\frac{18}{7} = \frac{7w}{7}

w = \frac{18}{7}

4 0
3 years ago
Football team had scores of 23, 15, 11, 29, and 17 in the last five games the team played. Which score is NOT a prime number?
exis [7]

Answer:

15

Step-by-step explanation:

15 is 5 * 3 so is not prime.

3 0
3 years ago
Read 2 more answers
Solve 3x2 − x = 10
Crazy boy [7]
Option number 2 I think.
3 0
3 years ago
What is 10x10, please help xd
Juliette [100K]

Answer:

100 lol

Step-by-step explanation:

ty for the points! <3

7 0
2 years ago
Read 2 more answers
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