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kompoz [17]
2 years ago
11

(-2,6) and (1,-1) whats the slope

Mathematics
2 answers:
Luda [366]2 years ago
7 0

Answer:

7/-3

Step-by-step explanation:

6--1=7

-2-1=-3

Effectus [21]2 years ago
7 0

Answer:

The slope is m=-7/3

m=y²-y¹/x²-x¹

m=(-1)-6/1-(-2)

m=-7/3

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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
Integral of sqrt(36+x^2)dx
AnnZ [28]
<span>Integral of sqrt(36 + x^2)dx = 1/2sqrt(36 + x^2)x + 18sinh^1 (x/6) + c </span>
4 0
2 years ago
Read 2 more answers
Can someone help me find out this question :) ? thanks &lt;3 for 8th grade algebra
Assoli18 [71]

Answer:

4,500,000 population in 1950

Step-by-step explanation:

the equation is 4p + 1,000,000 = 19,800,000

3 0
2 years ago
The Z-score is based on the concept of the normal distribution, the fact that we can expect 95% of the values in the distributio
Dennis_Churaev [7]

Answer:

C.) In perfect health.

Step-by-step explanation:

Given an average weight of 15kg and a standard deviation of 3kg for children of 4 years. Since the weight is based on a normal Z - distribution of 95% which is mean ± 2(standard deviations)

Mean weight interval is :

15 - 2(3) ; 15 + 2(3)

(9 ; 21) ; this weight interval could be interpreted to mean the normal or perfect weight value.

Therefore, given that the child weighs 12kg

Since, 12 kg falls within in the interval, we can conclude that the child is in perfect health.

7 0
2 years ago
What is the solution to the equation<br><br>1+1
sveta [45]

Answer:

2

Step-by-step explanation:

but I would personally say FISH

8 0
3 years ago
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