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3 years ago

Complete the equation of the line through (3,-1) and (4,7) (use exact numbers) Y=

Mathematics

1 answer:

Artemon [7]3 years ago

7 0

The line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by

$\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}$

Plug your values to get

$\dfrac{x-3}{4-3}=\dfrac{y+1}{7+1} \iff \dfrac{x-3}{1}=\dfrac{y+1}{8}$

Multiply both sides by 8 to get

$8(x-3)=y+1 \iff y=8x-24-1=8x-25$

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a 9ft ladder is placed 4.5 feet from the base of a wall. How high up will the ladder reach? Round to the nearest hundredth.

spin [16.1K]

Answer:

$\huge\boxed{7.79 \ \text{feet}}$

Step-by-step explanation:

We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.

This can be represented as a triangle, where x is the unknown side.

| \

x | \ 9

| \

|_____\

4.5

We can use The Pythagorean Theorem to find the value of x. The theorem states that $a^2+b^2=c^2$ , where a and b are the lengths of the legs and c is the length of the hypotenuse.

However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.

$a^2 + 4.5^2 = 9^2\\\\a^2 + 20.25 = 81\\\\a^2 = 60.75\\\\a \approx 7.79$

Hope this helped!

7 0

3 years ago

Round the weight 89 grams nearest kilogram

tatiyna

89 gram= 8.9 decagram = 0.89 hectograms = 0.089 kilogram

3 0

3 years ago

The following recipe serves 6 people tell how much of each ingredient you need to serve nine people then tell how much of each i

Paladinen [302]

9=5 3/4 cups of flour, 10 T butter, 3 eggs, and 3 cups of cocoa 3=1 3/4 cups of flour, 3 1/3 T butter, and 2/3 cups of cocoa I am sorry if I did anything wrong. I tried.

4 0

3 years ago

Simplify the expression 4x+3(5y−x)

Ipatiy [6.2K]

4x+3(5y-x)
Start by multiplying out the brackets
4x+15y-3x
Collect like terms
4x-3x+15y
Subtract the x's
X+15y
Hope this helps!

5 0

3 years ago

Read 2 more answers

Suppose you were given a 95% confidence interval for the difference in two population means. What could you conclude about the p

Savatey [412]

Answer:

(a) The population means are not same.

(b) The population means are same.

Step-by-step explanation:

The hypothesis to test whether there is a significant difference between two population means is:

H₀: There is no difference between the two population means, i.e. μ₁ - μ₂ = 0.

Hₐ: There is no difference between the two population means, i.e. μ₁ - μ₂ ≠ 0.

The decision rule based on confidence interval for the difference between two population means is:

If the confidence interval consists the null value of the difference, i.e. 0 then the null hypothesis will be accepted or else it will be rejected.

(a)

It is provided that the confidence interval for the difference between two population means does not contains 0.

Since the null value of the difference is not contained in the interval, it can be concluded that the null hypothesis will be rejected.

Thus, the population means are not same.

(b)

It is provided that the confidence interval for the difference between two population means does contains 0.

Since the null value of the difference is contained in the interval, it can be concluded that the null hypothesis will not be rejected.

Thus, the population means are same.

6 0

3 years ago

Read 2 more answers