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3 years ago

Which lines are parallel if m4 = m5? Justify your answer.

Mathematics

1 answer:

Andre45 [30]3 years ago

4 0

Ok to start with the answer,
Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4.
That means angle 1 = angle 5 as well. 

When a line intersects two parallel lines, the corresponding angles are equal. That is, if r and s are parallel, then the angles formed when l intersects r are the same s the angles formed when l intersects s.
Angle
1 = Angle 5,
Angle 2 = Angle 6, and so forth.
Since we know
angle 1 = angle 5,
we can conclude that r and s are parallel.

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Given y+6=10(x-9) What is the point used to write the equation?

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Answer:

Point (9, -6)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate
y₁ - y coordinate
m - slope

Step-by-step explanation:

Step 1: Define

y + 6 = 10(x - 9)

Step 2: Break Function

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Slope m = 10

Point (9, -6)

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3 years ago

A family member had some five-dollar bills and one-dollar bills in her wallet. Altogether she has 18 bills and s total of $62. W

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3 years ago

The coordinates of the endpoint of QS are Q(-9,8) and S(9,-4). Point R is on cue as such that QR:RS Is in the ratio 1:2. What ar

marishachu [46]

R(–3, 4)

Step-by-step explanation:

Let Q(-9,8) and S(9,-4) be the given points and let R(x, y) divides QS in the ratio 1:2.

By section formula,

$R(x, y)=R\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)$

Here, $x_{1}=-9, y_{1}=8, \text { and } x_{2}=9, y_{2}=-4 \text { and } m=1, n=2$

Substituting this in the section formula

$R(x, y)=R\left(\frac{1(9)+2(-9)}{1+2}, \frac{1(-4)+2(8)}{1+2}\right)$

To simplifying the expression, we get

$\Rightarrow R(x, y)=R\left(\frac{9-18}{3}, \frac{-4+16}{3}\right)$

$\Rightarrow R(x, y)=R\left(\frac{-9}{3}, \frac{12}{3}\right)$

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3 years ago

Suppose $1750 is put into an account that pays an annual rate of 4.5%

Yanka [14]

Answer:

The amount in the account after six years is $2,288.98

Step-by-step explanation:

In this question, we are asked to calculate the amount that will be in an account that has a principal that is compounded quarterly.

To calculate this amount, we use the formula below

A = P(1+r/n)^nt

Where P is the amount deposited which is $1,750

r is the rate which is 4.5% = 4.5/100 = 0.045

t is the number of years which is 6 years

n is the number of times per year, the interest is compounded which is 4(quarterly means every 3 months)

we plug these values into the equation

A = 1750( 1 + 0.045/4)^(4 * 6)

A = 1750( 1 + 0.01125)^24

A = 1750( 1.01125)^24

A = 2,288.98

The amount in the account after 6 years is $2,288.98

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3 years ago