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3 years ago

Write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

1 answer:

7 0

Question 1:

--------------------------------------------------------------------
Find Slope
--------------------------------------------------------------------
Equation: y = 5x - 2
Slope = 5
Slope of parallel line = 5

--------------------------------------------------------------------
Insert slope into the general equation y = mx + c
--------------------------------------------------------------------
y = 5x + c

--------------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------------
At point (2, -1)
y = 5x + c
-1 = 5(2) + c
c = -1 - 10
c = -11

--------------------------------------------------------------------
Insert y-intercept into the equation
--------------------------------------------------------------------
y = 5x + c
y = 5x - 11

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Answer: y = 5x - 11
--------------------------------------------------------------------

Question 2:

--------------------------------------------------------------------
Find Slope
--------------------------------------------------------------------
y = 9x
Slope = 9
Slope of the parallel line = 9

--------------------------------------------------------------------
Insert slope into the equation y = mx + c
--------------------------------------------------------------------
y = 9x + c

--------------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------------
y = 9x + c
At point (0, 5)
5 = 9(0) + c
c = 5

--------------------------------------------------------------------
Insert y-intercept into the equation
--------------------------------------------------------------------
y = 9x + c
y = 9x + 5

--------------------------------------------------------------------
Answer: y = 9x + 5
--------------------------------------------------------------------

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Step-by-step explanation:

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3 years ago

Complete the proof given below.

allochka39001 [22]

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS

Reasons:

The completed two column proof is presented as follows;

Statement ${}$ Reason

1. ABCD is a parallelogram ${}$ 1. Given

2. $\overline{AB}$ ≅ $\overline{DC}$ and $\overline{BC}$ ≅ $\overline{DA}$ ${}$ 2. Opposite sides of a parallelogram

3. $\overline{AC}$ ≅ $\overline{CA}$ ${}$ 3. Reflexive property of congruency

4. ΔABC ≅ ΔCDA ${}$ 4. SSS

The correct options are therefore;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

brainly.com/question/4218263

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8 0

2 years ago

A scientist had 3 1/2 liters of vinegar. He poured 2/3 of the vinegar into beaker. He then used 3/5 of the vinegar in the beaker

valentinak56 [21]

Answer:

A)2100 ml

Step-by-step explanation:

Given total vinegar is 3 1/2 liters and the used vinegar is 3/5 of the vinegar in the beaker:

#First calculate the amount of vinegar not poured in the beaker:

$V_o=V_t-V_b\\\\=3\frac{1}{2}(1-\frac{2}{3})\\\\=1\frac{1}{6}$

#Calculate amount of vinegar used in experiment:

$V_b=\frac{2}{3}V_t=\frac{2}{3}(3\frac{1}{2})=2\frac{1}{3}\\\\V_u=\frac{3}{5}V_b=\frac{3}{5}\times 2\frac{1}{3}=1\frac{2}{5}$

#The unused vinegar is therefore calculated by subtracting the used vinegar from the total at the start of the experiment:

$V_r=V_t-V_u\\\\=3\frac{1}{2}-1\frac{2}5}\\\\=2\frac{1}{10}\times 1000\ ml\\\\=2100\ ml$

Hence, the unused vinegar is 2100 ml

8 0

3 years ago

Simplify the expression (2x − 9)(x + 6)

kenny6666 [7]

Answer:

Simplified form of given expression (2x – 9 )( x + 6 ) is $2 \mathrm{x}^{2}+3 \mathrm{x}-54$

Solution:

We need to simplify following expression.

(2x – 9) ( x + 6)

For sake of simplicity lets first assume 2x – 9 = A

So expression becomes A(x+6)

= Ax + A6

Now replace A by 2x – 9

= (2x – 9 ) x + (2x – 9 ) 6

$=2 \mathrm{x}^{2}-9 \mathrm{x}+12 \mathrm{x}-54$

On simplification, we get

$=2 \mathrm{x}^{2}+3 \mathrm{x}-54$

Hence simplified form of given expression (2x – 9 )( x + 6 ) is $= 2 \mathrm{x}^{2}+3 \mathrm{x}-54$

7 0

3 years ago