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2 years ago

Identify the x and y intercepts from the give equation: 5x – 2y = 10

Mathematics

1 answer:

Iteru [2.4K]2 years ago

3 0

Answer:

x-intercept : (2, 0)

y-intercept : (0, -5)

Step-by-step explanation:

The x-intercept is where y = 0, and the y-intercept is where x = 0. To find the intercepts, substitute a zero in for the other variable, and solve.

So the x-intercept of 5x – 2y = 10 is

5x – 2y = 10 → 5x – 2(0) = 10 → 5x = 10 →

x = 2 → (2, 0).

So the y-intercept of 5x – 2y = 10 is

5x – 2y = 10 → 5(0) – 2y = 10 → -2y = 10 →

y = -5 → (0, -5).

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Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.

Nezavi [6.7K]

Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4

2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4

<u>Step-by-step explanation:</u>

Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = x² - 12x + 34

$y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}$

*******************************************************************************************

2) x = y² + 2y - 1

$x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}$

4 0

3 years ago

In 2018, the number of students at The Villages High School was 975 and is increasing at a rate of 2.5% per year. Write and use

avanturin [10]

Answer:

$A(t)=975(1.025)^t$

In 2025,the number of students at the villages high school=1159

Step-by-step explanation:

We are given that in 2018

Number of students at the villages high school=975

Increasing rate,r=2.5%=0.025

We have to write and use of exponential growth function to project the populating in 2025.

$A_0=975,t=0$

According to question

Number of students at the villages high School is given by

$A(t)=A_0(1+r)^t$

Substitute the values

$A(t)=975(1+0.025)^t=975(1.025)^t$

t=7

Substitute the value

Then, the number of students at the villages high school in 2025

$A(7)=975(1.025)^7=1158.96\approx 1159$

8 0

2 years ago

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Brut [27]

Answer:

1 and 5 I think

Step-by-step explanation:

5 0

2 years ago

Simiplify without using absolute value bars, Solve for |x +7| for x>=7

Pavlova-9 [17]

9514 1404 393

Answer:

x +7

Step-by-step explanation:

The argument of the absolute value function is positive for any x > -7. The required domain is a subset of that, so the absolute value function does not change its argument.

|x+7| for x ≥ 7 is x +7

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2 years ago

A right prism has a rhombus as a base. the height of the prism is 6 inches and the volume is 144 cubic inches. which could be th

Alex

The answer is C 6in by 8 in.

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2 years ago

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