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3 years ago

13

Andre withdrew spending money from his checking account that initially had $982. What was the amount of his withdrawal, w, if hi

s ending balance was $922.

1 answer:

Angelina_Jolie [31]3 years ago

3 0

Answer:

$60.00

Step-by-step explanation:

you subtract the original number with the new number to see the difference.

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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

Cameron is an electrician she charges and and initial fee of 32 plus 33 per hour if Cameron are 195 on the job how long did the

Svet_ta [14]

195 - 32 = 163

163 / 33 = 4.9 hr

8 0

3 years ago

Which of the following parabolas opens upward and appears narrower than y = −3x^2 + 2x − 1? A. y = 4x^2 − 2x − 1 B. y = −4x^2 +

Kamila [148]

Narrowing it down it's either a or c because the other 2 choices open downward (negative a).
Graphing the 2 parabolas choice c is narrower.
c

7 0

3 years ago

Help? with complete solution please help me please

serious [3.7K]

9514 1404 393

Answer:

13 ft
(a) 1 second; (b) t = 0, t = 1/2

Step-by-step explanation:

<h3>1. </h3>

Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...

5² +(w -1)² = w²

w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms

26 = 2w . . . . . . . . . . . . add 2w

13 = w . . . . . . . . . . . . divide by 2

The length of the wire is 13 feet.

__

<h3>2. </h3>

(a) When h = 0, the equation is ...

0 = -16t^2 +8t +8

Dividing by -8 puts this into standard form:

2t^2 -t -1 = 0

Factoring, we get ...

(2t +1)(t -1) = 0

The positive value of t that makes a factor zero is t = 1.

It will take 1 second for the gymnast to reach the ground.

__

(b) When h = 8, the equation is ...

8 = -16t^2 +8t +8

Subtract 8 and divide by 8 to get ...

0 = -2t^2 +t

0 = t(1 -2t) . . . . factor out t

Values of t that make the factors zero are ...

t = 0

t = 1/2

The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.

8 0

2 years ago

-5 ( p + 3/5) = -4 <br><br> topic is solving 2 step equations

lesya692 [45]

Answer:

1/5

Step-by-step explanation:

5 0

3 years ago