All categories

3 years ago

Write the vertex form of the equation of the parabola that has a vertex of (-6,-5) and passes through the point (-8,6)

Mathematics

1 answer:

Anastaziya [24]3 years ago

7 0

Answer:

Step-by-step explanation:

Find the parabola through ( − 8 , 6 ) with vertex ( − 6 , -5 ) .

Standard Form: y = − 11 /4x ²− 44 x − 170

Vertex Form: y = − 11 /4 ( x + 8 ) 2 + 6

Download docx

docx

You might be interested in

Solve the system by substitution -x-y-z= -8 -4x+4y+5z= 7 2x+2z= 4

Gennadij [26K]

- x - y - z = - 8 ------- (1)
- 4x + 4y + 5z = 7 -------- (2)
2x + 2z = 4 --------- (3)

From (3): x + z = 2
x = 2 - z --------- (4)

Substitute (4) into (1),
- x - y - z = - 8
- (2-z) - y - z = - 8
- 2 + z - y - z = -8
- 2 - y = - 8
2 + y = 8
Therefore, y = 6

Substitute y = 6 and (4) into (2),
- 4x + 4y + 5z = 7
- 4(2 - z) + 4(6) + 5z = 7
- 8 + 4z + 24 + 5z = 7
9z + 16 = 7
9z = - 9
Therefore, z = - 9

Substitute z = - 9 into (4),
x = 2 - z
x = 2 - (-9)
x = 2 + 9
Therefore x = 11

Solution:
x = 11
y = 6
z = -9

4 0

3 years ago

Read 2 more answers

Tickets for a school carnival cost 10$ for adult and 5 for children. last Saturday carnival sold 170 tickets worth a total of $1

riadik2000 [5.3K]

70 adults and 100 children attended the carnival.

Step-by-step explanation:

Given,

Cost of each adult ticket = $10

Cost of each child ticket = $5

Total tickets sold = 170

Total revenue generated = $1200

Let,

Number of adults = x

Number of children = y

According to given statement;

x+y=170 Eqn 1

10x+5y=1200 Eqn 2

Multiplying Eqn 1 by 10

$10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3$

Subtracting Eqn 2 from Eqn 3

$(10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500$

Dividing both sides by 5

$\frac{5y}{5}=\frac{500}{5}\\y=100$

Putting y=100 in Eqn 1

$x+100=170\\x=170-100\\x=70$

70 adults and 100 children attended the carnival.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

7 0

3 years ago

-7n - 15 ≥ 21? n ≥ -4 n ≥ 7.2 n ≤ -4 n ≤ 4

ollegr [7]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

$\diamond\large\textsf{\textbf{Question:-}}}}$

-7n-15≤21. find n

$\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}$

❖ Add 15 to both sides:-

-7n≤21+15

-7n≤36

❖ Now divide by -7 on both sides:-

n≥-5.14 or

n≥-5

The inequality sign changed because we divided both sides by a negative number.

- - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - -

7 0

2 years ago

What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8? an = 2(−8)n −

jonny [76]

Hello,

The question is
"What are the explicit equation and domain for a geometric sequence with a first term of 2 and a second term of −8?"

It is a geometric sequence =>U(2)=U(1)*r==>-8=2*r ==>r=-4

U(1)=2=2*(-4)^0
U(2)=-8=2*(-4)=2*(-4)^1
U(3)=32=-8*(-4)=2*(-4)(-4)=2*(-4)^2
U(4)=-128=32*(-4)=2*(-4)^3
...
U(n)=2*(-4)^(n-1) where n>=1.

Answer C

4 0

3 years ago

Simplify the radical expression.. square root of 128

Vaselesa [24]

Hello,

first we have to descompose the number:

128 | 2
64 | 2
32 | 2
16 | 2
8 | 2
4 | 2
2 | 2
1

So:
$128= 2x2x2x2x2x2x2 \\ 128=2^{6} *2$

Therefore:
$\sqrt{128}= \sqrt{2^{6} *2}$

You must know these properties:

$\sqrt{a*b} = \sqrt{a} * \sqrt{b}\\ \\ \sqrt[b]{x^a}= x^{ \frac{a}{b}}$

then:

$\sqrt{2^{6} *2} \\ =\sqrt{2^{6}}*\sqrt{2} \\ =2^{ \frac{6}{2}}*\sqrt{2} \\ =2^3*\sqrt{2} \\ \boxed{=8*\sqrt{2}}$

6 0

4 years ago