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3 years ago

Which equation has a graph that is a parabola with a vertex at (5,3)?

Mathematics

1 answer:

lara [203]3 years ago

6 0

Answer:

y = (x -5)² + 3.

Step-by-step explanation:

Given : parabola with a vertex at (5,3).

To find : Which equation has a graph that is a parabola.

Solution : We have given vertex at (5,3).

Vertex form of parabola : y = (x -h)² + k .

Where, (h ,k ) vertex .

Plug h = 5 , k= 3 in vertex form of parabola.

Equation :y = (x -5)² + 3.

Therefore, y = (x -5)² + 3.

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If 2x – 10y = -1 and 5x + 6y = 4 are true equations, what would be the value<br> of 7x - 4y?

Zigmanuir [339]

Answer:

Step-by-step explanation:

If the equations are true, they can be solved simultaneously.

Consider 2x-10y=-1 as Eq1 and 5x+6y=4 as Eq2

Multiplying Eq1 with 3 and Eq2 with 5 we get,

6x-30y=-3 -- Eq3 and 25x+30y=20 -- Eq4

Adding Eq3 and Eq4,

31x=17 Therefore, x=17/31

Plugin x=17/31 in Eq3,

6(17/31)-30y=-3 --- y=13/62

Plug In values of x and y in 7x-4y we get,

7(17/31)-4(13/62) = 3

So the value of 7x-4y = 3.

8 0

2 years ago

I need help i dot get it.

gayaneshka [121]

Answer:

the answer is about 8 cuz the answer shows 7.12 if you divide mentally

6 0

2 years ago

Read 2 more answers

A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential gr

Rufina [12.5K]

The answer is 138 million.

Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.

We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time

Step 1:
A = 120 million = 120 000 000
P = 114 million = 114 000 000
n = ?
x = 1997 - 1991 = 6
Therefore:
$120 000 000 = 114 000 000 * e ^{n*6} \\ e ^{n*6} =120 000 000 /114000000 \\ e ^{n*6} =1.05 \\$
Logarithm both sides of the equation:
$ln(e ^{n*6})=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = \frac{ln(1.05)}{6} \\ n = \frac{0.05}{6} \\ n = 0.0083$

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2014
A = ?
P = 120 000 000
n = 0.0083
t = 2014 - 1997 = 17
$A = 120 000 000 * e ^{0.0083*17} \\ 
A = 120 000 000 * e^{0.1411} \\ 
A = 120 000 000 * 1.15 \\ 
A = 138 000 000
$
Thus, the population will be 138 million in 2014

8 0

3 years ago

The heights of men in the United States are approximately normally distributed with mean 69.1 inches and standard deviation 2.9

Gre4nikov [31]

Answer:

Step-by-step explanation:

Let M be the heights of men in the United States and W be the heights of women in the United States

Given that M is N(69.1, 2.9) and W (63.7, 2.7)

For a husband and wife we have average height as

$\frac{x+y}{2}$ =Z (say)

$Mean =E(z) = \frac{1}{2} [E(M)+E(W)] = 66.4 inches$

Var (Z) = $Var (\frac{x+y}{2} )=\frac{1}{4}[Var(x)+ Var(y)+2 cov (x,y)]\\$

= $0.25[2.9^2+2.7^2+2*r*sx*sy]\\= 0.25(20.398)\\=5.0995$

Mean = 66.4" and std dev = 2.258

7 0

3 years ago

Jane uses 42 cups of dog food each week to feed her dog. Which number sentence should be used to find N the number of cups Jane

Natali5045456 [20]

Answer:

C) 42/7 = n

Step-by-step explanation:

A week is 7 days, so, to figure out how many cups of dog food she gives her dog daily, we would need to do her weekly amount, 42, divided by 7, the amount of days in a week :)

6 0

2 years ago