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2 years ago

Identify the vertex of the graph tell weather it is minimum or maximum

Mathematics

1 answer:

Contact [7]2 years ago

4 0

Vertex is (-2,-3) and it's a minimum.

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What are the solutions to the equation x² + 16x + 14 = 0?

poizon [28]

Answer:

-8+5√2 and -8-5√2

Step-by-step explanation:

Given the expression x² + 16x + 14 = 0

USing the general formulas

x = -16±√16²-4(14)/2

x = -16±√256-56/2

x = -16±√200/2

x = -16±10√2/2

x = -8±5√2

Hence the required solutions are -8+5√2 and -8-5√2

3 0

3 years ago

Solve the system of equations by substitution y = 2x + 1 and 3x + y = 16

Luden [163]

Answer: y=7,x=3

Steps:

y = 2x + 1

3x + y = 16

Substitute y = 2x + 1

3x + 2x + 1 = 16

Simplify

5x+1=16

Isolate x for 5x + 1 = 16: x = 3

For y = 2x + 1

Substitute x = 3

y = 2 · 3 + 1

Simplify

y = 7

The solutions to the system of equations are:

y = 7, x = 3

Hope This Helps!

6 0

2 years ago

A rectangular room is 11 feet by 18 feet. The ceilings are 10 feet high. If a gallon of paint covers 250 square feet. How many g

Bingel [31]

Answer:

2.32 gallons of paint

Step-by-step explanation:

First, find the area of all 4 sides of the room, with the equation A = lw

11(10)

= 110 (for 2 of the walls)

18(10)

= 180 (for the other 2 walls)

Add these up:

110 + 110 + 180 + 180

= 580

Then, divide this by 250:

580/250

= 2.32

So, 2.32 gallons of paint will be needed to paint the room.

5 0

3 years ago

The temperature is -3°F at 7:00 A.M. During the next 4 hours, the temperature increases 21°F. What is the temperature at 11:00 A

3241004551 [841]

Answer: 18°F

Step-by-step explanation: if you add 21 and -3 you get 18

4 0

3 years ago

A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am prepa

Crank

Answer:

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Step-by-step explanation:

Step(i):-

Given mean of the Population 'μ'= 25c.m

Given standard deviation of the Population 'σ' = 8c.m

Given sample size 'n' = 256

Let X₁ = 24

$Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2$

Let X₂ = 25

$Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0$

Step(ii):-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)

= P( Z≤0) - P(Z≤-2)

= 0.5 + A(0) - (0.5- A(-2))

= A(0) + A(2) ( ∵A(-2) =A(2)

= 0.000+ 0.4772

= 0.4772

Final answer:-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

4 0

3 years ago