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3 years ago

HELP IM IN DESPERATE NEED!!! What is the solution to this system of equations?

Mathematics

1 answer:

Paladinen [302]3 years ago

6 0

[Given]

{ x + y = 6

{ x = y + 4

[Plug-in our x value & solve]

[Given] x + y = 6

[ Plug-in] (y + 4) + y = 6

[Distribute] y + 4 + y = 6

[Combine like terms] 2y + 4 = 6

[Subtract 4 from both sides] 2y = 2

[Divide both sides by 2] y = 1

[Answer]

Third option - (5, 1)

-> You do not need to solve for x since this is the only option that has y = 1, but to solve for x we would do y + 4 = 1 + 4 = 5, so this answer fully checks correctly

Have a nice day!

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Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maxi

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Answer:

A) g(x) has a greater absolute maximum.

Step-by-step explanation:

Given graph of g(x) which is a Parabola

1. Opens downwards

2. The absolute maximum (vertex) is at around (3.5, 6)

i.e. value of absolute maximum is 6.

Another function:

$f(x) =-x^{2}+4x-5$

Let us convert it to vertex form to find its vertex.

Taking - sign common:

$f(x) =-(x^{2}-4x+5)$

Now, let us try to make it a whole square,

Writing 5 as 4+1:

$f(x) =-(x^{2}-4x+4+1)\\\Rightarrow f(x) =-((x^{2}-2 \times 2\times x+2^2)+1)\\\Rightarrow f(x) =-((x-2)^{2}+1)\\\Rightarrow f(x) =-(x-2)^{2}-1$

Please refer to attached graph of f(x).

We know that, vertex form of a parabola is given as:

$f (x) = a(x - h)^2 + k$

Comparing the equations we get:

a = -1 (Negative value of a means the parabola opens downwards)

h = 2, k = -1

Vertex of f(x) is at (2, -1) i.e. value of absolute maximum is -1

and

Vertex of g(x) is at (3.5, 6)

i.e. value of absolute maximum is 6.

Hence, correct answer is:

A) g(x) has a greater absolute maximum.

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3 years ago

A man and his young child have a race. The child starts out 120 feet ahead of the man. For every 5-foot stride of the man, the c

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Answer:

25.92 foot strides

Step-by-step explanation:

The man will take 120/5 = 24 five foot stride to cover the initial 120 foot advantage of the child.

Within this time, the child would have covered an additional 24/5 x 2 = 9.6 extra foot stride.

Within this 9.6 food stride of the child, the man will have to take an additional 9.6/5= 1.96 strides.

Total foot stride by the man will be 24 + 1.96 = 25.92 foot strides.

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4 years ago

What is 9×9+8-8÷10 Please And Thank You

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Order of operations

PEMDAS

There are no parenthesis

There are no exponents

Now, we do multiplication and division from left to right

(9x9) + 8 - (8/10)

81 + 8 - 0.8

Now, we do addition and subtraction from left to right

(81 + 8) - 0.8

89 - 0.8

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Answer:

Step-by-step explanation:

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Lucy fills a bathroom sink with water. Is the amount of water more than 1 liter, about 1 liter or less than 1 liter? Explain how

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Proposed Answer
Much more than 1 liter.

Make a guess.
Suppose the bathroom sink is about 15 inches across. That's actually not very big for a bathroom sink. But it makes up for the other estimate I'm going to make.

Suppose the sink is 7 1/2 inches deep at it's deepest point. So what you have is a 1/2 sphere. Figure this out in ccs. That way you have a simple conversion to make.

Conversion
1 in = 2.54 cm
7 1/2 in = x Cross multiply

x * 1 inch= 7 1/2 * 2.54
x = 6.5 * 2.54
x = 19.05 cm

x is actually the radius of the 1/2 sphere.
pi = 3.14
r = x = 19.05 cm

V = (4/3) pi * 19.05^3 / 2
V = 86831 / 6
V = 14471 ccs

1 L = 1000 cc
x = 14471 cc

x = 14.471 Liters. That's 14.5 times bigger than 1 Liter. Most sinks are about 7 1/2 inches deep but they are more across than 15 inches. So my answer is much more than 1 Liter. <<<<< Answer

Answer much more than a liter.

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