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Vladimir79 [104]

2 years ago

6

An architect designs an archway by resting the two bases of an arch on the floor. the shape of the arch can be modeled by the gr

aph of the function f in the CY plane above. if f is defined by f(x)= -2x^2 +20 x where x is in feet what is the value of the distance d in feet between the two base of an arch? A. 2
B. 10
C. 20
D. 40

1 answer:

d1i1m1o1n [39]2 years ago

6 0

Answer: OPTION B.

Step-by-step explanation:

Given the function:

$f(x)= -2x^2 +20x$

You can rewrite it with $f(x)=y$ . Then:

$y= -2x^2 +20x$

Now, in order to solve for "x", you can follow this procedure:

1- Substitute $y=0$ into the function:

$0= -2x^2 +20x$

2- Factor the equation:

$0= -2x(x-10)$

Therefore, you get:

$x_1=0\\\\x_2=10$

This means that the distance between the two bases (in feet) of the arch is:

$d=10\ ft$

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Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two dist

Lera25 [3.4K]

Answer:

$Sum = -81$

Step-by-step explanation:

See the comment for complete question.

Given

$c = 36$ ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

$x^2 + ax + 36 = 0$

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

$x = -\alpha$ and $x = -\beta$

Using the above roots, the equation can be represented as:

$(x + \alpha)(x + \beta) = 0$

Open brackets

$x^2 + (\alpha + \beta)x + \alpha \beta = 0$

To compare the above equation to $x^2 + ax + 36 = 0$ , we have:

$a = \alpha + \beta$

$\alpha \beta = 36$

Where: $\alpha, \beta$ and $\alpha \ne \beta$

The values of $\alpha$ and $\beta$ that satisfy $\alpha \beta = 36$ are:

$\alpha = -1$ and $\beta = -36$

$\alpha = -2$ and $\beta = -18$

$\alpha = -3$ and $\beta = -12$

$\alpha = -4$ and $\beta = -9$

So, the possible values of a are:

$a = \alpha + \beta$

When $\alpha = -1$ and $\beta = -36$

$a = -1 - 36 = -37$

When $\alpha = -2$ and $\beta = -18$

$a = -2 - 18 = -20$

When $\alpha = -3$ and $\beta = -12$

$a = -3 - 12 = -15$

When $\alpha = -4$ and $\beta = -9$

$a = -4 - 9 = -13$

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

$Sum = -37 -20 -15 - 9$

$Sum = -81$

7 0

2 years ago

Two cars are on the same straight road. Car A moves east at 55 mph and sounds its horn at 625 Hz. Rank from highest to lowest th

Fantom [35]

Answer:

1. Car B is moving east at 70MPh and is in from of car A

2.car B is moving west at 70 mph and is behind car A

Step-by-step explanation:

Use the cardinal point system to evaluate the problem first

8 0

2 years ago

A marble is selected at random from a jar containing 3 red marbles, 4 yellow marbles, and 6 green marbles. What is the probabi

alexgriva [62]

Answer: a) $\dfrac{3}{13},\ b)\dfrac{9}{13}\ c)\dfrac{9}{13},\ d)\dfrac{4}{13}$

Step-by-step explanation:

Since we have given that

Number of red marbles = 3

Number of yellow marbles = 4

Number of green marbles = 6

Total number of marbles = 3 +4 +6 = 13

a) the marble is red?

Probability of getting a red marble = $\dfrac{3}{13}$

b) the marble is not yellow?

Probability of not getting yellow = $\dfrac{3+6}{13}=\dfrac{9}{13}$

c) the marble is either red or green?

Probability of getting either red or green = P(red) + P(green) = $\dfrac{3}{13}+\dfrac{6}{13}=\dfrac{9}{13}$

d) the marble is neither red nor green?

Probability of getting neither red nor green = P(getting yellow) = $\dfrac{4}{13}$

Hence, a) $\dfrac{3}{13},\ b)\dfrac{9}{13}\ c)\dfrac{9}{13},\ d)\dfrac{4}{13}$

5 0

2 years ago

You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing th

finlep [7]

The <u>correct answer</u> is:

9.2 ft.

Explanation:

The distance from a point (m,n) to a line Ax+By+C=0 is given by the formula:
$d=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}$

We first need to write our equation in the form Ax+By+C=0.
y=(-6/7)x+7

First we will add 6/7x to each side:
y+6/7x=(-6/7x)+7+(6/7x)
y+6/7x=7

Now we will subtract 7 from each side:
y+6/7x-7=7-7
y+6/7x-7=0

It will be easier to work with this equation if we do not have fractions. We can accomplish this by multiplying everything by the denominator of the fraction, 7:
y(7)+(6/7x)(7)-7(7)=0
7y+(42/7)x-49=0
7y+6x-49=0

Now we rearrange the terms to the x term is in front:
6x+7y-49=0

This is in the form Ax+By+C=0, where A=6, B=7 and C=-49.

Substituting these into our formula above along with our coordinates from our point (m,n)=(6, 14) we have:
$d=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}
\\
\\d=\frac{|6(6)+7(14)-49|}{\sqrt{6^2+7^2}}
\\
\\d=\frac{|36+98-49|}{\sqrt{36+49}}
\\
\\d=\frac{|85|}{\sqrt{85}}=\frac{85}{\sqrt{85}}=9.2
$

7 0

2 years ago

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Paul bakes 300 bread loaves. I don’t know the question you’re asking for the second question.

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2 years ago

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