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madam
4 days ago
8

What is the equation of the line graphed below?

Mathematics
2 answers:
Inessa [8.9K]4 days ago
8 0
1/2x + y = 3

Rearrange the equation to achieve the slope-intercept form. (y=mx+b)

1/2x + y = 3

Eliminate 1/2x from both sides.

y = -1/2x + 3

The y-intercept (where the line intersects the y-axis) is three, and the slope (the change in y over the change in x) is -1/2.

Hope this helps!
AnnZ [9K]4 days ago
3 0

Response: A. \dfrac{1}{2}x+y=3

Here’s a detailed explanation:

To determine the equation of a line that traverses two coordinates (a,b) and (c,d), the following formula is used:-

(y-b)=\dfrac{d-b}{c-a}(x-a)

Thus, the equation of a line crossing through the points (0,3) and (6,0) is given by:-

(y-3)=\dfrac{0-3}{6-0}(x-0)\\\\\Rightarrow\ y-3=\dfrac{-1}{2}x\\\\\Rightarrow\ \dfrac{1}{2}x+y=3

Consequently, the equation depicted in the image provided is:-

\dfrac{1}{2}x+y=3

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Monica reads 7 1/2 pages of a mystery book in 9 minutes. What is her average rate in pages per minute
PIT_PIT [9101]

The answer is found by dividing the total pages by the total time in minutes.

Calculating 7.5 divided by 9 equals approximately 0.8333, so Monica reads around 0.83 pages each minute on average.

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1 month ago
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A hot air balloon descends to the ground. The function a(t) = 210 – 15t can be used to describe the altitude of the balloon as i
Inessa [8989]
When the balloon touches the ground, a(t) will equal zero.

To calculate the time it takes to reach the ground, the equation can be set up as follows:

210 - 15t = 0
Solving this yields t = 210/15, equating to 14 minutes.
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1 day ago
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Find a line that lies entirely in the set defined by the equation x2 + y2 − z2 = 1.
zzz [9066]

Response:

x=1\,,\,y=t\,,\,z=t

Step-by-step explanation:

A line is defined as a one-dimensional entity that lacks thickness and stretches infinitely in both directions.

A line segment contains two endpoints, while a ray consists of a single endpoint.

The equation given is x^2+y^2-z^2=1.

Objective: to identify a line completely within the set designated by this equation.

Solution:

Consider x=1\,,\,y=t\,,\,z=t.

Verification:

L.H.S=1^2+t^2-t^2=1+0=1=R.H.S.

Thus, x=1\,,\,y=t\,,\,z=t fulfills the criteria of the given equation.

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24 days ago
Which expression is equivalent to 15a^8b^4/5a^4b
AnnZ [9071]

Response: The provided expression \frac{15a^8b^4}{5a^4b} has been simplified to 3a^4b^3

Detailed explanation:

Given: expression \frac{15a^8b^4}{5a^4b}

Our task is to simplify the given expression \frac{15a^8b^4}{5a^4b}

Let’s examine the given expression \frac{15a^8b^4}{5a^4b}

We divide the numbers \frac{15}{5}=3

=\frac{3a^8b^4}{a^4b}

Using the exponent rule, \frac{x^a}{x^b}\:=\:x^{a-b}

We get,

\frac{a^8}{a^4}=a^{8-4}=a^4

=\frac{3a^4b^4}{b}

Cancel the common factor b,

Thus, we have

=3a^4b^3

Therefore, the simplified version of the given expression \frac{15a^8b^4}{5a^4b} is 3a^4b^3

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The time it takes a printer to print a job is an Exponential random variable with the expectation of 12 seconds. You send a job
Leona [9260]

Answer:

0.8753

Step-by-step explanation:

Determine the likelihood that your job will complete before 10:01 am.

In this scenario, the expected value of an Exponential distribution is E(X)=12.

To find the probability for the third job, we apply the Poisson Distribution with a parameter of 1/λ.

This gives us E(Y) =1/12.

Since the third job is expected to be ready by 10:01 AM, we have E(Y)=61/12.

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P(X\geq 3)=1-P(X

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8 0
17 days ago
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