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2 years ago

1. Fill in the blanks: For the line 3x - y=2 the 2-intercept is_ _and the y-intercept __

Mathematics

1 answer:

Alex777 [14]2 years ago

8 0

Answer:

x-intercept: (2/3,0)

y-intercept: (0, -2)

Step-by-step explanation:

To find the x-intercept, you plug in 0 for all y values.

To find the y-intercept, you plug in 0 for all x values.

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Rates Lin, Diego, and Elena are competing to see who can finish their book the fastest. Lin read the first 54 pages from a 270-p

Sav [38]

Answer:

Diego will finish first while Lin and Elena would finish reading their book at the same time

Step-by-step explanation:

Rates Lin, Diego, and Elena are competing to see who can finish their book the fastest.

Their rates is calculated as:

For Lin

Lin read the first 54 pages from a 270-page book in the first 3 days.

54 pages = 3 days

270 pages = x

Cross Multiply

54x = 270 × 3

x = 270 × 3/54

x = 15 days

For Diego

Diego read the first 100 pages from a 320-page book in the first 4 days.

100 pages = 4 days

320 pages = x days

Cross Multiply

100x = 320 × 4

x = 320 × 4/100

x = 12.8 days

For Elena

Elena read the first 160 pages from a 480-page book in the first 5 days.

160 pages = 5 days

480 pages = x days

Cross Multiply

160x = 480 × 5

x = 480 × 5/160

x = 15 days

If they continue to read every day at these rates, who will finish first, second, and third?

Diego will finish reading his book first while Lin and Elena would finish reading their book at the same time

4 0

2 years ago

Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=x2+4x−12.

xz_007 [3.2K]

The area of the isosceles triangle is 64 sq units.

<u>Solution:</u>

Part 1: x-intercepts

The x-intercepts occur at the points on the function where y=0

So, we need to solve

$x^2-4x-12=0$

The left side factors fairly easily into:

$(x-6)(x+2)=0$

So solution occur when

$x-6=0\rightarrow x=6$

and

$x+2=0\rightarrow x=(-2)$

So the x-intercepts are at (0,6) and (0,−2)

Part 2: vertex of the parabola

The vertex of a simple quadratic parabola occurs when the derivative of the quadratic is equal to 0.

The derivative of the given quadratic is

$\frac{dy}{dx}=2x-4$

By observation, this is equal to 0 when x=2

When x=2 the original equation becomes

$y=(2)^2-4(2)-12$

$y=-16$

Therefore the vertex of this parabola is at (2,−16)

The endpoints of the base of the isosceles triangle are (-6, 0) and (2, 0)

$\Rightarrow$ so its base is 8

The height of the triangle reaches from the midpoint of the base (-2, 0) and the vertex (2, -16)

$\Rightarrow$ so its height is 16

The area is $\frac{1}{2}\times \text { base }\times \text { height }=\frac{1}{2}\times8\times16=64 \text{ sq units }$

6 0

2 years ago

The manager of a grocery store wants to determine the average amount of money spent at his store as it compares to the average d

JulijaS [17]

For the manager's store

Population size: 15
Arithmetic mean (μ): 37.6
Standard deviation (σ): 11,056

For the competitor's store

Population size: 15
Arithmetic mean (μ): 48,533
Standard deviation (σ): 28,356

For the manager's store the average is a better representation of the data since it does not have Outlier points in the box diagram. Also the median is close to the average.

For the competition store the average of the data collected is not as good representation of the data since they are dispersed from the mean with a standard deviation of 28.35. It also presents Outliers points in the box diagram, such as 112 which is very far from the average

7 0

3 years ago

If the measure of angle 5 is (11x- 14) and x=6, which expression could represent the measure of angle 2?

Anna [14]

I don't really get the question but if you mean 11x-14 it's 52

6 0

2 years ago

Read 2 more answers

The following section is a statement from the rental agreement Tim signed when he rented his car this past weekend. “Upon checko

Gnom [1K]

Answer:

C. The representative failed to have Tim initial by the fuel level on the Check-Out sheet.

Step-by-step explanation:

After reading the paragraph, we can eliminate B, by seeing that the representative did give him a copy of the Check-Out sheet, as quoted. "Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.".

We can also eliminate A and D, as the contract stated nothing about dents or the oil level in the car.

The answer is C, as the representative failed to have Tim initial on the Check-Out sheet. That is a requirement for the contract to be valid, as stated. "The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter.". However, Tim never initialed by the fuel level, as stated here. "...the agency representative turned on the car, took note of the fuel level, and indicated it on the Check-Out sheet. Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.". No where here does it state that Tim initialed on the Check-Out sheet, meaning that he didn't. Him not doing so invalidates the contract.

3 0

2 years ago