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Daniel [21]
2 years ago
11

Line m contains points (1, -3) and (2, 2). Which of the following pairs of points define a line parallel to line m? f (0, 0) and

(1, 5) g (1, 1) and (6, 2) h (0, 0) and (-1, 1) j (-4, 0) and (5, 5)
Mathematics
1 answer:
Jet001 [13]2 years ago
7 0
The line will have the same slope as line m.

Slope of line m  =  (2 - -3) / (2 - 1) = 5

The answer is (0, 0) and (1, 5)     which has slope  (5-0) / (1 - 0) = 5 also.
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Sienna is solving the quadratic equation by completing the square. 3x2 + 9x – 4 = 0 3x2 + 9x = 4 A(x2 + 3x) = 4 What is the valu
bogdanovich [222]

Answer:

I am going to show you the first steps to complete squares for the given equation: 1) Starting equation: 3x^2 + 9x -4 = 0 2) Add 4 to both sides => 3x^2 + 9x - 4 + 4 = 4 => 3x^2 + 9x = 4 3) Extract common factor 3 in the left side => 3 (x^2 + 3x). Now, compare with a(x^2 + 3x) and you get a = 3. Answer: a = 3.

3 0
2 years ago
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Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours dur
Gelneren [198K]
I am setting the week hourly rate to x, and the weekend to y.  Here is how the equation is set up:

13x + 14y = $250.90
15x + 8y = $204.70

This is a system of equations, and we can solve it by multiplying the top equation by 4, and the bottom equation by -7.  Now it equals:

52x + 56y = $1003.60
-105x - 56y = -$1432.90

Now we add these two equations together to get:

-53x = -$429.30 --> 53x = $429.30 --> (divide both sides by 53) x = 8.10.  This is how much she makes per hour on a week day.

Now we can plug in our answer for x to find y.  I am going to use the first equation, but you could use either.

$105.30 + 14y = $250.90.  Subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40

Now we know that she makes $8.10 per hour on the week days, and $10.40 per hour on the weekends.  Subtracting 8.1 from 10.4, we figure out that she makes $2.30 more per hour on the weekends than week days.
7 0
2 years ago
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Use complete sentences to explain the relationship between tan 5pi/4 and tan pi/4. In your answer, reference specific values on
Kisachek [45]
Remark
pi/4 is between 0 and pi/2 which means that pi/4 is in the first quadrant.

5*pi / 4 is between pi and 3/2 pi which means that the angle is in the third quadrant. 

So you are talking about one two angles that are in the first and third quadrants.

Step One
Find the Tangent of pi/4 using the unit circle as a reference.

Since pi/4 is 1/2 way between 0 and pi/2 you are referring to something that has and x value of 0.707 for an x value and 0.707 for a y value. (They are equal)

That is the point where the opposite / adjacent = 0.707/0.707 = 1

Step Two
Find the tangent of 5pi/4 using the unit circle.
Using the same argument as pi/4 this time the opposite / adjacent = -0.707/-0.707 = 1 ( the two minus signs cancel out.)

 
8 0
2 years ago
Consider a single spin of the spinner.
alex41 [277]

Answer:

"landing on a shaded portion and landing on a 3"

"landing on an unshaded portion and landing on a number less than 2 "

Step-by-step explanation:

Mutually exclusive means the events will have no intersection.

Let's look at your first choice:

"landing on a shaded portion and landing on an even number"

Landing on a shaded portion would be 1 or 4.

Landing on an even number would be 2 or 4.

There is an intersection (they contain a common element), the 4.

These events are not mutually exclusive.

Let's look at your second choice:

"landing on a shaded portion and landing on a number greater than 3"

Landing on a shaded portion would be 1 or 4.

Landing on a number greater than 3 would be just 4.

There is an intersection; they both contain 4.

These events are not mutually exclusive.

Let's look at your third choice:

"landing on a shaded portion and landing on a 3"

Landing on a shaded portion would be 1 or 4.

Landing on 3 would just be 3.

There is no common elements in the lists listed.  These events have no intersection.

These events are mutually exclusive.

Let's look at your fourth choice:

"landing on an unshaded portion and landing on an odd number"

Landing on a unshaded portion would be 2 or 3.

Landing on an odd number would be 1 or 3.

There is an intersection; they both have 3 in common.

These events are not mutually exclusive.

Let's look at your fifth choice:

"landing on an unshaded portion and landing on a number less than 2 "

Landing on an unshaded portion would 2 or 3.

Landing on a number less than 2 would be 1.

There is no intersection.

These events are mutually exclusive.

6 0
2 years ago
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il63 [147K]

Let x represent the number of quarts of Tuscan sauce and

y represent the number of quarts of marinara sauce Tiffany makes.

A quart of Tuscan sauce requires 6 tomatoes and 1 cup of oil

x quarts requires 6x tomatoes and 1x cups of oil

A quart of her marinara sauce requires 5 tomatoes and 1.25 cups of oil

y quarts requires 5y tomatoes and 1.25 y cups of oil

She has 45 tomatoes and 10 cups of oil on hand.

So the constraints are

6x + 5y

1x + 1.25y < = 10

x>=0 and y>=0

4 0
2 years ago
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