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3 years ago

What is the equation for a line parallel to the line shown in the graph, that passes through the point (-3, 9)?

Mathematics

1 answer:

TiliK225 [7]3 years ago

3 0

Answer: option C is the correct answer.

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

c represents the y intercept

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

Slope = (y2 - y1)/(x2 - x1)

Slope = (8 - 5)/(4 - 0) = 3/4

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 3, 9) is 3/4

To determine the y intercept, we would substitute m = 3/4, x = - 3 and y = 9 into y = mx + c. It becomes

9 = 3/4 × - 3 + c

9 = - 9/4 + c

c = 9 + 9/4

c = 45/4

The equation becomes

y = 3x/4 + 45/4

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I am a fraction whose Numerator and denominator are both prime numbers less than 20. If you were to increase each term by 1‚ I w

11Alexandr11 [23.1K]

Answer:

$\frac{2}{5}$ .

Step-by-step explanation:

Let the unknown fraction be $\frac{x}{y}$ ,

where, x and y both are prime numbers less than 20.

Now, it is given that adding 1 to both numerator and denominator will make the fraction $\frac{1}{2}$ .

Thus,

$\frac{x+1}{y+1}$ = $\frac{1}{2}$

2(x + 1) = y + 1

2x + 2 = y + 1

2x + 1 = y.

Clearly if x will be any odd number , two times x will be odd and adding 1 to it will result in even number and y should be even number , which is not possible as only even prime is 2.

Thus , x should be the even prime which is 2.

And y will be 5.

Thus the required fraction is $\frac{2}{5}$ .

6 0

3 years ago

The area of the yellow region is 112 cm^2. find the value of x

mrs_skeptik [129]

<h3>Answer: x = 7</h3>

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Explanation:

The largest rectangle (composed of the green and yellow sections combined) has area of 11*12 = 132 cm^2.

The yellow region takes up 112 of those 132 sq cm. This must mean the green region takes up 132-112 = 20 cm^2.

The horizontal portion of the green rectangle is 12-x cm. The vertical portion is 11-x cm. We can form the area of the green rectangle as an algebraic expression like so

area = length*width

area = (11-x)*(12-x)

area = 132 - 11x - 12x + x^2 .... apply the FOIL rule

area = x^2 - 23x + 132

Set this equal to the 20 cm^2 we found earlier.

x^2 - 23x + 132 = 20

x^2 - 23x + 132-20 = 0

x^2 - 23x + 112 = 0

We could factor or we could use the quadratic formula. I'll go with the second option.

We'll plug in a = 1, b = -23, c = 112

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-23)\pm\sqrt{(-23)^2-4(1)(112)}}{2(1)}\\\\x = \frac{23\pm\sqrt{81}}{2}\\\\x = \frac{23\pm9}{2}\\\\x = \frac{23+9}{2}\ \text{ or } \ x = \frac{23-9}{2}\\\\x = \frac{32}{2}\ \text{ or } \ x = \frac{14}{2}\\\\x = 16\ \text{ or } \ x = 7\\\\$

One of these solutions isn't feasible. Note how if x = 16, then this exceeds both the 11 cm and 12 cm sides. So this x value is not possible.

However, x = 7 is possible.

If x = 7, then the horizontal portion of the green rectangle is 12-x = 12-7 = 5 cm. Also, the vertical portion of the green rectangle would be 11-x = 11-7 = 4 cm. The area then is length*width = 5*4 = 20 cm^2 which matches up with what we got earlier. So the answer is confirmed.

7 0

3 years ago

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

viva [34]

13 = 1.625 * 8
26 = 1.625 * 16
39 = 1.625 * 24
Therefore y vary directly with x.
Answer: C ) yes ; y = 1.625 x

8 0

3 years ago

4x + 6 = -x +1<br>what's x?

Setler [38]

Answer:

x=-1

Step-by-step explanation:

8 0

2 years ago

The measures of two sides of a triangle are 4in and 13in. Find all possible values that the third side of this triangle can be?

ElenaW [278]

Answer:

9 < x < 17 is the possible length of the third side of a triangle.

Step-by-step explanation:

The Triangle Inequality theorem defines that if we are given two sides of a triangle, the sum of any two given sides of a triangle must be greater than the measure of the 3rd side.

Given the two sides of the triangle

4 in

13 in

Let 'x' be the length of 3rd size.

According to the Triangle Inequality theorem,

The difference of two sides < x < The sum of two sides

13 - 4 < x < 13+4

9 < x < 17

Therefore, 9 < x < 17 is the possible length of the third side of a triangle.

5 0

3 years ago