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Stolb23 [73]
3 years ago
9

A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = y equals negative StartFractio

n 5 Over 3 EndFraction left-parenthesis x minus 2 right parenthesis.(x – 2). Which equations also represent this line? Select three options. y = y equals negative StartFraction 5 Over 3 EndFraction x minus 2.x – 2 y = y equals negative StartFraction 5 Over 3 EndFraction x plus StartFraction 10 Over 3 EndFraction.x + 3y = –5x + 10 3x + 15y = 30 5x + 3y = 10
Mathematics
2 answers:
arsen [322]3 years ago
4 0

Answer:

5x+3y=10

Step-by-step explanation:

Natali5045456 [20]3 years ago
3 0

Answer:

y=-\frac{5}{3} x+\frac{10}{3}  or what is the same: 5x+3y=10

Step-by-step explanation:

First we find the slope of the line that goes through the points (-4,10) and (-1,5) using the slope formula: slope=\frac{10-5}{-4-(-1)} =\frac{5}{-3} =-\frac{5}{3}

Now we use this slope in the general form of the slope- y_intercept of a line:

y=-\frac{5}{3} x+b

We can determine the parameter "b" by requesting the condition that the line has to go through the given points, and we can use one of them to solve for "b" (for example requesting that the point (-1,5) is on the line:

y=-\frac{5}{3} x+b\\5=-\frac{5}{3} (-1)+b\\5=\frac{5}{3}+b\\5-\frac{5}{3}=b\\b=\frac{10}{3}

Therefore, the equation of the line in slope y_intercept form is:

y=-\frac{5}{3} x+\frac{10}{3}

Notice that this equation can also be written in an equivalent form by multiplying both sides of the equal sign by "3", which allows us to write it without denominators:

y=-\frac{5}{3} x+\frac{10}{3}\\3*y=(-\frac{5}{3} x+\frac{10}{3})*3\\3y=-5x+10\\5x+3y=10

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ruslelena [56]

The length of the shorter rope is 20 cm.

<h3>How to find the original length of the rope using ratio?</h3>

He cut a rope into two pieces with lengths having a ratio of 5 to 2.

The shorter piece is 70 cm long.

The length of the original rope can be calculated as follows:

The ratio of the length of the rope is as follows;

5 : 2

let

x = length of the original rope

Therefore,

length of shorter piece = 2 / 7 × 70

length of shorter piece = 2 / 7 × 70

length of shorter piece =  140 / 7

length of shorter piece = 20 cm

Therefore, the length of the shorter rope is 20 cm.

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8 0
2 years ago
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3 years ago
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7 0
3 years ago
A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On
uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

h(x)=ax(x-7)             ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

4=a(3)((3)-7)

4=a(3)(-4)

\dfrac{4}{(3)(-4)}=a

-\dfrac{1}{3}=a

Putting a=-\dfrac{1}{3}, we get

h(x)=-\dfrac{1}{3}x(x-7)              ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

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A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)

h(1.5)=-(0.5)(-5.5)

h(1.5)=2.75

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

6 0
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Bingel [31]

Answer:

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0.6157 = height/300

height = 184.7 feet

5 0
3 years ago
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