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RoseWind [281]
2 years ago
15

What is the answer this is a math question

Mathematics
1 answer:
Elena L [17]2 years ago
6 0

Answer:

1221 - 321 = 900

Step-by-step explanation:

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1.
Eddi Din [679]

Answer:

a) y=\dfrac{5}{2}x

b) yes the two lines are perpendicular

c) y=\dfrac{5}{4}x+6

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form y = mx + c

5y = 7 - 2x

y = \dfrac{7 - 2x}{5}

y = \dfrac{7}{5} - \dfrac{2}{5}x

y = -\dfrac{2}{5}x+\dfrac{7}{5}

this is changed into the y = mx + c, and we easily see that -2/5 is in the place of m, hence m = \frac{-2}{5} is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

m_1m_2=-1.

here both slopesm_1 and m_2 are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

\dfrac{-2}{5}m_2=-1.

m_2=\dfrac{5}{2}.

Finally, we can find the equation of the line of the perpendicular using:

(y-y_1)=m(x-x_1)

we know that the line passes through origin(0,0) and its slope is 5/2

(y-0)=\dfrac{5}{2}(x-0)

y=\dfrac{5}{2}x is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether m_1m_2=-1 ?

the slopes can be easily found through rearranging both equations to y=mx+c

Line:1

2x + 3y =6

y =\dfrac{-2x+6}{3}

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

Line:2

y = \dfrac{3}{2}x + 4

this equation is already in the form we need.

the slopes of both equations are

m_1 = \dfrac{-2}{3} and m_2 = \dfrac{3}{2}

using

m_1m_2=-1

\dfrac{-2}{3} \times \dfrac{3}{2}=-1

-1=-1

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be m=\dfrac{-4}{5} and the y-intercept is c=6 the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

m_1m_2=-1

\dfrac{-4}{5}m_2=-1

m_2=\dfrac{5}{4}

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

(y-y_1)=m(x-x_1)

(y-6)=\dfrac{5}{4}(x-0)

y=\dfrac{5}{4}x+6

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0
3 years ago
A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. !e san
mina [271]
So if the sandwiches cost $7.75 each and the total was $113.50 that would mean that there were 14 sandwiches bought. So 14 times 7.75 is 108.50. 
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3 years ago
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Im confused on how to do this can someone explain???
sesenic [268]

Answer: you add them all up

Step-by-step explanation: you can get the answer from above and dont trust this answer.

3 0
3 years ago
Irina wants to build a fence around a rectangular vegetable garden so that it has a width of at least 10 feet. She can use a max
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<span>The answer to your question is l = 20 ft; w = 10 ft</span><span />
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What are the coordinates of point J’ after the rotation?
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Step-by-step explanation:

(5,4) is the coordinate of the point j after rotation

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