MATHEMATICS HIGH SCHOOL

Which statements about the system are true? Check all that apply. y = x – 4
3y – x = –7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y–intercept.
The equations represent the same line.
The lines intersect.

Answers

Answer 1
Answer:

Answer:

The correct answers are:

  • The system has one solution.
  • The lines intersect.

Step-by-step explanation:

We are given system of linear equations as:

y=x-4--------(1)

and 3 y-x= -7----------(2)

on substituting the value of 'y' from equation (1) into equation (2) we have:

3(x-4)-x=-7

⇒ 3x-3×4-x=-7

⇒ 3x-x= -7+12

⇒  2x=5

⇒ x=(5)/(2)

also putting the value of x into equation (1) we have:

y=(5)/(2)-4=(5-8)/(2)=(-3)/(2)

  • Hence, we get a unique value of x and y on solving the system of  linear equations.

             Hence, the system has one solution.

  • the slope for line y=x-4 is 1  ( since on comparing the equation with y=mx+c; where m denotes the slope of line and c is the y-intercept)

                y-intercept is -4

            but the slope of line 3y-x = -7 i.e.

           y=(x-7)/(3)=(x)/(3)-(7)/(3)

          hence the slope of second line is: (1)/(3).

                  and y-intercept is (-7)/(3).

  • They represent different lines.
  • the lines intersect at the point ((5)/(2),(-3)/(2))
Answer 2
Answer:

Answer and explanation:

Given : Equations y=x-4 and 3y-x=-7

To find : Which statements about the system are true? Check all that apply.

Solution :

First we solve the system of equations,

y=x-4  .....(1)

3y-x=-7  ......(2)

Substitute y from (1) in (2),

3(x-4)-x=-7

3x-12-x=-7

2x=5

x=(5)/(2)

Substitute the value of x in (1),

y=(5)/(2)-4

y=(5-8)/(2)

y=(-3)/(2)

1) The system has one solution i.e. ((5)/(2),-(3)/(2))

2) The system has solution which means it is not parallel lines.

Writing equation in slope from, y=mx+c

y=x-4 where m=1 and c=-4

3y-x=-7 where m=(1)/(3) and c=-4

3) Both lines have different slopes.

4) Both lines have the same y-intercept.

5) The equations represent the different lines.

6) The lines intersect at ((5)/(2),-(3)/(2))

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Marguerite drew a rectangle with vertices A(-2,-1) B(-2,-4) and C (1,-4) what are the coordinates of the fourth vortex?

Answers

Concept:

we use the vector method to solve this problem, take all the vertices in vector foam.

In the rectangle their exist two pair of parallel and equal sides, take the one pair and solve for unknown vertex.

BA=CD

A-B = D-C

(-2i-j)-(-2i-4j) = (xi+yj)-(1i-4j)

(-2i-j+2i+4j) = (xi+yj-1i+4j)

3j = xi+yj-1i+4j

i+3j-4j = xi+yj

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by comparing,

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Answers

Any number to the power of zero is one.  Think of it like this - a power is basically multiplying a certain number of the same integer together.  So, if we multiply 0 fours together, we just get 1.  Alternatively, consider it like this - 4 to the power of one divided by four to the power of one is equal to four to the power of zero, so 4/4=1 is 4 to the power of zero.  Therefore, 4^0 is 1.
any number to the zero power is equal to 1

an exponent is how many times you multiply something by itself
remember that x^2=x^2 times 1
when you have x^0 then that means x^0 times 1 and then since there are no x's, the resulting value is just 1

the answer is 1

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Answers

Answer:

angle 4 is 31

angle 5 is 59.

Step-by-step explanation:

M<4 and M<5 add up to a  right angle which is 90 degrees . so you put it in a equation form.

2x-5+4x-13=90

rearrange it

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6x-18=90

add 18 on both sides

6x=108

divide 6 from both sides

and you get x= 18

Plug in x for angle 4 =2(18)-5 =  31

plug in x for angle 5 = 4(18)-13 = 59

Irwin rode his bicycle from one end of a trail to another and back at a speed of 20 miles per hour. If the trail is 4 miles long, for how many hours was Irwin riding?0.2 hours
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Answers

Answer:

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Step-by-step explanation:

Hope this helps and please mark Brainliset!

Answer:

i would say 0.4

Step-by-step explanation:

i really really really hope this is right

if it's not I'm going to be very sad

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