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3 years ago

Hey i need help with system of equations. i uploaded a doxs file you can onpen it in google docs

Mathematics

1 answer:

Art [367]3 years ago

3 0

Answer:

Step-by-step explanation:

PART A:

The first equation is $x + y = 7\\y = 7 - x .............(a)$

The second equation is $3x - 2y = 1\\2y = 3x - 1$

Putting the value of y from (a) in the above equation, we get $2y = 3x - 1\\2(7 - x) = 3x - 1\\14 - 2x = 3x - 1\\x = 15$

From (a) we get y = 7 - x = 7 - 15 = -8

PART B:

Here the system of equations are $-x + 4y = 17........(a) and 3x - 5y = -30.........(b)$

From (a) we get, $x = 4y - 17$

Putting the above value of x in (b) we get, $3x - 5y = -30\\3(4y - 17) - 5y = -30\\12y - 51 - 5y = -30\\7y = 21\\y = 3$

Hence, $x = 4y - 17 = 12 - 17 = -5$

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Factorise (3m -2n)^2 +5p(3m - 2n)

monitta

Answer: if you factor it you will get this-->(3m−2n)(3m−2n+5p)

Step-by-step explanation:

8 0

3 years ago

Given: AB is the perpendicular bisector of IK.

mestny [16]

BI = BK bc bisecting it means cutting it in half

6 0

3 years ago

The surface areas of two similar solids are 384 yd squared and 1057 yd squared The volume of the larger solid is 1795. What is t

Arturiano [62]

This is the concept of scale factors, we are required to calculate for the volume of the smaller solid if the larger solid has a volume of 1975.
Area scale factor=(linear scale factor)^2
thus;
Area scale factor=(area of larger solid)/(area of smaller solid)=1057/384
linear scale factor=√(1057/384)=5.7019
the volume scale factor=(linear scale factor)^3=[volume of larger solid]/[volume of smaller solid]
The volume scale factor=(5.7019)^3=185.3772
therefore;
volume of smaller solid=[volume of larger solid]/[volume scale factor]

=1795/185.3772
=9.683
The answer is 9.683 yd^3

5 0

4 years ago

Help!! Please please answer quickly and in the next 9 hours! <br><br> Solve these questions.

lutik1710 [3]

Answer:

Please refer to step-by-step.

Step-by-step explanation:

Let's solve all of these one at a time.

15. -2x - y = -5

To find the x-intercept, we need to equate the value of y to 0.

-2x - 0 = -5

$\dfrac{-2x}{-2}=\dfrac{-5}{-2}$

$x=2.5$

To find the y-intercept, we need to equate the value of x to 0.

-2(0) - y = -5

Now since we cannot have a negative value, we need to divide both sides by -1.

$\dfrac{-y}{-1}=\dfrac{-5}{-1}$

$y=5$

To find the slope form, we can simply transpose the value of -2x to the other sides of the equal sign.

-y = 2x - 5

Now we cannot have a negative value for the slope, we need to divide both sides by -1, leaving us with.

y = -2x + 5

16. 6x + 3y = -9

Let's start with the x-intercept.

6x + 3y = -9

6x + 3(0) = -9

$\dfrac{6x}{6}=\dfrac{-9}{6}$

$x=1.5$

Now we solve for the y-intercept.

6x + 3y = -9

6(0) + 3y = -9

$\dfrac{3y}{3}=\dfrac{-9}{3}$

$y = -3$

Now for the slope.

3y = -6x - 9

Now we need to divide all our variables by 3 to get y.

$\dfrac{3y}{3}=\dfrac{-6x}{3}-\dfrac{9}{3}$

$y=-2x-3$

17. x - y = 4

Let's start with the x-intercept.

x - y = 4

x - 0 = 4

$x=4$

Now we solve for the y-intercept.

x - y = 4

0 - y = 4

-y=4

$\dfrac{-y}{-1}=\dfrac{4}{-1}$

$y = -4$

Now for the slope.

x - y = 4

-y = -x + 4

We need to divide all our variables by -1 to get y.

$\dfrac{-y}{-1}=\dfrac{-x}{-1}+\dfrac{4}{-1}$

$y=x-4$

18. 3x + 4y = 12

Let's start with the x-intercept.

3x + 4y = 12

3x + 4(0) = 12

$\dfrac{3x}{3}=\dfrac{12}{3}$

$x=4$

Now we solve for the y-intercept.

3x + 4y = 12

3(0) + 4y = 12

$\dfrac{4y}{4}=\dfrac{12}{4}$

$y = 3$

Now for the slope.

3x + 4y = 12

4y = -3x + 12

$\dfrac{4y}{4}=-\dfrac{3x}{4}+\dfrac{12}{4}$

$y=-\dfrac{3x}{4}+3$

19. -7x + 2y = -16

Let's start with the x-intercept.

-7x + 2y = -16

-7x + 2(0) = -16

$\dfrac{-7x}{-7}=\dfrac{-16}{-7}$

$x=-2\dfrac{2}{7}$

Now we solve for the y-intercept.

-7x + 2y = -16

-7(0) + 2y = -16

$\dfrac{2y}{2}=\dfrac{-16}{2}$

$y=-8$

Now for the slope.

-7x + 2y = -16

2y = -7x - 16

$\dfrac{2y}{2}=-\dfrac{7x}{2}-\dfrac{16}{2}$

$y=-\dfrac{7x}{2}-8$

20. x - 5y = 55

Let's start with the x-intercept.

x - 5y = 55

x - 5(0) = 55

x = 55

Now we solve for the y-intercept.

x - 5y = 55

0 - 5y = 55

$\dfrac{-5y}{-5}=\dfrac{55}{-5}$

$y=-11$

Now for the slope.

x - 5y = 55

-5y = x + 55

$\dfrac{-5y}{-5}=-\dfrac{x}{-5}+\dfrac{55}{-5}$

$y=-\dfrac{x}{5}-11$

8 0

3 years ago

Given the angles in the diagram, what is the measure of ∠C ?

Westkost [7]

Since quadrilaterals have interior angles that add up to 360, then subtract the known values from 360

360 - 90 - 90 - 146 = 64

Angle C = 64

8 0

3 years ago

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