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2 years ago

A given line has the equation 10x+2y=-2.

Mathematics

2 answers:

OLEGan [10]2 years ago

8 0

Answer:

Option 1 - $y=-5x+12$

Step-by-step explanation:

Given : A given line has the equation $10x+2y=-2$

To find : What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?

Solution :

The slope intercept form is $y=mx+c$

where, m is the slope and c is the y-intercept.

Writing given equation in slope intercept form,

Equation $10x+2y=-2$

Take x to another side,

$2y=-10x-2$

Divide both side by 2,

$y=-5x-1$

The slope intercept form of the equation is $y=-5x-1$

Where, m=-5 is the slope and c=-1 is the y-intercept.

When two lines are parallel their slopes are equal i.e. $m_1=m_2$

Let the equation be $y=mx+c$

As lines are parallel then m=-5

We have given lines passes through point (0,12).

Substitute in equation,

$12=-5(0)+c$

$c=12$

Substitute back in equation,

$y=-5x+12$

Therefore, The required equation is $y=-5x+12$

So, Option 1 is correct.

Karolina [17]2 years ago

4 0

Answer:

5x+y=12

Step-by-step explanation:

10x+2y=-2=5x+y=12

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The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism. Find the volume of each

Art [367]

Answer:

Step-by-step explanation:

Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT

Since VR = length * width and height

VR = 6*x*3

VR = 18x ft³

Also VT = Length *width * Height/2

VT = (7 * x * 4)/2

VT = 28x/2

VT = 14xft³

Since VR = 32 + VT

18x = 32+(14x)

collect like terms

18x-14x = 32

4x = 32

divide both sides by 4

4x/4 = 32/4

x = 8

Volume of the rectangular prism = 18x

Volume of the rectangular prism = 18*8

Volume of the rectangular prism = 144ft³

Volume of the right triangular prism = 14x

Volume of the rectangular prism = 14*8

Volume of the rectangular prism = 112ft³

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2 years ago

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Max's cell phone plan charges a monthly

ludmilkaskok [199]

Answer:

Step-by-step explanation:

7.41 / 0.13 = 57

57 - 15 = 42

42 / 2 = 21

21, 36

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2 years ago

HELP PLS>>> The vector (3, - 7) ) is rotated by an angle of (3pi)/4 radians and then reflected across the y-axis. If th

horsena [70]

Answer:

$a \approx -2.826$ , $b \approx 7.072$

Step-by-step explanation:

First, the vector must be transformed into its polar form:

$r = \sqrt{3^{2}+ (-7)^{2}}$

$r \approx 7.616$

$\theta \approx 2\pi - \tan^{-1}\left(\frac{7}{3} \right)$

$\theta \approx 1.629\pi$

Let assume that vector is rotated counterclockwise. The new angle is:

$\theta' = \theta + \frac{3\pi}{4}$

$\theta' = 2.379\pi$

Which is coterminal with $\theta'' = 0.379\pi$ . The reflection across y-axis is:

$\theta''' = \pi - \theta''$

$\theta''' = 0.621\pi$

The equivalent vector in rectangular coordinates is:

$a = 7.616\cdot \cos 0.621\pi$

$a \approx -2.826$

$b = 7.616\cdot \sin 0.621\pi$

$b \approx 7.072$

7 0

2 years ago

19. Bella is putting down patches of sod

Fofino [41]

Answer:

The dimensions of the two different rectangular regions are;

1st Arrangement:

W = 4 yards and L = 5 yards or W = 5 yards and L = 4 yards

2nd Arrangement:

W = 2 yards and L = 10 yards or W = 10 yards and L = 2 yards

The perimeter of the two different rectangular regions are;

1st Arrangement:

P₁ = 18 yards

2nd Arrangement:

P₂ = 24 yards

Step-by-step explanation:

Bella is putting down patches of sod to start a new lawn.

She has 20 square yards of sod.

We are asked to provide the dimensions of two different rectangular regions that she can cover with the sod.

Recall that a rectangle has an area given by

Area = W*L

Where W is the width of the rectangle and and L is the length of the rectangle.

Since Bella has 20 square yards of sod,

20 = W*L

There are more than two such possible rectangular arrangements.

Out of them, two different possible arrangements are;

1st Arrangement:

20 = (4)*(5) = (5)*(4)

Width is 4 yards and length is 5 yards or width is 5 yards and length is 4 yards

2nd Arrangement:

20 = (2)*(10) = (10)*(2)

Width is 2 yards and length is 10 yards or width is 10 yards and length is 2 yards

Therefore, the dimensions of two different rectangular regions are;

1st Arrangement:

W = 4 yards and L = 5 yards or W = 5 yards and L = 4 yards

2nd Arrangement:

W = 2 yards and L = 10 yards or W = 10 yards and L = 2 yards

What is the perimeter of each region?

The perimeter of a rectangular shape is given by

P = 2(W + L)

Where W is the width of the rectangle and and L is the length of the rectangle.

The perimeter of the 1st arrangement is

P₁ = 2(4 + 5)

P₁ = 2(9)

P₁ = 18 yards

The perimeter of the 2nd arrangement is

P₂ = 2(2 + 10)

P₂ = 2(12)

P₂ = 24 yards

So the perimeter of the 1st arrangement is 18 yards and the perimeter of the 2nd arrangement is 24 yards.

Note:

Another possible arrangement is,

20 = (1)*(20) = (20)*(1)

Width is 1 yard and length is 20 yards or width is 20 yards and length is 1 yard.

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2 years ago

PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of z

dimaraw [331]

1) $\frac{v(8)-v(0)}{8 - 0} = \frac{10-18}{8} = -1\frac{m}{s}$ .
2) $v(5) = 5^2-9*5+18 = 25-45+18 = -2\frac{m}{s}$ .
3) The particle is moving right when the velocity function is positive: $0\ \textless \ t\ \textless \ 3$ or $6\ \textless \ t\ \textless \ 8$ .
4) When $0\ \textless \ t\ \textless \ \frac{9}{2}$ the particle is slowing down because the acceleration is close to zero $\Rightarrow$ the particle is speeding up when acceleration is increasing away from zero: $\frac{9}{2}\ \textless \ t\ \textless \ 8$ .
5) $(\frac{1}{8})* \int\limits^8_0 {t^2-9t+18dt}=\frac{1}{8}*(\frac{t^3}{3}-(\frac{9}{2}*t^2+18t)_{0}^{8}= \\=(\frac{1}{8})*(\frac{8^3}{3}-(\frac{9}{2})*8^2+18*8)=\frac{8^2}{3}-(\frac{9}{2})*8+18=3\frac{1}{3} \frac{m}{s}$ .

3 0

2 years ago