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2 years ago

Solve the system of linear equations using any method. -6y + 2 = -4x y – 2 = x

Mathematics

1 answer:

Lilit [14]2 years ago

3 0

Answer:

x=-5 and y=-3

Step-by-step explanation:

-6y+2=-4x convert this into standard form

y=x+2

plug in the slope intercept form in to y

-6(x+2)+4x=-2

-6x-12+4x=-2

-2x-12=-2 now solve for x

-2x-12+12=-2+12

-2x=+10

x=-5 now solve for y

y=-5+2

y=-3

so basically x=-5 and y=-3

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At 3pm, the length of the shadow of a thin vertical pole standing on level ground is the same as the height of the pole. A while

aliya0001 [1]

Answer: The height of the pole is 175.97 ( approx )

Step-by-step explanation:

Let the height of the pole is x cm,

Also, let the angle of elevation of the sun to the pole at 3 pm is $\theta$

Thus, by the question,

$tan\theta = \frac{\text{ The height of the pole}}{\text{ The height of the shadow}}$

$\implies tan\theta = \frac{x}{x}$ ( at 3pm the height of shadow = height of the pole)

$\implies tan\theta = 1$

$\implies \theta = 45^{\circ}$

Again, according to the question,

When the angle of elevation is $(\theta - 12^{\circ})$ ,

The height of shadow = x + 95,

$\implies tan(45-12)^{\circ}=\frac{x}{x+95}$

$\implies tan 33^{\circ}=\frac{x}{x+95}$

$\implies tan 33^{\circ}x + 95\times tan33^{\circ}=x$

$\implies tan 33^{\circ}x - x = - 95\times tan33^{\circ}$

$\implies -0.3505924068 x = - 61.6937213538$

$x=175.969930202\approx 175.97\text{ cm}$

4 0

2 years ago

What is the slope of a line that contains the points (5, -3) and (7, 3)? *

Allisa [31]

Slope formula: y2-y1/x-x1

We can use the given points to solve.

3-(-3)/7-5

6/2

Best of Luck!

4 0

2 years ago

The area of a triangle is 30 square feet. If<br> the base is 4 feet, then what is the height?

ExtremeBDS [4]

Height=15

Explanation:
Area of a triangle= 1/2base x height
Plug in information
30=1/2 x 4 x h
Solve 1/2 x 4 = 2
30= 2 x h
Divide both side by two
30/2=2 x h/2
Solve:
15= h

6 0

2 years ago

At a cost restaurant the cost for a hot dog and a soft drink is $2.10. The cost for two hot dogs and three soft drinks is $5.15.

Alja [10]

Answer:

The cost of soft drink is $0.95

Step-by-step explanation:

Let the cost of hot dog be x

Cost of 2 hot dogs = 2x

Let the cost of soft drink be y

Cost of 3 soft drinks = 3y

At a cost restaurant the cost for a hot dog and a soft drink is $2.10.

So, x+y=2.10

The cost for two hot dogs and three soft drinks is $5.15

So, 2x+3y=5.15

Plot the lines on the graph:

x+y=2.10 --Purple line

2x+3y=5.15 --- Black Line

Intersection point =(x,y)=(1.15,0.95)

Hence The cost of soft drink is $0.95

7 0

2 years ago

A=1/2bh. A=200ft. H=10. What is b

Svetllana [295]

Answer:

B= $\frac{2A}{H}$

Step-by-step explanation:

If you noticed, A= $\frac{1}{2}$ BH is the formula for finding the area for a triangle. Your goal is to get B by it's self. Your first step will be to clear of the fraction first, so you will multiply both sides by 2. 2(A)=2( $\frac{1}{2}$ BH). On the left, you have 2×A= On the right side, you have 2( $\frac{1}{2}$ BH), but since you have a number in the equation, you will only use 2× $\frac{1}{2}$ . To solve 2× $\frac{1}{2}$ , you will cnacel out both 2's and you have 1. 1×BH will still equal BH, so you are now left will B×H.

(Your new equation looks like this by the way). 2A=BH

Since you need to get B by its self, the way to clear the H away from the B is by dividing. You will now divide the B and H aswell as 2A and H. (It will look like this) $\frac{2A}{H} = \frac{BxH}{H}$ . (Again when you have the same number or letter, you cross it out. When you divide, you won't change anything on the left side, and all you have to do on the right id to cross out the H next to the B and cross out the H on the bottom of the equation). You should be left with $\frac{2A}{H}$ = B. Now you can turn it around for your final answer. B= $\frac{2A}{H}$ .

Please let me know if i helped, how I did, and if you have any questions.

3 0

2 years ago