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3 years ago

The system of equations shown is solved using the linear combination method

1 answer:

4 0

Answer: When a system of two linear equations gives an answer of $0=0$ , there are infinitely many solutions. It also means that the graph represents parallel lines, so the answer is the third choice.

Step-by-step explanation: When it comes to systems of equations in algebra, you will see three types of solutions:

1. When you get an exact value & number for x and y, the system has one solution and is consistent/independent.

2. When you get $0=0$ like in this case, the system has infinitely many solutions and is consistent/dependent.

3. When you get numbers that are not equal, for example, $3\neq 5$ , you have many solutions and the system is inconsistent/independent.

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Julia is five years older than her sister Babs, and their ages add up to 31. How old is Babs?

Tresset [83]

Julia is X+5

x+x+5=31

Now we just solve the equation

2x=31-5
x=26/2
x=13 years old (Babs' age)

and we know that julia is 5 years older this gives us the conclusion that.

13+18=31

4 0

3 years ago

Read 2 more answers

The measures of the three of the interior angles of a quadrilateral are 60°, 110°, and 90°. What is the measure of the fourth an

irina [24]

The answer is C. 100 because the total measure of a quadrilateral is 360. When you add up the 3 interior angle measures, it adds up to 260. Then you subtract 360-260 to get 100 as the fourth angle measure. Hope that this helped!

6 0

3 years ago

The hypotenuse AB of the right triangle ABC is parallel to the axis of the abscess. Find the length of the hypotenuse if A (-1;

lukranit [14]

Answer:

10.25

Step-by-step explanation:

The slope of AC is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (-4 -1)/(3 -(-1)) = -5/4

Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

y -(-4) = 4/5(x -3) . . . . line CB

When y = 1 (to match the y-value of A), then ...

1 +4 = 4/5(x -3)

5(5/4) = (x -3) . . . . . multiply by 5/4

6.25 +3 = x = 9.25 . . . . add 3

Point B is (9.25, 1).

The length of the hypotenuse is ...

9.25 -(-1) = 10.25

6 0

2 years ago

A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 21 inches. The scoop is used to transfer molten st

eduard

Answer:

31.5 in

Step-by-step explanation:

Volume of a hemisphere = (2/3) $\pi$ r³
(where r is the radius)
Volume of a cylinder = $\pi$ r²h
(where r is the radius and h is the height)
radius r = (1/2) diameter

First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:

Volume = (2/3) $\pi$ x 21³ = 6174 $\pi$ in³

Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:

$\pi$ 14²h = 6174 $\pi$

196 $\pi$ h = 6174 $\pi$

Divide both sides by $\pi$ : 196h = 6174

Divide both sides by 196: h = 31.5

Therefore, the height of the molten steel in the storage tank is 31.5 in

3 0

2 years ago

8. A cellphone company charges $29.99 per month for the first 500 minutes of calls and $0.30 a minute for any calls over the 500

scZoUnD [109]

Answer:

C) $64.49

Step-by-step explanation:

let 'x' = #minutes

cost = 29.99 + 0.3(x-500)

= 29.99 + .3(115)

= 29.99 + 34.50

= $64.49

8 0

2 years ago