Two lines, A and B, are represented by the following equations: Line A: 4x + 4y = 16 Line B: x + y = 4 Which statement is true about the solution to the set of equations? It is (1, 2). There are infinitely many solutions. It is (1, 5). There is no solution.

Answers

Answer 1

Answer: Well it can't be (1,2) because that comes out to be 12 not 16, and it also can't be (1,5) because that comes out to be 20, but there is a solution, that i know of for sure which is (0, 4). So your answer would probably be there are infinitely many solutions.

Answer 2

Answer:

Answer:

The answer is B. There are infinitely many solutions.

Step-by-step explanation:

None of the other answers make sense and do not work.

Hope This Helps!

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lily is making granola she uses almonds walnuts and pecans in tge ratio 4:3:8 lily uses 40ounces of pecans

Answers

Well. im not 100% sure if this is correct. but what i did was did 5 x 8. which equals 40. so then i did 5 x 3. which equals 15. then i did 5 x 4. which equals 20. hopefully im correct. hope this helped! :)

A pool measuring 8 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 1008 square meters, what is the width of the path?

Answers

Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.

Combined Area = (2x + 26)*(2x + 8) = 1008

2x*(2x + 8) + 26*(2x + 8 ) = 1008

4x² + 16x + 52x + 208 = 1008

4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.

Multiply first and last coefficients: 1*-200 = -200

We look for two numbers that multiply to give -200, and add to give +17

Those two numbers are 25 and -8.

Check: 25*-8 = -200 25 + -8 = 17

We replace the middle term of +17x in the quadratic expression with 25x -8x

x² +17x - 200 = 0

x² + 25x - 8x - 200 = 0

x(x + 25) - 8(x + 25) = 0

(x+25)(x -8) = 0

x + 25 = 0 or x - 8 = 0

x = 0 -25 x = 0 + 8

x = -25 x = 8

The width of the path can not be negative.

The only valid solution is x = 8.

The width of the path is 8 meters.

A 13 foot board is cut into two pieces. If one piece is x feet long express the other length in terms of x

Answers

Since the foot board is 13 feet long, it can be said that the sum of the two pieces is 13. If one piece is x, the other piece can be expressed as the difference of 13, the total length of the foot board, and x, the length of the first piece. Hence, the other piece, in mathematical terms, is expressed as 13-x.

which are the roots of the quadratic function f(b) = b2 – 75? check all that apply. b = 5 square root of 3 b = -5 square root of 3 b = 3 square root of 5 b = -3 square root of 5 b = 25 square root of 3 b = -25 square root of 3

Answers

The answers are b = 5 square root of 3; b = -5 square root of 3. f(b) = b^2 – 75. If f(b) = 0, then b^2 – 75 ) 0. b^2 = 75. b = √75. b = √(25 * 3). b = √25 * √3. b = √(5^2) * √3. Since √x is either -x or x, then √25 = √(5^2) is either -5 or 5. Therefore. b = -5√3 or b = 5√3.

Answer:

$b=5√(3)$ and $b=-5√(3)$ are the roots of given quadratic equation.

Step-by-step explanation:

Given quadratic equation is $f(b)=b^2-75$

We have to check all the given options.

If the value of f(b) gives 0 when put the value of b in above equation then only that b value is the root of quadratic equation.

$b=5√(3): (5√(3))^(2)-75=75-75=0$

$b=-5√(3): (-5√(3))^(2)-75=75-75=0$

$b=3√(5): (3√(5))^(2)-75=45-75=30\neq 0$

$b=-3√(5): (-3√(5))^(2)-75=45-75=30\neq 0$

$b=25√(3): (25√(3))^(2)-75=1875-75=1800\neq 0$

$b=-25√(3): (-25√(3))^(2)-75=1875-75=1800\neq 0$

hence, only first two values $b=5√(3),-5√(3)$ gives the value of f(b)=0 .

⇒ $b=5√(3)$ and $b=-5√(3)$ are the roots of given quadratic equation.

Which equation represents the line that passes through the points (-3, 7) and (3, 3)?

Answers

Answer: y = 2/3 (x + 3) +7

Step-by-step explanation:

1. Find the slope

Slope is found by the change in y over the change of x.

(7-3)/(3--3)

2. Evaluate

4/6

3. Simplify

2/3

4. Find a point to use in the equation, so you can write the equation in point, slope form. For this problem, I have chosen the provided point, (-3, 7)

Point slope form: y = m(x - x1) + y1

5. Plug the point into the equation

y = 2/3 (x + 3) +7

A ceramic artist can shape a pot in 3 minutes. It takes 10 minutes to fire one batch of pots in the kiln. If there are p pots in a batch, which expression represents the time it takes to shape and fire one batch of pots? How long will it take the potter to form and fire a batch of 10 pots?

Answers

Answer:

t = 40 minutes for p = 10 pots

Step-by-step explanation:

given p pots in a batch.

Let t = time it takes to finish a pot

t = 3*p + 10

so if p = 10 pots,

t = 3*10 + 10 = 30 + 10 = 40 minutes

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