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3 years ago

7

Two intersecting lines l and m form an angle of 56° with each other. The reflection of a point (–4, 1) along the line l followed

by a reflection along line m will cause a ________ rotation. Question 18 options: A) 56° B) 112° C) 180° D) 28°

1 answer:

Tasya [4]3 years ago

7 0

Answer:

B) 112°

Step-by-step explanation:

After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:

2·56° = 112°

_____

In the attached, lines l and m are separated by 56°, as required by the problem statement.

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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% p

Stolb23 [73]

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

Then we know that the total amount of mixture will be:

$A + B = 80$

Then the total amount of pure fruit juice in the mixture will be:

$0.55A + 0.8B = 0.65 * 80$

$0.55A + 0.8B = 52$

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

$-0.8A -0.8B = -0.8*80$

$-0.8A -0.8B = -64$

$-0.8A -0.8B = -64$

+

$0.55A + 0.8B = 52$

--------------------------------------

$-0.25A = -12$

$A = \frac{-12}{-0.25}$

$A = 48\ pints$

We substitute the value of A into one of the two equations and solve for B.

$48 + B = 80$

$B = 32\ pints$

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2 years ago

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Rzqust [24]

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3 years ago

Read 2 more answers

Use the graph to the right to write an equation of the line. What is the equation?

Bingel [31]

Answer:

y = 1/4 x - 2

Step-by-step explanation:

To write the equation of a line, find from the line the slope and y-intercept. The y-intercept is where the line crosses the y-axis which here is at point (0,-2).

The slope of the line is found by writing a ratio between the vertical distance and the horizontal distance between points.

Slope is 1/4.

Substitute m = 1/4 and b = -2 into the slope intercept form y = mx + b.

y = 1/4 x - 2

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2 years ago

Drag the tiles to the correct boxes to complete the palrs.

Brut [27]

Answer:

(f+g)(2) = 4

(f-g)(4) = 8

(f ÷g)(2) = 7

(f x g)(1) = 0

Step-by-step explanation:

We are given these following functions:

$f(x) = 2x + 3$

$g(x) = x - 1$

(f+g)(2)

$(f+g)(x) = f(x) + g(x) = 2x + 3 + x - 1 = 3x - 2$

At $x = 2$

$(f+g)(2) = 3(2) - 2 = 6 - 2 = 4$

Then

(f+g)(2) = 4

(f-g)(4)

$(f-g)(x) = f(x) - g(x) = 2x + 3 - (x - 1) = 2x + 3 - x + 1 = x + 4$

At x = 4

$(f-g)(4) = 4 + 4 = 8$

Then

(f-g)(4) = 8

(f ÷g)(2)

$(f \div g)(x) = \frac{f(x)}{g(x)} = \frac{2x+3}{x-1}$

At x = 2

$(f \div g)(2) = \frac{7}{1} = 7$

Then

(f ÷g)(2) = 7

(f x g)(1)

$(f \times g)(x) = f(x)g(x) = (2x+3)(x-1) = 2x^2 -2x + 3x - 3 = 2x^2 + x - 3$

Then

$(f \times g)(1) = 2(1)^2 + 1 - 3 = 3 + 1 - 3 = 0$

So

(f x g)(1) = 0

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2 years ago

Jorge bikes to school each day. If he can travel 33 miles in 11 hours, how fast does he travel in one

Eddi Din [679]

33 miles divided by 11 hours will give you the mile per hour traveled.

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