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3 years ago

Gwen used elimination with multiplication to solve the system:

1 answer:

8 0

The correct answer for this question is this one:

Gwen used elimination with multiplication to solve the system:
2x + 6y = 3
x − 3y = −5

Her work to find x is shown. Complete the explanation of her error. Then solve the system. If necessary, enter your answer as a reduced fraction.
2(x − 3y) = −5 --> 2(x-3y) = 2(-5)
2x − 6y = −5 --> 2x - 6y = -10
2x + 6y = 3 --> 2x + 6y = 3
2x − 6y = −5 --> 2x - 6y = -10
4x + 0y = −2 --> 4x = -7
x = −2/4 --> x = -7/4

x - 3y = -5
4(-7/4 - 3y = -5)
-7 - 12y = -20
-12y = -13
y = 12/13

Gwen forgot to multiply the right side by 2.
What is the solution as an ordered pair

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Snow Dome Ski Resort has 75 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resor

Nastasia [14]

Answer:

a. See explanation for table

b. The 7th hour

Step-by-step explanation:

Given

Ski Resort

$Base\ Snow = 75in$

$Rate = 1in$ hourly

Mt. Winterpark

$Base\ Snow = 68in$

$Rate = 2in$ hourly

First, we need to illustrate the amount of snow as an equation in both cases.

$Amount = Base\ Snow + Rate * Time$

Let x be number of hours. and y be the amount of snow

So:

Ski Resort

$y= 75 + 1* x$

$y= 75 + x$

Mt. Winterpark

$y= 68 + 2 * x$

$y= 68 + 2x$

Next, we make a table to show the data.

When $x = 0$

Ski Resort: $y = 75 + 0 = 75$

Mt. Winterpark: $y = 68 + 2(0) = 68$

When $x = 1$

Ski Resort: $y = 75 + 1 = 76$

Mt. Winterpark: $y = 68 + 2(1) = 70$

When $x = 2$

Ski Resort: $y = 75 + 2 = 77$

Mt. Winterpark: $y = 68 + 2(2) = 72$

When $x = 3$

Ski Resort: $y = 75 + 3 = 78$

Mt. Winterpark: $y = 68 + 2(3) = 74$

When $x = 4$

Ski Resort: $y = 75 + 4 = 79$

Mt. Winterpark: $y = 68 + 2(4) = 76$

When $x = 5$

Ski Resort: $y = 75 + 5 = 80$

Mt. Winterpark: $y = 68 + 2(5) = 78$

When $x = 6$

Ski Resort: $y = 75 + 6 = 81$

Mt. Winterpark: $y = 68 + 2(6) = 80$

When $x = 7$

Ski Resort: $y = 75 + 7 = 82$

Mt. Winterpark: $y = 68 + 2(7) = 82$

When $x = 8$

Ski Resort: $y = 75 + 8 = 83$

Mt. Winterpark: $y = 68 + 2(8) = 84$

When $x = 9$

Ski Resort: $y = 75 + 9 = 84$

Mt. Winterpark: $y = 68 + 2(9) = 86$

When $x = 10$

Ski Resort: $y = 75 + 10 = 85$

Mt. Winterpark: $y = 68 + 2(10) = 88$

Hence, the table is:

x ---- Ski Resort ---- Mt. Winterpark

0 --------75 ----------- 68

1 --------76 ----------- 70

2 --------77 ----------- 72

3 --------78 ----------- 74

4 --------79 ----------- 76

5 --------80 ----------- 78

6 --------81 ----------- 80

7 --------82 ----------- 82

8 --------83 ----------- 84

9 --------84 ----------- 86

10 -------85 ----------- 88

(b)

From the table, the amount of snow is the same at the 7th hour and the snow is 82 inches

4 0

3 years ago

Harry earns 5% commission on his total sales. What was his commission if he had sales of $9,250?

Cerrena [4.2K]

5% as a decimal is = 0.05
then 9250 times 0.05 = 462.50
so Harry's commission was $462.50

3 0

3 years ago

A point P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t

Ivan

Answer:

sin t = $\frac{3}{5}$

cos t = $-\frac{4}{5}$

tan t = $-\frac{3}{4}$

csc t = $\frac{5}{3}$

sec t = $-\frac{5}{4}$

cot t = $-\frac{4}{3}$

Step-by-step explanation:

In the unit circle:

x-coordinate of a point on the circle represents cosine the angle between the + ve part of x-axis and the terminal side which joins the center of the circle and this point
y-coordinate of a point on the circle represents sine the angle between + ve part of x-axis and the terminal side which joins the center of the circle and this point

In the attached figure

∵ t represents the angle between + ve part of x-axis

and the terminal side drawn from the center of the circle to

point P

∴ The coordinates of point P are (cos t , sin t)

∵ The coordinates of P are ( $-\frac{4}{5}$ , $\frac{3}{5}$ )

∴ sin t = $\frac{3}{5}$

∴ cos t = $-\frac{4}{5}$

∵ tan t = $\frac{sin(t)}{cos(t)}$