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Keith_Richards [23]
2 years ago
6

Zack wants to make a profit of more than $300 for painting 4 identical rooms. The profit he makes is equal to the amount he is p

aid minus the cost of supplies. The cost of supplies is $32.50 for each room. Which inequality and solution represent the dollar amount, n, that zack must be paid for each room if he is to make a profit of more than 300$
A: n-4(32.5) > 300;n > 430
B: (n - 32.5) > 1,200; n > 332.5
C. (n-32.5)>300;n> 107.5
D 4n-32.5 > 300; n > 83.125
Mathematics
2 answers:
lianna [129]2 years ago
6 0

Answer: A

n-4(32.5) > 300;n > 430tep-by-step explanation:

given that Zack wants to make a profit of more than $300 for painting 4 identical rooms. That is

Profit > $300

Then, the profit he makes is equal to the amount he is paid minus the cost of supplies. The cost of supplies is $32.50 for each room. That is

n - 32.5 and

P + 32.5 × 4

Where 4 = number of rooms

P + 130

The minimum profit = 300 + 130 = $430

Therefore, the inequality and solution that represent the dollar amount, n, that zack must be paid for each room if he is to make a profit of more than 300$ is

n-4(32.5) > 300;n > 430

IgorC [24]2 years ago
5 0

Answer:

Step-by-step explanation:

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- In the following diagram of triangle QRS, QR = 8 and QS = 17. Determine the value of sin Q. Show how you
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Answer:

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Step-by-step explanation:

We draw the right triangle as shown in the image attached.

Δ QRS

Where R is the right angle

Given

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QS = 17

Now, using Pythagorean Theorem, we can find RS:

QR^2+RS^2=QS^2\\8^2+RS^2=17^2\\RS^2=17^2-8^2\\RS^2=225\\RS=\sqrt{225}\\RS=15

Now, we know the ratio Sine as:

Sin(\theta)=\frac{Opposite}{Hyotenuse}

Where \theta is the angle (here angle Q)

Opposite side is RS (which is 15)

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So,

SinQ=\frac{15}{17}

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2 years ago
Find the distance from (4, −7, 6) to each of the following.
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Answer:

(a) 6 units

(b) 4 units

(c) 7 units

(d) 9.22 units

(e) 7.21 units

(f) 8.06 units

Step-by-step explanation:

The distance d from one point (x₁, y₁, z₁) to another point (x₂, y₂, z₂) is given by;

d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Now from the question;

<em>(a) The distance from (4, -7, 6) to the xy-plane</em>

The xy-plane is the point where z is 0. i.e

xy-plane = (4, -7, 0).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(4, -7, 0)</em>

d = √[(4 - 4)² + (-7 - (-7))² + (0 - 6)²]

d = √[(0)² + (0)² + (-6)²]

d = √(-6)²

d = √36

d = 6

Hence, the distance to the xy plane is 6 units

<em>(b) The distance from (4, -7, 6) to the yz-plane</em>

The yz-plane is the point where x is 0. i.e

yz-plane = (0, -7, 6).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(0, -7, 6)</em>

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 6)²]

d = √[(4)² + (0)² + (0)²]

d = √(4)²

d = √16

d = 4

Hence, the distance to the yz plane is 4 units

<em>(c) The distance from (4, -7, 6) to the xz-plane</em>

The xz-plane is the point where y is 0. i.e

xz-plane = (4, 0, 6).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(4, 0, 6)</em>

d = √[(4 - 4)² + (-7 - 0)² + (6 - 6)²]

d = √[(0)² + (-7)² + (0)²]

d = √[(-7)²]

d = √49

d = 7

Hence, the distance to the xz plane is 7 units

<em>(d) The distance from (4, -7, 6) to the x axis</em>

The x axis is the point where y and z are 0. i.e

x-axis = (4, 0, 0).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(4, 0, 0)</em>

d = √[(4 - 4)² + (-7 - 0)² + (6 - 0)²]

d = √[(0)² + (-7)² + (6)²]

d = √[(-7)² + (6)²]

d = √[(49 + 36)]

d = √(85)

d = 9.22

Hence, the distance to the x axis is 9.22 units

<em>(e) The distance from (4, -7, 6) to the y axis</em>

The x axis is the point where x and z are 0. i.e

y-axis = (0, -7, 0).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(0, -7, 0)</em>

d = √[(4 - 0)² + (-7 - (-7))² + (6 - 0)²]

d = √[(4)² + (0)² + (6)²]

d = √[(4)² + (6)²]

d = √[(16 + 36)]

d = √(52)

d = 7.22

Hence, the distance to the y axis is 7.21 units

<em>(f) The distance from (4, -7, 6) to the z axis</em>

The z axis is the point where x and y are 0. i.e

z-axis = (0, 0, 6).

Therefore, the distance d is from <em>(4, -7, 6) </em> to <em>(0, 0 6)</em>

d = √[(4 - 0)² + (-7 - (0))² + (6 - 6)²]

d = √[(4)² + (-7)² + (0)²]

d = √[(4)² + (-7)²]

d = √[(16 + 49)]

d = √(65)

d = 8.06

Hence, the distance to the z axis is 8.06 units

5 0
2 years ago
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