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3 years ago

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Mel wants to buy a pair of shoes that costs $120. She has saved $45 and has a job that pays her $10 per hour. The number of hour

s she has to work to have enough to buy the shoes is given by the inequality 10x + 45 > 120, where x is the number of hours she works.

2 answers:

adelina 88 [10]3 years ago

8 0

Answer:

The solution for the inequality is x = (7.5,∞).

Mel needs to work more than 7.5 hours to buy a pair of shoes that costs $120.

Step-by-step explanation:

10x + 45 > 120<em> //substract 45 in both sides of the inequality.</em>

10x + 45 - 45 > 120 - 45

10x > 75

(10/10)x > 75/10<em> //divide by 10 both sides of the inequality.</em>

x > 7.5

iren2701 [21]3 years ago

7 0

120-45=75
10*8=80
80+45=125
so the answer would be 8

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NO LINKS!! Please help me with these graphs

Stella [2.4K]

Answer:

square: 9 square units
triangle: 24 square units

Step-by-step explanation:

Using a suitable formula the area of a polygon can be computed from the coordinates of its vertices. You want the areas of the given square and triangle.

<h3>Square</h3>

The spreadsheet in the first attachment uses a formula for the area based on the given vertices. It computes half the absolute value of the sum of products of the x-coordinate and the difference of y-coordinates of the next and previous points going around the figure.

For this figure, going to that trouble isn't needed, as a graph quickly reveals the figure to be a 3×3 square.

The area of the square is 9 square units.

<h3>Triangle</h3>

The same formula can be applied to the coordinates of the vertices of a triangle. The spreadsheet in the second attachment calculates the area of the 8×6 triangle.

The area of the triangle is 24 square units.

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<em>Additional comment</em>

We have called the triangle an "8×6 triangle." The intention here is to note that it has a base of 8 units and a height of 6 units. Its area is half that of a rectangle with the same dimensions. These dimensions are readily observed in the graph of the vertices.

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1 year ago

a fruit delivers its fruit in two types of boxes: large and small. a delivery of 3 large boxes and 5 small boxes has a total wei

Masteriza [31]

Answer:

The weight of a small box = 13.5 kg

The weight of 1 large box = 18.5 kg

Step-by-step explanation:

Let us assume the weight of a small box = m kg

And the weight of 1 large box = n kg

Now, the weight of 5 small box = 5 x (weight of 1 small box) = 5 m

Also, the weight of 3 large box = 3 x (weight of 1 large box) = 3 n

Here, 3 large boxes + 5 small boxes = of 123 kilograms

⇒ 5 m + 3 n = 123 .... (1)

Again, the weight of 2 small box = 2 x (weight of 1 small box) = 2 m

Also, the weight of 12 large box = 12 x (weight of 1 large box) = 12 n

Here, 12 large boxes + 2 small boxes = 249 kilograms

⇒ 2 m+ 12 n = 249 .... (2)

Now, solving both the given equations by ELIMINATION, we get:

5 m + 3 n = 123 x (2)

2 m+ 12 n = 249 x (-5)

we get the new set of equitation as:

10 m + 6 n = 246

- 10 m - 60 n = -1245

Adding both equation, we get

-54 n = 999

or, n = 18.5

Now, 5 m + 3 n = 123

So, 5 m = 123 -3 (18.5) = 123 - 55.5 = 67.5

⇒ m = 13.5

Hence, the weight of a small box = m kg = 13.5 kg

And the weight of 1 large box = n kg = 18.5 kg

8 0

3 years ago

Martine’s town is building a volleyball court based on a scale drawing that is 40cm to 80cm and uses the scale 1cm:22.5cm write

never [62]

Answer:

$y=22.5x$

Step-by-step explanation:

we have that

The scale drawing is

$\frac{1}{22.5}\frac{cm}{cm}$

we know that

Using proportion find out the actual dimensions of the volleyball court

Let

x -----> drawing court lengths in cm

y ----> court lengths in cm

For x=40 cm

$\frac{1}{22.5}\frac{cm}{cm}=\frac{40}{y}\frac{cm}{cm}\\\\y=40*22.5\\\\y=900\ cm$

For x=80 cm

$\frac{1}{22.5}\frac{cm}{cm}=\frac{80}{y}\frac{cm}{cm}\\\\y=80*22.5\\\\y=1,800\ cm$

Find the equation for the proportional relation ship between drawing court lengths x in centimeters and court lengths in y centimeters

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

For x=40 cm, y=900

substitute

$k=y/x$ -----> $k=900/40=22.5$

The equation is

$y=22.5x$

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3 years ago

Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new hou

Musya8 [376]

The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;

(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

(2) The longest installable sprinkler system is approximately 172.4 feet

<h3>How can the points where the line crosses the farmland be found?</h3>

1. The slope of the sewer line is found as follows;

m = (6 - 3)/(12 - 2) = 3/10 = 0.3

The equation of the sewer line can be expressed in point and slope form as follows;

(y - 3) = 0.3×(x - 2)

y = 0.3•x - 0.6 + 3

y = 0.3•x + 2.4

The equation of the circumference of the sprinkler can be expressed as follows;

(x - 8)² + (y - 3)² = 2²

Therefore;

(x - 8)² + (0.3•x + 2.4 - 3)² = 2²

Solving gives;

x= 6.53, or x = 8.48

y = 0.3×6.53 + 2.4 = 4.36

y = 0.3×8.48 + 2.4 = 4.9

Therefore;

The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

2. When the farmland does not cross the sewer line, we have;

sewer line is tangent to circumference of farmland

Slope of radial line from center of the land is therefore;

m1 = -1/0.3

Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;

y - 3 = (-1/0.3)×(x - 8)

Which gives;

y = (-1/0.3)×(x - 8) + 3

The x-coordinate is therefore;

0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3

x ≈ 7.5

y = 0.3 × 7.5 + 2.4 ≈ 4.65

The longest sprinkler system is therefore;

d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724

Which gives;

The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.

Learn more about the equation of a circle here:

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3 0

2 years ago

The phenomenon of bottle flipping has hit the nation. You design a machine that can randomly flip a bottle. You observe 2180 ran

krek1111 [17]

Answer:

The variable of interest is the proportion of flips that land the correct way when flipped randomly.

The necessary conditions $n\pi \geq 10$ and $n(1-\pi) \geq 10$ are present.

The 98% confidence interval for the overall proportion of bottles that land correctly when flipped randomly is (0.131, 0.167).

Step-by-step explanation:

Variable of Interest:

Proportion of flips that land the correct way when flipped randomly.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Necessary conditions:

The necessary conditions are:

$n\pi \geq 10$

$n(1-\pi) \geq 10$

You observe 2180 random, independent flips, and 325 land the correct way.

This means that $n = 2180, \pi = \frac{325}{2180} = 0.149$

Necessary conditions

$n\pi = 2180*0.149 = 325 \geq 10$

$n(1-\pi) = 2180*0.851 = 1855 \geq 10$

The necessary conditions $n\pi \geq 10$ and $n(1-\pi) \geq 10$ are present.

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.33$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 2.33\sqrt{\frac{0.149*0.851}{2180}} = 0.131$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 + 2.33\sqrt{\frac{0.149*0.851}{2180}} = 0.167$

The 98% confidence interval for the overall proportion of bottles that land correctly when flipped randomly is (0.131, 0.167).

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3 years ago