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Anettt [7]
2 years ago
13

Solve 5n -14≤11 *10 points*​

Mathematics
1 answer:
Sedbober [7]2 years ago
4 0

Answer:

n ≤ 5

Step-by-step explanation:

First, we add 14 to both sides. This gets us 5n ≤ 25. Next, we divide both sides by 5. This gets us n ≤ 5. I hope this helps!

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A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m². The surface area of the image is 315 m². T
Westkost [7]

The original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

<h3>How does dilation affect length, area, and volume of an object?</h3>

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k.

So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

<u><em>L = k × M</em></u>

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by <u><em>k²</em></u><em> </em>to get each other corresponding quantity from their similar figures' quantities.

<u><em>So </em></u><u><em>area </em></u><u><em>of </em></u><u><em>first figure </em></u><u><em>= k² × area of second figure</em></u>

Similarly,

<u><em>Volume </em></u><u><em>of first figure = k³ × volume of second figure.</em></u>

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

For this case, we're given that;

  • Surface area of pre-image = 35 m²
  • Surface area of dilated image = 315 m²
  • Height of pre-image = 5.8 m
  • Height of dilated image.

Let the scale fator of dilation be k.

Then:

<u><em>So area of pre-image = k² × area of dilated image</em></u>

Thus, we get:

35 = k^2 \times 315\\\\k = \sqrt{\dfrac{35}{315}} = 1/3

(took positive root as scaling is done by non-negative factors as only magnitude matters mostly)

Thus, we get:

Height of pre-image = (1/3) × Height of dilated image (say h)

5.8 = (1/3) \times h\\h = 3 \times 5.8 = 17.4 \rm \: m

Thus, the original object is called pre-image, and its dilated version is called image. The height of the image for the considered case is 17.4 m

Learn more about dilation here:

brainly.com/question/3266920

4 0
2 years ago
Read 2 more answers
3^2∙3^n simplifies to 3^20
yan [13]
2*3=6
6*3.33=20
3^20
i hope that helps
4 0
2 years ago
Which function is nonlinear?
lutik1710 [3]

Answer:

(-1,5), (0,4) ,(1,3) ,(3,1) is linear so dont pick it

(-4,-7), (-2,-6), (2,-4), (4,-3) is linear

you know what I'll just say it wait a minute is there like a other option

Step-by-step explanation:

U can tell by graphing them out yourself and if u see a straight line then it linear, and if you see a curved loop then it's non- linear. but I'll do it :)

4 0
3 years ago
a company is offering a job with a salary of $30,000 for the first year and a 5% raise each year after that. if the 5% raise con
Ber [7]
<span>First year is 30,000.
</span><span>Earn 5% raise every year.
</span>Growth factor is 1.05 this sounds a lot like a geometric ratio.

An = A1 × r^(n-1)Sn = A1 × (1 - r^n) / (1-r)<span>n = 40
A1 = 30,000
A40 = $30,000 * 1.05^39 = $201,142.53

S40 = A1 * (1 - 1.05^40) / (1-1.05) which becomes:
S40 = 30,000 * -6.039988712 / -.05 which becomes: 
</span>S40 = -181,199.6614 / -.05 which becomes:
S40 = $3,623,993.227

<span>The individual yearly calculations are shown below: </span>

8 0
3 years ago
How do I find the measurements of this triangle
Rudik [331]
Using sine law: 

9/sinc = 15/sin22 

sinc = 9sin22 / 15 = 0.225 

so c = sin^-1(0.225) = 12.99 degrees ~~ 13 degrees

if B was required:

B = 180  - C - A ~~  145 

8 0
2 years ago
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