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romanna [79]
3 years ago
9

How do I solve this properly?

Mathematics
1 answer:
o-na [289]3 years ago
6 0

Answer:

x \geq 4

Step-by-step explanation:

4x^2 - 64 \geq 0 ; move 64 over

4x^2 \geq 64 ; divide by 4

x^2 \geq 16 ; take square root of both sides

x \geq 4

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In a certain neighborhood, there's a sagging power line between two utility poles. The utility poles are 50 feet tall and 120 fe
e-lub [12.9K]
<h3>Answer:  33.75 feet</h3>

In fraction form, this value is equal to 135/4

33.75 ft is equivalent to 33 ft, 9 inches.

===============================================

Explanation:

Refer to the diagram below.

The key point to start with is point H, which is the vertex of the parabola.

Recall that vertex form is

y = a(x-h)^2 + k

What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.

So,

y = a(x-h)^2 + k

y = a(x-60)^2 + 30 .... plug in vertex

45 = a(0-60)^2 + 30 .... plug in y intercept coordinates

45 = a(-60)^2 + 30

45 = a(3600) + 30

45 = 3600a + 30

45-30 = 3600a

3600a = 15

a = 15/3600

a = 1/240

This then means:

y = a(x-h)^2 + k

y = (1/240)(x-60)^2 + 30

This is the equation of our parabola. Plug in x = 30 to determine the height of point K

y = (1/240)(x-60)^2 + 30

y = (1/240)(30-60)^2 + 30

y = (1/240)(-30)^2 + 30

y = (1/240)(900) + 30

y = 15/4 + 30

y = 15/4 + 120/4

y = 135/4

y = 33.75

Therefore, the height of the power line, when it is 30 feet away from one of the poles, is 33.75 feet. This is the y coordinate of point K.

Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches

8 0
2 years ago
Simplify the rational expression. state any restrictions on the variable. n^4-11n^2+30/n^4-7n^2+10
Andrej [43]
<span>For this case we have the following expression:
</span> \frac{n ^ 4-11n ^ 2 + 30}{ n ^ 4-7n ^ 2 + 10} &#10;&#10;
<span> We are going to make the following change of variables:
 </span>x = n ^ 2&#10;
 <span>Rewriting the expression we have:
 </span>\frac{(x ^ 2-11x + 30)}{(x ^ 2-7x + 10)} &#10;&#10;
 <span>Factoring the expression we have:
 </span>\frac{(x-5) (x-6)}{(x-5) (x-6)} &#10;
 <span>Canceling similar terms we have:
 </span>\frac{x-6}{x-2} &#10;
 <span>Returning the change we have:
 </span>\frac{n ^ 2-6}{n ^ 2-2} &#10;&#10;
<span> The resctrictions of the function are those that make the denominator equal to zero.
 We have then:
 </span>n ^ 2-2 = 0&#10;&#10;n = +/-  \sqrt{2} &#10;
<span> Answer:
 The simplified expression is:
 </span>\frac{n ^ 2-6}{n ^ 2-2}
 <span>The restrictions are:
 </span>n = \sqrt{2} &#10;
 n = -  \sqrt{2}
7 0
3 years ago
Evaluate ab - c. If a = 5, b = 3, and c = 4
irina1246 [14]
The answer is 11 The answer is 11 The answer is 11
5 0
2 years ago
Read 2 more answers
Which of the following fractions has the same value as the decimal number 0.65?
boyakko [2]

Answer:

13/20

Step-by-step explanation:

To find this, divide 13 by 20 to get .65

Hope this helped!

4 0
3 years ago
a mailing tube in the shape of cylinder has a height of 24 inches and a radius of 3 inches. what is the volume, in cubic inches,
TiliK225 [7]

ANSWER

The volume of the mailing tube is 678.6 square inches to the nearest tenth.

EXPLANATION

The volume of a cylinder is calculated using the formula;

V=\pi \:  {r}^{2} h

Since the mailing tube is in the form of a cylinder, we use this formula to find its volume.

We substitute h=24 and r=3 to obtain,

V=\pi \times {3}^{2} \times 24

V=216\pi  {in}^{2}

V=678.6{in}^{2}

8 0
3 years ago
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