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scZoUnD [109]
3 years ago
13

Select the correct properties of slope below.

Mathematics
1 answer:
Alinara [238K]3 years ago
3 0
<span>A. Lines that go up from left to right should have a positive slope.
B. Lines that go down from left to right should have a negative slope.
</span><span>D. The slope of a steep line should be bigger than the slope of a flat line.
E. The slope of a steep line should be smaller than the slope of a flat line.</span>
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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
Wanni cycled 6 km from her house to the school at a uniform speed, v km/h. If she increased her speed
Karolina [17]

Answer:

The quadratic equation in terms of v is   v² + 2 v + 180 = 0

Step-by-step explanation:

Given as :

The distance between house to the school = d = 6 km

The uniform speed = v km/h

So, Time = \dfrac{\textrm Distance}{\textrm speed}

or, t = \dfrac{\textrm d}{\textrm v}

Or, t = \dfrac{\textrm 6}{\textrm v}

<u>Now, Again</u>

The speed is increase by 2 km/h

i.e speed = (v + 2) km/h

So, Time taken = t' = (t - \dfrac{4}{60})hours

i.e t' =  (t - \dfrac{1}{15})hours

Now, Time = \dfrac{\textrm Distance}{\textrm speed}

So, (t - \dfrac{1}{15}) = \dfrac{\textrm d}{\textrm v}

Or,  (t - \dfrac{1}{15}) = \dfrac{\textrm 6}{\textrm (v + 2)}

Or , \dfrac{\textrm 6}{\textrm v} -  \dfrac{1}{15} = \dfrac{\textrm 6}{\textrm (v + 2)}

Or , \dfrac{\textrm 90 - v}{\textrm 15 v} = \dfrac{\textrm 6}{\textrm v + 2}

Or, (90 - v) × (v + 2) = 6 × 15 v

Or, 90 v - 180 - v² - 2 v = 90 v

Or,  v² + 2 v + 180 = 90 v - 90 v

Or,  v² + 2 v + 180 = 0

So, The quadratic equation in terms of v

v² + 2 v + 180 = 0

Hence The quadratic equation in terms of v is   v² + 2 v + 180 = 0   Answer

3 0
3 years ago
A quantity with an initial value of 160 grows continuously at a rate of 0.65% per hour.
dangina [55]

Answer:

167.10

Step-by-step explanation:

Here, we write out the general form for an exponential equation;

y = I (1 + r)^n

where y is the current value which we want to calculate

I is the initial value which is 160

r is the growth rate = 0.65% = 0.65/100 = 0.0065

402 minutes to hours will be 402/60 = 6.7 hours which is n

Substituting these values, we have

y = 160( 1 + 0.0065)^6.7

y = 160(1.0065)^6.7

y = 167.10

6 0
3 years ago
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I NEED HELP ASAP!!! I'LL GIVE BRAINLIEST FOR THE CORRECT ANSWER!!!
ASHA 777 [7]

Answer:

-x 7

Step-by-step explanation:

6 0
3 years ago
A circle in the zy-Plane has a center at(3/4,1/2) and a radius that is 3/5 units long. which of the following is an equation of
Contact [7]

Answer:b

Step-by-step explanation:

4 0
3 years ago
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