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to find the height of a pole, a surveyor moves 120 feet away from the base of the pole and then, with a transit of 8 feet tall, measures the angle of elevation to the top of the pole to be 36°. to the nearest foot, what is the height of the pole?


a. 87 feet
b. 95 feet
c. 71 feet
d. 79 feet

The key idea of the transformation called a rotation is moving a plane a specified Distance about a fixed Point

The value of cos of angle x of the dilated triangle would be exactly the same as in the first triangle cos (8/17).

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1)

The cosine ratio is a ratio of the two sides.

We have been given If the cos of angle x is 8/17 and the triangle was displayed to be two times big as the original.

In the first triangle, the ratio is 8/17.

In the second triangle, the ratio is 16/34.

The second triangle could be reduced back to 8/17 which produces the same cosine value.

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Answer:

correct answer 3x – 11 + 60/x+5

Step-by-step explanation:

Answer:

Melting points are determined by how much the molecules in the compound interact with the other molecules in the compound. Those that have many interactions with the other molecules have higher melting points.  

Of those listed, Ionic bonds have the most rigid interactions with other molecules so have the higher melting points.

For a better understanding of the solution provided here please go through the graph in the attachment. Please note that the solution provided here will be an approximate solution.

In the graph, the x axis is the number of months. 1 is January, 2 is February, so on and so forth.

The y axis is the expected number of daylight hours in those months. Each point has been depicted in the graph as shown.

Now, when we look at the graph we notice a pattern. The graph is nearly a cosine graph. Thus the equation that will best model the data will be an equation of the cosine form and will look like:

[tex] y=A cos(\omega t)+B [/tex]

where symbols have their usual meanings.

Let us find each term now:

We know that in December, the expected number of daylight hours is 9.25 hours. Thus, let us assume that the expected number of daylight hours in previous December was 9.25 hours too.

With this assumption let us proceed.

Amplitude=[tex] \frac{Highest - Lowest}{2} =\frac{15-9.25}{2} =2.875 [/tex]

The Vertical Shift Up is B=[tex] \frac{9.25+15}{2} = 12.125[/tex]

Also, the frequency can be calculated as: [tex] \omega=\frac{2\pi}{Period}= \frac{2\pi}{12}=\frac{\pi}{6} [/tex]

Thus, plugging in all the values, the final equation will be:

[tex] y=-2.875cos(\frac{\pi}{6}t)+12.125 [/tex]....(Equation 1)

The negative value of A suggests that the function starts below the horizontal y=12.125 line.

The above is the (Equation 1) that best models the given data.

Now, to find the expected number of daylight hours in March 2020, we just have to find the value of the time, t from January 2015 to March 2020.

Now, we know that each year has 12 months. So, 5 years from start of 2015 to end of 2019 will have 12 x 5=60 months. We need to add to this the first three months of the year 2020 to take us till March 2020. Thus, the value of t from January 2015 to March 2020 is 63.

Now, let us use the (Equation 1) to find the value of expected number of daylight in March 2020 by plugging in t=63 in it.

Thus,

Expected number of daylight in March 2020 is:

[tex] y=-2.875cos(\frac{\pi}{6}\times 63)+12.125 [/tex]

[tex] \therefore y=12.125 [/tex] hours.

Answer:

Step-by-step explanation:Close to 60 times but probably not exactly 60 times

Answer:

the answer is 24

Answer:

Its important because history repeats its self. some jobs won't be available in 5-10 years due to advance in technology, or a job that is fruitful/ profitable in one year may be completely dead and dry in the next.

Step-by-step explanation:

Answer:

B. 4.9%.

Step-by-step explanation:

We have been given that the assessed value of property in Enterprise County is $196,000,000. The county supervisors feel the county needs $9,525,000 in revenue.

To find the tax rate we need to find $9,525,000 is what percent of $196,000,000.

[tex]\text{Tax rate}=\frac{\$9,525,000}{\$196,000,000}\times 100[/tex]

[tex]\text{Tax rate}=0.0485969387755102\times 100[/tex]

[tex]\text{Tax rate}=4.85969387755102\%[/tex]

Upon rounding our answer to nearest tenth of percent we will get,

[tex]\text{Tax rate}\approx 4.9\%[/tex]

Therefore, the tax rate is 4.9% and option B is the correct choice.

Answer:

hope this helps :)

Cost of a pretzel is equals to $2.25.

" A system of equations is a finite set of equations for which we find the common solution."

According to the question,

'x' represents the cost of  pretzel

'y' represents the cost of lemonade

As per situation given system of equation are,

Situation1: The total cost of two pretzels and a lemonade is $5.75, which can be represented by equation:

[tex]2x + y = \$5.75[/tex]                              ____(1)

Situation2: The total cost of two lemonades is $0.25 more than the cost of a pretzel, which can be represented by equation:

[tex]2y = 0.25 +x[/tex]                                _____(2)

Multiply equation (1) by 2 we get,

[tex]4x + 2y = \$11.5[/tex]                              ______(3)

Substitute the value of 2y from (2) in (3) to get the cost of pretzel,

[tex]4x + 0.25 +x = \$11.5[/tex]

⇒ [tex]5x = 11.5 - 0.25[/tex]

⇒ [tex]5x = 11.25[/tex]

⇒ [tex]x =\frac{11.25}{5}[/tex]

⇒[tex]x=\$2.25[/tex]

Hence, cost of a pretzel is equals to $2.25.

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Let us suppose cost of 1 watermelon be x.

Cost of 6 watermelons = 6x.

It is given after buying 6 watermelons, he had $25.50 left.Total amount William spends on vegetable is $45.

We can form an equation with above information's

6x+25.50=45

To solve for x we isolate the x term .25.50 is added to the x term .

Opposite of addition is subtraction .Subtracting 25.50 both sides we have:

6x=45-25.50

6x=19.50

Dividing both sides by 6

x=3.25.

Cost of each watermelon is $3.25.

Answer:

B. f(x) = 7000x + 4000

Step-by-step explanation:

To find the best function for this situation, we need to list down all the things that we know first.

We currently have:

35000 total seats

4000 fans

11000 fans after an hour

So that means that after an hour, we had:

11000 fans - 4000 fans = 7000 fans

At one o'clock we had 7000 more fans arrive.

So we can assume that:

x = number of hours

f(x) = 7000x + 4000 will be the best function to use to find out if there that 90% of the stadium will be filled by game time.

To test this function let's use it:

f(1) = 7000(1) + 4000

f(1) = 11000

This is after hour 1.

Now let's see after hour 4 since the game starts at 4.

f(4) = 7000(4) + 4000

f(4) = 28000 + 4000

f(4) = 32000

So 90% of 35000 is:

35000 x 0.90 = 31500

By game time we have 32000 fans which is above 90% of the total number of seats.

So the stadium owners estimate is correct.