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1 year ago

11

A building 190 feet tall casts a 90 foot long shadow. if a person stands at the end of the shadow and looks up to the top of the

building, what is the angle of the person's eyes to the top of the building

1 answer:

Ivahew [28]1 year ago

5 0

Answer:

About 64.65 degrees

Step-by-step explanation:

$\tan(x) = \frac{190}{90}$

$x = { \tan}^{ - 1} \frac{190}{90} = 64.65$

Make sure your calculator is in degree mode.

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How do I do numbers 1, 2 and 3

stiks02 [169]

What you want to do for each of those is follow the formula, y-y[1]=m(x-x[1]). When I say y[1] and x[1], I mean the x and y values given. So the first one would be y-4=-3(x-(-1)). Then you solve for y by distributing the -3 to x and +1 (+1 because two negatives make a positive), making the equation
y-4=-3x-3. Then you subtract the 4. Answer #1. y=-3x-7.

#2.
y-1=1(x-4)
y-1=x-4
y=x-5

#3.
y-2=2(x-(-1))
y-2=2x+2
y=2x+4

Hope this helped you!

8 0

2 years ago

Semi annually means how many times a year?

Pie

Biannual and semiannual can be used interchangeably; they both mean “twice a year<span>.” But biennial describes something that occurs every two </span>years<span>.

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8 0

2 years ago

Jonathan calls his mother 2 times every week.

Dima020 [189]

Answer:

2w=c 2 times each week so 2 times how many weeks

5 0

2 years ago

1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating

elixir [45]

The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.

<h3>The equation of the theatre's income</h3>

The theatre charges $4.50 per student.

Assume the number of students is x, the equation of the theatre's income would be:

I(x) = 4.5x

<h3>The equation of the theatre's expenses</h3>

The theatre expense per student is $1.25, and the operating cost on the staff is $130

The equation of the theatre's expenses would be:

E(x) = 1.25x + 130

<h3>Complete the table</h3>

Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:

Students, x 0 10 20 30 40 50 60 70

Income, I 0 45 90 135 180 225 270 315

Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5

<h3>The graph of the theatre's income and expenses</h3>

See attachment

<h3>The pattern by which theatre's income and expenses increase</h3>

The functions I(x) and E(x) are linear functions.

So, the pattern with which the functions increase is a linear pattern.

<h3>The number of students when the theatre's income and expenses are equal</h3>

This means that:

I(x) = E(x)

So, we have:

4.5x = 1.25x + 130

Subtract 1.25 from both sides

3.25x = 130

Divide both sides by 3.25

x = 40

Hence, the number of students is 40

<h3>The theatre profit</h3>

This is the difference between the theatre expenses and their income.

So, we have:

P(x) = E(x) - I(x)

This gives

P(x) = 1.25x + 130 - 4.5x

Simplify

P(x) = 130 - 3.25x

<h3>Solution to the inequalities</h3>

We have:

E(x) < 255

This gives

1.25x + 130 < 255

Subtract 130 from both sides and divide by 1.25

x < 100 students

Also, we have:

I(x) > 675

This gives

4.5x > 657

Solve for x

x > 146 students

Hence, the number of students for the inequalities are less than 100 and greater than 146

Read more about linear equations and inequalities at:

brainly.com/question/11234618

8 0

2 years ago

Find the sum of the first 90 terms of the sequence -4,-1,2,5,8

telo118 [61]

Answer:

1655

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ]

Here a₁ = - 4, d = 3 and n = 90, thus

$S_{90}$ = $\frac{90}{2}$ [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655

4 0

2 years ago