A person standing 306 feet from the base of a church observed the angle of elevation to the church’s steeple to be 20°. How tall is the church. Give answer to the nearest whole number

All the x-values that satisfy the function - Domain

Translating the sine or cosine curve up or down - Vertical shift

How long a given function takes to repeat itself - Period.

A horizontal shift of a sine or cosine function- Phase shift

All the y-values that satisfy the function- Range

Distance from the horizontal axis or midline to the maximum and minimum points - Amplitude

Currently

Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.

In 5 years

Amy's age will be (x + 5) years.

Dianne's age will be:

The sum of their ages in 5 years is 91. Therefore, we have:

Solving, we have:

Amy is 29 years old. Therefore, Dianne will be:

ANSWER:

Amy is 29 years old, and Dianne is 52 years old.

Solution:

Let the total field to plow be 100 %

According to the question,

The field plowed before lunch is shown below:

15 acres field = 30%

30 % field = 15 acres

1 % field = 15/30 acres

The field plow after lunch is 70%.

Final Answer:

Therefore, the field to plow after lunch in order to finish the field is 35 acres.

1. slope= 2

2. slope=2

3. slope= 1/3

4. slope indefinite, vertical line

Explanation

Step 1

the equation is given in slope(m) - intercept(b)

Step 2

when you have two points of a line, P1 and P2 the slope is given by:

Let

P1(-2,-4) P2(-1,-2)

replace

Step 3

similar to the #1. ,the equation is given in slope(m) - intercept(b)

Step 4

let

Answer:

Step-by-step explanation:

If each value of x only has one corresponding value of y, it is a function. You can test this just by eye or by graphing and doing the vertical line test by rolling a pencil or other straight object across to make sure only one point is on the line at a time

Step-by-step explanation:

it is an equilateral triangle : all 3 sides are if equal length (indicated by the same symbol on each side).

automatically with that comes the conclusion that all 3 angles have the same size.

and since the sum of all angles in a triangle is always 180°, this means every angle is 180/3 = 60°.

therefore,

2x - 4 = 60

2x = 64

x = 32

and FYI

5y = 60

y = 12

Solution:

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. According to this, the correct answer is:

C.

Given:

The ship is moved from (-10,9) to (-1,-5) in the coordinate plane.

To find:

The transformation rule

Explanation:

The initial point can be written to obtain the terminal point as follow,

In general,

We write,

Final answer: Option C.

Step-by-step explanation:

since M is the midpoint, it means that AM = MB.

so,

b² + 5b = 3b + 35

b² + 2b - 35 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case (x is called b, don't get confused, as this is not the factor of x) this gives us

b = (-2 ± sqrt(2² - 4×1×-35))/(2×1) =

= (-2 ± sqrt(4 + 140))/2 = (-2 ± sqrt(144))/2 =

= (-2 ± 12)/2 = -1 ± 6

b1 = -1 + 6 = 5

b2 = -1 - 6 = -7

therefore, we have 2 solutions

b = 5

AM = 5² + 5×5 = 25 + 25 = 50

b = -7

AM = (-7)² + 5×-7 = 49 - 35 = 14

control, as AM = MB

MB = 3×5 + 35 = 15 + 35 = 50

or

MB = 3×-7 + 35 = -21 + 35 = 14

AM = MB in both cases, so, all is correct.

Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.

81 km=9 liters

9 km= 1 liter

She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.

By unitary method,

22 liters = 22 × 9 km

              = 198 km

Also, given that  if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.

We need to find the amount of fuel she would need.

Let 139.4 km = x liters

By unitary method,

x = 139.4 / 9

x = 15.5 liters

Therefore, Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

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Question:

Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.​

Solution:

A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:

In this case, the appropriate trigonometric identity is:

where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:

and solving for h, we get:

then, the correct answer is:

1) The best way to tackle questions like this is to locate the x-intercepts. Since according to the options the leading coefficient is 1, we just need to locate the zeroes and plug them into the quadratic equation form, in its factored form.

2) So now, let's write out the factored form and plug the zeroes into them:

Answer: 82 R1 or decimal form 82.031

Step-by-step explanation:

0082

. --------

-0

26

. - 0

. 262

. -256

65

-64

. 1

One can decide which rational number operations to use to solve problems based on the context of the information.

Studying rational numbers is significant because they illustrate how the world is so complex that we will never be able to comprehend it.

A rational number is defined as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer and 3/7, for example, are rational numbers.

A rational number is defined as the quotient of the fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number since q might be equal to 1.

In this case, the operation include addition, subtraction, division, etc. This will be based on the context.

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Let

x -----> the missing number

we know that

80%=80/100=0.80

so

0.80x=20

solve the linear equation for x

Divide by 0.80 both sides

x=20/0.80

x=25

the answer is 25

We need to solve the next expressions:

17. 19yd. 28in.- 16yd. 31in

We need to solve subtract each expression.

Then:

19yd. 28in.- 16yd. 31in =

19yd - 16yd and 28in-31in

3yd -3in

Then, we have the next equivalent.

1 yard = 36 in

So:

36 in - 3 in = 33 in

Therefore

19yd. 28in.- 16yd. 31in = 2 yard 33

18 61wk. 4da.- 18wk. 6da.

We need to subtract both expression:

Then

61wk - 18wk = 43kw

4da-6da = -2da

Where 1 week = 7 days

Then

7 da - 2da = 5 da

Hence, 43kw -1 wk = 42 wk.

The result is:

42 wk 5 da

21. 8tbsp. 2tsp. * 15

We need to convert 2ts into tbsp and then multiply the result by 15.

If

1 tsp ------- 0.333tbsp

Then

2tp ------ 2(0.333tbsp)= 0.66666 tbsp

Now

(8tbsp + 0.6666 ) * 15 = 130 tbsp

With each additional tree , the estimated time increases by 10 minutes .

in the question ,

a table with number of trees and time required to plant them is given .

For planting 1 tree 30 minutes is required to plant them .

for planting 2 trees 40 minutes is required to plant them .

increase in number of tree = 2 tree - 1 tree = 1 tree

change in time required = 40 min - 30 min = 10 min

for planting 3 trees , 50 minutes is required to plant them .

increase in number of tree = 3 trees - 2 trees = 1 tree

change in time required = 50 min - 40 min = 10 min

So, we can see that for every additional tree planted the time increases by 10 minutes .

Therefore , with each additional tree , the estimated time increases by 10 minutes .

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First, we graph the trapezoid and the line

If we reflect the figure across the line y = 1, then we get the following figure

As you can observe in the graph, the vertices would be J'(-4,-1), K'(-2,-5), L'(2,-5), and M'(3,-1).

The change of base formula states that:

this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.

In this case we have:

Then, using the change of base formula, we have:

Once we have the expression we just evaluate the expression on the right to get the appoximation we need:

Given two equations,

Comapring both equations,

Therefore, x = 1/3.

Constant of variation ( k ):

• y = 2/3

• x = 1/4

k = 8/3

Based on k we can find the value of y when x =3/4 as follows:

Answer:

• k = 8/3

• When ,x, = ,3/4,,, y = 2

Sara spent 15 minutes longer than (the difference is 15 min) Mia in her homework.

According to the question,

We have the following information:

Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40 minutes on reading and math homework.

So, it means that the total time spent by Sara in her homework is:

35+20 minutes

55 minutes

So, the differences between their time spent in her homework (will give us the more time taken by Sara) is:

Time spent by Sara in her homework-time spent by Mia in her homework

(55-40) minutes

15 minutes

Hence, Sara spent 15 more minutes than Mia.

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Use the formula for the area of a circle:

First, we need to find the radius r. Since the radius is half the diameter, then:

Substitute the value for r in the formula for the area of the circle:

Therefore, the area of a circle of diameter 10.5 in is approximately 86.6 squared inches.

As per given by the question,

There are given that a graph of line.

Now,

h

An angle in standard position has the vertex at the origin and the initial side is on the positive x-axis.

Thus, the initial side of the angle is:

Now, half the circumference measures pi, thus, pi/2 is a quarte of the circumference. As we want to find the angle -pi/2, then we need to rotate the terminal side clockwise:

Find the sine and the cosine.

The sine and the cosine in the unit circle are given by the coordinates as follows:

As can be seen in the given unit circle, the terminal side is located at:

Thus, the values of cosine and sine are:

x = 3, y = 2

The equations are:

x + y = 5......................(1)

y - 2x = -4...................(2)

Make x the subject of the the formula

x = 5 - y...............(3)

Substitute equation (3) into equation (2)

y - 2(5 - y) = -4

y - 10 + 2y = -4

3y = -4 + 10

3y = 6

y = 6 / 3

y = 2

Substitute the value of y into equation (3)

x = 5 - 2

x = 3

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

Work Shown:

5 blue + 4 red = 9 total

A = P(1st is red, 2nd is red)

A = P(1st is red)*P(2nd is red, given 1st is red)

A = (4/9)*(3/8)

A = 12/72

B = P(1st is blue, 2nd is red)

B = P(1st is blue)*P(2nd is red, given 1st is blue)

B = (5/9)*(4/8)

B = 20/72

C = P(2nd is red)

C = A+B

C = 12/72 + 20/72

C = 32/72

C = 4/9

Given:

The function used to compute the probability of x successes in n trials, when the trials are dependent.

Required:

To choose the correct option for the given statement.

Explanation:

The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.

Therefore the option c is correct.

Final Answer:

c ) hypergeometric probability function.

Answer:

Explanation:

What we want to answer in this question is simply, the area of the room that will be painted blue if he decides he would paint exactly have the room blue

So, we need to simply get the area of the room and divide this by half

Mathematically, the area of a rectangle is the product of its two sides

Thus, we have it that the area of the room is:

Now, to get the area painted blue, we divide this by 2 as follows or multiply by 1/2

We have this as: