how tall is a bridge if a 6-foot-tall person standing 100 feet away can see the top of the bridge at an angle of 30 degrees to the horizon

When starting a problem, almost every single problem needs to be understood by the person answering so they can see what needs to be done.  In this example, we are given an expression and told to solve the equation which means that we need to solve for the unknown, in this case x.

Now that we know what we must do, we can start to solve the problem. Looking at the problem we can see that the step that we must take is to distribute 3 into the parenthesis.

Distribute

Now that we distributed the values inside of the parenthesis we can move onto the next step which is to help isolate x.  What we should do is subtract 6 from both sides which will help leave x with its coefficient alone.

Subtract 6 from both sides

The next step that we should take to help solve for the unknown is to subtract 3x from both sides.

Subtract 3x from both sides

The final step that we must take to help isolate the unknown would be to divide both sides by 3.  This would remove the coefficient from x and we would get -21 divided by 3.

Divide both sides by 3

Therefore, after simplifying the expression that was given to solve for the unknown we were able to determine that the option that would best match the solution is option A, x = -7.

Answer:

a) x = -7

Step-by-step explanation:

Given: 3(2x + 2) = 3x - 15

1. Distribute:

3(2x) + 3(2) = 3x - 15

⟹ 6x + 6 = 3x - 15

2. Subtract 3x from both sides:

6x - 3x + 6 = 3x - 3x - 15

⟹ 3x + 6 = -15

3. Subtract 6 from both sides:

3x + 6 - 6 = -15 - 6

⟹ 3x = -21

4. Divide both sides by 3:

3x ÷ 3 = -21 ÷ 3

⟹ x = -7

5. Check your work:

3(2x + 2) = 3x - 15

3(2(-7) + 2) = 3(-7) - 15

3(-14 + 2) = -21 - 15

3(-12) = -21 - 15

⟹ -36 = -36 ✔

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Coordinates after 270 clockwise rotation is (-6,-2), (-3,-5) and  (-8, -5).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given coordinates are: (-2,6) , (-5, 3) and (-5, 8)

For 270° clockwise about the origin, we have the following rule:

(x, y)= (-y, x)

So,

coordinates  (-2,6) change into (-6,-2)

coordinates   (-5, 3) change into (-3,-5)

coordinates  (-5, 8) change into (-8, -5).

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The airplane reaches its maximum height of 95 feet after 10 seconds

The maximum height of an object the point where the velocity of the object is zero.

Given the function that represents the height of the airplane is expressed as h(t) = -(t-10)² + 95

The maximum height is the point where h'(t) = 0

h'(t) = -2(t-10)

0 = -2t + 10

2t = 10

t = 5secs

Substitute t =10 into the function

h(5) = -(10-10)² + 95

h(5) = -0 + 95
h(5) = 95feet

Hence the airplane reaches its maximum height of 95 feet after 10 seconds

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Answer:

140°

205°

Step-by-step explanation:

For A

The bearing of D from C is the angle at the line joining D and C while coming from the north pole in a clockwise direction.

from the diagram, the answer is = 140°

For B

The bearing of D from C is obtained same as A

so the answer is = 205°

Answer:

x=5 .........................................

In the 3rd quarter of year 5, the approximate total sales in the coastal region is; $7 million

The image of the graph showing the quarterly sales has been attached. From the graph, the red lines indicates the coastal region, the blue lines indicates the northern region, and the green lines indicates the southern region.

From the graph, in the third quarter, we can trace the total sales on the y-axis to be approximately $7 million dollars.

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The equation in the form (x + a)² = b is (x + 2)² = 16

The equation is given as:

x² + 4x = 12​

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)² = 4

Add this result to both sides of x² + 4x = 12​

x² + 4x + 4 = 12​ + 4

Evaluate the sum

x² + 4x + 4 = 16

Express as a perfect square

(x + 2)² = 16

Hence, the equation in the form (x + a)² = b is (x + 2)² = 16

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Answer:

x = 6

Step-by-step explanation:

Add the system of equations together:
2x - 3y = 12

4x + 3y = 24

you get

6x = 36

divide by the coefficient

6x/6 = 1

36/6 = 6

x = 6

Not sure if you need the y, but if so, let me know!

Hope this helps!

Answer:

see the attachment photo!

Answer: Choice B

A horizontal shift of 4 to the right.

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

Reason:

Replacing x with x-4 basically means we're decreasing each input by 4 units.

What this does is move the xy axis 4 units to the left. If we held the function curve fixed in place as the xy axis moved like this, then it would give the illusion the function is moving 4 units to the right.

Visual confirmation is shown below.

Using an exponential function, it is found that it will take 24 years for the current population of 4800 deer to reduce to 600.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, considering the initial value of 4800, and that the population halves every 8 years, the equation is given by:

[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]

The population will be of 600 when A(t) = 600, hence:

[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]

[tex]600 = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]

[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{600}{4800}[/tex]

[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{1}{8}[/tex]

[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \left(\frac{1}{2}\right)^3[/tex]

Hence:

t/8 = 3.

t = 24.

It will take 24 years for the current population of 4800 deer to reduce to 600.

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Considering the given graph, the number of solutions for the system of equations is given by:

b.) one

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In a graph, the number of solutions is given by the number of times the lines intersect. Hence, in this problem, the system has one solution, and option b is correct.

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Answer:

a^4

a^2×a^3= a^5(a^2+3)

a^5/a= a^4(a^5-1)

Answer:

Given function:

[tex]f(x)=2(3)^x[/tex]

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

[tex]\begin{aligned}\textsf{Average rate of change - Section A} & =\dfrac{f(1)-f(0)}{1-0}\\\\& =\dfrac{2(3)^1-2(3)^0}{1-0}\\\\& =\dfrac{6-2}{1}\\\\& =4 \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Average rate of change - Section B} & =\dfrac{f(3)-f(2)}{3-2}\\\\& =\dfrac{2(3)^3-2(3)^2}{3-2}\\\\& =\dfrac{54-18}{1}\\\\& =36 \end{aligned}[/tex]

[tex]\dfrac{\textsf{Average rate of change of Section B}}{\textsf{Average rate of change of Section A}}=\dfrac{36}{4}=9[/tex]

Therefore, the average rate of change of Section B is 9 times greater than Section A.

The function is an exponential function (with 3 as the growth factor) so the rate of change increases over time.

Answer:

No

Step-by-step explanation:

If you draw a line, it will not go through the origin and there isn't a constant rate of change.

Using an exponential function, it is found that you would have an amount of $64,060 in 45 years.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, considering the initial value of A(0) = 2000, with a growth rate of r = 0.26 each 3 years, the equation is given by:

[tex]A(t) = 2000(1.26)^{\frac{t}{3}}[/tex]

In 45 years, the amount will be given by:

[tex]A(45) = 2000(1.26)^{\frac{45}{3}} = 64060[/tex]

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Answer:

Simplest form = -4√44p

Step-by-step explanation:

● -2√2p × 2√22

⇒ (-2)(2)(√2p)(√22)

⇒ -4√44p ...Answer...

hope that helps...

Answer:

y=10°

Step-by-step explanation:

Here,

→(3x+18)°=(5x-4)°

→18°+4°=5x-3x

→22°=2x

→x=11°

Also,

3(4y+3)°+5x-4°=180°[The sum of the linear pair is 180°]

12y+9°+5x-4°=180°

12y+5°+5×11°=180°

12y+5°+55°=180°

12y=180°-60°

12y=120°

y=120°/12

y=10°

Opposite angles are equal

Now

linear pairs are supplementary

Answer:

For the first triangle:

[tex]2.75 units^{2}[/tex]

For the second triangle:

[tex]3.98 units^{2}[/tex]

Step-by-step explanation:

To find area of right triangles:

[tex]A=\frac{ab}{2}[/tex]

And you are good to go!

Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!

Have a great day!

:)

Answer:

290 take away 2 zeros wuxbeucheuxuejx

Answer:

X= 2.667  or X= -2.5

Step-by-step explanation:

sorry if this isn't correct </3

Answer:

B.80

Step-by-step explanation:

a straight line adds up to 180 degrees. you already have 100. 180-100=80

The right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is  0 to 40.

In setting the  vertical axis of a Bar Chart, note that it is vital for the categories to be natural as possible.

That is, the vertical axis should always begin with the number zero (0) and the scale values for the x axis must range from the lowest value on the left hand side to highest on the right hand side.

Therefore, due to the explanation given, the right method to use in order to represent the numerical data on the vertical axis of a Bar Chart is  0 to 40 as it range from 0 to the highest value.

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Answer:

A

Step-by-step explanation:

i think i can be wrong

Answer:

Tabled Function

Step-by-step explanation:

To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  -5 ≤ x ≤ 3

Therefore, a = -5  and  b = 3

[tex]f(3)=7[/tex]

[tex]f(-5)=-17[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]

[tex]f(3)=(3)^2-2=7[/tex]

[tex]f(-5)=(-5)^2-2=23[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]

From inspection of the graph:

[tex]f(3)\approx8[/tex]

[tex]f(-5) \approx 0[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]

Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.

Answer:

The answer is the first bullet. (number 1)