A person is standing 40 ft from a light post and can see the top of the light at a 35∘ angle of elevation. The person’s eye level is 5 feet from the ground. What is the height of the lightpost to the nearest foot. The height of the light post is feet.

Answer:

-10, -33, -125, -493, -1965

Step-by-step explanation:

a_1 = -10

a_n = 4a_(n - 1) + 7

The first five terms of the sequence are

a_1 =                                             -10

a_2 = 4(-10) + 7     =   -40 + 7 =    -33

a_3 = 4(-33) + 7    =  -132 + 7 =   -125

a_4 = 4(-125) + 7  = -500 + 7 =   -493

a_5 = 4(-473) + 7 = -1972 + 7 = -1965

Answer:

The expression used to find of 75 and 60 is 45.

Step-by-step explanation:

To find expression of 75 and 60, multiply decimals from left to right.

0.75*0.60=0.45 =45%

.75*.60=.45=45

45=45

True

45, which is our answer.

Answer:

C (-1,6).

Step-by-step explanation:

This is a horizontal line segment since A and B have the same y-coordinate.  Point P will also have the same y-coordinate since P is suppose to be on line segment AB.

So the only choice that has the y-coordinate as 6 is C. So we already know the answer is C.  There is no way it can be any of the others.  

So we are looking for the x-coordinate of point P using the x-coordinates of A and B.

A is at x=-3

B is at x=0

The length of AB is 0-(-3)=3.

AP+PB=3

AP/PB=2/1

This means AP=2 and PB=1 since 2+1=3 and AP/PB=2/1.

So if we look at A and we know P is 2 units away (after A) then -3+2=-1 is the x-coordinate of P.

OR!

IF we look at B and we know P is 1 unit away (before B), then 0-1=-1 is the x-coordinate of P.

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = x² - 2 → (1)

y = - 2x + 1 → (2)

Substitute y = x² - 2 into (2)

x² - 2 = - 2x + 1 ( subtract - 2x + 1 from both sides )

x² + 2x - 3 = 0 ← in standard form

(x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for corresponding values of y

x = - 3 : y = -2(- 3) + 1 = 6 + 1 = 7 ⇒ (- 3, 7 )

x = 1 : y = - 2(1) + 1 = - 2 + 1 = - 1 ⇒ (1, - 1 )

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x^2-2&(1)\\y=-2x+1&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\x^2-2=-2x+1\qquad\text{add 2x to both sides}\\x^2+2x-2=1\qquad\text{subtract 1 from both sides}\\x^2+2x-3=0\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1\\\\\text{put the value of x to (1):}\\\\for\ x=-3\\y=(-3)^2-2=9-2=7\\\\for\ x=1\\y=1^2-2=1-2=-1[/tex]

Answer:

f(x)=-3x+4

(can't see some of your choices)

Step-by-step explanation:

We want x to be independent means we want to write it so when we plug in numbers we can just choose what we want to plug in for x but y's value will depend on our choosing of x.

So we need to solve for y.

9x+3y=12

Subtract 9x on both sides

     3y=-9x+12

Divide both sides by 3:

     y=-3x+4

Replace y with f(x).

    f(x)=-3x+4

Answer:

The coordinates are  (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180°

 ∴ Its image is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Now lets solve the problem

∵ ABCD is a parallelogram

∵ Its vertices are A (1 , 1) , B (5 , 4) , C (7 , 1) , D (3 , -2)

∵ The parallelogram rotates about the origin by 180°

∵ The image of the point (x , y) after rotation 180° about the origin

   is (-x , -y)

∴ The images of the vertices of the parallelograms are

  (-1 , -1) , (-5 , -4) , (-7 , -1) , (-3 , 2)

∵ The parallelogram translate after the rotation 5 units to the right

   and 1 unit down

∴ We will add each x-coordinates by 5 and subtract each

   y-coordinates by 1

∴ A' = (-1 + 5 , -1 - 1) = (4 , -2)

∴ B' = (-5 + 5 , -4 - 1) = (0 , -5)

∴ C' = (-7 + 5 , -1 - 1) = (-2 , -2)

∴ D' = (-3 + 5 , 2 - 1) = (2 , 1)

* The coordinates of the parallelograms A'B'C'D' are:

  (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)

The given quadratic equation x² - 4x = -7 is rearranged into standard form and then solved using the quadratic formula -b ± √(b² - 4ac) / (2a). The roots of the equation are realized from solving this formula.

The subject of this problem is a quadratic equation in the form of ax²+bx+c = 0. The given equation is x² - 4x = -7, which can be rearranged into standard form as x² - 4x + 7 = 0. Thus, in this case, a=1, b=-4, and c=7.

The solutions or roots for this quadratic equation can be calculated using the quadratic formula, which is -b ± √(b² - 4ac) / (2a). Substituting the values of a, b, and c into the formula will give the roots of the given equation.

Doing that, we get: x = [4 ± √((-4)² - 4*1*7)] / (2*1)

The values that solve the equation are the roots of the quadratic equation.

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To solve the equation x^2 - 4x = -7 using the Quadratic Formula, we follow the steps of plugging the values of a, b, and c into the formula, evaluating the square root and simplifying to find the solutions.

To solve the equation x2 - 4x = -7 using the Quadratic Formula, we first need to make sure the equation is in standard form, which is ax2 + bx + c = 0. In this case, a = 1, b = -4, and c = 7. Plugging these values into the Quadratic Formula, we get:

x = (-(-4) ± √((-4)2 - 4(1)(-7))) / (2(1))

x = (4 ± √(16 + 28))/2

x = (4 ± √44)/2

x = (4 ± 2√11)/2

x = 2 ± √11

So the solutions to the equation x2 - 4x = -7 are x = 2 + √11 and x = 2 - √11.

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Answer:

[tex]1,207.6\ m[/tex]

Step-by-step explanation:

step 1

Find the perimeter of one lap

we know that

The perimeter of one lap is equal to the circumference of a complete circle (two half circles is equal to one circle) plus two times the length of 96 meters

so

[tex]P=\pi D+2(96)[/tex]

we have

[tex]D=35\ m[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]P=(3.14)(35)+2(96)[/tex]

[tex]P=301.9\ m[/tex]

step 2

Find the total meters of four laps

Multiply the perimeter of one lap by four

[tex]P=301.9(4)=1,207.6\ m[/tex]

Answer:

1207.6

Step-by-step explanation:

step 1

i got it right on the test

step 2

you get it right on the test

Answer:

V = 3053.63

Step-by-step explanation:

The volume of a sphere that has a radius of 9 is 3053.63.

V=4

3πr3=4

3·π·93≈3053.62806

Answer is provided in the image attached.

Answer:

C 1 hours 12 minutes

Step-by-step explanation:

We know distance is equal to rate times time

d= r*t

We know the distance is 30 miles and the rate is 25 miles per hour

30 = 25 *t

Divide each side by 25

30/25 = 25t/25

30/25 =t

6/5 =t

1  1/5 =t

Changing 1/5 hour to minutes.   We know there is 60 minutes in 1 hours so 1/5 of an hour is 60*1/5

1/5 *60minutes = 12 minutes

1 hours 12 minutes

Final answer:

Isabel's ride rotates 60° every two seconds. It takes 6 intervals (360° divided by 60°) to make a full rotation. Multiplying 6 intervals by 2 seconds gives us 12 seconds for Isabel to return to the starting position.

Explanation:

To determine how many seconds will pass before Isabel returns to her starting position on the ride, we need to establish the total degrees of rotation that equate to a full circle, which is 360°. Since the ride rotates 60° every two seconds, we can calculate the number of two-second intervals required to complete a full 360° rotation.

Firstly, divide 360° by 60° to find the number of intervals:

360° / 60° = 6 intervals

Since each interval takes 2 seconds, multiply the number of intervals by 2 to find the total time:

6 intervals × 2 seconds/interval = 12 seconds.

Therefore, it will take Isabel 12 seconds to return to her starting position on the amusement park ride.

Answer:

5

Step-by-step explanation:

16+24

--------------

30-22

Complete the items on the top of the fraction bar

40

----------

30-22

Then the items under the fraction bar

40

------------

8

Then divide

5

Step-by-step explanation:

First of all, solve the numerator.

16+24=40

Secondly, solve the denominator:

30-22 = 8

So now the fraction appear like this :

[tex] \frac{40}{8} [/tex]

40/8 = 5

Answer:

(2p - 9)(3p + 5)

Step-by-step explanation:

We have the polynomial: 6p2 – 17p – 45

Rewrite the middle term as a sum of two terms:

6p2 + 27p - 10p - 45

Factor:

3p(2p - 9) + 5(2p - 9)

→ (2p - 9)(3p + 5)

For this case we must factor the following expression:

[tex]6p ^ 2-17p-45[/tex]

We must rewrite the term of the medium as two numbers whose product is [tex]6 * (- 45) = - 270[/tex]

And whose sum is -17

These numbers are: -27 and +10:

[tex]6p ^ 2 + (- 27 + 10) p-45\\6p ^ 2-27p + 10p-45[/tex]

We group:

[tex](6p ^ 2-27p) + 10p-45[/tex]

We factor the maximum common denominator of each group:

[tex]3p (2p-9) +5 (2p-9)[/tex]

We factor[tex](2p-9)[/tex] and finally we have:

[tex](2p-9) (3p + 5)[/tex]

Answer:

[tex](2p-9) (3p + 5)[/tex]

Answer:

y=-(x-3)^2+2

Step-by-step explanation:

since the curve is convex up so the coefficient of x^2 is negative

and by substituting by the point 3 so y = 2

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (3, 2), hence

y = a(x - 3)² + 2

If a > 0 then vertex is a minimum

If a < 0 then vertex os a maximum

From the graph the vertex is a maximum hence a < 0

let a = - 1, then

y = - (x - 3)² + 2 → B

Answer:

2

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. Since midpoints will be involved, use multiples of 2 to name the coordinates for B, C, and D.

Answer:

2

Step-by-step explanation:

Well by definition a Rhombus is an equilateral paralelogram, AB =BC=CD=DA with all congruent sides, and Diagonals with different sizes.

Also a midpoint is the mean of coordinates, like E is the mean coordinate of A,C, and B, D

[tex]\frac{B+D}{2}=E\\  \\ B+D=2E\\ and\\\\  \frac{A+C}{2} =E\\ A+C=2E[/tex]

So the sum of the Coordinates B and D over two returns the midpoint.

And subsequently the sum of the Coordinates B +D equals twice the E coordinates. The same for the sum: A +C

Given to the fact that both halves of those diagonals coincide on E despite those diagonals have different sizes make us conclude, both bisect each other.

Answer:

y - 21 = 3(x - 5)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 3 and (a, b) = (5, 21), hence

y - 21 = 3(x - 5) ← in point- slope form

The point slope form of an equation is y - y1 = m(x - x1). Substituting the given point (5,21) and slope 3 into the equation, we get y - 21 = 3(x - 5). To remove the parenthesis on the y side, we simplify the equation to be y = 3x + 6.

The question asks for the writing of a point-slope equation of a line with a given slope of 3 that passes through a point (5,21). The point-slope form of an equation is generally denoted as:

y - y1 = m(x - x1)

Here, (x1, y1) = (5,21) and m (slope) = 3. Hence, substituting these values yields the equation:

y - 21 = 3(x - 5)

The asked equation without parenthesis on the y side would be:

y = 3x - 15 + 21

So, the final equation is:

y = 3x + 6

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Answer:

7t^2 + 21t

Step-by-step explanation:

You have 7 tiles of each t by t+3.

One tile has an area of

t * (t+3) = t^2 + 3t

So in total the area is

7* (t^2 + 3t)

7t^2 + 21t

Answer:

A. 18

Step-by-step explanation:

Median of a trapezoid: Its length equals half the sum of the base lengths.

So the sum of the lengths is 15 + 21 is 36 and half is 18.

18 inches long of a cut will John need to make so that he cuts the tiles along the median.

Given that, the top base of each tile is 15 inches in length and the bottom base is 21 inches.

The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.

The length of the median is the average of the length of the bases.

Now, add the top base and bottom base,

That is 15+21=36.

Now, divide that by 2

That is, 36/2= 18 inches.

Hence, the answer would be 18 inches.

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Answer:

[tex] D.~ 34.2~cm^2 [/tex]

Step-by-step explanation:

An arc measure of 20 degrees corresponds to a central angle of 20 degrees.

Area of sector of circle

[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]

where n = central angle of circle, and r = radius

[tex] area = \dfrac{20^\circ}{360^\circ}\pi (14~cm)^2 [/tex]

[tex] area = \dfrac{1}{18}(3.14159)(196~cm^2) [/tex]

[tex] area = 34.2~cm^2 [/tex]

Answer:

[tex]\large\boxed{f(x)=5x}[/tex]

Step-by-step explanation:

[tex]\begin{array}{c|c}x&f(x)\\1&5\\2&10\\3&15\end{array}\\\\\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\\Downarrow\\f(x)=5x[/tex]

For this case we must resolve the following expression:

[tex]6 + 2 ^ 3 * 3 =[/tex]

For the PEMDAS evaluation rule, the second thing that must be resolved are the exponents, then:

[tex]6 + 8 * 3 =[/tex]

Then the multiplication is solved:

[tex]6 + 24 =[/tex]

Finally the addition and subtraction:

30

Answer:

30

Answer: B

Step-by-step explanation:

Division of components are consistent  - the same

Answer:

B. -3, 3, -3, 3...

Step-by-step explanation:

There's two types of sequences, arithmetic and geometric.

Arithmetic equations are sequences that increase or decrease by adding or subtracting the previous number.

For example, take a look at the following sequence:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

Here, the numbers are increasing by +2. [adding]

So, this the sequence is arithmetic, since its adding.

Geometric sequences are sequences that increase or decrease by multiplying or dividing the previous number.

For example, take a look at the following sequence:

2, 4, 16, 32, 64, 128, 256, 512...

Here, the numbers are icnreasing by x2. [multiplying]

So, the sequence is geometric since its multiplying.

Based on this information, the correct answer is "B. -3, 3, -3, 3..." since its being multiplyed by -1.

Answer: 1) (x - 7)(x - 8)

               2) 2x(2x-7)(x + 2)

               3) (4x + 7)²

               4) (9ab² - c³)(9ab² + c³)

Step-by-step explanation:

1) x² - 15x + 56  → use standard form for factoring

                    ∧

                -7 + -8 = -15

  (x - 7) (x - 8)

************************************

2) 4x³ - 6x² - 28x      → factor out the GCF (2x)

2x(2x² - 3x - 14)         → factor using grouping

2x[2x² + 4x    - 7x - 14]    

2x[ 2x(x + 2)   -7(x + 2)]

2x(2x - 7)(x + 2)

*************************************

3) 16x² + 56x + 49     → this is the sum of squares

√(16x²) = 4x      √(49) = 7

              (4x + 7)²

******************************************************

4) 81a²b⁴ - c⁶          → this is the difference of squares

√(81a²b⁴) = 9ab²       √(c⁶) = c³

       (9ab² - c³)(9ab² + c³)

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6  = 20

Answer:

x=35

Step-by-step explanation:

We have the two angles (6x -82)  and (3x + 23) that are equal. To find 'x' we need to solve the system of equations:

6x -82 = 3x + 23

Solving for 'x':

3x = 105

x = 35

[tex]6x-82=3x+23\\3x=105\\x=35[/tex]

It's false, trapezoids are not rectangles.

Answer:

3(2x+3)=-3(-30+4)

6x+9=90+12

6x+9=102

6x=93

x=15.5

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Answer:

11½ = x

Step-by-step explanation:

6x + 9 = 78

- 9 - 9

-------------

6x = 69 [Divide by 6]

x = 11½ [3⁄6 = ½]

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

Answer:

466.27$ APEX

Step-by-step explanation:

Answer:

We have ; p = 2050

r = [tex]12/12/100=0.01[/tex]

n = [tex]3\times12=36[/tex]

But we will take [tex]36-5=31[/tex]

EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]

Substituting values in the formula we get;

[tex]\frac{2050\times0.01\times(1+0.01)^{31}}{(1+0.01)^{31}-1}[/tex]

= [tex]\frac{2050\times0.01\times(1.01)^{31}}{(1.01)^{31}-1}[/tex]

= $77.24

Now for further working you can see the sheet attached.

Total interest paid for the loan = $446.76

Answer:

OPTION B.

OPTION C.

Step-by-step explanation:

In order to know which numbers are less than [tex]\frac{9}{4}[/tex], you can convert this fraction into a decimal number. To do this, you need to divide the numerator 9 by the denominator 4. Then:

 [tex]\frac{9}{4}=2.25[/tex]

 Now you need convert the fractions provided in the Options A and B into decimal numbers by applying the same procedure. This are:

Option A→ [tex]\frac{11}{4}=2.75[/tex] (It is not less than 2.25)

Option B→ [tex]\frac{15}{8}=1.875[/tex] (It is less than 2.25)

The number shown in Option C is already expressed in decimal form:

Option C→ [tex]2.201[/tex] (It is less than 2.25)