In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.



Based on the given information, answer the questions below. Round each answer to the nearest tenth.

Part A: How tall is the pole? Show your work.

Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.

Part C: How long is Wire 1? Show your work.

Answer:

(- 25, 5 )

Step-by-step explanation:

- 3x - 6y = 45 → (1)

- 5y = x → (2)

substitute x = - 5y into (1)

- 3(- 5y) - 6y = 45

15y - 6y = 45

9y = 45 ( divide both sides by 9 )

y = 5

substitute y = 5 into (2)

- 5(5) = x , then

x = - 25

solution is (- 25, 5 )

The quadratic function f(x) = -3(x + 2)²  + 1is represented in the graph below

When graphing parabolas, we want to include certain special points in the graph. The y-intercept is the point where the graph intersects the y-axis. The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of the graph. Lastly, the line of symmetry (also called the axis of symmetry) is the vertical line through the vertex, about which the parabola is symmetric.

In the function given;

f(x) = -3(x + 2)² + 1

vertex of the function = (-2, 1)

Axis of symmetry =

This can be graphed using a graphing calculator;

Kindly find the attached image

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The probability that Rupert picked 2 green balls is 1/21.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. It's value ranges from 0 to 1.  

Main Body:

total balls = 7  , green balls =2

1st try:  

probability of getting green ball = 2/7

As there is no replacement so now,

total balls = 6  , green balls = 1

2nd try:  

probability of getting green ball = 1/6

total probability = (2/7)*(1/6)

                          = 1/21

Hence the answer is 1/21.

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The rate at which the height of the water changes when the water is 1m deep is; dh/dt = 1.5m/min

We are given;

width; w = 3m

Height; h = 4m

Length of trough; L = 10m

According to similar triangle property; w =3/4h

volume of water; V = 1/2×w×h×L = 1/2 × 3/4h × h × 10 = 15/4 h²

Differentiate using chain rule for both sides with respect to t gives;

dV/dt = (1/2)(15/2)h(dh/dt).

Now, we are given dV/dt = 5m³/min and we want to find the rate at which the height of water changes when the water is 1 m deep.

Thus;

5 = ×dh/dt

At h = 1m; 5 = 15(1)/2 × dh/dt

⇒ dh/dt = 2/3

dh/dt = 1.5 m / min

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Answer:

264,600

Step-by-step explanation:

249 ÷ 83 = 3

88,200 ×3 = 264,600

Answer:

The number is -36 or x = -36

Step-by-step explanation:

2x + 16 = -56
       2x = -72
         x = -36

Answer:

9x3

Step-by-step explanation:

x+9

/4

9x=8

x=2

+2=4

x=1+4234

After applying the distributive property, Ezra's expression was 8y + 16.

After he used the commutative property, his expression was 16 + 8y.

When using the distributive property, we are able to expand an expression with a bracket by multiplying the things in the bracket with the things outside:

8( y + 2)  becomes:

= (8 x y) + (8 x 2)

= 8y + 16

The commutative property on the other hand, means that when adding, the position of the number does not matter. For instance, a + b = b + a

When the commutative property is applied therefore, we get:
8y + 16 = 16 + 8y

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The value of y = 110.

What is slope intercept form?

The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

Rise of the water = 11

run = 1 min

slope m = 11/1 = 11.

The slope intercept form is

y = mx +b

after substituting the values, we get

m = 11,

x = 10and y = ?

y = 10 (11)

y = 110.

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10 + 10i

Apply Multiplicative Distribution Law: 12i - 9 x i^2 - 2i - i^2

Rewrite by definition: i^2 = -1:12i - 9 x (-1) -2i - (-1)

Remove the parentheses: 12i + 9 - 2i + 1

Combine like terms: 10 + 10i

Answer 10 + 10i

Answer:

10 + 10i

Step-by-step explanation:

Given expression:

[tex]3i(4 - 3i) - i (2 + i)[/tex]

Expand:

[tex]\implies 12i-9i^2-2i-i^2[/tex]

[tex]\implies 12i-2i-9i^2-i^2[/tex]

[tex]\implies 10i-10i^2[/tex]

Apply the imaginary number rule  i² = -1 :

[tex]\implies 10i-10(-1)[/tex]

Simplify:

[tex]\implies 10i+10[/tex]

Rewrite in standard complex form  a + bi:

[tex]\implies 10+10i[/tex]

well, looking at the picture we can see the blue rectangle is a 4x6 whilst the larger containing rectangle is a 14x15, well, we can simply get the area of the larger one and subtract the area of the smaller one.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{white~rectangle}{(14)(15)}~~ - ~~\stackrel{blue~rectangle}{(4)(6)}}\implies 210-24\implies \text{\LARGE 186}[/tex]

Answer:a. 24

b. 14

Step-by-step explanation:

a. 3ab=

3*a*b=

3*4*2=

12*2=24

b. a+5b=

a+5*b=

4+5*2=

4+10=14

Answer: a) 24

              b) 14

Step-by-step explanation:

step1: We have to substitute the numbers.

step2: Then finish the answer.

a) 3ab = 3 x 4 x 2 = 24

b) a+5b = 4 + 5 x 2 = 4 + 10 = 14

The amount of money that Amelia would spend on five bags of cat food is $22.5.

Amelia needs to buy some cat food. At the nearest store, three bags of cat food cost $13.50. We need to find out the amount of money that Amelia would spend on five bags of cat food.

Let the amount of money that Amelia would spend on 5 bags of cat food be represented by the variable M. We will use the unitary method. First of all, we will calculate the cost of one bag of cat food.

C = $13.50/3

C = $4.5

Now we need to find out the cost of five bags of cat food.

M = $4.5×5

M = $22.5

Hence, the amount of money that Amelia would spend on five bags of cat food is $22.5.

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The equation's graph is a straight line: y= 3/4x - 1/2.

acc to our question-

There are an endless number of solutions to a linear equation with two variables, and we can obtain each one as a pair of numbers.

Draw the two-variable linear equation's graph by plotting these values on a coordinate plane.

Using the slope and y-intercept is the simplest approach to graph something in slope-intercept form because that information is already available.

Follow all of the instructions listed below to plot the equation's graph.

Step 1: When x = 0, the y-intercept is 0, and y would then equal -1/2. (0, -1/2) are the points.

Step 2: Since the slope is 3/4 rise over run, go three up (rise) and four across (run).

Step 3: The slope of the line is upward since the slope in the  equation, not negative.

Step4; There are two points, draw a line connecting the two points.

hence,The equation's graph is a straight line: y= 3/4x - 1/2.

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The interest rate on the account would be 0.4.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

Compound interest

                  [tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Where,

    A = amount,

    P = principal

     t = no. of years

     r = annual interest rate

     n = no of times compounded  in a year.

By putting the values in the equations we get,

                  [tex]5067=4890(1+\frac{r}{10} )^{8.3}\\[/tex]

Solving this, we get

                  [tex]r = 0.356[/tex]

Rounding off to the nearest tenth of a percent we get

                  [tex]r=0.4[/tex]

Hence, the interest rate on the account will be [tex]0.4[/tex].

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Answer:

15 minutes

Step-by-step explanation:

The 3/4 of an hour is,

→ 60 × (3/4)

→ 180/4 = 45

Now required time spend on rope is,

→ 45 × (1/3)

→ 45/3 = 15 minutes

Hence, he had spend 15 minutes.

Answer:

87c

Step-by-step explanation:

Answer: Around 40 pages

Step-by-step explanation: Im not sure if this is the answer but from what I can do this would be the answer

Answer:

she will read 22 pages :)

Step-by-step explanation:

Answer:

$18

Step-by-step explanation:

She bought 2 garden hoses which both cost $30, so she already spent $60. The subtract 60 from 90, and get $36 left. Divide that by 2 because she buys 2 flower pots, and you arrive at the answer of $18 per flower pot.

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] x - 5 < 11 ( multiply through by 3 to clear the fraction )

2x - 15 < 33 ← equivalent inequality

to solve add 15 to both sides

2x < 48 ( divide both sides by 2 )

x < 24

Answer:

mary=x

andrew=8

jim=2*8=16

together=4*mary

total=8+16=24

24/4=x

x=6

Step-by-step explanation:

Answer:

The range is 9.

Step-by-step explanation:

The range of a data set is the difference between the maximum and the minimum values.

Let's begin by putting the set of values in order from lowest to highest.

12, 14, 15, 16, 17, 17, 21

The lowest value is 12, and the highest value is 21.

Let's subtract the minimum value from the maximum value to determine the range:

21 - 12 = 9

Hope this helps :)

Answer:

Step-by-step explanation:

Put them in order (lowest to highest)

so,

12, 14, 15, 16, 17, 17, 21

to find the range : highest - lowest

21 - 12 which is 9

Thanks

For Maia's birthday celebration, the bare minimum amount of packets of plates, napkins, and cups she needs to purchase is 15, 12, and 10, respectively.

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Answer:

Olumide will practice 40 minutes of playing the piano

Step-by-step explanation:

Olumide practices piano and guitar in the ratio of 5:8

64 minutes of guitar playing means that Olumide has had 8 individual practicing sessions of guitar (64 / 8 = 8), so he has also had 8 practicing sessions of piano.

5 x 8 = 40 minutes of piano practice

1. The length of RS is 5.

2. The length of JK is 6.

3. The length of RT is 4.

4. The perimeter of triangle JKL is 24.

What do you mean by right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

According to data in the diagram of the given question:

We have :

The ΔJKL, ΔRKS and ΔRTS are right-angle triangle.

The length of RK=3 and KS=4

We are using pythagoras theorem for determine the length of RS,

(RK)²+(KS)²=(RS)²

(3)²+(4)²=(RS)²

9+16=(RS)²

25=(RS)²

(5)²=(RS)²

RS=5

∴ The the length of RS is 5.

Now, we need to find the length of JK,

JK=2(RK)=2(3)=6

JK=6       [Because RK is midpoint of the side JK]

We have given value of KS=4 and the side KS is the opposite side of RT,

So, that's why the value of RT=4.

Now, we will find the perimeter of ΔJKL,

JK=6, KL=8 and we need to find the side JL,

(JK)²+(RL)²=(JL)²

(6)²+(8)²= (JL)²

36+64=(JL)²

100=(JL)²

(10)²=(JL)²

JL=10

The perimeter of the triangle ΔJKL,

Perimeter=6+8+10=24

Therefore, the perimeter of the triangle is 24.

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The solution to the linear system of equation is x = 3, y = 5, and z = -0.5

A system of linear equations is a set of linear equations that involve the same variable and which work or are operated (simultaneously) together

The system of linear equation is presented as follows;

2·x - 3·y + 6·z = -12...(1)

5·x + 2·y - 8·z = 29...(2)

7·x + 6·y + 4·z = 49...(3)

Multiplying equation (1) by 5 and equation (2) by 2, we get;

5 × Equation (1) ⇒ 10·x - 15·y + 30·z = -60...(4)

2 × Equation (2) ⇒ 10·x + 4·y - 16·z = 58...(5)

Subtract equation (4) from equation (5), to get;

10·x - 10·x + 4·y - (-15·y) - 16·y - 30·z = 58 - (-60) = 118

19·y - 46·z = 118...(6)

Multiplying equation (1) by 7 and equation (3) by 2, we get;

7 × Equation (1) ⇒ 14·x - 21·y + 42·z = -84...(7)

2 × Equation (3) ⇒ 14·x + 12·y + 8·z = 98...(8)

Subtracting equation (7) from equation (8), we get;

14·x - 14·x + 12·y - (-21·y) + 8·z - 42·z = 98 - (-84) = 182

33·y - 34·z = 182...(9)

Multiplying equation (6) by 33 and equation (9) by 19, we get;

627·y - 1,518·z = 3,894...(10)

627·y - 646·z = 3,458...(11)

Subtracting equation (10) from equation (11), we get;

627·y - 627·y -646·z - (-1,518·z) = 3,458 - 3,894 = -436

872·z = -436

z = -436 ÷ 872 = -0.5

z = -0.5

From equation (6), we have;

19·y - 46·z = 118

19·y - 46 × (-0.5) = 118

19·y - 46 × (-0.5) = 118

19·y = 118  + 46 × (-0.5) = 95

y = 95 ÷ 19 = 5

y = 5

From equation (1), we get;

2·x - 3·y + 6·z = -12

2·x - 3 × 5 + 6 × (-0.5) = -12

2·x = -12 + 3 × 5 - 6 × (-0.5) = 6

x = 6 ÷ 2 = 3

x = 3

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The average daily change  in temperature will be 3 degrees The temperature dropped to 24 degrees in 8 days

Since we know an average could be a single number taken as an agent of a list of numbers, as a rule, the whole of the numbers divided by how numerous numbers are within the list. We are said the temperature dropped to 24 degrees in the  8 days

So the average of it  will be =24 /8  = 3, which  means the temperature needed to drop for at least 3 degrees in order to get the sum  of 28  in 8 days.

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If a right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 degrees, the length of the each legs are 6.43 centimeter and 7.66 centimeter

The hypotenuse of the right triangle = 10 centimeter

The measure of angle = 40  degree

Here we have to use the trigonometric functions

sin θ = Opposite side / Hypotenuse

Substitute the values in the equation

sin 40 = Opposite side / 10

Opposite side = 10 × sin 40

= 6.43 centimeter

Similarly

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos 40 = Adjacent side / 10

Adjacent side = 10 × cos40

= 7.66 centimeter

Hence, if a right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 degrees, the length of the each legs are 6.43 centimeter and 7.66 centimeter

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The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

Given that,

The points (-7,9).

We have to find the image of the point after a rotation of 90° counterclockwise.

Because the hands of a clock move in a clockwise manner, we can rotate a point either in that direction or in the opposite direction when we rotate it. In mathematics, clockwise is defined as a negative rotation and counterclockwise as a positive rotation.

Consider the point on the coordinate plane (x,y). You may always swap the x- and y-coordinates and then multiply the new x-coordinate by -1 to rotate this point by 90 degrees around the origin in a clockwise orientation.

(x,y)→(y,-x)

(-7,9)→(9,7)

Therefore, The point (9,7) is the image of the point after a rotation of 90° counterclockwise.

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