A 6-foot- tall electric pole casts a shadow that is 24 feet long. What is the ratio
of the pole's height to its shadow?

Answer: 4.5

Step-by-step explanation:

We need to find the amount of time until Calire paints a total of 9 more square feet.

Since the difference in their rates is 2 square feet per hour, it will take 9/2 = 4.5 more hours.

Answer:

Q18: x = 21, y = 15

Q19: x = 16, y = 10

Q20: x = 24, y = 19

Step-by-step explanation:

Q18:

(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)

9x - 9 = 180

9x = 189

x = 21

11y - 32 = 6x + 7 (vertically opposite angles)

11y - 32 = 6(21) + 7

11y - 32 = 133

11y = 165

y = 15

Q19:

8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)

3x = 48

x = 16

(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)

8(16)-14 + (5y + 16) = 180

114 + 5y + 16 = 180

5y + 130 = 180

5y = 50

y = 10

Q20:

47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)

5x + 60 = 180

5x = 120

x = 24

5y - 23 = 3x (corresponding angles)

5y - 23 = 3(24)

5y - 23 = 72

5y = 95

y = 19

There are 52 cards in a deck.

There are 12 face cards in the deck, that is 3 face cards per suit.

The probability of getting at least from two draws is given to be:

Therefore, the probability is calculated using the formula:

Using the combination formula, we have the solution to be:

The LAST OPTION is correct.

System of inequalities

We are given the graph where two lines represent the solution of a system of inequalities.

The solution is the double-shaded region of the graph.

We need to find the equation of the blue line and the red line and then convert them to inequalities.

Let's start with the blue line. We need to find two clear points through which it passes. These are (0,6) and (2,0). Now we write the equation of the line when knowing two points (the point-point form):

For the red line, the points are (0,0) and (2,2):

Now we have the equations of the lines, we must convert the equation to inequality by inserting one of these symbols instead of the equal sign:

> ≥ < ≤

For the blue line, the equation of the line is:

y = -3x + 6

Testing the origin (0,0):

0 = 0 + 6

0 = 6

To convert this to a true inequality we must replace the = for < or ≤

Since the blue line is solid, the points on the line belong to the solution, thus the first inequality is:

y ≤ -3x + 6

Now for the red line. The equation is

y = x. Let's test the point (2,1)

1 = 2

We must use the sign ≤ to make the expression true, thus the second inequality is:

y ≤ x

Thus, the system of inequalities is:

y ≤ -3x + 6

y ≤ x

Answer:

Rhombus:  All sides congruent, two pairs of parallel sides

Parallelogram: Two pairs of parallel lines

Rectangle: 4 right angles, Two pairs of parallel sides

Step-by-step explanation:

ANSWER

EXPLANATION

When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:

where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.

Therefore, we have that:

Therefore, the coordinates of point C are:

Those are the coordinates of C.

Answer:

Z'(10, 14)

Explanation:

Taking into accoun that the vertex point X(2, 3) is mapped to X'(4, 8), we can say that the translation rule is:

(a, b) ----> (a + 2, b + 5)

Because

X(2, 3) ----> (2 + 2, 3 + 5)

----> X'(4, 8)

So, using this rule, we can find the coordinates for Z' as:

Z(8, 9) ----> (8 + 2, 9 + 5)

----> Z'(10, 14)

Therefore, the answer is Z'(10, 14)

EXPLANATION:

1.The first thing we must do is use a suitable method that allows us to find the value of y for the two equations of the line

2. The correct and most appropriate method is the matching method.

The exercise is as follows:

We will have the following:

From the polynomial we will have that:

*It falls to the left and rises to the right.

This can be seeing as follows:

The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤ 

Let the height of the third tree be x.

By the given condition, this will be:

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

The first relation will give x ≥ 32 - 24 = x ≥ 8

The second relation will give:

8 + 16 + x ≤  42

24 + x ≤  42

x ≤  42 - 24

x ≤  18

The inequality is 8 ≤ x ≤ 18.

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If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Let height of the third tree be x.

By the given condition

The sum of three palm tree heights range from 32 to 42 feet

8 + 16 + x ≥ 32 and 8 + 16 + x ≤  42

Solve these inequalities

8 + 16 + x ≥ 32

24+x ≥ 32

x≥ 32-24

x≥ 8

and 8 + 16 + x ≤  42

24+ x ≤  42

x≤  42-24

x ≤ 18

Hence the inequality is 8 ≤ x ≤ 18.

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The equation of a line in the slope intercept form is expressed as

y = mx + c

The given equation is

9x + 3y = 18

We would rearrange it so that it takes the form of the slope intercept equation shown above.

We would divide both sides of the equation by 3, we have

9x/3 + 3y/3 = 18/3

3x + y = 6

Subtracting 3x from both sides of the equation, we have

3x - 3x + y = 6 - 3x

y = 6 - 3x

The slope intercept form is

y = - 3x + 6

To plot the graph, we would substitute values of x into the equation to get corresponding y values. These x and y values would be plotted on the x and y coordinates of the graph. We have

For x = - 2, y = 6 - 3(- 2) = 6 + 6 = 12

For x = - 1, y = 6 - 3(-1) = 6 + 3 = 9

For x = 0, y = 6 - 3(0) = 6 - 0 = 6

For x = 1, y = 6 - 3(1) = 6 - 3 = 3

For x = 2, y = 6 - 3(2) = 6 -6 = 0

The graph is shown below

The solution to the compound inequality is x > 6 or x < -3

An inequality is a mathematical expression that has <, >, ≤ and ≥.

A compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality as follows:

2x - 4 > 8 or 3x - 1 < - 10

2x - 4 > 8

add 4 to both sides of the inequality

2x - 4 + 4 > 8 + 4

2x > 12

divide both sides by 2

x > 12 / 2

x > 6

3x - 1 < - 10

add 1 to both sides of the inequality

3x - 1 + 1 < - 10 + 1

3x < - 9

divide both sides by 3

x < -9 / 3

x < -3

Therefore, x > 6 or x < -3

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The solution to the compound inequality will be; x > 6 or x < -3

Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.

A compound inequality is defined as an inequality that combines two simple inequalities.

Therefore, solve the compound inequality that will be;

2x - 4 > 8 or 3x - 1 < - 10

2x - 4 > 8

Then add 4 to both sides of the inequality so,

2x - 4 + 4 > 8 + 4

2x > 12

Now, divide both sides by 2

x > 12 / 2

x > 6

3x - 1 < - 10

Again, add 1 to both sides;

3x - 1 + 1 < - 10 + 1

3x < - 9

Then divide both sides by 3;

x < -9 / 3

x < -3

Therefore, solution to the compound inequality is; x > 6 or x < -3

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The value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115

The expression is

[tex]10z^2[/tex]+7z+4

The expression is defined as the statements that have a minimum of two terms containing numbers or variables , connected by an operator in between. The operator maybe addition, subtraction, division, multiplication etc..

The expression is

[tex]10z^2[/tex]+7z+4

The value of z = 3

Substitute the value of z in the given expression

= [tex]10(3)^2[/tex]+ 7×3 + 4

= 10×9 + 21 + 4

Multiply the terms first

= 90 + 21 + 4

Add them together

= 115

Hence, the value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115

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The sphere has a surface area of 482.8064 square meters

From the question, the given parameters are:

Diameter, D = 12.4 meters

π = 3.14

The surface area of the sphere is calculated using the following formula

S = 4π(D/2)²

Substitute the given parameters in the above formula

So, we have

S = 4 * 3.14 * (12.4/2)²

Evaluate the exponent

This is represented as

S = 4 * 3.14 * 38.44

Evaluate the product

This is represented as

S = 482.8064

Hence, the surface area of the sphere is 482.8064 square meters

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The rates of changes of the given function for the corresponding intervals are:  [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.

What is function?

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).

The rate of change of a function can be calculate using the formula:

[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Putting the value from the question:

given [x₁, x₂] = [-5, -1]

f(-5) = 35 , f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-35}{-1 -(-5)}[/tex]

R = -32/4

R = -8

given [x₁, x₂] = [-4, -1]

f(-4) = 24, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-24}{-1 -(-4)}[/tex]

R = -21/3

R = -7

given [x₁, x₂] = [-3, -1]

f(-3) = 15, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-15}{-1 -(-3)}[/tex]

R = -12/2

R = -6

given [x₁, x₂] = [-2, -1]

f(-2) = 8, f(-1) = 3

Putting these value in formula:

[tex]R = \frac{3-8}{-1 -(-2)}[/tex]

R = -5/1

R = -5

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[tex]\frac{2(x-8)}{5}[/tex] = y

To Solve: value of y

Given: 2x-5y=16

Solution: The solution to this problem involves the following steps:

2x-5y-16=0

2x-16=5y

[tex]\frac{2x-16}{5}[/tex] = y

[tex]\frac{2(x-8)}{5}[/tex] = y

Answer: The final answer is : [tex]\frac{2(x-8)}{5}[/tex] = y

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Remember that

The y-intercept is the value of y when the value of x=0

In this problem

we have the equation

y=7x^2+4

For x=0

substitute

y=7(0)^2+4

y=4

Hello!

So, we are given the following to solve:

[tex]-m=9[/tex]

To solve this, simply divide both sides by -1.

[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]

Then, simplify the expression and you have your solution.

[tex]m=-9[/tex]

Hope this helps! If so, please lmk! Thanks and good luck!

Answer:

m= -9

Step-by-step explanation:

Divide both sides by -1

[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]

Simplify m = - 9

Answer:

1.2

Step-by-step explanation:

Answer:  Emma > Amelia > Brandon > Celesle > Damian

Step-by-step explanation:

We convert all the fractions to decimals (2 decimals).

Amelia      4.35 lbs

Brandon   [tex]4\frac{1}{3}= \frac{12}{3} +\frac{1}{3} =\frac{13}{3}[/tex] ≈ 4.33 lbs

Celesle     4.2 lbs

Damian    √15 ≈ 3.87 lbs

Emma       [tex]4\frac{2}{3} =\frac{12}{3} +\frac{2}{3} =\frac{14}{3}[/tex] ≈ 4.67 lbs

4.47 lbs > 4.35 lbs > 4.33 lbs > 4.2 lbs > 3.87 lbs

Emma  > Amelia > Brandon > Celesle > Damian

Given the function:

when x = 1.9

when x = 1.999

When x = 2.001

When x = 2.1

so, the limit of the function k(x) = 11

The answer is option A. 11

Answer:

Step-by-step explanation:

Answer:

The three numbers are:

4.62,

23.1, and

462.2

Step-by-step explanation:

Let X be the "first number."

B = What number is five times the first number:  5X

C = third number is 100 more than the first number:  100X

The sum of all three is 490:  X + B + C = 490

----

X + B + C = 490

X + 5X + 100X = 490

106X = 490

X = 4.622

Check:

X = 4.622

B = 5X = 23.11

C = 100X = 462.2

Check:

Sum (4.622 + 23.11 + 462.2) = 490

Answer:

The answer is D

Step-by-step explanation:

Check to see when the graph is increasing and decreasing from left to right.

It is decreasing from x = -5 to x = -3 or (-5,-3) These look like a points but are not. They are intervals.

Then, it increases from x = -3 to x = 0 or (-3,0)

Then, it stays constant from x = 0 to x = 2 or (0,2)

Lastly, it decreases from x - 2 to x = 5 or (2,5)

To summarize, the graph is increasing from (-3,0). Decreasing on (-5,-3) and (2,5). and constant on (0,2)

The only option that fits these conditions is D.

Answer: The points (9,-) and (9,3) Both have the same (y) coordinate.

Step-by-step explanation:

Answer: L= 9-.75x

Step-by-step explanation: since it starts at 9 inches tall and is melting at .75 inches per hour, it's going to be the initial length, 9, minus the rate, .75, times the time/hours past, so x