On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi

The expression is given as

(2+5) - (-6 +bi)

The above expression is a complex expression

So, we have the following expression

(2+5) - (-6 +bi)

Remove the brackets in the above expression

So, we have the following expression

(2+5) - (-6 +bi) = 2 + 5 + 6 - bi

Evaluate the like terms in the above equation

So, we have the following expression

(2+5) - (-6 +bi) = 13 - bi

Hence, the solution to the complex expression is 13 - bi

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Answer:

Step-by-step explanation:

$220=$10x+$50

x= hours

subtract $50 from both sides making sure to cancel the right side

$220-$50=$10x

$170=$10x

Divide both sides by $10 to leaving x by itself on the right side

$170/$10=x

17hrs=x

The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Cost of new pair of shoes = $220

In order to earn money for this, Keandre babysits his neighbor for $10 an hour.

And, He also has saved up his monthly allowance which totals $50.

Now,

Let number of minimum hours = x hour

So, We can formulate;

⇒ $10x + $50 = $220

Solve for x as;

⇒ $10x + $50 = $220

Subtract 50 both side, we get;

⇒ $10x + $50 - $50 = $220 - $50

⇒ $10x = $170

Divide by 10 both side, we get;

⇒x = 17

Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.

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Given:

To find:

The roots.

Explanation:

Here,

Using the quadratic formula,

On substitution we get,

Therefore, the solutions are,

Final answer:

The solutions are,

Answer:

hmmph..

(32, 31)

(33,30)

(34, 29)

(35, 28)

(36,27)

(37, 26)

Step-by-step explanation:

That all I got....

There will not be enough T-shirts for all the students

From the question, the given parameters are:

Number of T-shirt = 1437

From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred

When the number of T-shirts is approximated to the nearest hundred, we have

Approximation = 1400

By comparison, 1400  is less than 1437

This means that the T-shirts will not be enough

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The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)

From the question, we have the following parameters that can be used to determine system of inequalities

Represent the adult with y and the students with x

So, we have the following representations

x + y ≤ 300 ---- the ticket holders cannot exceed the capacity

11x + 15y ≥ 3630 --- the total sales cannot be less than $3630

x ≥ 0 -- the number of students cannot be negative

y ≥ 0 -- the number of students cannot be negative

Write out the inequalities

x + y ≤ 300

11x + 15y ≥ 3630

x ≥ 0

y ≥ 0

Next, we represent the inequalities on a graph

See attachment for the graph of the inequalities

To get the combination, we make use of the coordinate points that are in the shaded region of the graph

Using the above as a guide, we have

(70, 200), (150, 140) and (140, 150)

There are other points too

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The length of the diagonal of the napkin is 11 inches.

Here, we are given that a square napkin has a side of length 8 inches.

All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.

Thus, by using Pythagoras theorem, we can form the following equation-

[tex]side^{2} + side^{2} = diagonal^{2}[/tex]

Let the diagonal of the square be d. Then, we have-

[tex]8^{2} +8^{2} =d^{2}[/tex]

64 + 64 = [tex]d^{2}[/tex]

128 = [tex]d^{2}[/tex]

[tex]d^{2}[/tex] = 128

d = [tex]\sqrt{128}[/tex]

d = [tex]8\sqrt{2}[/tex]

the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,

d = 8 × 1.41

= 11.28

Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.

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To complete the square, we want a number such that:

because in this way we can writte the square as follows:

Hence the answer is the last option:

We are given the following information

Slope of the line = m = -3

The line passes through the point (5, -7)

Recall that the equation of a line in the point-slope form is given by

Where m is the slope and (x₁, y₁) is a point on the line.

Let us substitute the given values into the above equation

Therefore, the equation of the line in slope-intercept form is

The gross monthly income range to be for you to be able to rent this apartment is $1671 - $2340.

Let the monthly income be x.

Therefore, 25% of x = 585

0.25x = 585

Divide

x = 585/0.25

x = $2340

The maximum income is $2340.

The minimum income will be:

35% of x = 585

0.35x = 585

Divide.

x = 585 / 0.35

x = $1671

In this case, the minimum value is $1671 and the maximum value is $2340. This illustrates the concept for finding the range.

The range is $1671 - $2340.

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a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

Given that the actual distance from San Antonio to Houston is approximately 192 ​miles.

The scale factor from the map to the real world is;

 (actual)/( map) = (192mi)/(3 in) = 64 mi/in

Then the actual distance from Dallas to Houston will be;

 (3.75 in)(64 mi/in) = 0.058 mi

And from Dallas to San Antonio, the distance will be;

 (4.125 in)(64 mi/in) = 0.064 mi

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Answer:

$7,000

Explanation:

To find the simple interest on any principal, we use the formula:

From the given question:

• Principal = $50,000

• Rate= 7%

• Time = 2 years

Therefore:

The simple interest is $7,000.

To solve the question, we will follow the steps below:

To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1

That is:

f((fx)) = (x²-1)² - 1

Then we open the parenthesis

f(f(x)) = (x² - 1)(x² -1) - 1

=x²(x²-1)-1(x²-1) - 1

= x⁴ - x² - x² + 1 - 1

= x⁴ - 2x²

So the correct option is option D. which is x⁴ - 2x²

Area of the cricket pitch is 660 square feet

Given

1 chain is equal to 10 feet

There are 3 feet in a yard

And 22 yards in a chain

Hence it is evident that

One chain is equal to 22 x 3

1 chain = 66 Feet

Area of a rectangle is Length x Width

Length = 66

Width =  10

Hence Area = 66 x 10

Area = 660 Square feet

Hence area of the cricket pitch is 660 square feet.

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f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10

f(10) multiple of 12 is given as:

The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.

f(10) = (10+2)(100+20+2)

= (12)(122)

= 1220+244

= 1464

Hence, f(10) is a multiple of 12

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In order to determine the ordered pairs, look if the given points are on the curve.

Based on the graph, you can identify that the points are:

B. (0,1)

D. (2,4)

E. (3,8)

The space sample is the total quantity of possible results

for each toss there are 3 possible results

so the total results are 2x 3 = 6

The only option with 6 elements is B

so the answer is B.

Bar chart

For 20 charterers

Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.

What in mathematics is a polynomial?

4x² - 6x+1 = 0

x = -b ± √b² - 4ac/2a

x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4

x = -( 6) ± √36 - 16/8

x = - 6 ± √20/8

So, roots are x = - 6 + √20/8 and x = - 6 - √20/8

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The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:

y = -5*x + 3

We can find a general linear function in the slope-intercept form as:

y = m*x + k

Where m is the slope and k is the intercept of the y-axis.

If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:

m = (d - b)/(c - a)

In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:

m = (-7 - 18)/(2 + 3) = -5

So the line is something like:

y = -5*x + k

To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:

-7 = -5*2 + k

-7 = -10 + k

-7 + 10 = k

3 = k

So the linear function is:

y = -5*x + 3

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Answer:

slope would be 4/1

Step-by-step explanation:

its rise over run, so up 4 and out 1

have a good day!

we have that

Two times the sum of a number and 7 -----> 2(w+7)

Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6

the answer is

[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]

ATTACHED IS THE SOLUTION OF Y

BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.

Answer:

The anser is

Step-by-step explanation:

DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y

Part a: The relationship between x and y can be represented as y = 6.36 + 1.93x

Part b: The relationship between x and y is proportional

Part c: The value of the card in 2007 will be $25.66

Worth of the card in 1997 = $6.36

Increase in value each year = $1.93

Let x be the number of years the player has been in retirement and y be the value of the cards in dollars

Formulating the equations we get the following:

Value of the card = Worth of the card in 1997 + Increase in value each year*Number of years the player has been in retirement

Part a:

y = 6.36 + 1.93x

Part b:

The relationship between x and y is proportional as the increase in the value each year leads to an increase in the worth of the card

Part c:

Value of the card in 2007:

The number of years the player has been retired will be 10 years in this case

Formulating the equation we get the following:

y = 6.36 + 1.93(10)

= 25.66

So, the value will be $25.66

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ANSWER:

The value of x is 16

STEP-BY-STEP EXPLANATION:

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

Solving for x:

Answer:

16 is the answer

Answer:

x = 0 and 2pi/3

Explanation

Given the expression

cos(2x)=cos(x)

In trigonometry expression;

cos2x = 2xos^2x - 1

Substituting into the equation given;

cos(2x)=cos(x)

2xos^2x - 1 = cos x

Rearrange

2xos^2x - 1 - cosx - 1 = 0

Let P = cosx

2P^2 - P - 1 = 0

Factorize

2P^2 - 2P+P-1 = 0

2P(P-1)+1(P-1) = 0

2P+1 = 0 and P-1 = 0

P = -1/2 and 1

Recall that P = cosx

-1/2 = cosx

x = cos^-1(-1/2)

x = 120 degrees = 2pi/3

If P = 1

cosx = 1

x = cos^-1(1)

x = 0

Hence the value of x that satisfies the equation is 0 ad 2pi/3