Simplify 8-{x-(5+x)}

Answer:

The height of the tree is [tex]64.94\ ft[/tex]

Step-by-step explanation:

Let

y ----> the height of the tree

we know that

[tex]tan(33\°)=y/100[/tex] ----> the function tangent is equal to divide the opposite side angle of 33 degrees by the adjacent side angle of 33 degrees

Solve for y

[tex]y=(100)tan(33\°)=64.94\ ft[/tex]

The height of the tree can be calculated using the formula 'Height of tree = tan(33 degrees) * distance from the tree'. Substituting the given values, the tree should be approximately 65.45 feet tall.

John can measure the height of the tree using trigonometric principles. In this case, the problem involves a right triangle, where the height of the tree forms one side (opposite to the angle of elevation), the distance John is from the tree forms the base (adjacent to the angle of elevation), and the line of sight to the top of the tree forms the hypotenuse. The tangent of the angle of elevation (33 degrees in this case) is equal to the height of the tree divided by the distance from the tree.

Therefore, to calculate the height of the tree, we need to find the tangent of the given angle and multiply it by the distance from the tree:
Height of tree = tan(33 degrees) * distance from tree

= tan(33) * 100 feet
Approximately, the tree should be around 65.45 feet tall.

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Answer:

203 minutes

Step-by-step explanation:

This can be expressed as an arithmetic sequence, that is

20, 23, 26, 29,...

With first term a = 20 and common difference d = 3

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)d ], hence

[tex]S_{7}[/tex] = [tex]\frac{7}{2}[/tex] [ (2 × 20) + (6 × 3) ]

                        = 3.5 ( 40 + 18) = 3.5 × 58 = 203

Answer:

-3

Step-by-step explanation:

We have

y = F(x) = x + 3

so

x = y  - 3

so

F⁻¹(y) = y - 3

which we can write

F⁻¹(x) = x - 3

We solve

0 = F⁻¹(x) = x - 3

x = 3

Answer: 3

[tex]\bf \stackrel{\measuredangle A}{(5x-14)}+\stackrel{\measuredangle D}{(4x+5)}=\stackrel{\textit{linear angles}}{180}\implies 9x-9=180 \\\\\\ 9x=171\implies x=\cfrac{171}{9}\implies x=19 \\\\[-0.35em] ~\dotfill\\\\ \overline{DC}\implies -2x+54\implies -2(19)+54\implies -38+54\implies 16[/tex]

Answer:

DC = 12

Step-by-step explanation:

In a parallelogram consecutive angles are supplementary, that is

∠DAB and ∠ADC are consecutive and supplementary, thus

5x - 14 + 4x + 5 = 180

9x - 9 = 180 ( add 9 to both sides )

9x = 189 ( divide both sides by 9 )

x = 21

Hence

DC = - 2x + 54 = (- 2 × 21) + 54 = - 42 + 54 = 12

I think it is bottom right because it goes through the most points.

Answer:

Other division expression that have the same value as 61.12 divided by 3.2 are

122.24 divided by 6.4 AND

183.36 divided by 9.6

Step-by-step explanation:

61.12/3.2 = 19.1

Other division expression that have the same value as this:

122.24/6.4 = 19.1

183.36/9.6 = 19.1

Answer:

circle area = PI * radius^2

circle area = 11^2 * PI

circle area = 121 * PI

That would be the area for the ENTIRE area but the circle but we are only dealing with 135 degrees of a circle so the area equals

121 * (135 / 360) * PI

= 45.375 PI

Answer is C

Step-by-step explanation:

Answer:

It's option 2.

Step-by-step explanation:

- 1/2x > 6

Divide both sides by -1/2:

x < -12   (Note the inequality sign flips when we divide by a negative value).

Answer: {x |x ∈ R, x < -12}

Step-by-step explanation:

Given the following inequality:

[tex]-\frac{1}{2}x>6[/tex]

You can find the solution set by solving for the variable "x".

Then, to solve for the variable "x" you need to multiply both sides of the inequality:

[tex](-\frac{1}{2}x)(2)>(6)(2)[/tex]

[tex]-x>12[/tex]

And finally, you must multiply both sides of the inequality by (-1). Notice that the direction of the symbol of the inequality will change:

[tex](-x)(-1)>(12)(-1)[/tex]

[tex]x<-12[/tex]

Therefore, the solution set is: {x |x ∈ R, x < -12}

Answer:

Domain = {3,4,9}

Range = {2, 6, 8, 9.5}

Given relation is NOT a function.

Step-by-step explanation:

Given relation is relation is ((9,6), (3,8),(4,9.5), (9,2)}.

Now we need to determine if given relation is a function or not.

We also need to find the domain and range.

((9,6), (3,8),(4,9.5), (9,2)}

​Domain is basically the collection of x-values

So Domain = {3,4,9}

Range is basically the collection of y-values

So Range = {2, 6, 8, 9.5}

Since given relation contains repeated x-value "9".

So the given relation is NOT a function.

Answer:

The fourth

Step-by-step explanation:

It has 4 terms

ANSWER

4)x^3+ 5x^2- 9x- 45=0

EXPLANATION

Factoring by grouping is used to factor expressions that have four terms.

Among the given options, the fourth option is

[tex]x^3+ 5x^2- 9x- 45=0[/tex]

There are already four terms in this expression.

So we group the first two and the last two and factor.

We can see that x² is common to the first two terms and -5 is common to the last 2 terms.

The fourth choice is correct.

Answer:

21 + 4(3^2 - 5 = 37

Step-by-step explanation:

Answer:

[tex]\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}[/tex]

[tex]\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4[/tex]

Answer:

5

Step-by-step explanation:

(3 1/3)/(2/3) = (10/3)/(2/3) = 10/2 = 5

In the above, both the numerator fraction and the denominator fraction have the same denominator (3), so the result is the ratio of their numerators.

____

The other way to divide fractions is to "invert and multiply". For this, the denominator gets inverted (from 2/3 to 3/2) and that is then used to multiply the numerator.

(3 1/3)/(2/3) = (10/3) · (3/2) = (10·3)/(2·3) = 10/2 = 5

You will note that the denominators of 3 cancel, resulting in 10/2 as above.

Answer:

5

Step-by-step explanation:

Expression: 3 ¹/₃ ÷ ²/₃

Mixed to improper: ¹⁰/₃ ÷ ²/₃

Divide by fraction = multiply by its reciprocal:

Change: ¹⁰/₃ × ³/₂

Simplify: ¹⁰/₁ × ¹/₂

Simplify: ⁵/₁ × ¹/₁

Multiply: 5

Answer:

16) The area of the circle is 25.1 units²

17) JKLM is a parallelogram but not a rectangle

Step-by-step explanation:

16) Lets talk about the area of the circle

- To find the area of the circle you must find the length of the radius

- In the problem you have the center of the circle and a point on

 the circle, so you can find the length of the radius by using the

 distance rule

* Lets solve the problem

∵ The center of the circle is (1 , 3)

∵ The point on the circle is (3 , 5)

- Using the rule of the distance between two points

* Lets revise it

- The distance between the two points (x1 , y1) and (x2 , y2) is:

 Distance = √[(x2 - x1)² + (y2 - y1)²]

∴ r = √[(3 - 1)² + (5 - 3)²] = √[4 + 4] = √8 = 2√2 units

∵ The area of the circle = πr²

∴ The area of the circle = π (2√2)² = 8π = 25.1 units²

* The area of the circle is 25.1 units²

17) To prove a quadrilateral is a parallelogram, prove that every

     to sides are parallel or equal or the two diagonal bisect

     each other

* The parallelogram can be rectangle if two adjacent sides are

  perpendicular to each other (measure of angle between them is 90°)

 or its diagonals are equal in length

- The parallel lines have equal slopes, then to prove the

  quadrilateral is a parallelogram, we will find the slopes of

  each opposite sides

* Lets find from the graph the vertices of the quadrilateral

∵ J = (0 ,2) , K (2 , 5) , L (5 , 0) , M (3 , -3)

- The opposite sides are JK , ML and JM , KL

- The slope of any line passing through point (x1 , y1) and (x2 , y2) is

 m = (y2 - y1)/(x2 - x1)

∵ The slop of JK = (5 - 2)/(2 - 0) = 3/2 ⇒ (1)

∵ The slope of LM = (-3 - 0)/(3 - 5)= -3/-2 = 3/2 ⇒ (2)

- From (1) and (2)

∴ JK // LM

∵ The slope of KL = (0 - 5)/(5 - 2) = -5/3 ⇒ (3)

∵ The slope of JM = (-3 - 2)/(3 - 0)= -5/3 ⇒ (4)

- From (3) and (4)

∴ KL // JM

∵ Each two opposite sides are parallel in the quadrilateral JKLM

∴ It is a parallelogram

- The product of the slopes of the perpendicular line is -1

* lets check the slopes of two adjacent sides in the JKLM

∵ The slope of JK = 3/2 and the slope of KL = -5/3

∵ 3/2 × -5/3 = -5/2 ≠ -1

∴ JKLM is a parallelogram but not a rectangle

The height of the wall is calculated to be approximately 12 feet using the Pythagorean theorem with the given measurements.

This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, we have a triangle formed by the wall, the ground and the ladder. Let's say the ladder's length is 'c', the wall's height is 'a' and the base from the person to the wall is 'b'. According to the problem:

Using the Pythagorean theorem, we get:

a^2 + b^2 = c^2

Where a is the height of the wall. Substituting in the values we get:

a^2 + 9^2 = 15^2

Solving for 'a', we find that the height of the wall is approximately 12 feet.

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Using the Pythagorean theorem, the length of the ladder and subtract the person's height to find the wall's height is 4.82 feet.

To find the height of the wall, we can use similar triangles. The person's height and distance from the wall create a right triangle with the ladder. The ladder acts as the hypotenuse of this right triangle. Using the Pythagorean theorem, we can find the length of the ladder. Then, we subtract the person's height from this length to find the height of the wall.

Let's denote the height of the wall as h. The person's height is 6 feet and they are 9 feet from the wall. The foot of the ladder is 6 feet from the person, so it forms a right triangle with legs measuring 6 feet and 9 feet.

Using the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse, we have:

6^2 + 9^2 = c^2

36 + 81 = c^2

117 = c^2

c = sqrt(117) = 10.82 feet (rounded to two decimal places)

Therefore, the height of the wall is 10.82 feet - 6 feet (person's height) = 4.82 feet.

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Answer:

a ≈ 14 or 6

Step-by-step explanation:

264 = π × a × (20 - a)

a(20 - a) = [tex]\frac{264}{Pi}[/tex] ≈ 84 (rounded off to nearest whole number)

Opening the brackets we get;

a² - 20a + 84 = 0

Applying the quadratic formula we get:

a ≈ 14 or 6

Answer:

[tex]f(-1) = 1[/tex]

Step-by-step explanation:

Given

f(x) = [tex]-x^{3}-x^{2} +1[/tex]

Finding f(-1) means, we have to put -1 in the places of x in the function,

So, putting x=-1 in the function

[tex]f(-1) = (-1)^{3} - (1)^{2} +1[/tex]

As the power 3 is odd, the minus will remain the same, while in the 2nd term minus will be eliminated due to even power. So,

=> [tex]-1-1+1[/tex]

=> 1

Hence,

[tex]f(-1) = 1[/tex]

q=5 the first one is 2 so T1=2

and for the end we use the formula:

[tex]an = 2 \times {5}^{(n - 1)} [/tex]

Answer:

5/8

Step-by-step explanation:

Subtract the total computers from the old computers.

40-15=25

Then put the number of new computers over the total computers

25/40

Then, simplify

5/8

Answer:

I think the answer is 12 rides

Final answer:

After setting up a system of equations with Option A as C = 50 + 2x and Option B as C = 4.5x, we find that after 20 rides, the total costs for both options are the same.

Explanation:

To determine after how many rides the total costs of the two payment options will be the same for the express bus from the center of town, we can set up a system of equations. Option A includes a monthly pass costing $50 plus $2 per ride, and Option B is a flat rate of $4.50 per ride.

Let's define x to be the number of rides. Then for Option A, the cost will be $50 (monthly pass) plus $2 multiplied by x, which can be expressed as the equation C = 50 + 2x. For Option B, the cost is simply $4.50 multiplied by x, which can be written as C = 4.5x.

To find out after how many rides the costs are the same, we set the equations equal to each other: 50 + 2x = 4.5x. Solving for x, we get x = 20. After 20 rides, the total costs for both options A and B will be the same.

The answer is:

The distance that Adam should cover to get to the park is 108 miles.

To solve the problem, we need to write two equations with the given information about the times and his speed.

So,

For the first equation we have: Going to Disney Park

[tex]time=4hours[/tex]

[tex]Distance=v*4hours[/tex]

For the second equation we have: Going back from Disnery Park

[tex]time=4hours-2.5hours=1.5hours[/tex]

[tex]Speed=v+45mph[/tex]

[tex]Distance=(v+45mph)*1.5hours[/tex]

Now, if He covered the same distance going and coming back, we have:

[tex]v*4hours=(v+45mph)*1.5hours[/tex]

[tex]v*4hours=v*1.5hours+45mph*1.5hours[/tex]

[tex]v*4hours-v*1.5hours=45mph*1.5hours[/tex]

[tex]v*2.5hours=67.5miles[/tex]

[tex]v=\frac{67.5miles}{2.5hours}=27\frac{miles}{hour}=27mph[/tex]

We have that the speed when Adam was going to Disney Park was 27 mph.

Therefore, to calculate the distance, we need to substitute the obtained speed in any of the two first equations.

Then, substituting the speed into the first equation, we have:

[tex]Distance=v*4hours\\Distance=27mph*4hours=108miles[/tex]

Hence, we have that the distance that Adam should cover to get to the park is 108 miles.

Havea nice day!

The numbers added together resulted in 8419.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as an addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the addition of all 177 numbers.

First, we arrange in ascending terms, we get,

16, 17, 18, 19, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 31, 31, 32, 34, 35, 35, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 38, 38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 44, 45, 45, 45, 46, 46, 46, 47, 47, 47, 48, 48, 48, 48, 48, 48, 49, 49, 49, 49, 50, 50, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53, 53, 53, 53, 53, 54, 54, 54, 55, 55, 57, 60, 61, 61, 61, 61, 62, 62, 62, 62, 62, 63, 64, 64, 65, 65, 65, 67, 67, 68, 68, 68, 70, 70, 71, 72, 72, 73, 74, 75, 75, 75, 76, 78, 80, 82, 84, 85, 86, 89, 91, 93, 102, 104, 124.

Therefore, the sum is 8419.

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The question 'what is 48 35 26 31 27 52 55 63... added all together?' is asking for the sum of all the provided numbers. This can be calculated with a calculator or by manual addition. Be aware it may take time due to the large number of values.

To answer the question, 'what is 48 35 26 31 27 52 55 63 18 74 35 61 28 42 76 35 38 64 71 26 53 65 47 41 102 38 35 84 41 26 73 62 35 39 62 49 104 62 54 19 28 64 36 39 53 89 26 53 43 75 35 39 29 26 45 39 31 30 70 42 37 54 85 42 36 91 25 28 53 65 78 42 68 44 41 50 46 48 75 29 53 72 17 28 38 30 48 43 27 46 36 48 62 31 42 48 61 22 124 27 53 86 60 47 41 37 27 36 45 80 45 70 53 25 29 16 30 36 38 42 48 51 38 39 43 61 75 38 42 55 72 39 28 51 43 49 67 25 37 39 46 41 50 93 53 82 47 36 38 51 42 40 24 68 38 36 34 49 65 68 62 53 67 23 51 40 43 49 57 61 26 54 35 32 38 39 24 added all together?', you would have to add up all the numbers provided. Calculating this would involve simply adding the given values together. To get the answer, you can use a calculator or manually add each number, but it may take a bit of time due to the large number of values given.

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Answer:

Step-by-step explanation:

z score= x - mean/standard deviation

1.20= x -100/15

18= x -100

118=x

z score= x - mean/standard deviation

0.5=x-73/4

2=x-73

75= x

It might have come from

9/n  =  10/m

Answer: Hi, in the equation 9*m = 10*n the proportion is 9 to 10, which means that 9 times the number m is equal to 10 times the number n.

So n is proportional to m in the way that n= (9/10)*m

and m is proportional to n in the way that m= (10/9)*n

This means that the proportion can be written as 9 to 10, or 9:10.

Answer:

a) Domain: -∞ < x < ∞

b) Cost required to manufacture 3500 items is $15,900.

c) Number of items she can manufacture is 5208 if cost is kept at $20,000

Step-by-step explanation:

a) What is the reasonable domain of the function?

The function is C(x) = 7,500 + 2.4x

The domain of the function is the set of values for which the function is defined and valid.

In the given function there is no constraint or undefined points so domain is:

-∞ < x < ∞

b) What is the cost of 3,500 items?

We are given x = 3500 and we need to find the cost.

Putting values in the function given:

C(x) = 7,500 + 2.4x

C(x) = 7,500 + 2.4 (3500)

C(x) = 7500 + 8400

C(x) = 15,900

Cost required to manufacture 3500 items is $15,900.

c) If costs must be kept below $20,000 this month, what is the greatest number of items she can manufacture?

We are given cost, and we need to find x

C(x) = 7,500 + 2.4x

20,000 = 7500 +2.4x

20,000 - 7500 = 2.4x

12500 = 2.4 x

=> x = 12500/2.4

x= 5208.3 ≅ 5208

So, Number of items she can manufacture is 5208 if cost is kept at $20,000

Answer:

The value 1.8 represent the club's total number of members today or the present number of members

Step-by-step explanation:

Given an exponential function;

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

b is the base or the growth factor

a is the initial value, that is the value of y when x = 0

We have been given the exponential function;

[tex]y=1.8(1.02)^{12t}[/tex]

The value 1.8 simply represents the initial value of y. Plug in t = 0 in the equation;

[tex]y=1.8(1.02)^{12(0)}=1.8[/tex]

Therefore, the value 1.8 represent the club's total number of members today or the present number of members.

Answer:

TELL HIM TO STOP BEING SO CHEAP!!!!!!!!! <3

and i oop-

Step-by-step explanation:

Answer:

CD = 9

Step-by-step explanation:

DB is a perpendicular bisector, thus ΔADC is isosceles with

CD = AD = 9

The answer is D.

If you multiply them all together the answer (without simplifying), it should equal 210/9, you then simplify the numerator and denominator by 3 and you get 70/3.

Answer:

D

Step-by-step explanation:

Given

[tex]\frac{5}{3}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{21}{1}[/tex]

Multiply numerators/ denominators

= [tex]\frac{5(2)(21)}{3(3)(1)}[/tex]

= [tex]\frac{210}{9}[/tex]

Cancel the numerator/denominator by dividing both by 3

= [tex]\frac{70}{3}[/tex] → D

Answer:

D

Step-by-step explanation:

Using the midpoint formula

midpoint of 2 points (x₁, y₁ ) and (x₂, y₂ ) is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

let (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5), then midpoint is

[ [tex]\frac{1}{2}[/tex](- 1 + 5), [tex]\frac{1}{2}[/tex](5 + 5) ]

= (2, 5) → D

The midpoint of the segment is (2,5).

To find the midpoint of a line segment with endpoints [tex]\((-1, 5)\) and \((5, 5)\)[/tex], we can use the midpoint formula:

[tex]\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Given the endpoints:

[tex]\( x_1 = -1 \), \( y_1 = 5 \)[/tex] (coordinates of the first point)

[tex]\( x_2 = 5 \), \( y_2 = 5 \)[/tex] (coordinates of the second point)

Now, let's plug these values into the midpoint formula:

[tex]\[ \text{Midpoint} = \left( \frac{-1 + 5}{2}, \frac{5 + 5}{2} \right) \][/tex]

[tex]\[ = \left( \frac{4}{2}, \frac{10}{2} \right) \][/tex]

[tex]\[ = \left( 2, 5 \right) \][/tex]

Therefore, the midpoint of the segment is (2, 5)

Among the given options, the correct one is option D: (2, 5).