Please help !! Thank you so much !

Answer:

x = 35.5

Step-by-step explanation:

cos 65° = 15/x

cos 65° · x = 15

x = 15/cos 65°

x = 35.5

Part 1

There are many ways to go about this, but one possibility is the following:

You are building a tree house. Your ladder is 10 feet long and the portion in the tree you're trying to get to is 8 feet off the ground. How far should the base of the ladder be from the tree so you can reach that portion?

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Part 2

The drawing is shown below. The diagram is shown in 2D to keep things as simple as possible. Adding a third dimension greatly complicates everything.

We have a right triangle, so it has a 90 degree angle as shown by the square marker. The vertical leg is 8 feet. The horizontal leg is unknown. The hypotenuse (longest side) is 10 feet long to indicate the ladder.

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Part 3

Use the pythagorean theorem to get...

a^2 + b^2 = c^2

x^2 + 8^2 = 10^2

x^2 + 64 = 100

x^2 = 100-64

x^2 = 36

x = sqrt(36)

x = 6

The base of the ladder should be 6 feet away from the tree, so that you can reach 8 feet off the ground.

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

The correct number of candy is 1974 thousand candy bars (or 1,974,000 candy bars) must be sold to maximize revenue.

To maximize revenue, we need to determine the value of x that maximizes the function R(x) = p(x) * x, where R(x) represents the revenue generated by selling x thousand candy bars.

Given that p(x) = 141 - (x/28), we can substitute this expression into the revenue function:

R(x) = (141 - (x/28)) * x

Now, let's expand and simplify this equation:

\(R(x) = 141x - (x^2/28)\)

To find the value of x that maximizes the revenue, we need to find the critical point by taking the derivative of R(x) with respect to x and setting it equal to zero:

R'(x) = 141 - (2x/28) = 0

Simplifying this equation, we have:

141 - (2x/28) = 0

Multiplying through by 28 to eliminate the fraction, we get:

3948 - 2x = 0

Solving for x, we find:

2x = 3948

x = 3948/2

x = 1974

Therefore, 1974 thousand candy bars (or 1,974,000 candy bars) must be sold to maximize revenue.

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Answer: he would save (9) hours (44) minutes on an airplane.

Step-by-step explanation: its easy just subtract 11 &2 & you'll get 9 hours but you don't do anything with the 44 & 23 all you have to do is put down 9 - hours & 44 - minutes. it's a piece of cakeplease rate me with 5 stars & thank me & hit the little crown please and thank you and if you want to be friends we can just friend me please and thank you and your welcome!!!!

From the quadrilateral proof seen below we can prove that;

∠C + ∠D = 2∠AOB

The bisection of an angle simply means to divide an angle into two equal parts.

The sum of the interior angles of a quadrilateral is 360 degrees. Thus;

∠A + ∠B + ∠C + ∠D = 360°     ------(1)

In △AOB,

∠AOB + ∠A/2 + ∠B/2 = 180°

Multiply through by 2 to get;

2∠AOB + ∠A + ∠B = 360°

Thus;

∠A + ∠B = 360° - 2∠AOB

Put 360° - 2∠AOB for ∠A + ∠B in eq 1 to get;

360° - 2∠AOB + ∠C + ∠D = 360°

This simplifies to;

∠C + ∠D = 2∠AOB

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Complete question is;

Bisectors of two adjacent angles of angles A and B of quadrilateral ABCD intersect at a point O. Prove that 2∠AOB = ∠C + ∠D

Answer:

The answer is -5 and 5 because when you do absolute value if there is a negative number then it turns into a positive number. Negatives will always turn out as positives when doing absolute value. :)

Step-by-step explanation:

Answer: the two numbers that have the same absolute value is -5, and 5.

Step-by-step explanation:

Absolute will just make any negatives to positive.

So, the absolute value of -5 is 5,  or the absolute value of -3, is 3.

If it's already positive, then nothing happens; it stays the same

So, the absolute value of 8 is 8, nothing is changed.

Answer:

blue line: y = x + 2  ||      green line: y = -2x+3

Step-by-step explanation:

For blue line:

take two coordinates: (0,2),(1,3)

slope:

\(\frac{y2-y1}{x2-x1}\)

\(\frac{3-2}{1-0}\)

\(1\)

equation:

y - y1 = m(x - x1)

y - 2 = 1(x - 0)

y = x + 2

For green line:

take two coordinates: (0,3),(2,-1)

slope:

\(\frac{y2-y1}{x2-x1}\)

\(\frac{-1-3}{2-0}\)

\(-2\)

equation:

y - y1 = m(x - x1)

y - 3 = -2(x-0)

y = -2x+3

Answer:

The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Step-by-step explanation:

Allstars mean height:

= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15

= 1007 / 15

= 67.6 inches

Super Stars mean height:

= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15

= 912 / 15

= 60.2 inches

We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players

Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Answer:

75 \(feet^{3}\)

Answer:

a=11, b=10, c=32, and d=14.

Step-by-step explanation:

Answer:

67 units

Step-by-step explanation:

Perimeter  of a shape is the sum of all sides.

Perimeter = a + b + c + d

                = x +7  + 2x + 2 + 8x + x +10

                = x + 2x + 8x + x  +7 + 2 + 10

Combine like terms,

                 = 12x + 19

Now, substitute x = 4 in the above expression,

                  = 12*4 + 19

                  = 48 + 19

                  = 67

Answer:

b = 4\(\sqrt{3}\) , c = 8

Step-by-step explanation:

using the tangent and cosine ratios in the right triangle and the exact values

tan60° = \(\sqrt{3}\) , cos60° = \(\frac{1}{2}\) , then

tan60° = \(\frac{opposite}{adjacent }\) = \(\frac{b}{4}\) = \(\sqrt{3}\) ( multiply both sides by 4 )

b = 4\(\sqrt{3}\)

then

cos60° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{4}{c}\) = \(\frac{1}{2}\) ( cross- multiply )

c = 4 × 2 = 8

Using linear function concepts, it is found that the representation of the value of 4,000 is given by:

B the gallons of water initially in the pool.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the amount of water in the pool after x hours is modeled by:

y = -720 x + 4000.

4000 is the y-intercept, which is the initial amount of water in the pool, hence option B is correct.

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Answer:

because these angles are equal to right angle triangle

Answer:

Step-by-step explanation:

\(y=\frac12(x+4)(x-2)\quad\implies\quad x_1=-4\,,\ \ x_2=2\)

vertex is (p, q) where:

\(p=\dfrac{x_1+x_2}2=\dfrac{-4+2}2=\dfrac{-2}2=-1\\\\q=f(p)=\frac12(-1+4)(-1-2)=\frac12(3)(-3)=-\frac92=-4.5\)

So the vertex is: (-1, -4.5)

Answer:

\(a = \frac{(b - c)}{c} \\ ac = (b - c) \\ ac + c = b \\ c(a + 1) = b \\ c = \frac{b}{(a + 1)} \)

hope this helps.

For the octagon whose measure of angle is (9w + 8)°, the value of w is 14.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Angle of regular octagon = 9w + 8

Since, angle of an octagon is 135°

Equate 9w + 8 to 135,

9w + 8 = 135

9w = 127

w = 14.11

w = 14

The required value of w is 14.

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Answer:

he octagon whose measure of angle is (9w + 8)°, the value of w is 14.

Step-by-step explanation:

What is angle?

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Angle of regular octagon = 9w + 8

Since, angle of an octagon is 135°

Equate 9w + 8 to 135,

9w + 8 = 135

9w = 127

w = 14.11

w = 14

The required value of w is 14.

i hope this helps !!!!!

The Probability that the system does not fail for 2 days is 0. 053

Given ,

Mean (u) = 37 hours .

Step  1 : Calculate the rate parameter, λ.

λ = 1/ mean

λ = 1/ 37 = 0.02703

Step 2 : Find the probability that the system does not

fall for two days, P ( x\(\leq\)2 )  

P ( x\(\leq\)2 ) .= 1 - e power (lamda(x))

       = 1 - e - 2(lamda)

        = 1 - e power  -2(0. 02703 )

By solving,

P ( x\(\leq\)2 ) = 0.05263

P ( x\(\leq\)2 ) = 0. 053 [ upto three decimals]

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(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

What is Quadrant?

(i) When sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=41.81°,138.18°

So it lies in Ist and IInd quadrant.

A suitable graph is not provided here.

(ii) when cosФ=-1/2

Ф=cos^(-1)(-1/2)

Ф=120°,240°

So it lies in IInd and IIIrd quadrant.

A suitable graph is A and D.

(iii) when cotФ=3/4

Ф=cot^(-1)(3/4)

Ф=53.13°,233,13°

So it lies in Ist and IIIrd quadrant.

A suitable graph is E.

(iv) when cosecФ=3/2 or sinФ=2/3

Ф=sin^(-1)(2/3)

Ф=0.729°

So it lies in Ist quadrant.

A suitable graph is not provided here.

(i) When sinФ=2/3 → It lies in Ist and IInd quadrants and the suitable graph is not provided here.

(ii) when cosФ=-1/2 → It lies in IInd and IIIrd quadrants and the suitable graph is A and D.

(iii) when cotФ=3/4 → It lies in Ist and IIIrd quadrants and the suitable graph is E.

(iv) when cosecФ=3/2 → It lies in the Ist quadrant and the suitable graph is not provided here.

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The estimated margin of error can be found using the confidence interval provided by the store manager. The confidence interval of (44.9, 82.3) represents a range within which the true population mean price for textbooks is estimated to lie.

To find the estimated margin of error, we take half of the width of the confidence interval. The width of the confidence interval is obtained by subtracting the lower bound from the upper bound: 82.3 - 44.9 = 37.4. Since the margin of error is half the width, we divide this value by 2: 37.4 / 2 = 18.7.

Therefore, the estimated margin of error is 18.7 dollars. This means that, based on the provided confidence interval, the store manager estimates that the mean price for the population of textbooks is within 18.7 dollars of the sample mean.

However, the sample mean itself is not directly provided in the given information.

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Answer:

Step-by-step explanation:

D:  x ≥ -2.  This set includes x = -2 and all numbers greater than -2.

Answer: Choice D)  \(x \ge -2\)

Explanation:

We have a closed circle at -2, and shading to the right. This tells us x can equal -2, or it can be larger than -2. In short, x is greater than or equal to -2.

Symbolically, we'd write it as \(x \ge -2\)

If you wanted to graph \(x > -2\) instead, you would have an open circle to indicate "do not include this value in the solution set".

The correct time in the clock will be 8:40

The acute angles that are between the angle 30 and 60 is 35, 40,45, 50, 55 degrees.

According to the question, we are to determine the time in the clock if the angle between the minute hand and the hour hand of a clock is between 30 degree and 60 degrees.

The time 4:20 is wrong since the minute and hour hand are on each other while the time 10:45 D. 12:15 is wrong since the angle between the hands will be 90 degrees

Hence the correct time in the clock will be 8:40

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For z varies jointly with x and y. When x=5 and y=4, z=12.

a. Equation that models the relationship is z=(3/5)xy.

b. When x=15 and y=2 then z=18.

As given,

a. Equation that models relationship z varies jointly with x and y is:

z is directly proportional to product of x and y

⇒z∝ xy

⇒z=k xy

where k is symbol of proportionality.

When x=5 and y=4, z=12

12=k(5× 4)

⇒k=12/(5× 4)

⇒k=3 /5

Hence, z=(3/5)xy

b. When x=15 and y=2

z=(3/5)×15×2

 =18

Therefore, for z varies jointly with x and y, when x=5 and y=4, z=12.

a. Equation that models relationship is z=(3/5)xy.

b. When x=15 and y=2 then z=18.

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Answer:

I think -1/3

Step-by-step explanation:

Its negative bc the line is moving from left to right

Take 2 points from the line.

At the origin, (0,0)

And (6,-2) a point in fourth quadrant

m = y2 - y1

x2 - x1

m = -2 - 0

6 - 0

m = -1/3.

The 3rd option is the correct option.

ΔACD have AC=AD ⇒ ΔACD is a isosceles triangle

⇒ ∠ACD = ∠ADC = 67° ⇒ a° = 67°

ΔABD is a square triangle

⇒ ∠ABD = 90° - ∠ADC = 90° - 67° = 23° ⇒ b° = 23°

ok done. Thank to me :>

The values of b and a for the logarithmic function in this problem are given as follows:

The logarithmic function in the context of this problem has the format given as follows:

\(y = b\log_3{x + a}\)

The vertical asymptote is at x = -4, hence:

\(y = b\log_3{x - 4}\)

When x = 5, y = -1, hence the parameter b is obtained as follows:

\(-1 = b\log_3{5 - 4}\)

0.477b = -1

b = -1/0.477

b = -2.1.

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