Vertical/supplementary/Complementary Angles (Algebraic)​

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Answer:

Step-by-step explanation:

When reflecting coordinates about the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.

So, for the point (4, 6), the new coordinates after reflection about the y-axis would be (-4, 6).

For the point (12, 2), the new coordinates would be (-12, 2).

For the point (-1, 0), the new coordinates would be (1, 0).

Therefore, the new coordinates after reflecting these points about the y-axis are (-4, 6), (-12, 2), and (1, 0).

Answer:

Bruh so easy hahahahahaha

Answer: the distribution to the x and the 3 makes the solution 4

Step-by-step explanation: i got you broski

Answer:

Hi,

Answer B

Step-by-step explanation:

after 1.484 s the ball hit the ground à 22.019 feet

yes the ball will be at a height of 2.93506334 feet when time is 1.348 s and height is 20 feet

no the max height happens at 11.0 has no thing to do with hitting the grat 2.937 s the ball is at -68.2754 feet

ound

Answer:

Step-by-step explanation:

Use tan-1 (5÷7)

Answer: B i think

Step-by-step explanation:

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

The simplified expression is v2/15 / u1/5

To simplify the expression and eliminate any negative exponent(s), we need to use the rules of exponents. The rules of exponents state that when we multiply two expressions with the same base, we add the exponents. When we divide two expressions with the same base, we subtract the exponents. And when we raise an expression with an exponent to another exponent, we multiply the exponents.

Using these rules, we can simplify the expression:

(x-9/5 / y3/5)(x-6 / y-3)1/5

= (x-9/5 + -6 / y3/5 + -3)1/5

= (x-39/5 / y-12/5)1/5

= x-39/5 * 1/5 / y-12/5 * 1/5

= x-39/25 / y-12/25

To eliminate the negative exponents, we can use the rule that x-a = 1/xa:

= 1/x39/25 / 1/y12/25

= y12/25 / x39/25

So the simplified expression is y12/25 / x39/25.

Similarly, we can simplify the second expression:

(u1/2 / v-1/3)-2/5

= u1/2 * -2/5 / v-1/3 * -2/5

= u-1/5 / v2/15

= 1/u1/5 / v2/15

= v2/15 / u1/5

So the simplified expression is v2/15 / u1/5.

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The amount of money in the account after 17 years, to the nearest dollar, would be $76,956.

What is the formula for the future value?

The formula for the future value of an investment with continuous compounding is \(A = Pe^{(rt)}\) where A is the future value, P is the principal (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the number of years.

Putting in the given values,

\(A = 52000 \times e^{(0.021 \times 17) }\\ A ≈ 76,956.18\)

Therefore, the amount of money in the account after 17 years, to the nearest dollar, would be $76,956.

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Answer:

The pythagoras's theorem is the relation between the sides of a right-angles triangle, it shows that the square of the hypotenuse of the triangle will be equal to the sum of squares of the remaining sides

hypotenuse² = perpendicular² + base²

replacing the variables with the sides of the given triangle:

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17 mi

Answer:

the answer is 172cm cubed

Step-by-step explanation:

Answer: 1392 in cubed

Step-by-step explanation:

Lets start by solving for the volumes separately of the square pyramid and rectangular prism. Once we have those two volumes then we can add them together to get the total volume of the shape.

Rectangular Prism:

Formula: V = l * w* h

l = 12

w = 12

h = 7

Plug in values and solve.

V = 12 * 12 * 7

V = 1,008 in cubed

Square Pyramid:

Formula: V = A * (h/3)

A = the area of the base

A = 12^2 = 144

h = 8

Plug in values and solve.

V = 144 * ( 8/3)

V = 384 in cubed

Now we can add the two volumes together.

384 + 1,008 = 1392 in cubed

Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

Answer:

C?

Step-by-step explanation:

If I understand your description correctly...

Vertical Angles are angles on opposite sides of the X formed by intersecting lines, and are Congruent (equal in measure).

So, 4x-5 = x+16

      4x-x-5+5 = x-x+16+5

      3x = 21

      3x/3 = 21/3

      x = 7

Answer:

xsin∅

Step-by-step explanation:

If the ladder is x foot long, and it can safely make a maximum angle ∅  with the floor, then, the maximum height it can reach will be xsin∅

Answer:

Following the 4 to 1 ratio ladder rule

Step-by-step explanation:

set the base 1 foot out from the wall for every 4 feet it reaches up.

Answer: I would assume it to be 9 if you are allowed to round.

Step-by-step explanation: A sphere with a volume of 367cm^3 has a radius of 4.44. Diameter is radius * 2. This would most closely equal 8.88, which rounds to 9.

Given the word:

CARDINALS

The word has 9 letters.

To find the unique permutations of the letters, we have:

First check for the letters that appears more than once.

Letter A appeared twice

Therefore, the permutation is:

ANSWER:

72

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Answer:

The height is 16/80

Step-by-step explanation:

Answer:

126.9° and 323.°1

Step-by-step explanation:

I'll use x instead of theta and you can replace it by theta

5 sin x + 3 = 0

5 sin x = - 3

Sin x = - 3/5

Key angle = sin¯¹ 3/5 = 36.8698

Sin negative, so we use the third and fourth quadrants

X = 90+36.8698, 360-36.8698

X = 126.8698, 323.1302

Theta = 126.9°, 323.°1

Answer:

70 percent of what number is 90?

90 is 70% of 128.57

Steps to solve "90 is 70 percent of what number?"

We have, 70% × x = 90

or,

70

100

× x = 90

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 90 ×

100

70

x = 128.57

If you are using a calculator, simply enter 90×100÷70, which will give you the answer.

Answer:  70 % of 90 = 63

Step-by-step explanation:

   70 %  x  90.

= (70/100) x 90

= (70*90)/100

= 6300/100

= 63

n = 4

The given expression is:

-2 + 5n = 4n + 2

Collect like terms:

5n - 4n = 2 + 2

n = 4

6.25

-

the formula for finding percentage decrease would be:

[(start value - final value)/start value] · 100.

in this case, it would be 5/80 · 100.

5 ÷ 80= 0.0625 · 100= 6.25%.

sorry if this doesnt make sense, but hopefully you understand it !! (i also attacted scrap paper just in case)

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

16

Step-by-step explanation:

F(4)=3(4)+4=12+4=16

Answer:

n \(\geq\) -2

Step-by-step explanation:

1. Set up in an inequality

n-3 \(\geq\) -5

I set it up this way because if it is at least -5 then it can equal -5. It can also be more than -5 because -5 is the least it can be.

2. Add

n \(\geq\) -2

Add 3 to both sides to get n by itself.

The solution to the given inequality will be n  ≥-2.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that a number n minus, 3 is at least –5. Set up in an inequality

n-3 ≥ -5

I set it up this way because if it is at least -5 then it can equal -5. It can also be more than -5 because -5 is the least it can be.

n-3 ≥ -5

n ≥  -5 + 3

n  ≥-2

Therefore, the solution to the given inequality will be n  ≥-2.

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Answer: E. All of the above statements are true

Step-by-step explanation:

The mean of sampling distribution of the mean is simply the population mean from which scores were being sampled. This implies that when population has a mean μ, it follows that mean of sampling distribution of mean will also be μ.

It should also be noted that the distribution's shape is symmetric and normal and there are no outliers from its overall pattern.

The statements about the sampling distribution of the sample mean, x-bar that are true include:

• The sampling distribution is normal regardless of the shape of the population distribution, as long as the sample size, n, is large enough.

• The sampling distribution is normal regardless of the sample size, as long as the population distribution is normal. • The sampling distribution's mean is the same as the population mean.

• The sampling distribution's standard deviation is smaller than the population standard deviation.

Therefore, option E is the correct answer as all the options are true.

The option that gives the true statement about sampling distribution of the sample mean, x-bar, is;

Option E: All of the above.

Let us access each of the options;

A) There is a condition for normal distribution which states that sample size must be more than 30. So as long as the sample size is big enough, regardless of the shape, it is still a normal distribution.

B) This statement is also true because as long as the distribution of the population is normal, then it overrules every other thing as the sample distribution will have to be normal as a result.

C) This is true because by definition of population mean, it is the same as sample mean of the distribution.

D) This is true because the population is always more than the sample.

E) This is correct as all the above options are true.

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Answer:

cute scalene triangle.

Sides: a = 1   b = 2   c = 1.906

Area: T = 0.94

Perimeter: p = 4.906

Semiperimeter: s = 2.453

Angle ∠ A = α = 29.543° = 29°32'36″ = 0.516 rad

Angle ∠ B = β = 80.457° = 80°27'24″ = 1.404 rad

Angle ∠ C = γ = 70° = 1.222 rad

Height: ha = 1.879

Height: hb = 0.94

Height: hc = 0.986

Median: ma = 1.888

Median: mb = 1.147

Median: mc = 1.262

Inradius: r = 0.383

Circumradius: R = 1.014

Vertex coordinates: A[1.906; 0] B[0; 0] C[0.166; 0.986]

Centroid: CG[0.691; 0.329]

Coordinates of the circumscribed circle: U[0.953; 0.347]

Coordinates of the inscribed circle: I[0.453; 0.383]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 150.457° = 150°27'24″ = 0.516 rad

∠ B' = β' = 99.543° = 99°32'36″ = 1.404 rad

∠ C' = γ' = 110° = 1.222 rad

Step-by-step explanation: