Solve the right triangle. See image below.

Solve The Right Triangle. See Image Below.

Answers

Answer 1

Hi there! You still remember the Pythagorean Theorem, right? It's useful when it comes to finding a missing leg or side of a right triangle. If you forget then here it is:

[tex] \large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]

Define c = hypotenuse while a and b can be both adjacent and opposite (because a²+b²=b²+a² via addition property)

Since we are missing the adjacent side. Thus,

We define a = 6 and c = 14.

[tex] \large{ {6}^{2} + {b}^{2} = {14}^{2} } \\ \large{36 + {b}^{2} = 196} \\ \large{ {b}^{2} = 196 - 36} \\ \large{ {b}^{2} = 160} \\ \large{ b = \sqrt{160} \longrightarrow \boxed{b = 4 \sqrt{10} }}[/tex]

Put the value of b in a calculator then round to the nearest tenth and get 12.6

Thus, the value of b ≈ 12.6

Next we are going to find the angle in degree. We now know that b ≈ 12.6 or 4sqrt(10)

We can find the value of angle A by using tan or sin but I will use sin instead. Recall the sine ratio which is opposite to hypotenuse. Thus,

[tex] \large{sinA = \frac{6}{14} }[/tex]

Use arcsin(6/14) and put it in calculator.

Then put the decimal value of arcsin in sin and convert in degree form which we should get 24. 555°. Round to the nearest whole number and we get 25°

Thus, the angle A is 25°

Next is we are finding the value of angle B. We aren't going to use any formula or equation. Recall that three angles add up to 180°.

Thus, 25° + 90° + x = 180°

90° comes from a right angle.

115+x = 180

x = 180-115

x = 65°

Thus, the angle B is 65°

Answer

b ≈ 12.6 or 4sqrt(10)angle A = 25°angle B = 65°

Related Questions

Someone help me pls

Answers

Answer:

i think it's 4^ 19

4^11/4^-8

4^ 11 +8

4^19

what is the number 154 798 105 in expanded notation​

Answers


Expanded form:

1 × 100,000,000
+ 5 × 10,000,000
+ 4 × 1,000,000
+ 7 × 100,000
+ 9 × 10,000
+ 8 × 1,000
+ 1 × 100
+ 0 × 10
+ 5 × 1

I hope it helps :)

A window has the shape of a rectangle with a semicircle at the top. Find the approximate area of the window using the dimensions shown.

Answers

Answer:

9.57 ft²

Step-by-step explanation:

assuming the diigram attached is similar to the one required to complete the question,

From the diagram

Area of the window = Area of the rectangle+ Area of the semi circle.

A = lw+πr²/2................ Equation 1

Where A = area of the window, l = length of the rectangle, w = width of the rectangle, r = radius of the semi circle.

From the diagram,

Given: l = 4 ft, w = 2 ft, r = w/2 = 2/2 = 1 ft.

Constant: π = 22/7

Substitute these values into equation 1

A = (4×2)+(22/7×1²/2)

A = 8+1.57

A = 9.57 ft²

real answers only pls help!

Answers

Answer:

look at the picture i have sent

Answer:

d

Step-by-step explanation:

this shape is made up of a triangular prism and a rectangular prism. the formula for the volume of a prism (any prism, doesn't matter) is base area times height. the base areas of the rectangular prism can be found by multiplying 4*12, as these are the dimensions of the base rectangle. 4*12=48. we now multiply this number by the height of the rectangular prism as shown in the volume of a prism formula. the height of the rectangular prism is 14, so 48*14=672. the volume of the rectangular prism is 672 cm^3.

now for the triangular prism. the bases of the triangular prism are the two triangle shapes on the ends; a prism is named after the shape of its base, so be sure to note that you use the triangles for the formula and not the rectangle on the bottom. to find the area of one of these bases (they are both the same), we use the triangle area formula, 1/2*base*height. the base of the triangle shape is 4 units long, as seen by the measurements of the rectangle this triangle sits on top of. to find the height of this triangle, which isn't given, we must use the pythagorean theorem, a^2+b^2=c^2. c in this case is equal to 4 as that is the hypotenuse, and a and b are interchangeable. since the pythagorean theorem only works for right triangles, we must cut the base length in half to assume that the final side is a vertical line, which will give us the height of the original triangle. (note: halving the base length in order to apply the pythagorean theorem only works in this case because both of the other sides are equal length, as we can see on the far triangle, so make sure this applies before trying it in another context) the halved base length is 2, and this number can be either a or b, doesn't matter because the formula adds them. so: (2)^2+b^2=4^2. 2^2 is 4, and 4^2 is 16. 4+b^2=16. subtract 4 from both sides, leaving you with b^2=12, and to get rid of the square on b you take the square root of both sides. so the height of this triangle is the square root of 12, which doesn't need to be simplified if you have a calculator that can process square root input. so to find the area of this triangle, we convert the equation 1/2*base*height into 1/2*4*square root of 12. this gets you about 6.93. to find the total volume of this prism, you multiply the base area times height. as we just figured out, the base area is 6.93, and the height is 12, because this is the length between the two bases, which are the triangles. so, 6.93*12=83.16 is the volume of the triangular prism. the final step is to add this to the volume of the rectangular prism, which is 672. 672+83.16= 755.16 cm^3.

hope this helps! :)

Slope of the line that passes through (8,-9) and (14,-9)

Answers

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, - 9) and (x₂, y₂ ) = (14, - 9)

m = [tex]\frac{-9+9}{14-8}[/tex] = [tex]\frac{0}{6}[/tex] = 0

Someone help me right now pls

Answers

Answer:

90 degrees and 180 degrees

Step-by-step explanation:

90 degrees and 180 degrees

i will give brainiest if correct please hurry!!
You flip a coin 50 times and get 26 tails. What is the experimental probability of flipping heads? Write your answer as a simplified fraction or a percentage.

Answers

Answer:

12/25

Step-by-step explanation:

If you got 26 tails, that means you got 50 - 26 or 24 heads. The experimental  probability can be represented by the desirable flips over the total number of flips. We are looking for heads, so the amount of heads is the amount of desirable flips, and the total is 50. From this, we get the fraction 24/50 which simplifies to 12/25.

An angle measures 79.6° less than the measure of its complementary angle. What is the measure of each angle?

Answers

Answer:

y = 259.6/2 = 129.8 degrees. so x = 129.8 - 79.6 = 50.2 degrees.

Step-by-step explanation:

I got this answer from somewhere else. but it is correct. i hope this helped.

a car is going 40 miles per hour for 3 hours how far did the car go?
can anyone explain to me

Answers

Answer:

120miles

Step-by-step explanation:

I am not sure exactly I just guessed that since it's 40 miles an hour, it would be 40 x 3 ~ but am not sure... hope it works out!

btw am rlly bad at this :'')

- sry if am wrong

                           

what is the median !!! help!! alegbra 2. marking brainliest

Answers

Answer:

The answer is 8.5

Step-by-step explanation:

Just list all the numbers and cross them out one by one.

Add up all of the numbers and divide by the number of numbers in the data set. The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median.

hello please help i’ll give brainliest

Answers

Answer:

Volcanic Eruptions, Earthquakes, Erosion

I am very sorry if this is wrong

Have a great rest of your day and good luck!

Answer:

the answer is a, b, and d

Step-by-step explanation:

erosion is caused by wearing down overtime

hello please help i’ll give brainliest

Answers

nomads …………………………………….

use the matrix tool to solve the system of equations enter the answer as an ordered pair. 8x+5y=9 -x+y=7

Answers

Answer:

x = -44/13

y = -65/13

Step-by-step explanation:

Using matrix form means using the crammers rule

The matrix form of the expression is written as;

[tex]\left[\begin{array}{ccc}8&5\\-1&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}9\\7\\\end{array}\right][/tex]

AX = B

taking the determinant of A;

|A| = 8(1) - 5(-1)

|A| = 8 + 5

|A| = 13

After replacing the first row with the column matrix;

[tex]A_x =\left[\begin{array}{ccc}9&5\\7&-1\\\end{array}\right][/tex]

|Ax| = 9(-1)-5(7)

||Ax| = -9 - 35

|Ax| = -44

x = |Ax|/|A|

x = -44/13

similarly for y

[tex]A_x =\left[\begin{array}{ccc}8&9\\-1&7\\\end{array}\right][/tex]

|Ay| = 8(7)+9

|Ay| = 56+9

|Ay| = 65

y = |Ay|/|A|

y = -65/13

Ms. Masi is going to be paid $11.25 per day to look after Ms. Simms’ dog. She wants to save all of her earnings, but she owes her brother $72. After the first day of dogsitting, Ms. Masi uses her earnings to pay part of her debt to her brother. After the second day, she uses her earnings to pay more of her debt. Ms. Masi plans to save every dollar of her dog sitting money as soon as she has paid her brother in full.

How many days will it take for Ms. Masi to pay her brother in full? Explain.

Answers

Answer:

7 days

Step-by-step explanation:

So! Ms. Masi earns $11.25 everyday, and is paying her brother back everyday. Let's make an equation to solve for the number of days!

11.25d = 72 (d = # of days)

Now, we have to solve this equation to see how many days (d) it will take Ms. Masi to pay her brother back.

11.25d = 72

÷11.25   ÷11.25 (Divide by "11.25" to get the variable by itself)

d = 6.4

Since, she only gets 1 pay per day, Ms. Masi will have to wait til her 7th day to pay her brother back.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Select the correct answer. What is the approximate distance between points D and E? Round your answer to the nearest hundredth. A.

Answers

Answer:

The approximate distance between points D and E is 8.25

Step-by-step explanation:

The figure is as follows :

To find - What is the approximate distance between points D and E ?

Solution -

By Pythagoras Theorem, we get

(DE)² = (FE)² + (DF)²

        = (8)² + (2)²

        = 64 + 4

        = 68

⇒(DE)² = 68

⇒DE = √68

⇒DE = 8.246

∴ we get

The approximate distance between points D and E is 8.25

Find the degree measure of each angle in the triangle

Answers

Answer:

∠L = 43°

∠M = 121°

∠N = 16°

Step-by-step explanation:

Start by setting all sides equal to 180

3x - 5 + 7x + 9 + x = 180

Add like terms

11x + 4 = 180

Solve for x

11x + 4 = 180

      - 4     - 4

      11x = 176

     / 11     /11

        x = 16

Now, plug in 16 for all instances of x on the triangle and solve.

∠L = 43°

∠M = 121°

∠N = 16°

Give the domain.

y =2 / (5x - 4)(4x - 9)

Answers

Answer:

x ≠ 4/5, x ≠ 9/4

You can also write it as "all real numbers except 4/5 and 9/4."

Step-by-step explanation:

The denominator of a fraction cannot equal 0. We can write this relation to find what x does NOT equal:

(5x - 4)(4x - 9) ≠ 0

We can use the zero-product property to get two separate equations:

5x - 4 ≠ 0

5x ≠ 4

x ≠ 4/5

4x - 9 ≠ 0

4x ≠ 9

x ≠ 9/4

The answer above me is correct

In ⊙Q, mJLK= 170 and m∠1 = 36. What is mLM?

Answers

i believe it is also 170 degrees as the top angle mJLK

Dustin has a spinner that is divided into 5 equal-size sections colored pink, blue, orange, white, and green. What is the probability that Dustin spins pink on the 1st spin and then spins a color other than pink on the 2nd spin?

Answers

Answer:

1/6

Step-by-step explanation:

1st spin:

1 out of the 5 sections are pink, so the probability of spinning a pink on the 1st spin is 1/5.

2nd spin:

5 out of the 6 sections are not pink, so the probability of spinning a pink on the 2nd is 5/6.

Multiply the probabilities of the two spins to get the answer.

[tex]\frac{1}{5} *\frac{5}{6} =\frac{5}{30} =\frac{1}{6}[/tex]

What are all the zeros of the function f(x) = 4x^2 + 8x + 3?

Answers

Answer: -1/2 and -3/2

Step-by-step explanation:

X1= -3/2 x2= - 1/2

I think I’m not sure

A 2-quart carton of sour cream costs $4.32. What is the price per cup?

Answers

Answer:

0.54 cents

Step-by-step explanation:

4 cups per quart = 8 cups per 2 quarts

4.32/8 = .54

Find the value of each variable so that PQRS is a parallelogram. Explain what allows you to do this.

Answers

Answer:

[tex]x = 5[/tex]

[tex]y = 16[/tex]

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Find variables x and y

Solving for x, we have:

[tex]5x = 25[/tex] ---- Opposite sides of a parallelogram

[tex]\frac{5x}{5} = \frac{25}{5}[/tex] ------ Divide both sides by 5

[tex]x = 5[/tex]

Solving for y, we have:

[tex]3y - 1 = 47[/tex] ---- Opposite sides of a parallelogram

[tex]3y = 1 + 47[/tex] ------ Collect like terms

[tex]3y = 48[/tex]

[tex]\frac{3y}{3} = \frac{48}{3}[/tex] ---- Divide both sides by 3

[tex]y = 16[/tex]

Forty-five percent of what number is 15.75?​

Answers

45 percent (calculated percentage %) of what number equals 15.75? Answer: 35.

Answer:

35

Step-by-step explanation:

15.75 / 0.45 = 35

the value of the underlined digit in 4,596 is how many times the value of the underlined
--
digit in 481
--
a. 10

b.40

c.100

d.400

e.4,000

Answers

B! i hope this helps you out, and if you need any more help i’m here

* Required
1. Which function represents exponential growth?*
1. f(x) = 0.1(8)^x
2. f(x) = 5 (1/3)*x
3. f(x) = 8 (3/4)^x
4 f(x) = 16 (0.3)^x

Answers

Answer:

3

Step-by-step explanation:

1

It’s the only one multiplying by a whole number

Answer the following above

Answers

Answer:

true false true

Step-by-step explanation:

Help! it's easy but I need help

Answers

Answer:

no lol

Step-by-step explanation:

Answer:

i will tell you what to do and then you do the work

Step-by-step explanation:

arrange the numbers from lowest to largest

count the amount of numbers to find how many students wrote each test

to find the mean add all of the numbers up then divide by the amount of numbers there are

to find the mode it that is the number that appears the most or the most common value

to find the median is the middle number, when you put it from lowest to largest, it will be the middle number

hope this helps

If the diameter of a circle is increased by 6 cm, what is the increase in the circumference of the circle?
A. 6 cm

Answers

Answer:

A

Step-by-step explanation:

find the area of the triangle

Please help
need the correct answer
Urgent
Please do not answer from links
will give the brainliest!​

Answers

Answer:

[tex] \rm \displaystyle A_{ \text{triangle}} = \frac{147 \sqrt{7} }{2 } \quad \text{or} \quad 73.5 \sqrt{7} [/tex]

Step-by-step explanation:

we have a right angle triangle composited in a semi-circle we want to figure out the area of the triangle

in order to do so we need to figure out the adjacent side (height AB)

since the given triangle is a right angle triangle we can consider Pythagoras theorem given by

[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]

given that,a=21 and c=28

substitute:

[tex] \displaystyle {21}^{2} + {b}^{2} = {28}^{2} [/tex]

move left hand side expression to right hand side and change its sign:

[tex] \displaystyle {b}^{2} = {28}^{2} - {21}^{2} [/tex]

square root both sides:

[tex] \displaystyle {b}^{} = \sqrt{{28}^{2} - {21}^{2} }[/tex]

use algebraic indentity:

[tex] \rm \displaystyle {b}^{} = \sqrt{({28}^{} + 21) (28 - {21}^{})}[/tex]

simplify:

[tex] \rm \displaystyle {b}^{} = \sqrt{({49}) ( 7)}[/tex]

use redical property:

[tex] \rm \displaystyle {b}^{} = 7 \sqrt{ 7}[/tex]

now to figure out the area we can consider the following formula:

[tex] \displaystyle A_{ \text{triangle}} = \frac{1}{2} bh[/tex]

remember that,h=AB=7√7 and b=BC=21 thus substitute:

[tex] \displaystyle A_{ \text{triangle}} = \frac{1}{2} \times 21 \times 7 \sqrt{7} [/tex]

simplify multiplication:

[tex] \rm \displaystyle A_{ \text{triangle}} = \frac{147 \sqrt{7} }{2 } \quad \text{or} \quad 73.5 \sqrt{7} [/tex]

hence,

the area of the triangle is 194 (approximately)

note: you can also use horon's formula but I like to keep things simple

Please find attached photograph for your answer.

Can someone give me the answer with work to this problem?

Answers

Answer:

x=10

Step-by-step explanation:

4x-18=3x-8

4x-3x=-8+18

x=10

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