The sum of mZAOB and mZBOC is 218º. Find the measure of ZBOC.

Answer:

[tex]tanC=\frac{c}{b},[/tex] [tex]sinB=\frac{b}{a},[/tex] [tex]tanB=\frac{b}{c},[/tex] and [tex]cosB =\frac{c}{a}[/tex]

Step-by-step explanation:

We can use the phrase SOH-CAH-TOA to help us with this problem. SOH-CAH-TOA stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. This phrase helps to remember which sides of a right triangle get divided by which.

First, we'll evaluate [tex]cosB[/tex]. Referencing CAH (Cosine = Adjacent / Hypotenuse), we know that [tex]cosB[/tex] is equal to the length of the adjacent leg to ∠B, which is c, divided by the length of the hypotenuse of the right triangle, which is a. Therefore, [tex]cosB =\frac{c}{a}[/tex].

As for [tex]tanC[/tex], we can refer to TOA (Tangent = Opposite / Adjacent), which means that [tex]tanC[/tex] is equal to the length of the opposite leg to ∠C, which is c, divided by the length of the adjacent leg to ∠C, which is b. Therefore, [tex]tanC=\frac{c}{b}[/tex].

As for [tex]sinB[/tex], we can refer to SOH (Sine = Opposite / Hypotenuse), which means that [tex]sinB[/tex] is equal to the length of the opposite leg to ∠B, which is b, divided by the length of the hypotenuse of the right triangle, which is a. Therefore, [tex]sinB=\frac{b}{a}[/tex].

Finally, we'll evaluate [tex]tanB[/tex]. As TOA tells us, [tex]tanB[/tex] is equal to the length of the opposite leg to ∠B, which is b, divided by the adjacent leg to ∠B, which is c. Therefore, [tex]tanB=\frac{b}{c}[/tex].

Hope this helps!

Answer:

i believe the answer is D (which is 10)

Step-by-step explanation:

i just took the test. so you have to isolate X, so you add 2 to both sides and on the right you get answer of "5". so then you have to multiply both sides by "2/1" (which is the reciprocal of 1/2) and so on the left side so you're left with just "x", and on the right side you have 2/1 times 5/1 which equals "10".

Answer:

I would say $24?

Step-by-step explanation:

20/5=4

20+4=24

This is because $20 is for 5/6 of an hour, $24 would be for the entire hour.

Answer: its 24

Step-by-step explanation:

i have confirmed!!

9514 1404 393

Answer:

  D.  16.8 years

Step-by-step explanation:

The multiplier each year is 1-3% = 0.97, so the multiplier after x years is 0.97^x. You want to know the value of x when that multiplier is 60%, or 0.60.

  0.97^x = 0.60

  x·log(0.97) = log(0.60) . . . . . . take logarithms

  x = log(0.60)/log(0.97) ≈ 16.8

At the given rate, it will be 16.8 years before 60% of the species remains.

Answer:

x = -6.

Step-by-step explanation:

5 -2x = -4x - 7

Add '4x' to both sides:

5 - 2x + 4x + -4x + 4x -7

5 + 2x = -7

Subtract '5' from both sides:

5 - 5 + 2x = -7 - 5

2x = -12

Divide both sides by '2':

x = -6.

Answer:

3

Step-by-step explanation:

[tex]\frac{h^{2}-1 }{h+3}[/tex]=

[tex]\frac{5^{2}-1 }{5+3}[/tex]=

[tex]\frac{25-1}{8}[/tex]=

[tex]\frac{24}{8}[/tex]=

3

Answer:

B. 1.67%

Step-by-step explanation:

The periodic rate is the annual interest rate divided by the number of periods.

Therefore, we divide the annual interest rate by 12.

[tex]20\% \div 12 =1.67\% $(correct to two decimal places)[/tex]

Therefore, the periodic interest rate for Jack's credit card from June 3

to July 2 is 1.67%.

Answer:

27.5

Step-by-step explanation:

this is the trigonometric ratio.. we are looking for d... that is the opposite... any side facing the angel is the opposite.... so the longest side of the right angle triangle is the hypotenuse........ so you are looking for the opposite and you are giving the hypotenuse.... so the easiest way to know how to find it is by using this way...... SOH CAH TOA..... the first words stand for sin cosine and tangent of angles.... we are using sin.... because it says opposite / hypotenuse... and as you can see the angle which is 39 degree we will use sin 39.....what will be sin 39=d/30m....then ull cross multiply.... d=30m* sin 39.....

d = 30m *0.963

d = 28.8

but since 27.5 is dere....

you can round up to 1 sig. f =28

Answer:

53

Step-by-step explanation:

f(x) = x^2 – (x + 3)

Let x = 8

f(8) = 8^2 – (8 + 3)

      =64 - (11)

       =53

Answer:

19%

Step-by-step explanation:

1. Decrease by 10% = 0.9 times

2. Repeat decrease by 10% = 0.9*0.9= 0.81 times

0.81 times decrease equals to 100%-81%= 19% decrease

The length of AB is 10 units.

look at the attached picture

Hope it will help you

Good luck on your assignment

The right answer is 2√6

look at the attached picture

Hope it will help you

Good luck on your assignment

[tex]3\sqrt{6} = \sqrt{9}*\sqrt{6} = \sqrt{9*6} = \sqrt{54}[/tex]

The rule I'm using is

[tex]\sqrt{x}*\sqrt{y} = \sqrt{x*y}[/tex]

note how I rewrote "3" into the square root of 9, so that everything would have a square root over it, and that allows me to use that rule above.

[tex]\sqrt{54}[/tex] equivalent to the expression [tex]3\sqrt{6}[/tex].

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given expression

[tex]3\sqrt{6}[/tex]

We have the property [tex]\sqrt{x}[/tex] × [tex]\sqrt{y}[/tex] = [tex]\sqrt{x.(y)}[/tex]

[tex]3\sqrt{6}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{9.(6)}[/tex]

= [tex]\sqrt{54}[/tex]

[tex]\sqrt{54}[/tex] equivalent to the expression [tex]3\sqrt{6}[/tex].

Find out more information about expression here

https://brainly.com/question/14961928

#SPJ3

Answer:

fall dance cost more money?

Step-by-step explanation:

Answer:

Step-by-step explanation:

G(x) is transformed from the parent function f(x)=x^2 by:

right 4 units

since we all know that the vertex form of a quadratic equation is y=a(x-h)^2+k

since 4 is h, and k is 0 ( graph is on the x-axis), we can write the equation of this graph:

g(x)=(x-4)^2, which is C

Answer:

123.5 square inches

Step-by-step explanation:

Given: To find the area of a rectangle, you have to multiply base times height.

To find the area of a triangle, you have to do base times height devided by 2.

Finding the area: Let's break up this shape into polygons. At the bottom there is a rectangle. We know that to find the area of the rectangle you have to do base times height. 13in•7in will give you 91in square for the rectangle.

Now for the triangle. If you can see, if you break the triangle in half, there are 2 right triangles. Let's look at the right one for now. Since we know that to find the area of a triangle you have to do base times height divided by 2,  you do 5in•6.5in=32.5in. 32.5in divided by 2 is 16.25in square which is the area of one triangle. You might be wondering why i did 5•6.5, and that's because at the bottom of the rectangle you can see it's 13in, and 13in÷2=6.5in.

We already found the area of the rectangle and one triangle. The other triangle is equal to it so we can just do 16.25+16.25=32.5in square for both of the triangles.

Now we add it all up: 32.5+91=123.5 square inches

Answer:

4

Step-by-step explanation:

The right answer is 4.

look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

List of expenses is attached below.

Total Income = $160 + $6245 = $6405

As mortgage payment has increased, we replace $1580 with $1632 in the table

Replace student loans with roof expense, we replace $544 with $500 in the table.

Find Total Expenses by adding all the values from the table.

Total Expenses = $6660.17

Total Income  =$6405

They have a deficit

Deficit = $6660.17 - $6405 = $255.17

Deficit = $255.17

Savings = 10% of income = 10% OF $6405

Savings = (10/100)· $6405 = $640.5

New total expenses = $6660.17 - $640.5

New total expenses = $6019.67

Balance = Total income - New total expenses = $6405 - $6019.67

Balance = $295.33

Yes, they had to remove the savings to fulfill their expenditures. Otherwise, they would have been spending more than their income, which couldn't last very long

Answer:

2/3

Step-by-step explanation:

6 friends share 4 pizzas, each get 4/6 = 2/3 pizza

Answer:

CORRECT answer is -3

Step-by-step explanation:

Answer:

BD = 1 unit

AD = 1 unit

AB = 1.6 units

AC = 1.6 units

Step-by-step explanation:

In the picture attached, the triangle ABC is shown.

Given that triangle ABC is isosceles, then ∠B = ∠C

∠A + ∠B + ∠C = 180°

36° + 2∠B = 180°

∠B = (180° - 36°)/2

∠B = ∠C  = 72°

From Law of Sines:

sin(∠A)/BC = sin(∠B)/AC = sin(∠C)/AB

(Remember that BC is 1 unit long)

AB = AC = sin(72°)/sin(36°) = 1.6

In triangle ABD, ∠B = 72°/2 = 36°, then:

∠A + ∠B + ∠D = 180°

36° + 36° + ∠D = 180°

∠D =  180° - 36° - 36° = 108°

From Law of Sines:

sin(∠A)/BD = sin(∠B)/AD = sin(∠D)/AB

(now ∠A = ∠B)

BD = AD = sin(∠A)*AB/sin(∠D)

BD = AD = sin(36°)*1.6/sin(108°) = 1

Answer:

x = 36.

Step-by-step explanation:

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

Answer:

15

Step-by-step explanation:

The constant is the term without the variable

5x+3y=15

15 is the constant

Answer: it’s (3,2)

Step-by-step explanation:

Answer:

|-0.073| < |0.73|​

Step-by-step explanation:

since it is absolute value |-0.073| = .073

and |0.73|​= .73

|-0.073|  |0.73|​

Hello! The answer to your question is:

I believe it is 0.073 < 0.73

I hope this helped you!

Answer:

18.75 or 18 3/4

Step-by-step explanation:

assuming 5 cups is for 1 batch we can just multiply 5 and 3 3/4 to get our answer.

Step-by-step explanation:

[4 2] ×[-2/7 5/-1]

[4×(-2)+4×5/4×7+4×(-1) 2×(-2)+2×5/2×7+2×(-1)]

[-8+20/28+(-4) -4+10/14+(-2)]

[12/24 6/12]

Answer:

x = 36 and √x = 6; total 42 children

Step-by-step explanation:

Number of boys:  x

Number of girls:  √x

Total number of kids:  x + √x = 42.

Find x.

Rewrite x + √x = 42 as √x = 42 - x.  Then square both sides:

x = 1764 - 84x + x^2, or

x^2 - 85x + 1764 = 0

Check out Answer C:  x = 36.  Is the above equation true for x = 36?  YES

Check out Answer A:  x = 49.  Is the above equation true for x = 49?  YES

Assume that x = 36.  This would be the number of boys.  The number of girls would be √36, or 6.  Does the sum of 36 and 6 equal 42?  YES.  So the number of boys is 36 and the number of girls is 6.

Assume that x = 49.  This would be the number of boys.  The number of girls would be √49, or 8.  Does the sum of 49 and 7 equal 42?  NO.  So we reject x = 49 as the number of boys and accept x = 36 as being correct.