Which equation can be used to solve for b? b = (8)tan(30o) b = b = (8)sin(30o) b =
Answers
tan30 = b/8
b=8tan30
In a right angle triangle the three sides are represented by the letters a, b and c .
a represents the side adjacent with given angle .
b represents the side opposite to the given angle.
c represents the hypotenuse of the triangle .
Check the attached image for clear picture of the right angle triangle with angle 30 degrees .
Using the trigonometric ratio we can write the ratio as
[tex]\frac{b}{a} = tan(30^0)[/tex]
Multiplying both sides by a , we get
[tex]b =a * tan(30^0)[/tex]
since a=8 so
[tex]b = 8* tan(30^0)[/tex]
Related Questions
144=8x what is the answer please help me
Answers
To solve for x in this equation, we need to divide both sides of the equation by 8 to isolate x.
144/8=8x/8
18=x
x=18
Hope this helps!
Here, it is multiplied by 8. We perform the inverse operation, divide by eight (or multiply by one eighth), on both sides of the equation.
[tex]144=8x[/tex]
[tex] \dfrac{144}{8}= \dfrac{8x}{8} [/tex]
[tex]x=18[/tex]
How many square feet of outdoor carpet will we need for this hole?
Answers
Answer:
44 square feet
Step-by-step explanation:
We are given a rectangle of dimension 12ft×4ft and a square of dimension 2ft×2ft.
Then, the required outdoor carpet will be:
Outdoor carpet required=Area of the outer hole that is the rectangle - Area of the inner hole that is the square
=[tex](length)(breadth)-(side)^{2}[/tex]
=[tex](12)(4)-2^{2}[/tex]
=[tex]48-4[/tex]
=[tex]44[/tex] square feet.
Beulah took out a loan for $1225 at an 11.4% APR, compounded monthly, to buuy a foosball table. If she will make monthly payments of $101.75 to pay off tghe loan, how many total payments will she have to make?
Answers
To answer this problem, get first the Future Value (FV) of the loan for a year. Given the APR and the amount of loan, FV is computed as follows: FV = $1225 x (1+.0095)¹² = $1372.18
Note that the APR and period were changed to 0.95% and 12, respectively because it has to be compounded monthly.
Now, divide the FV by the monthly payment of $101.75.
Number of payments = $1372.18/$101.75 = 13.48 ≈ 13
Answer:
13
Step-by-step explanation:
APEX
This figure consists of a rectangle and semicircle.
What is the perimeter of this figure?
Use 3.14 for pi.
19.42 cm
20.28 cm
23.42 cm
32.84 cm
Answers
1. for the semicircle p₁=πr=3.1415*3≈9.4248 cm., where r=3 radius of the semicircle;
for the rectangle p₂=4*2+6=14 cm.
2. totaly: p=p₁+p₂=14+9.4248≈23.4248 cm.
answer: 23.42 cm.
Answer:
The perimeter of the figure is [tex]23.42\ cm[/tex]
Step-by-step explanation:
we know that
The perimeter of the figure is equal to the perimeter of the rectangle plus the circumference of a semicircle minus the length of [tex]6\ cm[/tex]
Step 1
Find the perimeter of rectangle
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
In this problem we have
[tex]L=6\ cm[/tex]
[tex]W=4\ cm[/tex]
substitute
[tex]P=2(6+4)=20\ cm[/tex]
Step 2
Find the circumference of a semicircle
The circumference of a semicircle is equal to
[tex]C=\pi r[/tex]
we have
[tex]r=6/2=3\ cm[/tex] -----> the radius is half the diameter
substitute
[tex]C=3\pi\ cm[/tex]
Step 3
Find the perimeter of the figure
[tex]20\ cm+3\pi\ cm-6\ cm=(20+3.14*3-6)=23.42\ cm[/tex]
Part A: What is the group of points labeled P called? What is the point labeled T called? Give a possible reason for the presence of point T.
Part B: Describe the association between students' test scores and the number of hours they exercise.
Answers
in an election for sheriff 210 people voted if there where 1260 possible voters write a ratio to compare the number of people who voted to the numbernof possible voters
Answers
The ratio of the number of people who voted to the number of possible voters in the sheriff election is 1:6 after simplifying the original ratio of 210:1260.
Explanation:In an election for sheriff where there are 1260 possible voters and only 210 people voted, the ratio of the number of people who voted to the number of possible voters can be written as 210:1260. To simplify this ratio, you divide both numbers by the greatest common divisor, which in this case is 210. So, when you divide both 210 and 1260 by 210, the simplified ratio is 1:6. This means that for every one person who voted, there were six possible voters.
The number of people who voted is 210 and the number of possible voters is 1260. So the ratio is 210:1260. Simplifying this ratio by dividing both numbers by their greatest common divisor, which is 30, we get 7:42. Therefore, the ratio to compare the number of people who voted to the number of possible voters is 7:42.
meg runs 1 1/2 miles and walks 2 1/4 miles each day of the week. how far does meg run and walk in al each week? explain. remember, you can write an equivalent fraction fir 1 1/2
Answers
Meg walks and runs 3 3/4 in total each week.
We can find this answer by adding the two numbers, 1 1/2 and 2 1/4
Hope this helps :)
To solve this problem, you first add the numbers 1 1/2 and 2 1/4:
1 + 2 = 3
Try finding the Lowest Common Denominator (LCD) of the fractions. . .
1/2 = 2/4
1/4 = 1/4
2/4 + 1/4 = 3/4
1 + 2 = 3
4 = 4
(Since both have the same denominator, the final denominator stays the same.)
3 + 3/4 = 3 3/4
Since there are 7 days in a week, multiply 7 x 3 3/4 . . .
7 = 7/1
3 3/4 = 15/4
7 x 15 = 105
1 x 4 = 4
105/4 = 26 1/4 <------------
Meg runs 26 1/4 miles overall in each week.
Hope this helps you.
Have a great day!
Yesterday, the price of a gallon of gas at five gas stations was $3.64, $3.79, $3.70, $4.01, and $3.91, respectively, but today each gas station raised its price by $0.08. What is today's mean price of a gallon of gas at the five stations?
A. $3.81
B. $3.89
C. $3.73
D. $3.97
PLEASE BE CORRECT.
Answers
0.08 * 5 = 0.40
19.05 + 0.40 = 19.45
19.45 / 5 = 3.89
Answer is B
Option: B is the correct answer.
B. $ 3.89
Step-by-step explanation:The price of a gallon of gas at five gas stations is given by:
$3.64, $3.79, $3.70, $4.01, and $3.91
The mean of these data values is given by:
[tex]Mean=\dfrac{3.64+3.79+3.70+4.01+3.91}{5}\\\\\\Mean=\dfrac{19.05}{5}\\\\\\Mean=3.81[/tex]
We know that if each of the quantity of the data set is increased by a fixed amount then the mean of the data set also increases by that fixed amount.
As we are given that each gas station raised its price by $0.08.
This means that the mean is also increased by $ 0.08
i.e. Today's mean price of a gallon of gas at the five station is given by:
[tex]Mean=3.81+0.08\\\\\\Mean=3.89[/tex]
Hence today's mean is:
$ 3.89
What is the area of the trapezoid? Enter your answer in the box. in2 The figure shows a trapezoid. The parallel bases of the trapezoid are horizontal, and top base is shorter than the bottom base. Vertical line segments are drawn inside the trapezoid from the upper vertices perpendicular to the bottom base. These segments are each 6 inches and divide the trapezoid into two right triangles and a rectangle. The rectangle lies between the two triangles. The bases of the triangles and rectangle make up the bottom base of the trapezoid. The base of each triangle is 4 inches, and the base of the rectangle is 8 inches.
Answers
Answer: [tex]\text{Area}=72\ inches^2[/tex]
Step-by-step explanation:
By the given description of trapezoid we get,
The height of the trapezoid h= 6 inches
The base of triangle = 4 inches
The base of rectangle (a)= 8 inches
The bottom base of the trapezoid (b)= 2×base of triangle +base of rectangle
The bottom base of the trapezoid (b)= [tex]2(4)+8=8+8=16\ inches[/tex]
The area of trapezoid is given by :-
[tex]\text{Area}=\frac{1}{2}(a+b)h\\\\\Rightarrow\text{Area}=\frac{1}{2}(8+16)(6)\\\\\Rightarrow\text{Area}=72\ inches^2[/tex]
Answer:
72
Step-by-step explanation:
Find an explicit rule for the nth term of the sequence.
-5, -25, -125, -625, ...
Answer Choices
A) an = -5 • 5n
B) an = 5 • -5n + 1
C) an = 5 • -5n
D) an = -5 • 5n - 1
Answers
an = a1. r^(n -1)
= -5 . 5^(n - 1)
Its D
Final answer:
The explicit rule for the nth term of the sequence is an = -5 * 5ⁿ that is option A is correct.
Explanation:
The explicit rule for the nth term of the sequence is an = -5 * 5ⁿ
To find this rule, we notice that each term is 5 times the previous term but negative. So, the nth term can be represented as an = -5 * 5^(n-1), which simplifies to an = -5 * 5ⁿ.
Therefore, the correct answer choice is A) an = -5 * 5ⁿ.
Which of the following functions is quadratic? f(x)=3(x-4)(x+3), f(x)=5^2, f(x)=2/x, f(x)=2x^3+3x^2-5
Answers
In C f(x) = 2/x is a function of a reciprocal, not a quadratic.
In D f(x) = 2x^3 + 3x^2 - 5 is a cubic. A cubic is not a quadratic. The highest power of a quadratic is x^2
That leaves A. When you expand the brackets, you get
3(x^2 + 3x- 4x - 12)
2(x^2 - x - 12) when you remove the brackets you get
2x^2 - 2x - 24. The highest power of x is x^2. This is your quadratic.
A<<<< answer.
Final answer:
The function f(x)=3(x-4)(x+3) is the only quadratic function provided in the options, as it can be expanded to a second-order polynomial form.
Explanation:
The student asks which of the given functions is quadratic. A quadratic function is a second-order polynomial with the highest exponent of the variable being 2. Given the options, the function f(x)=3(x-4)(x+3) is quadratic because it can be expanded to the form ax2 + bx + c, where a, b, and c are constants. The given function will simplify to a quadratic equation once we expand it. No other provided functions display the characteristics of a quadratic equation; f(x)=52 is a constant, f(x)=2/x is a rational function, and [tex]f(x)=2x^3+3x^2-5[/tex] is a cubic function.
There were 25 melons at the grocery store. The store sold 3/5 of the melons. How many melons were sold?
Answers
Convert 3/5 to a decimal by dividing its numerator by its denominator.
3 ÷ 5 = 0.6
Next, multiply the total amount of melons in the store by the decimal.
25 × 0.6 = 15
ANSWER:
15 melons were sold.
Simplify 3a • 3b ÷ 3c ÷ 3d. The exponent on 3 is _____.
Answers
The correct answer is 2.
To simplify the expression 3a • 3b ÷ 3c ÷ 3d, we need to apply the laws of exponents and combine the coefficients and variables.
Given expression: [tex]3a \cdot 3b \div 3c \div 3d[/tex]
[tex]\text{Step 1: Rewrite the expression using exponents}[/tex]
[tex](3^1 \cdot a) \cdot (3^1 \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]\text{Step 2: Apply the laws of exponents for multiplication and division}[/tex]
[tex](3^1 \cdot 3^1 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]= (3^{1 + 1} \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]= (3^2 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]\text{Step 3: Simplify the expression by combining the exponents and coefficients}[/tex]
[tex](3^2 \cdot a \cdot b) \div (3^1 \cdot c) \div (3^1 \cdot d)[/tex]
[tex]= (3^2 \cdot a \cdot b) \div (3^{1 + 1} \cdot c \cdot d)[/tex]
[tex]= (3^2 \cdot a \cdot b) \div (3^2 \cdot c \cdot d)[/tex]
[tex]= \frac{a \cdot b}{c \cdot d}[/tex]
Therefore, the simplified expression is [tex]\frac{a \cdot b}{c \cdot d}[/tex], and the exponent on 3 is 2.
Simplify: 4x + 4y + 4z A) 4 + xyz B) 4x3y3z3 C) 4xyz D) 4x + 4y + 4z
Answers
A regular hexagon has a side of 18 cm, find the area of the regular polygon
Answers
Judy built a rectangular patio that is 9 meters wide and has a perimeter of 40 meters what is the length of Judy’s patio
Answers
Final answer:
The length of Judy's rectangular patio is 11 meters, calculated using the perimeter formula for rectangles and the given width and perimeter measurements.
Explanation:
To find the length of Judy's patio, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Judy's patio has a known width of 9 meters and a perimeter of 40 meters. Substituting these values into the perimeter formula, we get:
40 = 2l + 2(9)
40 = 2l + 18
To solve for the length l, we first subtract 18 from both sides:
40 - 18 = 2l
22 = 2l
Now, we divide both sides by 2 to find the length:
22 / 2 = l
11 meters = l
Therefore, the length of Judy's patio is 11 meters.
Josie has $80. Addie has $60.
In how many months will they both have the same amount of money if Josie saves $30 per month and Addie saves $40?
Answers
13 is 20% of what number
Answers
65 is your answer
(5 because 20 * 5 is 100)
13 ÷ .20 = 65
65 × .2 = 13
Answer: 65
Last question pls help!
A rectangle has a side of 12 inches and another side of 6 inches...
whats the perimeter? whats the area? what would be the area and permieter combined?
Answers
Area = 72 in.
Perimeter = 36 in.
Hope this helps :))
To find perimeter, add the sides. . .
12 + 12 = 24
6 + 6 = 12
24 + 12 = 36 <------ The perimeter is 36 inches.
To find area, multiply the two sides. . .
12 x 6 = 76 <------ the area is 76 inches.
To combine the area and perimeter, add the numbers 76 and 36. . .
36 + 76 = 112 <--- the area and perimeter combined is 112 inches.
Hope this helps you.
Have a great day!
your elapsed time is 9 and 3/4 and you finishrd at 6:00 pm. what ime did you start?
Answers
if the elapsed time is in minutes then you started at 5:50pm 15 seconds in
You paid $80 for a tennis racket. If you found the racket under a sign stating 1/4 off, what must the original retail price have been?
Answers
1. You have that you paid $80 for a tennis racket which was under a sign stating 1/4 off. Therefore, you can express this with the following equation:
[tex] x-x/4=80 [/tex]
Where [tex]x[/tex]is the original retail price.
2. When you solve for [tex]x[/tex], you obtain:
[tex]3/4x=80 \\ x=106.67[/tex]
The answer is: [tex]106.67 dollars [/tex]
What is the mean of the data set un the box below?
- 7,- 10,- 1,0,- 4,- 7,3,- 2,1
Answers
The data set is: (-7), (-10), (-1), 0, (-4), (-7), 3, (-2),1
You find mean by adding up all of the values and dividing them by the number of values.
-7 + -10 + -1 + 0 + -4 + -7 + 3 + -2 + 1 = -27
you divide this by 9 because there are 9 seperate values.
-27/9 = -3
The mean of the data set is -3
Hope I helped!
Let me know if you need anything else!
~ Zoe
1 tin of 500ml blue paint costs $11.50. to finish a bedroom i need 4litre of blue paint. how much wi this cost me.
Answers
Knowing this, all we need to do is multiply $23 • 4 which should give us $92.
So, the total of how much you will need to pay in this scenario to paint a room is $92 for 4 litres of blue paint.
Good luck!
subtracting unlike fractions 8/9 - 5/6
Answers
Here is your answer:
The proper answer to your question is "1/18".
Here is how:
8*6=48
9*6=54
-
5*9=45
6*9=54
48-45=3
Which is 3/54!
3/3=1
54/3=18
Which means your answer is 1/18!
If you need anymore help feel free to ask me!
Hope this helps!
lungimea unei gradini de 78 m iar perimetrul este de 256 m.Afla latimea gradinii
Answers
L= 78 si P=256
P=2L+2W w e width(latime)
256=2*78+2w
256=156+2w
256-156=2 w
100=2w
w=50
Is 90 g less than, greater than, or equal 9kg
Answers
9 kg = 9000 grams since 1 kg is equal to 1000 grams (kilo = thousand)
So comparing "90 g to 9kg" is the same as "90 g to 9000g"
90g is smaller than 9000 g
therefore, 90 g is smaller than 9 kg
To the model estimated in table 8.1, add the interaction term, e401k · inc. estimate the equation by ols and obtain the usual and robust standard errors. what do you conclude about the statistical significance of the interaction term?
Answers
Signed General Penguin
P - potassium
S - sodium
L - lithium
M - magnesium
C - calcium
A - aluminium
Z - zinc
I - iron
L - lead
H - hydrogen
C - copper
S - silver
G - gold
P - platinum
number 248682 rounded off to the nearest hundred becomes what
Answers
Movie A took in $142.44 million on it’s first weekend. This topped the previous opening weekend revenue set by movie B by $4.14 million. How much did movie B take in on its opening weekend?
Answers
According to the given statement, revenue of movie A was $4.14 million more than the revenue of movie B in their first weekends.
So, we can write:
Revenue of movie A = Revenue of movie B + $4.14 million
Revenue of movie B = 142.44 million - 4.14 million = $ 138.30 million.
Thus movie B take in $138.30 million on its opening weekend.
James gets headaches. the time between one headache and the next is an exponential random variable. he has noticed that, after having a headache, there is a 50% chance of having another headache within the next 4 days. james has not had a headache in 5 days. what is the probability that he will go for at least 5 more days before the next headache?
Answers
For an exponential distribution,
λ=rate of occurrence=mean number of headaches per day.
probability distribution function
=pdf(x, λ ) = λ e^(- λ x)
cumulative probability distribution function,
cdf(x, λ ) = 1 - e^(- λ x)
We are given probability of having no headaches in 4 days is 0.5,
this means x=4 in
cdf(4, λ ) = 0.5, =>
1 - e^(-4 λ )=0.5
Solve for λ
λ = -log(0.5)/4 = 0.1732868 [log(x)=natural log of x]
=>
interpretation: the mean number of headaches is 0.1732868 per day.
Using the cdf, for x=5 days,
cdf(5,0.1732868)=1-e^(-0.173868*5)=0.57955
=>
interpretation: probability of having a headache in 5 days = 0.57955
Therefore
probability of NOT having a headache in 5 days is (1-0.57955)=0.42045