Answers
Answer:
BC = 6 units
Given following:
AC = 4 unitstan(A) = 3/2Solve for BC:
Formula:
[tex]\rightarrow \sf tan(A) =\dfrac{opposite}{adjacent}[/tex]
insert values and make them proportional
[tex]\rightarrow \sf tan(A) =\dfrac{BC}{AC} = \dfrac{3}{2} = \dfrac{6}{4}[/tex]
So, BC is 6 units.
Answer:
1) BC = 6
2) B = 33.7° (nearest tenth)
3) [tex]\sf AB=2\sqrt{13}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Question 1Given:
Angle = ASide opposite angle = BCSide adjacent angle = AC = 4Substituting the values into the tan ratio:
[tex]\implies \sf \tan A=\dfrac{BC}{AC}=\dfrac{BC}{4}[/tex]
Given:
[tex]\sf \tan A=\dfrac{3}{2}[/tex]
Therefore:
[tex]\implies \tan \sf A = \tan \sf A[/tex]
[tex]\implies \sf \dfrac{BC}{4}=\dfrac{3}{2}[/tex]
[tex]\implies \sf BC=\dfrac{4 \cdot 3}{2}=6[/tex]
Question 2Given:
Angle = BSide opposite angle = AC = 4Side adjacent angle = BC = 6Substituting the values into the tan ratio and solving for B:
[tex]\implies \sf \tan B=\dfrac{AC}{BC}[/tex]
[tex]\implies \sf \tan B=\dfrac{4}{6}[/tex]
[tex]\implies \sf B=\tan ^{-1}\left(\dfrac{4}{6}\right)[/tex]
[tex]\implies \sf B=33.69006753...^{\circ}[/tex]
[tex]\implies \sf B=33.7^{\circ}\:(nearest\:tenth)[/tex]
Question 3Pythagoras’ Theorem
[tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = AC = 4b = BC = 6c = ABSubstituting the values into the formula and solving for AB:
[tex]\implies \sf AC^2+BC^2=AB^2[/tex]
[tex]\implies \sf 4^2+6^2=AB^2[/tex]
[tex]\implies \sf 16+36=AB^2[/tex]
[tex]\implies \sf AB^2=52[/tex]
[tex]\implies \sf AB=\sqrt{52}[/tex]
[tex]\implies \sf AB=2\sqrt{13}[/tex]
Related Questions
Which figures demonstrate a single translation?
Select each correct answer.
Answers
Translation of a figure is the situation when a figure is moves from one place to another place. The size of the figure does not changes in translation. The figure does not rotate in the translation. As the option 3 (below the first option) and 4 demonstrate the single translation hence, option 3 and 4 is the correct option.
Given-Given option shows the different translation and rotation of the original figure. It has to be known about the translation before checking the correct option.
What is translation?Translation of a figure is the situation when a figure is moves from one place to another place. The size of the figure does not changes in translation. The figure does not rotate in the translation.
In option 1 the object flips to the opposite side of the figure figure. Thus the option 1 does not demonstrate the single translation.In option 2 (right to the first option) the figure flips to the opposite side of the original figure and then translate to other location. Thus the option 2 does not demonstrate the single translation.In option 3 (below the first option) the figure moves to southeast direction to its position. Thus the option 4 demonstrate the single translation. Therefore option 4 is the correct option.In option 4 the figure moves to right from its location. Thus the option 3 demonstrate the single translation. Therefore option 3 is the correct option.As the option 3 (below the first option) and 4 demonstrate the single translation hence, option 3 and 4 is the correct option.
Learn more about the translation here:
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22 out of the 55 teachers in a
school staff meeting were first-year
teachers. What percentage of the
teachers in the meeting were first-
year teachers?
Answers
Answer:
40%
Step-by-step explanation:
Our fraction would be 22/55. You can divide and then multiply by 100 to get your percentage.
Use the box plots comparing the number of boy dogs and number of girl dogs attending doggy daycare each day for a month to answer the questions.
Answers
The boxplots 1 and 2 represent the distribution of data using a five number summary for the male and the female attendance
(a) The IQR of the male's dataThe first box plot represents the male's boxplot.
So, we have:
Upper quartile (Q3) = 14Lower quartile (Q1) = 2The IQR is the difference between the above values
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2 = 12
So: the IQR for the males' data is 12
(b) The difference in the median valuesFrom the first and second boxplots, we have:
Median male = 10Median female = 18The difference (d) between these values is
d = 18 - 10
d = 8
So: the difference between the median values of each data set is 8
(c) The distribution of dataThis is dependent on whether the dataset has an outlier or not.
From the figure, we have:
Male's data: presence of an outlier - use medianFemale's data: absence of an outlier - use meanSo: the male dataset is measured by median, while the mean is a better measure of center for the female's data
(d) Reason for outliersA possible reason for outliers is sampling problems
Read more about boxplots at:
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Answer:
I took the test but my quewstion was a little different sorry
In slope-intercept form, write the equation of the line parallel to y=3x+4 that passes through (−5, 8).
y=_x+_
fill in the blanks
Answers
Answer:
y = 3x+13
Step-by-step explanation:
I would like to ask you if you know how to differentiate an equation to get a slope ?. I always use calculus to get a slope. The slope i found was 3 so i used y-y1 = m(x-x1) formula.
Answer: y = 3x+13
Step-by-step explanation:
The slope i found was 3 so i used y-y1 = m(x-x1) formula.
3. A _ is a figure that extends endlessly in all directions.
Answers
Answer:
A plane is a flat surface that extends endlessly in all the directions.
PLS MARK ME AS THE BRAINLIST!!
*2.) Which trinomial is equivalent to 4(x - 5)^2– 3(x - 2)?
Answers
Answer:
4x² - 43x - 106
Step-by-step explanation:
4(x - 5)²– 3(x - 2)
4(x - 5)(x - 5) - 3 (x - 2)
distribute
4(x(x - 5) - 5(x - 5)) - 3 (x - 2)
4(x² - 5x - 5x - 25) - 3 (x - 2)
↓
combine like terms ↓
4(x² - 10x - 25) ((( ↓
distribute again ↓
4x² - 40x - 100 ↓
↓
distribute ↔ ↓
4x² - 40x - 100 - 3 (x - 2)
4x² - 40x - 100 - 3x + 6
add
4x² - 40x - 106 - 3x
combine
4x² - 43x - 106
A pair of shoes cost $92. What would be the total cost with 7% sales tax
Answers
Answer:
$98.44
Step-by-step explanation:
take $92 x .07 = $6.44 (tax amount)
$92+$6.44=$98.44
What is the volume of the rectangular prism?
Type the answer in the boxes below.
Answers
Answer:
3.75 cubic centimeters
Step-by-step explanation:
1.5*2.5*1 cubic centimeters
Answer:
3/20
Step-by-step explanation:
1/2 x 3/5 x 1/2
L x W x H is the formula
Length x Width x Height
count the squares, they're each 1/2 so multiply the number of squares with 1/2.
For example, the rectangular prism is 3 squares high, which means it's 3/6, and that simplifies to 1/2. Now you have your height. You do the same for the width and length.
Hope this helps <3
1. DC↔ means “ _____ DC”
A. line DC
B. ray DC
C. line segment DC
D. angle DC
2. ST→ means “_____ ST”
A. line ST
B. ray ST
C. angle ST
D. line segment ST
Answers
2. ray
how this helps
i need help with 7th grade math please need help ASAP + brainleist
Answers
Answer:
Area : π mm²
Circumference : 2π mm
Step-by-step explanation:
Finding area :
πr²π x 1²π mm²Finding circumference :
2πr2 x π x 12π mmSum and Difference Identities
Find the value of the expression.
cos(-pi/12)
What would -pi/12 be the sum or difference of?
Answers
Notice that
1/6 - 1/4 = -1/12
Then
cos(-π/12) = cos(π/6 - π/4)
cos(-π/12) = cos(π/6) cos(π/4) + sin(π/6) sin(π/4)
cos(-π/12) = (√3/2) (1/√2) + (1/2) (1/√2)
cos(-π/12) = (√6 + √2)/4
units and Lino Plots
More
Bags of Oranges
х
Jordan fills several bags with oranges. This line plot
shows the weight of each bag.
How many more pounds does one of the heaviest
bags weigh than one of the lightest bags?
Enter your answer as a mixed number by filling in the
boxes.
х
х
х
х
х
х
х
х
xx
xx
X X
X X
X X X
х
х
х
х
х
х
х
х
X
8
8
4 44 45 46 45 5 5 5 5 5
55 55
Weight (lb)
Ib
1
2
3
4
4
5
6
1
Answers
Answer:
1 1/8 or 9/8
Step-by-step explanation:
5 1/2 - 4 3/8 = 1/ 1/8
The Math Campers are grouped into groups with 9 members each. Each group is asked to form a circle and they will be sitting on the ground. If the seating arrangement is circular, in how many possible ways can the 9 members be seated?
A. 40320
B. 362880
C. 5040
D. 720
Answers
Answer:
B. 362880
Step-by-step explanation:
! means permutation which means
arrangement of people or things in
sequence or
linear order
9! = 362880
9! = 9*8*7*6*5*4*3*2*1 = 362880
a number minus 4 is less than thirteen
Answers
please answer asap!! show work!
12. What is (f - g)(x)?
f(x) = 4x4 - 5x2 + 2
g(x) = x3 - 2x2 + x - 4
Answers
Answer:
[tex]4x^4-x^3-3x^2-x+6[/tex]
Step-by-step explanation:
1. [tex](f-g)(x)=(4x^4-5x^2+2)-(x^3-2x^2+x-4)[/tex]
2. [tex]4x^4-5x^2+2-x^3+2x^2-x+4[/tex]
3. Simplify = [tex]4x^4-x^3-3x^2-x+6[/tex]
Estimate the value of
Answers
Answer:
The given equation results in 1.98, so the answer is D) 2
✏ [tex]\sf Solve[/tex]
[tex]\sqrt{2} = 1.41\\\\1.41 * 3.14 = 4.4274\\\\\sqrt{5} = 2.23\\\\\frac{4.4274}{2.23} = 1.98[/tex]
Select the correct answer.
E
B
2
7
B
C
0
b D
Polygon ABCDE is reflected to produce polygon ABCDE. What is the equation for the line of reflection?
ОА У-0
OB. X=0
OC x=2
OD. y=1
Answers
Answer:
B. x = 0
Step-by-step explanation:
we notice that a point and it’s image have the same y-coordinate and opposite x-coordinates
Example :
A(-2 , 2) is a point and A(2 , 2) it’s image by the reflection
[tex]y_{A}=2=y_{A^{\prime }}[/tex]
[tex]x_{A}=-2=-x_{A^{\prime }}[/tex]
Then the reflection is across the y-axis
Or The equation of the y-axis is x = 0
2xy - 3x2y2 + 2xy +5x2y2
Answers
Kevin invest $2,000 at 4.6% compounded continuously. How long will it take him to have $3,700
Answers
Answer:
t=In(37/20)/0.046
Step-by-step explanation:
p=2000
r=0.046
A=3700
t=?
3700=2000e^0.046t
switch sides
2000e^0.046t=3700
Divide both sides by 2000
$2000e^0.046t/2000=$3700/2000
Simplify
e^0.046=37/20
Apply exponent rules
0.046=37/20
Solve 0.046t = ln(37/20)
t=In(37/20)/0.046
Match the graph with the correct equation.
y-1 = -4(x + 5)
y-1 = -1/4(x + 5)
y+1 = -1/4(x + 5)
y-1 = -1/4(x + 5)
Answers
30% tip on a bill of $150.47
Answers
Answer:
45.141 or if you round 45.14
Step-by-step explanation:
150.47 x 0.30 = 45.141
Give one solution for in each of the following statements.
25≡ 5
36≡ 8
50≡ 9
Answers
So
#1
25=5xx=25/5x=5#2
36=8xx=36/8x=9/2x=4.5#3
50=9xx=50/9x=5.55Answer:
25 = 5
x = 25 - 5
x = 20
38 = 8
x = 38 - 8
x = 30
50 = 9
x = 50 - 9
x = 41
The sides of a triangle are 77, 56, and 59. Use the Pythagorean Theorem to determine
if the triangle is right, acute, or obtuse.
the
The triangle is y because the square of the largest side
sum of the squares of the other two sides.
Answers
Step-by-step explanation:
59^2+56^2=77^2
3481+3136=5929
no not right triangle
im guessing its and acute triangle
i don't understand what else your trying to ask after that
Answer:
obtuse and greater than
Step-by-step explanation:
obtuse and greater than
What is the inverse of the function below?
f(x) = 3^x
---
OA 1-1(x) = logg
.
B. -() = log, 3
c. 1-2(1) = 3log(7)
D. 12() = log(31)
Answers
Original: y = 3^x
---To find the inverse, switch the x and y, then solve for y.
Inverse: x = 3^y
---Take the log base 3 of both sides to get y by itself
Answer: [tex]log_{3}(x) = y[/tex]
[tex]y = log_{3}(x)[/tex]
Hope this helps!
Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.
f (x) = 2 x squared. G (x) = negative 2 x squared
a.
f opens downward; g opens upward; both pass through different y-intercepts
b.
both open downward; both pass through (0, 0)
c.
both open upward; both pass through different y-intercepts
d.
f opens upward; g opens downward; both pass through (0, 0)
Answers
The function f(x) opens upwards, while g(x) opens downwards, and both functions pass through (0, 0), so the correct option is d.
What are the similarities/differences observed?
Here we have the two functions:
[tex]f(x) = 2x^2[/tex]
[tex]g(x) = -2x^2[/tex]
Notice tat g(x) = -f(x), which means that g(x) is a reflection across the x-axis of f(x).
The graphs of these functions can be seen below, the one that opens upwards is f(x), the one that opens downwards is g(x).
Then we can conclude that the true statement is:
"f opens upward; g opens downward; both pass through (0, 0)"
If you want to learn more about functions:
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10 POINTS PLEASE HELP
Answers
Answer:
m∠A = 49°
Step-by-step explanation:
According to Angle Sum Property,
angles of the Δ add up to 180°∠A + ∠B + ∠D = 180°5x - 6 + 7x - 24 + 78 = 18012x + 48 = 180x + 4 = 15x = 11m∠A
5x - 65(11) - 655 - 649°
Use the image of the L-shaped composite figure formed by two rectangular prisms to answer the question.
4 cm
8 cm
2 cm
14 cm
20 cm
What is the volume for the figure in cubic centimeters?
Enter your answer as a number, like this: 42
Do not enter units.
Answers
Just to have fun, I have written a transcript scenario. Your answer is in the paragraph as if I was teaching it! Hope this improves the quality of the answer, if it hasn't just give your review! Have a nice day!
All right. So you want the surface area for this composite figure? So, the surface area, we're going to split into two different shapes. So, I'm gonna do this shape here. That's kind of up. And then I'll do this one. That's kind of flattered. Okay, so when we look at the base, because our surface area formula, let's start with. That is perimeter times high plus two times the area of the base. So, I need the perimeter of this. This is my base, right? I'm thinking about the one that's on the bottom that I can't see. So this is 20 and four. So when you do perimeter, I'm gonna say 20 plus 20 Plus four Plus 4. That's perimeter. The height is eight plus two. And then my area of the base is the two numbers I used in the first parentheses. So four times 20. Okay, so let's see. 20 plus 20 is 40, 40-plus 8 is 48. 48 times eight Is 3 84. Okay. Plus four times 20 is 80, maybe times two is 1 60. If I add all this together And your calculator or do it by hand, you get 5:44. So that is the surface area for the shape that I drew mostly over just now. Let me do it in red for the next one. So my base for this one, I'm actually gonna use 20 and 14 for my perimeter. So the same kind of steps, 20 plus 20 plus 14 plus 14. And then my height is too Plus two times the area of the base. So 20 times 14. So 40 plus 28. Because that's what 14 plus 14 is is 68 68 Times two for the height. So I get 1 36 plus And now 20 times 14 gives you 2 80 times two. It's 5 60 Plus 1 36. So I'm adding these together now And you get 6 96. Alright, We're almost done. Now. We have to take our first answer and add it To our second answer. So 6 96. So 6 96 plus 5 44. You can use your calculator, you get 1240. And if you wanted to use correct units it's centimeters squared. Alright. I hope this helps.
Image attatched is the actual problem.
Answer:
did u guys ever figure it out
Step-by-step explanation:
Write a cosine function that has a midline of 2, an amplitude of 4 and a period of pi/2.
Answers
y = Acos(Bx) + D;
D = 4, A = 2. Now T = 2π/B = 5π/8, B = 2π/(5π/8) = 16/5
WE get y = 2cos(16/5x) + 4
Yesterday the price of a can beans at five supermarkets was $2.02, $2.11, $1.99,$2.32, and $2.26, respectively but today each supermarket raised it's price by $0.10. what today's mean price of a can of beans at five supermarkets?
a.2.14
b.2.34
c. 2.24
d.2.04
Answers
Answer:
the answer is C
Step-by-step explanation:
add them all together with the 0.10C increase which gives you 11.2 then divide by the number of different beans which is 5 and it gives you 2.24
Reasoning: add together all the values + $0.50 ($0.10 for 5 supermarkets), then divide that number with 5 to get the mean or average.
Enter the number that belongs in the green box.
y=[?]
Answers
Answer:
60 degrees
Step-by-step explanation:
As shown, this is a equilateral triangle which has the same angle measures.
According to the Triangle Sum Theorem, the sum of all three angles in a triangle is 180 degrees.
Thus,
180 (The sum of all angles in a triangle) /3 (The amount of angles in a triangle) = 60 degrees.
60 because all of the side are equal so it would be 180 divided by 3.