Question 4 of 5
Drag each label to the correct location on the triangle. Not all labels will be used.
Find the unknown measurements. Round all values to the nearest tenth.
cm
8.9 cm
65°
Answers
Answer:
long side: 19.1 cmmissing angle: 25°hypotenuse: 21.1 cmStep-by-step explanation:
You can use this information to "guess" at the answers without doing any "work."
The sum of angles in a triangle is 180°.The shortest side is opposite the smallest angle.__
qualitative solutionThe missing angle is the complement of the marked acute angle in the right triangle, so is ...
C = 90° -65° = 25°
This angle is opposite the side of length 8.9 cm. The next-smallest angle is 65°, which is more than double the smallest angle. Hence the side opposite 65° will not be either of 3.8 or 9.8.
Of the two remaining measures, the longer one, 21.1, will be the hypotenuse, BC. The shorter of those, 19.1, will be the long side, AC.
Our solution is ...
AC = 19.1 cmC = 25°BC = 21.1 cm__
quantitative solutionThe mnemonic SOH CAH TOA reminds you of the relations between trig functions and right triangle sides. Here, we're given an angle and the length of its adjacent side. We are asked for the opposite side and for the hypotenuse. This suggests useful relations might be ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
Solving the first of these for the hypotenuse gives ...
hypotenuse = adjacent/cos(65°)
BC = 8.9 cm/cos(65°) ≈ 21.059 cm ≈ 21.1 cm
Solving the second relation above for the opposite side gives ...
opposite = adjacent×tan(65°)
AC = 8.9 cm×tan(65°) ≈ 19.086 cm ≈ 19.1 cm
As above, the missing angle is the complement of the given one:
C = 90° -65° = 25°
Then the quantitative solution is ...
AC = 19.1 cmC = 25°BC = 21.1 cm_____
Additional comment
If AC were 9.8 cm, the angle at B would be about 48°. That is, the two acute angles in the triangle would be very nearly equal.
We know that the side ratios in a 30°-60°-90° right triangle are 1 : √3 : 2. This triangle has a larger angle greater than 60°, so its longer side will be more than √3 times the short side. That means a length of 9.8 cm is way too short.
Related Questions
20 points pls help quick
Let f(x) = 3x² + mx + 5 and g(x) = nx² - 4x - 2. The functions are combined to
form the new function h(x)=f(x)xg(x). Points (1,-40) and (-1,24) satisfy the new
function. Determine f(x) and g(x).
Answers
Answer:
[tex]\displaystyle f(x) = 3x^2 + 2x + 5\text{ and } g(x) =2x^2 - 4x -2\text{ or } \\ \\ f(x) = 3x^2 + 5 \text{ and } g(x) = x^2 - 4x -2[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = 3x^2 + mx +5 \text{ and } g(x) = nx^2 - 4x -2[/tex]
And that:
[tex]\displaystyle h(x) = f(x)\cdot g(x)[/tex]
With the given conditions that (1, -40) and (-1, 24) satisfy the new function, we want to determine functions f and g.
First, find h:
[tex]\displaystyle \begin{aligned} h(x) & = f(x)\cdot g(x) \\ \\ & = (3x^2 + mx +5)(nx^2 - 4x -2) \end{aligned}[/tex]
Because (1, -40) and (-1, 24) are points on the graph of h, we have that h(-1) = 40 and h(-1) = 24. In other words:
[tex]\displaystyle \begin{aligned} h(1) = -40 & = (3(1)^2 + m(1) +5)(n(1)^2 - 4(1) -2) \\ \\ & = (3 + m +5)(n-4 -2) \\ \\ & = (m+8)(n-6) \\ \\ -40 &= mn-6m+8n-48 \end{aligned}[/tex]
And:
[tex]\displaystyle \begin{aligned} h(-1) = 24 & = (3(-1)^2 + m(-1) +5)(n(-1)^2 -4(-1) -2) \\ \\ & = (3 - m +5)(n + 4 -2) \\ \\ & = (-m+8)(n+2) \\ \\ 24 & = -mn -2m + 8n +16 \end{aligned}[/tex]
Solve the system of equations. Adding the two equations together yield:
[tex]\displaystyle -16 = -8m+16n - 32[/tex]
Solve for either m or n:
[tex]\displaystyle \begin{aligned} -16 & = -8m + 16n - 32 \\ \\ 16 & = -8m + 16n \\ \\ 8m & = 16n - 16 \\ \\ m & = 2n -2\end{aligned}[/tex]
Substitute this into one of the two equations above and solve:
[tex]\displaystyle \begin{aligned} -40 & = mn - 6m + 8n - 48 \\ \\ 0 & = (2n-2)n -6 (2n-2) + 8n -8 \\ \\ &= (2n^2 - 2n) + (-12n + 12) +8 n - 8 \\ \\ & = 2n^2 -6n + 4 \\ \\ & = n^2 - 3n + 2 \\ \\ &= (n-2)(n-1) \\ \\ & \end{aligned}[/tex]
Therefore:
[tex]\displaystyle n = 2 \text{ or } n = 1[/tex]
Solve for m:
[tex]\displaystyle \begin{aligned}m &= 2n-2 & \text{ or } m & = 2n-2 \\ \\ & = 2(2) - 1 &\text{ or } & =2(1) -2 \\ \\ &= 2 &\text{ or } & = 0 \end{aligned}[/tex]
Hence, the values of n and m are either: 2 and 2, respectively; or 1 and 0, respectively.
In conclusion, functions f and g are:
[tex]\displaystyle f(x) = 3x^2 + 2x + 5\text{ and } g(x) =2x^2 - 4x -2\text{ or } \\ \\ f(x) = 3x^2 + 5 \text{ and } g(x) = x^2 - 4x -2[/tex]
I can’t figure this out…going on 4 hours now
Answers
Answer:2: 95/215, 3: 95/580, 4: 210/330 5: 365/580
Step-by-step explanation:probability=outcome in question/the total number in the given category
Are 100 10 and 5 1 equivalent rates ? Pls answer quick
Answers
Answer:
No
Step-by-step explanation:
I don't think so
what is the answer to thiss
Answers
Hi Student!
This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression. So let's plug in the values and solve.
Plug in the values
[tex]m^2 + 5[/tex][tex](9)^2 + 5[/tex]Factor out the exponent
[tex](9*9) + 5[/tex][tex]81 + 5[/tex]Combine
[tex]86[/tex]Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.
find the smallest number by which 84 must be multiplied to make a perfect square?
Answers
Step-by-step explanation:
84=2×2×3×7
perfect square has all twice no.
so it is multiply by 7 x 3 =21
to get perfect square of 42
Evergreen Corporation manufactures circuit boards and is in the process of preparing next year's budget. The pro forma income statement for the current year is presented below.
Sales $ 3,500,000
Cost of sales:
Direct Material $ 500,000
Direct labor 250,000
Variable Overhead 275,000
Fixed Overhead 600,000 1,625,000
Gross Profit $ 1,875,000
Selling and General & Admin. Exp.
Variable 750,000
Fixed 250,000 1,000,000
Operating Income $ 875,000The break-even point (rounded to the nearest dollar) for Evergreen Corporation for the current year is:
$1,724,138.
$2,625,000.
$2,155,172.
$1,865,672.
Answers
The break-even point (rounded to the nearest dollar) for Evergreen Corporation for the current year is: A. $1,724,138.
Break-even pointFirst step is to calculate the Variable costs
Variable costs = $500,000 + $250,000 + $275,000 + $750,000
Variable costs = $1,775,000
Second step is to calculate the Contribution margin ratio
Contribution margin ratio = (Sales - Variable costs) / Sales
Contribution margin ratio= ($3,500,000 - $1,775,000) / $3,500,000
Contribution margin ratio= 0.493×100
Contribution margin ratio =49.3%
Now let calculate the Break-even point
Break-even point = Fixed costs / Contribution margin ratio
Break-even point= ($600,000 + $250,000) / 0.493
Break-even point= $1,724,137.9
Break-even point =$1,724,138 (Approximately)
Therefore the break-even point (rounded to the nearest dollar) for Evergreen Corporation for the current year is:$1,724,138.
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Luke was asked to find the median of the following numbers:
16, 24, 12, 7, 30, 11, 22
The work below shows the steps he used.
The numbers 7, 11, 24, and 30 are crossed out. StartFraction 16 + 22 Over 2 EndFraction = StartFraction 38 Over 2 EndFraction = 19.
What error did Luke make?
He forgot to put the numbers in order first.
He crossed off the low and high pairs incorrectly.
He left out a number when putting the numbers in order.
He did not make an error.
Answers
The mistake made by Luke is that he forgot to arrange the numbers in order first before finding the median.
How to find the median of a data?The median is the middle number of a distribution when arrange in ascending or descending order.
7, 11, 12,16, 22, 24, 30
The number has been arrange from the smallest to the largest.
Therefore, the median can be calculated as follows:
median = 16
Therefore, Luke forgot to put the numbers in order first.
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Answer: (C)
100% Correct Answer! Pls, give me brainliest. Thank You!
PLEASE HELLPPPP Ms. Rudolph randomly selects one student from a group of students.
are wearing a black shirt, 6 students are wearing a red shirt, and 9 students are
wearing a blue shirt.
Show your work to determine the PROBABILITY that the selected student is
wearing a BLACK shirt?
You may write your answer as a FRACTION or DECIMAL.
Answers
Using it's concept, it is found that the probability that the selected student is wearing a black shirt is given by:
[tex]p = \frac{n}{n + 15}[/tex]
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that out of n + 6 + 9 = n + 15 students, n are wearing black shirts, hence the probability is given by:
[tex]p = \frac{n}{n + 15}[/tex]
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Translate (10,8) down 5
Answers
Answer:
A (10,3)
Step-by-step explanation:
In a study of patients arriving at a hospital emergency room, the gender of the patients is considered, together with whether the patients are younger or older than 30 years of age, and whether or not the patients are admitted to the hospital. It is found that 45% of the patients are male, 30% of the patients are younger than 30 years of age, 15% of the patients are females older than 30 years of age who are admitted to the hospital, and 21% of the patients are females younger than 30 years of age. What proportion of the patients are females older than 30 years of age who are not admitted to the hospital?
Answers
The probability of patients are females older than 30 years of age who are not admitted to the hospital is 0.19
How to calculate the probability?The probability of patients who are females and are admitted will be 0.15. The probability of those younger than 30 years will be 0.21.
The proportion of the patients are females older than 30 years of age who are not admitted to the hospital will be:
= [(1 - 0.45) - 0.21] - 0.15
= 0.19
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Two spheres have volumes of 87pi cm³ and 64pi cm³. If the surface area of the smaller sphere is 16pi cm², what is the
surface area of the larger sphere?
O 64pi cm²
O 96pi cm²
O 128pi cm²
O 256pi cm²
Answers
The surface area of the large sphere is 128π cm²
Complete questionTwo spheres have volumes of 8π cm3 and 64π cm3. If the surface area of the smaller sphere is 16π cm2, what is the surface area of the larger sphere?
How to determine the larger area?The given parameters can be represented using the following ratio:
Small Area : Large Area = Small Volume : Large Volume
Substitute the given parameters
16π : Large Area = 8π : 64π
Express as fraction
Large/16π = 64π/8π
Multiply both sides by 16π
Large = 128π
Hence, the surface area of the large sphere is 128π cm²
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Translate the given phrase into an algebraic expression and simplify if possible: the quotient of 12 and the product of 3 and 4.
Note: Enter only the simplified result.
Answers
Answer: 1
Step-by-step explanation:
First, we will translate this into an algebraic expression.
-> Quotient means we will be using divison
-> Product means we will be using multiplciation
the quotient of 12 and the product of 3 and 4
[tex]\displaystyle \frac{12}{\text{the product of 3 and 4}}[/tex]
[tex]\displaystyle \frac{12}{3*4}[/tex]
Now, I will simplify.
Given:
[tex]\displaystyle \frac{12}{3*4}[/tex]
Multiply:
[tex]\displaystyle \frac{12}{12}[/tex]
Divide:
1
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A skydiver is falling at a rate of 1.1 × 10 2 miles per hour. About how long will it take him to fall 5 miles?
Answers
Answer:
See below
Step-by-step explanation:
distance / rate = time
5 miles / 110 m/hr = .04545 hr = 2.727 min = 2 min 44 sec = 1/22 hr
Enter a positive value for d that makes this statement true: 18 *d less than 18 but greater than 0
Answers
Answer:
d=0.5
Step-by-step explanation:
18 x 0.5=9
9 is less than 18 and greater than 0
Answer:
9
Step-by-step explanation:
(07.03 MC)
What is the solution to the following equation? (1 point)
4(3x − 11) + 23 = 5x − 14
0
1
10
14
Answers
Answer:
1
Step-by-step explanation:
[tex]~~~~~~4(3x-11) +23 = 5x -14\\\\\implies 12x -44 + 23 -5x +14 = 0\\\\\implies 7x-7=0\\\\\implies 7x = 7\\\\\implies x = \dfrac 77 \\\\\implies x = 1[/tex]
Answer:x=1
Step-by-step explanation: did the test
The rectangle shown is rotated about line k.
Rectangle A B C D is shown. A line of rotation goes through the midpoint of sides A B and D C to cut the side into two equal lengths of 5 inches. Side A D has a length of 4 inches.
What is the approximate base area of the resulting figure?
Area of a circle: A = πr2
31 sq. in.
50 sq. in.
79 sq. in.
314 sq. in.
Answers
The approximate base area of the resulting figure is 79 in²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The resulting figure formed from the rotation is a cylinder with a radius of 5 inches and height of 4 inches
Area of base = π * radius² = π * 5² = 79 in²
The approximate base area of the resulting figure is 79 in²
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Markson and Sons leases a copy machine with terms that include a fixed fee each month plus a charge for each copy made. Markson made 8,000 copies and paid a total of $980 in January. In April, they paid $760 for 6,000 copies. What is the variable cost per copy if Markson uses the high-low method to analyze costs? If required, round your answer to two decimal places.
Answers
The variable cost per copy if Markson uses the high-low method to analyze costs. will be $0.11.
How to calculate the cost?It should be noted that the variable cost per unit will be calculated as:
= Difference in cost between high and low level activities / Difference in units
= (980 - 760)/(8000 - 6000)
= 220/2000
= 0.11
Therefore, the variable cost per copy if Markson uses the high-low method to analyze costs. will be $0.11.
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Which of the following is the solution to the
inequality below?
-4x-7<5
A. x>-1
B. x < -¹/
C. x>-3
D. x<-3
Answers
Answer:
the answer to this problem Is C. x>-3
Which sentence illustrates the distributive property
Answers
Answer:
4th option
Step-by-step explanation:
the distributive property is
a(b + c) = ab + ac
that is each term in the parenthesis is multiplied by a
Answer:
a(b+c)=ab+ac
Step-by-step explanation:
The distributive property is when it distributes the outside variable with whatever is in the parenthesis.
For example, 2(1+3) is 2(1)+2(3)= 2+6=8.
SOMEONE PLEASE HELP IVE BEEN WAITING FOREVER
Answers
Answer:
Only option A. cannot be simplified; is in its simplest form.
Step-by-step explanation:
In order for A. to have a simplified form, it must have a specified degree or leading term, which it does not have, making it impossible to simplify.
This year a small business has a total revenue of $21,700. If this is 38% less of their total revenue the previous year what was their total revenue the previous year?
Answers
Answer:
29946
Step-by-step explanation
Multiply the value by 1.38.
Amanda's math certificate is 7 inches tall and
11 inches wide. Amanda wants to put the
certificate in a fancy frame that costs $3.00
per inch. How much will it cost to frame
Amanda's math certificate?
Answers
Answer:
ten inches
Step-by-step explanation:
because the frame will focus on it wider the tall will not fall in so you will divide the wide inches and you will mutiple it by the tall inches
15 (y - 4 ) - 2 ( 9y - 11 ) = 4 (8z - 13)
Answers
Answer to the given equation is 32z + 3y = 14.
Step 1: Given data: The given equation is 15 (y - 4) - 2 (9y - 11 ) = 4 (8z - 13)Step 2: Solving the above equation,15y - 60 - 18y + 22 = 32z - 52
- 3y - 38 = 32z - 52
- 3y + 52 - 38 = 32z
- 3y + 14 = 32z
32z + 3y = 14
Hence, we get 32z + 3y = 14
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Leslie set up a fruit stand to sell some of her crop of oranges. The first person who came by bought 1/3 of her oranges. The second person bought 4 oranges. The thrid person bought 1/4 of the REMAINING oranges. Leslie took the last 15 oranges home to make orange juice. How many oranges did Leslie have at the beginning?
Answers
Answer:
36
Step-by-step explanation:
Let's say Leslie starts with x oranges.
The first person buys 1/3 of the oranges, leaving behind 2/3 x.
The second person buys 4 oranges, leaving behind 2/3 x − 4.
The third person buys 1/4 of the remaining oranges, leaving behind:
3/4 (2/3 x − 4)
This amount equals 15. Solving for x:
15 = 3/4 (2/3 x − 4)
20 = 2/3 x − 4
24 = 2/3 x
36 = x
Help Me please . I want to know cube root of 512 and 997002999 . please man fast
Answers
Answer:
8,999
Step-by-step explanation:
Cube root of 512 is 8.
cube root of 997002999 is 999.
A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the number of calories, numbered 3 to 27. A straight line with a positive slope begins at point (0, 0) and ends at point (6.8, 27).
The graph shows the relationship between the number of strawberries eaten and the approximate number of calories consumed. Which statement is true?
Each strawberry contains 4 calories.
Each strawberry contains 3 calories.
Twenty-four strawberries contain 6 calories.
Four strawberries contain 15 calories.
Answers
From the equation y = 4x, each strawberry contains 4 calories.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the number of calories in x strawberries. Hence:
y - 0 = [(27 - 0)/(6.8 - 0)](x - 0)
y = 4x
From the equation y = 4x, each strawberry contains 4 calories.
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Answer:
a
Step-by-step explanation:
Consider the function represented by the table.
For which x is f(x)=–3?
–7
–4
4
5
Answers
Step-by-step explanation:
-7 because i now this by myself aND blah blah blah blah blah blah blah blah blah blah blah blah blah blah step by step nice
nice nice
Answer:
A: -7
Step-by-step explanation:
Taking the test rn and just happened to see this :)
Please help I am so confused
Evaluate -6b+8t where b=-9 and t=-9
Answers
Answer:
-18
Step-by-step explanation:
If you plug the number values into the equation, it would be -6(-9)+8(-9) when then turns out to be 54+(-72) which is -18
k dived by 11 is 7
solve for k
Answers
Answer:
k = 77
Step-by-step explanation:
[tex]\frac{k}{11} =7\\\\\rightarrow 11 * 7 = 77\\\rightarrow 77 \div 11 = 7[/tex]
Answer:
k = 77
Step-by-step explanation:
The question in equation form is :
[tex]\frac{k}{11} =7[/tex]
Now we multiply both sides by 11 to solve for k :
k = 7×11
k = 77
Hope this helped and brainliest please
What is the distance between the points (-4,-8) and (6,16), to the nearest tenth of a units?
A. 8.2 units
B.676.0 units
C.21.8 units
D.26.0 units
Answers
Answer:
D.26.0 unitsStep-by-step explanation:
Given : the points A(-4,-8) and B(6,16),
Let d be the distance between A and B.
Then
[tex]d=\sqrt{\left( 16-\left( -8\right) \right)^{2} +\left( 6-(-4)\right)^{2} }[/tex]
[tex]=\sqrt{\left( 24\right)^{2} +\left( 10\right)^{2} }[/tex]
[tex]=\sqrt{676 }[/tex]
[tex]=26[/tex]