Answer:
Step-by-step explanation:
22
Answer:
Factored :
2 (5x-3)(x^2+5)
Roots :
[tex]x=\frac{3}{5} , i\sqrt{5} , -i\sqrt{5} \\[/tex]
Step-by-step explanation:
While looking at some reports, a store manager notes that carousel horses that retail for $620 end up costing customers $651 once the sales tax is added. What is the sales tax percentage?
Answer:
[tex]\large \boxed{5.0 \, \% }[/tex]
Step-by-step explanation:
1. Calculate the amount of tax
Total cost = selling price + sales tax
Sales tax = total cost - selling price
Total cost = $651
-Selling price = - 620
Sales tax = $ 31
2. Calculate the percent tax
[tex]\text{\% Tax} = \dfrac{\text{\$31}}{\text{\$620}} \times 100 \, \% = \mathbf{5.0 \, \%}\\\\ \text{The sales tax percentage is $\large \boxed{\mathbf{5.0 \, \% }}$}[/tex]
To write the explicit rule, we need some information about the following series:
3, 6, 12, 24, 48, ...
In Blank 1: a1 =
In Blank 2: r =
Answer:
see explanation
Step-by-step explanation:
Note the common ratio r between consecutive terms of the sequence
r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
The explicit rule for a geometric sequence is
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 3 and r = 2, thus
[tex]a_{n}[/tex] = 3[tex](2)^{n-1}[/tex] ← explicit rule
PLZ HELP 5 QUESTIONS FOR 50 POINTS
Answer:
3. 113.04
4. 137.1
5. $9.24
Answer:
3. 113.04
4. 137.1
5. $9.24
The Neolithic Revolution
led people to lead lives based on hunting and gathering
allowed people to live in permanent settlements
reduced people’s need for food and resources
prevented the advance of civilization
i wel give the branlist to howe answers it carect
The Neolithic Revolution allowed people to live in permanent settlements.
Explanation:
The Neolithic Revolution is the phase of transition in which many of the human cultures in the world shifted their lifestyle to permanent settlement and agriculture from hunting and gathering.
This era is also named as First Agricultural Revolution or Neolithic Demographic Transition. The agricultural practices led the cultures to develop the knowledge of domestication of animals and they began to observe and experiment with the plants (to learn or know how they grow and develop).
Neolithic period is named as revolution because this period changed the way of life of most of the communities. This first occurred in so-called "Fertile Crescent" or Mesopotamia (modern Iraq).
The Neolithic Revolution allowed people to live in permanent settlements.
Answer: Option B
Step-by-step explanation:
This phase 'Neolithic Revolution' witnessed the change in the behavior of the people, notably the development of habits like hunting and gathering of animals and fruits.Although it is a development of habits, people refer to it as a revolution because it changed the lifestyle of the communities.It dates back to prehistoric times which is said to have happened almost nine thousand years ago. Thereby concluding that, the Neolithic revolution allowed people to live in permanent settlements.You just purchased 3 pairs of pants for $75.25, $30.95 and $90.35. You also purchased 2 hats for $50 each. The sales tax is 7.5%; what is the amount of your total purchased?
Answer:
$318.79
Step-by-step explanation:
To do this problem, to find the real end amount paid, you must add up all the prices and add the sales tax. To do this, you add them to 296.55, and multiply it by the decimal form of the sales tax added to 1, so 1.075 which is 318.791 rounded to 318.79
A line contains the points (4, 2) and (0, -1). What is the equation of the line? Show your work.
Answer:
[tex]\large\boxed{y=\dfrac{3}{4}x-1}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept (0, b)
We have two points (4, 2) and (0, -1) → b = -1.
Calculate the slope:
[tex]m=\dfrac{-1-2}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}[/tex]
Finally:
[tex]y=\dfrac{3}{4}x-1[/tex]
The equation of the line that passes through the points (4, 2) and (0, -1) is y = 0.75x + 1.
Explanation:The subject of this question is Mathematics, and it involves finding the equation of a line given two points. To find the equation of the line that contains the points (4, 2) and (0, -1), we first find the slope (m) using the formula m = (y2 - y1) / (x2 - x1).
Substituting the given points into the formula, we get m = (-1 - 2) / (0 - 4) = -3 / -4 = 0.75.
We then use the point-slope form of a linear equation, y - y1 = m(x - x1), and substituting m = 0.75, x1 = 4, and y1 = 2, we get the equation of our line as: y - 2 = 0.75(x - 4), which simplifies to y = 0.75x + 1.
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plz help I don't want to be awake the whole night
Answer:
Therefore
[tex]75\div 5 - [(9-7)\times 3 ]\times 2 = 3[/tex]
Step-by-step explanation:
To Find:
Value of expression
75 ÷ 5 - [( 9 - 7 ) × 3 ] × 2
Solution:
PEDMAS rule
It explains the order of operations to solve an expression.
According to Pedmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.),
then division, multiplication, addition and subtraction from left to right.
P - parenthesis
E- exponent
D/M - Div or Multiply which ever comes first
A/S - Add or Sub which ever comes first.
So first we will solve the Parenthesis we get
Step 1. Parenthesis operation
75 ÷ 5 - [( 2 ) × 3 ] × 2
Step 2. Parenthesis operation
[tex]75\div 5 - [(2)\times 3 ]\times 2[/tex]
Step 3. Division
[tex]15 - [6]\times 2[/tex]
Step 4. Multiplication
[tex]15 - 12[/tex]
Step 5. Subtraction
3
Therefore
[tex]75\div 5 - [(9-7)\times 3 ]\times 2 = 3[/tex]
in the right triangle shown, angle A=30 and AC=18 how long is AB?
Answer:
[tex]AB=9\sqrt{3}\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC
The cosine of angle of 30 degrees is equal to divide the adjacent side to angle of 30 degrees by the hypotenuse
so
[tex]cos(30^o)=\frac{AB}{AC}[/tex]
we have
[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]
[tex]AC=18\ units[/tex]
substitute
[tex]\frac{\sqrt{3}}{2}=\frac{AB}{18}[/tex]
solve for AB
[tex]AB=(18)\frac{\sqrt{3}}{2}[/tex]
[tex]AB=9\sqrt{3}\ units[/tex]
Answer:
T
Step-by-step explanation:
Angle X and angle Y are supplementary angles. Angle Y measures 33 degrees. what is the measure of angle X?
Answer: 147
Step-by-step explanation:
Supplementary: Angles that equal 180
180-33=147
147+33=180
The measure of supplement angle X is 147°.
Given that, angle X and angle Y are supplementary angles.
What are supplementary angles?Supplementary angles refer to the pair of angles that always sum up to 180°. These two angles are called supplements of each other.
Here,
∠X+∠Y=180°
⇒ ∠X+33°=180°
⇒ ∠X=180°-33°
⇒ ∠X=147°
Hence, the measure of supplement angle X is 147°.
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Please help me out this kind of confused me thank you in advance!
Answer:
In the quotient [tex]x^4+2x^3+x^2+5x+10=0[/tex] , the coefficient of x is 5.
Step-by-step explanation:
Given rational expression is [tex]\frac{-x^5+3x^3-3x^2+20}{x-2}[/tex]
Nicolette used synthetic division to solve the given rational expression.
Nicolette's work is given below:
Given that x-2 is a zero of given rational expression
By using synthetic division for the given rational expression.
2_| -1 0 3 -3 0 20
0 -2 -4 -2 -10 -20
____________________________
-1 -2 -1 -5 -10 | 0
Therefore the simplified expression can be written as below
[tex]-x^4-2x^3-x^2-5x-10=0[/tex]
Taking negative sign outside.
[tex]-(x^4+2x^3+x^2+5x+10)=0[/tex]
Multiply negative sign with "0" we get "0"
Therefore [tex]x^4+2x^3+x^2+5x+10=0[/tex]
In the quotient [tex]x^4+2x^3+x^2+5x+10=0[/tex], the coefficient of x is 5.
Farrah bought a new car in 2016 one year later the car had depreciated in value by 2300 and was worth $20,140 find the value of her car when she purchased it in 2016
Answer:
Farrah purchased the car in 2016 at the price of $22,440.
Step-by-step explanation:
Given:
Cost of the car in 2017 = $20,140
Depreciation in the cost after 2016 was = $2300
To find cost of the car in 2016.
Solution:
Let cost of the car in dollars in 2016 be = [tex]x[/tex]
Depreciation in value after a year was by = $2300
Thus, cost of car in dollars in 2017 will be = [tex]Original\ cost-Depreciation\ =x-2300[/tex]
Given cost of car in 2017 = $20,140
So, we have:
[tex]x-2300=20140[/tex]
Solving for [tex]x[/tex]
Adding 2300 both sides.
[tex]x-2300+2300=20140+2300[/tex]
∴ [tex]x=22440[/tex]
Thus, cost of the car in 2016 was = $22,440
A recipe for 8 apple dash cinnamon muffins calls for 1 cup of flour. The number of muffins that can be made varies directly with the amount of flour used. There are 1 and three fourths cups of flour available. How many muffins can be made?
Answer:
you can make 14 muffins
Step-by-step explanation:
To get this answer you first need to know that 1 cup makes 8 muffins. Next know that there's 1 3/4 cups of flour. Because you know that 1 cup makes 8 muffins you need to figure out how many muffins 3/4 a cup of flour can make. To do this you divide 8 by 4. Hence 8 divided by 4 is 2. So know you know that for every 1/4 cup you can make 2 muffins. Now since there's 3/4 cup of flour you then multiply 2 by 3 which is 6. Now you have to add 1 cup ( 8 muffins) to 3/4 cup ( 6 muffins ) of flour which then equals 14. You then get the answer , 1 3/4 cups of flour can make 14 muffins. Hope this helped ;)
Can you spend 1/5 of his allowance on a movie 3/8 on snacks and 2/7 on games if his allowance was $20 how much did Ken have
For this case we assume that the initial amount of money is $20.
So:
[tex]\frac{1} {5}[/tex] of $20 in movies:[tex]\frac {1} {5} (20) = 4[/tex]
[tex]\frac {3} {8}[/tex] of $20 in snacks:[tex]\frac {3} {8} (20) = 7.5[/tex]
[tex]\frac {2} {7}[/tex] of $20 in games:[tex]\frac {2} {7} (20) = 5.71[/tex]
Adding we have:
[tex]4 + 7.5 + 5.71 = 17.21[/tex]
Ken has:
[tex]20-17.21 = 2.79[/tex]
Answer:
Ken can spend what he planned and he has $2.79 left.
Monica built a porch that contained 2 different colors of bricks to create a pattern. She purchased the red bricks for $7 each and the gray bricks for $4 each.
Write a system to find how many red bricks did Monica purchase if she spent $193 on 40 bricks?
What is the system that models this situation? Equation #1: Equation #2:
How many red bricks did Monica purchase?
Equation #1: x+y=40
Equation #2: 7x+4y=193
Monica bought 11 red bricks.
Step-by-step explanation:
Given,
Cost of one red brick = $7
Cost of one gray brick = $4
Total spent on bricks = $193
Total bricks bought = 40
Let,
x represents the number of red bricks bought.
y represents the number of gray bricks bought.
What is the system that models this situation?
Equation #1: x+y=40
Equation #2: 7x+4y=193
How many red bricks did Monica purchase?
Multiplying Eqn 1 by 4
[tex]4(x+y=40)\\4x+4y=160\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](7x+4y)-(4x+4y)=193-160\\7x+4y-4x-4y=33\\3x=33[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{33}{3}\\x=11[/tex]
Monica bought 11 red bricks.
Keywords: linear equation, elimination method
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15. Mr. Clements painted his barn for hours in the morning. He painted
the barn for 5 hours in the afternoon. For 154-15c, select True or False
for each statement.
15a. A common denominator of
the mixed numbers is 20.
O True
False
O True
O False
15b. The amount of time spent
painting in the morning can be
rewritten as 3 hours.
False
15c. Mr. Clements spent 2 hours O True
longer painting in the afternoon
than the morning
16. Tom exercised hour on Monday and hour on Tuesday.
Answer:
15a) True 15b) False 15c) True
16)[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
Step-by-step explanation:
*Rewriting the question with Retrieved missing information:
15. Mr. Clements painted his barn for hours in the morning. He painted his barn [tex]3\frac{3}{5}[/tex] hours in the morning. He painted the barn for [tex]5\frac{3}{4}[/tex] hours in the afternoon.Select True or False for each statement.
15a. A common denominator of the mixed numbers is 20.
15b. The amount of time spent painting in the morning can be rewritten as [tex]3\frac{15}{20}[/tex]
15c. Mr. Clements spent [tex]2\frac{3}{20}[/tex]
hours longer painting in the afternoon than the morning.
16. Tom exercised:
[tex]\frac{4}{5}[/tex]
hour on Monday and
[tex]\frac{5}{6}[/tex]
hour on Tuesday. Part A. Complete the calculations below to write equivalent fractions with a common denominator.
15a) True
Turning the Mixed Numbers into Improper ones:
He painted the his barn:
[tex]3\frac{3}{5}=\frac{18}{5}[/tex] Keep the denominator, and for the numerator multiply the denominator 5 by 3 and add 3 = 18. (In the morning).
[tex]5\frac{3}{4}=\frac{23}{4}[/tex] (In the afternoon)
The Prime factorization [tex]\frac{23}{4},\frac{18}{5}[/tex] help us to obtain the common denomination, i.e. 20
15b) False
This is a matter of simplification. In this mixed number, the fraction can be simplified this way:
[tex]3\frac{15}{20}=3\frac{15:5}{20:5}\Rightarrow 3\frac{3}{4}[/tex]
15c) True
Subtracting the working hours, knowing the common denominator by prime factorization is 20.
For Mixed Numbers:
[tex]5\frac{3}{4}-3\frac{3}{5}=5\frac{15}{20}-3\frac{12}{20}=2\frac{3}{20}[/tex]
For the same mixed numbers turned into improper fractions:
[tex]\frac{23}{4}-\frac{18}{5}=\frac{115-72}{20}=\frac{43}{20}[/tex]
Notice that:
[tex]2\frac{3}{20}==\frac{43}{20}=2.15[/tex]
16A
Equivalent fractions are fractions multiplied by a same constant, on the numerator and denominator:
[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]
[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]
15a is False as a common denominator isn't clear; 15b is False because the time in the morning is undefined; 15c is True assuming the morning was 3 hours. 16 needs further clarification.
15a ⇒False. To find the common denominator, we need to look at the fractions given. If there are fractions involved, more context is needed to validate this statement. Please provide relevant fractions.15b ⇒False. There is no concrete information given about the exact time spent in the morning to confirm this statement. If he spent 5 hours in the afternoon and the total time spent isn't specified, we cannot conclude the morning time is 3 hours.15c ⇒True. Since he painted for 5 hours in the afternoon, and we assume the morning time to be 3 hours (as per previous interpretations), Mr. Clements painted 2 hours longer in the afternoon (5 - 3 = 2).So, correct answer is 15a. False 15b. False 15c.True
Which describes the amount of product a seller is able to make?
A. Market
B. Demand
C. Supply
D. Can’t tell
Answer:
c) supply
Step-by-step explanation:
Answer:
supply
Step-by-step explanation:
15 more than twice a number
Answer:
15×2x
Step-by-step explanation:
Answer:
15 more than twice a number if it is a certain number u would multiply 15 times what ever number u chose
Step-by-step explanation:
What is solution to equation ? 4x + 5 = -3
Answer:
x=-2
Step-by-step explanation:
Solve for x:4x (+ 5-5) = -3-5
4x = -8
4x/4 = -8/4
x=-2
Checking Answer:4(-2) + 5= -3
-8 + 5 = -3
-3 = -3
Answer is Correct.
Answer:
[tex] \: \: \: \: \: \: 4x + 5 = - 3 \\ = > 4x = -3 - 5 \\ = > 4x = - 8 \\ = > x = \frac{ - 8}{4} \\ = > x > - 2[/tex]
BRAINLIEST!!! 10 POINTS!!
Make a list of the possible outcomes from the table.
Answer: The answer is A my friend.
Step-by-step explanation:
All possible outcomes:
Yellow shirt, white trouser
Yellow shirt, black trouser
Green shirt, white trouser
Green shirt, black trouser
Hope this helps. Please hit the thanks button if it is right. I would appreciate it. :)
∫x(x-6)³dx by using substitution u=x-6
Answer:
[tex]\large\boxed{\int\bigg(x(x-6)^3\bigg)dx=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C}[/tex]
Step-by-step explanation:
[tex]\int\bigg(x(x-6)^3\bigg)dx\Rightarrow\left[\begin{array}{ccc}x-6=u\\x=u+6\\dx=du\end{array}\right]\Rightarrow\int\bigg((u+6)u^3\bigg)du\\\\=\int(u^4+6u^3)du=\dfrac{1}{5}u^5+\dfrac{6}{4}u^4+C=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C[/tex]
what's 20 times 2 and add 4?
Answer:
20*2 is 40
add 4?
its 44
Answer:
44
Step-by-step explanation:
20 * 2 = 40
40 + 4 = 44
Hope this helps :)
how do you find if these are similar solids?
Step-by-step explanation:
Compare the ratios of their heights, widths, and lengths. If they're the same, then the solids are similar.
10/5 = 2
6/3 = 2
6/3 = 2
The ratios are the same, so the solids are similar.
9.
A wholesaler buys pairs of sunglasses
for $5.50 each. He then marks up the
wholesale cost 80% to create a retail
price for his customers. Customers must
then pay an additional 7% tax on the
retail price. What is the total cost of a
pair of sunglasses to the wholesaler's
customers, including tax, rounded to
the nearest penny?
A customer will pay $10.59, including sales tax, for a pair of sunglasses.
Step-by-step explanation:
Given,
Purchase price of sunglasses = $5.50
Mark up = 80%
Amount of mark up = 80% of purchase price
Amount of mark up = [tex]\frac{80}{100}*5.50=0.80*5.50[/tex]
Amount of mark up = $4.40
Retail price = Purchase price+mark up
Retail price = 5.50+4.40 = $9.90
Sales tax = 7% of retail price
Sales tax = [tex]\frac{7}{100}*9.90=0.07*9.90[/tex]
Sales tax = $0.69
Total paid by customer = retail price + sales tax
Total paid by customer = 9.90 + 0.69 = $10.59
A customer will pay $10.59, including sales tax, for a pair of sunglasses.
Keywords: addition, percentage
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I
10
11
12
13
Miguel bought 6 cos that were each the same price. Including sales tax, he paid a total of $99.60. Each CD had a tax of $1.30. What was the price of each CD
before tax?
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Answer:
The price of each CD before tax was $15.30.
Step-by-step explanation:
Given:
Miguel bought 6 CDs that were each the same price.
Including sales tax, he paid a total of $99.60.
Each CD had a tax of $1.30.
Now, to find the price of each CD before tax:
So, to get the price of 1 CD including tax by using unitary method:
Total price of 6 CDs including tax = $99.60.
So, the price of 1 CD including the sales tax = $99.60 ÷ 6 = $16.60.
Thus, the price of each CD including tax = $16.60.
Tax on each CD = $1.30.
Now, by subtracting we get the price of each CD before tax:
[tex]\$16.60-\$1.30[/tex]
[tex]=\$15.30.[/tex]
Therefore, the price of each CD before tax was $15.30.
how manet times dose 50 go into 1,000
Answer:
20 times
Step-by-step explanation:
1,000 divided by 50 will be 20 try using lone division :)
Answer:
20 times
Step-by-step explanat
Find X.
pls & thank you :)
Answer:
The correct answer is D. 69
Step-by-step explanation:
Let's recall that if an exterior angle has its vertex where two rays share an endpoint outside a circle, the measure of that exterior angle is found by dividing the difference between the measures of the intercepted arcs by two.
Therefore, we have:
x = (Measure of arch CD - Measure of arch BD)/2
Replacing with the real values:
x = (210 - 72)/2
x = 138/2 = 69°
The correct answer is D. 69
I need the answer I tried to do the work but my work is wrong so can you help me
Answer:
$545
Step-by-step explanation:
Let the total cost per year be y.
He spent a flat amount of $125 per year.
Then he spend an additional $35 per months. There are 12 months in a year so that's a total of 35*12=$420.
Add up the cost
y = 125 + 420 = $545
When two of the three numbers are added at a time, the possible sums are 32, 39, 23. What is the sum of all three numbers?
Please explain.
Answer:
47
Step-by-step explanation:
Let a, b, and c be those three numbers.
When two of the three numbers are added at a time, the possible sums are 32, 39, 23. Let
[tex]a+b=32\\ \\a+c=39\\ \\b+c=23[/tex]
Add these three equations:
[tex]a+b+a+c+b+c=32+39+23\\ \\2a+2b+2c=94[/tex]
Divide this equation by 2:
[tex]a+b+c=47[/tex]
The sum of all three numbers is 47.
To find the quotient of 8 divided by 1/3, multiply 8 by?
Answer:
Multiplying 8 by 3 will give the same quotient.
Step-by-step explanation:
We have to find the quotient of 8 divided by [tex]\frac{1}{3}[/tex], so, we have to follow the following steps.
[tex]8 \div \frac{1}{3} = \frac{8}{\frac{1}{3}} = 8 \times 3 = 24[/tex]
So, it is clear from the above steps that dividing 8 by [tex]\frac{1}{3}[/tex] is equivalent to multiplying 8 by 3.
Therefore, multiplying 8 by 3 will give the same quotient. (Answer)
Answer:
3/4 divied by 8 im sorry if it wrong im not to smart cuz my mom or dad doesnt help me :( and im homeschooled
Step-by-step explanation:
Help please I have to do all
Question # 1 (Top Left)
Step-by-step Explanation:
To determine:
We have to determine the missing side x.
Given:
Given angle = 29°Right angle = 90°The missing side x can be calculated by the formula:
sinФ = opposite ÷ hypotenuse
sin(29°) = x ÷ 3
0.4848 = x ÷ 3
x ÷ 3 = 0.4848
x = 0.4848 × 3
x = 1.45 cm
Hence, x = 1.45 cm is the length of missing side.
Question # 2 (Top Center)
Step-by-step Explanation:
To determine:
We have to determine the missing side x.
Given:
Given angle = 21°Right angle = 90°The missing side x can be calculated by the formula:
tanФ = opposite ÷ adjacent
tan(21°) = x ÷ 4
0.3838 = x ÷ 4
x ÷ 4 = 0.3838
x = 0.3838 × 3
x = 1.15 cm
Hence, x = 1.15 cm is the length of missing side.
Question # 3 (Top Right)
Step-by-step Explanation:
To determine:
We have to determine the missing side x.
Given:
Given angle = 66°Right angle = 90°The missing side x can be calculated by the formula:
cosФ = adjacent ÷ hypotenuse
cos(66°) = x ÷ 8
0.4067 = x ÷ 8
x ÷ 8 = 0.4067
x = 0.4067 × 8
x = 3.25 cm
Hence, x = 3.25 cm is the length of missing side.
Question # 4 (Bottom Right)
Step-by-step Explanation:
To determine:
We have to determine the missing side x.
Given:
Given angle = 29°Right angle = 90°The missing side x can be calculated by the formula:
cosФ = adjacent ÷ hypotenuse
cos(29°) = 3.7 ÷ x
0.8746 = 3.7 ÷ x
x = 3.7 ÷ 0.8746
x = 4.23 cm
Hence, x = 4.23 cm is the length of missing side.
Question # 5 (Bottom Center)
Step-by-step Explanation:
To determine:
We have to determine the missing side x.
Given:
Given angle = 37°Right angle = 90°The missing side x can be calculated by the formula:
sinФ = opposite ÷ hypotenuse
sin(37°) = 5.1 ÷ x
0.6018 = 5.1 ÷ x
x = 5.1 ÷ 0.6018
x = 8.47 cm
Hence, x = 8.47 cm is the length of missing side.
Question # 6 (Bottom Right)
Step-by-step Explanation:
To determine:
We have to determine the missing side x.
Given:
Given angle = 54°Right angle = 90°The missing side x can be calculated by the formula:
tanФ = opposite ÷ adjacent
tan(54°) = x ÷ 5.9
1.3763 = x ÷ 5.9
x ÷ 5.9 = 1.3763
x = 1.3763 × 5.9
x = 8.12 cm
Hence, x = 8.12 cm is the length of missing side.
Keywords: missing angle, tanФ, cosФ, sinФ, hypotenuse
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