of estion Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. 60° X y 93 2 y
Answers
The 30-60-90 ratio is a special right triangle that always has angles with measures: 30º, 60º, and 90º. Its side lengths have also the same relationship one with another.
For any 30-60-90 the ratio is as follows:
The side opposite to the 30º angle has length: z
The side opposite to the 60º angle has a length z√3
The side opposite to the 90º angle has a length: 2z
Following these ratios, you can determine the side lengths of the triangle.
The measure opposite to the 60º angle is z√3 = 9√3 → From this we can determine the value of z, which is z=9
Once we know the value of z, we can calculate the values of the sides opposite to the other angles.
The side opposite to the 30º angle is y= z= 9
The side opposite to the 90º angle is x= 2z= 2*9 = 18
Related Questions
3/9 - 6/9 = ?
,,,,,,,,,,,,,,,,,,,,,,,
Answers
Answer:
-3/9 or -1/3
Step-by-step explanation:
:]
Answer: -1/3
Step-by-step explanation- To subtract fractions, you first make the the denominators the same. The denominator is the bottom number. To make the denominator the same, you look for the lowest common denominator. Making the answer -1/3
Help?
(ii) Not sure what scale factor is
(ii) And I’ve never learnt this
Answers
This video from khan academy should clear up your confusion on scale factors.
https://www.khanacademy.org/math/7th-engage-ny/engage-7th-module-1/7th-module-1-topic-d/v/identifying-scale-factors
Capital Gate Tower is
150 meters tall
(measured vertically
from the ground) and
makes a 72° angle
with the ground. If
you were to climb to
the top and then
accidently drop your
keys, how far from
the base of the tower
would they land?
Answers
Answer:
Step-by-step explanation:
[tex]\frac{150}{x} =tan72 \\x=150 cot~72=150 cot(90-18)=150 ~tan ~18 \approx 48.74 ~meteres[/tex]
Explain how you can use addition of groups to show that 4 x ( -3) = 12
Answers
The technique of repeated addition involves combining equal groups.
4 x ( -3) = 12.
Repeated addition is the combining of equal groupings. It offers a basis for comprehending multiplication. For instance, 3 x 5 can be expressed as 5 + 5 + 5 to represent 3 groups of 5 counters.
We have been given that
4 x ( -3) = 12
By using repeated addition for multiplication
Add 4 three times or add 3 for times ..
In question negative 3 is given so we add negative 4 , three times
(-4) + (-4) + (-4)
-12.
Or
Add negative 3 , four times
(-3) + (-3 )+ (-3) + (-3)
-12.
Hence, we solved given multiplication by the using repeated addition method.
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Given m∥n, find the value of x
Answers
Answer:
x=55
Step-by-step explanation:
2x+6+x+9=180
3x=165
x=55
:]
Simplify the expression 7(6t+2)+3-5(t-1).
Answers
We are given the following expression:
[tex]7(6t+2)+3-5(t-1)[/tex]To simplify the expression, we will first use the distributive property on the parenthesis, like this:
[tex]7\times6t+7\times2+3-5\times t+5\times1[/tex]Solving the operations:
[tex]42t+14+3-5t+5[/tex]Now we add like terms:
[tex](42t-5t)+(14+3+5)[/tex]Solving the operations:
[tex]37t+22[/tex]This is the most simplified form of the equation
can you help me find the answer to this question find the area of this figure round your answer to the nearest hundredth use 3.14 to approximate tt. a= ? ft 2
Answers
First, let's calculate the area of the triangle.
[tex]A=\frac{1}{2}b\cdot h[/tex][tex]A=\frac{1}{2}\cdot6\cdot8=\frac{48}{2}=24\text{ ft2}[/tex]Now let's calculate the area of the semicircle.
[tex]A=3.14\cdot\frac{r^2}{2}[/tex][tex]A=3.14\cdot\frac{4^2}{2}=25.12\text{ ft2}[/tex]The total area of the figure is:
24+25.12 ft2 = 49.12 ft2
Tina couldn't wait to share the 36 cookies she made with her friends. If she shares with 8 friends, how many cookies (c) will each of them get?
Answers
Given:
Total number of cookies is, N = 36.
Number of friends is, n(f) = 8.
The objective is to find the number of cookies (c) will each of them get while sharing.
Consider the required number of cookies to each person as (c).
The value of c can be calculated as,
[tex]\begin{gathered} c=\frac{\text{Number of cookies (N)}}{Number\text{ of friends n(f)}} \\ =\frac{36}{8} \\ =4.5 \end{gathered}[/tex]Hence, each of them will get 4 and a half cookies.
1messageJosh wants to estimate the mean age in a population of trees. He'll sample n trees and build a 95% confidence interval for the mean age. He doesn't want the margin of error to exceed 3 years. Preliminary data suggests that the standard deviation for the ages of trees in this population is 16 years.Which of these is the smallest approximate sample size required to obtain the desired margin of error?11 trees110 trees144 trees43 trees87 trees
Answers
The formula for the margin of error is
[tex]\begin{gathered} \text{MOE}=SE\times critical\text{ value} \\ SE\Rightarrow\text{standard error} \end{gathered}[/tex]The critical value for 95% confidence interval is 1.96
The standard error is
[tex]\begin{gathered} SE=\frac{\sigma}{\sqrt[]{n}} \\ \sigma\Rightarrow standard\text{ deviation} \\ n\Rightarrow\text{sample size} \end{gathered}[/tex]To know which of the list of options will yield approximately the desired margin of error, we will have to calculate the margin of error with the following values
For 110 trees, n= 110, standard dev. =16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{110}}=1.53 \\ \text{MOE}=1.53\times1.96=2.9988 \end{gathered}[/tex]For 144 trees, n=144, standard dev=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{144}}=\frac{16}{12}=1.33 \\ \text{MOE}=1.33\times1.96=2.61 \end{gathered}[/tex]For 43 trees, n=43 , standard dev.=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{43}}=2.44 \\ \text{MOE}=2.44\times1.96=4.782 \end{gathered}[/tex]For 87 trees, n= 87, standard dev=16
[tex]\begin{gathered} SE=\frac{16}{\sqrt[]{87}}=1.72 \\ \text{MOE}=1.72\times1.96=3.3712 \end{gathered}[/tex]Hence, from the above calculations, the most prefered is the sample size of 110 trees (because the margin of error of 2.9988 is approximately 3 )
Answer is 110 trees
question 1.P(A)=0.25 P(B)=0.65 P(A or B)=?a.0.45b.0.2c.0.65d.0.9question 2P(A)=0.45 P(B)=0.35 P(A or B)=?a.0.75b.0.85c.0.8d.0.35
Answers
Given,
1)P(A) = 0.25
P(B) = 0.65
The value of P( A or B) is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)_{} \\ P(A\cup B)=0.25+0.65 \\ P(A\cup B)=0.90 \end{gathered}[/tex]Hence, option d is correct.
2)P(A) = 0.45
P(B) = 0.35
The value of P( A or B) is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)_{} \\ P(A\cup B)=0.45+0.35 \\ P(A\cup B)=0.80 \end{gathered}[/tex]Hence, option c is correct.
The safe load, L. of a wooden beam supported at both ends varies jointly as the width, w, the square of the depth, d. and inversely as the length. I. A wooden beam 8 in. wide. 6 in. deep, and 10 ft long holds up 1966 lb. What load would a beam 3 in. wide 9 in. deep and 11 ft long of the same material support? (Round off your answer to the nearest pound.)
Answers
The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17
Analyzing the given conditions in the question, we get
The safe load, L is directly proportional to width (w) and square of depth (d²)
also,
L is inversely as length (l) i.e L = k/l
combining the above conditions, we get an equation as:
L = k(wd²/l)
now, for the first case we have been given
w = 8 in
d = 6 in
l = 10 ft
L = 1966 lbs
thus,
1966 lb = k ((8 × 6²)/10)
or
k = 68.26 lbs/(ft.in³)
Now,
Using the calculated value of k to calculate the value of L in the second case
in the second case, we have
w = 3 in
d =9 in
l = 11 ft
Final Safe load L' = 68.26 × (6 × 3²/12)
or
L' =307.17 lb
Therefore, The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17
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Write an equation describing the relationship of the given variables
Answers
Towson Corporation issued $150,000 of 7% ten year bonds at 103 on the semi-annual interest date. Towson uses the straight line method to amortize any bond premium or discount. What is the amount of bond amortization for each six month period? Answer in whole dollars (no cents).
Answers
The amount of bond amortization for each six month period is [tex]\$225[/tex].
In the given question,
Towson Corporation issued [tex]\$150,000[/tex] of [tex]7\%[/tex] ten year bonds at [tex]103[/tex] on the semi-annual interest date.
Towson uses the straight line method to amortize any bond premium or discount.
We have to find the amount of bond amortization for each six month period.
Cash issued [tex]=\$150,000[/tex]
Rate [tex]=7\%[/tex] ten year bond at [tex]103[/tex] n the semi-annual interest date.
So the cash proceed on issue of bond = Cash issued [tex]\times103[/tex] [tex]/100[/tex]
Cash proceed on issue of bond [tex]=\$150,000\times\frac{103}{100}[/tex]
Firstly simplifying ratio
After simplification of ratio
Cash proceed on issue of bond [tex]=\$150,000\times1.03[/tex]
Now simplifying after multiplication
Cash proceed on issue of bond [tex]=\$154,500[/tex]
Hence, the cash proceed on issue of bond is [tex]\$154,500[/tex].
Now we find the premium that issued in the bond.
Premium on issue of bond [tex]=\$154,500-\$150,000[/tex]
Simplifying
Premium on issue of bond [tex]=\$4,500[/tex]
Hence, the premium on issue of bond is [tex]\$4,500[/tex]
Now finding the amount of bond amortization for each six month period.
Bond Amortization = (Premium on issue of bond/10 years) * 1/2
Bond Amortization [tex]=(\frac{\$4500}{10})\times\frac{1}{2}[/tex]
Simplifying the ratio
Bond Amortization [tex]=\$450\times0.5[/tex]
Bond Amortization [tex]=\$225[/tex]
Hence, the amount of bond amortization for each six month period is [tex]\$225[/tex].
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Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6. How many different lottery numbers are possible? O 720 lottery number O 7776 lottery numbers
Answers
As per the concept of probability, there are 7776 different lottery numbers are possible.
Probability:
Probability means the concept that is based on the possible chances of something to happen.
Given,
Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6.
Here we need to find how many different lottery numbers are possible.
Through the given question we know that,
The number of digits in a lottery ticket = 5
Side in cube = 6
So, in each time they will roll the dice 5 times to get one number.
So, the possible options of that event are,
For the first time we have 6 options
Second time we got 6 options
Third time also we got six option
Fourth time = 6 options
Fifth time = 6 options.
Therefore, it can be written as,
=> 6 x 6 x 6 x 6 x 6
=> 6⁵
=> 7776.
Therefore, there are 7776 different lottery numbers are possible.
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identify the mapping diagram that represents the relation and determine whether the relation is a function
Answers
F is the correct answer (option A) that is, the relation is like many to one. So, it is a function.
Given mapping diagram that represents the relation.
We have to determine whether the relation is a function.
(-8, -6), (-5, 2), (-8, 1), (7, 3)
Here,
Domain = (-8, -5, 7)
Range = (-6, 2, 1, 3)
A function is a relation where each input has only one output.
Here,
F. The relation is like many to one. So, it is a function.
G. The relation is many to one. So, it is a function.
H. The relation is one to many. It is not a function.
G. The relation is one to many. It is not a function.
So, F is the correct answer (option A) that is, the relation is like many to one. So, it is a function.
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Which analytical model best represents the data in the table below?
Answers
When x = 0, y = 2, then the constant term of the polynomial must be 2. This discards the last 2 options.
When x = 1, y = 11. Substituting x = 1 into the first two options, we get:
[tex]\begin{gathered} y=9\cdot1^2+2=9+2=11 \\ y=9\cdot1^2+11\cdot1+2=9+11+2=22 \end{gathered}[/tex]Then, y = 9x² + 2 is correct.
Simplify the expression 5(-7 + 3k)
Answers
The given expression is,
[tex]5(-7+3k)[/tex]Opening the brackets and multiplying each term inside the bracket with 5, we get,
[tex]\begin{gathered} \lbrack5\times(-7)\rbrack+(5\times3k)=-35+15\text{ k} \\ 15k=35 \\ k=\frac{35}{15}=2.33 \end{gathered}[/tex]The simplified expression is 15k = 35 and the value of k is 2.33.
damion started solving this equation in an even different way what did he do first
Answers
With the help of Linear equation we can say that Damion added 12 on both sides.
What is linear equations?Equations with variables whose maximum power is 1 are said to be linear equations. A linear equation has a straight line as its graph.The given equation was,
12x + 4 = 20x-12If we will add 12 on both sides ,
12x + 16= 20xHence we can say that Damion added 12 to both sides.
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calcula la suma de los quince primeros multiplos de 9
Answers
Answer:
Step-by-step explanation:
9*(15/2)[2+14] = 9*15*16 = 2160.
In triangle DEF, m∠D = (2x + 19)°, m∠E = (3x + 24)°, and m∠F = 87°. Determine the degree measure of the exterior angle to ∠D.
54°
39°
141°
126°
Answers
The value of x is equal to 10 and the exterior angle to angle d is equal to 141 degrees.
Exterior AnglesTo solve this problem, we have to recall that the sum of angles in a triangle is equal to 180 degrees.
Applying that formula here;
[tex]m < d + m < e + m < f = 180^0\\(2x + 19) + (3x + 24) + 87 = 180\\x = 10[/tex]
But the exterior angle to angle D can be found assuming the angle lies on a straight line, then the sum of angle D and it's exterior angle would be equal to 180 degrees.
Let y = exterior angle
[tex]m < d + y = 180\\2x + 19 + y = 180\\x = 10\\2(10) + 19 + y = 180\\20 + 19 + y = 180\\39 + y = 180\\y = 141^0[/tex]
The value of the exterior angle to d is equal to 141 degrees.
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Answer: its C
Step-by-step explanation: i got it right
In gym class, a student can do 40 sit-ups in 60 seconds and 100 sit-ups in 150 seconds.
Graph the proportional relationship.
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 60
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 30
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 60 comma 50
graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30
Answers
Answer:
(a) graph with line through (90, 60)
Step-by-step explanation:
You want a graph of the proportional relationship between sit-ups and seconds if a student can do 40 sit-ups in 60 seconds.
GraphSeconds are plotted on the x-axis, and sit-ups are plotted on the y-axis The graph will match that shown in the attachment.
<95141404393>
The cranes shown in the figure are lifting an object that weighs 20,290 pounds. Find the tension in the cable of each crane. (Round your answers to the nearest whole number.)TL= lbsTR= lbs
Answers
we have that
TLy+TRy=20,290 ------> equation A
and
sin(24.3)=TLy/TL
TLy=TLsin(24.3) ------> equation B
sin(44.5)=TRy/TR
TRy=TRsin(44.5) ------> equation C
and
TLx=TRx
TLcos(24.3)=TRcos(44.5)
TL=TRcos(44.5)/cos(24.3) --------> equation D
substitute equation B and equation C in equation A
TLsin(24.3)+TRsin(44.5)=20,290 -------> equation E
substitute equation D in equation E
(TRcos(44.5)/cos(24.3))sin(24.3)+TRsin(44.5)=20,290
solve for TR
factor TR
TR[cos(44.5)/cos(24.3))sin(24.3)+sin(44.5)]=20,290
TR=19,835 pounds
Find TL
TL=(19,835)cos(44.5)/cos(24.3)
TL=
10. A recipe calls for 5 cups of flour. If you only have a ½ cup to measure, how many ½ cups will you need for
the recipe?
Answers
Explanation: 1/2 goes into one twice. So, if you have 5 cups, you need to multiply it by 2 to account for every 1/2 a cup
there are 13 porters carrying total weight of 195 kg on an expeditioin. extra porters joined the group so, they carry average weight of 13kg of baggage. find the number of portes added
Answers
Answer: 2 porters joined the group
Step-by-step explanation:
First, you are told that "13 porters are carrying a total weight of 195kg". You can use this information to create an equation to find the average weight carried by each porter.
[tex]\frac{195 kg}{13}=15kg[/tex]
^195kg (total weight) divided by 13 (the number of porters) is equal to 15kg (the average weight carried by each of the 13 porters).
You are then told that "extra porters join the group, so they carry an average weight of 13 kg of baggage". because some porters joined the group, you'll have to add p (p = number of porters) to the original equation and change the average weight from 15kg to 13kg.
[tex]\frac{195kg}{13 +p} = 13kg[/tex]
^195kg (total weight) divided by 13+p (total number of porters after some joined group) is equal to 13kg (new average weight)
You can then use your new equation to solve for "p" and find the number of porters added.
p = 2
A 250 N force acts on a 20 kg object. What would be the acceleration of the object?
Answers
Answer:
a = 12.5 m/s2
Step-by-step explanation:
anwser 12.5
In isosceles triangle ABC,AB=BC. AB and Bc are called_____a.bases b.verticesc.hypotenused. legs
Answers
In an isosceles triangle, there are
2 legs (equal sides)
1 base
The 2 legs are the equal sides
The base is the third side
In the isosceles triangle ABC:
Since AB = BC, then
AB and BC are the legs of the triangle, then
AB and BC are called legs
The answer is d
6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6
Answers
The value of 6 to the negative 3rd power times 6 to the 2nd power times 6 to the 5th power times 6 is 6^5.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, the numbers will be expressed as:
6^-3 × 6^2 × 6^5 × 6
= 6^5
It's important to note that they've the same base. Therefore, the powers will be added thus:
= -3 + 2 + 5 + 1
= 5
This gives 6^5. This illustrates the concept of exponents.
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Complete both transformations below.
Then enter the final coordinates of the figure.
A(-1,3)
B(2,1)
C(1-1)
1) <2,3>
2) Dilate K = 2
A" ([?], [])
B" ([][])
C" ([],[])
Enter
Answers
Answer:
A" (2, 12)
B" (8,8)
C" (6, 4)
Step-by-step explanation:
For each point P(x, y) of the image, the translations are as follows:
Translate P(x, y) by <2, 3> [tex]\longrightarrow[/tex] P'(x + 2, y + 3) [tex]\longrightarrow[/tex] P'(x', y')
Dilate P'(x', y') by 2 [tex]\longrightarrow[/tex] P'' (x'', y'') [tex]\longrightarrow[/tex] P(2x', 2y')
Point [tex]\longrightarrow[/tex] Translate <2, 3> [tex]\longrightarrow[/tex] Dilate by 2
A(-1, 3) [tex]\longrightarrow[/tex] A'(-1 +2, 3 + 3) => A'(1, 6) [tex]\longrightarrow[/tex] A''(2, 12)
B(2, 1) [tex]\longrightarrow[/tex] B'(2 + 2, 1 + 3) => B'(4, 4) [tex]\longrightarrow[/tex] B"(8, 8)
C(1, -1) [tex]\longrightarrow[/tex] C'(1 + 2, -1 + 3) => C'(3, 2) [tex]\longrightarrow[/tex] C"(6, 4)
How much interest is earned in an investment if $720 is deposited monthly at 7.8% compounded monthly if the term of the investment is 6 years?$__________Round to the nearest cent
Answers
Given:
The initial investment is, P = $720.
The rate of interest is, r = 7.8% = 0.078.
The number of years of investment is, t = 6 years.
Explanation:
The general formula to find the compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n represents the number of times compounded in a year. It is given that the amount is compounded monthly, so the value of n = 12.
To find total amount after 6 years:
Now, substitute the given values in the general equation.
[tex]\begin{gathered} A=720(1+\frac{0.078}{12})^{12(6)} \\ =720(1+0.0065)^{72} \\ =1147.95 \end{gathered}[/tex]Thus, the total amount earned is $1147.95.
To fnd interest amount:
Now, the amount of interest can be calculated as,
[tex]\begin{gathered} I=A-P \\ =1147.95-720 \\ =427.95 \end{gathered}[/tex]Hence, the interest amount earned is $427.95 and the total amount earned is $1147.95.
how far apart is -1 1/3 and 4 2/5 on a number line