What is the value of b?
Round your answer to the nearest tenth.
15.7 yd
24.1 yd
35.1 yd
36.2 yd
The figure shows acute triangle A B C. The measure of angle B is 34 degrees. The length of side A B is 28 yard. The length of side B C is 22 yard. The length of side C A is b.
Answers
You are trying to find length b, so
b^2 = a^2 + c^2 - 2ab cos B
b^2 = 22^2 + 28^2 - 2(22)(28) cos 34
b^2 = 484 + 784 - 1232 cos 34
b^2 = 1268 - 1232 cos 34
b^2 = 246.6257
b = 15.7 yards
Hope this helps!
Answer:
A. 15.7 yards.
Step-by-step explanation:
Please find the attached file.
We have been given that in triangle ABC, the measure of angle B is 34 degrees. The length of side AB is 28 yards and the length of side BC is 22 yards. The length of side CA is b.
We will use law of cosines to find the length of side 'b'.
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]CA^2=22^2+28^2-2\times 22\times 28\times cos(34^{\circ})[/tex]
[tex]CA^2=484+784-1232\times 0.829037572555[/tex]
[tex]CA^2=1268-1021.37428938776[/tex]
[tex]CA^2=246.62571061224[/tex]
Taking square root of both sides we will get,
[tex]CA=\sqrt{246.62571061224}[/tex]
[tex]CA=15.70432139929\approx 15.7[/tex]
Since the length of side CA is b, therefore, the value of b is 15.7 yards and option A is the correct choice.
Related Questions
A radio tower casts a shadow of 8.2 ft long and a 36-inches and a fourth-grader walking home cast a shadow of 1.5 inches. How tall is the radio tower?
Answers
Answer: 196.8
Step-by-step explanation:
Start off by reading the problem.
A radio tower casts a shadow of 8.2 ft long and a 36-inches and a fourth-grader walking home cast a shadow of 1.5 inches. How tall is the radio tower?
Then take what you know from the problem and put it in a fraction looking thing:
like this:
1.5 8.2
__ = __
36 x
So after you've done this you will want to:
Multiply 36 x 8.2 = 295.2
take 295.2 then Divide by 1.5
=196.8
Answer:
196.8
Step-by-step explanation:
The common stock of air united had annual returns of 13.7 percent, 4.8 percent, -6.7 percent, and 27.9 percent over the last four years, respectively. what is the standard deviation of these returns?
Answers
What is the sum of the geometric sequence -4,24,-144...if there are 8 term? A.-959,781 B. 29,637 C. 26,661 D. 959,780 PLEASE HELP
Answers
Answer:
The sum of 8 terms of series is 959,780
D is correct
Step-by-step explanation:
Given: -4, 24, -144, ......
There are 8 terms.
We need to find the sum of 8 terms.
First term, a=-4
Common ratio, r=-6
[tex]a_n=-4\cdot(-6)^{n-1}[/tex]
Sum of 8 term
[tex]Sum=a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8[/tex]
[tex]Sum=\sum_{n=1}^{8}a_n[/tex]
[tex]Sum=-4+24-144+864-5184+31104-186624+1119744[/tex]
[tex]Sum=959,780[/tex]
Hence, The sum of 8 terms of series is 959,780
2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft^3
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain. Answer:
Answers
As the table can only support 200 lbs the aquarium should not be put on the table.
(b) No the deisity of the water is a constant
(a)
3*3*3=27
27*62=1674
Your answer: 1674
(b)
No, no matter how much water there is, the density will never change.
Question 4 :)))))))$$$))))$$
Answers
£19 is your answer.
The original vertices of a quadrilateral are (-2,3), (4,6), (4,2), and (3, -2). After a transformation, the new coordinates are (-1,1.5), (2,3),(2,1), and (1.5,-1). Are the two images similar? Justify your answer.
A) no; The transformation is not rigid; therefore, the quadrilaterals are not similar.
B) no; The transformation is a translation which only results in the size of the quadrilaterals being preserved.
C) yes; This is a rigid transformation which preserves angle measurement and size of the original quadrilateral.
D) yes; The transformation is a dilation which results in similar quadrilaterals by preserving angle measurements.
Answers
The answer would be D) yes; The transformation is a dilation that results in similar quadrilaterals by preserving angle measurements.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The original vertices of a quadrilateral are (-2,3), (4,6), (4,2), and (3, -2).
After a transformation, the new coordinates are (-1,1.5), (2,3),(2,1), and (1.5,-1).
As we know that dilation is a process for creating similar figures by changing the size.
This means that the two images are similar, as they have the same shape and size, despite having different positions and orientations in the coordinate plane.
Hence, the given transformation is a dilation that results in similar quadrilaterals by preserving angle measurements.
To learn more about the transformations click here :
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Claire has received scores of 85, 88, 87, and 80 on her algebra tests. what is the minimum score she must receive on the fifth test to have an overall test score average of at least 82 ?
Answers
85+88+87+80+x/5=82
340+x=410
410-340=70
HHHEEELLLPPP PLEASE
1] Amanda’s gross annual salary is $62,112.
What is the maximum amount of rent she can afford to pay?
Round your answer to the nearest dollar.
A $2588
B $1866
C $1449
D $1236
2] Jonathan is signing a lease for an apartment that rents for $1240/month.
How much will he pay to move in if he must pay the first and last months’ rent and a security deposit equal to 80% of his monthly rent?
A $2976
B $3472
C $3542
D $3720
Answers
Rule of thumb for month rent: Rent ≤ 28% of monthly gross income
Then,
Month gross income = $62,112/12 = $5,176
Affordable rent = 0.28*5176 = $1,449.28
Rounding to nearest dollar;
Affordable rent = $1,449.
The correct answer is C.
Part 2
Monthly rent = $1240
Security deposit = 80% of rent = 0.8*1240 = $992
Amount to be paid = 1240*2 + 992 = $3472
The correct answer is B.
Answer:
first one would be c
Step-by-step explanation:
Find the distance d from (6.1, 5.9) to (-5.9, -4.1) .
A.
6.63
B.
15.62
C.
22.00
D.
244.00
Answers
√(x1-x2)^2+(y1-y2)^2
Answer:
your answer is B
Step-by-step explanation:
Brian made 5 free throws at basketball practice. ethan scored 3 more than twice the number of free throws brian made. which equation could be used to find the number of free throws, t, ethan made?
Answers
b=5
e=3+2b
will be the equation of finding free throws.
Find the surface area of the equilateral triangular pyramid.
Answers
tan 49 = x/400
please solve
Answers
Therefore, 400tan49 = x (simple algebra)
X = 460.147
What is the following quotient?
3^√60
------------
3^√20
Answers
Answer:
its 3√3 bud
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
BRAINLIESTTT ASAP!
please answer
Answers
2x+8+5x-2=90
7x+6=90
7x=84
x=12
Now, we substitute x and solve for the angles.
2x+8
2(12)+8
32 degrees
5x-2
5(12)-2
58 degrees
To double check our answer, we can add the two angles together and see if we get 90.
32+58=90 yes
Our answer is correct
Need help to write equations for 5, 6 & 7
Answers
Read my note at the end of problem 5 in another post.
You already know this table represents an exponential function
since each y-coordinate is always the previous y-coordinate multiplied by 6.
That means b = 6, and you have
y = a(6)^x
Now we find "a". When x = 0, y = 5. That means a = 5.
The equation is
y = 5(6)^x
Solve the equation. 20 = –d + 16
A. 4
B. –10
C. –6
D. –4
Answers
The correct answer to this question would be D: negative 4
This is because the negatives from negative 4 and negative d would cancel each other out, to make it a positive 4, resulting in the equation being: 20 = 4 + 16 , which is true
I hope this helped ^^
What is the length of segment CE if AE = 15 inches and ED = 5 inches and EB = 3 inches?
A. 45 inches
B. 9 inches
C. 15 inches
D. 14 inches
Answers
We have to determine the length of segment CE if AE = 15 inches and ED = 5 inches and EB = 3 inches.
Since ,we can observe that AB and CD are chords intersecting at point E.
Therefore, by intersecting chord theorem which states:
" When two chords intersect each other inside a circle, the products of their segments are equal"
So, [tex] AE \times EB= CE \times ED [/tex]
[tex] 15 \times 3= CE \times 5 [/tex]
[tex] 45= CE \times 5 [/tex]
[tex] CE = \frac{45}{5} [/tex]
CE = 9 inches.
So, the measure of segment CE is 9 inches.
So, Option B is the correct answer.
Expenses that are bi-weekly are paid twice a week twice a month every two weeks every two months
Answers
Answer:
Expenses that are bi-weekly are paid every two weeks.
Step-by-step explanation:
Expenses that are bi-weekly are paid every two weeks.
A bi-weekly pay schedule is the most commonly used pay period by employers. It is also called every other week pay period.
This payment method results in 26 paychecks in a year.
Three different bags of pretzels are sold at the store. which bag of pretzels is the best buy? bag a:10 ounces for $1.10 bag b:12 ounces for $1.38 bag
c.6 ounces for $0.84
Answers
Bag a:
----------------------
10 ounces = $1.10
1 ounce = $1.10 ÷ 10 = $0.11
----------------------
Bag b:
----------------------
12 ounces = $1.38
1 ounce = $1.38 ÷ 12 = $0.115
----------------------
Bag c:
----------------------
6 ounces = $0.84
1 ounce = $0.84 ÷ 6 = $0.14
--------------------------------------------------
Answer: Bag A is the best buy.
--------------------------------------------------
In a circle, a 225 degrees sector has area 490pi in2. What is the radius of the circle?
Answers
area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree
r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=(∅/2)*r²--------> when ∅ is in radians
r=√[2*(area of a sector)/∅]
let's calculate the radius of the two ways
1) r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=490*pi in²
∅=225°
r=√[360°*(490*pi)/(225°*pi)]-------> r=√784-----> r=28 in
2) r=√[2*(area of a sector)/∅]
area of a sector=490*pi in²
∅=225°-----> convert to radians-----> ∅=225°*pi/180-----> ∅=1.25*pi
r=√[2*(490*pi)/(1.25*pi)]----> r=√[980/1.25]---> r=√784----> r=28 in
the answer is
the radius is 28 in
the value 5 is a an upper bound for the zeros of the function shown below f(x)=x^4+x^3-11x^2-9x+18
A. TRUE
B. FALSE
Answers
Answer:
Answer to this question is TRUE.
Step-by-step explanation:
The graph of the function:
[tex]f(x)=x^4+x^3-11x^2-9x+18[/tex] is attached to the answer.
Clearly by looking at the graph we could see that the zeros of the function f(x) are -3, -2, 1 and 3.
All the zeros are distinct.
" Also upper bound of a number 'p' means the set of all those numbers which are greater than 'p' ".
Here 5 will be an upper bound for the zeros of the function f(x) since all the 4 zeros of f(x) are less than 5.
Hence, the given statement that the value 5 is an upper bound for the zeros of the function f(x) is TRUE.
Answer:
true
Step-by-step explanation:
Write the prime factorization of 18. Use exponents when appropriate and order the factors from least to greatest (for example,
2
2
3
5
).
Submit
Answers
For example, the number 18.
18/2 = 9
9/3 = 3
So the prime factorization is 2,3,3
As it says use exponents: There are 2 threes. 3 x 3 is the same as 3²
3² x 2 should be your answer
hope this helps
The prime factorization of 18 is 2 x 3², dividing 18 first by 2 and then by 3 twice.
Explanation:The prime factorization of a number represents that number written as the product of its prime factors. Let's take 18 as an example. First, we will find the smallest prime number that can divide 18, which is 2. When 18 is divided by 2, the quotient is 9. Then, we continue to divide 9 by the smallest possible prime number, which is 3. We can divide 9 by 3 two more times. Therefore, the prime factorization of 18 is 2 x 3², where 2 and 3 are the prime factors and ² is an exponent indicating that 3 is a factor twice.
Learn more about Prime Factorization here:https://brainly.com/question/33295472
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Simplify the radical expression.
square root of 20
A. 2√10
B. 5√2
C. 2√5
D. 2
if anyone has the answers to the unit test let me know :)
Answers
Suppose y varies directly with x and y=-25 when x=5. find y when x=3
Answers
Final answer:
To solve for y when x = 3, we first determined the constant of proportionality (k) using the given values (y = -25 when x = 5). With k found to be -5, we then calculated y for x = 3 to find that y = -15.
Explanation:
The question asks us to find the value of y when x = 3 given that y varies directly with x and that y = -25 when x = 5. Because y is directly proportional to x, we can write the relationship as y = kx, where k is the constant of proportionality.
First, we solve for k:
Set up the equation based on the given information: y = kx
Substitute the known values: -25 = k(5)
Solve for k: k = -25 / 5 = -5.
Now that we have found k, we can use it to find y when x = 3:
Use the determined value of k: y = -5(3)
Multiply to find y: y = -15.
Therefore, when x = 3, y is -15.
Last week christi spent 2 3/4 hours playing piano this week she spent 3 2/4 hours playing the piano how much more time did she play the piano this week
Answers
3 2/4-2 3/4
Converting the above into proper fraction we get:
14/4-11/4
=(14-11)/4
=3/4
Thus she spent and extra 3/4 hours=45 minutes this week
It’s 3/4 hours which is 40 mins how I did this was I did that then I finished BOOM DONE KID
NEED HELP PLEASE I BEG!!!!!!
The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations.
What is the survey’s margin of error?
Enter your answer in the box. ± ___ %
The answer goes on the underscores
Answers
[tex]C.I.=\hat{p}\pm M.E.[/tex]
where: [tex]\hat{p}[/tex] is the sample proportion, which is midway between the two intervals and M.E. is the margin of error which is the difference between each of the intervals and the sample proportion.
i.e.
[tex]\hat{p}= \frac{76+84}{2} \% \\ \\ = \frac{160}{2} \%=80\%[/tex]
Therefore, the margin of error is 4%.
Final answer:
The margin of error for the survey, given a range between 76% and 84% satisfaction for seat locations, is calculated to be ±4%.
Explanation:
The margin of error in a survey indicates how much the survey results might differ from the actual opinions of the total population.
In this case, the survey indicates a satisfaction range between 76% and 84% for seat locations among season ticket holders.
The margin of error is half of the width of the range, which is the difference between the upper and lower percentage bounds of the confidence interval divided by two.
To calculate the margin of error, subtract the lower percentage (76%) from the upper percentage (84%) and then divide by 2. That is, (84 - 76) / 2 = 8 / 2 = 4.
Thus, the margin of error for the survey is ±4%.
Graciela is working to earn 200$ . she earns 25$ mowing her grandmas lawn and 60$ for a day of housecleaning what decimal represents the part of money graciela still needs to earn
Answers
What is the range of the data set
2 | 1, 3, 8, 8
5 | 2, 4, 6, 6, 7
6 | 0, 1, 1
Key: 6| 0 means 60 please help i do not get this plz solve
Answers
The highest value is 61.
The lowest value is 21.
range = highest value - lowest value = 61 - 21 = 40
The english alphabet contains 21 consonants and five vowels. how many strings of six letters, each of which is drawn from the english alphabet, contain (a) exactly one vowel?
Answers
Answer: 20 420 505
What is the lateral area of the prism? Assume the figure is resting on its base.
Answers
the lateral area, namely the area of the sides, as you see in the picture, is really just the area of 6 rectangles.
front and back, two rectangles of 5x25,
left and right, two rectangles of 2x25.
simply get the area of each and sum them up, that's the lateral area of the prism.
[tex]\bf \stackrel{\textit{front and back}}{2(5\cdot 25)}~~~~+~~~~\stackrel{\textit{left and right}}{2(2\cdot 25)}[/tex]