In triangle ABC, a = 9, c = 5, and B = 120°. Find b2.
61
83.5
128.5
151
Answers
Answer:
The correct answer is 151.
Step-by-step explanation:
Given,
In triangle ABC,
BC = a = 9 unit,
AB = c = 5 unit,
m∠B = 120°,
We have to find : b² or AC²,
By the cosine law,
[tex]b^2=a^2+c^2-2ac cosB[/tex]
[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]
[tex]=81+25-90\times -0.5[/tex]
[tex]=81+25+45[/tex]
[tex]=151[/tex]
Hence, the value of [tex]b^2[/tex] is 151.
Answer:
Option D) [tex]b^2 = 151[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]
We have to find [tex]b^2[/tex]
The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,
[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]
Putting the values, we have,
[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]
Option D) [tex]b^2 = 151[/tex]
Related Questions
Mrs blanda truck holds 19.7 gallons of gas she used 4 full tanks of gas last month and paid $3 for each gallon how much did mrs blanka spend on gas last month
Answers
multiply 19.7 x 4 for total gallons
19.7 * 4 = 78.8 total gallons
multiply that by price:
78.8 * $3 = $236.40 total price
Mrs. Blanka spent $236.4 on gas last month by filling up her truck's 19.7-gallon tank 4 times at a price of $3 per gallon.
Explanation:To calculate how much Mrs. Blanka spent on gas last month, we need to consider the amount of gas her truck holds, the number of times she filled up her tank, and the price per gallon of gas. Mrs. Blanka's truck holds 19.7 gallons of gas, and she used 4 full tanks of gas last month. Given the price of gas was $3 per gallon, the calculation would be as follows:
First, find the total gallons of gas used: 19.7 gallons/tank × 4 tanks = 78.8 gallons.Next, calculate the total cost: 78.8 gallons × $3/gallon = $236.4.Therefore, Mrs. Blanka spent $236.4 on gas last month.
A data firm records a large amount of data. historically, 1.0% of the pages of data recorded by the firm contain errors. if 200 pages of data are randomly selected?
a. what is the probability that six or more pages contain errors?
b. what is the probability that more than 10 pages contain errors?
c. what is the probability that none of the pages contain errors?
d. what is the probability that fewer than five pages contain errors?
Answers
a) P(X >= 6) = 0.0160
b) P(X > 10) ≈ 6.88 x 10^-6
c) P(X = 0) ≈ 0.1339
d) P(X < 5) ≈ 0.9482
a. Probability of six or more pages with errors:
This is the sum of probabilities for 6, 7, 8, ..., 200 errors:
P(X >= 6) = 1 - [P(X < 6)] = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]
Using a calculator or statistical software, we can find these individual probabilities and sum them up. Alternatively, we can use binomial distribution tables or functions available in programming languages.
P(X >= 6) ≈ 0.0160
b. Probability of more than 10 pages with errors:
Similar to part (a), but calculating from 11 errors onwards:
P(X > 10) = 1 - [P(X=0) + P(X=1) + ... + P(X=10)]
P(X > 10) ≈ 6.88 x 10^-6 (very small probability)
c. Probability of none of the pages containing errors:
P(X = 0) = (0.99)^200 ≈ 0.1339
d. Probability of fewer than five pages containing errors:
P(X < 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
P(X < 5) ≈ 0.9482
Based on the graph of the line below, which describes the relationship between the value of the y-intercept and the value of the slope?
Answers
(-9,0)(0,3)
slope = (3-0)/(0+9) = 1/3
answer
A. y intercept is 3 and slope is 1/3
A protective cover for a wireless tablet has a height of 8 inches and base of 7 inches. What is the area of the cover?
Answers
Answer: The area of the cover = 56 square inches.
Step-by-step explanation:
We know that the shape of a tablet is rectangle.
Thus to calculate the area of the protective cover we apply the formula to calculate area of rectangle.
The area of rectangle is given by :-
[tex]\text{Area}=\text{Length*width}\\\\\Rightarrow\text{Area}=8\times7\\\\\Rightarrow\text{Area}=56\text{ inches}^2[/tex]
Therefore, the area of the protective cover is 56 square inches.
Richard estimates that he can apply fertilizer to 4,485 square feet of grass in 3/4 of an hour. How many square feet of grass can Richard fertilize per hour?
Answers
We know that Richard can apply fertilizer to 4485 square feet = 3/4 hour
To solve this problem, one approach is to find 1/4 then multiply by 4 to get the whole 4/4 or 1 hour.
So the solution would be:
4485/3=1495
Then multiply this by 4.
1495 multiplied by 4 is equal to 5980 square feet.
So Richard can apply fertilizer to 5980 square feet in 1 hour.
Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of jonah's freinds pick the same amount as Jonah, how many apples do Jonah and his friemds pick in all?
Answers
75 + 60 = 135
Four friends split equally a lunch bill of 36.96 plus 20% tip. How much did each person pay
Answers
P = [(36.96)(0.20) + 36.96]/4
Solve for P to find your answer.
suppose an isosceles triangle abc has a=pi/6 and b=c=5. what is the length of a^2?
Answers
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)
Answers
z-score = (x - m)/s
where x is the data point, m is the mean, and s is the standard deviation. Substituting the known values,
z-score = (11 - 8)/ 3 = 1
This translates to 0.84.
ANSWER: 0.84.
the difference of twice a number and 3
Answers
the difference means divide 2 times(multiply)a number
Find two consecutive odd integers such that their product is 71 more than 3 times their sum.
Answers
x = y + 2
The constraint is:
xy= 3(x+y) + 71 Simplify
xy = 3x + 3y + 71 Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71 Simplify
y² + 2y = 3y + 6 + 3y + 71 Subtract 6y from both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7
When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143
Our values work!
Answer: 11, 13
Use place value to find the product 3x600=3x
Answers
which of the following steps were applied to abc obtain a'b'c'
Answers
Answer:
Shifted 2 units left and 4 units up
Step-by-step explanation:
Given are two triangles
ABC is having vertices as (4,6) (7,6) and (5,9)
The transformed image A'B'C' has vertices as
(2,10) (5,10) (3,13)
On comparing the vertices corresponding we find a certain pattern.
X coordinate is reduced by 2 and y coordinate is increased by 4.
This implies the transformation is
Shifted 2 units left and 4 units up
What is m∠PTS?
Enter your answer in the box.
Answers
Their measures are equal.
11(y - 10) = 4y - 5
11y - 110 = 4y - 5
7y = 105
y = 15
m<PTS = 11(y - 10) = 11(15 - 10) = 11(5) = 55
m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
Angle is shown by the sign ∠
Given the line segments, PQ and SR is intersecting at T
Thus m∠PTS and m∠RTQ will be vertically opposite angles
m∠PTS = m∠RTQ
Given that,
m∠PTS = 11(y - 10)
m∠RTQ = 4y - 5
11(y - 10) = 4y - 5
11y - 110 = 4y - 5
11y - 4y = -5 + 110
7y = 105
y = 15
Therefore m∠PTS = 11(15 - 10)
m∠PTS = 55°
Hence "m∠PTS and m∠RTQ are vertically opposite angles thus both will be the same so the measure of m∠PTS will be 55°".
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Ahmad is fertilizing his garden. The garden is in the shape of a rectangle. Its length is 12 feet and its width is 10 feet. Suppose each bag of fertilizer covers 30 square feet. How many bags will he need to cover the garden?
Answers
Hope it helps!
Find the product of 4×7×25tell which strategy you used
Answers
The basic recipe for split pea soup serves 8 people. Find the amount of each ingredient needed to serve 32 people.
Answers
so, 4 time as much the recipe, or 4 times as much of each ingredient.
Round 354,738 to the nearest thousand?
Answers
Hope this helps!
354,738 rounded to the nearest thousand is 355,000.
What is a place value?In Mathematics and Euclidean Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.The number in the thousand place in the number 354,738 is 7 and it is greater than or equal to 5. This ultimately implies that, we would round up the number 4 to 5.
354,738 ≈ 355,000.
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Prove the quotient of any two rational numbers is a rational number
Answers
In the equation the {x} values would be most likely described as {2}. Since 2 was the quotient that was being repeating hence that equation not being rational. Hope this helps!
The quotient of any two rational numbers is always a rational number. This can be proved by expressing the division as multiplication by the reciprocal and demonstrating that the result is a rational number. Therefore, the property of being rational is preserved under division.
Let's define rational numbers first. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. Mathematically, if a and b are integers and b ≠ 0, then r = a/b is a rational number.
Consider two rational numbers r1 and r2.Suppose r1 = a/b and r2 = c/d, where a, b, c, and d are integers, and b ≠ 0 and d ≠ 0.To find the quotient q of these two rational numbers, we compute r1 ÷ r2:
q = (a/b) ÷ (c/d)This division can be written as multiplication by the reciprocal:
q = (a/b) × (d/c) = (a × d) / (b × c)Since the product of two integers is also an integer, a × d and b × c are integers.We can write the quotient as:
q = (a × d) / (b × c), where (b × c) ≠ 0 because neither b nor c is zero.Therefore, q is the quotient of two integers where the denominator is not zero, which means q is a rational number.
Thus, we have proved that the quotient of any two rational numbers is a rational number.
Max has a monthly salary of $1,100 and also earns 7.5% commission on his sales. If Max had $43,000 in sales last month, what were his total earnings for the month? a. $3,225 b. $4,050 c. $4,325 d. $5,150
Answers
1100+3225=4325
An equation is formed when two equal expressions. Max's total earnings for the given month are $4,325. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that Max has a monthly salary of $1,100 and also earns a 7.5% commission on his sales. Therefore, the equation that can represent Max's monthly salary for any month is,
y = $1,100 + $(0.075x)
where y is the month's salary and x is the number of sales he made.
Given in the last month Max had $43,000 in sales last month. Therefore, Max's total salary for the given month is,
Max Salary = $1,100 + $(0.075x)
= $1,100 + $(0.075 × 43,000)
= $1,100 + $3,225
= $4,325
Hence, Max's total earnings for the given month are $4,325.
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Choose the answer. 3. (1 pt) Suzanne cut a ribbon into 9 equal pieces. She sewed 5 pieces onto her quilt. Which number line shows a dot representing the fraction of the ribbon that was sewn onto the quilt? A. B. C. D.
Answers
A number line with 9 partitions with a dot marked on the 5th partition.
Find the simple interest. Principal $2300 rate 20% time 27 months The interest is $ ?
Answers
George spent 70 % of his saving to buy a camera. The camera cost $574 . How much did he originally have in savings?
Answers
820 $
You walk north for 2.5 miles. then you walk east a distance of 3.0 miles. how many miles from the starting point are you?
Answers
This would give u 5.5
Correct me if i'm wrong, but i hope it helps
Joshua earns $8.20 per hour when he works at the college library. How much money does he earn by working at the library for $4.5 hours.
PLEASE HELP!!!
Answers
he earns $36.90
How to determine if the function has x-axis sym, y-axis sym, and origin sym
y^2 -xy =2
Answers
To check for symmetry on the x axis, replace y with –y
-y^2 –x(-y) =2
Apply the product rule, since the equation is not identical tot eh original equation it is not symmetric about the x axis
Now do the same for y axis by replacing x with –x
Again using product rule the equations are not identical, so it is not symmetric about the y axis
To check the origin,
Replace both x & y with –x & -y
Again using product rule, the equations are not identical so it is not symmetric about the origin
To check for symmetry, replace x with -x and y with -y in the equation. Upon doing that for y^2 -xy =2, we find it lacks x-axis, y-axis, and origin symmetry.
Explanation:To determine whether a function has x-axis symmetry, y-axis symmetry, or origin symmetry, we have to replace x with -x and y with -y and see whether we get the same function.
X-axis symmetry: Replace y with -y. The equation becomes (-y)^2-(-y)x=2 which simplifies to y^2+xy=2. This is different from the original function, so there is no x-axis symmetry.Y-axis symmetry: Replace x with -x. The equation becomes y^2-(-x)y=2 which simplifies to y^2+xy=2. This is different from the original function, so there is no y-axis symmetry.Origin symmetry: Replace x with -x and y with -y. The equation becomes (-y)^2-(-y x -x)=2, which simplifies to y^2+xy=2. This is different from the original function, so there is no origin symmetry.Learn more about Symmetry of Functions here:https://brainly.com/question/16710816
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the value of the 7 in 507,264 is 10 times the value of the 7 in which number?
Answers
7000=10 x 700
7000=7000
Answer:
The value of the 7 in 507,264 is 10 times the value of the 7 in number 2
Step-by-step explanation:
Given Number : 507,264
To find : Number in which the value of the 7 in 507,264 is 10 times the value of the 7 .
Starting from the left ,
4 is in ones place
6 is in tens place
2 is in hundreds place
7 is in thousands place
0 is in ten thousands place
5 is in lakhs place
Here, 7 is in thousands place
7000 = 10 x 700
2 is in hundreds place
200 = 2 × 100
Therefore, the value of the 7 in 507,264 is 10 times the value of the 7 in number 2 .
A car is traveling at a rate of 40 miles per hour. What is the car's rate in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answers
1 mile = 1.6 kilometers
multiply 40 mph by 1.6 = 64
car's rate = 64 kilometers per hour
multiply kilometers per hour by 4 = 256
car will travel 256 kilometers in 4 hours
Write an equation for "eight less than a number is seventy-five". What is the number? n - 8 < 75; -67 n - 8 = 75; 67 n - 8 = 75; 83 n - 8 < 75; 67
Answers
n is the number
so number minus 8 equals 75
n-8=75
n is the number
so number minus 8 equals 75
If the product of two numbers is 14 and one of the numbers is 3 ½ times the other, then what is the sum of the two numbers?
Answers
product of the two numbers is 14 which translates to
xy=14
either x or y are 3.5 times big as the other one
so 3.5x=y
substituting in xy=14
x(3.5x)=14
[tex]3.5 {x}^{2} = 14[/tex]
[tex] {x}^{2} = \frac{14}{3.5} = 4 [/tex]
then x must be equal to 2 or -2
x+y=
by substituting
x+3.5x=
if x =2 then 2+7=9 or if x=-2 then -2-7=-9