Use the law of cosines to find each missing side. Round to the nearest tenth
Answers
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As per the law of cosine, the measure of angle x can be written as,
[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]
Hence, the value of x is 117.8°. thus, the correct option is A.
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Related Questions
Find the length of diagonal BC of ABCD to the nearest hundredth.
Answers
The length of BC as shown in the diagram is 6.32units
Calculating distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
Given the following coordinate points (3, 6) and (5, 0)
Substitute
BC = √(0-6)²+(5-3)²
BC = √(36+4)
BC = √40
BC = 6.32 units
Hence the length of BC as shown in the diagram is 6.32units
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What is the area of triangle ABC?
Answers
Answer:
3 square units
Step-by-step explanation:
Use BC as the base = 2
Use y -axis to C (or B) as the height = 3
Area of triangle = 1/2 * base * height = 1/2 * 2 * 3 = 3 units^2
Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
Answers
Which expression is equivalent to?
Answers
The expression obtained is 2g³-5g² +6 , Option C is the correct answer.
What is an Expression ?An expression is a mathematical statement that consists of constant , variable and mathematical operators.
The expression given is
[tex]\rm \dfrac{(5g^4 +5g^3 -17g^2 +6g) -(3g^4 +6g^3-7g^2 -12)}{g+2}[/tex]
On subtracting the numerator
2g⁴-g³-10g²+6g+12
Now dividing the numerator by denominator
The expression obtained is 2g³-5g² +6
Therefore Option C is the correct answer.
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In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys simple equations
Answers
Answer:
Boys = 605
Girls = 675
Step-by-step explanation:
Let x be the number of boys in school.
So, girls = (x+70)
Total no. of students = 1280
x + x + 70 = 1280
2x + 70 = 1280
2x = 1280 - 70
2x = 1210
x = 1210/2
x = 605
Hence, no. of boys = 605
no. of girls = 605 + 70 = 675
* GEOMETRY
please help me show the work for 9, 10, and 11!!
Answers
9) Diagonals of a parallelogram bisect each other, so KN=NM. Thus, KM=13.5+13.5=27 cm
10) Opposite sides of a parallelogram are congruent, so LM=KJ=17 cm
11) Based on Question 9, MN=13.5 cm
30 point!!!! Help me fast!!!PLS!!Question is attached!!!
Answers
Answer:
This is an extremely easy question bro!
1. 3²
2. 3 (Base) ² (Exponent)
3. Expanded form: (9 * 1)
Standard form: 9
Step-by-step explanation:
Well, there's none.
Please mark me as Brainliest! Thanks! :)1) 5^3
2) Base = 5; Exponent = 2
3) Expanded Form = 5 * 5
Standard Form = 25
What is sin and cos
Answers
Sin and cos are trigonometry functions used to find measurements in a right triangle.
[tex]\displaystyle sin=\frac{\text{opposite side}}{hypotenuse}[/tex]
[tex]\displaystyle cos=\frac{\text{adjacent side}}{hypotenuse}[/tex]
find x and y. Please help me with my math
Answers
Answer: Read attachment.
Step-by-step explanation: Attached below is my work. Hope it helps!
P(x)⋅Q(x)=R(x); if P(x)=x+1 and R(x)=2x3+2x2+3x+3, what is Q(x)?
A. 2x2+2
B. 2x2+3
C. 2x2−3
D. 2x2−2
Answers
Answer: B
Step-by-step explanation:
[tex]P(x) Q(x)=R(x) \implies Q(x)=\frac{R(x)}{P(x)}\\\\Q(x)=\frac{2x^{3}+2x^{2}+3x+3}{x+1}={2x^{2}(x+1)+3(x+1)}{x+1}=\boxed{2x^{2}+3}[/tex]
(6 + 7) + 8 = 21
Choose an equivalent addition sentence that shows the associative property of addition.
Answers
Answer:
6 + (7 + 8) = 21
Step-by-step explanation:
the associative property of addition is: (a + b) + c = a + (b + c)
So the equivalent addition sentence would be:
(6 + 7) + 8 = 6 + (7 + 8) as they both equal 21
1kg of sugar costs ₹25.30 . Find the cost of 13.5kg of sugar
Answers
Answer:
₹ 341.55
Step-by-step explanation:
Cost of 1 kg sugar = ₹ 25.30
Cost of 13.5 kg sugar = 25.30 × 13.5 = 341.55
Hence, the cost of 13.5 kg is ₹ 341.55
If you are writing, write statements too as in my school they give extra marks.
Thankyou and have a great day ahead.
Answer:341.55
Step-by-step explanation:
If one KG of sugar does cost ₹25.3 and if you want to know how much 13.5 kg costs you just would have to multiply/times ₹25.3 by 13.5 and what is 25.3 x 13.5. ₹341.55 and that's your answer!
775 tickets were sold for a game for a total of $1,587.50. If adult tickets sold for $2.50 and childrens tickets sold for $1.50,how many of each kind of tickets were sold?
Answers
350 tickets sold of children and 425 tickets sold for adult.
What is algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Let x be the number of adult tickets that were sold and y be the number of children's tickets that were sold.
Total 775 tickets were sold for the game.
So,
x + y = 775
If adults tickets sold for 2.50 and children's tickets sold for 1.50 and all the tickets were sold for a total of 1587.5, it means that
2.5x + 1.5y = 1587.5
put x = 775 - y
2.5(775 - y) + 1.5y = 1587.5
1937.5 - 2.5y + 1.5y = 1587.5
-y = 1587.5- 1937.5
y = 350
and, x = 775 - y = 775 - 350
x = 425
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Venn diagram ( attached image )
Answers
Assessing the given Venn diagram and the data related to it, we can answer the required question:
Q1. How many people were surveyed = 86.
Q2. What is the probability that a customer chosen at random:
a) takes salt P(S) = 46/85.
b) takes both salt and vinegar P(S ∩ V) = 13/85.
c) takes salt or vinegar or both P(S ∪ V) = 66/85.
The number of people who take salt chips n(S) = 46.
The number of people who take vinegar chips n(V) = 33.
The number of people who takes both n(S ∩ V) = 13.
The number of people who take neither n((S ∪ V)') = 19.
Therefore, the total number of people surveyed n(U) = n(S) + n(V) - n(S ∩ V) + n((S ∪ V)') = 46 + 33 - 13 + 19 = 85.
The number of people who takes salt or vinegar or both n(S ∪ V) = n(U) - n((S ∪ V)') = 85 - 19 = 66.
The probability that a customer chosen at random takes salt P(S) = n(S)/n(U) = 46/85.
The probability that a customer chosen at random takes both salt and vinegar P(S ∩ V) = n(S ∩ V)/n(U) = 13/85.
The probability that a customer chosen at random takes salt or vinegar or both P(S ∪ V) = n(S ∪ V)/n(U) = 66/85.
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How many solutions does the system have?
x + y = 5
x + y = 6
Onone
O one
O two
O infinite
Answers
Answer:
none
Step-by-step explanation:
please mark me as brainlest
Find the nature of the graph of the function y = -9x3 + 5x2 - 2x using end behavior.
Answers
The graph goes upwards on the left side and downwards on the right side, so the correct option is the first one.
How is the end behavior of the function?
We have the function:
[tex]y = -9*x^3 + 5*x^2 -2x[/tex]
This is a cubic polynomial with a negative leading coefficient.
So, when x takes large negative values, because the leading coefficient is negative, y will take large positive values.
And when x takes large positive values, because the leading coefficient is negative, y will take large negative values.
So the nature is:
The graph goes upwards on the left side and downwards on the right side. The correct option is the first one.
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evaluate the expression below when x is 4
3x^2 +5 =
Answers
Answer:
[tex]\fbox {53}[/tex]
Step-by-step explanation:
⇒ 3x² + 5
Substitute x = 4 :
⇒ 3(4)² + 5
⇒ 3(16) + 5
⇒ 48 + 5
⇒ 53
3(4)^2+5
*note*
(4)^2= 4•4=16
3(16)+5
48+5= 53
Examine the equation.
-2(-x + 9) = 2(x - 9)
2x 18 = 2x - 18
This equation has
Infinite solutions
One solution
No solution
Answers
Answer:
No solution
Step-by-step explanation:
In order to create a system of equations that has the same solution as the system
x+y=4
2x+y = 7
complete three steps.
1
Step 1: Multiply the equation x + y = 4 by _[blank A]__.
Step 2: Add the equations 2x + y = 7 and _[blank B]_.
Step 3: Write the new system of equations as _[blank C]__.
Match each blank with the system or statement that correctly fills in that blank.
Answers
#Step1
Multiply by -2It will result -2x-2y=-8
#2
-2x-2y=-8#3
add
-y=-1y=1Find x
x+1=4x=3Work out (6 × 10²) ÷ (3 × 105)
Give your answer in standard form.
Answers
Answer: 40/21
Step-by-step explanation:
[tex]3 \times 105=315\\\\6 \times 10^{2}=600\\\\\implies \frac{6 \times 10^{2}}{3 \times 105}=\frac{600}{305}=\boxed{\frac{40}{21}}[/tex]
The frequency table shows the results asking people how many hours they spend online per week
Answers
The histogram is attached with the answer.
What is a Histogram ?It is a mathematical representation of data in a bar shaped graph , the range is user defined.
The histogram is drawn and the shape of the histogram is left skewed as the peak of the graph lies to the left of the centre.
The histogram is attached with the answer.
The complete question is
the frequency table shows the results of a survey that asked people how many hours they spend working in the yard per month. display the data in a histogram. describe the shape of the distribution
The data is attached with the answer.
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can someone please help mee (20 points and i will give brainliest!!!)
Answers
Answer:
Step-by-step explanation:
Quick
Check
Match each power of a power expression with its simplified expression.
Answers
In a family the ages of children arranged from youngest to oldest are 2,6,y,14 and z if the square of ages is in an a.p what is the ratio of z and y
Answers
Answer:
y=10
z=18
Step-by-step explanation:
2,6,y,14,z
there are 4 years different between the childrens.
2-6-10-14-18
Four students are trying to determine what number must replace the question (x^2)^?=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? In words explain why.
Answers
Joe is correct as the unknown number is 6.
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
Given :
[tex](x^2)^?=x^4\times x^8[/tex]
Let the question mark exponent outside the bracket be y, which needs to be determined
[tex](x^2)^y=x^4\times x^8[/tex]
Simplify the equation by applying exponent rules to either side of the equation:
Apply the rule [tex](a^b)^c = a^{b \times c}[/tex]
[tex](x^2)^y=x^4\times x^8[/tex]
[tex](x)^{2y}=x^4\times x^8[/tex]
Now apply [tex]a^b \times a^c = a^{b+c}[/tex]
[tex](x)^{2y}=x^{4+8}\\\\(x)^{2y}=x^{12}[/tex]
So, the base is the same the exponent will be the same also,
2y = 12
y = 6
Hence, Joe is correct as the unknown number is 6.
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HELPPPPPPPPPPPPPPPPP PLEASE
Answers
X=2
Yeah that’s all I got to say lol
Solve for the value of x:-
4x+3(x-1)=67
Answers
Answer:
x = 10
Step-by-step explanation:
4x + 3(x - 1) = 67 ← distribute parenthesis and simplify left side
4x + 3x - 3 = 67
7x - 3 = 67 ( add 3 to both sides )
7x = 70 ( divide both sides by 7 )
x = 10
Hi. . .
✦•···················•✦•···················•✦
A n s w e r : -[tex]\boxed{\fbox{\huge{x = 10}}}[/tex]
E x p l a n a t i o n :Let's solve your equation step-by-step ~
➳ Step 1: Simplify both sides of the equation.
[tex]\sf{4x \: + \: 3(x \: - \: 1) = 67}[/tex]
[tex]\sf{4x \: + \: (3)(x) \: + \: (3)(-1) = 67} \: (Distribute)[/tex]
[tex]\sf{4x \: + \: 3x \: + \: -3 = 67}[/tex]
[tex]\sf{(4x \: + \: 3x) \: + \: (-3) = 67} \: (Combine \: like \: terms)[/tex]
[tex]\sf{7x \: + \: 7 \: -3 = 67}[/tex]
[tex]\sf{7x \: - \: 3 = 67}[/tex]
➺ Step 2: Add 3 to both sides.[tex]\sf{7x \: - \: 3 \: + \: 3 = 67 \: + 3}[/tex]
[tex]\sf{7x = 70}[/tex]
➽ Step 3: Divide both sides by 7.[tex]\sf{\frac{7x}{7} = \frac{70}{7}[/tex]
[tex]\boxed{\fbox{\huge{x = 10}}}[/tex]
Hope It Helps...
Estimate
12.4 × 18
—————-
0.012
Answers
Answer: 12.4 x 18
-------------- = 18600
0.012
It takes 6 hours for 2 people to build a swing set. Can you use the proportion 2 - 6 = 5 - h to determine the number of hours h it will take 5 people to build the swing set? Explain.
Answers
The number of hours, h it will take 5 people to build the swing set is; 2.4 hours
What is the number of hours it will take 5 people to build the swing set?From the task content, it follows that it took 6 hours for 2 people to build the swing set, hence, it follows that it'd take 12 hours for 1 person to build the swing.
However, when the work is divided between 5 People, the time taken is therefore; 12/5 = 2.4hours.
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A bakery has a sale on cookies. If a customer buys a dozen cookies for $15, each additional single cookie is $0.75. What is an equation that shows how the total cost depends on the number of single cookies purchased? (Assume that the order starts with a dozen cookies.) How much would a dozen cookies plus six single cookies cost?
Answers
Answer:
T = 15 + 0.75c
T = $19.5
Step-by-step explanation:
Assume that T stands for total cost and c stands for number of single cookies purchased, the equation would be:
T = 15 + 0.75c
Therefore, a dozen cookies plus six single cookies would cost:
T = 15 + 0.75(6)
T = 15 + 4.5
T = $19.5
