Use the law of cosines to solve for the measure of the largest angle in triangle abc.
Answers
The law used for determining the measure of unknown sides and angles of a triangle. The measure of the largest angle in triangle abc is 98.25 degrees
Law of cosinesThe law used for determining the measure of unknown sides and angles of a triangle. It is expressed as:
c² = a² + b² - 2abcosC
Given the following
c = 16
a = 12
b = 9
Substitute
16² = 12² + 9² - 2(9)(12)cosC
256 = 144 + 81 - 216cosC
31 = -216cosC
cosC = -31/216
C = 98.25 degrees
Hence the measure of the largest angle in triangle abc is 98.25 degrees
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Related Questions
A class consists of 60 boys and 40 girls. If two students are chosen at random, what is the probability that i) both are boys ii) both are girls iii) one boy and one girl?
Answers
Without replacement
i) P(b and b) = 60/100 * 59/ 99 = 59/165 = 0.358
ii) P(g and g) = 40/100 * 39/99 = 0.158
iii) we can solve this question using hyper geometric distribution:
(60C1 * 40C1)/ 100C2 = 0.48
(i) Both are boys = 0.3575757576, (ii) Both are girls = 0.1575757576 and (iii) one boy and one girl = 0.48484848 are the probabilities.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A class consists of 60 boys and 40 girls.
To find the probability if two students are chosen at random:
The probability is ¹⁰⁰C₂.
(i) Both are boys,
The probability is ⁶⁰C₂ ÷ ¹⁰⁰C₂.
⁶⁰C₂ ÷ ¹⁰⁰C₂ = 60! / {2! x (60-2)!} ÷ 100! / {2! x (100-2)!}
⁶⁰C₂ ÷ ¹⁰⁰C₂ = 30 x 59 / 50 x 99
⁶⁰C₂ ÷ ¹⁰⁰C₂ =0.3575757576
(ii) Both are girls,
The probability is ⁴⁰C₂ ÷ ¹⁰⁰C₂.
⁴⁰C₂ ÷ ¹⁰⁰C₂ = 40! / {2! x (40-2)!} ÷ 100! / {2! x (100-2)!}
⁴⁰C₂ ÷ ¹⁰⁰C₂ = 20 x 39 / 50 x 99
⁴⁰C₂ ÷ ¹⁰⁰C₂ =0.1575757576
(iii) one boy and one girl,
The probability is ⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂.
⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂ =
40! / {1! x (40-1)!}x 60! / {1! x (60-1)!} ÷ 100! / {2! x (100-2)!}
⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂ = 40x60 / 50 x 99
⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂=0.48484848
Therefore, the probabilities are (i) Both are boys = 0.3575757576, (ii) Both are girls = 0.1575757576 and (iii) one boy and one girl = 0.48484848
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Is this congruent yes or no and explain why
Answers
Answer:
Yes, it is because the triangles are about the same shape.
Step-by-step explanation:
Answer: Yes, it is because the triangles are about the same shape. So I think they are congruent.
Use the low of Cosines to solve the given triangle. Round your answer to two decimal places. a = 51, b = 21, c = 68
Answers
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is given as:
a² = b² + c² - 2bc * cosA
Given that a = 51, b = 21, c = 68, hence:
51² = 21² + 68² - 2(21)(68) * cosA
A = 30.37°
21² = 51² + 68² - 2(51)(68) * cosB
B = 12.02°
68² = 21² + 51² - 2(21)(51) * cosC
C = 137.61°
Using the cosine rule, the measure of the triangles is a = 51, b = 21, c = 68, A = 30.37°, B = 12.02° and C = 137.61°
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Soon-yi’s house has a hexagonal window made up of six identical equilateral triangles as pictured below. a triangular section has a height of 14 inches and a base of 16 inches. which expression is equivalent to the area of one triangular section? one-half times 7 times 8 one-half times 14 times 16 one-sixth times 14 times 16 one-half times 7 times 7
Answers
Answer:
16*14*1/2
Step-by-step explanation:
The area of a triangle can be found in 1/2bh.
Therefore, 16 is our base, and 14 is our height.
16*14*1/2 should be your answer, from the choices that I see.
Answer:
[tex]\frac{1}{2} *14*16[/tex]
Correct Answer 100%. Pls. give me brainliest. Thank You.
4. Factor:
j) x(x+2) + y (x + 2) - 5(x + 2)
k) 5y2 - 10y3
l) ax + ay + az
5. Factor:
m) yx(y+1) + 4x(y + 1) - 5(y + 1)
n) 6p2 - 3p3
o) 4x4 + 2x
Answers
The results of factoring are presented below for each algebraic expression.
x(x-3)+y(x+2)-105y²(1-2y)a(x+y+z)y(xy +5x-5)-13p²(2-p)[tex]2x(2x^3+1)[/tex]FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: y²-y= y(y-1), where y is a common term.
You should apply the factor out a common term for solving the question.
Exercise 4 - letter jx(x+2) + y (x + 2) - 5(x + 2)
x²+2x+xy+2y-5x-10
x²-3x+xy+2y-10
x(x-3)+y(x+2)-10
Exercise 4 - letter k[tex]5y^2 - 10y^3[/tex]
5y²(1-2y)
Exercise 4 - letter lax+ay+az
a(x+y+z)
Exercise 5 - letter myx(y+1) + 4x(y + 1) - 5(y + 1)
xy²+xy+4xy+4-5y-5
xy²+5xy-1-5y
y(xy +5x-5)-1
Exercise 5 - letter n[tex]6p^2 - 3p^3[/tex]
3p²(2-p)
Exercise 5 - letter o[tex]4x^4 + 2x[/tex]
[tex]2x(2x^3+1)[/tex]
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In which two of these numbers does the digit
6 have a value of 0.6?
16.7
61.28 14.63 28.16 96.77 85.62
Answers
Answer:
Step-by-step explanation:
In this numbers:
14.63
85.62
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
To determine in which two numbers the digit 6 has a value of 0.6, we need to examine the place value of 6 in each number.
Let's go through each number:
1. 16.7: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
2. 61.28: The digit 6 is in the ones place, so its value is 6 (not 0.6).
3. 14.63: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
4. 28.16: The digit 6 is in the hundredths place, so its value is 6 * 0.01 = 0.06.
5. 96.77: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
6. 85.62: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
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You buy vegan ricotta cheese in 5 lb containers. One batch of ravioli requires 24 ounces of vegan ricotta cheese. How many batches can be made with one container
Answers
Answer:
3
Step-by-step explanation:
there are 16 ounces in a pound
so that means that 5 pounds (lbs) equals 80 ounces, you find this out by multiplying 16 and 5.
to find out how many batches are in a 5lb container then you just divide 80 and 24 which equals... 3.333333 but you just need to round it.
Find the surface area of the composite figure. 4 cm 3 cm 5 cm 3 cm 4 cm 5 cm 6 cm 4 cm If you'd like, SA = [ ? ] cm2 you can use a calculator.
Answers
The surface area of the composite figure is 144 square cm after calculating separately.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is the name given to this novel 3D object.
We have a composite figure made up of a triangular prism and a cuboid
First we calculate the surface area of the triangular prism:
= 2(area of one triangle) + area of three rectangles
= 2[(1/2)6×4] + 3×5 + 3×5
= 24 + 15 + 15
= 54 square cm
Surface area of rectangle(with three faces) = 2(4×3 + 4×6) + 3×6
= 2(12 + 24) + 18
= 72 + 18 = 90 square cm
Total surface area of figure = 54+ 90 = 144 square cm
Thus, the surface area of the composite figure is 144 square cm after calculating separately.
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Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. How much fabric will he need?
A square pyramid with a base of 4 meters by 4 meters and triangular side heights of 3 meters.
Answers
The area of a 2D form is the amount of space within its perimeter. The total surface area of the square pyramid is 40 meters².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. Therefore, the amount of fabric that Henri will need is equal to the total surface area of the square pyramid.
Total surface area = Area of the base + 4(Area of the triangle)
= (4m × 4m) + 4(0.5×4m×3m)
= 16 meters² + 24 meters²
= 40 meters²
Hence, the total surface area of the square pyramid is 40 meters².
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Which of the following functions best models the data represented by the scatterplot shown below?
A: y=160x-100
B: y=2^x+12
C: y=8x^2+10
D: y=25x+20
Answers
Answer:
C: y = 8x^2 + 10.
Step-by-step explanation:
It looks close to being a parabola so I think it is probably a function in x^2.
Try 8x^2 + 10
Checking against the plot
When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200
Calculating y for other values:
When x = 7, y = 8(7)^2 + 10 = 402, and on graph y = 400.
When x = 11, y = 978 , and on graph = 1000.
When x = 17, y = 2322, and on graph y = about 2350.
lmk if u can figured it out
Answers
Answer:
see explanation
Step-by-step explanation:
since the triangles are congruent , then corresponding sides and angles are congruent.
(1)
Δ HIJ ≅ Δ LMN
sides angles
--------- -----------
HI ≅ LM ∠ H ≅ ∠ L
HJ ≅ LN ∠ I ≅ ∠ M
IJ ≅ MN ∠ J ≅ ∠ N
(2)
Δ XYZ ≅ Δ JKL
sides angles
-------- ------------
XY ≅ JK ∠ X ≅ ∠ J
XZ ≅ JL ∠ Y ≅ ∠ K
YZ ≅ KL ∠ Z ≅ ∠ L
Answer:
1. ΔHIJ ≅ ΔLMN
sides: HI ≅ LM, IJ ≅ MN, HJ ≅ LN.angles: ∠H ≅ ∠L, ∠I ≅∠M, ∠J ≅∠N.2. ΔXYZ ≅ ΔJKL
sides: XY ≅ JK, YZ ≅ KL, XZ ≅ JL.angles: ∠X ≅ ∠J, ∠Y ≅∠K, ∠Z ≅∠L.Step-by-step explanation:
I believe it's asking to list the corresponding sides and pairs of angles in the congruent triangles.
Look at the order of the letters HIJ and LMN. There are 3 letters, which represent 3 sides and 3 angles. The first, second, and third letters of the first triangle correspond to the first, second, and third letters of the second triangle.
1. ΔHIJ ≅ ΔLMN
sides: HI ≅ LM, IJ ≅ MN, HJ ≅ LN.angles: ∠H ≅ ∠L, ∠I ≅∠M, ∠J ≅∠N. (these can also be written as ∠HIJ ≅ ∠LMN, ∠HJI ≅ ∠LNM, ∠IHJ ≅ ∠MLN... but it depends on what the instructor wants really).2. ΔXYZ ≅ ΔJKL
sides: XY ≅ JK, YZ ≅ KL, XZ ≅ JL.angles: ∠X ≅ ∠J, ∠Y ≅∠K, ∠Z ≅∠L.If the slope of the line that goes through the points (2, 7) and (5, a) is -3, what is the value of a?
Answers
Answer:
a = -2
Step-by-step explanation:
I graphed the given point (2,7) and then I used that point and plugged the point and the slope into the point-slope formula, which is (y-y₁)=m(x-x₁). Then, I just looked for where x=5 on the line and it was -2
Jenny wants to start an after-school club, so she decides to survey the student body to determine which club would be the most popular: French Club, Architecture Club, or Anime Club. She decides (with Mrs. Howell's permission) to survey the first 25 students who show up to her class one day.
Does her survey comprise an accurate representation of the Reach student body? Why or why not?
Answers
Answer:
no because it just reaches one class, not the student body
Step-by-step explanation:
If f(x) = 2(3x) + 1, what is the value of f(2)
Answers
Answer:
x=−2 in the formula for F(x) . Therefore, F(−2)=3(−2)2+1=3(4)+1=13 .
HELP ME PLEASE ON MATHEMATICS!!
Answers
Answer:
1)526 kw
2)1943 m³
3) 33
4) 43 m³
5) 5010 kw
Step-by-step explanation:
1) 7675-7149= 526
2) 462+ 1481= 1943
3) 168-135 = 33
4) 1499 -l456= 43
5) 4945+65= 5010
Yesterday a car rental agency rented 4 vehicles, of which 2 were pickup trucks. what is the experimental probability that the first vehicle rented today will be a pickup truck?
Answers
Using it's concept, it is found that the experimental probability that the first vehicle rented today will be a pickup truck is of 0.5 = 50%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, we have that out of 4 vehicles, 2 are pickup trucks, hence the experimental probability is given by:
p = 2/4 = 1/2 = 0.5.
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a parallelogram has an area of 153
cm and height of 17 cm what is the length of the base
Answers
Answer:
9 cm
Step-by-step explanation:
Formula :
Area (parallelogram) = Base × Height
=========================================================
Given :
⇒ Area = 153 cm²
⇒ Height = 17 cm
===========================================================
Solving :
⇒ 153 cm² = 17 cm × Base
⇒ Base = 153/17
⇒ Base = 9 cm
Answer:
Base = 9 cm
Step-by-step explanation:
Given dimensions:
Area of the parallelogram: 153 cm^2 ( It should be cm^2 not cm )Height of the parallelogram: 17 cmTo Find:
The baseSolution:
This question is a bit tricky.Usually,the height and the base are given. We'll use the formula of area of parallelogram , then substitute/plug the values of height and area of parallelogram, with the exception of base as it's not given.
So recall the formulae of area of parallelogram:
[tex] \rm \: Area_{(Parallelogram)} = b \cdot{h}[/tex]
Here,b = baseh = heightPlug/substitute the values of area of parallelogram & height:
[tex]\rm \: 153 \: cm ^2 =b \cdot17 \: cm[/tex]
We created an equation.Solve it now.
Transpose 17 cm to the LHS:[tex] \implies \rm \cfrac{153 \: cm^2}{17 cm} = base[/tex]
Cancel 153/17 by 17:[tex] \implies \rm9 \; cm = \: base[/tex]
[tex] \implies \rm \: Base = 9\; cm[/tex]
Yes! We're done!
Hence,the base is 9 cm of the parallelogram.
[tex] \rule{225pt}{2pt}[/tex]
If the grain pile has a diameter of 30 feet and a height of 16 feet, what is the volume of the grain pile? In terms of TT.
Answers
Answer: 75TT
(When you answer in terms of pi, don’t multiply pi but leave it in your answer)
Step-by-step explanation:
assuming the grain pile is a pyramid, V=1/3 TT r^2
(1/3) (TT) (15^2). Remember radius is 1/2 of diameter
(1/3) (225) TT
Answer 75TT
You sold a combined total of 25 of item A and item B. You made $88.
Item A: 3$
Item B: 4$
How much of each item did you sell?
Answers
Answer:
x = 25 - y = 2
Step-by-step explanation:
Let x represent the number of item A that you sold.
Let y represent the number of item B that you sold.
The total number of item A and item B sold is 25. This means that
x + y = 25
The cost of item A is $3, the cost of item B is $4 and if the total amount of money made is $88, this implies
3(x) + 4(y) = 88 (Substitute x = 25 - y)
→ 3(13 - y) + 4y = 88
→ 39 - 3y + 4y = 88
→ 39 + y = 16
→ y = 23
If y = 23, then x = 25 - y = 2
23.21
Which equation represents the relationship between the number of liters, x, and the number of liquid pints, y?
O y = x + 5.55
Oy=x-5.55
O y = 2.11x
O Y - 211
Answers
The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
How to determine the equation?The attached table of values represents the missing piece in the question.
Start by calculating the rate of change using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (14.77 - 10.55)/(7- 5)
Evaluate
m = 2.11
The equation is then calculated using:
y = m(x - x1) + y1
This gives
y = 2.11(x - 5) + 10.55
Evaluate
y = 2.11x - 10.55 + 10.55
y = 2.11x
Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
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A scientist has two solutions, which she has labeled solution a and solution b. each contains salt. she knows that solution a is 65% salt and solution b is 90% salt. she wants to obtain 110 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
Answers
Answer:
All
Step-by-step explanation:
I done this question before
Select the correct answer. you have 7 balls that are each a different color of the rainbow. in how many distinct ways can these balls be ordered? a. 1 b. 7 c. 49 d. 343 e. 5,040
Answers
Because the factorial of 7 is 5040
7(6)(5)(4)(3)(2)(1)
Factorial is to calculate combinations which in this case is finding different ways they can be ordered in.
Answer:
E. 5,040
Step-by-step explanation:
For plato users
any help is great find the missing length?
Answers
Answer:
3Step-by-step explanation:
Similar = proportional
solve with an equation
12 : 9 = 4 : x
x = 4 * 9 : 12
x = 3
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. which constraint could be part of the scenario? the pool is 1 meter deep. the pool is 2 meters deep. the toy falls at a rate of at least a negative one-half meter per second. the toy sinks at a rate of no more than a negative one-half meter per second.
Answers
The answer choices which could be a constraint to the scenario are;
the pool is 1 meter deep.the pool is 2 meter deep.Which constraint could be part of the scenario?It follows from the task content that the scenario is modelled by means of a system of inequalities. However, only the variables in the model can be constrained and hence, only time and depth factors could be part of the constraints.
On this note, the constraints area as indicated above.
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Answer:
A
Step-by-step explanation:
A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?
The pool is 1 meter deep.
The pool is 2 meters deep.
The toy falls at a rate of at least a Negative one-half meter per second.
The toy sinks at a rate of no more than a Negative one-half meter per second.
The graph of a linear function is given below.
f(x)
-8
8
What is the zero of the function?
OA. -3
OB. -
OC.
-
-2
6
6 +
2
2
6
N
a
00
X
Answers
The zero of the linear function is -2
How to determine the zero of the function?This is the point where the line of the equation crosses the x-axis
From the attached figure, the line cross the graph at:
x = -2
Hence, the zero of the function is -2
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Over what interval is the function in this graph constant?
OA. -3≤x≤2
B. -4sxs-2
OC. -2≤x≤3
OD. -5≤x≤5
Answers
A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The interval of the function for which the given graph is constant is when the value of x is less than -2 and when the value is greater than -4. Therefore, we can write this interval as -4< x < -2.
Hence, the correct option is B.
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Measure of the following
Answers
Answer: [tex]35^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle BIG=90^{\circ}[/tex] since the lines are perpendicular, meaning that [tex]m\angle HIG=90-30-25=\boxed{35^{\circ}}[/tex]
Find f¹(x) for the function
f(x) = -4.
2
f¹(x) = [?]x + [ ]
Answers
Answer:
[tex] {f}^{ - 1}(x) = 2x + 8[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{x}{2} - 4 \\ \\ y = \frac{x}{2} - 4 \\ \\ y = \frac{x - 8}{2} \\ \\ x = 2y + 8 \\ \\ {f}^{ - 1} (x) = 2x + 8[/tex]
Ali is about 2,760,000 minutes old. Write this age as a number multiplied by a power of 10. Use ^ to represent an exponent (power)
Answers
Answer:
27600x10^10
Step-by-step explanation:
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Show all steps.
!BRAINLIEST AND 5 STARS TO BEST ANSWER AND FULL
EXPLANATION ONLY!
Answers
The coordinate of point P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 is [tex](-\frac{22}3, \frac{23}6)[/tex]
How to determine the coordinates of P?The given parameters are:
A = (-9,3)
B = (1, 8)
m : n = 1 : 5
The coordinate of point P is then calculated using:
[tex]P = \frac{1}{m + n} (mx_2+nx_1,my_2+ny_1)[/tex]
Substitute known values
[tex]P = \frac{1}{1 + 5} (1 * 1 + 5 * -9, 1 * 8 + 5 * 3)[/tex]
Evaluate
[tex]P = \frac{1}{6} (-44, 23)[/tex]
Evaluate the product
[tex]P = (-\frac{22}3, \frac{23}6)[/tex]
Hence, the coordinate of point P is [tex](-\frac{22}3, \frac{23}6)[/tex]
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