Given:
The measure of three sides of a triangle are 8, 7 and 14.
To find:
The measure of the angle opposite the side of length 8.
Solution:
According to the Law of Cosine:
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
Let a=8, b=7 and c=14, then by using Law of Cosine, we get
[tex]\cos A=\dfrac{7^2+14^2-8^2}{2(7)(14)}[/tex]
[tex]\cos A=\dfrac{49+196-64}{196}[/tex]
[tex]\cos A=\dfrac{181}{196}[/tex]
Taking cos inverse on both sides.
[tex]A=\cos^{-1}\dfrac{181}{196}[/tex]
[tex]A=22.561328[/tex]
[tex]A\approx 22.6[/tex]
Therefore, the measure of the angle opposite the side of length 8 is 22.6 degrees.
The answer is A
You’re welcome
Answer:
so you answered your own question?
solve the triangle a=? b=7m c=10m
Answer:
[tex]\sqrt{149}[/tex]
Step-by-step explanation:
The third side of a triangle can be any value in the range of -
1 ≤ a < 17.
What is a triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique planeGiven are two sides of a triangle as b = 7m and c = 10m.
The sum of two sides of a triangle is always greater than the third side. Mathematically -
a < {b + c}
a < {7 + 10}
a < 17
a ∈ [1, 16]
Therefore, the third side of a triangle can be any value in the range of -
1 ≤ a < 17.
To solve more questions on triangles, visit the link below -
https://brainly.com/question/12538366
#SPJ2
The vertex of a parabola is (-1, -8) and the zeros are (-5, 3) Determine the equation of the parabola in standard and factored form
Answer:
Part A
The equation of the parabola in standard form is f(x) = 0.5·x² + x - 7.5
Part B
The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)
Step-by-step explanation:
The coordinates of the vertex of the parabola, (h, k) = (-1, -8)
The zeros of the parabola = -5, 3
Part A
The quadratic equation representing the parabola can be written as follows;
y = a·(x - h)² + k
The standard form of the equation is f(x) = a·x² + b·x + c
k = c - b²/(4·a)
h = -b/(2·a)
c = k + a·h² = -8 + a
From the zeros of the parabola, we have;
f(-5) = a × (-5)² + b×(-5) + c = 25·a - 5·b + c = 0
f(3) = a × (3)² + b×(3) + c = 9·a + 3·b + c = 0
Therefore, we have;
25·a - 5·b + c = 0...(1)
9·a + 3·b + c = 0...(2)
From which we have;
25·a - 5·b + c = 25·a - 5·b - 8 + a = 26·a - 5·b - 8 = 0
9·a + 3·b + c = 9·a + 3·b - 8 + a = 10·a + 3·b - 8 = 0
We then have;
26·a - 5·b = 8...(3)
10·a + 3·b = 8...(4)
Making 'b', the subject of both equations (3) and (4), equating the values, we find the value of 'a' as follows;
From equation (3), we have;
26·a - 5·b = 8
∴ b = (26·a - 8)/5
From equation (4), we have;
10·a + 3·b = 8
∴ b = (8 - 10·a)/3
From b = b, by transitive property, we have;
(26·a - 8)/5 = (8 - 10·a)/3
3 × (26·a - 8) = 5 × (8 - 10·a)
78·a - 24 = 40 - 50·a
∴ 128·a = 64
a = 64/128 = 1/2 = 0.5
a = 0.5
∴ b = (26·a - 8)/5 = (26 × 0.5 - 8)/5 = (13 - 8)/5 = 1
b = 1
c = -8 + a
∴ c = -8 + 0.5 = -7.5
c = -7.5
The equation of the parabola in standard form is therefore presented as follows;
f(x) = 0.5·x² + x - 7.5
Part B
The equation of the parabola in factored form is given as follows;
With the aid of a graphing calculator, we have;
f(x) = 0.5·x² + x - 7.5 = 0.5×(x² + 2·x - 15) = 0.5·(x + 5)·(x - 3)
The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)
I NEED HELP PLEASE Which is the better buy?
14 rolls of paper towels for $18
or
10 rolls of paper towels for $12
what is the unit rate for the 14 roll option
Answer: The second one, 10 rolls for $12. 1.29 (Rounded)
Step-by-step explanation:
14/18 is 1.29 (Rounded)
10/12 is 1.20.
The unit rate is cheaper, therefore making it the better buy
Camden is going to invest $600 and leave it in an account for 12 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Camden to end up with $920?
Answer:
320 i think lol
Step-by-step explanation:
Answer:
3.56
Step-by-step explanation:
Find the SLOPE between (-8,9) and (-4,12) Write answer as a SIMPLIFIED FRACTION.
What is the measure of the missing angles?
Answer:
[tex]x = 64 + 45 \\ x = 109[/tex]
Write the inequality to represent the graph.
Answer:
x > -1
Step-by-step explanation:
Open circle so the sign is not inclusive. The point is at -1 and goes to the right so it is more than.
In order to become a member of the library all star members club there is a $40 signup fee and a $2 monthly fee
Answer:
do you need an equation? if so it would be 2x+40
Step-by-step explanation:
I need help right now I’m in my class plz help
Answer:
1/3x + 1/2
Step-by-step explanation:
combine like terms 1/3x plus 2/3x equals 3/3x - 2/3x = 1/3x
and 3/4-1/4 = 2/4.
Answer:
1/3x+1/2
Step-by-step explanation:
1/3x+2/3x-2/3x+3/4-1/4 eliminated +2/3x-2/3x
1/3x+3/4-1/4
1/3x+2/4 simplify 2/4 to 1/2
1/3x+1/2
T m = the number of minutes it will take Beck to finish his homework. Choose the equation that can be used to find the solution to the problem
Answer:
[tex]0.3 m = 12[/tex]
Step-by-step explanation:
See comment for complete question
Given
30% in 12 minutes
Required
Time to complete the homework
From the question: m represents the required minutes
This implies that:
[tex]30\% * m = 12[/tex]
Convert to decimal
[tex]0.30 * m = 12[/tex]
[tex]0.3 m = 12[/tex]
Hence:
The equation is: [tex]0.3 m = 12[/tex]
Please help me!!!!!!
Answer: 72.5
Step-by-step explanation:
The average of 2 points is the midpoint so if I add 70 and 75 to get 145 and divide by the number of numbers which is 2 I get 72.5
Pls helppp due soon!!
Answer:
I think the answer is B
Step-by-step explanation:
Sorry if it's wrong
Answer: i think its b
Step-by-step explanation:
I NEED THIS ANSWERED QUICKKKK
Answer:
2/4=4/8
Step-by-step explanation:
you do 2×2=4 and 4×2=8. You multiply both denominators by 2.
I need help with part b and c pretty p please show your work so I can do this
43 lbs of bananas cost $86. How many
lbs of bananas can you get with $100 ?
will get brainliest
Answer:
$200
Step-by-step explanation:
Hey There!
So first we want to find the price of each pound of banana
To do this we divide the cost by amount of bananas bought
86/43=2
so each pound of bananas cost $2
now we just multiply 2 and 100
2x100=200
so 100 pounds of bananas would cost $200
hope this helps :)
Answer:
50
Step-by-step explanation:
Calculate how much 1lbs of bananas cost by dividing 86 by 43. getting you 2. That means each lbs of bananas is $2. Then divide $100 by $2 getting you 50 because you have $100. So you can get 50lbs of bananas with $100.
Richie is solving the equation x^2 – 12x = 28 by completing the square. What number should he add to
both sides of the equation to complete the square? Pleaseee Help
Answer:
Richie should add the number 36 to both sides.
Step-by-step explanation:
To complete the square, you need to divide b by 2, square it, then add it to both sides. In this case, you'd do this:
12/2=6
6^2=36
(m - 8) ÷ 2 in standard form (no links)
Answer:
1/2m - 4
Step-by-step explanation:
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 andthe chicken wrap costs $3.10. Today they made $268.30 from the 136 wraps sold. How many of the wraps
sold were vegetarian?
a. 57 wraps
c. 63 wraps
d. 75 wraps
b. 73 wraps
Answer:
I think it is 73
Step-by-step explanation:
Because i tryed all of the other numbers and they didnt work
HOPE THIS HELP !!!!!!!!!!!!!!!! :)
The slope is -8. The point
(3, 12) lies on the line. What is the equation for each linear
Help! Check if my answer is right please, I’m marking brainliest!!!
A. 46.1
B. 50.1 - (my answer)
C. 76
D. 54.2
Show work, if possible. Thanks❤️
Answer:
its B
Step-by-step explanation:
54-1/7 y i = 9x -4 help
Let's solve for i.
54−(
1
7
y)(i)=9x−4
Step 1: Add -54 to both sides.
−1
7
iy+54+−54=9x−4+−54
−1
7
iy=9x−58
Step 2: Divide both sides by (-y)/7.
−1
7
iy−y7=
9x−58−y7i=
−63x+405y
Answer:i=
−63x+406y
PLEASE HELP ITS DUE BY 11!! I NEED ALL QUESTIONS SOLVED AND I WILL MARK BRAINLIEST
Answer:
∠A = 60°
∠B = 42°
∠C = 78°
Step-by-step explanation:
∵ In a triangle, sum of all the three interior angles is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ (4x)° + (3x - 3)° + (5x + 3)° = 180°
∴ (4x + 3x - 3 + 5x + 3)° = 180°
∴ (12x)° = 180°
∴ 12x = 180
∴ x = 180/12
∴ x = 15
∠A = (4x)° = (4× 15)° = 60°
∠B = (3x-3)° = (3× 15-3)° =(45-3)°= 42°
∠C = (5x+3)° = (5× 15 + 3)° =(75 + 3)°= 78°
find the lateral surface area of the figure below
Answer:
242
First is 9 times 10 which is 90, then 4 times 8 is 32 divided by 2 which is 16 times 2 since there are two, 32 again. 8 times 10 is 80. 4 times 10 is 40.
90 + 32 + 80 + 40 = 242
Step-by-step explanation:
Select the correct answer.
A machining company needs to manufacture more than 20 fixtures in a day. The company uses five identical machines to make the fixtures. If each machine produces x fixtures, which inequality represents this situation?
A.
5x > 20
B.
5x < 20
C.
5x > 20 + 5
D.
5x < 20 + 5
Answer:
I thinks its D.
Step-by-step explanation:
Select the expression that has a value of 23.
6 + (9 x 3) ÷ 3 + 8
(6 + 9) + 3 ÷ 3 + 8
6 + 9 x 3 ÷ (3 + 8)
(6 x 9 x 3) ÷ 3 + 8
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Pleaseee needing helppp
Answer:
You were correct.
Step-by-step explanation:
If the input to the function y = 4x - 3 is 2 Then
y = 4 * 2 - 3
= 8 - 3
= 5
Hope it helps :)
y = -3x + 4
y = 3x - 2
graph
Answer:
Look at the graph bellow
Step-by-step explanation:
use the slope and y-intercept to graph.
Which of the following graphs represents the equation
2x + y = 12?
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation: