Answer:
A. The length of the third side is approximately 5 feet.
B. A = [tex]88^{o}[/tex], B = [tex]60^{o}[/tex] and C = [tex]32^{o}[/tex].
Step-by-step explanation:
Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.
A. Let side a = 6 feet and c = 3 feet, thus;
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] - 2ac Cos B
= [tex]6^{2}[/tex] + [tex]3^{2}[/tex] - 2(6 x 3) Cos [tex]60^{o}[/tex]
= 36 + 9 - 36 x 0.5
= 45 - 18
[tex]b^{2}[/tex] = 27
b = [tex]\sqrt{27}[/tex]
= 5.1962
b = 5.2 feet
b ≅ 5 feet
The length of the third side is approximately 5 feet.
B. Given that B = [tex]60^{o}[/tex], then let us apply the Sine rule to determined the measure of A.
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]
So that,
[tex]\frac{6}{Sin A}[/tex] = [tex]\frac{5.2}{Sin60^{o} }[/tex]
Sin A = [tex]\frac{0.886*6}{5.2}[/tex]
Sin A = 0.99923
A = [tex]Sin^{-1}[/tex] 0.99923
= 87.75
A ≅ [tex]88^{o}[/tex]
Since the sum of angle in a triangle = [tex]180^{o}[/tex].
Then,
A + B + C = [tex]180^{o}[/tex]
[tex]88^{o}[/tex] + [tex]60^{o}[/tex] + C = [tex]180^{o}[/tex]
[tex]148^{o}[/tex] + C = [tex]180^{o}[/tex]
C = [tex]180^{o}[/tex] - [tex]148^{o}[/tex]
= [tex]32^{o}[/tex]
C = [tex]32^{o}[/tex]
Thus,
A = [tex]88^{o}[/tex], B = [tex]60^{o}[/tex] and C = [tex]32^{o}[/tex].
The value of a new car decreases by about 15% in the first year. How much will a car be worth after one year if its initial value was $1,500? If you get stuck, consider using diagrams or a table to organize your work.
Answer:
$12,750
Step-by-step explanation: when you do the math you get it your welcome my G
what is the answer to 2.6=-0.2t
Answer:
-13
Step-by-step explanation:
Answer:
t = -13
Step-by-step explanation:
2.6 = -0.2t Equation
2.6 / -0.2 . = -0.2t/-0.2 Divide -0.2 on both sides
t = - 13 Simplify
Danielle is making a quilt with triangles and squares. There are 4 colored triangles inside each square. The base and height of each triangle is x + 4 inches as shown. Which polynomial represents the area of the colored triangles in square inches?
Answer:
[tex](2x^2+16x+32)\ \text{sq. inches}[/tex]
Step-by-step explanation:
b = h = Base = Height of triangle = [tex](x+4)\ \text{inches}[/tex]
Area of one triangle
[tex]A=\dfrac{1}{2}bh=\dfrac{1}{2}(x+4)(x+4)[/tex]
There are 4 colored triangles so total area of the triangles is
[tex]4A=4\times \dfrac{1}{2}(x+4)(x+4)\\\Rightarrow 4A=2(x+4)^2\\\Rightarrow 4A=2(x^2+8x+16)\\\Rightarrow 4A=2x^2+16x+32[/tex]
The area of the colored triangles is [tex](2x^2+16x+32)\ \text{sq. inches}[/tex]
4x-y= -2
2х + Зу = 13
Answer:
x = 1/2
y = 4
Step-by-step explanation:
4x - y = -2 --------------------(I)
2x + 3y = 13 --------------------(II)
Multiply equation (I) by 3 and then add
(I)*3 12x - 3y = -6
(II) 2x + 3y = 13 {Now add and so y will be eliminated}
14x = 7
x = 7/14
x = 1/2
Plugin x = 1/2 in equation (I)
[tex]4*\frac{1}{2}-y = -2[/tex]
2 - y = -2
-y = -2 - 2
-y = -4
y = 4
Answer:
x=1/2
y=4
Step-by-step explanation:
4x-y=-2
-y=-4x-2
y=4x+2
2x+3y=13
2x+3(4x+2)=13
2x+12x+6=13
14x=7
x=1/2
y=4x+2
y=4(1/2)+2
y=2+2
Y=4
Solve and Graph: 12 – ⅔ x > 6
Answer:
There's the graph
But the answer is x<9
X is all values below 9.
After adding a tip, the total lunch cost was $32.24. What percentage tip did they give? Enter your answer to the nearest percentage. the original cost was 27.32
Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop. How did you determine the pair(s) (x, y) that Leah could work to meet the given conditions in item 15?
Answer:
Babysitting= 13.3 hours
Icecream shop= 6.6 hours
Step-by-step explanation:
Step one:
let the hours for babysitting be x
and the hours for icecream shop be y
we are told that Leah would like to earn $120 monthly
She babysits for $5 per hour and
works at an ice cream shop for $8 per hour
5x+8y=120---------------1
Leah cannot work more than a total of 20 hours per month
x+y≤20-------------2
The system of equation for the situation is
5x+8y=120
x+y≤20
x=20-y
put x=20-y in eqn 1
5(20-y)+8y=120
100-5y+8y=120
3y=120-100
3y=20
y=20/3
y=6.6 hours
put y=6.6 in eqn 2
x+6.6≤20
x≤20-6.6
x=13.3hours
What is the solution to the system graphed below?
Answer:
I'm pretty sure it is (2,0)
please help it's the SLOPE
Answer:
3/2
Step-by-step explanation:
do rise over run
rise is 3
run is 2
3/2
hope this helps <3
Answer:
slope is 1.5
Step-by-step explanation:
slope=rise over run
3/2=1.5
look at point
(1,-3) then go up 3 and right 2
lands in point
(3,0)
Carrie read a total of 18 books over 6 months. If Carrie has read 30 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
? months
Answer:
10 months
Step-by-step explanation:
If we divide 18 and 6, you would get 3. This means that Carrie reads 3 books per month and we can divide 30 and 3 to figure out how many months that she read which is 10.
PLEASE HELP ME HURRY
2/5 of the class is male
40% of the class is male
3/5 of the class is female
60% of the class is female
Not sure if this is right, but this is what I got.
A point on the ocean floor is 5,962 m below sea level. Express this elevation as an integer.
the elevation as an integer is ___ m.
Answer:
-5,962 m
Step-by-step explanation:
Since the point is below sea level, it will be a negative number as an integer.
it is 5,962 m below sea level, so as an integer, it will be -5,962 m.
So, the elevation as an integer is -5,962 m
A recipe requires 1/3 cup of milk for each 1/4 ounce of sugar. How many ounces of sugar are needed for each cup of milk? Answer quickly please!
Answer: 3/4 ounces of sugar for one cup.
Step-by-step explanation: Since we know that we have 1/3 cup, we can simply times the 1/4 by 3. If it helps, just imagine pouring 1/4 ounce of sugar three times.
Hope this helps :)
please show work
23 lbs of onions cist $250.70. How much will 50 lbs cost
Answer:
$545.00
Step-by-step explanation:
250.7 / 23 = 10.9
$10.9 is the cost of every lb of onions.
Then we multiply 10.9 by 50 because there are 50 lbs. like this
10.9 * 50 = 545
So $545.00 is our answer.
The graph shows the cost of buying tickets to a concert.
What is the cost of buying 10 tickets?
I need help pleaseee
Solve for x. assume that lines which appear to be diameters are actual diameters.
Answer:
x=10
Step-by-step explanation:
5x+17 = 67
The angles are vertical angles which means they are equal. This means the arc lengths are equal
5x+17-17 = 67-17
5x = 50
5x/5 = 50/5
x =10
Can someone do this please
What’s the equation?
please answer this. thank you
can anyone help with this question
Step-by-step explanation:
GCF of 2 prime numbers is always 1, because prime number only have two factors, themselves and 1.
LCM of 2 prime numbers will be simply multiplying them together.
Sasha can do that by; finding the HCM of two factors.
Razi will tell Jake to find the LCM you have to find the least common factor of the numbers,and then that's your answer.
Explanation:Hope this helps:)!
there are 50 kilometers in 31 miles. which representation does NOT show the same relationship?
Answer:
There's no options
Step-by-step explanation:
Answer:
Options please
Step-by-step explanation:
CAN YOU HELP ME???
Laura borrowed $105,000 at a rate of 6% simple interest for 12 years. How much interest will Laura pay?
Group of answer choices
$75,600
$37,800
$180,600
$256,200
Answer:
Laura will pay an interest of $75,600.
Step-by-step explanation:
Our formula: A = P(1 + rt)
Principal = $105,000
Rate = 6%
Time = 12 years
A (amount)= 105,000(1 + (0.06 × 12)) = 180,600
$180,600 - $105,000 = $75,600.
HELP PLEASE!!!! I need someone to help me!!!!
Answer:
A
Step-by-step explanation:
Answer:
It's C or the one u just clicked on
Step-by-step explanation:
I went to get dinner at a restaurant. The bill for the meal was $60. I want to
leave a 20% tip. What will be my total cost including the tip? *
Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d=−6.
Answer:
a(45) =-209
Step-by-step explanation:
a(n) = a +(n-1)d
d=-6
we have to get a1
By using:
a(10) = a1 +(10-1)-6=1
a(10) = a1 +(9)-6 =1
a1 =1+54=55
So:a(45) = 55 +(45-1)-6=-209
hope this helps
pls help me fast like asap
Answer:
Im pretty sure its D
Step-by-step explanation:
HELP MEEE PLEASEEEEE!!!!! I NEED HELPPP!!
Which the ordered pair that is a solution of the system for linear equations?
Answer:
(2,2)
Step-by-step explanation:
Lets check:
(2,2)
2(2)-2=2 Correct !
2=-2+4 correct !
Hope this helps plz hit the crown :D
Answer:
i believe the answers (2,2)
Step-by-step explanation:
if you add it in for y and x you will see it right
**FIRST CORRECT ANSWER GETS BRAINLEST**
y varies directly as x, and y = 0.5 when x = 0.4.
A.) y = 4/5 x
B.) y = 0.1 x
C.) y = 5/4 x
D.) y = 0.9 x
Answer:
C.) y = 5/4 x
Step-by-step explanation:
5/4 multiplied by 0.4 is 0.5
Let x=
-
11
8
and y=
11
4
0
Which expression has a negative value?
Copyright 2017 Open Up Resources
Select one
OA. x+y
OB. xy
OC. x.y
OD. x/y
Answer:
OD. x/y
Step-by-step explanation: