Answer:
63.6mm
Step-by-step explanation:
According to cosine rule;
AB² = BC²+AC²-2(BC)(AC)cos m<C
Substitute the given values
AB² = 70²+40²-2(70)(40)cos 64
AB² = 4900+1600-5600cos64
AB² = 6500-5600(0.4384)
AB² = 6500-2,454.87
AB² = 4,045.12
AB = √4,045.12
AB = 63.6mm
Hence the length of AB is 63.6mm
There are 6 animals in the pen some are quails and some are goats if there are 20 legs in all how many quails and how many goats are there?
Answer:
4 goats
Step-by-step explanation:
Let us represent
Number of quails = x
Number of goats = y
Quails have 2 legs
Goats have 4 legs
Hence:
There are 6 animals in the pen some are quails and some are goats
x + y = 6...... Equation 1
x = 6 - y
if there are 20 legs in all how many quails
2x + 4y = 20..... Equation 2
We substitute 6 - y for x in Equation 2
2(6 - y) + 4y = 20
12 - 2y + 4y = 20
Collect like terms
- 2y + 4y = 20 - 12
2y = 8
y = 8/2
y = 4 goats
The number of goats there are 4 goats
What is p / r equal to?
Using our trig functions, we know that tan x = opposite side of a right triangle divided by the adjacent side of the right triangle.
So, tan x = p/r.
Answer: tan x°
The trigonometric function gives the ratio of different sides of a right-angle triangle. The ratio of p and r can be written as tan(x°) and sec(y°).
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
As per the given figure, the ratio of the p\r can be written as shown below,
In terms of angle x,
tan(x°) = p units / r units
tan(x°) = p/r
In terms of angle y,
tan(y°) = r / p
1 / tan(y°) = r/p
sec(y°) = r/p
Hence, the ratio of p and r can be written as tan(x°) and sec(y°).
Learn more about Trigonometric functions:
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Plsssssss help plsss plssss plsss
Answer:
7/24
Step-by-step explanation:
in order to get the fraction, you need to add all of the books read together; you should get 120.
Then add all of the books read in even classes(2nd grade and 4th grade) and you should get 35.
Then place 35 on top of 120 to form the fraction: 35/120.
Then simplify the fraction by finding the greatest common factor, which is 5, and divide 35 and 120 by 5 to get 7 and 24.
Find the percent of change. Round your answer to the nearest tent necessary, Please explain.
Original price: $185
New price: $160
Original number of students: 56
New number of students: 77
Answer:
No answer just clues
Step-by-step explanation:
x/100*160/1=185/1
y/100*56/1=77/1
I just can't do anymore metal math today, sorry.
It had the same slope as y = 3 and passes through (1,5).
Answer:
y=5
Step-by-step explanation:
It has same slope of y=3, which means it is also a horizontal line. A horizontal slope will only have one y value. So, if we use the point (1, 5), we can say that the equation is y=5.
Given the following expression, what is the rate of decay (write in decimal form, not as a percentage)? 15000 (.87)^7
Answer:
0.87
Step-by-step explanation:
y = ab^x
b is the rate of decay if it is between 0 and 1. Here, b = 0.87.
Answer: 0.87
How far from zero is 5.5?
Answer: 5.5
When you subtract 5.5 from 5.5 you get 0
You have a cup containing 4 green skittles, 5 red skittles, 7 yellow skittles, and 10 purple skittles. What is the probability of not pulling a purple skittle?
Answer:
about 62%
Step-by-step explanation:
add all of the numbers
subtract the number of purple skittles
do 16÷26
multiply your answer by 100
get 61.5
round up
Carter, Michelle, and Jen work at a coffee shop. All three of them worked 6 hours on Monday. Michelle and Jen worked 7 hours on Tuesday. On Wednesday, Carter worked 5 hours. On Thursday, Carter and Michelle worked 4 hours, and Jen worked 8 hours. Use a matrix to organize the number of hours all three employees worked Monday through Thursday.
please help, i will give brainliest!! <3
Sorry i dont know what a matrix is but the answer to all 3 of the workers time is, 66
$7,000 is invested in an account that earns 1.5% annual interest, compounded quarterly. What is the value of the account after 18 years?
Answer:
$9,151.38
Hopefully that is correct!!
Help with pic please as siin as possibke SIMPLIFY....
Answer:
[tex]2x^3y^3[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{2x^5y^7} * \sqrt[3]{4x^4y^2} \\\\2x^3y^3[/tex]
Part B
What is the density of the plne log? Show your work.
Answer:
Please Provide the an attachment.Then i can show u my answer
John bought a crate of floor tiles $100. The crate had 5 boxes of floor tiles. Each box contained 40 floor tiles. What is the cost per tile ?
help me plzzzzzzzzzzzz
Find the length of the third side. If necessary, write in simplest radical form 8 5
Answer: c = [tex]\sqrt{89}[/tex]
8² + 5² = c²
64 + 25 = c²
[tex]\sqrt{89}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]\sqrt{89}[/tex] = c
The length of the third side is 9.4.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Applying Pythagorean theorem.
Third side = x
x² = 8² + 5²
8 x 8 = 64 and 5 x 5 = 25
So,
x² = 64 + 25
x² = 89
x = √89
x = 9.4333
Rounding to the nearest tenth
x = 9.4
Thus,
The length of the third side is 9.4.
Learn more about the Pythagorean theorem here:
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Which expression is equivalent to the following: 5(6f + 5)
Answer:
30f+25 I hope it is a right answers
I hope this answers is useful for you
HELP PLEASE 20 POINTS
Find the slope of the line that passes through the points M of the line in the graph below.
Answer:
The slope is 4
Step-by-step explanation:
rise over run
Find the coefficient of x for the expression y²x + y.
Answer:
y^2
step-by-step-explanation:
Nabil earns $2100 a month. He spends 30 % of it and saves the rest. How much does he save each month?
$ 1470
$ 1400
$ 1450
Answer:
$1470
Step-by-step explanation:
$2100 * 70% = $1470
Evaluate the expression when b=5 and c=7
Answer:
7×7-5/7+3(5)
49-5/7+15
44/22
=2
so c squared - b
over c+3b is =2
2 meters into km
2.002 Km
2.02 Km
2.2 Km
PLEASE PLEASE PLEASEEEEE HELP ME PLEASEEE!!!
Answer:
V = 0.523598776
Step-by-step explanation:
Which point represents the unit rate?
A
B
C
D
Answer:
d
Step-by-step explanation:
PLZZZZ HELP
A. 178.3
B. 196.5
C. 250.8
D. 292.5
E. 297. 1
Answer:
E, 297.1
Step-by-step explanation:
First, find the area of the triangle using the formula a= (bh) / 2
Base x height would be 16 x 12, which is 192
192 / 2 is 96 sq meters
Then, find the area of the circle using the formula a= Pi (r^2)
If the diameter is 16, the radius would be 8 because you divide by 2
8^2 is 64, 64 times Pi is approximately 201.1
Finally, add the areas together, 96 + 201.1 is 297.1 or E
A 30-foot long escalator forms a 41° angle at the second floor. Which is the closest height of th
141
30 feet
A 20 feet
B. 22.5 feet
C. 24.5 feet
D. 26 feet
Answer:
[tex]\huge\boxed{\text{B) } 22.5 \ \text{feet}}[/tex]
Step-by-step explanation:
We can use basic trigonometric functions to find the closest height of the escalator.
Let's set up a picture from what we already know. The length of the escalator is 30 feet, and it forms a 41 degree angle with the top. Since it will form a 90 degree angle with the ground, we can find the angle between the ground and the beginning of the escalator.
Since all triangles have an angle sum of 180:
[tex]90+41+x=180[/tex] [tex]131+x=180[/tex] [tex]x = 180-131[/tex] [tex]x=49[/tex]Now we know that the triangle looks something like this.
/ | 41°
/ |
/ |
/ |
30 / |
/ |
/ |
/ |
/__________| 90°
49°
We need to find the length of the side between the 41 and 90° angle.
To find which trigonometric operation to use on this triangle, we can use the acronym SOH CAH TOA.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
We can use the sine of the 49 degree angle (opposite / hypotenuse) to find our missing side (since we know the hypotenuse).
Let's set up an equation and solve with our calculator.
[tex]\text{sin}(49) = \frac{\text{opposite}}{\text{hypotenuse}}[/tex] [tex]\text{sin}(49) = \frac{x}{\text{30}}[/tex] [tex]30 \cdot \text{sin}(49) = x[/tex]We can calculate the sine of 49 with our calculator. We'd end up multiply 30 and that value and get 22.6.
Since the closest value to 22.6 on the answer choices is 22.5, the correct answer would be B) 22.5 feet.
Hope this helped!
Answer:
The answer is B.
Step-by-step explanation:
B. 22.5 feet
Lucas deposits $4,000.00 for 6 years at 2% interest, compounded monthly. How much interest does he earn at the end of the 6 years? Round to the nearest cent. SHOW THE WORK PLEASE
Answer:
$12644.56
Step-by-step explanation:
one year = 12 month
4,000 * (1.02)^(6*12) = 16644.5615
16644.5615-4000 = 12644.5615
Answer:
Step-by-step explanation:
[tex]A=P(1+r/c)^{ct}\\ \\ A=4000(1+.02/12)^{12(6)}\\ \\ A\approx \$ 4509.54[/tex]
)) Evaluate the expression for b = 7.
11b - 75 =
Answer:
The answer is 2.
Step-by-step explanation:
11(7) - 75
77-75
=2
what is the product of (8-3a)(8-3a)
Answer:
i think is is 64a
Step-by-step explanation:
Answer:
[tex](8 - 3a)(8 - 3a) \\ 8(8 - 3a) - 3a(8 - 3a) \\ 64 - 24a - 24a + 6a {}^{2} \\ 64 - 48a + 6a {}^{2} \\ 6a {}^{2} - 48a + 64[/tex]
what are the coordinates for the center of the circle in the length of the radius X squared plus Y squared minus X minus 2Y -11 over four equals zero
Given:
The equation of a circle is:
[tex]x^2+y^2-x-2y-\dfrac{11}{4}=0[/tex]
To find:
The center of the circle and its radius.
Solution:
The standard form of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, (h,k) is center and r is the radius of the circle.
The given equation of the circle is:
[tex]x^2+y^2-x-2y-\dfrac{11}{4}=0[/tex]
Write the given equation in standard form of a circle.
[tex](x^2-x)+(y^2-2y)-\dfrac{11}{4}=0[/tex]
[tex]\left(x^2-x+\left(\dfrac{1}{2}\right)^2\right)+(y^2-2y+1^2)-\dfrac{11}{4}-\left(\dfrac{1}{2}\right)^2+1^2=0[/tex]
[tex]\left(x-\dfrac{1}{2}\right)^2+(y-1)^2-\dfrac{11}{4}-\dfrac{1}{4}-1=0[/tex]
[tex]\left(x-0.5\right)^2+(y-1)^2-\dfrac{12}{4}-1=0[/tex]
On further simplification, we get
[tex]\left(x-0.5\right)^2+(y-1)^2-3-1=0[/tex]
[tex]\left(x-0.5\right)^2+(y-1)^2-4=0[/tex]
[tex]\left(x-0.5\right)^2+(y-1)^2=4[/tex]
[tex]\left(x-0.5\right)^2+(y-1)^2=2^2[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]h=0.5,k=1,r=2[/tex]
Therefore, the center of the circle is (0.5,1) and radius is 2 units.
Amir buys a new car for £16470. The value of the car will depreciate by 2% each year. Work out how much amir's car will cost after 23 years
Answer:
Amir's car will cost £10348.88 after 23 years.
Step-by-step explanation:
I finally found a UK human!
This is compound interest so you have to find a decimal multiplier and multiply that with £16470 to the power of 23.
The decimal multiplier would be 0.98. This is because you do 100% - 2% as depreciating basically means a decrease, which gives you 98% and then you divide that by 100 to get your decimal multiplier - 0.98.
16470 × [tex]0.98^{23}[/tex] = £10348.88
I hope that helps you!! ^-^