Answers
Answer:
32.7 degress
Step-by-step explanation:
In this question we are to find the value of the angle
The best way to do with the information given is the cosine rule
Mathematically that would be;
y^2 = x^2 + z^2 -2xzCosY
where x = 90 ft , y = 55ft and z = 50 ft
Plugging the values we have;
55^2 = 90^2 + 50^2-2(90)(50)CosY
-7575 = -9000cosY
cosY = 7575/9000
cosY = 0.841666666667
Y = cos^-1 0.841666666667
Y = 32.68 degrees which is 32.7 to the nearest tenth
Answer:
32.7
Step-by-step explanation:
Related Questions
Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri ¼ hour to make the round trip. What was her average speed for the entire trip?
Answers
Answer:
Terri’s speed can be calculated like this:
her speed- [tex]\frac{6km}{0.25h}[/tex]=24km/h
Step-by-step explanation:
Given 8x + 2 = 3 - x; x =
Answers
Answer:
x = 1/9
Step-by-step explanation:
8x + 2 = 3 - x
Add x to both sides.
9x + 2 = 3
Subtract 2 from both sides.
9x = 1
Divide both sides by 9.
x = 1/9
Answer:
x = 1/9
Step-by-step explanation:
We are given the equation:
8x + 2 = 3 - x
In order to solve for the variable x, we need to isolate it; in other words, we need to combine all the x terms and move everything else to the other side.
First, add x to both sides:
8x + x + 2 = 3
9x + 2 = 3
Now subtract 2 from both sides:
9x = 3 - 2 = 1
Divide both sides by 9:
x = 1/9
The answer is thus 1/9.
~ an aesthetics lover
In an arithmetic series, what is the sum of the first 22 terms if the first term is 12 and the common difference is 3?
Answers
Answer:
561
Step-by-step explanation:
an = dn - (a-d)
The difference is 3.
The first term is 12.
an = 3n - (12-3)
an = 3n - 9
Put n as 1, 2, 3, 4, 5 ....22.
3(1) - 9 = -6
3(2) - 9 = -3
3(3) - 9 = 0
3(4) - 9 = 3
3(5) - 9 = 6
...
3(22) - 9 = 57
Add the first 22 terms.
-6+-3+0+3+6+9+12+15+18+21+24+27+30+33+36+39+42+45+48+51+54+57
= 561
Pls help me with trig!!!
for 32 but if you understand 33 pls i need the help
Answers
I’m guessing number 32 is true, since it asks you to round to the nearest integer.
To solve this problem, use the Pythagorean Theorem, which is a^2 + b^2 = c^2, where c is the hypotenuse. The hypotenuse of the triangle is always the longest side, meaning the hypotenuse would be 15.23.
To ensure these measurements can be used in order to make a right triangle, substitute the numbers into the Pythagorean Theorem.
6^2 + 14^2 = 15.23^2.
36 + 196 = 231.9529
232 = 231.9529
Because we were asked to round, that makes the equation 232 = 232, meaning the answer is true.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)
Answers
Answer:
4 (20) + 6(6) = 120
4(20) + 4 (6) = 100
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations with the information given:
Build time (hours) = 4c + 6a = 120
Test time (hours) = 4c + 4 a = 100
Where c represents the number of child bikes and a represents adult bikes.
So, for 20 child bikes and 6 adult bikes:
4 (20) + 6(6) = 120
4(20) + 4 (6) = 100
Feel free to ask for more if needed or if you did not understand something.
Choose the graph represents the function y-3=3/2(x-4)?
Answers
Hope this helps have a nice day! :)
If four of the exterior angles of a convex pentagon measure
60°, find the measure of the fifth exterior angle.
Answers
Answer:
120°
Step-by-step explanation:
all exterior angles of any polygon add up to 360 therefore 4 x 60 = 240
360 - 240 = 120
The measure of the fifth exterior angle is 120 degrees if the four of the exterior angles of a convex pentagon measure 60°.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have:
If four of the exterior angles of a convex pentagon measure 60°
The sum of the total interior angles = 360
The sum of the four of exterior angles = 4(60) = 240 degrees
The measure of the fifth exterior angle = 360 - 240 = 120 degrees
Thus, the measure of the fifth exterior angle is 120 degrees if the four of the exterior angles of a convex pentagon measure 60°.
Learn more about the regular polygon here:
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PLEASE HELP. Thanks to the two people who have helped me on the other two maths questions today :) much appreciated. <3
Answers
Answer: hope this helps
Step-by-step explanation:
7kg of nuts = £10
350g nuts into bags= 75p
convert 7kg into g which is 7000g
then do 7000 divide by 350 which is 20
so then you do 0.75 times 20 which is £15.00
so your answer is £15.00 hope it helps
Area of the cone when the radius is 4cm and the height is 12cm. Rounded to the nearest tenth
Answers
Explanation:
Use this formula to figure it out
Pi x r(r + sqrt h^2 + r^2)
Help please!!!! Thanksss
Answers
Answer:
Correct option: E
Step-by-step explanation:
The group must have 1 man and 1 woman.
So, for the woman slot, we have 4 possible choices, because we have 4 women and 1 slot to occupy.
For the man slot, we have 2 possible choices, because we have 2 men and 1 slot to occupy.
So the number of different groups we can make is the product of the number of possibilities for each slot:
Number of groups = 4 * 2 = 8
Correct option: E
the illumination due to a source of light varies directly as the strength of the source and inversely as the square of the distance from the source. two sources are 6 meters apart and one of them is 8 times stronger than the other. at what distance from the weaker source on the line segment joining them is the illumination the least
Answers
Answer:
Point is at x = 4 m
Step-by-step explanation:
From the question, we can write the formula for intensity as;
I = strength/distance²
Now,
- Let x be the position from the stronger source
- Let k be the strength of the weaker light source
- 8k will be the strength of the stronger light source.
We are told that the two sources are 6 meters apart and one of them is 8 times stronger than the other.
Thus, the total illumination is;
I(x) = (8k/x²) + k/(6 - x)²
Using chain rule to get the critical points, let's find the first derivative and equate to zero;
I'(x) = -16k/x³ + 2k/(6 - x)³ = 0
Adding -16k/x³ to both sides, we have;
2k/(6 - x)³ = 16k/x³
Cross multiply to get;
2kx³ = 16k(6 - x)³
Dividing both sides by 16k to give;
x³/8 = (6 - x)³
Taking cube root of both sides to give;
x/2 = 6 - x
Multiply both sides by 2 to give;
x = 12 - 2x
x + 2x = 12
3x = 12
x = 12/3
x = 4 m
simplify radical sign 16a^8b^-2
Answers
Answer:
[tex] \frac{ {4a}^{4} }{b} [/tex]solution,
[tex] \sqrt{16 {a}^{8} {b}^{ - 2} } \\ [/tex]
Use negative power rule:
[tex] {x}^{ - a} = \frac{1}{ {x}^{a} } [/tex]
[tex] \sqrt{ {16}^{8} \times \frac{1}{ {b}^{2} } } \\ [/tex]
Simplify:
[tex] \sqrt{ \frac{ {16a}^{8} }{ {b}^{2} } } \\ = \frac{ \sqrt{ {16a}^{8} } }{ \sqrt{ {b}^{2} } } \\ [/tex]
Use this rule:
[tex] \sqrt{ab} = \sqrt{a} . \sqrt{b} [/tex]
[tex] \frac{ \sqrt{16. \sqrt{ {a}^{8} } } }{ \sqrt{ {b}^{2} } } [/tex]
Since, 4*4=16 ,the square root of 16 is 4
[tex] \frac{ \sqrt{ {4}^{2} } \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 \sqrt{ {a}^{8} } }{ \sqrt{ {b}^{2} } } [/tex]
Simplify:
[tex] \frac{4 \: \sqrt{ {(a}^{4) ^{2} } } }{ \sqrt{ {b}^{2} } } \\ = \frac{4 {a}^{4} }{b} [/tex]
Hope this helps...
Good luck on your assignment...
What is the approximate distance between points A and B? A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair 4, 3 is labeled as A, and the ordered pair negative 2, negative 4 is labeled as B 3.61 9.22 10.35 12.62
Answers
Answer:
[tex]\large \boxed{9.22}[/tex]
Step-by-step explanation:
The formula for the distance between two points is
[tex]d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]
x₂ - x₁ = 4 - (-2) = 9
y₂ - y₁ = 3 - (-4) = 7
The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.
[tex]\begin{array}{rcl}AB & = & \sqrt{6^{2} + 7^{2}}\\& = & \sqrt{36 + 49}\\& = & \sqrt{85}\\& \approx & \mathbf{9.220} \end{array}\\\text{The approximate distance between the points is $\large \boxed{\mathbf{9.220}}$}[/tex]
The approximate distance between points A and B will be equal to 9.220.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. The length of the line segment between two places represents their distance.
Most notably, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula for the distance between two points is,
[tex]D =\sqrt{(x_2-x_1)+y_2-y_1)^2[/tex]
x₂ - x₁ = 4 - (-2) = 9
y₂ - y₁ = 3 - (-4) = 7
The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.
AB = √( 6² + 7² )
= √ ( 36 + 49 )
= √85
= 9.22
Therefore, the approximate distance between points A and B will be equal to 9.220.
To know more about Coordinate geometry follow
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A top costs £48 in a sale after a 20% reduction. What is the original cost of the top before the sale?
Answers
Answer:
£60
Step-by-step explanation:
Let the original cost be x.
x × (1 - 20%) = 48
0.8x = 48
x = 48/0.8
x = 60
The original cost was £60 before the sale.
Answer:
£57.60
Step-by-step explanation:
find 20% of £48, which is £9.60
then add that to £48, which will give you the answer of £57.60
help me with trig Pls !!
using given triangle, calculate length of the altitude
Answers
hope it will be helpful.......
What is the smallest positive integer n for which [tex]n^{2}[/tex] is divisible by 18 and [tex]n^{3}[/tex] is divisible by 640?
Answers
Answer:
120
Step-by-step explanation:
n^2 has a factor of 18, so factors of 3^2·2. Since n^2 is a perfect square, we know n must have a factor of 3·2 = 6.
n^3 has a factor of 640, so factors of 2^7·5. Since n^3 is a perfect cube, we know n must have a factor of 2^3·5 = 40.
The least common multiple of 6 and 40 is 120.
The smallest positive integer n is 120.
_____
Check
120^2/18 = 800
120^3/640 = 2700
Can any one please help me in this the teacher did not explain this it have to be in the lowest term also no decimal answer thank you please help me
Answers
Answer:
a. -5 + 3x = -41
3x = -36
x = -12
b. 7x - 4 = -2x + 11
9x = 15
x = 15/9 = 1 and 2/3
c. (-4x) / 5 = 8
-4x = 40
x = -10
d. x / 3 - 1/2 = 1/4
4x - 6 = 3 (multiply by lcm of 3, 2 and 4 which is 12)
4x = 9
x = 9/4 = 2 and 1 / 4
e. -4(6x + 1) + 3 = 11 + 2(x + 2)
-24x - 4 + 3 = 11 + 2x + 4
-24x - 1 = 2x + 15
-26x = 16
x = -8/13
Jasmine knows that the area of a rectangle is the product of its base and height. Help her write an expression that represents the area of this rectangle, and then use the expression to find the area when b = 10
Answers
Answer:
Area of rectangle = H × B
Area of rectangle = 10(H)
Step-by-step explanation:
Given:
Base (B) = 10
Height = H
Find:
Area of rectangle
Computation:
Area of rectangle = Height × Base
Area of rectangle = H × B
So,
Area of rectangle = H × B [Base (B) = 10]
⇒ Area of rectangle = H × 10
⇒ Area of rectangle = 10(H)
Answer:
The expression that represents the area of this rectangle is 8b
When b = 10, the area of the rectangle is 80 square units.
Step-by-step explanation:
The rectangle’s base is b units, and its height is 8 units. The area of the rectangle is the product of its base and height, which is 8b.
To find the area of the rectangle when b = 10, substitute 10 for b in the expression:
8b= 8(10)
=80
The current cost of a loaf of bread is $2.89. At the time of this writing, the CPI for bread is 323.0. What was the cost of a loaf of bread in 1983 to the nearest cent?
This is a fill in the blank problem, please help me.
Answers
Answer:
The cost of a loaf of bread in 1983 to the nearest cent is $0.89
Step-by-step explanation:
The cost of the loaf of bread in 1983 can be computed using the below formula:
cost of a loaf of bread in 1983=$2.89/current CPI *100
cost of a loaf of bread in 1983=$2.89/323*100=$ 0.89
It is obvious that the cost of a loaf of bread in the year 1983 is $0.89
Which are steps in the process of completing the square used to solve the equation 3 – 4x = 5x2 – 14x? Check all that apply 3 = 5(x2 + 2x) 3 = 5x2 – 10x 4 = 5(x2 – 2x + 1) 8 = 5(x2 – 2x + 1) 3 = 5(x – 1)2 4 = 5(x – 1)2 StartFraction 8 Over 5 EndFraction = (x – 1)2
Answers
Answer:
1. 3 = 5x2 – 10x
2. 8 = 5(x2 – 2x + 1)
3. StartFraction 8 Over 5 EndFraction = (x – 1)2
Step-by-step explanation:
3-4x=5x^2-14x
3=5x^2-14x+4x
3=5x^2-10x
5x^2-10x-3=0
1. 3 = 5x2 – 10x
2. 8 = 5(x2 – 2x + 1)
8=5x^2-10x+5
8-5=5x^2-10x
3=5x^2-10x
3. StartFraction 8 Over 5 EndFraction = (x – 1)2
8/5=x^2-2x+1
Cross product
8=5(x^2-2x+1)
8=5x^2-10x+5
8-5=5x^2-10x
3=5x^2-10x
Answer:
2,4,7
Step-by-step explanation:
An irregular parallelogram rotates 360° about the midpoint of its diagonal. How many times does the image of the parallelogram coincide with its preimage during the rotation?
Answers
Answer:
2
Step-by-step explanation:
The question, is basically asking for the order of rotational symmetry for the parallelogram. This is 2, which means while spinning the parallelogram around its centre point 360 degrees, it looks exactly the same, or matches with its original at 2 points
Find, in terms of π, the surface area of a sphere generated by rotating a semicircle of radius 6 inches about its diameter.
Answers
Answer:
[tex]144\pi in^2[/tex]
Step-by-step explanation:
Given
Shape: Circe
Radius = 6 inches
Required
What is the surface area of a sphere when the circle
When a circle is rotated about its diameter, the resulting sphere maintains the same radius and diameter as the circle, before rotation;
This implies that
Radius [of sphere] = 6 inches
[tex]Surfare\ Area = 4\pi r^2[/tex]
Substitute 6 for r
[tex]Surfare\ Area = 4\pi* 6^2[/tex]
[tex]Surfare\ Area = 4\pi* 6 * 6[/tex]
[tex]Surfare\ Area = 4\pi*36[/tex]
[tex]Surfare\ Area = 144\pi[/tex]
Hence, the surface area of the resulting sphere is 144 pi inches square
Guys I need help what is 8+[4+(-9)] please.
Answers
Answer:
-9 + 4 = 4 - 9 = -5
-5 + 8 = 8 - 5 = 3
3 is the answer
Step-by-step explanation:
8+[4+(-9)]
-9 + 4 = 4 - 9 = -5
-5 + 8 = 8 - 5 = 3
3 is the final answer.
Find the sum of the arithmetic series for which a_1 = 7, n = 31, and a_n = 127.
Answers
Answer: 2077
There are 31 terms.
S₃₁ = 31(a₁+a₃₁)/2 = 31(7+127)/2 = 2077
A basketball player's total points scored for the season went from 158 to 231 over a period of 5 games. What was his scoring rate per game over those 5 games?
Answers
Answer:
14.6
Step-by-step explanation:
(231 - 158) / 5 = 14.6
I need help with this
Answers
dalanay enlarges a photograph tahst is 3 inches long and 2 inches wide. the length of the enlarged photograph is 15 inches. what is the width of the enlarged photograph, in inches?
Answers
Answer:
10 inches
Step-by-step explanation:
Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?
Hence, L1/L2 = W1/W2
∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches
if a 10-pound turkey costs $20.42.how much does a 21-pound turkey cost
Answers
Answer:
$42.88
Step-by-step explanation:
Let's create a proportion using the following setup:
cost/pounds=cost/pounds
We know that it costs $20.42 for a 10 pound turkey.
$20.42/10 pounds= cost/pounds
We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.
$20.42/ 10 pounds= $x/ 21 pounds
20.42/10=x/21
We want to find x, by getting x by itself.
x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.
21*(20.42/10)=(x/21)*21
21* 20.42/10=x
21*2.042=x
42.882=x
Round to the nearest cent, or hundredth.
42.88=x
x= $42.88
A 21 pound turkey costs $42.88
There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. d How many sets can be formed (including empty set)
Answers
Answer:
1,024Step-by-step explanation:
The number of sets that can be generated from the given set is determined by calculating the power of the set. Power of a set is expressed as 2ⁿ where:
n represents the number of elements in the set.
Given the set S = {0,1,2,3,4,5,6,7,8,9}.
n(S) = 10
The Power of the set = 2^n(S)
Power of the set = 2^10 = 1,024
This means that 1,024 different sets can be formed from the given set including the empty set.
Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0? The constant term is 8.
Answers
Answer:
false
Step-by-step explanation:
the constant term is 3 not 8
hope this helps