Answer:
A
Step-by-step explanation:
[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]
[tex] \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) [/tex]
Will give brainliest. Find the length and measure of each arc. Show your work.
Problem 1
The circumference is the full perimeter around the circle. You can think of it as the combination of "circle" and "fence" to get "circumference", but there might be other tricks to remember the term.
Anyways, the formula to get the circumference of a circle is
C = 2*pi*r
In this case, r = 14 is our radius so,
C = 2*pi*r
C = 2*pi*14
C = 28pi .... exact circumference in terms of pi
We only want a portion of this circumference as shown by the piece of the circle darkened. The fractional portion we want is 135/360 of a circle. Divide the angle by 360 to get the fractional portion you want. If the angle was say 180 degrees, then 180/360 = 1/2 is the fractional portion.
So we take 135/360 and multiply it by the value of C found earlier
arc length = (fractional portion)*(circumference)
arc length = (135/360)*28pi
arc length = 10.5pi
That's the exact arc length in terms of pi. Use a calculator to find that
10.5pi = 32.9867228626929
Or you could use pi = 3.14 to say
10.5*pi = 10.5*3.14 = 32.97
Which is fairly close to what the calculator is saying
-----------------
Summary:Exact arc length = 28pi
Approximate arc length (using calculator) = 32.9867228626929
Approximate arc length (using 3.14 for pi) = 32.97
Units are in feet
When I write "using calculator", I mean using the calculator's stored version of pi, instead of pi = 3.14
======================================================
Problem 2
We could use the same idea as problem 1, or we could use the formula below. The formula is just a quick way of encapsulating what I discussed earlier.
L = arc length
x = central angle
L = (x/360)*2*pi*r
L = (150/360)*2pi*13
L = (65/6)pi .... exact arc length
L = 34.0339204138894 .... approx arc length (using calculator)
L = 34.0166666666667 .... approx arc length (using 3.14 for pi)
-----------------
Summary:Exact arc length = (65/6)pi
Approximate arc length (using calculator) = 34.0339204138894
Approximate arc length (using 3.14 for pi) = 34.0166666666667
Units are in meters
Matilda has 16 3/4 hours to finish 3 consulting projects. How much time may she spend on each project, if she plans to spend the same amount of time each?
A. 5 6/7
B. 5 3/7
C. 5 9/11
D. 5 7/12
Answer: D
Step-by-step explanation:
To find how much time she need on each project divide the time by 3 because there are 3 projects and to get to 1 project you will need to divide by 3.
16 3/4 = 67/4
[tex]\frac{67}{4}[/tex] ÷ [tex]\frac{3}{1}[/tex] = [tex]\frac{67}{12}[/tex] = 5 7/12
Answer:
Step-by-step explanation:
Find the area. Round to the nearest tenth.
6 ft
3 ft
12.16 ft
9.16 ft
Answer:
100.5 ft^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w
A = 12.16 * 6
A =72.96 ft^2
Then find the area of the triangle
A = 1/2 bh
The base is 12 ft - 6ft = 6ft
The height is 9.16 ft
A = 1/2 ( 9.16) * 6
A = 27.48 ft^2
Add them together
27.48+72.96
100.44 ft^2
Round to the nearest tenth
100.5 ft^2
Answer:
[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]
Step-by-step explanation:
To find the area of the shape, we can add the area of the rectangle with the area of the triangle.
Area of rectangle :
base × height
6 ft × 12.16 ft
72.96 ft²
Area of triangle :
base × height × 1/2
(12 ft - 6 ft) × 9.16 ft × 1/2
6ft × 9.16 ft × 1/2
27.48 ft²
Adding the areas.
72.96 ft² + 27.48 ft²
100.44 ft²
≈ 100.4 ft² (rounded to nearest tenth)
Which graph represents 7x+2y< 8
Answer:
Graph C.
Step-by-step explanation:
Hi there!
Well let’s first put,
7x + 2y < 8
We need to single out y.
7x + 2y < 8
-7x to both sides
2y < -7x + 8
Divide everything by 2,
y < -7/2x + 4
Well the shade on the graph should be going down because it is y is less than,
And the y intercept should be at 4 with a dotted line and a slope of -7/2.
So graph C. Is correct.
Hope this helps :)
The graph that represents the inequality 7x + 2y < 8 will be graph C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The inequality is given as,
7x + 2y < 8
Simplify the equation in slope-intercept form, then we have
7x + 2y < 8
2y < 8 - 2x
y < (8 - 2x) / 2
The value of the variable 'y' is less. Then the graph that represents the inequality 7x + 2y < 8 will be graph C.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
Express in standard form : a) 0.000000056 b) 56780000000 c) 1923.8 (will mark brainly
Answer:
Step-by-step explanation:
a) 5.6 x 10∧-8
b) 5.678 x 10∧10
c) 1.9238 x 10∧3
Match the property of equality with the corresponding definition given that a = b.
multiplication property of equality
a+c=b+c
subtraction property of equality
a(c) = b(c)
addition property of equality
a-c=b-c
division property of equality
ale = b c
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]a = b[/tex]
Required
Match proper type of equality
Each of the equality properties can easily be identified with their names; For multiplication property of equality, same term must be multiplied on both sides;
For addition, same term must be added on both sides;
Same thing implies for division and subtraction
Multiplication:
[tex]a(c) = b(c)[/tex]
Subtraction
[tex]a - c = b - c[/tex]
Addition
[tex]a + c = b + c[/tex]
Division
[tex]a/c = b/c[/tex]
Barbara Cusumano worked 60 hours last week. Of those hours, 40 hours were paid at the regular-time rate of $12.50 an hour, 18 hours at the time-and-a-half rate, and 2 hours at the double-time rate. What was Barbara's gross pay for the week?
Answer:
$887.50
Step-by-step explanation:
Her gross pay is the sum of the pay amounts for each of the hour amounts:
pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)
= (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)
pay = 887.50
Barbara's gross pay for the week was $887.50.
how many are 4 raised to 2 ???
Answer:
[tex]\huge \boxed{16}[/tex]
Step-by-step explanation:
4 raised to 2 is 4 squared or 4 to the power of 2.
[tex]4^2 =4 \times 4 = 16[/tex]
Please answer answer question now
Answer:
Area= 97.9 km²
Step-by-step explanation:
Angle at w = 180-119-34
Angle at w = 27°
Side XV= x
x/sin27= 26/sin119
x= sin27(26/sin119)
x= 0.454(26/0.8746)
x= 13.5 km
Side WX = y
y/sin 34= 26/sin119
y= sin34(26/sin119)
y= 0.559(26/0.8746)
y= 16.6 km
S= (16.6+13.5+26)/2
S= 56.1/2
S=28.05
Area = √(28.05(28.05-26)(28.05-13.5)(28.05-16.6))
Area=√(28.05(2.05)(14.55)(11.45))
Area=√(9579.772744)
Area=97.8763
Area= 97.9 km²
Which of the following statements is true about odd
and/or even numbers?
F. The sum of any 2 even numbers is odd.
G. The sum of any 2 odd numbers is ood.
H. The quotient of any 2 even numbers is odd.
J. The quotient of any 2 even numbers is even.
K. The product of any 2 odd numbers is odd.
Answer:
k) the product of ant 2 odd numbers is odd
I don't know.
Let's check um out.
For each choice, I'll try to find an example to show that it's false.
F. The sum of any 2 even numbers is odd.
2+2=4. 4 is even. This one is false.
G. The sum of any 2 odd numbers is ood.
3+3=6. 6 is even. This one is false.
H. The quotient of any 2 even numbers is odd.
8÷4=2. 2 is even. 10÷4=2.5. 2.5 is neither odd nor even. This one is false.
J. The quotient of any 2 even numbers is even.
10÷2=5. 5 is odd. This one is false.
K. The product of any 2 odd numbers is odd.
I can't find an example where this is false.
So I'm gonna say that this is the true one.
Can you help Jorge organize the results into a two-way frequency table?
Answer:
Top left: 6
Bottom left: 8
Top right: 7
Bottom right: 3
Step-by-step explanation:
To solve this problem, we need to look at the table to see what missing information we need to solve for. On the table, it asks us how many students:
Play a musical instrument and sportDoesn't play anythingPlays sportsPlays an instrumentOn the first intersection (top left), we are asked how many students played an instrument and sport. That is easy to solve because the information they provide us already gives us that number: 6.
On the second intersection (bottom left), things get a little more challenging. The information states that 14 students in total play sports, so that is not the number of people who only play sports. Since 14 people in total play sports and 6 people play both an instrument and sport, we subtract 6 from 14 to get our answer, 8.
On the third intersection (top right), it asks us how many people play an instrument but doesn't play a sport. Let's look at the remaining values first. There is: 6, 8, 3. When we add those together, we get 17, and when we subtract that from the total (24), we get our answer: 7.
On the last intersection (bottom right), the information already provides us with the answer to how many people don't play anything: 3.
What two numbers multiply to negative 12 and add up to negative 13
Answer:
−13.8654599313 and 0.8654599313
Step-by-step explanation:
The two numbers of interest will be the solutions to ...
xy = -12
x +y = -13
Substituting for y, this becomes the quadratic ...
x(-13 -x) = -12
x^2 +13x = 12 . . . . . multiply by -1
x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square
(x +6.5)^2 = 54.25
x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5
x ≈ -13.865499313 or 0.8654599313
The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.
Please help
Maths....
6 cm from what im seeing
Answer: 7 cm
Step-by-step explanation:
PLEASE HELP How can a company use a scatter plot to make future sale decisions
Answer:
From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.
Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).
Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).
Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.
find the gcd of 12 18 and 24
Answer:
6
Step-by-step explanation:
the solution in photo :)
Answer:
6
Step-by-step explanation:
→ Prime factorise each number
12 = 2² × 3 ⇒ 2 × 2 × 3
18 = 2 × 3² ⇒ 2 × 3 × 3
24 = 2³ × 3 ⇒ 2 × 2 × 2 × 3
→ Find which number there are in each one
2 and 3
→ Multiply them together
2 × 3 = 6
solve 2(1/9)× = 2/81 for x
Answer: x=1/9
Step-by-step explanation:
[tex]2\left(\frac{1}{9}\right)x=\frac{2}{81}[/tex]
[tex]\frac{2}{9}x=\frac{2}{81}[/tex]
multiply both sides by 9
[tex]9\cdot \frac{2}{9}x=\frac{2\cdot \:9}{81}[/tex]
[tex]2x=\frac{2}{9}[/tex]
divide 2 on both sides
[tex]x=\frac{1}{9}[/tex]
Evaluate the expression 18C4
Answer:
3,060
Step-by-step explanation:
Given:
18C4
nCr=n! / r!(n-r)!
=18! / 4!(18-4)!
18!=18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
=6,402,373,705,728,000
4!=4*3*2*1
=24
(18-4)!=14!
=14*13*12*11*10*9*8*7*6*5*4*3*2*1
=87,178,291,200
18! / 4!(18-4)!
=6,402,373,705,728,000 / 24*87,178,291,200
=6,402,373,705,728,000 / 2,092,278,988,800
=3,060
Duke wants to hire someone to re-tile his bathroom. The research he found for three local tilers is presented in the table below. He was able to find the average area of their tiling jobs and the time it took the tilers to complete the job.
Tiler Area Tiled
(square feet) Time
(hours:minutes)
Toni's Tiles 803 2:12
Bob's Bathrooms 1,460 4:00
Rhonda's Restroom Redos 753 1:30
Calculate the unit rate for each tiler above to determine if proportional relationships exist.
The rates at which Toni's Tiles and Bob's Bathrooms tile are ?
to one another.
The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are ?
to one another.
The rates at which Bob's Bathrooms and Rhonda's Restroom Redos tile are ?
to one another.
Two items are in a proportional relationship if they ?
the same unit rate.
Answer:
Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate
Step-by-step explanation:
The given parameters are;
, Area Tiled (ft²) Time (Hr:min)
,
Toni's Tiles, 803 2:12
Bob's Bathrooms, 1,460 4:00
Rhonda's Restroom Redos 753 1:30
The unit rate for each tiler
Toni's Tiles = 803/2:12 = 803/(2×60 + 12) = 6.083 ft²/min
Bob's Bathrooms = 1460/(4×60) = 6.083 ft²/min
Rhonda's Restroom Redos = 753/(60 + 30) = 8.37 ft²/min
Therefore we have;
The rates at which Toni's Tiles and Bob's Bathrooms tile are to one another = 6.083 to 6.083 = 1:1
The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502
The rate at which Bob's Bathrooms and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502
Therefore, Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate.
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
x = 22, y = 11[tex]\sqrt{3}[/tex]
x = 11, y = 22[tex]\sqrt{3}[/tex]
x = 22[tex]\sqrt{3}[/tex], y = 11
x = 11[tex]\sqrt{3}[/tex], y = 22
Answer:
D
Step-by-step explanation:
Since this is a right triangle, and we are given that one of the other angles is 30°, we have a 30°, 60°, 90° triangle.
In a 30°, 60°, 90° triangle, the side lengths are all related as shown below.
We should determine a first. a is the measure of the side opposite to the 30° angle. Thus:
[tex]a=11[/tex]
The side opposite to the 60° angle is given by a√3. Since a = 11, the side opposite to the 60° angle or x is:
[tex]x=(11)\sqrt{3}=11\sqrt3[/tex]
Finally, the hypotenuse will be 2a. Since a = 11, the hypotenuse or y will be:
[tex]y=2(11)=22[/tex]
Hence, x = 11√3 and y = 22.
Our answer is D.
An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 5% and 95% confidence. To gauge the size of the problem, the agency first picks 50 cars and finds 12 with faulty emissions systems. How many should be sampled for a full investigation?
Answer:
197
Step-by-step explanation:
Sample proportion is; p^ = 12/50 = 0.24
Margin of error of 5% is given by the formula;
ME = (z_0.05) √[p^(1 - p^)/n]
Let's make n(number of sample) the subject.
n = ((z_0.05)/ME)²((p^)(1 - p^))
From tables, the z-score of 0.05 is 1.645
Thus;
n = ((1.645)/0.05)²(0.24(1 - 0.24))
n ≈ 197
Final answer is x=4
Help me out with question 4
Answer: x = 4/5
Step-by-step explanation:
[tex]\tan\ y=\dfrac{\text{side OPPOSITE y}}{\text{side ADJACENT to y}}=\dfrac{1}{6}\\\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \dfrac{x}{x+4}=\dfrac{1}{6}\\\\\\\text{Cross multiply, distribute, and solve for x:}\\6(x)=1(x+4)\\6x=x+4\\5x=4\\\\\large\boxed{x=\dfrac{4}{5}}[/tex]
What is the formula to find the area of the sector?
Answer:
There are 3 ways
Step-by-step explanation:
The formula for a sector's area is:
1. A = (sector angle / 360 ) * (pi *r2)
2. A = (sector angle / (2*pi)) * (pi * r2)
3. A = (fraction of the circle) * (pi * r2)
NEED HELP ASAP solve for x : 3/5 = x-1/8
a.5 b.29/5 c.23/5 d.19/5
Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{ \frac{29}{5} }}}}}[/tex]Option B is the correct option.
Step-by-step explanation:
[tex] \sf{ \frac{3}{5} = \frac{x - 1}{8} }[/tex]
Apply cross product property
⇒[tex] \sf{ 5(x - 1) = 3 \times 8}[/tex]
Distribute 5 through the parentheses
⇒[tex] \sf{5x - 5 = 3 \times 8}[/tex]
Multiply the numbers
⇒[tex] \sf{5x - 5 = 24}[/tex]
Move 5 to right hand side and change it's sign
⇒[tex] \sf{5x = 24 + 5}[/tex]
Add the numbers
⇒[tex] \sf{5x = 29}[/tex]
Divide both sides of the equation by 5
⇒[tex] \sf{ \frac{5x}{5} = \frac{29}{5} }[/tex]
⇒[tex] \sf{x = \frac{29}{5} }[/tex]
Hope I helped!
Best regards!!
If 2x+5=8x, then 12x=?
Answer:
[tex]\boxed{10}[/tex]
Step-by-step explanation:
[tex]2x+5=8x[/tex]
[tex]\sf Subtract \ 8x \ from \ both \ sides.[/tex]
[tex]2x+5-8x=8x-8x[/tex]
[tex]-6x+5=0[/tex]
[tex]\sf Subtract \ 5 \ from \ both \ sides.[/tex]
[tex]-6x+5-5=0-5[/tex]
[tex]-6x=-5[/tex]
[tex]\sf Divide \ both \ sides \ by \ -6.[/tex]
[tex]\displaystyle \frac{-6x}{-6} =\frac{-5}{-6}[/tex]
[tex]\displaystyle x =\frac{5}{6}[/tex]
[tex]\sf Evaluate \ 12x.[/tex]
[tex]\displaystyle 12 \cdot \frac{5}{6} =\frac{60}{6} =10[/tex]
Answer:
10
Step-by-step explanation:
2x+5=8x: First, you are going to subtract 2x from both sides of the equation.
5=6x: Now divide 6x from each side of the equation.
x=5/6: now plug in 5/6 by multiplying this number by 12.
Your final answer should be 10.
Melissa, of Melissa's Lawn and Landscaping Service, needs to replace her mowers.
She has ordered four new gas mowers, at $499 each, and a negotiated Trade
Discount Rate of 9%, with terms of 2/10 EOM, and FOB Shipping Point. The
seller has agreed to prepay the shipping charge of $80, which is not included in the
invoice amount. The invoice from the manufacturer is dated July 26.
Determine:
A)
By what date does Melissa have to pay in order to be able to take the cash
discount?
B)
What is the payment amount assuming that Melissa pays before the end of
the discount period?
Answer:
A) 10th of August
B) $1780.03
Step-by-step explanation:
A) From the payment terms of 2/10 EOM, Melissa is to receive a 2% discount if she pays within 10 days from the end of the month
From the date on the invoice, July 26, the date at which Melissa has to pay to take the cash discount is before the 10th of August
B) The payment amount will be 2% off the original payment amount
The total cost of the four new gas mowers less the trade discount = 499 × 4 × (100 - 9)/100 =$1816.36
The 2% discount will then be $1816.36 × (100 - 2)/100 = $1780.03
The payment amount assuming Melissa pays before the end of the discount period = $1780.03.
Evaluate 2x+3x+2 for x= -2
Answer:
-8
Step-by-step explanation:
2(-2) +3(-2) +2
-4 -6 +2
-10 +2
-8
math be like 0-0????
Answer: A & C
Step-by-step explanation:
HL is Hypotenuse-Leg
A) the hypotenuse from ΔABC ≡ the hypotenuse from ΔFGH
a leg from ΔABC ≡ a leg from ΔFGH
Therefore HL Congruency Theorem can be used to prove ΔABC ≡ ΔFGH
B) a leg from ΔABC ≡ a leg from ΔFGH
the other leg from ΔABC ≡ the other leg from ΔFGH
Therefore LL (not HL) Congruency Theorem can be used.
C) the hypotenuse from ΔABC ≡ the hypotenuse from ΔFGH
at least one leg from ΔABC ≡ at least one leg from ΔFGH
Therefore HL Congruency Theorem can be used to prove ΔABC ≡ ΔFGH
D) an angle from ΔABC ≡ an angle from ΔFGH
the other angle from ΔABC ≡ the other angle from ΔFGH
AA cannot be used for congruence.
8 m minus 6 less or equal than 10
Hi there! :)
Answer:
[tex]\huge\boxed{m\leq 2}[/tex]
Equation:
8m - 6 ≤ 10
Add 6 to both sides:
8m ≤ 16
Divide both sides by 8:
8m/8 ≤ 16/8
m ≤ 2
Answer:
8m - 6≤ 10
m≤2
Step-by-step explanation:
8m - 6≤ 10
Add 6 to each side
8m - 6+6≤ 10+6
8m ≤ 16
Divide each side by 8
8m/8 ≤16/8
m≤2
The graph of g(x) is a translation of the function f(x)=x^2. The vertex of g(x) dislocated five units above and seven units to the right of the vertex of f(x). which equation represents g(x)
[tex]f(x)[/tex] passes through origin, i.e. $(0,0)$
if you move 5 units up, it should pass through $(0,5)$
so you'll add 5 to $y$ i.e. $y+5=x^2$ this satisfies $(0,5)$
and to move right, it should pass through $(7,0)$ so you'll subtract $7$ from $x$ i.e. $y=(x-7)^2$
now combine both translations
$g(x)=(x-7)^2-5=x^2-14x+45$
What is the multiplier that corresponds to 12% exponential decay(answer choices in picture)?
Answer:
[tex] 0.88^x [/tex]
Step-by-step explanation:
Exponential decay formula is given as [tex] a(1 - r)^x [/tex], where,
a is the initial amount
r is the decay rate
x is the time interval
Therefore, the multiplier that corresponds to 12% decay is [tex] (1 - r)^x = (1 - \frac{12}{100})^2 = (1 - 0.12)^x = 0.88^x [/tex]
