Answer:
A = pi/2
Step-by-step explanation:
Area of a sector is given by
A = 1/2 r^2 theta when theta is given in radians
We know the area of the circle (pi * r^2) so we multiply by pi/pi
A = 1/2 pi/pi r^2 theta
A = 1/(2* pi) * pi r^2 theta
= 1/(2* pi) * Ac theta where Ac is the area of a circle
Substituting what we know Ac = 9 pi and theta = 1/9 * pi
A = 1/(2* pi) * 9*pi 1/9 * pi
A = 1/(2* pi) * pi^2
A = 1/2 * pi
A = pi/2
Answer:
Its [tex]\frac{\pi }{2}[/tex] .
Step-by-step explanation:
Because the work shown below will show you how:
[tex]\frac{\theta}{2\pi } = \frac{A_s}{A_c}\\\frac{1}{9} /2\pi = \frac{A_s}{9\pi } \\\frac{1}{18} = \frac{A_s}{9\pi } \\\frac{1}{18} * 9\pi = A_s\\=\pi/2[/tex]
Colin and Rosie had the same number of cashews at first. Each day, Colin ate 5 cashews and Rosie ate 8 cashews. When Rosie had 4 cashews left, Colin had 10 times as many cashews left as Rosie. How many cashews did each child have at first?
The ordered pairs model an exponential decay function.
{(−1,30), (0,21), (1,14.7), (2,10.29)}
What is the function equation?
Enter your answer in the box.
f(x)=
Answer to your question:
f(x)= 12x
Answer:
f(x)=12 Hope this helps you!
what is the slope of the line shown
(4, 2) (-4, -2)
m=?
(4, 2) (-4, -2)
Slope is the change in Y over the change in X
From the two points given:
Slope =( -2 - 2 ) / ( -4 -4)
Slope = -4 / -8
Slope = 1/2
m = 1/2
Evaluate − a + ( − b ) −a+(−b) where a = 6 . 0 5 a=6.05 and b = 3 . 6 1 1 b=3.611.
Answer:
-19.322
Step-by-step explanation:
− a + ( − b ) −a+(−b)
First step is to combine like terms
-a -a + -b + -b
-2a -2b
We know a = 6.05 and b = 3.611
-2 (6.05) -2(3.611)
-12.1 - 7.222
-19.322
Answer:
Step-by-step explanation:-9.661
list the angles of the triangle in order from smallest to largest
Answer:
correct choice is C
Step-by-step explanation:
Triangle KLM has three known lengths of sides:
KL=4.1 units;LM=6.4 units;MK=3.2 units.The greatest angle is opposite to the greatest side. The greatest side is LM, then the greatest angle is angle K. The smallest angle is opposite to the smallest side. The smallest side is MK, then the smallest angle is angle L.
Therefore, the list the angles of the triangle in order from smallest to largest is ∠L, ∠M, ∠K.
Based on the angle and side relationship of the triangle given, the angles of the triangle from smallest to the largest would be: C. ∠L, ∠M, ∠K
Triangle Angles and Sides RelationshipThe longest side of a triangle is opposite the biggest angle measure.The shortest side of a triangle is opposite the smallest angle measure in a triangle.Thus, based on the angle and side relationship of the triangle given, the angles of the triangle from smallest to the largest would be: C. ∠L, ∠M, ∠K
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Write the expression (4x-6) x 6(2x+7)
Answer:
48x² + 96x - 252
Step-by-step explanation:
(4x - 6) × 6(2x + 7) Reorder the factors
= 6(4x – 6)(2x+ 7) Multiply the binomials
= 6(8x² + 16x - 42) Remove parentheses
= 48x² + 96x - 252
Jake wants to estimate 15.92+0.85 . How can he use rounding to estimate the sum? What is the estimate?
Answer:
17
Step-by-step explanation:
15.92 is close to 16
0.85 is close to 1
15.92 + 0.85 is close to 16 + 1
16 + 1 = 17
15.92 + 0.85 is approximately 17
The vertical axis is called the x-axis and the horizontal axis is called the y-axis. The entire plane containing these is called the xy-plane
TRUE OR FALSE
Please help please help
Answer:
reeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
What is the equation of the line?? Please help!!
The point-slope form of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -4 and the point (8, -7). Substitute:
[tex]y-(-7)=-4(x-8)[/tex] use distributive property
[tex]y+7=-4x+32[/tex] subtract 7 from both sides
[tex]y=-4x+25[/tex] add 4x to both sides
[tex]\boxed{4x+y=25}[/tex]
What is Perimeter of triangle ABC?
ΔABC and ΔFEG are congruent. Therefore we have the equation:
7x - 19 = 2x + 11 add 19 to both sides
7x = 2x + 30 subtract 2x from both sides
5x = 30 divide both sides by 5
x = 6
AB = 24
AC = 2x + 11 → AC = 2(6) + 11 = 12 + 11 = 23
BC = 6x - 8 → BC = 6(6) - 8 = 36 - 8 = 28
The perimeter of ΔABC = 24 + 23 + 28 = 75
Answer: 75 feetSamuel has 2 1/4 cups of flour. She uses 1/3 of the flour to make pancakes. How many cups of flour did he use? Please try to explain this to me the best you can
Answer:
Samuel uses 1 11/12 cups of flour.
Step-by-step explanation:
Okay, this is assuming he uses the rest of the flour she didn't use.
The first step would be to find the Greatest Common Factor(GCF) of the fractions
2 1/4 and 1/3 have different denominators, but they both can divide into 12.
1/4 * 3/3 = 3/12
1/3 * 4/4 = 4/12
Now we can also convert 2 3/12 into an improper fraction to make it easier
2* 12/12 = 24/12
24/12+ 3/12 = 27/12
Here's the part were we subtract the two numbers.
27/12- 4/12 = 23/12
The last step is to simplify the fraction
23/12 = 1 11/12 cups
estimate 782 divided by 50
Answer: about 15.72
Step-by-step explanation: i used a calculator
Find the Nonpermissible replacement for y in this expression y-9/y+3
Answer:
y = - 3
Step-by-step explanation:
Providing you mean (y - 9)/(y + 3) then it is always the variable in the denominator that is going to cause trouble. If it equals zero at any point, it's game over.
It's a little better if you get a result like 0/0. That problem has a "depends" as an answer, but by and large, you don't want to monkey around with 0 in the bottom of a fraction.
y + 3 = 0 Subtract 3 from both sides.
y + 3 - 3 = 0 - 3 Combine
y = - 3
PLEASE HELP I HAVE 49 POINTS!
show work
Answer:
1. y = 2x-4
2 y = -1/2x+3
Step-by-step explanation:
Slope intercept form of the equation is y= mx+b
where m is the slope and b is the y intercept
1. y- 2x = -4
We need to solve for y
Add 2x to each side
y -2x+2x = 2x-4
y = 2x-4
2 y-3 = -1/2 x
We need to add 3 to each side
y-3+3 = -1/2x +3
y = -1/2x+3
Answer:
1. y = 2x - 4
y = -1/2x + 3
Step-by-step explanation: You have to isolate or get y by itself.
1:
y - 2x = -4
+ 2x + 2x
y = 2x - 4
2:
y - 3 = -1/2x
+ 3 + 3
y = -1/2x + 3
You are working as a locksmith. Of the 50 customers you had today, 15 of them needed a new key for their car. What percentage of today’s customers needed a new key for their car?
How do i figure this out ??
A.0.030%
B.0.3%
C.3%
D.30%
E.300%
Which sign makes the statement true 17/20 ? -11.95
To make the statement '17/20 ? -11.95' true, the correct symbol to use is '>'. We find this by comparing the result of 17 divided by 20 (which is 0.85) with -11.95.
Explanation:The question is asking us to find the correct sign (either less than '<', equal '=', or greater than '>') to make the mathematical statement '17/20 ? -11.95' true.
To solve this, we first need to divide 17 by 20 to get 0.85. Then, we compare this result with -11.95.
Since 0.85 is greater than -11.95, we use the '>' symbol. Thus, the statement '17/20 > -11.95' is true.
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Find the equation that represents a line that passes through the point (7,-5) and has slope -4/7
Answer:
The equation would be y = -4/7x - 1
Step-by-step explanation:
Given that we have the slope and the point, we can solve for the equation using point-slope form.
y - y1 = m(x - x1)
y + 5 = -4/7(x - 7)
y + 5 = -4/7x + 4
y = -4/7x - 1
The equation that represents a line that passes through the point (7,-5) and has a slope of -4/7 is,
⇒ 7y = - 4x - 7
The equation of a line in point-slope form passing through the point
(x₁ , y₁) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Given that,
The equation of line passes through the point (7,-5) and has a slope of -4/7.
Here we have,
[tex](x_1 , y_1) = (7, - 5)[/tex]
And, [tex]m = \frac{- 4}{7}[/tex]
Substitute the given values in the above equation,
[tex]y - y_1 = m (x - x_1)[/tex]
[tex]y - (- 5) = \frac{-4}{7} (x - 7)[/tex]
[tex]y + 5 = \frac{-4}{7} (x - 7)[/tex]
Multiply by 7 on both sides,
[tex]7 (y + 5) = - 4 (x - 7)\\7y + 35 = - 4x + 28\\ 7y =- 4x 28 - 35\\ 7y = - 4x- 7\\[/tex]
So, the equation of a line is,
7y = - 4x - 7
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javier opens a savings account with a starting balance of $200 and plans to deposit $75 each week after opening the account and savings over time is represented by the graph below how would the graph change if javier open his account with a starting balance of $300 instead
If Javier starts with a higher initial balance of $300, the initial point on his savings graph would be higher by $100, and all subsequent points would reflect this initial increase, though the slope of the graph would remain unchanged.
If Javier opens a savings account with a starting balance of $300 instead of $200 and then deposits $75 each week, the graph representing his savings over time would change in the following way:
The initial point on the graph, representing the starting balance, would be higher.
This is because the starting balance would be $300 instead of $200.
After this initial change, the slope of the graph, representing the weekly deposits of $75, would remain the same.
However, every point on the graph after the initial deposit would be $100 higher than it was before because each point on the savings graph accumulates the effects of the higher starting balance.
What is the cheapest way to go to a ball game if the admissions options are as shown? A) $10 for a single B) $15 for a couple C) $20 for a triple D) $35 for a group of four E) $50 for a group of five
Answer: C
Step-by-step explanation: A = 10 for one person. B = 7.5 for one person. C = 6.67 for one person. D = 8.75 for one person. E = 10 for one person.
Out of all of these, C is the cheapest.
HELP PLEASE WILL GIVE 30 POINTS !!!!!! Determine the amount you need to invest to have $22,000 dollars in 4 years if you invest at 5% annual interest, compounded quarterly. ADD WORK PLEASE
Answer:
$18 034.42
Step-by-step explanation:
The formula for the future value of an account paying 5 % annual interest compounded quarterly for four years is
[tex]A = P(1 +\frac{r }{n })^{nt}[/tex]
A = $22 000
r = 0.05
n = 4 times per year
t = 4 years
[tex]22 000 = P(1 +\frac{0.05 }{4 })^{4\times4}[/tex]
[tex]22 000 = P(1 + 0.0125)^{16}[/tex]
[tex]22 000 = P(1.0125)^{16}[/tex]
22 000 = P x 1.220
P = 2 000/1.220
P = $18 034.42
You must invest $18 034.42.
to the nearest whole degree what angle measure has a tangent of 5.6922
Answer:
80° has a tangent of 5.6922..Step-by-step explanation:
We are given value of tangent trigonometric ratio = 5.6922.
We need to find the angle in degrees whose measure has a tangent of 5.6922..
So, we need to find the value of [tex]tan^{-1}(5.6922)[/tex].
On plugging [tex]tan^{-1}(5.6922)[/tex]in calculator, we get
80.03°.
Now, we need to round it to the nearest whole degree.
Therefore, 80.03°≈ 80°.
Therefore, 80° has a tangent of 5.6922..The ratio of blueberry bagels to all bagels is 1:4. Does this ratio represent a part to part or part to whole ratio
Answer:
Part to whole ratio
Step-by-step explanation:
The 1 represents the blueberry bagels. This is just a part of the entire variety that is offered, so this is a part.
The 4 represents all of the bagels. It is the whole amount, which makes this the whole.
This means it is a part to whole ratio.
Select the two figures that are similar to the 5 by 10 figure that is shown
Answer:
Figure (i) and (iv)
Step-by-step explanation:
We need to find two figures that are similar to the 5 by 10 figure.
that is we need to find the figure that is similar to 5 X 10 figure.
Observe that in a figure m X n, the letter m represent the number of rows and the letter n represents the number of columns.
Observe that in the given figure 5 by 10, the number of rows is 5 and number of columns is 10, that is, the number of columns is double of that the number of rows.
so we need to find two such figures whose number of columns is double of the number of rows.
from the given figures, we can see that in the figure (i) the number of rows is 2 and number of columns is 4, which is double of number of rows. so it is similar to 5 by 10 figure.
And the figure in (iv), the number of rows is 4 and number of columns is 8. so here since the number of columns is double the number of rows, so it is similar to the figure 5 by 10.
Thus the two figures that are similar to 5 by 10 figure are given in (i) and (iv).
The two figures that share a similarity with the 5 by 10 figure based on the doubling relationship between columns and rows are represented by options (i) and (iv).
In the provided 5 by 10 figure, it's evident that the number of columns is twice the number of rows.
Therefore, our goal is to identify two other figures with the same relationship.
Upon examination of the given options, we can see that in figure (i), there are 2 rows and 4 columns, which maintains the same doubling relationship between columns and rows as the 5 by 10 figure.
Thus, figure (i) is similar to the 5 by 10 figure.
Similarly, in figure (iv), there are 4 rows and 8 columns, and this also maintains the doubling relationship between columns and rows. Therefore, figure (iv) is another figure similar to the 5 by 10 figure.
In summary, the two figures that share a similarity with the 5 by 10 figure based on the doubling relationship between columns and rows are represented by options (i) and (iv).
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a-5/a divided by 4/a
Answer:
[tex]\frac{a-5}{4}[/tex]
Step-by-step explanation:
the given equation is
[tex]\frac{a-5}{a} /\frac{4}{a}[/tex]
from the multiplication rules we know that
[tex]\frac{a}{b}/\frac{c}{d}=\frac{a}{b}*\frac{d}{c}[/tex]
so for the given equation changing the sidn of division to multiplication
the equation becomes
[tex]\frac{a-5}{a} * \frac{a}{4}[/tex]
a cancels out from both numerator and denominator
so it becomes
[tex]\frac{a-5}{4}[/tex]
which is the answer
I don't get this problem from maths.
Answer:
100/3 or 33.33
Step-by-step explanation: If the perimeter of the whole figure is 220, we can use that number to solve the equations on the trapezoid.
2(2x-3) + 2(4) + 2(4x+1)
4x - 6 + 8 + 8x + 2
12x + 2
Now we have to set the equation equal to the perimeter to find the value of x
12x + 2 = 220
12x = 218
x = 109/6
Since we are only finding the length of PS, we will plug x into its equation (2x - 3).
2(109/6) - 3
109/3 - 3
109/3 - 9/3
100/3
check the picture below.
[tex]\bf \stackrel{\textit{perimeter of the trapezoid}}{(4x+1)+(4x+1)+(4)+(4)+(2x-3)+(2x-3)} \implies 12x+4[/tex]
The area of a triangle is twice the area of a square. If the base of the triangle and a side of the square are equal, what is the ratio of the height of the triangle to the side of the square?
Answer:
1:1
Step-by-step explanation:
If you're square is a true square, than the height and base will be the same. If one is larger than the other, it's a rectangle.
If you slice a square diagonally, you still have the original height of the square.
Final answer:
To find the ratio of the triangle's height to the square's side, set the area of the triangle (1/2 × base × height) to be twice that of the square (side²). Simplify by equating base to side as they are the same length and solve for the height. The resulting ratio of the height of the triangle to the side of the square is 4:1.
Explanation:
The question involves finding the ratio of the height of a triangle to the side of a square where the area of the triangle is twice that of the square, and they have one side in common. The area of a square is given by side² (s²), and the area of a triangle is given by 1/2 × base × height (1/2 × b × h). To solve this, we set the triangle's area to be twice the square's area: 1/2 × b × h = 2 × s². Since the base of the triangle (b) is equal to the side of the square (s), they can be represented by the same variable. Hence, the equation simplifies to 1/2 × s × h = 2 × s². Canceling s from both sides leaves us with h = 4 × s. Therefore, the ratio of the height of the triangle to the side of the square is 4:1.
Change each improper fraction into an equal mixed number.
a. 15⁄4
b. 41⁄9
c. 67⁄8
d. 135⁄11
e. 107⁄20
f. 493⁄17
A.) 3 3/4
B.) 4 5/9
C.) 8. 375 - I couldn't solve this one
D.) 12 3/11
E.) 5 7/20
F.) 29
if you have 10 cookies and you want to give 1/2 of them to a friend. How many do you give to your friend
Answer: You would give your friend 5 cookies
Step-by-step explanation:
One half of the cookies, is basically saying divided by two. 10 divided by 2 is 5. To check that answer, multiply 5 by 2, and you will get 10
What is 575 written as a mixed number
The 575 written as a mixed number is A. 5 3/4 . Therefore , A. 5 3/4 is correct .
You have correctly outlined the steps to convert 575% to a mixed number. Let me summarize the process:
Convert the Percentage to a Decimal:
Divide the percentage by 100 to convert it to a decimal:
[tex]\frac{575}{100}[/tex]% = 5.75.
Separate the Whole Number and Decimal Part:
Separate the whole number part from the decimal part:
5.75=5+0.75.
Convert the Decimal to a Fraction:
Convert the decimal part to a fraction with a denominator of 100:
0.75× [tex]\frac{100}{100}[/tex] = [tex]\frac{75}{100}[/tex] .
Combine the Whole Number and Fraction:
Combine the whole number and the fraction into a mixed number:
5 + [tex]\frac{75}{100}[/tex] =5 [tex]\frac{3}{4}[/tex] .
Therefore, 575% written as a mixed number is 5 [tex]\frac{3}{4}[/tex] .
This means there are 5 whole units and [tex]\frac{3}{4}[/tex]of an additional unit in the given percentage.
It's a clear and accurate way to represent a percentage as a mixed number.