Answers
14.1 in
Explanation:
The equation relating the length of arc, radius of circle and angle is:
S = rθ
where:
S is the length of the arc
r is the radius of the circle = 6 in
θ is the angle in radians = 135 degrees = (135*π) / 180 = 0.75 π radian
Substitute with the givens in the above equation to get the length of the arc as follows:
S = rθ
S = 6 * 0.75π
S = (9/2) π which is approximately 14.1in
Hope this helps :)
Related Questions
This figure is made up of a triangle and a semicircle. What is the area of this figure? Use 3.14 for pi. Round only your final answer to the nearest tenth. Enter your answer, as a decimal, in the box. units²
https://static.k12.com/nextgen_media/assets/8124428-GA_GMT_IT_03_DP100_885_008.png
Answers
The area of the figure that is made up of a triangle and a semicircle is 23.137 units².
What is the area of a triangle?The area of a triangle is half the product of its base and its height.
[tex]Area \triangle = \dfrac{1}{2}\times base \times height[/tex]
In order to solve the problem, we will divide the given figure into two parts such that the first one will be a right-angled triangle while the second one is a semi-circle as shown below.
As we can see in the ΔABC, the height of the triangle is 3 units, while the length of the base of the triangle is 6 units. therefore, the area of the triangle can be written as,
[tex]\begin{aligned}\triangle ABC &= \dfrac{1}{2} \times height \times base\\\\&= \dfrac{1}{2} \times BC \times AB\\\\& = 0.5 \times 3 \times 6\\\\& = 9\rm\ unit^2 \end{aligned}[/tex]
Now, if we look at the semi-circle we will find that the diameter(BC) of the semi-circle is 3 units, therefore, the area of the semi-circle can be written as,
[tex]\begin{aligned}\text{Area of Semi-circle} &= \dfrac{\pi}{2}d^2\\\\ &= \dfrac{\pi}{2}(3)^2\\\\&= 14.137\rm\ units^2 \end{aligned}[/tex]
Further, in order to get the total area of the figure, simply add the two areas, therefore,
The area of the figure = Area of triangle + Area of the semi-circle
= 9 + 14.137
= 23.137 units²
Hence, the area of the figure that is made up of a triangle and a semicircle is 23.137 units².
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Find the constant of variation for the quadratic variation.
x 2 3 4 5 6
y 24 54 96 150 216
A. 12
B. 6
C. 30
D. 18,
Answers
y = kx^2
Use any coordinate in the set.
The missing is k, to find it, use the equation
24 = k(2^)
= 4k
k = 6
Least common denominator for -3/a and 1/4a^2
Answers
How much would $300 invested at 4% interest compounded monthly be worth after 8 years? Round your answer to the nearest cent.
here's the equation: A(t)=P(1+r/n)^nt
i just don't know what to put where please help,
Answers
The equation you have provided is correct:
A(t)=P(1+r/n)^nt
Where P = principal amount
r = interest rate
n = number of times the amount is compounded in a year
t = time in years
The value of n is 12 since it is compounded monthly.
Substituting the amount to the formula:
A(t) = $300 ( 1 + 4%/12)^(12)(8)
A(t) = $300 (1 + 0.003333)^96
A(t) = $300 (1.376351)
A(t) = $412.91
32 = 4m + 8 solve each equation
Answers
32= 4m+8
Subtract 8 on both sides.
24=4m
Divide 4 on both sides.
m=6
I hope this helps!
~kaikers
Subtract 8 from each side.
4m + 8 (-8) = 32 - 8.
Solve.
4m = 24.
Divide each side by 4.
m = 6.
Hope it helps! :)
Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b – 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which student’s first step was incorrect, and why? Amelia’s, because the variable term must be isolated on the left side Luis’s, because he flipped the inequality sign when he subtracted Shauna’s, because she did not apply the subtraction property of equality properly Clarence’s, because the terms he added together were not like terms
Answers
What will affect the symbol is when you divide or multiply by a negative because this means the opposite.
Answer:
B
Luis’s, because he flipped the inequality sign when he subtracted
Step-by-step explanation:
got it right on Edge
please mark as Brainliest
(P.S. Luis is my first name)
Let f be a differentiable function such that f(0) = -5 and f'(x) is less than or equal to 3 for all x. Of the following, which is not a possible value for f(2)?
A) -10 B) -5 C) 0 D) 1 E) 2
Answers
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.
Using the Mean Value Theorem, we can determine the possible values for f(2) which is D) 1
Explanation:To find the possible values for f(2), we can use the Mean Value Theorem. Taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values.
Since f(0) = -5 and f'(x) is less than or equal to 3 for all x, we know that f(2) must lie between -5 and -5 + 3(2) = 1.
Therefore, 1 is not a possible value for f(2), making the correct answer choice D) 1.
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Please Help!!!
The only coins Alexis has are dimes and quarters.
Her coins have a total value of $5.80.
She has a total of 40 coins.
Which of the following systems of equations can be used to find the number of dimes,d, and the number of quarters, q, Alexis has. Explain your choice.
A.) d + q = 5.80
40d + 40 q= 5.80
B.) d + q = 40
0.25d + 0.10q = 5.80
C.) d + q = 5.80
0.10d + 0.25q = 40
D.) d + q = 40
0.10d = 0.25q = 5.80
Answers
The correct answer is (d). If d represents the number of dimes and q the number of quarters, the total number of coins would be d+q, which is given as 40 in the prompt: d+q=40
Since each dime is worth ten cents and each quarter worth twenty-five cents, their total value would be 0.10d+0.25q which would total 5.80.: 0.10d+0.25q=5.80 I HOPE THIS HELPS YOU
0.10d+0.25q=5.80
Find all possible values for θ if 0° < θ < 360° and tanθ = -1.
a. -225°
b. -45°
c. 135°
d. 225°
e. 315°
Answers
To find all possible values for θ if 0° < θ < 360° and tanθ = -1, we need to determine in which quadrants the tangent function is negative and then find the specific angles in those quadrants where the tangent equals -1.
The tangent function is negative in the second and fourth quadrants. Since tan(45°) = 1, we are looking for angles where the reference angle is 45° and the tangent is negative.
In the second quadrant, the angle that meets these criteria is 180° - 45° = 135°.
In the fourth quadrant, the angle that meets these criteria is 360° - 45° = 315°.
Therefore, the correct values for θ are:
c. 135°
e. 315°
The correct answer is [tex]135^{0}[/tex], [tex]225^{0}[/tex]
To find all possible values of θ if 0° < θ < 360° and tan θ = -1, we need to consider the values of θ in the different quadrants where the tangent function is negative.
In the first quadrant (0° < θ < 90°), the tangent function is positive, so there are no solutions in this range.
In the second quadrant (90° < θ < 180°), the tangent function is negative, and tan(135°) = -1.
In the third quadrant (180° < θ < 270°), the tangent function is also negative, and tan(225°) = -1.
In the fourth quadrant (270° < θ < 360°), the tangent function is positive, so there are no solutions in this range.
Therefore, the possible values of θ satisfying the given conditions are:
[tex]\theta = 135^\circ and \theta = 225^\circ[/tex]
Analyzing the given options:
a. [tex]-225^\circ[/tex] is not a solution, as it lies outside the given range of 0° < θ < 360°.
b. [tex]-45^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.
c. [tex]135^\circ[/tex] is a solution, as tan(135°) = -1.
d. [tex]225^\circ[/tex] is a solution, as tan(225°) = -1.
e. [tex]315^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.
Therefore, the correct options are c. 135° and d. 225°.
The function rule for this graph is y =__ x +__
Answers
It is -1/2x + 2...she just didnt add the negative sign
The equation of line will be -
y = [tex]-\frac{1}{2} x[/tex] + 2
We have a graph as shown in the figure.
We have to find out the equation of this straight line in the graph.
What is the general form of the equation of a Straight line?The general form of a equation of a straight line is -
y = mx + c
where -
m - slope of line
c - the y - intercept
We have -
The y intercept of the straight line as = (0, 2)
The x intercept of the straight line as = (4, 0)
The slope of the line will be m = [tex]\frac{2 - 0}{0 - 4}[/tex] = - [tex]\frac{1}{2}[/tex]
The y-intercept is at (0, 2) , therefore the value of c = 2.
Substituting the values in the general equation of line we get -
y = mx + c
y = [tex]-\frac{1}{2} x[/tex] + 2
Hence, the equation of line will be -
y = [tex]-\frac{1}{2} x[/tex] + 2
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I Really Need Help With This Problem, Please
Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. The order does not matter.
Answers
1 and 8 are alternate exterior
2 and 6 are corresponding
2 and 7 are alternate exterior
3 and 5 are alternate interior
3 and 6 are consecutive interior
3 and 8 are corresponding
4 and 5 are consecutive interior
4 and 6 are alternate interior
4 and 7 are corresponding
Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .
Alternate interior angles : 4 & 6 , 3 & 5
Alternate exterior angles : 1 &8 , 2 & 7
Consecutive interior angles : 4 & 5, 3 & 6
Step-by-step explanation:The corresponding angles are the angles that are in the same position made by a line cutting through two or more other lines.The alternate interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal. The alternate exterior angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. The consecutive interior angles are the pair of angles which are formed on one side of the transversal when two lines are intersected by transversal line .By using the above definitions,
Corresponding angles : 1 & 5 , 2 & 6 , 4 & 7 , 3 & 8 .
Alternate interior angles : 4 & 6 , 3 & 5
Alternate exterior angles : 1 &8 , 2 & 7
Consecutive interior angles : 4 & 5, 3 & 6
Help anyone please???
Answers
Look at the picture.
The expression square root of 576/64 in simplest form is
Answers
I see you have doubts, so I will explain each step.
Step 1: simpliy 576 / 64. In this case when you divide 576 by 64 you get 9 that is a whole number, so that is its simplest form.
Step 2: Calculate the square root of 9, which is 3.
If you use a simple calculator you will obtain that, but the square root of 9 is a calculation that you should know by yourself.
Remember that the square root a number N is the number that multiplied by itself results in the number N. For example the squere root of 4 is 2, because 2 times 2 is 4. So, the square root of 9 is 3 because 3 times 3 is 9.
It will be very helpful for you to learn the 12 first squares because with that you will be able to tell the square roots of the most elemental numbers:
1^2 = 1 => √1 = 1
2^2 = 4 => √4 = 2
3^2 = 9 => √9 = 3
4^2 = 16 => √16 = 4
5^2 = 25 => 25 = 5
6^2 = 36 => √36 = 6
7^2 = 49 => √49 = 7
8^2 = 64 => √64 = 8
9^2 = 81 => √81 = 9
10^2 = 100 => √100 = 10
11^2 = 121 => √121 = 11
12^2 = 144 => √144 = 12
Answer:
Just did it
The answer is 3
Step-by-step explanation:
Reflection across the y -axis
Answers
Answer:
G (-6,-8) H(-2,-2) F(0,-4)
Step-by-step explanation:
So really you add an negitive symbol to each number then its reflected acroos the x axis
Someone help me and remember to show your work so I know how to do it!
Answers
n = 12
Suppose the test scores of students in a class are normally distributed with a mean of 92 and a standard deviation of 3.
What is the z-score for a student who scored 86 on a test?
−6
−2
2
6
Answers
What is the solution set?
−4.9x+1.3>11.1
Enter your answer in the box.
Answers
1.3> 11.1 + 4.9x This way you never have to remember to turn the > into < when dividing by a minus.
Subtract 11.1 from both sides
-9.8 < 4.9x Divide by 4.9
-9.8 / 4.9 < x
-2 < x
To solve the inequality -4.9x + 1.3 > 11.1, subtract 1.3 from both sides and then divide by -4.9, flipping the inequality sign to get x < -2. The solution set is x < -2.
To solve the inequality -4.9x + 1.3 > 11.1, follow these steps:
Subtract 1.3 from both sides to isolate the term with x:-4.9x > 11.1 - 1.3
-4.9x > 9.8Divide both sides by -4.9 and remember to flip the inequality sign because you are dividing by a negative number:
x < -9.8 / -4.9
x < -2
The solution set for the inequality is x < -2.
Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection y=x+2 y=−12x+5
Answers
What is the greatest common factor of 7ab and 8b^3
Answers
7 and 8 have nothing in common.
ab and b^3 have b in common.
The greatest common factor is b.
Find each missing length to the nearest tenth
Answers
a²+b²=c²
(2.7)²+b²=(6.5)²
7.29+b²=42.25
b²=34.96
b=√34.96
b=5.91
MEDAL!!!@#$%
7. According to the plate tectonics model, what layer from Earth's rigid, mobile plates?
A. inner and outer core
B. upper and lower mantle
C. crust only
D. crust and upper mantle <---
i think D is the answer,
Answers
Sarah and Azhar both invest $10,000. Sarah invests her $10,000 at a rate of x% compound interest per year. Azhar invests his $10,000 in a bank that pays 2% simple interest per year. After 7 Years, their investments are worth the same amount. Calculate the value of x.
Answers
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the number of years
With this formula we will find the final amount Azhar's investment after 7 years. We know from our problem that [tex]P=10000[/tex], [tex]r= \frac{2}{100}=0.02 [/tex], and [tex]t=7[/tex]. Lets replace those values in our formula to find [tex]A[/tex]:
[tex]A=10000(1+(0.02)(7))[/tex]
[tex]A=10000(1.14)[/tex]
[tex]A=11400[/tex]
Now, since Sarah is investing in a compound interest account, we are going to use the compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the number of years
Notice that we know from our problem that after 7 years their investments are worth the same amount, so [tex]A=11400[/tex]. We also know that [tex]P=10000[/tex], [tex]r= \frac{x}{100} =0.01x[/tex], and [tex]t=7[/tex]. Since the interest are compounded per year, [tex]n=1[/tex]. Lets replace all the vales in our compound interest formula and solve for [tex]x[/tex] to find our rate:
[tex]11400=10000(1+ \frac{0.01x}{1} )^{(1)(7)} [/tex]
[tex] \frac{11400}{10000} =(1+0.01x) ^{7} [/tex]
[tex](1+0.01x) ^{7} =1.14[/tex]
[tex]1+0.01x= \sqrt[7]{1.14} [/tex]
[tex]0.01x= \sqrt[7]{1.14} -1[/tex]
[tex]x= \frac{ \sqrt[7]{1.14}-1 }{0.01} [/tex]
[tex]x=1.89[/tex]
We can conclude that the interest rate of Sarah's investment is approximately 1.89%, so x=1.89%.
Complete the two- column proof
Given: 11x - 6y = -1; x = 8
Prove: 98/6 = y
11x - 6y = -1; x = 8
88 - 6y = -1
-6y = -89
y = 89/6
89/6 = y
a. Given: b. Symmetric Property of Equality; c. Subtraction Property of Equality; d. Division Property of Equality; e. Reflexive Property of Equality
a. Given; b. Substitution Property; c. Subtraction Property of Equality; d. Division Property of Equality; e. Symmetric Property of Equality
a. Given; b. Substitution Property; c. Subtraction Property of Equality; d. Division Property of Equality; e. Reflexive Property of Equality
cant put it all in h
Answers
Explanation:
The first line of your proof just restates what was given to us; therefore the reason is "given."
Between the first step and the second step, 11x was changed to 88; this is because x=8, and we substitute that in for x. That would give us 11*8=88, with the justification being substitution.
Between the second line and third line, 88 is cancelled from the left side and the -1 becomes -89; this happens because in order to cancel a positive 88, you must subtract it from both sides. This is the subtraction property of equality.
Between the third line and fourth line, -6 is cancelled from the left side and on the right side, -89 is changed to 89/6. This happens because in order to cancel the -6 that is beside the y (which means multiplication), we must divide both sides; this is the division property of equality.
The last step is to rewrite the equation with y on the left and the answer on the right; the reflexive property allows us to do that.
The correct properties of equality used to solve the equation given x = 8 are Given, Substitution Property, Subtraction Property of Equality, Division Property of Equality, and Symmetric Property of Equality.
Explanation:The student has shared the steps of solving an equation and is asking for the correct sequence of properties used to solve it:
Given: 11x - 6y = -1; x = 8Substitute x: 88 - 6y = -1Subtract 88 from both sides: -6y = -89Divide by -6: y = 89/6State that 89/6 = yThe correct properties of equality should be applied as follows:
Given: Both the equation and x = 8 are provided information.Substitution Property: x = 8 is substituted into the equation for x.Subtraction Property of Equality: 88 is subtracted from both sides of the equation.Division Property of Equality: Both sides of the equation are divided by -6 to solve for y.Symmetric Property of Equality: Rearranges the equation to y = 89/6 for clarity.WILL GIVE THE BRAINLIST!!!
In the table below, x represents miles traveled and y represents the cost to travel by train.
What is the y-intercept of this function?
2.25
4.00
6.50
17.13
Answers
Answer:
Option B. 4
Step-by-step explanation:
By the table mentioned by you in the comments that the correct table is
x(miles) 2 5 8 12
y(cost) 8.5 15.25 22 31
As we know that the standard equation of a linear function is represented as
y = mx + c
For the points (2, 8.5) and (5, 15.25)
[tex]Slope(m)=\frac{15.25-8.5}{5-2}=\frac{6.75}{3}=2.25[/tex]
y = 2.25x + c
This function passes through (2, 8.5)
8.5 = 2.25×2 + c
c = 8.5 - 4.5 = 4
Therefore, y- intercept of the function will be option B. 4.
The y-intercept of this line is (4). Therefore, the estimated y-intercept of the function represented by the given data is 4.
To find the y-intercept of the function from the provided table, we look for the point where (x = 0), which represents the cost when no miles are traveled.
However, in the given table, there is no entry for \(x = 0\), which means we don't have a direct value for the y-intercept from the given data.
To estimate the y-intercept, we can use the concept of linear interpolation.
We can assume that the relationship between miles traveled and cost is linear, so we can find the slope of the line passing through two consecutive points and use it to estimate the cost when (x = 0).
Using the points (2, 8.5) and (5, 15.25) from the table:
[tex]\[ \text{Slope} = \frac{{15.25 - 8.5}}{{5 - 2}} = \frac{6.75}{3} = 2.25 \][/tex]
Now, we can use the slope and one of the points to find the y-intercept using the point-slope form of the equation of a line: [tex]\(y - y_1 = m(x - x_1)\).[/tex] Let's use the point (2, 8.5):
y - 8.5 = 2.25(x - 2)
y - 8.5 = 2.25x - 4.5
y = 2.25x + 4
The y-intercept of this line is (4). Therefore, the estimated y-intercept of the function represented by the given data is [tex]\(\boxed{4.00}\)[/tex].
Complete question:
By the table mentioned by you in the comments that the correct table is
x(miles) 2 5 8 12
y(cost) 8.5 15.25 22 31
In the table below, x represents miles traveled and y represents the cost to travel by train.
What is the y-intercept of this function?
2.25
4.00
6.50
17.13
Roger and Sulee each decomposed 1 1/6.Roger wrote 1/6+1/6+2/6+3/6.Sulee wrote 3/6+4/6. who is correct? Explain
Answers
Find the number of moles in 508 g of ethanol (C2H5OH).
Answers
M(C2H5OH) = 2*M(C) + 6*M(H) + M(O)
M(C2H5OH) = 2* 12.01 + 6* 1.008 + 16
M(C2H5OH) = 46.068g
This is mass of one mole of ethanol. Total mass of ethanol can be calculated by using formula:
m = N * M
Where:
m = total mass
N = number of moles
M = molar mass
We rearrange formula for N:
N = m / M
N = 508 / 46.068
N = 11.03
508g of ethanol contains 11.03 moles.
Solve for x: x^19 − 2x^18 + 7x^17 − 12x^6 + 6x^15 = 0
A) 0,1, +/-6i
B) -1,0, +/-√6i
C)-1, 0, +/-6i
D) 0,1, +/-√6i
Answers
x¹⁹ -2x¹⁸ +7x¹⁷ -12x¹⁶ +6x¹⁵ = 0
x¹⁵(x -1)²(x² +6) = 0
x = 0, 1, ±(√6)i . . . . . . . selection D is appropriate
Lyla is an editor reviewing short story submissions for a literary magazine. She collected data showing that she's an efficient reviewer and wants to leverage this to get a raise.
For a week, Lyla recorded the number of words in each short story submission, x, and how long it took her to review that story (in minutes), y.
The least squares regression line of this data set is:
ŷ=0.003x+32.164
Complete the following sentence:
For each additional word in a story, the least squares regression line predicts that it would only take Lyla ____ more minutes to review it.
Answers
This is the slope value, which is the number in front of the x in the least squares regression line. Each time x increases by 1, y increases by 0.003
This is the predicted y value of course.
which of the following represents the ratio of the hypotenuse to the given side 45 and 45
Answers
we know that
[the ratio of the hypotenuse to the given side]=(6√2)/(6)-----> √2/1
therefore
the answer is the option A) √2/1
A ratio shows us the number of times a number contains another number. The correct option is C.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The complete answer is mentioned in the below image.
The ratio of the hypotenuse to the given side is,
Ratio = (6√2)/ 6 = √2 : 1
Hence, the correct option is C.
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Help a fella out. Explain this to me.
Answers
HELLO
add x with exponent 2 to 5x then you get 6x with exponent 2
(if there one x with out a number it = 1x)
change the exponent like time it by its base so its 6*6=36
answer 36x +6 I think the answer is b or c I'm not very sure
have a wonderful Wednesday
can I get brainlest plz