Answers
Answer:
17) Length of arc QPT = 20.9 inches
18) Length of arc QR = 12.6 feet
19) Length of arc PQR = 39.3 meters
20) x = 161°
21) x = 123°
22) x = 24 units
23) EB = 4 units
24) EB = 14 units
Step-by-step explanation:
∵ The length of any arc = Ф/360 × 2πr
where Ф is the central angle subtended by this arc
17) ∵ m∠RZQ = 60° ⇒ central angle
∵ m∠QZP = 90° ⇒ centeral angle
∵ m∠RZT = 180° ⇒ Z ∈ TR
∴ m∠TZP = 180 - 90 - 60 = 30°
∴ m∠QZT = 90 + 30 = 120° ⇒ central angle
∵ ∠QZT subtended by arc QPT
∵ m∠QZT = 120 , r = 10 inches
∴ Length arc QPT = 120/360 × 2π × 10 = 20.9 inches
18) ∵ m∠QZR = 60° ⇒ central angle subtended by arc QR
∵ r = 12 feet
∴ The length of arc QR = 60/360 × 2π × 12 = 12.6 feet
19) ∵ m∠PZR = 60° + 90° = 150°⇒ central angle subtended
by arc PQR
∵ r = 15 meters
∴ The length of arc PQR = 150/360 × 2π × 15 = 39.3 meters
20) ∵ SU = ST
∴ Measure of arc SU = measure of arc ST
∵ The measure of the circle is 360°
∵ Measure of arc UT = 38°
∴ x = (360 - 38) ÷ 2 = 161°
21) ∵ AB = AC
∴ Measure of arc AB = measure of arc AC
∵ The measure of the circle is 360°
∵ Measure of arc BC = 114°
∴ x = (360 - 114) ÷ 2 = 123°
22) ∵ The two arcs are equal
∴ Their chords are equal in length
∴ 2x - 12 = 36 ⇒ 2x = 36 + 12 ⇒ 2x = 48
∴ x = 24
23) In circle A
∵ AB is a radius and CD is a chord
∵ AB ⊥ CD
∴ AB bisects CD at point E
∵ AB = 20 , CD = 24
∴ CE = 24/2 = 12
In ΔAEC
∵ m∠ AEC = 90
∵ AC = 20 ⇒ radius
∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem
∴ AE = √(20² - 12²) = 16
∵ AB = 20 ⇒ radius
∴ EB = 20 - 16 = 4
24) In circle A
∵ AB is a radius and CD is a chord
∵ AB ⊥ CD
∴ AB bisects CD at point E
∵ AB = 35 , CD = 56
∴ CE = 56/2 = 28
In ΔAEC
∵ m∠ AEC = 90
∵ AC = 35 ⇒ radius
∵ AE = √[(AC)² - (CE)²] ⇒ Pythagoras theorem
∴ AE = √(35² - 28²) = 21
∵ AB = 35 ⇒ radius
∴ EB = 35 - 21 = 14
Related Questions
Evaluate ³√-8
please help.
Answers
-8=-2^3 so the answer is -2.
-8 to the 1/3 power is -2
Two equations are given below:
m + 4n = 8
m = n − 2
What is the solution to the set of equations in the form (m, n)?
(4, 6)
(2, 4)
(0, 2)
(6, 8)
Answers
The solution to the set of equations is (0,2).
Reasoning:
m + 4n = 8 -> 0 + 4(2) = 8
m = n - 2 -> 0 = 2 - 2
Answer:
Yes, B is correct.
Step-by-step explanation:
Han has 10 cubes, each 5 inches on a side. A) Find the total volume of Han’s cubes. Express your answer as an expression using an exponent. B) Find the total surface area of Han’s cubes. Express your answer as an expression using an exponent.
Answers
Answer:
A) Vol_10_cubes = 2*(5^4) inch^3
B) Area_10_cubes = (2^2)*3*(5^3) inch^2
Step-by-step explanation:
A)The volume of a cube, as all sides are equal:
Vol_cube = (side)^3
side = 5 inches
Vol_cube = 5^3 inch^3
Since we have 10 cubes
10 = 2*5
Vol_10_cubes = 2*(5^4) inch^3
B) A cube has six faces, each with area equal to its squared side
Area_cube = 6*(side)^2
Area_cube = 6*(5)^2 inch^2
Area_10_cubes = 2*5*6*(5)^2 inch^2
Area_10_cubes = (2^2)*3*(5)^3 inch^2
The total volume of Han's cubes is given by the expression 10 × 5³ cubic inches, and the total surface area can be expressed as 10 × 6 × 5² square inches.
Explanation:The question asks for the calculation of volume and surface area of cubes with a given side length.
Volume Calculation
To find the volume of a single cube, we use the formula V = s³, where s is the length of a side of the cube. Because each side of the cube is 5 inches, the volume of one cube is V = 5³ inches³, which equals 125 cubic inches. Now, Han has 10 cubes, so the total volume is 10 times the volume of one cube, which can be expressed as:
Total Volume = 10 × 5³ inches³
Surface Area Calculation
The surface area of a single cube is found using the formula SA = 6s², since there are six sides to a cube. With a side length of 5 inches, the surface area of one cube is SA = 6 × 5² square inches, which equals 150 square inches. For 10 cubes, the total surface area is 10 times the surface area of one cube, which can be expressed as:
Total Surface Area = 10 × 6 × 5² square inches
I need help with this
Answers
The answer is circle, because the shape is a cylinder. Cylinders have a circle on the bottom.
Use the distributive property to factor the expression.
8yz − 16xy
The answer is 8y(yz-2x
Answers
Answer:
8y(z - 2x)
Step-by-step explanation:
The two given terms have the following factors in common: 8 and y.
Thus, the product in question is 8y(z - 2x).
Real Answer:
8y(z - 2x)
Thank you altavistard they helped me!
The length of a rectangular prism is four times the width. The height of the prism is 8 ft. If the volume of the prism is 160 ft3, what is the width of the prism? Round to the nearest tenth of a foot.
A. 8.9 ft
B. 2.2 ft
C. 4.5 ft
D. 10.8 ft
Answers
Answer:
2.2
Step-by-step explanation
(guess and check)
2.2 x 4 = 8.8
2.2 x 8.8 x 8 = 160
The width of the prism is approximately 2.2 feet.
Explanation:Let's assume that the width of the prism is x feet. Since the length of the prism is four times the width, the length can be represented as 4x feet. Given that the height is 8 feet, we can use the formula for the volume of a rectangular prism: Volume = Length x Width x Height. Plugging in the given values, we get the equation 160 = 4x * x * 8. By solving this equation, we find that the width of the prism is approximately 2.2 feet (when rounded to the nearest tenth).
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Jeremy made 2 quarts of lemonade. Which expression can be used to find the number of fluid ounces of lemonade, Jeremy made.
A: 2×2×2
B:2×2×8
C: 2×2×2×2
D:2×2×2×8
Answers
The correct answer is D.
There are 32 fluid ounces in a quart so 2 quarts would have 64 fluid ounces and the last equation represents this.
I hope this makes sense and is helpful.
Answer:
D
Step-by-step explanation:
I just need help with 4-6
Answers
4-6=-2
Solve the equation.
12=2+z/-6
Answers
Answer:
[tex]\boxed{\bold{z=-60}}[/tex]
Step-by-step explanation:
Switch Sides
[tex]\bold{2+\frac{z}{-6}=12}[/tex]
Subtract 2 From Both Sides
[tex]\bold{2+\frac{z}{-6}-2=12-2}[/tex]
Simplify
[tex]\bold{\frac{z}{-6}=10}[/tex]
Multiply Both Sides By -6
[tex]\bold{\frac{z\left(-6\right)}{-6}=10\left(-6\right)}[/tex]
Simplify
[tex]\bold{z=-60}[/tex]
The value of z is -60
Step-by-step explanation:see the image
The graph of a system of parallel lines will have no solutions. (1 point) Select one: a. Always b. Sometimes c. Never
Answers
Answer:
Always
Step-by-step explanation:
They never intersect
Answer:
Always
Step-by-step explanation:
The solution to a system of equations graphically is at the point of intersection of the graphs.
If the lines are parallel then they never intersect and so there is no solution.
I just need to know if it’s right. Thanks!
Answers
You are correct! It’s C
Which of the following equations describes a relationship of inverse variation between input and out put ?
Answers
Answer:
option A
output = constant / input
Step-by-step explanation:
Inverse relationship between two input and output means that they both moves in opposite directions, if one increases than other decreases.
Equation to describe relationship of inverse variation between input and output will be as following
output ∝ 1 / inputto remove this sign of proportionality
output = k / inputwhere k is a constant
Find the amplitude and the equation of the midline of the periodic function
Answers
Answer:
amplitude: 3; midline is y = 2
Step-by-step explanation:
Note that the range of this function is [-1, 5], values that are 6 units apart. The amplitude is half that, or 3 units.
The midline is the horiz. line halfway between -1 and +5.: y = 3.
These values correspond to the last (fourth) answer choice.
The amplitude and midline of a periodic function can be determined from the function's equation. The amplitude is the absolute value of the coefficient attached to the sine or cosine, and the midline (or vertical shift) is the constant added or subtracted in the function.
Explanation:From the equation of a periodic function, we can determine the amplitude and midline. The amplitude is the absolute value of the coefficient of the function while the midline (or the vertical shift) can be found as the constant added or subtracted in the equation.
Let's consider your periodic function as y = A sin(kx) + D. Here, |A| is the amplitude and D is the midline of the function. However, the function itself is not provided in your question.
For instance, in the function y=0.2 m sin(6.28 m¯¹x − 1.57 s¯¹t), the amplitude, wave number, and angular frequency can be read directly. The amplitude here is 0.2 m (the multiplier of the sine term). It and doesn't seem to be any shifts up or down, so the midline is y = 0 (the x-axis).
So, you can find the amplitude and midline of a periodic function from the equation itself, however, you need the specific equation of your function to do that.
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What is the value of X? show all of your work
Answers
Answer:
5
Step-by-step explanation:
We need to use Pythagoras' theorem.
For this we can use the pythagoras formula a^2+b^2=c^2 and rearrange this
We then will have 8^2+b^2=89
(because 89(sqrt) squared is 89)
We can then solve for what x is.
We take away 64 from 89 which is 25
the square root of 25 is 5
Therefore x=5
Which system of linear inequalities is represented by the graph?
Answers
Answer:
The system of inequalities is
[tex]y\leq -\frac{1}{3}x+2[/tex]
[tex]y>\frac{2}{3}x+3[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid red line
Let
[tex]A(0,2),B(3,1)[/tex]
Find the slope
[tex]m=(1-2)/(3-0)=-1/3[/tex]
The equation of the line is
[tex]y=-\frac{1}{3}x+2[/tex]
The solution of the inequality is the shaded area below the solid red line
therefore
The inequality is
[tex]y\leq -\frac{1}{3}x+2[/tex]
step 2
Find the equation of the dashed blue line
Let
[tex]A(0,3),B(3,5)[/tex]
Find the slope
[tex]m=(5-3)/(3-0)=2/3[/tex]
The equation of the line is
[tex]y=\frac{2}{3}x+3[/tex]
The solution of the inequality is the shaded area above the dashed blue line
therefore
The inequality is
[tex]y>\frac{2}{3}x+3[/tex]
The system of inequalities is
[tex]y\leq -\frac{1}{3}x+2[/tex]
[tex]y>\frac{2}{3}x+3[/tex]
Examine the equation: 4x = 2 − y Which equation represents the equivalent equation in slope-intercept form?
Answers
Answer:
2 - y = 4x
y - 2 = -4x
y = -4x + 2
Solve the equation f(x) = g(x) by graphing the functions f(x)= 2^x + 1 and g(x) = 5 on the same set of coordinate axes.
Which statements about the solution to the equation are true?
Select each correct answer.
a. The ordered pair that contains the solution to the equation lies in Quadrant II.
b. there are 2 solutions to the equation.
c. The ordered pair that contains a solution to the equation lies in Quadrant I.
d. The solution to the equation is x = 2.
e. The ordered pairs that contain the solutions to the equation lie in Quadrant I and II.
Answers
Answer:
C) The ordered pair that contains a solution to the equation lies in Quadrant I.
D) The solution to the equation is x = 2
Step-by-step explanation:
we have
[tex]f(x)= 2^x + 1[/tex]
[tex]g(x)= 5[/tex]
[tex]f(x)=g(x)[/tex]
we know that
The solution is the x-coordinate of the intersection point both graphs
using a graphing tool
The intersection point is [tex](2,5)[/tex]
therefore
The solution is [tex]x=2[/tex]
see the attached figure
Verify each statement
case A) The ordered pair that contains the solution to the equation lies in Quadrant II
The statement is False
The ordered pair that contains the solution to the equation lies in the first quadrant
case B)There are 2 solutions to the equation
The statement is False
The equation has only one solution
case C) The ordered pair that contains a solution to the equation lies in Quadrant I.
The statement is True (see the procedure)
case D) The solution to the equation is x = 2
The statement is True (see the procedure)
case E) The ordered pairs that contain the solutions to the equation lie in Quadrant I and II
The statement is False
The ordered pair that contain the solution to the equation lie in Quadrant I
consider the following graph of a linear function which equations have the same slope as the graph above select all that apply
Answers
Answer:
Step-by-step explanation:
which graph?
A fair number cube , labeled with digits 1 through 6, is rolled four times. What is the probability of rolling a 6 all four times?
Answers
Answer:
Step-by-step explanation:
chance of rolling a 6 once on a die: 1/6
1/6 * 1/6 * 1/6 * 1/6 = 1/(36^2)= 1/1296
plz help me with this
Answers
Answer:
1,887
Step-by-step explanation:
i added all the calories i believe it is the answer unless there are more steps
Tonya bought a sweater that cost $29.99 plus $1.60 tax. She used a coupon for $10 off. She paid the cashier $25. How much change should Tonya receive?
Answers
29.99 + 1.60 = 31.59
31.59 - 10 = 21.59
25 - 21.59 = 3.41
Tonya’s change she will receive will be $3.41
I hope this helps.
Tonya should receive $3.41 in change from the cashier after using a $10 coupon and paying $25.
Tonya's change:
Original total cost ,, = $29.99 + $1.60 = $31.59Total with the $10 coupon = $31.59 - $10 = $21.59Change received = $25 - $21.59 = $3.41Plz help me i need it
Answers
Answer: a) k(x) = 2ˣ
Step-by-step explanation:
[tex]g(x) = 3(2^x)\qquad h(x)=2^{x+1}\\\\k(x) = (g-h)(x)\\.\qquad =3(2^x)-2^{x+1}\\.\qquad =3(2^x)-2^x\cdot 2^1\\.\qquad =3(2^x)-2(2^x)\\.\qquad =1(2^x)\\.\qquad =\large\boxed{2^x}[/tex]
A scale drawing of a rectangular parking lot is shown. The width of the parking lot is smaller than the length. The width of the actual parking lot is 48 feet
Answers
Sorry, but is there a picture or anything to see the parking lot? Also what do you need?
Select the points you need to calculate the average rate of change from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet.
(0, 80)
(5, 40)
(10, 20)
(15, 10)
Answers
Answer:
EDGE 2020:
Step-by-step explanation:
It's A: (0,80) and D: (15,10)
The next part is B: -14,3
trust me
The points you need to calculate are the average rate of change from the beginning of the slide (0, 80) and (15, 10).Options A and D are correct.
What is the distance between the two points?The length of the line segment connecting two places is the distance between them. The distance between two places is always positive, and equal-length segments are referred to as congruent segments.
The given coordinate in the problem is;
(x₁,y₁)=(0, 80)
(x₂, y₂)=(15, 10)
The distance between the two points on the x-axis is found as;
d = 15 -0 feet
d = 15 feet
The points you need to calculate the average rate of change from the beginning of the slide to when the slide has covered a horizontal distance of 15 feet will be (0, 80) and (15, 10)
Hence, options A and D are correct.
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two carts have 22 bags of groceries between them. The larger one has 13 bags. How many bags are in the smaller one?
Answers
Answer:
9 bags
Step-by-step explanation:
22 - 13 = 9
Since there is two carts and we know that in one of them (bigger one) is 13 bags and that we know there is in sum of two 22 bags, we will need to subract sum of bags from two carts by bags from bigger cart to get amount of bags in small cart (in which one we finding that there will be 9 bags).
The smaller cart contains 9 bags.
How to find the number of bags in the smaller cart as given in the question ?It is given that two carts have 22 bags of groceries between them.
Also given that the larger one has 13 bags in it .
Therefore to find the bags in the smaller cart is =
(22 - 13) = 9 bags.
Therefore the smaller cart contains 9 bags.
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Name the following segment or point.
Given: L,M,N aw midpoints
Altitude to AB
Answers
Answer:
Segment CR.
Step-by-step explanation:
We have been given an image of a triangle. We are asked to find the segment that is altitude to segment AB.
We know that the altitude of triangle is the perpendicular drawn from a vertex of triangle to opposite side.
We can see that vertex opposite to segment AB is [tex]\angle ACB[/tex]. We can see that there are two lines drawn from vertex C that are segment CR and CN.
We have been given that points L, M and N are midpoints for our given triangle. We know that segment that is midpoint of triangle is known as median of triangle, therefore, CN is not a correct choice.
We can see that segment CR is perpendicular to segment AB, therefore, option B is the correct choice.
Answer: CR
hope this helps have a nice day
i need to answer and explain
Answers
Answer:
parallel
Step-by-step explanation:
Solve both equations for y to make it easier to compare them.
2x - 5y = 0 ↔ 5y = 2x, or y = (5/2)x.
y = (5/2)x - 3
Since the slopes are the same, the two lines are parallel.
If your in 6th grade and you got offered to go to algebra honors next year and do pre-algebra math over the summer would you do it?Please help me decide
Answers
Answer:
YESSSSSS
Step-by-step explanation:
i myself skipped pre-algebra and let me tell you it was the best decision ever. pre-algebra is by far the easiest and probably the most useless math course followed by geometry/trigonometry.
Yes
I would because it is a great opportunity to be ahead for when you get in 9th grade
Pls help meh and explain this:/
Answers
answer is b because you can see that it breaks the cycle
PLS HELP! FREE POINTS! I NEED THIS QUESTION ANSWERED AS QUICK AS POSSIBLE!
What is the simplest form of the ratio 40 : 16?
A. 20 : 8
B. 10 : 4
C. 5 : 4
D. 5 : 2
E. 10 : 8
Answers
The answer is D 5:2
4:16
10:4
5:2
All you have to-do is simplify the ratio until you get the lowest number. I divided 40 : 16 by 4 which gave me 10 : 4. I divided 10 : 4 by 2 which gave me the answer 5:2.