The chord and the diameter are perpendicular.
Suppose that chord AB is bisected by a diameter, which interserct the chord at point C.
Now, focus on triangles OAC and OBC. They have:
OA = OB because they are both radiiOC in commonAC=BC because the diameter bisects the chordSo, they are congruent. In particular, this means that angles ACO and BCO are equal. Since they sum up to 180, each of them must be 90°, so the diameter is perpendicular to the chord.
In a circle, if a diameter bisects a chord (that is not a diameter), then it must also be the perpendicular bisector of that chord.
What is a perpendicular bisector?A perpendicular bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.
If a diameter bisects a chord in a circle, then it must also be the perpendicular bisector of that chord. This is because the diameter is the longest possible chord in the circle, and it passes through the center of the circle, which is the point of concurrency for all the perpendicular bisectors of chords in the circle.
Therefore, it must also be the perpendicular bisector of that chord when the diameter bisects a chord.
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A similar scale model of the motorcycle shown stands 3 inches high and is 6 inches long. How high does the actual motorcycle stand?
Answer:
48 in.
Step-by-step explanation:
Scales are based on proportions. The proportion in this scenario is:
96/6 = x/3
Cross multiply. You are left with the equation:
96x3 = 6x
Simplify.
288 = 6x
288/6 = x
48 = x
Hope this helps :)
A model's scale ratio is the proportionate ratio of dimensions. The actual motorcycle stands at a height of 48 inches.
What is the scale ratio?A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.
The length of the motorcycle is 96 inches, while the length of the scale model of the motorcycle is 6 inches. Therefore, the scale ratio can be written as,
[tex]\rm Scale\ Ratio = \dfrac{\text{The actual length of the motorcycle}}{\text{The model length of the motorcycle}}\\\\Scale\ Ratio = \dfrac{96}{6} = 16[/tex]
Using the same ratio the height of the motorcycle can be written as,
[tex]\rm Scale\ Ratio = \dfrac{\text{Actual height of the motorcycle}}{\text{Model height of the motorcycle}}\\\\\\16=\dfrac{\text{Actual height of the motorcycle}}{3}\\\\\\{\text{Actual height of the motorcycle}} = 16 \times 3 = 48\ inches[/tex]
Hence, the actual motorcycle stands at a height of 48 inches.
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HELP! let f(x) = 7x - 4. what is f(6)
Answer:
the answer was 38 sorry
Step-by-step explanation:
Answer:
F(6) = 38
Step-by-step explanation:
F(x) = 7x - 4
Plug in 6 where x is
F(6) = 7(6) - 4
Multiply
F(6)= 42 -4
Subtract
F(6) = 38
Find the value of x. Give the answer in simplest radical form.
Answer:
X = 8√2.
Step-by-step explanation:
In a 45-45-90 triangle the ratio of the sides are x:x:√2 x.
So here, x = 8 and the side X = 8√2.
Would anyone please be able to help me??
Answer:
a. = 111 inches squared b.= 506 inches squared c.=143 inches squared
Step-by-step explanation:
a.
To find the area I broke the shape into two parts one where you multiply 7 and 9 to get the area and one where you multiply 12 and 4 to get the area. The first area is 63 and the second is 48 and together the entire area is 111 inches squared
b.
To find the area here you do the same thing as a. you break the shape into two parts a part where you multiply 29 and 14 and a part where you multiply 20 and 5. In all you get 506 inches squared.
c.
I this problem you find the area of the triangle and the rectangle.The formula of the triangle is b times h times 1/2 in this case. 6 times 13 times 1/2 which is 39. the area of the rectangle is 8 times 13 = 104. So the total area is 143
Sorry i took so long I had to do something
Write 3.01 as a mixed number in simplest form
Answer:
3 1/100
Step-by-step explanation:
That is just the answer
Answer:
3 1/100
Step-by-step explanation:hope this helps god bless
The number of hours of TV watched each week by 8 seventh grade students is shown below.
11, 7, 9, 3, 3, 8, 10, 5
a. What is the mean number of hours of TV watching?
b. Mean absolute deviation =
c. Explain the meaning of the mean absolute deviation as it relates to the number of hours of TV watched.
Answer:
(a)Mean=7 Hours
(b)Mean Absolute Deviation=2.5 Hours
Step-by-step explanation:
Given the number of hours of TV watched each week by 8 seventh grade students shown below.
11, 7, 9, 3, 3, 8, 10, 5
(a)Mean
[tex]Mean=\dfrac{\text{Addition of all the terms}}{\text{Number of Terms}} \\=\dfrac{11+7+9+3+3+8+10+5}{8} \\=\dfrac{56}{8} \\$Mean Number of Hours=7[/tex]
(b)Mean absolute deviation
[tex]M.A.D=\dfrac{|11-7|+|7-7|+|9-7|+|3-7|+|3-7|+|8-7|+|10-7|+|5-7|}{8} \\=\dfrac{4+0+2+4+4+1+3+2}{8} \\=\dfrac{20}{8}\\$Mean Absolute Deviation=2.5 Hours[/tex](c)The Mean Absolute Deviation tells us how far, on average, all values are from the mean. The Mean absolute deviation of 2.5 Hours tells us that each hour is on the average far from the mean number of hours by 2.5 Hours.
Which is the most efficient way to solve this equation?
x−57=135
A. Do nothing because the equation is already solved.
B. Subtract 135 from both sides of the equation so all terms will be on the same side of the equal sign.
C. Subtract 57 from 135 because x equals 78.
D. Add 57 to both sides of the equation because addition is the inverse operation of subtraction.
Answer: The Answer is D.
Step-by-step explanation: You are trying to get x by itself, and in order to do that, you need to get the 57 away from it. In order to do THAT, you need to do the opposite of what s already being done. Since your already subtracting it, in order to get it away from x, you need to add it to itself, and then add it to the other side, because what you do to one side, you do to one side, you must do to the other.
You start at (7,0). You move up 1 unit.
Consider this system of equations. Which equation represents the first equation written in slope-intercept form?
5 x minus 2 y = 10. y = one-fourth x + 1.
y = five-halves x minus 5
y = five-halves x + 10
y = negative five-halves x + 10
y = negative 5 x minus 5
Answer:
y= 5/2x - 5
Step-by-step explanation:
5x - 2y = 10
-5x -5x (Subtract both sides by 5x to leave y by itself)
-2y = -5x + 10
-2y/-2 = -5/-2 + 10/-2
(Divide both sides by -2 to leave y with no coefficient. -5/-2 = 5/2 because there are two negatives. 10/-2 = -5.
y = 5/2 - 5
Answer:
A
Step-by-step explanation: i think tell me if im wrong
A circle with area 9π has a sector with a central angle of 17π/9 radians. What is the area of the sector?
Answer:
8.5pi
Step-by-step explanation:
We can solve this problem with a rule of three.
The area of the whole circle is represented by a sector with central angle of 2*pi. So, if we want to find the area of a sector that has a central angle of 17pi/9, we can use the following logic:
sector of 2pi -> area equal to 9pi
sector of 17pi/9 -> area equal to X
2pi / (17pi/9) = 9pi / X
18 / 17 = 9pi / X
X = 17 * 9pi / 18 = 17pi / 2 = 8.5pi
x² - x - 6
x - 3
Perform the division
Answer:
x+2 is answer by division
Which expression is equivalent to 36+12m?
Answer:
The second one
Step-by-step explanation:
Answer:
12(3+m)
Step-by-step explanation:
36 + 12m
Factor out 12
12*3 + 12*m
12(3+m)
13. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (u, P, o) for the indicated
parameter.
A psychologist claims that more than 4.1% of the population suffers from professional problems due to extreme shyness. Use P, the true percentage
of the population that suffers from extreme shyness.
OHo:p> 4.1%
Hips 4.1%
OHo: P = 4.1%
H:p> 4.1%
OHo: p < 4.1%
Hip 24.1%
OHo: P = 4.1%
Hip < 4.1%
Answer:
Null Hypothesis, [tex]H_0[/tex] : P = 4.1%
Alternate Hypothesis, [tex]H_A[/tex] : P > 4.1%
Step-by-step explanation:
We are given that a psychologist claims that more than 4.1% of the population suffers from professional problems due to extreme shyness.
Let p = true percentage of the population that suffers from extreme shyness.
So, Null Hypothesis, [tex]H_0[/tex] : P = 4.1%
Alternate Hypothesis, [tex]H_A[/tex] : P > 4.1%
Here, null hypothesis states that % of the population who suffers from professional problems due to extreme shyness is equal to 4.1%.
On the other hand, alternate hypothesis states that more than 4.1% of the population suffers from professional problems due to extreme shyness.
So, the above hypothesis would be appropriate for conducting the test.
4. Find the lateral and total surface area of
the prism.
What single transformation was applied to quadrilateral A to get to quadrilateral B
a.)translation
b.)rotation
c.) reflection
d.) Dilation
Answer:
B. a rotation
Step-by-step explanation:
The shape appears to have the same size, but it has been moved in a way that is not reflection. Through the process of elimination, the answer is rotation.
Answer:
D.) dilation
Step-by-step explanation:
Rolling a number less than 6 on a number cube labeled 1 through 6
Answer:
Any number from 1-5
Step-by-step explanation:
Less than 6!
What is 220kg increased by 12.5%
Answer:
247.5
Step-by-step explanation:
220 + (12.5% × 220)
220 + 12.5% × 220
(1 + 12.5%) × 220
(100% + 12.5%) × 220
112.5% × 220
112.5 ÷ 100 × 220
112.5 × 220 ÷ 100
24,750 ÷ 100 = 247.5
The average not chocolate solo per nour auring Juanas Shirt was
The coffee shop where Juana works makes a profit of $312.50 for every 250 hot chocolates sold. How much
profit do they make on each hot chocolate sold?
Answer:
1.25
Step-by-step explanation:
Find the area of the circle. Round to the nearest tenth.
Answer:
28.27
Step-by-step explanation:
Area= pi x radius squared
Radius is 1/2 the diameter which in this case is 6 ft
So, pi x 3 squared (9)
= 28.27
Answer:
28.3
Step-by-step explanation:
Hello!
To find the area of a circle we use πr².
In this case, all we have to do is divide 6 by 2 and square that.
6 ÷ 2 = 3. 3² = 9.
9 × π = 28.2743....
Rounding to the nearest tenth:
28.3
Thus, the area of the circle is [tex]\boxed{28.3}[/tex].
Hope this helps!
Multiply. Express your answer in simplest form. 1 7/8 x 2 1/3
Answer:
4 3/8
Step-by-step explanation:
8 × 1 + 7 = 15/8
3 × 2 + 1 = 7/3
Now, we'll multiply both numerator and denominators.
(numerators) 15 × 7 = 105
(denominators) 8 × 3 = 24
= 105/24
Now, we'll find the simplest form of 105/24
= 4 3/8
The pyramids have always fascinated Kristina, so she wants to build two model pyramids to put on her mantel. She wants her model of Khufu’s pyramid to have a volume of 73.5 cubic inches and a height of 4.5 inches. What would the side length of the base of the pyramid be? Is this number rational or irrational? Why?
Answer:
Side length = 7 inches
This number is a rational number, because it is a whole number and it can be represented as a fraction (7 = 14/2 for example)
Step-by-step explanation:
The volume of the pyramid can be calculated as:
V = (1/3)*A*h
Where V is the volume, A is the area of the base and h is the height.
If the volume is 73.5 in3 and the height is 4.5 in, we can find the area of the base:
73.5 = (1/3)*A*4.5
A = 73.5*3/4.5 = 49 in2
As the pyramid have a square base, we can calculate the side length of the base:
A = L*L (L = length)
49 = L^2
L = 7 inches
This number is a rational number, because it is a whole number and it can be represented as a fraction (7 = 14/2 for example)
Answer:
7 rational a rational number is a whole number
Step-by-step explanation:
11. Dominika wykonała dwa pudełka z przykrywkami: jedno w kształcie prostopadłościanu, a drugie w kształcie sześcianu. Do łączenia ścian użyła nici. Na które pudełko zużyła więcej kartonu.
Dam naj, 5gwiazdek i dziękujke.
Answer:
I pudełko:
a=15cm
b=20cm
H=10cm
P=2*a*b+2*a*H+2*b*H
P=2*15cm*20cm+2*15cm*10cm+2*20cm*10cm
P=600cm2+300cm2+400cm2
P=1300cm2
II pudełko:
a=15cm
P=6*a*a
P=6*15cm*15cm
P=1350cm2
1350cm2-1300cm2=50cm
Na drugie pudełko zużyła więcej kartonu
Step-by-step explanation:
An angle measures 30 degrees.
What is the measure of its complement (i.e., the complementary angle)?
The measure of the complimentary angle is 60 degrees.
Complimentary angle:The complimentary angle is the angle where the sum of angles should be 90 degrees
Since An angle measures 30 degrees.
So, the measure of an angle should be
= Sum of angles - one measurement of angle
= 90 - 30
= 60 degrees
Therefore we can conclude that The measure of the complimentary angle is 60 degrees.
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Find the degree of the monomial -4/9
Answer:
Step-by-step explanation: the degree is 0
Final answer:
The degree of the monomial -4/9 is 0 since it contains no variables and can be considered to have variables with an exponent of 0.
Explanation:
The degree of a monomial is the sum of the exponents of all its variables. In the case of the monomial -4/9, there are no variables present, which means that the degree is 0. This is because the monomial can be considered to have variables raised to the power of 0, and any number (except zero) raised to the power of 0 is 1, which does not affect the value of the coefficient (-4/9).
How does the value of log 100 compare with the value of log 20?
The value of log 100 is about 4 times the value of loge 20
The value of log2100 is about 7 times the value of loge 20
The value of log2100 is about 3 times the value of log 20
O
The value of log2100 is about 3 times the value of loge 20
Answer:
option A
Step-by-step explanation:
log_2(100)
we can simplify it
we can use base change formula
log_2 (100)=\frac{ln\left(100\right)}{ln\left(2\right)}
log_2 (100)=6.643856
Second value is :
log_6(20)
we can simplify it
we can use base change formula
log_6(20)=\frac{ln\left(20\right)}{ln\left(6\right)}
log_6(20)=1.67195
so, we know that
6.6438 is almost 4 times of 1.67195
The value of log₂ (100) is about 4 times the value of log₆(20). The correct answer would be an option (A).
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
According to the problem, we will use some of the basic logarithmic properties,
The logarithms expression is given, as follows:
log₂(100)
It can use the base change formula,
log₂ (100) = ln (100) / ln (2)
log₂ (100) = 6.643856
The second value is :
log₆(20)
It can use the base change formula
log₆(20) = ln (20) / ln (6)
log₆(20) = 1.67195
Since 6.6438 is almost 4 times 1.67195
Hence, the correct answer would be option (A).
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Solve using substitution. x + 2y = 4 and –4x − 7y = –9
Step-by-step explanation:
Given
x + 2y = 4
x = 4 - 2y.......... equation 1
-4x -7y = - 9.......equation 2
Putting equation 1 in equation 2
- 4 ( 4 - 2y) - 7y = - 9
-16 + 8y - 7y = -9
y = - 9 + 16
y = 7
Now
x = 4 - 2* 7 = 8 - 7 = 1
hope this helps.
Answer:
X=-10 y=7
Step-by-step explanation:
1) in first equation subtract 2y on both sides
X=4-2y
Substitute as "x" in the second equation:
-4(4-2y)-7y=-9
-16+8y-7y=-9
-16+y=-9
Y=7
Substitute y as 7 to get x)
X=4-2(7)
X=4-14
X=-10
Hope this helps
In the graph below, find the coordinate of the image point. O is the origin and P is the point (4,3). Ry and Ry are
reflections around the x- and y-axes.
R p,90 • R o, -90 : (-1,1) ->
A.) (-7, 9)
B.) (-1, -1)
C.) (6, -2)
(See image for graph)
The coordinate of the point is (-1,-1).
The answer is option B) (-1, -1).
How do you find a coordinate on a graph?To identify the x-coordinate of a point on a graph, read the number on the x-axis directly above or below the point. To identify the y-coordinate of a point, read the number on the y-axis directly to the left or right of the point. Remember, to write the ordered pair using the correct order (x,y).
What is graph coordination?An ordered pair (x, y) represents a position of a point on a coordinate graph, where x is the number on the x-axis that the point lines up with and y is the number on the y-axis that the point lines up with. The numbers x and y in the ordered pair (x, y) are called coordinates.
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If both coordinates of a point are positive, in which quadrant is that point located?
A) I
B) II
C) III
D) IV
Answer:
A
Step-by-step explanation:
Both points are positive in the 1st quadrant.
Answer:
A. l
Step-by-step explanation:
Both coordinates are in quadrant 1 because both x and y in quadrant 1 must be positive.
Find the slant height of the pyramid shown.
Answer:
B is the correct answer ( square root of ten)
Step-by-step explanation:
I just did it and got it right
The slant-height of the pyramid having perpendicular height as 3 units, base as 1 unit is : (b) √10.
A Pyramid is a three-dimensional geometric shape with a polygonal base and triangular faces that meet at a single point called the apex. The base can be any polygon, and the number of sides of the base determines the type of pyramid (e.g., a square base yields a square pyramid)
The "Slant-Height" of the given pyramid can be calculated by using Pythagoras-Theorem, which states that; (slant-height)² = (perpendicular)² + (base)²;
Substituting Perpendicular height as 3 units, base as 1 unit, and slant-height as "x";
We get,
⇒ 3² + 1² = x²,
⇒ x² = 9 + 1,
⇒ x² = 10,
⇒ x = √10,
Therefore, the slant-height is √10, option (b) is correct.
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Which is greater .13 or .3
Answer:
.3 is greater.
Step-by-step explanation:
.13
.3 or .30
These are the same, and obviously .30 is larger than .13.
Answer:
.3 is greater cause it is also read as .30