15. What is the relationship between angle a , angle b and angle c?
H
Answers
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles.
figure51
Vertical angles are always congruent, which means that they are equal.
Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap.
figure52
The size of the angle xzy in the picture above is the sum of the angles A and B.
Two angles are said to be complementary when the sum of the two angles is 90°.
figure53
Two angles are said to be supplementary when the sum of the two angles is 180°.
figure54
If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is called a transversal
When a transversal intersects with two parallel lines eight angles are produced.
figure55
The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.
Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles.
Angles that are on the opposite sides of the transversal are called alternate angles e.g. 1 + 8.
All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.
Example
figure56
The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?
6 and 8 are vertical angles and are thus congruent which means angle 8 is also 65°.
6 and 2 are corresponding angles and are thus congruent which means angle 2 is 65°.
6 and 4 are alternate exterior angles and thus congruent which means angle 4 is 65°.
Related Questions
There are 20 students in a class. Everyone in the class scored 6 out of 10
in a test. What is the range of their scores?
Answers
Answer: 0
Step-by-step explanation:
Range = Highest number - lowest number
range = 6 - 6
range = 0
0.16 divided by 6.08 helpp me pls I need to show my work on this one
Answers
This I believe would be in terms of long division, correct? If so, follow the steps below to guide you through the process.
___________________________________________________
First, you must multiply both the numerator and denominator by 100.
\(\frac{6.08}{0.16}\)
\(\frac{608}{16}\)
Next, convert the problem into long division format and solve.
__38
16| 608
\(\frac{48}{128}\) \(\frac{128}{0}\)Hence, the solution for Long Division of 6.08/0.16 would be 38.
Hope this helps! Please lmk if it does. Good luck!
what is the probability, to the nearest hundredth, that a point chosen randomly inside the rectangle is in the triangle?
Answers
The probability that a point chosen randomly inside the rectangle is in the triangle is 1/3, or approximately 0.33 to the nearest hundredth.
The probability that a point chosen randomly inside the rectangle is in the triangle is equal to the area of the triangle divided by the area of the rectangle.
To find the area of the triangle, we need to first find its base and height. The base of the triangle is the length of the rectangle, which is 8 units. To find the height, we need to draw a perpendicular line from the top of the rectangle to the base of the triangle. This line has a length of 4 units. Therefore, the area of the triangle is (1/2) x base x height = (1/2) x 8 x 4 = 16 square units.
The area of the rectangle is simply the length times the width, which is 8 x 6 = 48 square units.
Therefore, the probability that a point chosen randomly inside the rectangle is in the triangle is 16/48, which simplifies to 1/3.
In conclusion, the probability that a point chosen randomly inside the rectangle is in the triangle is 1/3, or approximately 0.33 to the nearest hundredth.
To know more about probability visit:
brainly.com/question/31828911
#SPJ11
Salama makes fruit baskets with oranges and bananas.
She uses between 8 and 16 oranges and bananas in a ratio of 3 oranges to 2 bananas.
Answers
Answer: 9 oranges: bananas
Step-by-step explanation:
The ratio is 3 oranges: 2 bananas. They add up to 5 fruits, so some possible values are 5, 10, 15, 20, 25. We need a value between 8 and 16. This means that we need 15/5 = 3 portions of fruits and since the ratio is 3:2
We multiply this by the original ratio to get 9 oranges: 6 bananas
Answer:
6:4
Step-by-step explanation:
3+2=5, but 5 is not enough so we multiply 3 and 2 to make 6 and 4. Now 6+4= 10 which is between 8 and 16 as we need. So the answer is 6:4
Solve for the value of s.
(s+1)°
(2S-1)°
Answers
Answer
90*
Step-by-step explanation:
Answer:
s = 30
Step-by-step explanation:
The three angles lie on a line.
The sum of angles on a line are supplementary, meaning they add up to 180 degrees.
s + 1 + 90 + 2s - 1 = 1803s = 90s = 30I need to know where to place the dot
Answers
Answer:
in your but
Step-by-step explanation:
nah jk its 3,-3
Tom borrowed $8,000 for 4 years to make improvements on his home. if he repaid a total of 10,320, what interest rate did he borrow the money at?
Answers
Tom borrowed the money at an interest rate of 29%. This is calculated by dividing the interest paid ($2,320) by the loan amount ($8,000). The calculation assumes simple interest and does not consider compounding or additional fees.
To find the interest rate, we need to consider the total amount repaid and the original loan amount. The difference between the total amount repaid and the loan amount represents the interest paid. In this case, the interest paid is $10,320 - $8,000 = $2,320.
Next, we divide the interest paid by the loan amount to determine the interest rate. In this scenario, $2,320 divided by $8,000 equals approximately 0.29, or 29% when expressed as a percentage. Therefore, Tom borrowed the money at an interest rate of 29%.
By calculating the interest paid relative to the loan amount, we can determine the interest rate at which Tom borrowed the money. It's essential to note that this calculation assumes a simple interest calculation and does not account for compounding interest or any additional fees that may be associated with the loan.
Learn more about interest here:
https://brainly.com/question/30706630
#SPJ11
Calculate.
\(\sqrt{(-4.5)^{4}}\)
Answers
Answer:
Step-by-step explanation:
\(\sqrt{(-4.5)^{4}}=\sqrt{(-4.5)*(-4.5)*(-4.5)*(-4.5)}\\\\= (-4.5) * (-4.5)\\\\= 20.25\)
which of these sentences contains an example of hyperbole?
Answers
Answer:
choose the most exagerrated one
Step-by-step explanation:
hyporbole is really exageratted really wild, not to ne taken literally
"I could eat a horse!"
Answer: The room was almost as hot as an oven.
Step-by-step explanation:
A line is drawn on a coordinate grid by the equation y = 1. Which of the following lines would represent a row perpendicular to it?
A. a line containing the point (5,2)
B. y = 1
C. x = 4
D. y = 3
Answers
Answer:
C
Step-by-step explanation:
In the Cartesian coordinate system, a line perpendicular to the line that's across the Y axis is a row across the X axis. You see Y=1 is the line across Y axis, so we need a row that's across the X axis. So C. X=4 is the ideal choice.
If a line is drawn on a coordinate grid by the equation y = 1 then x=4 would represent a row perpendicular to it.
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
A line is drawn on a coordinate grid by the equation y = 1.
The equation y = 1 represents a horizontal line on the coordinate grid, passing through all the points where y-coordinate is 1.
A line that is perpendicular to a horizontal line is a vertical line.
The vertical line x = 4 passes through all the points where x-coordinate is 4, and is perpendicular to the horizontal line y = 1.
Hence, if a line is drawn on a coordinate grid by the equation y = 1 then x=4 would represent a row perpendicular to it.
To learn more on Coordinate Geometry click:
brainly.com/question/27326241
#SPJ2
PLEASE HELP! 5TH GRADE MATH! Select the best estimate of the product of Select the best estimate of the product of 52 x 89 = ____
Answers
Answer:
400
Step-by-step explanation:
50x80=400, you just ignore the ones digits so its easy to solve. (5x8x100)
how will the z-scores compare if you use your height in inches verses centimeters?
Answers
The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.
The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.
The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.
Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.
Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.
To know more about z-scores, here
https://brainly.com/question/15016913
#SPJ4
Suppose T: V → W is a linear transformation. Let n = dim V m = dim W and r = rank(T).
(a) (3pts) If T is one-to-one, what is the relationship between m, n, and r?
(b) (3pts) If T maps V onto W, what can you say about m, n, and r?
(c) (2pts) If T is one-to-one and maps onto W, what can you say about m, n, and r?
(d) (2pts) If T is not one-to-one and does not map onto W, what can you say about m, n, and r?
Answers
(a) If T is one-to-one, it means that every vector in V is mapped to a distinct vector in W. In this case, the rank of T, denoted as r, is equal to the dimension of V, denoted as n. Therefore, the relationship between m, n, and r is that m = r = n. The dimension of W, denoted as m, is not directly related to the one-to-one property of T.
(b) If T maps V onto W, it means that every vector in W is the image of at least one vector in V. In this case, the rank of T, denoted as r, is equal to the dimension of W, denoted as m. Therefore, the relationship between m, n, and r is that r = m. The dimension of V, denoted as n, is not directly related to the onto property of T.
(c) If T is both one-to-one and maps onto W, it means that T is a bijective linear transformation or an isomorphism. In this case, every vector in V is uniquely mapped to a vector in W, and every vector in W has a pre-image in V. Therefore, m = n = r, and the dimensions of V, W, and the rank of T are all equal.
(d) If T is not one-to-one, it means that there exist vectors in V that are mapped to the same vector in W. If T does not map onto W, it means that there are vectors in W that do not have a pre-image in V. In this case, the rank of T, denoted as r, will be less than the dimension of W, denoted as m. The relationship between m, n, and r is that m ≥ r and n ≥ r, but m and n can be larger than r since there may be more dimensions in V and W that are not utilized by T.
To know more about vector refer here
https://brainly.com/question/29740341#
#SPJ11
help please ill give you thanks 5stars and Brainliest
Answers
Use differentials to estimate the amount of metal in an open top rectangular box that is 12 cm long, 8 cm wide, and 10 cm high inside the box if the metal on the bottom and in the 4 sides is 0.1 cm thick.
59.2 cm³
192 cm³
96 cm³
29.6 cm³
49.6 cm³
Answers
Among the given answer choices, the closest approximation to 57.6 cm³ is 59.2 cm³.
To estimate the amount of metal in the box, we need to calculate the volume of the metal used for the bottom and the four sides of the box.
The metal on the bottom of the box is a rectangle with dimensions 12 cm long and 8 cm wide. Since the metal is 0.1 cm thick, the volume of the metal for the bottom is approximately (12 cm) * (8 cm) * (0.1 cm) = 9.6 cm³.
The metal on the four sides of the box can be thought of as a rectangular prism with dimensions 12 cm long, 10 cm high, and 0.1 cm thick. The volume of the metal for each side is approximately (12 cm) * (10 cm) * (0.1 cm) = 12 cm³. Since there are four sides, the total volume of the metal for the four sides is 4 * 12 cm³ = 48 cm³.
the estimated amount of metal in the box is the sum of the volume of the metal for the bottom and the four sides: 9.6 cm³ + 48 cm³ = 57.6 cm³.
To know more about volume visit;
brainly.com/question/28058531
#SPJ11
The measure of an angle is 63.9 what is the measure of its supplementary angle?
Answers
Answer:
116°10"
Step-by-step explanation:
180°-63.9°=179°60"-63°50"=116°10"
Al vender una refrigeradora, gané s/. 580. Si después de la venta gasté s/. 1 260 y me queda s/. 480, ¿Cuánto costó la refrigeradora?
Answers
Answer:
english plz
Step-by-step explanation:
For a process in control, we expect % of the points on a process control chart to fall within the UCL and the LCL. would like to Show Work for this question: Open Show Work 0.27 95 99.73 100
Answers
We expect approximately 99.43% of the points to fall within the UCL and LCL on the process control chart.
Find out the percentage of points expected to fall on (UCL) and (LCL)?To determine the percentage of points expected to fall within the Upper Control Limit (UCL) and Lower Control Limit (LCL) on a process control chart, we can use the concept of the Normal Distribution.
Assuming the process follows a normal distribution, we can refer to the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of data falling within certain ranges.
According to the empirical rule:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Given that the process is in control and using the empirical rule, we can calculate the percentage of points falling within the UCL and LCL.
Let's assume the UCL is 100 and the LCL is 0.27. We'll calculate the percentage of points between the LCL and UCL.
Step 1: Calculate the mean (μ) of the process.
The mean of the process is the midpoint between the UCL and LCL.
μ = (UCL + LCL) / 2
μ = (100 + 0.27) / 2
μ = 50.135
Step 2: Calculate the standard deviation (σ) of the process.
The standard deviation can be estimated using the range divided by the control chart constant (typically 3 for a 3-sigma control chart).
σ = (UCL - LCL) / (3 * control chart constant)
σ = (100 - 0.27) / (3 * 3)
σ ≈ 33.243
Step 3: Calculate the percentage of points falling between the LCL and UCL.
We'll calculate the percentage of points within three standard deviations of the mean (μ ± 3σ) since the process is in control.
Percentage = (99.7% - 0.27%) * 100
Percentage ≈ 99.43%
Learn more about Percentages
brainly.com/question/32040800
#SPJ11
Find each angle or arc measure
Answers
Answer:
17
Step-by-step explanation:
34/2 because the measure of the arc is half of what it would normally be because it touched the other side
Write down the roots of x(squared)-4x-5=0
Answers
What is n?
The answer format is
n=
Answers
Answer:
n=3
Step-by-step explanation:
q² × q^n = q^5
q^(2+n) = q^5
=> 2+n=5
n = 5-2
n=3
CAN SOMEONE PLEASEEEE HELP/EXPLAIN THIS ASAP !!!
Answers
Answer:
5th figure is not symmetrical
comment if doubt
HELP DOES ANYONE KNOW HOW TO DO THIS?
Answers
Answer:
im pretty positive its exponential
Step-by-step explanation:
Answer:
Linear a good app to do this work is Desmos graph the pairs to see if they are straight
Jose is looking up at a flagpole.
• He is standing 40 ft from the flagpole. • He can see the top of the pole at a 35 degree angle of elevation
• His eyes are 5 ft from the ground.
What is the total height of the flagpole? Round to the nearest tenth of a unit if necessary.
(trigonometry)
Answers
The total height of the flagpole on the basis on the information given that Jose is standing at a distance of 40 ft from flagpole, angle of elevation is 35° from his eyes which are at height of Jose is 5 ft is 33 ft with the help of trigonometric-ratios.
What are trigonometric-ratios?
Greek is the language of measurement, and the word "metric" is Greek for triangle. The trigonometric ratios are particular measures of a right triangle, which is a triangle having a 90° angle. The legs are the two sides of a right triangle that are linked at the right angle, while the hypotenuse is the third longest side.Trigonometric ratios are the ratios of the sides of a right triangle. The sine, cosine, tangent, secant, cosecant, and cot are six trigonometric ratios.
Consider the ΔECD,
AB=EC=40 ft
∠E=35°
EA=BC=5ft
tan A =\(\frac{side opposite to the angle}{side adjacent to the angle\\}\)
tan 35=\(\frac{CD}{EC}\)
0.7002=\(\frac{CD}{40}\)
CD= 0.7002 x 40
CD=28.008
CD≈28 ft
Total height of flagpost=BD
BD=BC+CD
BD=EA+CD
BD=5+28
height of falgpole=33 ft
To know more about trigonometric-ratios , visit:
https://brainly.com/question/25122825
#SPJ1
write v as a linear combination of u1, u2, and u3, if possible. (if not possible, enter impossible.) v = (14, −13, 5, 3), u1 = (3, −1, 3, 3), u2 = (−2, 3, 1, 3), u3 = (0, −1, −1, −1) v = u1 u2 u3
Answers
v = u1, u2, u3. This can be answered by the concept of Matrix.
To determine if v can be written as a linear combination of u1, u2, and u3, we need to check if the system of equations:
a u1 + b u2 + c u3 = v
has a solution for the unknowns a, b, and c.
Setting up the augmented matrix and performing row operations, we get:
[3 -2 0 14 | a]
[-1 3 -1 -13 | b]
[3 1 -1 5 | c]
[3 3 -1 3 | v]
R2 + R1 -> R2:
[3 -2 0 14 | a]
[2 1 -1 1 | b + a]
[3 1 -1 5 | c]
[3 3 -1 3 | v]
R3 - R1 -> R3:
[3 -2 0 14 | a]
[2 1 -1 1 | b + a]
[0 3 -1 -9 | c - a]
[3 3 -1 3 | v]
R4 - R1 -> R4:
[3 -2 0 14 | a]
[2 1 -1 1 | b + a]
[0 3 -1 -9 | c - a]
[0 5 -1 -11 | v - a]
R4 - (5/3)R2 -> R4:
[3 -2 0 14 | a]
[2 1 -1 1 | b + a]
[0 3 -1 -9 | c - a]
[0 0 -2/3 -2/3 | v - (5/3)b - (1/3)a]
The last row represents the equation:
-(2/3)c + (2/3)a + (5/3)b = v4
where v4 is the fourth component of v. Since the coefficient of c is non-zero, we can solve for c:
c = (2/3)a + (5/3)b - (3/2)v4
This means that v can be written as a linear combination of u1, u2, and u3:
v = a u1 + b u2 + ((2/3)a + (5/3)b - (3/2)v4) u3
Therefore, v = u1, u2, u3.
To learn more about Matrix here:
brainly.com/question/28180105#
#SPJ11
2. The admission fee at a small fair is $1.50 for children and $4 for adults.
On a certain day, 220 people enter the fair and $505 is collected. How
many children attended the fair that day?
Answers
Answer:
26 children
Step-by-step explanation:
Step 1 Create a system of equations
Firstly, we know that it cost $1.50 for children and $4 for adults and we know that 505$ is the total amount collected
So if x = number of children and y = number of adults
Then 1.50x + 4x = 505
We also know that 220 total people entered which consists of adults and children.
Again, if x = number of children and y = number of adults
Then we can say that x + y = 220
So we now have the two equations
1.50x + 4y = 505 and x + y = 220
Step 2 Solve the equation
There are many methods you can use to solve this equation however I'd recommend the substitution method as we can easily solve for x or y in the equation x + y = 220 and isolate one of the variables, we can then easily substitute that into the other equation.
Isolating y
x + y = 220
==> subtract x from both sides
y = 220 - x
We now substitute y into the other equation and solve for x(# of children)
1.5x + 4y = 505
==> plug in y = 220 - x
1.5x + 4(220 - x) = 505
==> distribute 4
1.5x + 440 - 4x = 505
==> combine like terms
-2.5x + 440 = 505
==> subtract 440 from both sides
-2.5x = -65
==> divide both sides by -2.5
x = 26
So 26 children attended the fair that day.
Which expression is equivalent to log 20 + 2 log x - log y ? a) log(20x^2y) b) log(10x/y) c) log(20/x^2 y) d) log(20x^2 /y)
Answers
OPTION D
log(20x²/y)
is the correct answer
the answer is D!
Step-by-step explanation:
hope it helped!have a nice day!!!
Find the derivative of the function. B(t) = 8 + 8e-8t B'(t) 64e-8t x
Answers
We get: B'(t) × 64e^(-8t) × x = -64x . This can be answered by the concept of Differentiation.
The function B(t) is given as B(t) = 8 + 8e^(-8t). We are required to find the derivative of B(t), denoted as B'(t), and then use it to find B'(t) when multiplied by 64e^(-8t) and x.
To find B'(t), we need to use the chain rule of differentiation. Let u = -8t, then we have B(t) = 8 + 8e^(u). Using the chain rule, we get:
B'(t) = d/dt [8 + 8e^(u)] = d/dt [8] + d/dt [8e^(u)] = 0 + 8e^(u) × d/dt [u]
Now, d/dt [u] = d/dt [-8t] = -8, since the derivative of a constant multiple of a variable is the constant itself. Thus, we have:
B'(t) = 8e^(u) × (-8) = -64e^(-8t)
Finally, multiplying B'(t) by 64e^(-8t) and x, we get:
B'(t) × 64e^(-8t) × x = -64x
To learn more about Differentiation here:
brainly.com/question/24898810#
#SPJ11
for khan academy math please answer, thank you!
Answers
Answer:
7pi/theta = radius
Step-by-step explanation:
So we are using the arc length, central angle(in radians), and radius.
We know arc length, which is 7pi.
We don't know theta, which does not matter.
And finally, we don;t know radius, which is what we are looking for.
To find radius, we use:
arc length/theta=radius
Lets plug in our values:
7pi/theta=radius.
So the answer to the khan acadamy question is
7pi/∅
Here are some othr things that may help:
Radian * Radius = arc length
This solves for arc length
Here is another one:
Arc length/radius= radian
This solves for radians
Hope these help! :)
Find the solution(s) to (x- 3) = 49. Check all that apply.
OA X=-10
B. Xx=-4
C. x-7
OD. X=-7
OE. X= 10
Answers
Answer:
B.x= -4 and E. x= 10 are the answers