line bd is tangent to a circle with diameter ab. explain why the measure of angle bca must equal the measure of angle abd.
Answers
The measures of the angles BCA and ABD are equal because they are both right angles.
The line segment BD is a tangent to the circle with diameter AB. We need to find out the reason why the measure of angle BCA must be equal to the measure of angle ABD. The diagram is attached below.
Since AB is the diameter of the circle, it makes an angle equal to 180 degrees at the center of the circle. So the measure of the angle BCA is half of the angle produced by the diameter.
∠BCA = (1/2)×180° = 90°
Since the line BD is tangent to the circle, it will be perpendicular to the diameter. Hence, the angle formed by the diameter and the tangent must be the right angle.
∠ABD = 90°
Hence, both the angles are equal to each other.
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Related Questions
PLS HELP !! ITS DUE tommorow!!
Answers
In the given square, the values of f and g are equal that is 4√3cm.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.So, the values of f and g are:
From the given diagram we know that ABCD is a square.So, all sides are the same.The area of ABCD is 48cm².
Now, calculate for sides as follows:The formula for the area of the square: A = s²Then,
A = s²48 = s²s = √48s = √2×2×2×2×3s = 2×2√3s = 4√3Since f and g are 2 sides of the square, their values are 4√3cm.
Therefore, in the given square, the values of f and g are equal that is 4√3cm.
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Colin buys a car for £45500. It depreciates at a rate of 6% per year. How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
The answer is 33,710 euros.
Step-by-step explanation:
Start by multiplying 45,550 by 6%. This will give 2,730. over the next three years the price decreases, so multiply 2,730 by 3, which is 8,190. Finally, subtract 45,550 by 8,190 to get 33,710.
In the triangle below, with right angle G, suppose that m/F= (3x-14)° and mZH=(5x-16)°.
Find the degree measure of each angle in the triangle.
Answers
The degree measure of each angle in the triangle is
∠H = 59°
∠F = 39°
Angle sum property of triangle says that sum of all the triangle is always equal to 180°
∠G is given to us as 90°
So by applying the property we an say that
90 + (3x - 14) + (5x - 16) = 180
8x = 180 - 90 + 14 + 16
8x = 120
x = 15
∠H = 5x - 16
∠H = 5*15 - 16
∠H = 75 - 16
∠H = 59°
∠F = 3x - 14
∠F = 3*15 - 14
∠F = 45 - 14
∠F = 39°
Therefore ∠H = 59° and ∠F = 39°
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its easy but im lazy please helppppp
Answers
y=1/58x
because in 3 hours its 174 miles.
let y=miles
x=time
so 174y=3x
divide by 3 on both sides
58y=x
isolate y by dividing by 58 on both sides
therefore you get the answer
There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.
a. Find the percentage of marbles that are not blue.
b. Find the number of marbles that are not blue
Answers
Step-by-step explanation:
There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.
a. Find the percentage of marbles that are not blue.
100% - 40% = 60%
b. Find the number of marbles that are not blue.
60% = 0.6
0.6 * 185 = 111 marbles
cheyenne needs to cut a piece of paper so that she has exactly 1/3 of it. if the length of the paper is 11 inches, how long will be the piece that she cuts?
Answers
The lengths of the piece she should cut is = 3 2/3
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
1/3 of 11=1/3*11=11/3=3 2/3hence,The lengths of the piece she should cut is = 3 2/3
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What is wrong I need help
I don’t understand it
Answers
Answer:
Step 2 is incorrect
Step-by-step explanation:
Step 2 is where you are distributing out -5. Step 2 should be distribution rather than division property of equality.
Direct and Inverse Variations
Answers
The value of y is 24 when x is 7.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
There are direct variations
y= 24 when x=2
We need to find value of y when x =7
This can be found by forming an equation.
Let the value of unknown y be a
2/24=7/a
Apply cross multiplication
2a=24(7)
2a=168
We need to divide by 2 on both sides
a=24
Hence the value of y is 24 when x is 7.
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Graph the points of the given function with the x-values x=−4 , x = 0, and x = 5. f(x)=−2x+4−−−−√
Answers
The graph is attached and the table of value of the graph is as follows
x y
-4 12
0 4
5 -6
How to get the table of valuesThe function y = −2x + 4 is a linear function and will have a straight line graph
The table of values is gotten form the equation y = −2x + 4
solving for x = -4,
y = −2 * -4 + 4 = 12
solving for x = 0
y = −2 * 0 + 4 = 4
solving for x = 5,
y = −2 * 5 + 4 = -6
x y
-4 12
0 4
5 -6
The graph is plotted by finding the points in the table in the Cartesian plane and joining the points together
Other values are solved for in similar step
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Answer:Here is your answer
Step-by-step explanation:
Hey, guys! How is your day? (°ω°)
Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
Answers
The time it takes to paint the whole bookcase is 50 minutes.
How to calculate the value?From the information, Wilson paints 40% of a bookcase in 20 minutes.
Let the time taken to paint the whole bookcase be x. This will be illustrated as:
20/x = 40/100
Cross multiply
40x = 100 × 20
40x = 2000.
Divide
x = 2000 / 40
x = 50
The time taken is 50 minutes.
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Is it a, b, or c, and if A what goes in the box
Answers
Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.
Given equation,
[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]
For values (-∞,-7)
equation stands true
For values (-7,5)
equation stands false
For values (5,12)
equation stands true
For values (12,∞)
equation stands false
Hence, x ∈ (-∞,-7)∪(5,12).
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(sec(t)-cos(t))/sin(t)
Answers
The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)
How to simplify trigonometric ratios?There are different trigonometric ratios such as;
sin x
tan x
cos x
sec x
cosec x
cot x
Now, we want to simplify the trigonometric expression;
(sec(t) - cos(t))/sin(t)
We know that;
sec (t) can be written as 1/cos t
Thus;
(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t
= (1/(sint cos t) - cos t/ sin t
= (1 - cos²t)/(sin t cos t)
= sin²t/(sin t cos t)
= sin t/cos t
= tan t
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8x + 24 I was solutions
Answers
Step-by-step explanation:
8x + 24 is a simplified expression.
It is not an equation, so it can't be solved.
There are two terms in 8x + 24, 8x and 24.
The two terms are unlike terms, so they cannot be combined together.
Find the initial population size
Answers
The numeric values for the population function are given as follows:
Initial population: 49 individuals.Population after eight years: 292 individuals.How to find the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, each instance of the input variable in the function or in the expression is replaced by the value at which we want to find the numeric value.
The function giving the population after t years is defined as follows:
[tex]P(t) = \frac{340}{1 + 6e^{-0.45t}}[/tex]
The initial population is the numeric value at t = 0, that is, the lone instance of t is replaced by zero, hence:
[tex]P(0) = \frac{340}{1 + 6e^{-0.45(0)}} = \frac{340}{7} = 49[/tex]
After eight years, the population is given by the numeric value at t = 8, hence:
[tex]P(8) = \frac{340}{1 + 6e^{-0.45(8)}} = 292[/tex]
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an iq test is designed to have scores that have a standard deviation of . a simple random sample of students at a large university will be given the test in order to construct a confidence interval for the mean iq of all students at the university. how many students must be tested so that the margin of error will be equal to points?
Answers
The sample size required in this case is 71 pupils, which must be tested in order for the margin of error to be equal to 3 points.
When it comes to statistics, selecting a relatively small representative sample and conducting hypothesis testing on it typically makes it easier to analyze a large population. By boosting the sample size, the margin of error, which represents the sampling procedure's statistical precision, can be decreased.
From standard normal tables,
P( -2.326 < Z < 2.326) = 0.98 here
The sample size required here is computed as:
n = [(z * α) / МОЕ]² = [(2.326 * 18) / 5]² = 70.12
Therefore, the required sample size, in this case, is 71.
To ensure that the margin of error is equivalent to 3 points, 71 students must be assessed.
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COMPLETE QUESTION:
An IQ test is designed to have scores that have a standard deviation of a 10. A simple random sample of students at a torgo university will be given the test in order to construct a 95% confidence interval for the mean 10 of all students at the university. How many students must be tested so that the margin of error will be equal to 3 points? The sample size required for the desired margin of error is.(Round your answer to next whole number.)
mary invests £12000 in a savings account.
the account pays 1.5% compound intrest per year.
y is inversely proportional to x.
when y=7, x=9
a) work out an equation connecting y and x.
b) work out the value of y when x=21.
pls show step by step working out.
Answers
Using a proportional relationship, it is found that:
a) The equation is: y = 63/x.
b) When x = 21, the numeric value is of y = 3.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables are inversely proportional, we have a inverse proportional relationship, in which the output variable y is obtained by the division of k by the input variable x, as follows:
y = k/x.
For this function, when y = 7, x = 9, hence the constant is obtained as follows:
7 = k/9
k = 9 x 7
k = 63.
Hence the equation is:
y = 63/x.
The numeric value of the function when x = 21 is given as follows:
y = 63/21 = 3.
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Find the perimeter of \triangle PQR△PQR. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answers
154.5
Step-by-step explanation:
left triangle and right triangle has the same degree.
M to Q 107/2 = P to R 53.5
O to N 110/2 = R to Q 55
Find X
M to N 92/2 = P to Q 46
Perimeter- 53.5+ 55+ 46= 154.5
What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answers
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust
Write an equation in slope-intercept form
to represent the relationship between x
and y shown in the table.
X
Y
-10 -5 0 5
55
20
-15
-50
10
-85
Answers
Answer:
665-09
Step-by-step explanation:
Describe the transformation of
f(x) = -2|x + 1 + 5
Shift Up__units.
Shift Down__units.
Shift Right__units.
Shift Left__units.
Compress by a factor of__
Stretch by a factor of__
Reflect over__axis.
Answers
The transformation of the equation f(x) = -2|x + 1| + 5 is
Shift Left 1 units
Shift Up 5 units
Compress by a factor of 2
Reflect over x axis
Interpretation of the transformationsTransformation involves movements of image or object usually described in a cartesian plane
starting from |x| at the origin
|x + 1| is a shift to the left 1 unit
|x + 1| + 5 is a shift on the y axis, it represents a shift up 5 units
2|x + 1| + 5 is a vertical compression by a factor of 2
-2|x + 1| + 5 the negative sign shows reflection over x axis turning the graph over
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PLEASE HELP!
629 students at a school each pay £6 to go on a school trip. How much money do they pay in total?
Show all your working.
Answers
Answer:
£3,774
Step-by-step explanation:
629 students at a school each pay £6 to go on a school trip. How much money do they pay in total?
629 * £6 = £3,774
Answer:
no of students= 629
amount paid each =£6
amount paid by all the students =no of students × amount paid each
:: 629
× 6
£3774
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52?
0.23 × 52
23% of $52 is $
11.96
.
An easy way to check your answer is to use the friendly
50%
and divide 52 by
2
to get
13
.
Am i right???
Answers
Answer:
yeah i think so
Answer:
$11.96
Step-by-step explanation:
Now we have to,
→ find the 23% of $52.
Let's solve the problem,
→ 23% of $52
→ (52/100) × 23
→ 0.52 × 23
→ $11.96
The similar expression is,
→ 0.23 × 52
→ $11.96
Hence, answer is $11.96.
XY
Y
a. (1, 1) and (7,5)
Answers
The slope of the line that passes through (1, 1) and (7, 5) is 2/3
How to calculate the slope of the line?From the question, the points are given as
a. (1, 1) and (7,5)
Rewrite the above points properly
So, we have the following ordered pairs
(1, 1) and (7,5)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (1, 1) and (7,5)
Substitute the known values in the above equation
So, we have the following equation
Slope = (5 - 1)/(7 - 1)
Evaluate
Slope = 2/3
Hence, the slope of the line is 2/3
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Possible question
Find the slope of the line that passes through a. (1, 1) and (7,5)
Suppose that A and B are points on the number line.
If AB=5 and B lies at 12, where could A be located?
If there is more than one location, separate them with commas.
:0
Location(s) of A :
0.0....
X
Answers
Answer:
locations of A are 7, 17
Step-by-step explanation:
since B is positioned at 12 and AB = 5 , then
A = 12 - 5 or 12 + 5 = 7 , 17
Help please I will give brainliest this is due in an hour!!!
Answers
Answer:
yes for helena: not sure for edwin
Step-by-step explanation:
for helena, it would be a 270 cc rotation and then scale
for edwin, again im not sure, but it could be a refection and then scale
Barney just bought stock in Purple Dinosaur Industries. He paid a total of $7,380. The price of the stock is $12 for one share. How many shares did he buy?
Answers
The number of shares he buy is $615.
Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.
We want to find the number of shares Barney buys.
The total amount barney should pay is $7380.
The price of the stock for one share is $12.
The total number of shares barney buy is 7380/12=615.
Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.
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Complete the function table. Function: t = 5d − 2
Answers
The table for the linear equation is summarized below:
d t
3 13
4 18
5 23
6 28
How to complete a table related to a linear function
In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:
d = 3
t = 5 · 3 - 2
t = 15 - 2
t = 13
d = 4
t = 5 · 4 - 2
t = 20 - 2
t = 18
d = 5
t = 5 · 5 - 2
t = 25 - 2
t = 23
d = 6
t = 5 · 6 - 2
t = 30 - 2
t = 28
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Ray buys a computer game for $38. He uses a coupon to receive 15% off the price of the game. After the coupon is deducted, he must pay 6% sales tax. What is the tota cost of the game, to the nearest cent? A $28.00 C. $34.58 D. $36.56
Answers
Find the least common denominator. Then express each fraction using the least common denominator. 3/4 and 5/6
I need a answer
Answers
Answer:
The least coomon denominator is 12, so
9/12 and 10/12
What is an equation of the line that passes through the point (2,-2)and is perpendicular to the line 5x-2y=4
Answers
Answer:
y=-0.4x - 1.2
