1) Because \(\angle ACB\) is a central angle, \(m\angle ACB=72^{\circ}\).
Since \(\angle ACB\) and \(\angle BCD\) are supplementary, they form a linear pair, and thus \(m\angle BCD=180^{\circ}-72^{\circ}=\boxed{108^{\circ}}\)
5) Tangents drawn from an external common point are congruent, so CR=CP=8 and RB=BQ=4. This means that QA=11, and so PA=11 as well. Adding CP+PA, we get AC=19.
6) By the inscribed angle theorem, angle QPR measures 36 degrees.
Write the equation of the line that is parallel to y-axis and passing through the point (3,-5)
Answer:
\(x=3\)
Step-by-step explanation:
Because this line is parallel to the y-axis, it is a vertical line. This is a special case where the formatting of its equation is different:
\(x=d\) where d is the x-intercept, or the value of x when the line crosses the x-axis
We're given that the line passes through the point (3,-5). Because this is a vertical line, the x-coordinates of the points it passes through will always stay the same. Therefore, the x-intercept (d) is 3.
\(x=3\)
I hope this helps!
wh at is the smallest number of rectangles, each measuring 2cm by 3cm, which are needed to fit together without overlap to form a rectangle whose sides are in the ratio 5:4 ?
The smallest number of rectangles required will be 30.
Given:- The sides of the rectangle are in the ratio of 5:4
let, length=5x
breadth=4x
Area = 20x²
Area of smaller rectangle =2*3
=6cm²
Now, take numbers which are in the ratio of 5:4;
suppose, Case 1=10:8
Case2 = 15:12
For Case 1;
number of rectangles needed =10*8/2*3
=13.3333
This means it is overlapping hence, not possible.
For Case 2;
number of rectangles needed=15*12/2*3
=30
therefore, the smallest number will be 30.
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int \( a[4]=\{1,2,3,4\} \) int \( { }^{*} p=a \); What is the value of \( *(p+3) ? \)
The value of the expression is 4.
The code :
int a[4] = {1, 2, 3, 4};
int *p = a;
what is *(p + 3)?
The variable a is an array of integers, and the variable p is a pointer to the first element of the array.
The expression *(p + 3) is the value of the element of the array that is 3 elements after the element that p points to.
Since p points to the first element of the array, the expression *(p + 3) is the value of the fourth element of the array, which is 4.
Therefore, the value of the expression is 4.
Here is a breakdown of the code:
int a[4] = {1, 2, 3, 4}: This line declares an array of integers called a and initializes it with the values 1, 2, 3, and 4.
int *p = a; This line declares a pointer to an integer called p and initializes it with the address of the first element of the array a.
what is *(p + 3)?: This line asks what the value of the expression *(p + 3) is.
The expression *(p + 3) is the value of the element of the array that is 3 elements after the element that p points to.
Since p points to the first element of the array, the expression *(p + 3) is the value of the fourth element of the array, which is 4.
Therefore, the value of the expression is 4.
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Correct Question :
Int a[4]={1,2,3,4}, int *p=a. What is the value of *(p+3)?
find a power series representation for the function. f(x) = x^8 tan^−1(x^3)
The Power series representation of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)
What is Maclaurin series?The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.
What is power series?
An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.
The Maclaurin series will be used in this instance to expand the function:
\(tan^-^1x\) = \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}\)
and for \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}\)
=> \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\) -------(i)
and f(x) = \(x^8tan^-^1x^3\)
now we need to multiply \(x^8\) in the above equation to get the power series expansion of f(x)
\(x^8tan^-^1x^3\) = \(x^8\) \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)
=> \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}\)
=> \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)
so the expansion of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)
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which equation represents a line that is parallel to y = 4x + 3 and passes through the point (-3, 2)
50 points
Answer:
it should be y= -4x + 10
Step-by-step explanation:
hope this helps.
HELP PLEASEEEE!!!
Parallelogram EFGH is similar to parallelogram JKLM. What is the scale factor of a dilation from EFGH to JKLM? Enter your answer, as a decimal, in the box.
Answer:this is a little late but i think its 0.4
Step-by-step explanation:
The scale factor of a dilation from parallelogram EFGH to parallelogram JKLM is \(2.5cm.\)
What is Scale Factor ?Scale Factor is defined as the ratio of size of new image formed to the size of old image.
What is Parallelogram?Parallelogram is defined as the quadrilateral whose opposite sides are equal and opposite to each other.
Here, we have parallelogram EFGH and parallelogram JKLM,
it is given that,
parallelogram EFGH is similar to parallelogram JKLM.
In parallelogram EFGH we have,
EF\(=28 cm\), EH\(=14cm\)
and
In parallelogram JKLM we have,
JK\(=11.2cm\) JM\(=5.6cm\)
So, according to question,
Scale factor \(=\) \(\frac{EF}{JK}\)
\(=\frac{28}{11.2}\)
\(=2.5\) cm
Hence, we can say that Scale factor of dilation of parallelogram EFGH to parallelogram JKLM is \(2.5 cm\).
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A. Let Q(n) be the predicate "n2 ≤ 30", write Q(2), Q(-2), Q(7), Q(-7), and indicate whether each statement is true or false
B. Let B(x) = "-10 < x < 10". Find truth set for x∈D , where D=Z+ is the set of all positive integers.
A.
To evaluate the predicate Q(n) = "n^2 ≤ 30", we substitute different values for n and determine whether the statement is true or false.
1.
2^2 = 4, which is less than 30. Therefore, Q(2) is true.
2.
(-2)^2 = 4, which is less than 30. Therefore, Q(-2) is true.
3.
7^2 = 49, which is not less than or equal to 30. Therefore, Q(7) is false.
4.
(-7)^2 = 49, which is not less than or equal to 30. Therefore, Q(-7) is false.
B.
The predicate B(x) = "-10 < x < 10" defines a range of values for x. In this case, we are looking for the truth set of B(x) when x belongs to the set of positive integers, D = Z+.
The set of positive integers, D = Z+, includes all numbers greater than zero without any fractional or decimal values.
Therefore, the truth set for B(x) where x ∈ D = Z+ is the set of positive integers between -10 and 10, excluding -10 and 10.
In set notation, the truth set can be expressed as:
{1, 2, 3, 4, 5, 6, 7, 8, 9}
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First Class Airlines has 40 pilots for every 15 aircrafts. If they employ 250 pilots, how many aircrafts does First Class Airlines own?
(Answer is ratio or proportion)
Answer:
250÷ 40 = 6.25
6.25 x 15 = 94
pls help me quick erg
The distance Chyna ran is 7 1 / 2 kilometres.
How to find the distance Chyna ran?Ronaldo ran 9 / 10 fewer kilometres than Chyna ran. Ronaldo ran 6 3 / 5
kilometres
Therefore, the distance Chyna ran in kilometres can be calculated as follows:
Therefore,
Distance Ronaldo ran = 6 3 / 5 = 33 / 5 kilometres
Hence,
Distance Chyna ran = 33 / 5 + 9 / 10
Distance Chyna ran = 66 + 9 / 10
Distance Chyna ran = 75 / 10
Therefore,
Distance Chyna ran = 7 5 / 10
Distance Chyna ran = 7 1 / 2 kilometres
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is f(x)=7(x-1)+8, what is the value of f(11)?
Answer:
f(11) = 78
Step-by-step explanation:
f(x) = 7(x-1) + 8
f(11)
this means that the problem wants us to find what the value of this function is when x is 11
x = 11
f(11) = 7(11-1) + 8
=7(10) + 8
= 70 + 8
= 78
Evaluate the function below for the given value of x
Answer:
Step-by-step explanation:
- 4 ≤ 3 , then f(- 4) = \(\frac{1}{2}\) ( - 4) + 1 = - 1
2 ≤ 3 , then f(2) = \(\frac{1}{2}\) (2) + 1 = 2
3 ≤ 3 , then f(3) = \(\frac{1}{2}\) (3) + 1 = 2.5
5 > 3 , then f(5) = 9×5 - 4 = 41
HELP! BRainliest +20
A function f is defined such that 8f(x)=f(\(\frac{1}{8}\)x) for all values of x, and f(4) = 24. What is the value of f(32) ?
The value of f(32) is 3
What is a Function ?A function is a mathematical statement used to relate two variables .
It is given that
8f(x) = f((1/8)x)
It is also given that
f(4) = 24
now to determine the value of f(32)
8 * f(32) = f((1/8) *32)
8 * f(32) = f(4 )
f(32) = 24 /8 = 3
Therefore the value of f(32) is 3
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Which numerical expression provides the solution to the equation 2p2 - 7p - 13 = -10?
The numerical expressions that provides the solution to the equation 2p2 - 7p - 13 = -10 are (2p -1) and (p-3)
How to determine the expressionsWe have the quadratic equation given as;
2p2 - 7p - 13 = -10
Using the factorization method, we take the following steps
collect like terms
2p² - 7p - 3
Find the pair factors of -6 that sums up to -7, then substitute the values, we get the expression as;
2p² - 6p - p - 3
Group the expression into two
(2p² - 6p) - (p -3)
Factorize the expressions
2p(p -3) - 1(p-3)
Hence, the expressions are (2p -1) and (p-3)
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Which graphs represent functions with the following key features?
- positive on (-∞, ∞)
- increasing on (-∞, ∞)
- approaches 0 as x approaches -∞
Answers:
• Graph U
• Graph V
• Graph W
• Graph X
• Graph Y
• Graph Z
Ayuden por favor, no entiendo este problema
We will get that the angle theta is:
θ = β/2
How to find the value of theta?Remember that the sum of the interior angles of any triangle must be equal to 180°.
Now, looking at the triangle in the left, we can see that the top angle is equal to:
180 - 2α
The right angle is equal to:
180 - 2β
And the left angle is α
Then we can write:
α + (180 - 2α) + (180 - 2β) = 180
-α - 2β = -180
α = 180 - 2β
Now we can go to the other triangle, where theta is, and write:
α + β + 2θ = 180
Replacing what we found above, we get:
180 - 2β + β + 2θ = 180
-β + 2θ = 0
θ = β/2
That is the best simplification we can get with the given diagram.
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Can someone plz help me. There is an equation and the cost too.
Answer:
C = 40p
Cost for 15 people: 600 dollars
Step-by-step explanation:
The amusement park charges $40 per person.
That can be represented as 40 × P or 40P.
C is equal to the cost of admission for P people.
So, C = 40P
C = 40P
C = 40(15)
C = 600
The cost of admission for 15 people is 600 dollars.
Hope that helps.
PLEASE ANSWER ASAP! How does the volume of a triangular prism change if it’s height is cut in half
Triangular prism formulas
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length.
area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.
Mariah runs a minimum of 25 miles a week to prepare for the 5k in Oklahoma City next Spring Break. She runs an equal amount on Tuesday and Thursday and 3 times that amount on Saturday. What is the least she must run on Tuesday?
Answer:
5 miles
Step-by-step explanation:
Set it up in terms of x. She'll run x miles on Tuesday, x miles on Thursday, and 3x miles on Saturday. If she runs 25 miles in a week (even though she can run more, we're only concerned with minimums in this problem), then 25 = x + x + 3x. This can be simplified down into 25 = 5x. All you need to do here is isolate x by dividing both sides by 5 to get x = 5. Don't forget your units! (:
Match the graph with the correct equation
A: Y= -2X + 5
B: Y= -X + 3
From: SLOPE-INTERCEPT FORM: PART 1
Answer:
The equation for this picture(graph) is:
y = -x+3
Slope: Rise/run
= 3/3
= 1
= -1 (negative because the slope is decreasing).
Y-intercept is where the line touches the y-axis
I NEED HELP WITH THESE TWO QUESTIONS ASAP PLEASE!!!
Answer:
6. (2,1) 7. (2,2)
Step-by-step explanation:
Number 6, Since it is a dilation of .5 you divide the x and y coordinate by 2 to get (2,1). X - 4/2=2, Y - 2/2=1
Number 7, Since it's rotating 90 degrees counterclockwise you switch the x and y coordinates. So from (x,y) to (y,x) and also when going counterclockwise you have to make the y coordinate becomes negative, so the counterclockwise equation is (-y,x) plug in your numbers and you get (2,2) as your 90 degree counterclockwise rotated coordinates.
Given inverse demand function P=342-190, what does the price need to be so that sales are Q=10?
a, 18
b.36
c.152
d.171
The calculated price is -1558. However, since prices cannot be negative in most real-world scenarios, we need to consider the valid range of prices. None of the options are correct.
To find the price at which sales are equal to Q=10, we need to substitute Q=10 into the inverse demand function P=342-190 and solve for P.
Let's start by substituting Q=10 into the inverse demand function:
P = 342 - 190 * Q
P = 342 - 190 * 10
P = 342 - 1900
P = -1558
The calculated price is -1558. However, since prices cannot be negative in most real-world scenarios, we need to consider the valid range of prices.
Given the options provided (a, 18; b, 36; c, 152; d, 171), we can see that none of them match the calculated price of -1558.
Therefore, none of the options are correct.
It is important to note that the calculated price of -1558 may not be realistic or feasible in the context of the problem. It is possible that there may be some error or inconsistency in the information provided.
If you have any additional information or if there are any constraints or limitations mentioned in the problem, please provide them, and I will be happy to assist you further.
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can anyone help me with this
Answer:
137
Step-by-step explanation:
3*4=12
12^2=144
-2*4=-8
144-8+1
144-7
137
Simplify the expression.
options:
52
152
512
25
Answer:
The correct answer is 152
The two polygons below are similar.
True
False
Answer:
true
Step-by-step explanation:
well same I'd everything looks alike but similar is the basics
is 3/17 rational or irrational
Answer:
A rational number is a number that can be put in the form p / q where p and q are integers.
3 and 17 are integers
3 / 17 is rational
Solve for the value of m.
6 X m = 54
Answer:
m=9
Step-by-step explanation:
m = 9/x
xm = 54/6
xm = 9
m=9/x
which type of article provides a quantitative summary of the evidence?
A type of article that provides a quantitative summary of the evidence is a systematic review and meta-analysis.
A systematic review is a comprehensive and rigorous approach to synthesizing existing research literature on a specific topic. It involves a systematic search for relevant studies, an assessment of their quality and relevance, and a synthesis of the findings.
A meta-analysis, on the other hand, is a statistical method that combines the results of multiple studies to generate a quantitative summary of the evidence.
Systematic reviews and meta-analyses are considered the highest level of evidence in evidence-based medicine and other fields. They provide an objective and rigorous assessment of the available evidence, helping to guide clinical practice, policy decisions, and further research.
By pooling data from multiple studies, meta-analyses can provide more precise estimates of treatment effects or other outcomes of interest.
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how to calculate 71-5(3)-(4*4)
Answer:
40
Step-by-step explanation:
first do what is in the parentheses (4*4) which is 16 then rewrite the whole equation. 71-5(3)-16. then you'll want to multiply 5 times 3 because if there is no sign before the parentheses then it is automatically multiplication. 5 times 3 is 15. rewrite the equation again. 71-15-16 then simply subtract.
Hope this helps! :)
an envelope contains eight bills: ones, fives, tens, and twenties. two bills are drawn at random without replacement. what is the probability that their sum is $ or more?
Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when two bills are drawn randomly without replacement.
We have an envelope contains 8 bills;
Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.
When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.
Total outcomes = 2 x 2 x 2 x 2 = 16
Total possible outcomes, more than 20;
(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases
That is,
The total possible outcomes is 8.
Now,
The probability of bill to be $20 or more = Possible outcome / Total outcome
Probability = 8/16 = 1/2=0.5
Hence, When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 0.5.
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(Complete question)
an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is the probability that their sum is $20 or more?
Presents of equal size are in a boxes each with dimensions of 10 inches length, 4 inches width, and 2 inches height. How many presents can be gift wrapped if you have a roll of 600 square inches of wrapping paper? Show all work
Answer:
You can make 7.5 gifts presents (or just 7)
Step-by-step explanation:
First I calculated the area of 1 box, which is 80 inches squared. Then I just divided the 600 square inches with the 80 inches. 600/80= 7.5. Therefore, you can make 7 presents (since you cannot wrap half of a present (0.5))
Hope this helps !