The square of the radius of the given circle is [tex]$OP^2 = 703$[/tex]
What is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus. Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties.
We can use the concept of the power of a point, which states that the square of the distance of a point from a line is equal to the product of the distances of the point from the two tangents to the line that are drawn from the point.
Let [tex]$O$[/tex] be the center of the inscribed circle.
The power of point O with respect to AB and CD is [tex]$(OPOQ) = (1937) = 703$[/tex]
Since the Circle is tangent to AB and CD at P and Q respectively, so [tex]$OP = OQ$[/tex]
So, [tex]$OP^2 = 703$[/tex]
Hence, the square of the radius of the circle is [tex]$OP^2 = 703$[/tex]
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Complete question is: A circle is inscribed in quadrilateral [tex]$A B C D$[/tex], tangent to [tex]$\overline{A B}$[/tex] at [tex]$P$[/tex] and to [tex]$\overline{C D}$[/tex] at [tex]$Q$[/tex]. Given that [tex]$A P=19, P B=26, C Q=37$[/tex], and [tex]$Q D=23$[/tex], find the square of the radius of the circle.
how many 1/3 inch cubes does it take to fill a box with width 1 1/3 inches, length 1 1/3 inches, and height 1 2/3 inches?
The number of 1/3 inch cubes that will fill the box is 26.
Volume of an object.The volume of an object is the amount or quantity of substance that it would conveniently contain. Different objects has their method of determining their volume depending on their shapes.
Given a cube of length 1/3 inch. The volume of the cube can be determined as;
volume of a cube = length x width x height
The volume of the cube = 1/3 * 1/4 * 1/3
= 1/9 cube inches
The volume of the box can be determined as;
Volume of the box = length x width x height
= 1 1/3 * 1 1/3 * 1 2/3
= 2.963 cubic inches
Volume of the box = 2.963 cubic inches
The number of 1/3 inch cubes that will fill the box = 2.963/ (1/9)
= 26.667
The number of 1/3 inch cubes that will fill the box is 26.
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please help me out will give brainliest
Answer:
I think it would be 10 inches but I am not sure
How do you solve an inequality equation?
There are four fundamental types of inequality: less than ( < ), larger than( > ), less than or equal to ( ≤ ), and more than or equal to( ≥ ).
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
Steps to solve the inequality:
First, get rid of all fractions by multiplying all terms by the fractions' lowest common denominator. (There is no difference when we multiply by a positive number.)Second, simplify the inequality by merging like words on either side. The sameThird To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts. The sameFourth, multiply each term in the inequality by the unknown coefficient. The inequality will not change if the coefficient is positive. Inequality will also be reversed if a negative coefficient exists. The crucial distinction between equations and inequalities is this.To know more about inequalities refer to:
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Find the missing length of the triangle. a= ? b=4 c=12 1/3
Answer:
a = 12.93
Step-by-step explanation:
Convert to decimal: 12 1/3 = 12.3
Pythagoras (a^2 = b^2 + c^2):
4^2 = 16
12.3^2 = 151.29
16+151.29 = 167.29
a = √167.29
a = 12.93 (rounded to two decimal places)
The solution is :
the missing length of the triangle is a = 12.93.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
Convert to decimal: 12 1/3 = 12.3
so, we have,
Pythagoras (a^2 = b^2 + c^2):
4^2 = 16
12.3^2 = 151.29
16+151.29 = 167.29
a = √167.29
we get,
a = 12.93 (rounded to two decimal places)
Hence, the missing length of the triangle is a = 12.93.
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The sum of two integers is 10. Their difference is 4. What are the two integers?
A) -3 and 1
B) -3 and 13
C) 3 and 7
D) -1 and 3
Answer:
The answer is 3 and 7.
Step-by-step explanation:
31. A curious accountant at a large firm would like to know if moncy can buy happiness. She selects a random sample of 30 of her wealthy clients and contacted them to ask "On a scale of 1-100, how happy are you?" The resulting 95 percent confidence interval for the true mean happiness rating for all wealthy customers is (67.5, 89.5). Which of the following statements best summarizes the meaning of 95% confidence?
Answer:
(E) - About 95% of all random samples of 30 wealthy customers from this population would result in a 95 percent confidence interval that captures the population mean happiness rating.
Step-by-step explanation:
The correct answer is (E). When we select a random sample from a population and use it to construct a confidence interval, the confidence level tells us what proportion of all such random samples we can expect to give confidence intervals that will capture the population parameter.
A board is 85 inches long. How long is it in feet and inches?
Answer: 7.083
Step-by-step explanation: all you have to do is divide 85 by 12 since there are 12 inches in one foot :)
Math help quick guys where ya at
The required dimensions are solved using linear pair and vertical angle to get the result as
x = 40y = 35Angle AED = angle CEB = 125 degreesAngle DEB = Angle AEC = 55 degreesHow to find the value of x and yThe value of x and y is calculated using linear pair theorem, the theorem implies that
solving for x
(3x + 5) + (x + 15) = 180
3x + x + 5 + 15 = 180
collecting like terms
4x = 180 - 15 - 5
4x = 160
x = 40
solving for y
(y + 20) + (4y - 15) = 180
y + 4y + 20 - 15 = 180
collecting like terms
5y = 180 - 20 + 15
5y = 175
y = 35
Angle AED
= 3x + 5
= 3 * 40 + 5
= 125 degrees
Angle AED = angle CEB = 125 degrees (vertical angles)
Angle DEB
= x + 15
= 40 + 15
= 55 degrees
Angle DEB = Angle AEC = 55 degrees (vertical angles)
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a. 96°
b. 132°
c. 137°
d. 89°
Answer:
b. 132°
Step-by-step explanation:
A coach formed teams of 8 from all the players in a soccer league. There are 14 teams. How many players are in the league?
Answer:
112
Step-by-step explanation:
8 players time 14 teams = 112
8*14=112
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square. What is the surface area of the solid? (1 point) a 18 square inches b 27 square inches c 36 square inches d 45 square inches
The correct option regarding the surface area of the solid is given as follows:
d. 45 square inches.
How to calculate the surface area?The surface area of a solid is composed by the sum of the areas of all the pars of the figure.
The composition of the figure in this problem is given as follows:
4 triangles of base 3 and height 6.One square of side length 3.Thea area of a triangle is given by half the multiplication of the base by the height, hence the area of the four triangles in this problem is given as follows:
At = 4 x 1/2 x 3 x 6
At = 36 square inches.
The area of a square is given by the square of the side length, hence:
As = 3³
As = 9 square inches.
Thus the surface area of the solid in this problem is given as follows:
S = At + As
S = 36 + 9
S = 45 square inches.
Meaning that option d is correct.
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An 80% confidence interval is found to be (12, 20). What is the margin of
error?
Answer:4
Step-by-step explanation:
If A = 5 units, then what is the volume of the cube shown above?
Answer:
125 square units
Step-by-step explanation:
YYWW :)
How do you call 2 angles with the sum of 90?
The two angles that have the sum of angles as 90° are called as Complementary Angles .
What are Complementary Angles ?
The two angles are said to be complimentary Angles when the sum of two angles is 90° .
In other words, we can say that if the measure of two angles add up to form a right angle, then these angles are called as Complementary Angles. We can also say that the two angles complement each other.
For Example : the angles having the measure of 30 degree and 60 degree can be called as Complimentary as their sum adds up to 90 degree .
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question in in the image
Answer:
Step-by-step explanation: The answer will be D isolate the variable x by dividing by the factors.
Evaluate the expression when x=3
, y=−4
, and z=−6
.
z−2xy=
z
−
2
x
y
=
The evaluation of the expression z − 2xy when x = 3, y = -4 and z = -6 is 18
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: z − 2xy
Values: x = 3, y = -4 and z = -6
Substitute the known values in the above equation, so, we have the following representation
z − 2xy = -6 - 2 * 3 * -4
Evaluate the products
This gives
z − 2xy = -6 + 24
Evaluate the like terms in the equation
So, we have the following representation
z − 2xy = 18
Using the above as a guide, we have the following:
The solution is 18
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How do you solve a 3 sided triangle?
It is impossible to solve a 3-sided triangle because triangles require 3 sides and 3 angles in order to be solved.
A triangle is a three-sided polygon, and the sum of its angles is always 180 degrees. In order to solve a triangle, you must know the length of all three sides and the measure of all three angles. If you know two sides and the angle between them (the angle opposite to one of the sides), you can use the Law of Sines to determine the other angle. If you know two angles and a side, you can use the Law of Cosines to determine the other two sides. With all three sides and angles known, you can use the Pythagorean Theorem to check your work. However, if you only have three sides, it is impossible to solve the triangle because you do not have enough information.
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8
In the expression (3) (0.2)³(0.8)5, which value
represents the number of successes?
0.8
C. 0.8 D. (0.8)5
A. 8/3 B. 0.2 C.
Answer: In the expression (3)(0.2)³(0.8)5, the value that represents the number of successes is 0.8.
This value is associated with the probability of success in the given expression, usually represented as "p" in a binomial distribution.
0.8 is probability of success
(0.8)5 represents number of successes.
It is important to note that 0.8 is a probability of success which means the probability of getting a success outcome in a single trial, and (0.8)5 is the probability of getting five successful outcomes in five trials.
Step-by-step explanation:
Please help me to find the slope
Answer:
Step-by-step explanation:
the formula for the slope is y2 - y1 / x2 - x1
so 1 - 0 / -3 --3/7
on the calculator
- 7 / 18
(a) 26 is what percent of 40? 65% (b) 85% of 80 is what number?
If p is inversely proportional to the square of q and p is 3 when he was 12 determine p when q is equal to 3
Answer:
p = 48
Step-by-step explanation:
If p is inversely proportional to the square of q
This is written Mathematically as:
p ∝ 1/q²
p = k × 1/q²
p = k/q²
Cross Multiply
k = pq²
k = Constant of Proportionality
Step 1
We find k
When p is 3 when q was 12
k = pq²
k = 3 × 12²
k = 432
Step 3
determine p when q is equal to 3
p = k/q²
p = 432/3²
p = 48
HELP ASAP WILL MARK BRAINLIEST PART 2
Answer:
6) 2nd option
7) 1st option
8) [tex]\sqrt{576} = 24[/tex] in
Answer:
Q6. A = s²
Q7. s = √A
Q8. 24 inches
Step-by-step explanation:
Q8.
√576 = 24in.
PLS HELP!!!! WILL GIVE BRAINLIEST!!! EDGE. PERFORMANCE TASK STEP FOUR
5W = 24D is the expression that represents the change in the rate of dosage as per the weight.
What is an expression?A mathematical expression is a sentence that includes numbers, variables, or both. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.
Given the relation between dosage and the weight of a medicine
Children's Fever Medicine
(given every 4-6 hours, as needed)
Weight: 24 lbs 36+ lbs 48+lbs 60+lbs 72+ lbs
Dosage: 5 mL 7.5 mL 10 mL 12.5 mL 15 mL
ratio of weught and dose
24/5 = 36/7.5 = 48/ 10 = 60/12.5 = 75/15
=> 4.8 = 4.8 = 4.8 = 4.8 = 4.8
Since weight is directly proportional to the dosage
let W be the weight of the child and D be the Dose of the medicine
Thus, Relation between them:
=>W/D = 24/5
=> 5W = 24D
Therefore, The formula that describes the change in dosage rate in relation to weight is 5W = 24D.
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What is the measure? Would appreciate any help!
Answer:
If I'm not wrong, angle O should be 62°!
Step-by-step explanation:
since triangle MON and triangle DAY are equal, if we add 75° and 43° it would be 118°. We then subtract 118° from 180° and it should be 62°. :)
Answer:
43
Step-by-step explanation:
measure angle M = measure angle D = 75
measure angle O = measure angle A = 43
measure angle N = measure angle Y = 180 - (43 + 75) = 62
and each angle of MON corresponds to that of DAY
Help please yes ok lol
a. The ratio of rows of corn to beans is 13 : 12 or 13/12 or 13 to 12.
b. The ratio of rows of lettuce to the total number of rows in the garden is 5 : 52 or 5 to 52 or 5/52.
a. The ratio using the word 'to' is corn to beans.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
We know a ratio between a and b can be written as a : b, a/b or a to b.
From the given information the ratio of rows of corn to beans is,
corn/beans = 13/12 Or 13 : 12 Or 13 to 12.
The ratio of rows of lettuce to the total number of rows in the garden is,
lettuce/total number of rows in the garden = 5/52 Or 5 : 52 Or 5 to 52.
The ratio using the word 'to' is corn to beans.
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NEED HELP ASAP MAKE IT NEAT AND NOT TOO LONG!!!!
Use the function f(x) = 2x^2 − 3x − 5 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
Answer:
Step-by-step explanation:
A
(2x - 5)(x + 1)
B)
The x intrcepts occur when the factors equal zero.
2x - 5 = 0
2x = 5
x = 5/2
x = 2 1/2
C
I will give the the minimum from completing the square
y = 2(x - 0.75)^2 - 6.125
as x approaches + infinity, y approaches + infinity.
as x approaches - infinity, y approaches + infinity.
It's a quadratic. The y values go to plus infinity, when x goes from - infinity to + infinity.
D
Desmos is the most useful tool for this part of the question. What it shows is the two roots and the minimum at (0.75,-6.125. A parabola does what the end behavior describes. The roots are clearly labeled as is the minimum.
Need help #’s 18-24 show work and answers please
Answer:
hope this helps you out good luck
Describe and explain the possible values of s, the number of student tickets sold, and e, the number of tickets sold to nonstudents.
Answer:
(20,0) , (0,16) , (5,12) , (10,8) , (15,4)
Step-by-step explanation:
Total amount of tickets sold = 80
Per ticket price for students = 4 ; Per ticket price for non students = 5
Let no. of students be s , no. of non students be x
Equation : 4s + 5x = 80
So, Maximum number of student tickets sold (assuming all student, no 'non student' tickets) = 80 / 4 = 20
Maximum number of non student tickets sold (assuming all 'non student', no 'student' tickets) = 80 / 5 = 16
Other possible values {s,x} , as per equation = (5,12) , (10,8) , (15,4)
tara is trying to solve the following equation 4.5x-4=14
Answer:
[tex]4.5x - 4 = 14 \\ 4.5x = 14 + 4 \\ 4.5x = 18 \\ x = \frac{18}{4.5} \\ x = 4[/tex]
Answer: x=4
Step-by-step explanation: 4.5x-4=14
4.5x−4+4=14+4
4.5x/4.5=18/4.5
x=4
What is the value of x in simplest radical form?
Answer:
x = 20
Step-by-step explanation:
To solve this problem we first observe the Pythagoras equation. If a= 16 and b=12 are the lengths of the legs of a right triangle and c=x is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
This relationship is represented by the formula: a*a + b*b = c*c
[tex]\sqrt{16^2 + 12^2}[/tex] = x