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.
write as complete square root 3√5
Dean Wormer wants to compare the grade point average of athletes at Faber College with the overall grade point average at Faber College. She randomly selects three students from each team and determines that their combined grade point average, 2. 3, is the same as that of all students at Faber. In this example, what is the population
yes it is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number
What is the definition of a population?
In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.
When the distribution is normal, we use the z-score formula.
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
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I NEED HELPPPPppppppp
Check the picture below.
The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
The area of a right-angled triangle is represented by the expression
x(x + 2) = 24 having area 24 square feet.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a right-angled triangle is (1/2)×base×height.
Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.
Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).
Therefore, The area of the triangle is,
(1/2)×x(x + 2) = 24.
x(x + 2) = 24.
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If triangle NPZ ~ triangle HBZ find the measure of angle B.
Please show the steps
The measure of angle B is m ∠B = 107°.
What is similar triangles?
Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects include all equilateral triangles and squares with any side length. To put it another way, if two triangles are similar, then their corresponding angles and sides are congruent and equal in size.
Given: Δ NPZ ~ Δ HBZ
As the triangles NPZ and triangle HBZ are similar that means the corresponding angles are congruent.
⇒ ∠N = ∠H, ∠P = ∠B, ∠Z = ∠Z
Since,
∠P = (8x - 37)°, ∠Z = 42°, ∠H = (2x - 5)°
⇒ 2x - 5 = ∠H, ∠B = 8x - 37, Z = 42°
Since, the sum of three angles of triangle is 180°.
⇒ ∠H + ∠B + ∠Z = 180°
(2x - 5)° + (8x - 37)° + 42° = 180°
10x - 42° + 42° = 180°
10x = 180°
x = 18°
So,
∠B = (8x - 37)° = 8(18) - 37 = 144 - 37 = 107°.
Hence, the measure of angle B is m ∠B = 107°.
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Two vehicles start from the same point traveling in the same direction. One vehicle travels 55.5 miles per hour (mph) and the other 45 ¼ mph. When will the two cars be 350 miles apart?
The number of hours after which the cars will be 350 miles apart is 34 hours.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Vehicle 1.
Speed = 55.5 mph
Distance(1) = 55.5 x Time
Vehicle 2.
Speed = 45(1/4) mph
Distance(2) = 45(1/4) x Time
The difference in the distance = 350 miles.
Distance(1) - Distance(2) = 350
55.5 x Time - 45(1/4) x Time = 350
55.5 x Time - (181/4) x Time = 350
(55.5 - 181/4) x Time = 350
Time = 350 / (55.5 - 45.25)
Time = 350 / 10.25
Time = 34 hours.
Thus,
The car will be 350 miles apart after 34 hours.
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What is the name of the point where the two axes cross?
As per the concept of graph, the name of the point where the two axes cross is origin.
Graph in math is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Here we have to identify the name of the point where the two axes cross.
As we all know that the horizontal axis in the coordinate plane is called the x-axis and the vertical axis is called the y-axis.
Here we have also know that the point at which the two axes intersect is called the origin.
Where the origin is at 0 on the x-axis and 0 on the y-axis.
And these intersecting x- and y-axes divide the coordinate plane into four sections
Finally all these four sections are called quadrants.
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What is the horizontal asymptote * 1 point?
Copy and complete each of the Diamond Problems below.
The pattern used in the Diamond Problems is shown at right.
b.
a.
0.32
12
"1
J
c.
9
2
d.
234
31
Core Connections, C
"
J
The provided schematic must be followed in order to answer these diamond problems. You must multiply the values on the left (x) and right (y) cells in order to find the value that belongs in the top cell.
we have,
For Diamond Problems a
x+y=1.2
xy=.32
so value of x= .8 and y = .4.
for Diamond Problems b
x= 11
x+y=25.
so y= 14 and xy=11*14=154.
for Diamond Problems c
x=-7
y=-9
so x+y=-16 and xy= 63.
for Diamond Problems d
x+y=31
xy=234
x=13 and y=18
Is figuring out puzzles a skill?Because puzzles engage both the left and right sides of your brain, solving them aids in the development of your problem-solving abilities. Solving puzzles with others is a terrific method to improve your communication and cooperation skills in addition to your problem-solving and critical thinking abilities.
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For what value of k does the pair of linear equations 3x +5y 3 6x KY 8 do not have any solution?
The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.
We can rewrite the equations as:
3x + 5y = 3
6x + ky = 8
To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:
6x + 10y = 6
-18x - 3ky = -24
Now we can add the two equations together and get:
-12x - 3ky = -18
Since the coefficient of x is 0, this equation does not have any solution for any value of k.
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(Car Sales) Of the cars sold during the month of July, 85 had air conditioning, 102 had automatic transmission, and 54 had power steering. 8 cars had all three of these extras. 24 cars had none of these extras. 25 cars had only air conditioning, 56 cars had only automatic transmissions, and 26 cars had only power steering. 11 cars had both automatic transmission and power steering. How many cars had exactly two of the given options
24 cars lacked power steering but did have air conditioning and an automatic gearbox.
According to the question,
No. of cars with Air conditioning = 88
No. of cars with Automatic transmission = 96
No. of cars with power steering = 76
All three = 4
None of these extras = 19
Only air conditioning = 23
Only automatic transmissions = 61
Only power steering = 28
Power steering and automatic transmission both = 11
The calculation for missing values:
11 - 4 = 7
96-61-4-7 = 24
88-24-4-23=37
It is obvious that 24 cars lacked power steering but did have air conditioning and an automatic gearbox.
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The table shows the balances of two bank accounts for 3 months. In what month will the balance of account A be equal to the balance of account B?
As per Given data,
The month in which the balance of two bank accounts A is become equal to the balance of account B is 30thmonths,
How to find unknown values?Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
Month Account A Account B
0 $ 100 $ 250
1 $ 125 $ 270
2 $ 150 $ 290
Clearly
The amount in account A is growing with $25 each month. Thus, the amount in this account in nth month is,
100+25[tex]n[/tex]
The amount in account B is just growing with $20. Thus, the amount in this account in nth month is,
250+20[tex]n[/tex]
x month
balances of two
account becomes equal,
then
100 + 25x =250 + 20x
25x - 20x = 250 - 100
5x = 150
x =30
Therefore, in 30th month balance of account A equal to balance of account B
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Q. The table shows the balances of two bank accounts for 3 months. In 30th month will the balance of account A be equal to the balance of account B?
Month Account A Account B
0 $100 $250
1 $125 $270
2 $150 $290
What is the coefficient of the variable in the expression 4 − 3x − 7 6 3 points?
The coefficient of the variable x in the expression 4a+3x +a is 3
Given that,
The expression is 4a+3x +a which can be simplified as 4a+3x +a
To find : The coefficient of the variable x in the expression
The coefficient of x in 4a+3x +a is 3
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
Coefficient is the number that is beside the variable in the equation.
As we can see that the term that is in multiplication with x is 3
Hence, the coefficient of x in the equation is 3
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Torrin rode his bike to school at 13. 5 km/h. He returned home using the same route at 10. 5 km/h. Torrin took a total of 36 min to ride to school and back. Express your answer to the nearest hundredth. A) how many minutes did torrin take to ride to school? B)how far is it from Torrins house to school?
To ride a bike to school Torrin takes 15.75 min to ride to school and 3.54 km is the distance from his house to school.
Let v₁ = 13.5 km/h the speed to school
v₂ = 10.5 km the speed returning home
t = the time of the ride to school in minutes
36 - t = the time of the ride from school in minutes
Since, distance = speed × time
⇒v₁ × t/60 = v₂ × (36 - t)/60
⇒13.5 × t/60 = 10.5 × (36 - t)/60
⇒t = 15.75 min
Now, the distance = v₁ × t/60 = 13.5 × 15.75/60 = 3.54 km.
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y<3x+12, y≥5x+7
The solution of the system of linear inequalities.
Answer: nswer ; x , we can find ; y with the first equation :.
1 answer
·
We know that y=5x−7 so we are just going to replace the y in the other equation : −3x−
Step-by-step explanation:
What are the AGI and taxable income? Responses $35,468 and $23,068 $35,468 and $23,068 $47,468 and $35,468 $47,468 and $35,468 $47,868 and $12,400 $47,868 and $12,400 $35,468 and $12,400 $35,468 and $12,400 Gross Income $35,468 Adjustments 0 1 Exemption $12,400 Deduction 0
The amount of GI is $35,468.
The amount of taxable income is $23,068.
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Gross income = $35,468
Exemption = $12,400
Deduction = 0
Adjustment = 0
Taxable income.
= Gross income - Exemption
= 35,468 - 12,400
= $23068
Thus,
GI and taxable income are $35,468 and $23,068
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What is the degree of the polynomial 2x² 5x²³ 7?
The degree of the polynomial [tex]2xA^2 5xA^2A^37[/tex] is 9
A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.
The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).
Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]
The polynomial has a degree of 6.
This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.
As per question, polynomial is: [tex]2xA^2 5xA^2A^37[/tex]
The total sum of power is: 1+2+1+2+3=9
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These are the numbers and I need the ratio
to thank you!
help me please it's due tomorrow !!!!!!!!!!
help please
ill get in trouble!!!!
Answer: 1:3
Step-by-step explanation:
I'd say 1:3 but I could be wrong
Melody has two different posters to put up in her bedroom. Poster A has an area of 450 square inches. Poster B has an area of 326 square inches. How much area of Melody's bedroom wall will the two posters cover, in square inches?
The two posters will cover 776 square inches of Melody's bedroom wall.
To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.
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The diagram shows two proportional right triangles.
What is the perimeter of the larger triangle?
The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary surrounding the figure.
Two triangles that have proportional dimensions are similar triangles
The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;
First (larger) triangle side lengths; 24, 32, and xSecond (smaller) triangle side lengths; 9, 12, and 15The similarity of the triangles (proportional corresponding sides, indicates that we get;
[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]
Therefore, by cross multiplication, we get;
32 × 15 = 12 × x
x = 32 × 15 ÷ 12 = 40
The perimeter of the larger triangle is; 24 + 32 + 40 = 96
The perimeter of the larger triangle is 96 units.Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.
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The number of pages in an Algebra 1 book is 99 less than the number of pages in a geometry book. Write and solve an equation to find the number n of pages in the geometry book. (big ideas)
On solving the provided question we can say that *629 = n - 99 is an equation. The textbook contains 728 pages*.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
In other words, the geometry book is 99 pages LONGER than the algebra book, which is 99 pages SHORTER. The solution can be obtained using this equation. I'm sorry, but 530 is not the solution.
629 = n - 99 is an equation. The textbook contains 728 pages*.
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When a calcium atom forms an ion, it loses two electrons. what is the electrical charge of the calcium ion? responses −2 negative 2 −1 negative 1 1 1 2
When a calcium atom forms an ion, it loses two electrons. The electrical charge of the calcium ion is +2
What do you meant by electrical charge of a calcium ion?Calcium ions are net positive two charges. In calcium, when it has assumed its most stable state, the relationship between the quantity of protons (20) and the quantity of electrons (18) is represented by the +2 charge.
In the event that calcium (Z = 20) picks up two electrons, the resultant ion will have 18 electrons and 20 protons, giving it a charge of +2. (two more positive protons than negative electrons). It's a cation, this ion. Using the Ca2+ symbol, we can identify a calcium ion.
Atoms that lose electrons acquire a positive charge as there are fewer electrons left with negative charges to balance the positive charges of the protons in the nucleus. Positively charged ions are known as cations.
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30PTS 30PTS don’t explain just answer.
Answer:
y = 90°
Step-by-step explanation:
Tues
1.There were 32 brown ducklings at a pond. Twice as
many white ducklings arrived., 1/2 of the brown ducklings
flew away. How many ducklings are there now, at the
pond?
Answer:
80 ducks (16+64)
Step-by-step explanation:
So if there were 32 brown ducks in the pond at first, then twice the amount of brown ducks (32).
32x2=64 white ducks
So now their are 64 white ducks at the pond. We still have to add how many brown ducks their were so…
64+32=96 ducks in total
But then as the white ducks came in half of the brown ducks flew away.
32/2=16 brown ducks left in the pond.
Lastly add the remaining brown ducks with the white ducks and that is you answer!
16+64=80 total amount of ducks
Final Answer:
80 ducks
I hope this helps! I am sorry if I got it wrong!
A B. C A3 x 3 matrix is above. It has a pattern going both horizontally across the rows and vertically down the columns. The pattern is not necessarily the same in both directions. There is one object that fits correctly in the bottom right corner of the matrix. Choose this object from the list below the matrix Select one: a. A ОБ. В Ос, с d. D e. E f.F 8.G h. H
We can conclude from answering the above question that the first two patterns of the matrix form a sequence in the third from top with the numbers 4-2-6.
what is matrix i?A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.
We can conclude from answering the above question that the first two patterns of the matrix form a sequence in the third from top with the numbers 4-2-6.
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please answer **ASAP** (WORTH 50pts)
in a sequence the first term of 4 and the common difference is 8 find a fifth term
EXPLAIN
The fifth term of the given arithmetic sequence is 36.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d
Given that, in a sequence the first term of 4 and the common difference is 8.
Here, a=4 and d=8
Now, the fifth term is
a₅=4+(5-1)×8
= 4+32
= 36
Therefore, the fifth term of the given arithmetic sequence is 36.
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Carl deposited $1220 in a bank that pays 9% interest, compounded monthly. Find the amount he will have at the end of 3 years.
a.
$3431.45
c.
$1549.40
b.
$1596.55
d.
$1334.44
The amount he will have at the end of 3 years is $1596.55.
Option B is the correct answer.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $1220
r = 9%
n = 12
t = 3 years
Amount = P [tex](1 + r/n)^{nt}[/tex]
A = 1220 [tex](1 + 9/12)^{36}[/tex]
A = 1220 [tex](1 + 0.75)^{36}[/tex]
A = 1220 x [tex]1.75^{36}[/tex]
A = $1,596.55
Thus,
The amount after 3 years is $1596.55.
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i dont know how to do it
Answer:
x = 4
y = 28
Step-by-step explanation:
1) y = 7x
2) y = 2x + 20
substitute y = 7x into equation 2:
7x = 2x + 20 now you can solve for x:
7x - 2x = 20
5x = 20
x = 20/5 = 4
Plug x = 4 into either equation 1 or 2 to solve for y:
y = 7x = 7(4) = 28
Random students from a high school were surveyed to determine if there was enough interest to start a Ukulele Club.
Identify the population:
A. Students of high schools across the country
B. Students of the high school
C. Citizens of the city
D. Every citizen of the country
Answer:
b
Step-by-step explanation:
Answer:
B. Students of the high school
Step-by-step explanation:
It is high school because you just want to ask that area.
A bag contain 27 ball. The ratio of red to blue to yellow ball i 6:1:2 find how many red, blue and yellow ball there are
On solving the provided question we can say that by linear equation number of, Red Balls = 6x 18; Blue Balls = 3; Yellow Balls = 6
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
A bag contains 27 balls
• The ratio of red to blue to yellow balls is 6:1:2
To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6X+X+2x = 27
9x = 27
x = 3
Hence the number of,
Red Balls = 6x 18
Blue Balls = 3
Yellow Balls = 6
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