1. The rational expression representing the charge each attendee will have to pay is 300 + 55x.
2. Each attendee will have to pay $65 in order to cover the total cost.
The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
All real numbers are thought to be adequately explained by the four basic operations, sometimes known as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.
1. We are given that it costs $300 plus $55 per person attending to host an event.
Let the number of attendees be x.
We get the expression as 300 + 55x.
2. We are given that 30 people are attending the event.
So, substituting x = 30 in the expression, we get
⇒ Total cost = 300 + (55 * 30)
⇒ Total cost = 300 + 1650
⇒ Total cost = $1950
Now, using the division operation, we get
⇒ Per person charge = 1950 ÷ 30
⇒ Per person charge = $65
Hence, the required solutions have been obtained.
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Question: To host an event at a popular convention center, it costs $300 plus $55 per person attending.
1. Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x be the number of attendees.
2. In the previous step you determined that for x number of people, the total cost for hosting the event is 300+55x. Now, adjust the expression to represent what each attendee would need to be charged to cover the total cost if 30 people were attending.
Triangle L M N LMN is similar to triangle O P R OPR. Find R O RO. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
This shows a function. F(x)=4x^3+8 which statement describes f(X)? A. The function does not have an inverse function because F(x) fails the vertical line test. B. The function does not have an inverse function because f(x) fails the horizontal line test. C. The function has an inverse function because f(x) passes the vertical line test. D. The function has an inverse function because f(x) passes the horizontal line test
Answer:
Step-by-step explanation:
The statement that describes the function f(x) = 4x^3 + 8 is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
To see why this is the correct answer, let's first define what the vertical line test and the horizontal line test are.
Vertical line test: A function passes the vertical line test if any vertical line intersects the graph of the function at most once. This means that no two points on the graph have the same x-coordinate.
Horizontal line test: A function passes the horizontal line test if any horizontal line intersects the graph of the function at most once. This means that no two points on the graph have the same y-coordinate.
Now, let's look at the function f(x) = 4x^3 + 8. We can graph this function by plotting points or by using a graphing calculator. The graph of the function looks like a curve that goes up and to the right.
If we draw a vertical line anywhere on the graph, we can see that it intersects the graph at most once, which means that f(x) passes the vertical line test. However, if we draw a horizontal line on the graph, we can see that it intersects the graph at more than one point. This means that f(x) fails the horizontal line test.
The fact that f(x) fails the horizontal line test tells us that there are some values of y that correspond to more than one value of x. This means that f(x) is not a one-to-one function, and therefore it does not have an inverse function.
Therefore, the correct statement that describes the function f(x) is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
Simplify and leave your answer in indices form. (2² × 32)6 ÷ (3⁹ × 26)
A block weighing 25№ has dimensions 34cm * 25 *
10em. what is the greatest pressure and the least.
the ground?
pressure it can
exert on
As a result, the maximum pressure the block may impose on the ground angles is 25 N/cm2 and the minimum pressure is 0.029 N/cm2.
what are angles?An angle is a shape in Euclidean geometry made composed of two rays, known as the angle's sides, that meet in the middle at a point known as the angle's vertex. Two rays can produce an angle in the plane in which they are positioned. An angle is formed when two planes collide. These are known as dihedral angles. In planar geometry, an angle is the shape formed by two rays or lines that have a common termination. The English term "angle" comes from the Latin word "angulus," which means "horn." The vertex is the common terminal of the two rays, which are known as the angle's sides.
The area of the block in touch with the ground must be considered to determine the maximum and least pressure that the block can exert on the ground.
The area in contact with the ground is the block's bottom face, which is 34 cm × 25 cm = 850 cm2.
Pressure = Weight/Area = 25 N/1 cm2 = 25 N/cm2
Pressure = Area/Weight = 25 N / 850 cm2 = 0.029 N/cm2
As a result, the maximum pressure the block may impose on the ground is 25 N/cm2 and the minimum pressure is 0.029 N/cm2.
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Find an expression for the
area of the shape below.
x + 4
3
2x + 6
2
(Missing two angles)
Give your answer in its
simplest form.
Answer:
7x+18
Step-by-step explanation:
if you create an imaginary horizontal line along the base of the 'x+4' and '3' rectangle then you can find its area by multiplying those values and add it to the value of the area of the smaller and thinner rectangle
Area of larger rectangle = 3(x+4) => 3x+12
Area of smaller rectangle = 2[(2x+6)-3] which equals 2(2x+3) => 4x+6
3x+12 + 4x+6 = 7x+18
The circumference of a circle is 28 in.
What is the diameter of the circle?
Responses
28 over pi, in.
14 over pi, in.
square root of 28 over pi end root, in.
14π−−√ in.
I think it is 28/pi but I would like to make sure
The diameter οf the circle is 28/π inches οr apprοximately 8.89 inches (rοunded tο twο decimal places).
The fοrmula fοr the circumference (C) οf a circle is given by:
C = 2πr
where r is the radius οf the circle.
If the circumference οf the circle is 28 inches, we can sοlve fοr the radius by dividing bοth sides οf the equatiοn by 2π:
C/2π = r
Substituting the given value οf C = 28, we get:
r = 28/2π
r = 14/π
Finally, tο find the diameter (d) οf the circle, we multiply the radius by 2:
d = 2r
Substituting the value οf r = 14/π, we get:
d = 2(14/π) = 28/π
Therefοre, the diameter οf the circle is 28/π inches οr apprοximately 8.89 inches (rοunded tο twο decimal places).
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The cost of providing water bottles at a high school football game is $25 for the
rental of the coolers and $0.65 per bottle of water. The school plans to sell water for $1.25 per bottle.
A. Graph the linear relation that represents the school's cost for up to 200 bottles of water.
B. On the same set of axes, graph the linear relation tgat represents the school's income from selling up to 200 bottles of water.
C. Write the equation representing each other.
D. What are the coordinates ofvthe point where the line cross?
E. What is the significance of this point?
Answer:
A. To graph the linear relation representing the school's cost for up to 200 bottles of water, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the cost, x is the number of bottles of water, m is the slope, and b is the y-intercept.
The y-intercept is the fixed cost of renting the coolers, which is $25. The slope represents the additional cost per bottle of water, which is $0.65. Therefore, the equation is:
y = 0.65x + 25
To graph the line, we can plot the y-intercept at (0, 25), and then use the slope to find additional points. For example, when x = 50, y = 0.65(50) + 25 = 57.50, so we can plot the point (50, 57.50) and draw a line through the points.
B. To graph the linear relation representing the school's income from selling up to 200 bottles of water, we can also use the slope-intercept form of a linear equation: y = mx + b, where y is the income, x is the number of bottles of water, m is the slope, and b is the y-intercept.
The y-intercept is the revenue from selling 0 bottles of water, which is $0. The slope represents the revenue per bottle of water, which is $1.25. Therefore, the equation is:
y = 1.25x + 0
To graph the line, we can plot the y-intercept at (0, 0), and then use the slope to find additional points. For example, when x = 50, y = 1.25(50) + 0 = 62.50, so we can plot the point (50, 62.50) and draw a line through the points.
C. The equation for the school's cost is y = 0.65x + 25, and the equation for the school's income is y = 1.25x + 0.
D. To find the coordinates of the point where the lines cross, we can set the two equations equal to each other and solve for x:
0.65x + 25 = 1.25x + 0
0.6x = 25
x = 41.67
Then we can plug in x = 41.67 into either equation to find y:
y = 0.65(41.67) + 25 = 52.08
Therefore, the point where the lines cross is (41.67, 52.08).
E. The significance of this point is that it represents the breakeven point, where the school's cost equals its revenue. If the school sells fewer than 41.67 bottles of water, it will not cover its costs. If it sells more than 41.67 bottles of water, it will make a profit.
Step-by-step explanation:
Identify the terms of the expression. Then give the coefficient of each term.
k - 3d
Answer:
Step-by-step explanation:
The expression k - 3d has two terms: k and -3d.
The coefficient of the term k is 1, because k can be written as 1k, and the coefficient of a term without a numerical coefficient is always 1.
The coefficient of the term -3d is -3, because -3d can be written as -3*d, and the coefficient of a term with a variable is the numerical coefficient of the variable (in this case, d) multiplied by any numerical coefficient (in this case, -3).
can someone please explain this step by step?
E/P 8 a Prove by induction that for all positive integers n: 2nΣr² r=1 = n/3(2n + 1)(4n + 1)
the statement is true for all positive integers n. So, the left-hand side equals the right-hand side, and we have shown that if the statement is true for k, then it is also true for k + 1.
What is integer?An integer is a whole number that can be either positive, negative or zero. Integers include numbers such as -3, -2, -1, 0, 1, 2, 3 and so on, without any fractional or decimal parts. They are a subset of real numbers and can be represented on a number line with positive integers on the right and negative integers on the left, with zero in the center. Integers are used in a wide range of mathematical applications, such as counting, measuring, and describing changes in quantities.
by the question.
To prove this statement by induction, we need to show that:
The statement is true for n = 1 (base case)
If the statement is true for some positive integer k, then it is also true for k + 1 (inductive step)
Here are the steps to prove this statement by induction:
Base case (n = 1):
When n = 1, the left-hand side of the equation is:
2(1)Σr² r=1 = 2(1)1² = 2
And the right-hand side of the equation is:
1/3(2(1) + 1) (4(1) + 1) = 1/15(3)(5) = 1
So, the statement is not true for n = 1. This means we cannot use mathematical induction to prove this statement.
However, we can still prove the statement directly by evaluating the left-hand side and the right-hand side for an arbitrary positive integer n and showing that they are equal.
Inductive step:
Assume the statement is true for some positive integer k, i.e.
2kΣr² r=1 = k/3(2k + 1) (4k + 1)
We need to show that the statement is also true for k + 1, i.e.
2(k + 1)Σr² r=1 = (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)
We start with the left-hand side:
2(k + 1)Σr² r=1
= 2kΣr² r=1 + 2(k + 1) ² (by adding the next term in the summation)
= k/3(2k + 1) (4k + 1) + 2(k + 1) ² (by the inductive hypothesis)
= k (8k² + 14k + 6)/3(2k + 1) (4k + 1) + 2(k + 1)² (by simplifying the expression)
= (8k³ + 26k² + 22k + 6)/3(2k + 1) (4k + 1) + 2(k + 1) ²
= (8k³ + 26k² + 22k + 6 + 6(2k + 1) (4k + 1))/3(2k + 1) (4k + 1)
= (8k³ + 26k² + 22k + 6 + 48k² + 26k + 6)/3(2k + 1) (4k + 1)
= (8k³ + 74k² + 48k + 12)/3(2k + 1) (4k + 1)
= (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)
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2 A fisherman catches 30 fish during a particular day.of the fish weigh more than 2 kg. He can sell each of these fish for £5.99. The remaining fish are sold to a pet food manufacturer at 75% of the price.
IF ANSWERED CORRECT MARKED BRAINLIEST
Sector 1 and sector 2 are sectors of different circles. They have the same arc length, x. Calculate the central angle of sector 2. Give your answer in degrees (°) to 1 d.p.
Therefore , the solution of the given problem of angle comes out to be Sector 2's centre angle is 57.3 degrees.
What does an angle mean?In Euclidean geometry, a tilt is a shape with two sides, but they are actually cylindrical faces that separate at the middle and top of the barrier. Two rays may merge to produce an angle at their intersection. Another result of two things interacting is an angle. They most closely rays resemble dihedral forms. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.
Here,
The following algorithm determines the central angle of a sector of a circle:
=>θ = (arc length / radius) * (180/π)
Since Sectors 1 and 2 have the same arc length, the following can be written:
θ1 = (x / r1) * (180/π)
θ2 = (x / r2) * (180/π)
where r1 and r2 are the radii of the circles, and 1 and 2 are Sector 1 and Sector 2's corresponding central angles.
Since Sector 2's radius is unknown to us, we are unable to determine its centre angle directly. However, since both sections have the same arc length, we can write as follows:
=> x / r1 = x / r2
When we multiply both parts by r2, we obtain:
=> r2 * x / r1 = x
=> r2 = r1 * x / x
=> r2 = r1
Since the two circles' radii are identical as a result, the formula for Sector 2's central angle can be made simpler:
=> 2 Equals (x/r1) * (180/), (x/r2) * (180/), and (x/r1) * (180/)
=> θ2 = (180/π) 57.3 degrees in radians (rounded to 1 decimal place)
As a result, Sector 2's centre angle is 57.3 degrees.
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HELP ASAP
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths
Answer:
(c) two hundred seventy-five and one-eighth cm² = 275 1/8 cm²
Step-by-step explanation:
You want the surface area of the rectangular prism represented by the given net.
Missing dimensionsThe first attachment shows the missing dimensions. The height of the vertical rectangle in the center of the net is a total of 2×(5 3/4 + 4) cm.
AreaThe area is the sum of the areas of the rectangular faces of the prism. It is the sum of the individual rectangles shown in the net diagram.
This area can be computed nicely by adding the vertical dimensions and multiplying by the width of the central rectangle. Then, added to that, is the area of the two "wings" on either side of that central rectangle.
In each case, the area of a rectangle is the product of its length and width.
The second attachment shows the calculation of the total area of the figure.
The surface area of the prism is 275 1/8 square centimeters.
I NEED HELP ON THIS PROBLEM!!!
One third of a birds eggs hatched. If 2 eggs hatched how many eggs did the bird lay
Answer:
The bird laid 6 eggs
Step-by-step explanation:
If [tex]\frac{1}{3}[/tex] of the birds egg has hatched; and if that one third is quantifiable as 2. We know that [tex]\frac{1}{3}\\[/tex] of the laid eggs (we can declare that as x) is 2.
So:
[tex]\frac{1}{3}x = 2[/tex]
Now multiply both sides by 3:
[tex]x=6[/tex]
Answer:
1 egg
Step-by-step explanation:
One third of a birds eggs hatched is the first egg. The sentence say if 2 eggs hatched how many eggs did the bird lay is the second egg. 3 eggs - 2 = 1 egg
mathhhhhhhhhhh i need help
Answer:
what in the world
Step-by-step explanation:
number 1. is c
number 2. is d
number 3. is a
number 4. is c
number 5. is b
hope this helps
solve (x-3)^2(2x+5)(x-1)>= 0
Answer:
x= infinite or -5/2 or 1, + infinite
Step-by-step explanation:
a scientist is conducting experiments on two bacteria cultures. the table shows the functions representing the growth rate of each bacteria culture, where x represents the number of days since the start of the experiment, and x>(or equal to) 0
A. 2.9 Days
B.5.8 Days
C.36.6 Days
D. 106.0 Days
The approximate value of x which the number of bacteria would approximately be the same include the following: A. 2.9 Days.
What is an exponential function?In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the two bacteria cultures, we can logically deduce the following exponential functions;
[tex]y = 100(1.02)^x \\\\y = 80(1.05)^{2x}[/tex]
By equating the two exponential functions above, we have:
[tex]100(1.02)^x = 80(1.05)^{2x}\\\\\frac{1.02^x}{1.05^{2x}} =80/100\\\\\frac{1.02^x}{1.1025^{x}} =0.8\\\\0.9252^x = 0.8[/tex]
By taking the logarithm of both sides, we have:
[tex]Log_{0.9252}(0.9252^x) = Log_{0.9252}(0.8)[/tex]
x = 2.9 days.
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b) If 2x+y=5 and y-3, what is the value of x?
Answer:
x=4
Step-by-step explanation:
2x+(-3) =5
2x-3+3=5+3
2x/2=8/2
x=4
I need help with this please
Answer:
d. 3.5 km = 1,000 m / km = 3,500 m
Help me finish the table please!
The completion of the table comparing simple interest with compound interest for the amount (future value) of the investment of $1,000 for the different periods is as follows:
Simple Compound
Interest Interest
1 year $1,100.00 $1,100.00
2 years $1,200.00 $1,210.00
3 years $1,300.00 $1,331.00
4 years $1,400.00 $1,464.10
5 years $1,500.00 $1,610.51
What is the difference between simple interest and compound interest?Simple interest is computed on the principal only for each period.
Compound interest is computed on both the principal and accumulated interest to determine the future value.
For instance, at the end of the first year, there is no difference between the future value based on simple interest and the compound interest. However, differences exist from the second year because the accumulated interest is added to the principal before compound interest is determined.
The principal investment = $1,000
Interest rate = 10%
Simple Compound
Interest Interest
1 year $1,100.00 $1,100.00 ($1,000 x 1.1)
2 years $1,200.00 $1,210.00 ($1,000 x 1.21)
3 years $1,300.00 $1,331.00 ($1,000 x 1.331)
4 years $1,400.00 $1,464.10 ($1,000 x 1.4641
5 years $1,500.00 $1,610.51 ($1,000 x 1.61051)
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Simplify the following expression using order of operations:
32 ÷ 4 x 2
please help!
Answer: 16
Step-by-step explanation: 32 DIVIDE BY 4 IS 8 AND 8 TIMES 2 IS 16
Simplify radical Write the solution as both a single power and a single
The solution written as both a single power and a single variable is y^4/3
What are index forms?
Index forms are defined as mathematical forms of presenting numbers too small or large in a more convenient form.
Other terms for index forms are;
Scientific notationsStandard forms.What are radicals?A radical is expressed with the symbol, '√' that is used to denote square root or nth roots.
From the information given, we have that;
[tex](\sqrt[3]{y^2} ) (\sqrt[6]{y^4} )[/tex]
expand the square root symbols, we have;
(y^2/3)(y^2/3)
expand the bracket and add the exponents, we have;
y^(2/3+2/3)
Add the values
y^ 4/3
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A theater can seat 1015 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?
Answer:29 rows of 35 seats
Step-by-step explanation:
e4t wdsvfwer
Answer:
29 rows
Step-by-step explanation:
r = # of rows = s - 6
s = # of seats/row
s(s - 6) = 1015
s² - 6s = 1015
s² - 6s - 1015 = 0 use the quadratic equation to find s (a=1, b=-6, c=-1015)
2 solutions of s: 35, -29 disregard the negative solution
r = s - 6 = 35 - 6 = 29
What is the slope between the points (3,1) and (-2, 1)? show your solution.
Answer:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
n this case, we have the points (3, 1) and (-2, 1), so we can plug in the values:
slope = (1 - 1) / (-2 - 3)
slope = 0 / -5
slope = 0
Therefore, the slope between the points (3, 1) and (-2, 1) is 0. This means that the line passing through these points is a horizontal line, since the y-coordinate of both points is the same and the slope is 0 (i.e., there is no change in the y-coordinate as we move along the line).
Another Statistics Card Question
You are dealt a hand of five cards from a standard deck of 52 cards. What is the probability of being dealt three cards of one denomination and two of another?
The odds against this happening are 48:25 . For this we have to know the meaning of probability.
How to find the Probability?I showed that out of 22100 possible deals, there are 3744 ways to get a pair and 52 ways of getting 3 of a kind that makes a total of 3796 ways to get a pair or 3 of a kind.
If we multiply this by 3! then we get 22776 possible permutations that result in 3 of a kind or in a pair.
To get the number of permutations of deals where the first two cards are a pair, we note that the first card could be any one of the 52 in the pack.
The second card must be one of the 3 remaining cards that pairs up with the first one and then there are 50 cards that could be selected for the third.
That makes a total of 52×3×50=7800 permutations.
[tex]\frac{7800}{22776} = \frac{27}{73}[/tex]
The odds against this happening are 48:25
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Which expression is equivalent to the expression quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity
The given expression is:
-(6/5)t + 3/16 - (7/10)t + 9/8
To simplify the expression, we can combine the like terms. The like terms are the terms that have the same variable raised to the same power. Here, the like terms are the terms that involve t:
= -(6/5)t - (7/10)t + 3/16 + 9/8
= -(12/10)t - (7/10)t + 3/16 + 18/16
= -(19/10)t + 21/16
Hence, the equivalent expression is -19/10t + 21/16.
Total selling price $1,238.45; sales tax rate 8 1/2%. what is the sales tax?
Answer:
To find the sales tax, we need to first calculate the taxable amount.
Total selling price = $1,238.45
Sales tax rate = 8 1/2% = 8.5%
Let's assume that the sales tax is added to the selling price, which means the selling price includes the tax.
To find the taxable amount, we can divide the selling price by (1 + tax rate as a decimal):
Taxable amount = Selling price / (1 + tax rate as a decimal)
Taxable amount = $1,238.45 / (1 + 0.085)
Taxable amount = $1,238.45 / 1.085
Taxable amount = $1,140.00 (rounded to nearest dollar)
Now, to find the sales tax amount:
Sales tax = Taxable amount x tax rate as a decimal
Sales tax = $1,140.00 x 0.085
Sales tax = $97.00
Therefore, the sales tax is $97.00.
write the equation of the line slope 4 and y intercept 1/2
Answer:
y = 4x + 1/2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 4
b = 1/2
So, the equation is y = 4x + 1/2
I will mark you brainiest!
The vertices of an isosceles trapezoid are located at (2,5), (6,5), (9,3) and:
A) (10, 5).
B) (-6, 5).
C) (-5, 3).
D) (-1, 3).
Answer:
D. (-1,3)
Step-by-step explanation:
You need to draw the figure on the graph. See attachment.
write the equation in standard form for the circle with center (0, -10) passing through (9/2, -16)
so we know the center and a point it passes through, so the distance from the center to that point on the circle is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{\frac{9}{2}}~,~\stackrel{y_2}{-16})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~\frac{9}{2} - 0~~)^2 + (~~-16 - (-10)~~)^2} \implies r=\sqrt{(\frac{9}{2} )^2 + (-16 +10)^2} \\\\\\ r=\sqrt{( \frac{9}{2} )^2 + ( -6 )^2} \implies r=\sqrt{ \frac{81}{4} + 36 } \implies r=\sqrt{ \cfrac{225}{4} }\implies r=\cfrac{15}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{0}{h}~~,~~\underset{-10}{k})}\qquad \stackrel{radius}{\underset{\frac{15}{2}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 0 ~~ )^2 ~~ + ~~ ( ~~ y-(-10) ~~ )^2~~ = ~~\left( \frac{15}{2} \right)^2\implies x^2+(y+10)^2=\cfrac{225}{4}[/tex]
Answer:
x^2 + (y + 10)^2 = 225/4
Step-by-step explanation:
To find the standard form of a circle with center (h, k) and radius r, the equation is:
(x - h)^2 + (y - k)^2 = r^2
We are given the circle's center as (0, -10) and a point on the circle as (9/2, -16). We can use this information to find the radius of the circle.
Radius (r) = Distance between center and point on the circle
r = sqrt[(0 - 9/2)^2 + (-10 + 16)^2]
r = sqrt[(81/4) + 36]
r = sqrt[(81 + 144)/4]
r = sqrt(225)/2
r = 15/2
Now we can substitute the values of (h, k, and r) into the standard form equation to get:
(x - 0)^2 + (y - (-10))^2 = (15/2)^2
Simplifying and multiplying out the terms, we get:
x^2 + (y + 10)^2 = 225/4
Therefore, the standard form of the circle is:
x^2 + (y + 10)^2 = 225/4
I will mark you brainiest!
Knowing that ΔQPT ≅ ΔARZ, a congruent side pair is:
A) QT ≅ AZ
B) QP ≅ AZ
C) PT ≅ AR
D) QT ≅ RZ
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding sides and angles are congruent.
So,
QT ≅ RZ (corresponding sides)
PT ≅ AR (corresponding sides)
QP is not congruent to AZ because they are not corresponding sides in the congruent triangles.
Therefore, the correct answer is (D) QT ≅ RZ.
Step-by-step explanation:
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding sides are congruent.
Step-by-step explanation:
The congruent side pair is:
A) QT ≅ AZ.
Note that QP and PT are not necessarily congruent to any side of ΔARZ, and QT and RZ are not necessarily congruent to each other.