State the postulate or theorem that can be used to prove the triangles congruent.If you cannot prove the triangles congruent, write not enough information.
Answers
To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.
What are the postulates?The postulates are:
SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.
ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.
SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.
AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.
HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.
From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.
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Related Questions
Which of the following could be the vertex of a parabola with x-intercepts of (-12, 0) and (14, 0)?
A: (1, 9)
B: (3, 7)
C: (7, 3)
D: (9, 1)
Answers
What is the solution to the equation 5(3x-1)=10?
Answers
Answer: x = 1
Step-by-step explanation:
5(3x-1) = 10
Use distributive property and multiply 5 times 3x and 5 times -1.
15x-5 = 10
Move -5 to the right of the equal sign making it positive.
15x = 10+5
Solve.
15x = 15
Divide both sides of the equal side by 15.
15x÷15 = 15÷15
Solve.
x=1
Hope this helps :)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5(3x - 1) = 10}[/tex]
[tex]\mathsf{5(3x) + 5(-1) = 10}[/tex]
[tex]\mathsf{15x - 5 = 10}[/tex]
[tex]\textbf{ADD 5 to BOTH SIDES}[/tex]
[tex]\mathsf{15x - 5 + 5 = 10 + 5}[/tex]
[tex]\textbf{SIMPLIFY it}[/tex]
[tex]\mathsf{15x = 10 + 5}[/tex]
[tex]\mathsf{15x = 15}[/tex]
[tex]\textbf{DIVIDE 15 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{15x}{15} = \dfrac{15}{15}}[/tex]
[tex]\textbf{SIMPLIFY it}[/tex]
[tex]\mathsf{x = \dfrac{15}{15}}[/tex]
[tex]\mathsf{x = 1}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 1}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
what is 345 divided by 2:3
Answers
Answer:
Est: 517
Answer: 517.499999974
Step-by-step explanation:
Louis has 1 green counter, 2 white counters
and 2 yellow counters in a box.
Louis takes one counter at random from the
box, puts it back, and takes another
counter from the box.
Answers
The probability that Louis takes two green counters is 1/9, since there is only one green counter in the box.
What is random probability? Random probability is a mathematical concept that describes the likelihood of a given event occurring. It is a measure of the chance that a certain event will happen, expressed as a percentage or a fraction. Random probability is based on the idea that all outcomes of a situation are equally likely to occur, and the probability of any event occurring is the same as any other event. For example, the probability of rolling a six on a standard die is 1/6, or 16.7%. Random probability is used in many different fields, from gambling to weather forecasting. It is also used in scientific experiments and research, to determine the likelihood of a certain outcome occurring. Random probability can be used to measure the probability of success in any given situation. For example, a company may use random probability to determine how likely it is for a particular product to be successful in the market. By understanding random probability, companies can make more informed decisions about their products and services, and gain a better understanding of their risks and rewards.To learn more about probability refer to:
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A fruit juice company include 1. 751 ounce of juice in a 6. 45
-ounce bottle of a mixed fruit juice. How much of the bottle of mixed fruit juice i NOT juice?
Answers
73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.
To find out how much of the 6.45-ounce bottle is not juice, we need to subtract the amount of juice in the bottle, which is 1.751 ounces, from the total volume of the bottle, which is 6.45 ounces.
6.45 ounces - 1.751 ounces = 4.699 ounces
So, 4.699 ounces of the 6.45-ounce bottle is not juice.
Alternatively, we can express the answer as a percentage of the total volume of the bottle:
(4.699 / 6.45) x 100 = 73.14 %
So, 73.14 % of the 6.45-ounce bottle of mixed fruit juice is not juice.
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1. Parker Electronics sold 450 cell phones in January. Since then, their cell phone sales have increased at a rate of 4.75% per month.
Answers
a) The exponential function defining the monthly cell phones sold is given as follows: y = 450(1.0475)^t.
b) The predicted amounts are given as follows:
April: 542.October: 716.How to model the exponential function?The general format of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.The parameters for this problem are given as follows:
a = 450.b = 1 + 0.0475 = 1.0475. (increase of 4.75%).Hence the function is defined as follows:
y = 450(1.0475)^x.
Then the amounts are given as follows:
April: y = 450 x (1.0475)^4 = 542. -> Month 4.October: y = 450 x (1.0475)^10 = 716. -> Month 10More can be learned about exponential functions at https://brainly.com/question/25537936
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How do you graph logarithms?.
Answers
Step 1: Find some points on the exponential f(x). The more points we plot the better the graph will look.
Step 2: Switch the x and y values to obtain points on the inverse.
Step 3: Determine the asymptote.
Graph the following logarithmic functions. State the domain and range.
A logarithmic scale (or log scale) is a way of displaying numerical facts over a completely extensive range of values in a compact manner—typically the biggest numbers inside the data are loads or even lots of times large than the smallest numbers.
Logarithmic scales are useful for quantifying the relative alternate of a fee in place of its absolute distinction. moreover, because the logarithmic feature log(x) grows very slowly for huge x, logarithmic scales are used to compress massive-scale scientific statistics.
A logarithm is an exponent or power to which a base need to be raised to yield a given quantity. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logo n. for example, 23 = 8; therefore, 3 is the logarithm of eight to base 2, or 3 = log2 eight.
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Is the domain of a function always all real numbers?.
Answers
The domain of a function is not always all real numbers.
We know that the domain of function is the set of all possible input values for which the function is well defined.
And the range of function is the set of all possible output values for given input.
As we know the domain of a function, f(x), is all real numbers when there are no restrictions on what we can take input for x, as all real numbers would make function f(x) true.
But the domain of a function is not always all real numbers.
consider the function f(x) = 1/x
This function is not defined for x = 0
So, the domain of above function f(x) is R - {0}
Also, we know that the domain of a logarithmic function is all non-zero positive real numbers.
Thus, the domain is not always set of all real numbers.
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26
1 point
N
Rose is filling her swimming pool with water. She needs to pump 2000 gallons into the pool, and the water flows at a rate of r gallons
per hour. Which of the following expresses the amount of time it will take to fill the pool?
2000
2000
T
2000 + T
2000r
Answers
T = 2000/r expresses the amount of time it will take to fill the pool.
What is Rate of Gallons?The volume of liquid that can be poured, dispensed, or eaten in an hour is measured in gallons per hour.
It gauges how quickly a liquid may travel from one location to another. The flow rate of liquids in pipes, tanks, and other vessels can be determined using the rate of r gallons per hour.
The flow rate of liquids through pumps and other mechanical devices can also be measured using this technique.
You may calculate the amount of liquid utilized or consumed in an hour using the rate of r gallons per hour.
This can be useful for estimating how much water will be consumed over a certain length of time.
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Rina ha been viiting the coffee hop everyday for 7 day. Each day, he pent a dollar more than he did the day before. If he tarted going to the coffee hop on Monday, pending $ 1, how much did he pend on average daily for that week?
Answers
Rina has been visiting the coffee shop every day for 7 days and he spent an average of $1 each day he visited the coffee shop during the week.
He started on Monday, spending $1, and each day he spent a dollar more than he did the day before. By the end of the week, he had spent $7. To calculate the average amount he spent each day, add up the total amount of money he spent that week and divide it by 7 (the total number of days he visited the shop).
7/7=1
In this case, the total amount of money spent was $7, so when divided by 7, the average amount spent each day is $1. Therefore, Rina spent an average of $1 each day he visited the coffee shop during the week.
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Wyatt is typing his science paper. He can type 50 words per minute. Write an equation that shows the relationship between the number of minutes Wyatt types, x, and the number of words he types, y. y=
Answers
Answer:
Step-by-step explanation:The equation that shows the relationship between the number of minutes Wyatt types, x, and the number of words he types, y, is:
y = 50x
This equation shows that the number of words Wyatt types is directly proportional to the number of minutes he types. For every 1 minute he types, he types 50 words.
This equation can also be read as "y is equal to 50 multiplied by x" which means that for any given number of minutes, x, that Wyatt types for, the number of words he types will be 50 times that value.
HELP ME I NEED IT ITS DUE TODAY!!!
Math on the Spot Manda wants to know the distance
between her front door and her neighbor's. She located
points P, Q, and R. How can she find MN?
Answers
Answer:
mn = 20ft is the answer (I hope it helps)
10. Christian sold tickets to the Golden Knights hockey game. Lower Level seats were $50 each and Upper
Level seats cost $20 each. 2100 people attended and paid $66000. Write a system of linear equations that
can be used to find how many Lower Level seats (x) and how Upper Level seats (y) were sold. How many
of each type of seat were sold?
Answers
1500 Lower Level seats and 600 Upper Level seats were sold.
What is linear equation?Linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x is a variable. In this equation, a is referred to as the coefficient of x and b is referred to as the constant. Linear equations are used to represent relationships between two variables and can be used to solve for either variable. Linear equations are used in many different fields of mathematics, including algebra, calculus, and geometry.
System of linear equations:
50x + 20y = 66000
x + y = 2100
Solving the system of equations gives:
x = 1500
y = 600
Therefore, 1500 Lower Level seats and 600 Upper Level seats were sold.
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x+y=4 in slope intercept form
Answers
Answer:
y=-x+4
Step-by-step explanation:
have a good day
Answer:
y=-x+4
slope intercept form is y = mx+c
m is 1 and c is 4
y=- x +
Step-by-step explanation:
URGENT!
find the value of x in each supplementary angle pair
Answers
Answer: X=9
180 -108=72
72/8=9
Answer:
x = 9° (or) 8x = 72°
Step-by-step explanation:
Now we have to,
→ find the required value of x.
We know that,
→ Straight line is always 180°.
Forming the equation,
→ 8x + 108° = 180°
Then the value of x will be,
→ 8x + 108° = 180°
→ 8x = 180° - 108°
→ 8x = 72°
→ x = 72° ÷ 8
→ [ x = 9° ]
Hence, the value of x is 9°.
The jazz band sells 30 large boxes of fruit and 75 smallboxes of fruit for a fundraiser
a. Use the Distributive Property to write and simplify an expression for
the profit
b. A large box of fruit costs $7 and a small box of fruit costs $3. What is the juz band's profit?
Answers
Jazz Band Makes $785 in Profit.
What is the juz band's profit ?31 huge boxes and 74 little boxes of fruit are sold by the jazz band.
The cost is $x and the price is $20 for each huge fruit box.
Price minus Cost is referred to as profit.
Profit therefore equals 20 - x for one large fruit box.
31 huge fruit boxes at a profit (20 - x)
Each little fruit box costs $10 and costs $10 per small fruit box.
Each tiny fruit box has a profit of 10–y.
74 little fruit boxes worth of profit (10 - y)
For 74 small boxes and 31 large boxes, the overall profit will be:
Profit overall equals 31 (20-x) + 74. (10 - y)
We can reduce the problem above by using the distributive property as follows:
Total profit is equal to 31(20)-31x + 74(10)-74y.
Profit total = 1360 - 31 x - 74 y
Part B)
Each large package is estimated to cost $9.
Accordingly, x = 9.
Each tiny box is stated to cost $4.
Therefore, y = 4.
We can determine the Jazz Band's profit by using the x and y numbers from the profit equation.
Profit of Jazz Band = 1360 - 31(9) - 74. (4)
Jazz Band Makes $785 in Profit
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triangle k a p is congruent to Triangle akr by rule
Answers
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. The rules to show this include SSS, SAS, ASA.
How to explain the triangle congruenceSide-Side-Side (SSS) Rule The SSS rule states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent
The SAS rule states that if two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
The ASA rule states that if two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.
An overview was given due to the incomplete information.
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The scatter plot shows the systolic blood pressure of people of several different ages. The equation represents the linear model for this data. Y = x + 95 according to the model, how much does the systolic blood pressure increase for each year of age? responses 1 mm hg per year 1 mm hg per year 5 mm hg per year 5 mm hg per year 15 mm hg per year 15 mm hg per year 95 mm hg per year 95 mm hg per year 110 mm hg per year 110 mm hg per year.
Answers
The true statement is that blood pressure increases by 1 mm HG per year.
In geometry, we have seen the lines drawn on the coordinate plane. To predict whether the lines are parallel or perpendicular or at any angle without using any geometrical tool, the best way to find this is by measuring the slope. In this article, we are going to discuss what a slope is, slope formula for parallel lines, perpendicular lines, slope for collinearity with many solved examples in detail.
What is a Slope?
The equation that represents the linear model is:
y =x+95
Linear regression is represented as:
y=mx+b
Where:
m represents the slope
b represents the y-intercept
By comparison, we have: m=1
This means that:
The blood pressure increases by 1 mm HG per year.
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What substitution should be used to rewrite 4x12 5x6 14 0 as a quadratic equation U x2 U x3 U x6 U x12?.
Answers
The substitution that should be made to rewrite the given equation 4x¹² - 5x⁶ - 14 = 0 as a quadratic equation is (c) U = x⁶ .
The Quadratic Equations can be defined as a type of polynomial equations which has the highest degree of 2 , it is a algebraic equation of the second degree in x .
The given equation is ; 4x¹² - 5x⁶ - 14 = 0 ;
we have to make this equation a quadratic equation ,
If we substitute , U = x⁶ in the given equation ,
we get ;
⇒ 4(x⁶)² - 5x⁶ - 14 = 0;
⇒ 4(U)² - 5U - 14 = 0 ;
the equation becomes ⇒ 4U² - 5U - 14 = 0, which is a quadratic .
Therefore , the substitution of U = x⁶ , should be used .
The given question is incomplete , the complete question is
What substitution should be used to rewrite 4x¹² - 5x⁶ - 14 = 0 as a quadratic equation
(a) U = x²
(b) U = x³
(c) U = x⁶
(d) U = x¹²
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What is the value of f of 2?.
Answers
The value of f of 2, which means f(2), is 6.
As we know,
f'(x) = [tex]\[ \lim_{h\to0}[/tex] [f(x+h) - f(x)]/h
= [tex]\[ \lim_{h\to0}\\[/tex] [f(3x + 3h)/3 - f(3x + 0)/3]/h
= [tex]\[ \lim_{h\to0}\\[/tex] [{2 + f(3x) + f(3h)}/3 - {2 + f(3x) + f(0)}/3]/h
∴f'(x) = [tex]\[ \lim_{h\to0}\\[/tex] [f(3h) - f(0)]/3h-0 = f'(0)
⇒ f′(2) = f′(0) = 2 [∵f′(2) = 2]
⇒f′(x) = 2
Now, apply integration on the above equation with respect to x
∴f(x) = 2x + c (1)
Substituting x = 0 = y in f{(x+y)/3} = {2 + f(x) + f(y)]/3
⇒3f(0) = 2 + f(0) + f(0)
∴f(0) = 2
By equation (i) f(0) = 2.0 + c
∴c = 2 [∵f(0) = 2]
Now (1) becomes
∴f(x) = 2(x + 1)
Put x = 2
f(2) = 2(2 + 1) = 2 × 3 = 6
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Could someone please help me on this? The answer is NOT c.
Answers
Answer:
The answer is D the second quadrant.
Step-by-step explanation:
HAVE A GREAT DAY!!!!!
2x^ 3 +17x^ 2 +20x+6 is divided by 2 x + 1
Answers
Answer:
The quotient is x^2 + 9x + 6 with a remainder of 6.
Step-by-step explanation:
I used the polynomial long division method to divide the polynomial 2x^3 + 17x^2 + 20x + 6 by 2x + 1.
First, I divided the leading coefficient of the dividend (2x^3) by the leading coefficient of the divisor (2x). This gave me x^2 as the first term of the quotient.Next, I multiplied the divisor (2x + 1) by the first term of the quotient (x^2) to get 2x^3 + x^2.I then subtracted this product from the dividend (2x^3 + 17x^2 + 20x + 6) to get 17x^2 + 20x + 6 as the new dividend.I then brought down the next term of the dividend (17x^2) and divided it by the leading coefficient of the divisor (2x) to get 8.5x as the next term of the quotient.I then multiplied the divisor (2x + 1) by this term (8.5x) to get 17x^2 + 8.5x.I subtracted this product from the new dividend (17x^2 + 20x + 6) to get 0.5x + 6 as the new dividend.I brought down the next term of the dividend (0.5x) and divided it by the leading coefficient of the divisor (2x) to get 0.25x as the next term of the quotient.I multiplied the divisor (2x + 1) by this term (0.25x) to get 0.5x.I subtracted this product from the new dividend (0.5x + 6) to get 6 as the remainder.So the quotient is x^2 + 8.5x + 0.25x which simplifies to x^2 + 9x + 6 and the remainder is 6.
Answer:
[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]
Step-by-step explanation:
[tex] \sf \frac{2x^ 3 +17x^ 2 +20x+6}{ 2 x + 1}[/tex]
2x³/2x = x²
[tex] \sf \frac{x^ 2 +17x^ 2 +20x+6}{ 1}[/tex]
[tex] \sf x^ 2 +17x^ 2 +20x+6[/tex]
for each sequence,find the first 4th terms and the 10th terms.
a)10-n
b)6-2n.
Answers
The numbers for the sequences are 10-n = 9, 8, 7, 6, 0, and 6-2n = 4,2, 0, -2, and -14.
What is a sequence?A sequence is a series of numbers that follow the sample principle in terms or order. In this case, the sequence is determined by the equations given, and based on this the numbers are calculated.
What are the numbers in these sequences?10-n:
10 - 1 = 9
10 - 2 = 8
10 - 3 = 7
10 - 4 = 6
And the 10th term is
10- 10 = 0
6-2n:
6 - 2 = 4
6 - 4 = 2
6- 6 = -0
6 - 8 = -2
And the 10th term is
6 - 20 = -14
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4. Triangle XYZ with vertices X(-6, 4), Y(0, 6), and Z(-4, 2):
a) 180° counterclockwise rotation about the origin
b) dilation with scale factor of 3/2 centered at the origin
X')
Y')
Z'
Answers
a) X'(-6, -4), Y'(0, -6), Z'(-4, -2)
b) X'(-9, -6), Y'(0, -9), Z'(-6, -3)
Rotation and dilation in geometry
This question uses the concepts of rotation and dilation in geometry.For the rotation of 180° counterclockwise about the origin, we will use the rotation formula:
(x, y) → (xcosθ - ysinθ, xsinθ + ycosθ)
Where θ is the angle of rotation.
For our 180° rotation, θ = 180°.
We calculate the new coordinates for each vertex:
X(-6, 4) → X'(-6, -4):
(-6cos180° - 4sin180°, -6sin180° + 4cos180°)
Y(0, 6) → Y'(0, -6):
(0cos180° - 6sin180°, 0sin180° + 6cos180°)
Z(-4, 2) → Z'(-4, -2):
(-4cos180° - 2sin180°, -4sin180° + 2cos180°)
For the dilation of the triangle with a scale factor of 3/2 centered at the origin, we will use the dilation formula:
(x, y) → (kx, ky)
Where k is the scale factor.
For our dilation, k = 3/2.
We calculate the new coordinates for each vertex:
X(-6, 4) → X'(-9, -6):
(-6*3/2, 4*3/2)
Y(0, 6) → Y'(0, -9):
(0*3/2, 6*3/2)
Z(-4, 2) → Z'(-6, -3):
(-4*3/2, 2*3/2)
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How do you know if the inverse of a function is a function?.
Answers
Answer:
function-function relation
Step-by-step explanation:
To determine if the inverse of a function is a function, we can use the horizontal line test.
A function is a set of ordered pairs (x, y) where each x value corresponds to one and only one y value. The inverse of a function is a set of ordered pairs (y, x) where each y value corresponds to one and only one x value.
To use the horizontal line test, we draw a horizontal line on a graph of the original function. If the line intersects the graph in more than one point in any vertical section, the inverse is not a function. But if the horizontal line intersects the graph in at most one point in any vertical section, the inverse is a function.
Another way to check if the inverse of a function is a function is to check that the original function is a one-to-one function, meaning that each x value corresponds to one and only one y value. If the original function is not one-to-one, then the inverse is not a function.
It's also possible to check if the inverse of a function is a function by analyzing the equation of the function. If the original function is a one-to-one function, its inverse is also a function
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x-3y=18
Answers
The slope intercept form of a line is,
⇒ y = x - 6
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The equation is,
⇒ 3x - 3y = 18
Now, We know that;
The slope intercept form of the equation is,
⇒ y = mx + b
Here, The equation of line is,
⇒ 3x - 3y = 18
Take 3 as common,
⇒ 3(x - y) = 18
Divide by 3;
⇒ x - y = 18/3
⇒ x - y = 6
⇒ x - 6 = y
⇒ y = x - 6
Thus, The slope intercept form of a line is,
⇒ y = x - 6
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Under what conditions is a radical expression in simplest form?.
Answers
Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both).
Three conditions must be satisfied for a radical expression to be in its simplest form, that is, first, No radicands other than 1 have perfect square factors.
Secondly, there isn't a fraction in any radicand and finally, the fraction's denominator has no radicals.
A radical expression can be reduced to a simple form by first factoring it into primes, then finding the radical's index, and finally moving the group of numbers either inside or outside the radical.
The expressions both inside and outside the radical can then be made simpler by adding up all the numbers inside the radical.
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Mikaela wants to do a poll of everyone at Martin Luther King High School. Which of
these is the best way to get an accurate response?
A.Poll only students in 9th and 11th grades.
B.Poll a random selection of teachers, students and staff.
C.Poll only female teachers and students.
D.Poll only staff who have worked at the school for less than five years.
Answers
Poll only students in 9th and 11th grades would be the best way to get an accurate response. Thus, option A is correct.
What is poll?In electoral campaigns, math is frequently used. The goal of polling is to predict how the electorate will vote overall by taking a small sample of voters and extrapolating their results to the entire population. Pollsters must ensure that their sample of respondents is representative of the entire electorate, or if it is not, they must use a variety of statistical techniques to increase the representativeness of their findings.
In essence, this means that a survey is conducted, and not only are respondents' voting intentions recorded, but also their age, gender, race, and other demographics. As a result, it is possible to make predictions about the voting intentions of various social groups.
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Question- A circle has a circumference of 10π inches and a center of (9, 2). What is the standard form equation of this circle?
Answers:
A. (x-9)^2 + (y-2)^2 = 10
B. (x-9)^2 + (y-2)^2 = 25
C. (x-9)^2 + (y-2)^2 = 3.14
D. (x-9)^2 + (y-2)^2 = 100
Answers
Answer:
[tex]\sf{Choice \;B.\;\; (x-9)^2 + (y-2)^2 = 25[/tex]
Step-by-step explanation:
The standard form equation of a circle with center (a, b) and radius r is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
where (a, b) is the center of the circle.
Here we are given that the circle has center (9, 2)
So the equation becomes
[tex](x-9)^2 + (y-2)^2 = r^2\cdots(1)[/tex]
All we have to do is find the radius and we are done
Circumference of a circle with radius r
[tex]= 2 \pi r\\[/tex]
Given circumference [tex]= 10\pi[/tex]
[tex]10\pi = 2\pi r\\\implies r = 10/2 = 5[/tex]
Substitute this into equation (1):
[tex](x-9)^2 + (y-2)^2 = 5^2\\\\(x-9)^2 + (y-2)^2 = 25\\[/tex]
This corresponds to option B.
The equation of a circle is (x - 9) + (y - 2) = 25.
Option B is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
The equation of a circle is (x - h) + (y - k) = r² _____(A)
Where (h, k) is the center and r is the radius.
Now,
Centre = (9, 2)
This means,
(h, k) = (9, 2) _____(1)
Circumference = 10π
This means,
2πr = 10π
2r = 10
r = 5 in ____(2)
Now,
Substituting (1) and (2) in (A).
(x - h) + (y - k) = r²
(x - 9) + (y - 2) = 5²
(x - 9) + (y - 2) = 25
Thus,
The equation of a circle is (x - 9) + (y - 2) = 25.
Learn more about circle here:
https://brainly.com/question/11833983
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Tomas buys a bag of 5 peaches for 3. 55. Write ans solve an equation to find how much money, m, Tomas has left
Answers
Answer:
Step-by-step explanation:
so if x is the money he had in the beginning, than
m=x-5(3.55)
m=x-$17.75
