Answers
Given:
The equation is,
[tex]\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}[/tex]Explanation:
Simplify the right hand side of equation.
[tex]\begin{gathered} -8x-3-\frac{53}{ax-2}=\frac{(-8x-3)(ax-2)-53}{ax-2} \\ =\frac{-8ax^2-3ax+16x+6-53}{ax-2} \\ =\frac{-8ax^2+(-3a+16)x-47}{ax-2} \end{gathered}[/tex]From left side and right side of equationn it can be observed that,
[tex]-8ax^2=24x^2\text{ and (-3a+16)x=}25x[/tex]Simplify the equation for a.
[tex]\begin{gathered} -8a=24 \\ a=\frac{24}{-8} \\ =-3 \end{gathered}[/tex]OR,
[tex]\begin{gathered} -3a+16=25 \\ -3a=25-16 \\ a=\frac{9}{-3} \\ =-3 \end{gathered}[/tex]So value of a is -3.
Option B is correct.
Related Questions
All of the triangles are dilations of Triangle D. The dilations use the same center P, but different scale factors. 1) What do Triangles A, B, and C have in common? 2) What do Triangles E, F, and G have in common? 3) What does this tell us about the different scale factors used?
Answers
Triangles A, B, and C have a scale factor less than 1 in common
Triangles E, F, and G have a scale factor greater than 1 in commonDifferent scale factors would give different sizes after dilationWhat Triangles A, B, and C have in commonThe figure that completes the question is added as an attachment
From the figure, we can see that triangles A, B, and C are smaller than the original triangle i.e. the triangle D
This means that triangle D is dilated by a scale factor less than 1 to form each of these triangles
What Triangles E, F, and G have in commonThis has just a slight difference to (a)
From the figure, we can see that triangles E, F, and G are bigger than the original triangle i.e. the triangle D
This means that triangle D is dilated by a scale factor greater than 1 to form each of these triangles
What this tell us about the scale factorsThe conclusion about the scale factors is that
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A ball was dropped from the Empire State Building observatory. The height of the ball in feet is described by the function f(x) = 1048 - 16[tex]x^{2}[/tex], where x is the time in seconds.
Find the inverse function [tex]f^{-1}[/tex](x) and explain its meaning.
Answers
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.
What is the inverse function f^-1(x) and its meaning?
Given:
[tex]f(x) = 1048 - 16x^{2}[/tex]
Since the function f(x) is the height (h), we can write the function as :
[tex]h = 1048 - 16x^{2}[/tex]
We will make x the subject:
[tex]16x^{2} = 1048 - h[/tex]
[tex]x^{2} = \frac{1048 - h}{16}[/tex]
[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]
[tex]x = \sqrt{65.5 - 0.0625h }[/tex]
Since:
[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]
Thus:
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]
Therefore, the inverse function is [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.
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what is BIDMAS?
Please answer
Answers
Answer:
BIDMAS is a math term that is used to describe these 6 terms.
Brackets
Indices, which is another word for exponents
Division
Multiplication
Addition
Subtraction
Answer:
It is the order of operation in order to know how to calculate an equation starting from which order.
Step-by-step explanation:
Brackets first
Indices second
Division and multipaction third. From left to right
Addition and subtraction last. From left to right
When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
Answers
Answer:
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
Explanation:
To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.
Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so
r² = 537/1986
r² = 0.2704
r = √0.2704
r = 0.52
Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so
For 1 hour
Amount left = 1986(0.52) = 1032.7 grams
In the same way, the amount left after 3 and 4 hours is
For 3 hours
Amount left = 537(0.52) = 279.2 grams
For 4 hours
Amount left = 279.2(0.52) = 145.2 grams
Therefore, the complete table is
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
REVIEW & REFRESH
42. Tell whether x and y are proportional.
43. What number is 60% of 35?
44. 27 is what percent of 75?
Just do 42 and 44
Answers
Using proportions, it is found that:
42. x and y are not proportional.
43. The number 21 is 60% of 35.
44. The number 27 is 36% of the number 75.
How to verify if two variables are proportional?Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.
From the table, the ratios are given as follows:
6/4 = 1.5.8/6 = 1.25.Different ratios, hence the variables x and y are not proportional.
Percentage of a numberTo find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.
The decimal equivalent of a percentage of 60% is:
60/100 = 0.6.
Hence the percentage of 35 is calculated as follows:
0.6 x 35 = 21.
The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:
27/75 x 100% = 36%.
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two students each use a random number generator to pick an integer between 1 and 8 inclusive. what is the probability that they pick the same number? (enter your answer as a fraction.)
Answers
The probability that they pick the same number is 1/8.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
As given two students each use a random number generator to pick an integer between 1 and 8 inclusive.
So, the possible choices are,
8 - 1 + 1 = 8 Possible choices: 1, 2, 3, 4, 5, 6, 7, 8.
So, the probability is, 1/8.
Therefore, the probability that they pick the same number is 1/8.
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2/3x - 8 when x = 12
Answers
1) For this question, all we need to do is to plug it in the value for x.
So,
2/3x -8 =0 Plugging into x the value x=12
2/3(12) -8 =0
8 -8 =0
0
So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.
A groundskeeper needs grass seed to cover a circular field 290 ft in diameter a store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square ft. What is smallest number of bags there groundskeeper must buy to cover the circular field
Answers
Using the concept of area, we got 165 bags is the smallest number of bags there groundskeeper must buy to cover the circular field.
The branch of mathematics which deals with measuring is known as Mensuration. It was basically first used for land surveys and other civic works in Egypt. The father of mensuration is known as Archimedes. Mensuration is a discipline of mathematics which studies the measurements of various geometrical forms possible and their areas, perimeters, and volumes, among other things.
Diameter of the field = 290 feet, radius = 145 feet
Area of the circular field =[tex]\pi r^{2}[/tex]
=>[tex]\pi[/tex]×145×145 =66018.5 square feet.
No of bags to be brought = 66018.5/400=165bags,
Hence, the smallest number of bags is 165 which groundskeeper must buy to cover the circular field.
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Question 5
Fill in the blank question.
Jack wants to buy a coat that costs $74.95. The sales tax rate in his city is 612% . What is the total cost for the coat?
Answers
The coat has a total cost of $533.644
How to determine the total cost for the coat?From the question, the given parameters are:
Cost of a coat = $74.95
Sales tax in the city = 612%
Using the sales tax, the total cost for the coat is calculated using
Total cost of coat = Cost of a coat + Cost of a coat * Sales tax in the city
Substitute the known values in the above equation
So, we have the following equation
Total cost of coat = 74.95 + 74.95 * 612%
Evaluate the products
Total cost of coat = 74.95 + 458.694
Evaluate the sum
Total cost of coat = 533.644
Hence, the total cost of the coat is $533.644
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EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
c = 23
Step-by-step explanation:
To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.
(2c + 51)° = 97°
Next, you want to subtract 51 from both sides.
(2c + 51) - 51 = 97 - 51
2c = 46
Lastly, you isolate c by dividing 46 by 2.
c = 46 ÷ 2
c = 23
a bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after that which statement is true
Answers
The equation for the cost when the bowling alley charges $14 for the first game $10 for the second game is 24 + 5x.
What is a equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
In this case, the bowling alley charges $14 for the first game $10 for the second game and $5 per game for every game after.
Let the number of games be illustrated as x.
Therefore, the equation will be:
14 + 10 + (5 × x)
= 24 + 5x
This illustrates the cost.
An overview was given as the information given is incomplete.
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-3/2x = 6 solve for x and simplify your answer as much as possible
Answers
Answer: x = -4
Step-by-step explanation:
Multiply both sides by 2 to get:
-3x = 12
Then, divide both sides by -3 to get:
x = -4
Hope this helps!
Answer:
x = -4
Step-by-step explanation:
Two large and 1 small pump can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool?
Answers
Answer: It will take just 1 hour & 36 minutes with 4 large pumps & 4 small pumps
Step-by-step explanation:
Where do I put the dots at
Answers
The numbered disks shown are placed in a boxand one disk is selected at random. Find theprobability of selecting an odd number, given that agreen disk is selected.Find the probability of selecting an odd number, given that a green disk is selected.(Type an integer or a simplified fraction.)
Answers
Given that the numbered disks are placed in a box, you need to find the probability of selecting an odd number, given that a green disk is selected.
Therefore, you need to use the Conditional Probability Formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, let be "A" the event of selecting an odd number, and "B" the event of selecting a green disk.
You can identify that:
- There are a total of 8 disks.
- There are 4 green disks that have odd numbers.
- There are a total of 7 green disks.
Therefore, you can determine that:
[tex]P(A\cap B)=\frac{4}{8}=\frac{1}{2}[/tex]And:
[tex]P(B)=\frac{7}{8}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]P(A|B)=\frac{\frac{1}{2}}{\frac{7}{8}}=\frac{1\cdot8}{2\cdot7}=\frac{8}{14}=\frac{4}{7}[/tex]Hence, the answer is:
[tex]\frac{4}{7}[/tex]On the map, 0.1 inches represents
25 miles. If the real distance between
two cities is 112.5 miles, what is the
distance between their locations on
the map?
A. 0.45 in
B. 2 in
C. 0.2 in
D. 1 in
Answers
The distance between the two cities on the map is 0.45 inches , the correct option is (A) 0.45inches .
In the question ,
it is given that
the scale factor of the map is 25 miles = 0.1 inches
So, 1 mile = 0.1/25 inches
= 0.004 inches
So , on the map 1 mile is represented by 0.004 inches
Given that the real distance between the two cities is 112.5 miles
So , on the map 112.5 miles = 112.5*0.004 inches
= 0.45 inches
Therefore , the distance between the two cities on the map is 0.45 inches , the correct option is (A)0.45inches .
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Angle JKL and angle MKQ are complementary angles. The measures of angle JKL is twice the measure of angle MKQ.• Write one equation to find x, the measure of angle MKQ• Solve for X
Answers
Answer : x = 30 degrees
< JKL and < MKQ are complementary
Let < MKQ = x
Angle JKL is twice the measure of angle MKQ
JKL = 2 x MKQ
Sum of a complementary angles = 90 degrees
< JKL + < MKQ = 90
< JKL = 2MKQ
Substitute the value of < jkl
2(<2MKQ + Since, Therefore,
2x + x = 90
3x = 90
Divide both sides by 3
3x / 3 = 90/3
x = 30 degrees
2) Choose the correct answer.
A given line passes through the points (2, 3) and (2, 3). Determine the equation of the
line that is perpendicular to the given line and passes through the point (1,5).
y = 5
x = -1
x=5
y= -1/2x + 13/3
y = -1
Answers
There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
What is meant by equation?The definition of an equation in algebra exists as a mathematical statement that demonstrates the equality of two mathematical expressions.The equation of a perpendicular line to a line in point-slope form is expressed as:
y - y1 = -1/m(x - x1)m is the slope(x1, y1) is any point on the lineDetermine the slope:
Slope = -3-3/2-2y = ∞Since there is no slope, hence the equation of the line will be in the form y = b.
Where b exists the y-coordinate of the point. Hence the required equation of the line is y = 5Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
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Correct question:
2) Choose the correct answer.
A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).
(A) y = 5
(B) x = -1
(C) x=5
(D) y= -1/2x + 13/3
(E) y = -1
Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.
Answers
The image above represents a proof of the Pythagorean Theorem is image B.
What is Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle.
It states that the sum of the squares of the leg lengths equals the square of the hypotenuse length.
This is illustrated as:
a² = b² + c²
The values in image 2 will be used to ascertain this. Therefore,
5² + 12² = 13²
25 + 144 = 169
169 = 169
Therefore, B is correct as the value is gotten.
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Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation:
The marked price of an article is Rs.2080. After allowing d% discount and levying(d-2)% VAT,the cost of the article becomes Rs 1997.84. find the discount amount and VAT amount
Answers
The discount rate is 15% and the VAT rate is 13%
What is the value of the discount?The following can be deduced:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)
Add VAT:
2080*(1 - 0.01d) + (d - 2)%
2080*(1 - 0.01d) * (1 + (d -2)/100)
2080*(1 - 0.01d) * (0.98 + 0.01d)
= 1997.84
(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
0.98 + 0.01d - 0.0098d - 0.0001d²
= 0.9605
- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
0.0001d²- 0.0002d - 0.0195 = 0
d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Therefore discount is 15%
VAT rate = d - 2 = 15% - 2% = 13%
The concept shown above is the calculation for the discount and the amount of the value added tax.
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Alexis can run 5/2 miles in 1/4hrs. What is her speed in miles per hour?
Answers
Solution
We are given
Distance = 5/2 miles
Time = 1/4 hours
Answer:
The speed would [tex]10~\text{mph}[/tex].
Step-by-step explanation:
Step 1: State the formulas required
The formula for speed is:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Step 2: Substitute the values into the formula
The distance is [tex]\frac{5}{2}~\text{miles}[/tex] and the time is [tex]\frac{1}{4}~\text{hours}[/tex].
Substitute these values into the formula:
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}\\\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\[/tex]
Step 3: Calculate
[tex]\text{Speed}=\frac{\frac{5}{2}}{\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\div {\frac{1}{4}}\\\\\text{Speed}={\frac{5}{2}}\times 4\\\\\text{Speed}={\frac{20}{2}}\\\\\text{Speed}=10[/tex]
So, the speed is [tex]10~\text{miles per hour}[/tex] or [tex]10~\text{mph}[/tex].
If a and b are two events defined on the same sample space, given that p(a) = 0.28 and p(aub) =0.51, find the p(b) such that a and b are mutually exclusive
Answers
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional.
Occurrence to determine the conditional probability. P(A and B) = P(A) * P if A and B are two Independent events (B).
How can you calculate the likelihood of two occurrences, A and B, coming together?
The probability of their union, or the event that either A or B occurs, is equal to the total of their probabilities less the sum of their intersection if two occurrences A and B are not disjoint. P(A) + P(B) - P(A and B) (A and B).
The answer is then (0.28 + P(B) - (0.51 = 0.23).
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SOS I NEED HELP ASAP I MEED IT NOW
Answers
Answer: do c to my very ecucated guess bc c is always right
Step-by-step explanation:
Step-by-step explanation:
PLEASE HELP!!!! Solve using the quadratic formula
Answers
Answer:
Step-by-step explanation:
Given Equation
3x^2 + x = - 2x - 7
Solution
Add 2x + 7 to both sides
3x^2 +x + 2x + 7 = -2x - 7 + 2x + 7 Combine like terms
3x^2 + 3x + 7 = 0
Givens
a = 3b = 3 c = 7x = (-b +/(√b^2 - 4ac))/2
x = (-3 +/- (√3^2 - 4(3 *7)) / 2*3
x = (- 3 +/- (9 - 84)) / 2 *3
x = (- 3 +/- √ (-75))/6
x = (- 3 +/- 8.660i ) / 6
x = -.5 +/-1.443i
Answer
x = -.5 + 1.443.i
x = -.5 - 1.443i
The distance between the points (-2,y) and (3, -7) is 13 units.What are the possible values of y?
Answers
To calculate hte possible values of y you have to apply the Pythagoras theorem:
[tex]a^2+b^2=c^2[/tex]Where
c will be the distance between the given points, and the hypothenuse of a right triangle
a will be the base of a theoretical triangle below the hypothenuse, you calculate it as (x2-x1)
b= will be the heigth of said triangle, you calculate it using the y-coordinates (y2-y1)
So:
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ c=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]Replace the expression with the given measurements to calculate the y-coordinate of the first point:
[tex]\begin{gathered} c=\sqrt[]{(3_{}-(-2))^2+(-7-y)^2} \\ 13=(3+2)+(-7-y) \\ 13=5-7-y \\ 13=-2-y \\ 13+2=-y \\ -15=y \end{gathered}[/tex]The possible values for y, since its
. The population of Star, ID was 1800 people in the year 2000. The population has been growing at a rate of 9.9% annually. a. Write a function that models the population of Star, ID in years since 2000.b. Use your function to predict the population of Star, ID in 2050.c. The function g(x)=11000(1.056)^x models the population of Eagle, ID in years (x) since 2000. Which city is growing faster? How do you know?
Answers
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
Part A:
The function that models the population of Star, ID in years since 2000 is:
[tex]f(x)\text{ = 1800 }(1\text{ + }\frac{9.9}{100})^t[/tex]Part B :
Use your function to predict the population of Star, ID in 2050
[tex]\begin{gathered} \text{Given } \\ f(x)\text{ = 1800 ( 1 + }\frac{9.9}{100}^{})^t \end{gathered}[/tex]The year 2050 means that t= 50, we have that:
[tex]\begin{gathered} f(x)=\text{ 1800 ( 1 + }\frac{9.9}{100})^{50} \\ f(x)=1800X(1+0.099)^{50} \\ f(x)\text{ =}1800(1.099)^{50} \\ f(x)=201,909.6734 \\ f(x)\approx\text{ 201, 910 ( to the nearest whole number)} \end{gathered}[/tex]Part C:
The function:
[tex]g(x)\text{ = 11000 ( 1}.056)^x[/tex]models the population of Eagle, ID in years (x) since 2000.
Which city is growing faster? How do you know?
Answer:
From this equation, we can see that the growth rate is 5.6% annually.
Comparing this, with the initial function:
[tex]f(x)=1800(1.099)^{50}[/tex]We can see that the annual growth rate of f(x) is 9.9 %
CONCLUSION:
The population of Star ID, with the function, g (x) has a faster growth rate.
Rewrite expression (4^-2)^3 using positive exponents
Answers
The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
The given expression is [tex](4^{-2})^3[/tex].
What is a positive exponent?A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
The given expression can be simplified as follows
[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]
So, the positive exponent = [tex]\frac{1}{4^6}[/tex]
Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
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[tex]\sqrt{x} x^2+2x-3[/tex]
Answers
The result of the expression given is 3x - 3
Simplification of Linear EquationTo solve this problem, we have to simplify the equation, and write the expression.
Given that
[tex]\sqrt{x^2}+ 2x -3[/tex]
In the square root, we can eliminate the square and square root using the square root rule.
Lets apply that in this expression
[tex]\sqrt{x^2} + 2x - 3\\x + 2x - 3[/tex]
Lets solve the expression
[tex]x + 2x - 3\\3x - 3[/tex]
The value of the expression given is 3x - 3
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Malika buys 20 bottles of cranberry juice at the corner store for a total cost of $20. If each bottle costs the same amount, how much is each bottle of juice?
Answers
Answer: 1 dollar per bottle
Step-by-step explanation:
If they cost $20 and she bought 20 bottles, we can use division.
$20 / 20 bottles = 1 dollar per bottle
What is the midpoint of a segment with endpoints at (-4.-8) and (8.10)? O A. (-6,-9) OB. (-6,1) OC. (2,-9) OD. (2,1)
Answers
Answer
Option D is correct.
Midpoint = (2, 1)
Explanation
The midpoint of two coordinates is obtained by respective x-coordinates together and dividing by 2 and then doing similarly for the y-coordinate.
(-4, -8) and (8, 10)
Midpoint = (x, y)
x = (-4 + 8)/2 = (4/2) = 2
y = (-8 + 10)/2 = (2/2) = 1
Hope this Helps!!!