Answer:
The required points of the given line segment are ( - 7, - 4 ).
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( - 2, 3 ) and point A is ( 3, 10), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] )then the mid points M are-
M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )
Here,
Let A ( 3, 10 ), B ( x, y ) with midpoint M ( - 2, 3 ) -
then by the midpoint formula M are-
( - 2, 3 ) = ( [tex]\frac{ 3 + x}{2}[/tex] , [tex]\frac{ 10 + y}{2}[/tex] )
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{ 3 + x}{2}[/tex] = - 2 , [tex]\frac{ 10 + y}{2}[/tex] = 3)
( 3 + x = - 4, 10 + y = 6 )
( x = - 4 - 3, y = 6 - 10 )
( x = - 7, y = -4 )
Hence the required points A are ( - 7, - 4 ).
We can also verify by putting these points into Midpoint formula.
Final answer:
To find the other endpoint of a line segment with a known endpoint (3, 10) and midpoint (-2, 3), use the midpoint formula in reverse to calculate the coordinates, resulting in the other endpoint being (-7, -4).
Explanation:
To find the other endpoint of a line segment when given one endpoint and the midpoint, you can use the midpoint formula in reverse. The midpoint formula in two dimensions is
( (x1+x2)/2, (y1+y2)/2 ), where (x1, y1) and (x2, y2) are the endpoints of the line segment. Given that (3, 10) is one endpoint and (-2, 3) is the midpoint, we can set up equations to find the coordinates of the unknown endpoint (x2, y2).
To find x2, we use the formula for x-coordinate of the midpoint: (-2 + 3)/2 = (x2 + 3)/2. Solving for x2 gives us x2 = -2 - 3 = -7.
To find y2, we use the formula for y-coordinate of the midpoint: (3 + 10)/2 = (y2 + 10)/2. Solving for y2 gives us y2 = 2*3 - 10 = 6 - 10 = -4.
Therefore, the other endpoint of the line segment is (-7, -4).
This rectangle has a perimeter of 120
centimeters. If the width is 20 cm, what is
measure of the length?
20 cm
x cm
The length of the rectangle, given a perimeter of 120 cm and a width of 20 cm, is 40 cm.
Explanation:This question pertains to the calculation of the dimensions of a rectangle given its perimeter and one side. In a rectangle, the perimeter is given by the formula 2(Length + Width). In this case, the perimeter is 120 cm, and the width is 20 cm. We can set up the following equation based on the given information: 120 = 2(Length + 20). After simplifying, we get 120 = 2*Length + 40, which leads to 2*Length = 120 - 40 or 2*Length = 80. Finally, solving for Length gives Length = 80 / 2 = 40 cm. Therefore, the length of the rectangle is 40 cm.
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How do you write 33% as a fraction
Answer:
1/3 simplified or 33/100
Step-by-step explanation:
33% is around one third of 100%. Aka, you multiply 33(.33)% by 3 to get 100% or you can leave it as 33/100.
the ratio of the point (-3,k) divides the line segment joining the points (-5,-4) and (-2,3) also find the value of k
Answer:
Step-by-step explanation:
midpoint theorem : (mx₂+nx₁/m+n , my₂+ny₁/m+n)
(-3, k) = ( -3*-2 + k*-5/-3+k , -3*3 + k*-4/-3+k)
(-3, k) = (6-5k/-3+k , -9-4k/-3+k)
Compare x values of both side ;
-3 = 6-5k/-3+k
-3 *( -3+k) = 6-5k
-3*-3 +k *-3 = 6-5k
9 -3k = 6- 5k
5k -3k = 6 - 9
2k = -3
k= -3/2
an exponential function has an
Answer:
Step-by-step explanation:
Exponential functions have the form
f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.
Answer:
Exponential functions have the form
Step-by-step explanation:
There is 1/3 gallon of water in a 3-gallon container. What fraction of the container is filled?
Answer:
3/3 i think sorry if its wrong
Step-by-step explanation:
Answer:
1/3 of the container is filled.
Step-by-step explanation:
One counting number is 4 times great as a counting number.The product of the two number is 36.What is the sum of the two number
Answer:
The sum of the two numbers is 15
Step-by-step explanation:
Let the counting numbers be x and y.
Then we can write the following equations
x=4y.......1 (one is four times greater )
x(y)=36.....2 (the product of the two)
Putting equation 1 into equation 2, we get
4y(y)=36
[tex] {4y}^{2} = 36 [/tex]
Dividing through by 4,we get
[tex] {y}^{2} = \frac{36}{4} [/tex]
[tex] {y}^{2} = 9[/tex]
Taking square root of both side, we obtain
y=3
Putting the value of y into equation , we get
x=4(3)=12
Hence the numbers are 3 and 12
Therefore the sum of the two numbers is 3+12=15
One counting number is 4 times greater as the other counting number. The product of the two numbers is 36. The sum of the two numbers is 15.
Explanation:Let's assume the smaller counting number as X. According to the question, one counting number is 4 times greater than the other, so the larger counting number is 4X. The product of the two numbers is 36, so we can set up an equation: X * 4X = 36. Simplifying, we get 4X^2 = 36. Divide both sides by 4 to get X^2 = 9. Taking the square root of both sides, we find X = 3. Therefore, the two numbers are 3 and 4 times 3 which is 12. The sum of these two numbers is 3 + 12 = 15.
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8. How is the graph of log (x + 3) translated from the graph of log x?
Answer:
shift 3 units left.
Which of the following numbers has a prime factorization of 2 x 5 x 5?
Answer:
5×5
Step-by-step explanation:
the factorazation is 5×5
Final answer:
The number with a prime factorization of 2 x 5 x 5 is 50, which is obtained by multiplying 2 by 5 squared (2 x 25).
Explanation:
The student asked which of the following numbers has a prime factorization of 2 x 5 x 5. The prime factorization given can also be written as 2 x 52, since 5 x 5 equals 52 or 25. Therefore, we are looking for a number that is the product of 2 and 25.
By multiplying 2 by 25, we find that the correct answer is 2 x 25 = 50. Thus, the number that has a prime factorization of 2 x 5 x 5 is 50.
HELP ASAP. Gotta get this done.
Answer:
C
Step-by-step explanation:
The ratio of frames : containers can be calculated using values from table.
3 : 12 = 7 : 28 = 9 : 36 = 1 : 4 ← in simplest form, thus
Number of containers is 4 times the number of frames
Thus for 5 picture frames the number of containers = 5 × 4 = 20 → C
If the expression (2x^4) was written as ax^b form which of the following would be the sum of a and b?
Answer:
6
Step-by-step explanation:
2x^4
a = 2
x = x
b = 4
a + b
2 + 4
6
The sum of a and b for the expression (2x^4) in ax^b form is 6, where a is 2 and b is 4.
Explanation:The expression given is (2x^4), which is already in ax^b form. In this expression, a is the coefficient of the x term, and b is the exponent applied to the x variable. In this case, a is 2 and b is 4.
To find the sum of a and b, you simply add the two numbers together.
The sum of a and b is:
2 + 4 = 6
This result is achieved by recognizing that a represents the constant in front of the x term, and b represents the power to which x is raised.
Adding these two values gives us the sum of the coefficients and exponents in the ax^b expression.
Is p = 6m + 9m a proportional relationship?
Answer:
yes
Step-by-step explanation:
A football team loses a total of 12 yards in 4 plays. On average how many yards did the team move the ball per play?
The team moved the ball -3 yards per play.
Step-by-step explanation:
Given,
Total yards lost = 12 yards
Total plays = 4 plays
As the yards are lost, therefore, we will use negative sign.
Yards per play = [tex]\frac{Number\ of\ yards}{Number\ of\ plays}[/tex]
Yards per play = [tex]\frac{-12}{4}[/tex]
Yards per play = -3
The team moved the ball -3 yards per play.
Keywords: division, unit rate
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Samantha is measuring the snowfall in a snow Gog for her science project. The first week she measured 3 3/4 inches of snow the second week she measured twice as much snow, and the third weekShe measured half as much snow as the first week. It did not snow at all in the fourth week. How much snowfall did Samantha measure for the entire month? Explain
Samantha measured [tex]13\frac{1}{8}[/tex] inches for the entire month
Step-by-step explanation:
Samantha is measuring the snowfall in a snow Gog for her science project
The first week she measured 3 3/4 inches of snowThe second week she measured twice as much snow, and the third week she measured half as much snow as the first weekIt did not snow at all in the fourth weekWe need to find how much snowfall Samantha measured for the entire month
∵ She measured [tex]3\frac{3}{4}[/tex] inches of snow in the 1st week
- Change the mixed number to improper fraction
∵ [tex]3\frac{3}{4}=\frac{(3)(4)+3}{4}=\frac{12+3}{4}=\frac{15}{4}[/tex]
∴ She measured [tex]\frac{15}{4}[/tex] inches of snow in the 1st week
∵ She measured twice as much snow as the 1st week in the 2nd week
- Multiply the value of the 1st week by 2
∵ [tex]\frac{15}{4}[/tex] × 2 = [tex]\frac{30}{4}[/tex]
∴ She measured [tex]\frac{30}{4}[/tex] inches of snow in the 2nd week
∵ She measured half as much snow as the 1st week in the 3rd week
- Multiply the value of the 1st week by 1/2
∵ [tex]\frac{15}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{15}{8}[/tex]
∴ She measured [tex]\frac{15}{8}[/tex] inches of snow in the 3rd week
∵ It did not snow at all in the fourth week
- Add the values of the three weeks above to find the amount
of snowfall she measured for the entire month
∵ The amount of snowfall = [tex]\frac{15}{4}+\frac{30}{4}+\frac{15}{8}[/tex]
- To add the fraction you must make all the denominator same number
so multiply the 1st and 2nd fractions by 2 up and down to make all
the denominator equal 8
∴ The amount of snowfall = [tex]\frac{30}{8}+\frac{60}{8}+\frac{15}{8}[/tex]
- Add the numerators and put the sum over 8
∴ The amount of snowfall = [tex]\frac{105}{8}[/tex]
- You can change the improper fraction to mixed number by divide
105 by 8 and put the reminder over 8
∵ 105 ÷ 8 = 13 and 1/8
∴ The amount of the snowfall = [tex]13\frac{1}{8}[/tex] inches
Samantha measured [tex]13\frac{1}{8}[/tex] inches for the entire month
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A company plans to sell purses for $20 each. The company's business manager estimates that the
cost, y, of making x purses is a quadratic function
with a y-intercept of 1,989 and a vertex of (500,4,489).
Which linear equation models the company’s income from selling x purses?
A.) y=x+20
B.)20x
C.)x/20
D.)20/x
Step-by-step explanation:
the answer is B: y = 20x on edge.
The income for selling x purses is given by the linear equation:
y = $20*x
Which linear equation models the income for selling x purses?
A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
In this case, we know that each purse is sold by $20. So, if the company sells x purses, the income will be x times $20.
So the linear equation is:
y = $20*x
Then the correct option is B
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NEED HELP ASAP!!!!!
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y = seven divided by square root of quantity eight x plus ten.
Answer:
B
Step-by-step explanation:
To find [tex]y=f(g(x))[/tex], substitute the value of [tex]g(x)[/tex] into the the function f(x) instead of x.
Consider option B:
Given
[tex]f(x)=\dfrac{7}{\sqrt{x}}\\ \\g(x)=8x+10[/tex]
So,
[tex]f(g(x))\\ \\=f(8x+10)\ [\text{Expression } 8x+10\text{ has a role of }x]\\ \\=\dfrac{7}{\sqrt{8x+10}}[/tex]
This is exactly what you need as answer.
Whats the range of y=2x-7
Answer:
(-∞,∞) or {y|y∈R}
Step-by-step explanation:
Question 1
You answer 24 questions on a 100-point test correctly and earn a 96%.
a. All of the questions are worth the same number of points. How many questions are on the test? How many points is each question worth?
There are
questions on the test.
Each question is worth
points.
Question 2
b. Your friend earns a grade of 76% on the same test. How many questions
did your friend answer correctly?
Your friend answered
questions correctly.
plz help
Answer:
a) There are Total 25 Question on the test.
Each question is worth 4 points.
b) Your friend answered 19 questions correctly.
Step-by-step explanation:
Given:
Question answered =24
Percent earn = 96%
Total point test = 100
We will first solve for part a.
We need to find Total Question on the test and Points worth each question.
Now We know that percent earn is equal to Question answered divided by Total Question on test and ten multiplied by 100.
Framing in equation form we get;
[tex]Percent\ earn = \frac{\textrm{Question Answered}}{\textrm{Total question on test}}\times 100\\ \\\textrm{Total question on test} = \frac{\textrm{Question Answered}}{\textrm{Perecent earned}}\times 100[/tex]
Substituting the given values we get;
Total question on test = [tex]\frac{24}{96}\times 100 =25[/tex]
Hence There are Total 25 Question on the test.
Now we will find each question worth points.
each question worth points can calculated by dividing Total Point test with total number of question on the test.
Framing the equation we get;
each question worth points = [tex]\frac{100}{25} = 4\ points[/tex]
Hence Each question is worth 4 points.
Now Solving for part b.
Given:
Percent earn by friend = 76%
we need to find number of question answered correctly.
question answered correctly = [tex]\frac{\textrm{Percent earned by friend}\times \textrm{Total Number of question}} {100}[/tex]
Substituting the values we get;
question answered correctly = [tex]\frac{76\times 25}{100} = 19[/tex]
Hence Your friend answered 19 questions correctly.
Answer:
a) There are Total 25 Question on the test.
Each question is worth 4 points.
b) Your friend answered 19 questions correctly
Step-by-step explanation:
Write a word problem for 3x + 15 = 42
Final answer:
The math problem 3x + 15 = 42 is represented by a word problem involving a teacher preparing for a math contest, aiming to have 42 pencils for students, leading to a solution where 9 students can participate.
Explanation:
Consider a scenario where a teacher is preparing a math contest for school and decides to include a question about buying pencils for students. The teacher figures that for every student participating, they will need 3 pencils. Along with these, the teacher wants to have an additional 15 pencils just in case. The total number of pencils the teacher aims to have is 42.
To solve, we can write the equation representing this scenario as 3x + 15 = 42. Here, x represents the number of students participating in the contest. Solving this equation will help us find how many students can participate if the teacher wants to achieve their goal of having 42 pencils ready for the math contest.
To find the number of students, we subtract 15 from both sides to get 3x = 27, and then divide both sides by 3 to get x = 9. Therefore, 9 students can participate in the math contest.
The mid-segments of opposite sides of a triangle are parallel to each other?
True
False
Answer:
False
Step-by-step explanation:
The mid segments are the lines between midpoints on the triangle. They aren't parallel, because they form a triangle inside the triangle.
Please Help!
A function is represented by the values in the table.
x y
22 26
20 22
16 20
14 18
10 14
Choose from the drop-down menu to complete the statement. The function represented in the table (Is or is not) linear.
Pick one: Is or is not.
A function is a relationship between inputs where each input is related to exactly one output.
The coordinates of the table are: (22, 26), (20, 22), (16, 20), (14, 18),
(10, 14).
The graph of the coordinates formed from the table must show a linear graph.
This means a straight line.
The graph is shown below and it is not a straight line.
The function represented in the table is not linear.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function is represented by the values in the table.
x y
22 26
20 22
16 20
14 18
10 14
Now,
We can find the coordinates of the given function.
(22, 26)
(20, 22)
(16, 20)
(14, 18)
(10, 14)
The graph of these coordinates must show a linear graph.
This means a straight line.
The graph is shown below and it is not a straight line.
Thus,
The function represented in the table is not linear.
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Factor each polynomial expression and explain the factoring process used.
Answers:
b) [tex]x(25x-1)[/tex]
c) [tex]x^{2}-4(x-3)[/tex]
d)[tex]4x(x-5)+25[/tex]
e)[tex]2(3x^{2}+11x+14)[/tex]
Step-by-step explanation:
b) We have the following expression:
[tex]25x^{2}-x[/tex]
Applying common factor [tex]x[/tex]:
[tex]x(25x-1)[/tex]
c) We have the following expression:
[tex]x^{2}-4x+12[/tex]
Applying common factor [tex]4[/tex]:
[tex]x^{2}-4(x-3)[/tex]
d)We have the following expression:
[tex]4x^{2}-20x+25[/tex]
Applying common factor [tex]4x[/tex]:
[tex]4x(x-5)+25[/tex]
e)We have the following expression:
[tex]6x^{2}+22x+28[/tex]
Applying common factor [tex]2[/tex]:
[tex]2(3x^{2}+11x+14)[/tex]
Devin inveated $750 in a CD that pays 6% simple interest, calculated quarterly. How much money will Devin earn in 3 years?
Answer:
$896.70
Step-by-step explanation:
Amount( A) Devi earned can be calculated from the formula below
[tex]A =P ({ 1 + \frac{r}{m} })^{mt}[/tex]
Where,
P= principal=$750
r=rate=6%=0.06
m=compounding frequency=4
t=time=3yrs
[tex]A =750 ({ 1 + \frac{0.06}{4} })^{(4 \times 3)}[/tex]
[tex]A =750 ({ 1 + 0.015)}^{12}[/tex]
[tex]A =750 \times ({ 1.015)}^{12}[/tex]
[tex]A =750 \times 1.1956[/tex]
[tex]A = 896.70[/tex]
Answer:
135
885-750 is 135 on financial literacy
The population of a town went from 100000 to 137000 in 5 years. What was the percent increase in the town's population over that time?
Answer: 37%
Step-by-step explanation:
Initial Population = 100,000
Population after 5 years = 137,000
Population increase = 137,000 - 100,000
= 37,000
Therefore % increase = 37,000/100,000 x 100
= 37%
the local music activities coordinator sold 300 tickets to the orchestra concert. student tickets were $4 and adult tickets were $6. if the total sales were $1,600 how many student tickets were sold
100 children tickets and 200 adult tickets were sold.
Step-by-step explanation:
Given,
Cost of one student ticket = $4
Cost of one adult ticket = $6
Total sales = $1600
Number of tickets sold = 300
Let,
x represent the number of children tickets sold.
y represent the number of adult tickets sold.
According to given statement;
x+y=300 Eqn 1
4x+6y=1600 Eqn 2
Multiplying Eqn 1 by 4
[tex]4(x+y=300)\\4x+4y=1200\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](4x+6y)-(4x+4y)=1600-1200\\4x+6y-4x-4y=400\\2y=400[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{400}{2}\\y=200[/tex]
Putting y=200 in Eqn 1
[tex]x+200=300\\x=300-200\\x=100[/tex]
100 children tickets and 200 adult tickets were sold.
Keywords: linear equation, elimination method
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Which of the following numbers is irrational? (1 point)
a fraction with numerator negative 15 and denominator 4, a fraction with numerator negative 7 and denominator 9, square root of 4, π
a fraction with numerator negative 15 and denominator 4
a fraction with numerator negative 7 and denominator 9
square root of 4
π
Answer:
The correct answer is D. π
Step-by-step explanation:
Let's recall that rational numbers are those that can be written as a ratio or fraction of two integers. Quite the opposite, irrational numbers can't be written as a ratio or fraction of two integers.
Upon saying that we have:
A. A fraction with numerator negative 15 and denominator 4 is a rational number because we can represent it: -15/4
B. A fraction with numerator negative 7 and denominator 9 is a rational number because we can represent it: -7/9
C. √4 is a rational number because we can represent it: 2 or 2/1
D. π is the most known irrational number because we can't represent it as a ratio or fraction: 3.14159265358979....and more can't be written as a ratio or fraction.
The correct answer is D. π
There are 136 people waiting for a river raft ride. Each raft holds 8 people. Silvia used the work below to find the number of rafts needed to hold 136 people. Explain how her work helps to find out how many rafts are needed.
8 % 136
-80
= 56 - 56 =0
Answer:
17 rafts are needed for 136 people.
Step-by-step explanation:
Given:
Total number of people waiting for river raft ride = ?
Number of people the raft holds = 8
To Find:
The number of rafts needed =?
Solution:
Let X be the total number rafts needed to accommodate all the 136 people waiting for the River Raft ride.
So now X will be
X= [tex]\frac{\text{Total number of people}}{\text{number of people a raft can hold}}[/tex]
X= [tex]\frac{136}{8}[/tex]
X = 17
How many seconds are in a leep year
Answer:
3.162e+7
Step-by-step explanation:
10 out of every 65 students order pizza for lunch. There are 416 students at her school. How many students will eat pizza at her school?
Answer:
64
Step-by-step explanation:
First, you divide 416 by 65. This gets you 6.4. But it's not 1 in 65 eating pizza, it's 10 out of 65, so then you multiply 6.4 by 10, getting 64.
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
X - 12y = - 11
X- y = -11
Answer:
x=-11, y=0. (-11, 0).
Step-by-step explanation:
x-12y=-11
x-y=-11
-------------
x=y+(-11)
x=y-11
y-11-12y=-11
-11y=-11+11
-11y=0
y=0/-11=0
x-0=-11
x=-11+0=-11
Simplify
Please help
Answer:
D
Step-by-step explanation:
Given
- 4x² - 5(x + 3) + x² ← distribute the parenthesis by - 5
= - 4x² - 5x - 15 + x² ← collect like terms
= - 3x² - 5x - 15