Mathematics Middle School

Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.

Answers

Answer 1

Final answer:

The coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).

Explanation:

To find the coordinates of the point that divides the line segment AB in the ratio of 1:4, we can use the formula:

x = (x1 + 1/n * (4 * x2)) / (1 + 1/n)

y = (y1 + 1/n * (4 * y2)) / (1 + 1/n)

Substituting the given coordinates into the formula, we have:

x = (10 + 1/4 * (4 * 2)) / (1 + 1/4) = 8

y = (4 + 1/4 * (4 * 8)) / (1 + 1/4) = 6

Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).

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Related Questions

An electrolyte solution has an average current density of 1 ampere per square decimeter (A/dm^2). What is the current density of the solution in A/m^2?

Answers

We should know that ⇒⇒⇒ 1 meter = 10 decimeters
1 m = 10 dm

∴ 1 m² = 100 dm² ⇒⇒⇒ 1 dm² = 0.01 m²

For the given dimension
1 (A/dm²) = [tex] 1 \frac{A}{dm^2} = 1 \frac{A}{0.01 \ m^2} = 1 * \frac{1}{0.01 } \frac{A}{m^2} = 100 \ \frac{A}{m^2}[/tex]

note: 1/0.01 = 100

Answer:

the density of electrolyte solution is 100 ampere per square meter

Step-by-step explanation:

We know that the Average current density of the solution = 1 ampere per square decimeter and we need to find the average current density of the solution in ampere per square meter. So

Add the two expressions. 4.6x−3 and −5.3x+9 Enter your answer, in simplified form, in the box. PLEASE ANSWER FAST THIS IS A BIG DEAL!!!

Answers

So you have 4.6x − 3 and −5.3x + 9. You can only add like terms, which are terms where their variables (and the exponents on the variable) are the same. That means you can add 4.6x and −5.3x, and you can also add −3 and 9:
[tex]4.6x - 3 + - 5.3x + 9\\ = (4.6x - 5.3x) + (-3 + 9)\\ = -0.7x + 6[/tex]

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Answer: -0.7x + 6

An expression is defined as a set of numbers, variables, and mathematical operations. The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The addition of the two given expressions (4.6x-3) and (-5.3x+9) is,

(4.6x-3) + (-5.3x+9)

= 4.6x - 3 - 5.3x + 9

= -0.7x + 6

Hence, The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).

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What is the formula for the perimeter of a rectangle?

Answers

A= L x W / 2 length times width divided by 2

A survey shows that 67% of peanut butter lovers prefer chunky-style. Out of 850 people surveys, how many can be predicted to say they prefer chunky-style peanut butter?

Answers

ANSWER: 569.5
All you have to do is make you % into a decimal is multiply by 850

Hope this helps :-)

I like to use this formula cause it's really useful when it comes to these problems:

Part Percent

________ = _________

Whole 100

So, you basically plug in the numbers into the equation, it's really easy:

??? 67%

________ = ________

850 100

Then, you cross multiply. 67% x 850 = 56,950 / 100 =

And the answer to your question is: 569.6 or rounded is 570.

Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line. How many solutions should Sudhanshu find?

Answers

It all depends on the speeds of the cars. If they are going the same speed, the lines could never cross. Or they could could cross once, if one car passes the other.
However, if the speeds are changing, then there could be multiple solutions.

Answer:

The lines would only cross ONCE. So the answer is ONE.

Step-by-step explanation:

If using a graphing calculator you will see that the lines are at different slopes and will soon cross at (5,20) on a graph. Which means that the second cars is also faster even though the first car had a head start.

Find sine cosine and tangent

Answers

I am just going to assume that you are looking the sine, cosine, and tangent of both A and B.

SOHCAHTOA (used for reference).

[tex]Sin A = \frac{8}{10} = \frac{4}{5} \\Cos A = \frac{6}{10} = \frac{3}{5} \\Tan A = \frac{8}{6} = \frac{4}{3} \\Sin B = \frac{6}{10} = \frac{3}{5} \\Cos B = \frac{8}{10} = \frac{4}{5} \\Tan B = \frac{6}{8} = \frac{3}{4} \\[/tex]

What is the value of x in the solution to this system of linear equations? 4x - 3y = 3

Answers

4x-3y=3
x-y=2

Multiply the bottom equation by -3

4x-3y=3
-3x+3y=-6

Add the two equations together
The y’s cancel each other out
So your left with:

X=-3

The value of x is -3

Who can help me with this algebra 2 work Need help

Answers

Change the following to logarithmic or exponential form.
Note:
log_a c=b can be written as:
aᵇ=c
hence:
1. log₄ 16=2
will be written in exponential as:
4²=16

2. 25^(1/2)=5
will be written in logarithmic form as:
log₂₅5=1/2

3. Which function represents exponential growth?
#N/B For an exponential function:
y=a(b)^x
when b>1 it exponential growth
when b<1 it is an exponential decay
F: y=1/20(4)ˣ
b=4>1
exponential growth

G: y=16(0.4)ˣ
b=0.4<1
exponential decay

H: 20(1/8)ˣ
b=1/8<1
exponential decay

I. y=8x³
The above function does not have a growth factor, thus
it is a polynomial function not an exponential function.

4. Solve log₄3+log₄x=log₄18
when we add log functions we can multiply them as follows:
log₄(3*x)=log₄18
the log₄ will cancel and we shall remain with:
3x=18
solving for x we get:
(3x)/3=18/3
thus
x=6

5. Solve log₇36x-log₇2=log₇9
Dividing log functions is like subtracting them, thus we shall have:
log₇(36x/2)=log₇9
simplifying this we get:
log₇ 18x=log₇9
log₇ will cancel because of the same base and we shall have:
18x=9
thus
x=9/18
x=1/2

Expand the following:
Remember:
Multiplying logs is the same as adding them
Subtracting logs is the same as dividing them
thus

6. log₃ 4xy
expanding the above give us:
log₃4+log₃x+log₃y
Answer: log₃4+log₃x+log₃y

7. log₅ (xy²)/3
expanding this gives us:
log₅x+log₅y²-log₅3

Answer: log₅x+log₅y²-log₅3

Condense the following logarithms:
Using the concept from 6 and 7 we shall have:
8. log₈2+log₈7-log₈x
condensing this will give us:
log₈[(2*7)/x]
simplifying gives us:
log₈(14/x)

9. log₇9+3log₇y-4log₇2
Condensing the above gives us:
log₇9+3log₇y-4log₇2
=log₇9+log₇y³-4log₇2
=log₇(9*y³)/2
=log₇(9y³/2)

A researcher randomly surveyed a sample of high school students in a town to find out which career area they were most interested in pursuing. This table shows the results of the sample. The town has a total of 1000 high school students.

Art Science Finance Health Law Education
26 24 16 21 18 20
Based on this sample, how many high school students in the school are predicted to be most interested in pursuing a career in health?

Enter your answer in the box.

Answers

total of students sampled:
26 + 24 + 16 + 21 + 18 + 20 = 125 total
21 picked health so 21 / 125 = 0.168 of the students picked health
multiply that by total students:
1000 * 0.168 = 168 total students will pick health

The total number of students who will pick health is 168 if a researcher randomly surveyed a sample of high school students in a town.

What is a survey?

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

A researcher randomly surveyed a sample of high school students in a town to find out which career area they were most interested in pursuing.

The town has a total of 1000 high school students.

Total of students sampled = 26 + 24 + 16 + 21 + 18 + 20

= 125 total

21 picked health:

= 21 / 125

= 0.168 of the students picked health

Total students will pick health:

= 1000×0.168

= 168

Thus, the total number of students will pick health is 168 if a researcher randomly surveyed a sample of high school students in a town.

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Find f(x) if it is known that f(3k)=3k+7.

Answers

f(3k)=3k +7 Equals 9k+7. So 9k+7 would be the Answer.

Since f(3k) = 3k+7 (Equation 1)

We have to determine the value of f(x).

That is we have to replace 3k by x,

3k = x

Substituting the value of 3k in equation 1.

So, f(x) = x + 7

Therefore, f(x)=x+7 is the required function.

Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x – 3)?

Answers

D (-6,0) is the correct answer

Answer:

(-6,0) and (3,0)

Step-by-step explanation:

we have the function [tex]f(x)=(x+6)(x-3)[/tex] and the x-intecept of the function will be when y=0 then:

[tex]f(x)=(x+6)(x-3)\longrightarrow 0=(x+6)(x-3)[/tex]

Then the result will be 0 when x=-6 or x=3

Which of the following is the correct way to write 6 * 6 * 6 as a base and exponent?

Answers

To write this equation in the correct form would look something like this :

[tex] 6^{3} [/tex] .

6 to the 3rd power, or 6 cubed, would equal :

6 x 6 x 6 = 216.

Hope this helps.

ANSWER ASAP PLEASE!!!
Johnny wants to know how many students in his school enjoy watching science programs on TV. He poses this question to all 26 students in his science class and finds that 75% of his classmates enjoy watching science programs on TV. He claims that 75% of the school's student population would be expected to enjoy watching science programs on TV. Is Johnny making a valid inference about this population?
A. Yes, it is a valid inference because his classmates make up a random sample of the students in the school
B. Yes, it is a valid inference because he asked all 26 students in his science class
C. No, it is not a valid inference because he asked all 26 students in his science class instead of taking a sample from his math class
D. No, it is not a valid inference because his classmates do not make up a random sample of the students in the school

Answers

The answer is D. No, it is not a valid inference because his classmates do not make up a random sample of the students in the school.

Answer:D

Step-by-step explanation:

i got it right onn a test

what does a highter and lower standard deviation tell you!!!!?
what does a higher and lower z-score tell you ?
what does the varience tell you?

Answers

The larger the standard deviation, the more spread out the data values will be. A smaller standard deviation, and the values are more closely grouped together. The variance is equal to the standard deviation squared. In terms of symbols
V = s^2
where V = variance and s = standard deviation
So the variance can also be used to determine how grouped or spread out the data values are

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The z score tells us where this score is located in terms of the group. If the z score is positive, then it is above the mean. If the z score is negative, then it is below the mean. The further the z score is from zero, the further the raw score is from the mean. A score of z = 0 is right at the mean.

Cheryl used 40% of her money to buy a dress and 1/5 of the remainder to buy a pair of shoes. She then donated $60 to charity and had $132 left How much money did Cheryl have at first?

Answers

Let the amount be a
Amount used for dress= 40% of a
amount left =60% of a
amount used for shoe= 1/5*60a/100=3a/25
left=60a/100-12a/100=48a/100
=>48a/100-60=132
=>a=192*100/49=400
She had $400 at first.
Hope I helped, good luck.

Let the amount of money she has at first be x.

Dress = 40% x = 0.4x

Amount left = x - 0.4x = 0.6x

Shoes = 1/5 x 0.6x = 0.12x

Amount left = 0.6x - 0.12x = 0.48x

Donated $60 and had $132 left:
⇒ 0.48x - 60 = 132

Solve x:

0.48x - 60 = 132

0.48x = 192

x = $400

Answer: $400

How many lawns were mowed?

What is the difference between the greatest amount and least amount of gasoline used to mow lawns?

Answers

How many lawns were mowed ?
11 lawns because there are 11 x’ s

What is the difference between the greatest amount and least amount of gasoline used to mow lawns ?
4/8 of to simplify it’s 1/2

if i started a business making braclets for $2 and necklaces for $3 with a budget >200 what would be the inequality equation?
How would I graph

Answers

If i started a business making braclets for $2 and necklaces for $3 with a budget >200 what would be the inequality equation?
How would I graph

Solution:
let x= number of bracelets
y= number of necklaces

Thus, the equation would be:
$2x+$3y>200

In graphing this equation, you just have to substitute any number for the values of x and y as long as when substituted, their sum is greater than 200

Determine whether quantities vary directly or inversely and find the constant of variation. It takes three identical water pumps 8 hours to fill a pool. How long would it take four of these same pumps to fill the pool, assuming they all pump at the same rate?
PLEASE HELP!!

Answers

8 * 3 = 24
24/4 = 6 HOURS

A bag is filled with marbles. You take out and mark 80 marbles. Then you put the marbles back in the bag and mix the marbles. In a sample of 20 marbles, 4 of the marbles are marked. About how many marbles are in the bag?

Answers

About 400 marbles. You simply set up a proportion and solve it as I did in the photo attached.

there are about 400 marbles

charlene is a video game designer and wants to make sure that her game can be played on all types of screens. In order for the games to work on both devices with a standard aspect ratio and those with widescreen aspect ratios, the playable area of the games should an aspect ratio of 3:2. This means that the width is equal to 3/2 times the height. On one type of tablet , the playable area of the game on the screen is 54 square inches. Write and solve a system of equations to determine the dimensions of the playable are.

A) width=6 height=9
B) width=6 height=4
C) width=13.5 height=9
D) width=9 height=6

Answers

The correct answer is D) width=9, height=6.

Let w represent the width and h represent the height. The first equation we write deals with the area of the screen:
A=wh

Our playable area is 54, so we have
54=wh

Now we write the equation relating the width and the height. The width is 3/2 times the height; this means
w=3/2h

We will use substitution to solve this. Substitute the value for w from the second equation into the first equation:
54=wh
54=(3/2h)h
54=3/2h²

Divide both sides by 3/2:
54 ÷ 3/2 = 3/2h² ÷ 3/2
54/1 ÷ 3/2 = h²
54/1 × 2/3 = h²
108/3 = h²
36 = h²

Take the square root of both sides:
√36 = √h²
6 = h

The height is 6. Substituting this into our first equation,
54=wh
54=w(6)

Divide both sides by 6:
54/6 = w(6)/6
9=w

The width is 9.

370x1/10 = please help

Answers

37,
It is thirty seven, use a calculator

Answer: 37
This is because 370 times 1/10 is the same as 370 times 0.1 which would be equal to 37

Find the future value of $1800 deposited at 8% for 5 years if the account pays simple interest, and the account pays interest compounded annually.

Answers

For one year:
0.08(1800) + 1800
But because it is 5 years:
5(0.08(1800)) + 1800
0.4(1800) + 1800
We can make it simpler:
1.4(1800)
Multiply:
2520
YOU NOW HAVE $2520

Answer:

The answer is 2,644.79.

You would have to calculate the three variables to get and complete your answer.

Step-by-step explanation:

The equation below shows The area of a trapezoid, a, with a height of 9 cm, and one base 35 cm. A=9/2(b+35)
Which formula correctly solves for the other base, b?

Answers

For this case we have the following equation:
A = 9/2 (b + 35)
We must clear b from the equation, to obtain the value of the other base.
Clearing b we have:
(b + 35) = (2/9) A
b = (2/9) A - 35
Answer:
A formula that correctly solves for the other base, b is:
b = (2/9) A - 35

Please help me!
Which of the following is the best definition of the sample space of a probability event?

Answers

It’s the set of all possible outcomes

Answer: D. The set of all possible outcomes

Step-by-step explanation:

The set of all possible outcomes is the collection of all possible outcomes of an experiment.In the theory of probability the sample space of an random experiment is the set of all possible results of that particular experiment.

Therefore, the best definition of the sample space of a probability event is the set of all possible outcomes.

what does x equal
5x+2y=3
1x+2y=6

Answers

[tex]\underline{-\left\{\begin{array}{ccc}5x+2y=3\\x+2y=6\end{array}\right }\ \ \ \ |subtract\ both\ sides\\\\4x=-3\ \ \ |:4\\\\x=-\dfrac{3}{4}\to x=-0.75[/tex]

A rectangle has vertices at these coordinates. (5, −3), (5, −8),(8, −3) What are the coordinates of the fourth vertex of the rectangle? Enter the coordinates in the boxes.

will give brainlest

Answers

Answer:

Coordinate of 4th vertex of the rectangle is ( 8 , -8 ).

Step-by-step explanation:

Given Vertices of Rectangle are ( 5 , -3 ) , ( 5 , -8 ) , ( 8 , -3 )

To find: Coordinate of Fourth Vertex of the rectangle.

First, Plot all given three points on the graph.

Graph is attached.

We know that Opposite sides of the rectangle are equal and parallel.

Also All angles of rectangles are right angle.

So to satisfy these properties of rectangle.

4th coordinate must be on line x = 8 and y = -8.

⇒ Fourth coordinate = ( 8 , -8 )

Therefore, Coordinate of 4th vertex of the rectangle is ( 8 , -8 ).

simplify this expression 6q/20(q+r)

Answers

For this case we have the following expression:
6q / 20 (q + r)
Rewriting the expression we have:
(6/20) (q / (q + r))
Simplifying we have:
(3/10) (q / (q + r))
Answer:
The simplified expression is given by:
(3/10) (q / (q + r))

The answer would be (3/10) (q / (q + r))
Equation:
6q / 20 (q + r)
=(6/20) (q / (q + r))
Simplify it :
(3/10) (q / (q + r))

The simplified expression is given by:
(3/10) (q / (q + r))

Jamie is 5 years older than Ella. Jamie's age is 11 years less than three times Ella's age. The system below models the relationship between Jamie's age (j) and Ella's age (e):

j = e + 5
j = 3e – 11

Which of the following methods is correct to find Jamie's and Ella's age? (4 points)

Solve j + 5 = 3j – 11 to find the value of j.

Write the points where the graphs of the equations intersect the x-axis.

Write the points where the graphs of the equations intersect the y-axis.

Solve e + 5 = 3e – 11 to find the value of e.

Answers

The correct answer is to solve e+5=3e-11 for e.

The correct method is to use the equation

e + 5 = 3e - 11

on solving, we get e = 8 and j = 13

Other methods are complicated.

Which expression repressents “6 more than x”?

Answers

I would say the 2nd option because its adding 6 to the X which means 6 more

Hope this helps I would appreciate brainliest

Hello there, and thank you for posting your question here on brainly.

Short answer: C. x + 6

Why?

When you're referring to addition, you can use words like 'more than, higher than, added, etc.' In this case, we have 6 more than x, so the correct answer would be the one that shows addition, which is x + 6.

Hope this helped you! ♥

What type of triangle is this
1. right isosceles
2. obtuse isosceles
3. equilateral equilangular
4. acute scalene
5. right scalene
6. obtuse scalene
7. acute isoceles

Answers

It is an pbtuse triangle

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