Find the coordinates of point B along a directed line segment from A(3,4) and
C(3,9) so that the ratio of AB to BC is 4:1.

Answers

Answer 1

We have been given two points. [tex]A(3,4)[/tex] and [tex]C(3,9)[/tex]. We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.

We will use segment formula to solve our given problem.

When a point P divides segment any segment internally in the ratio [tex]m:n[/tex], then coordinates of point P are:

[tex][\right x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}\left][/tex]

[tex](x_1,y_1)=(3,4)[/tex] and [tex](x_2,y_2)=(3,9)[/tex].

[tex]m=4,n=1[/tex]

Upon substituting our given information in above formula, we will get:

[tex][\right x=\frac{4(3)+1(3)}{4+1},y=\frac{4(9)+1(4)}{4+1}\left][/tex]

[tex][\right x=\frac{12+3}{5},y=\frac{36+4}{5}\left][/tex]

[tex][\right x=\frac{15}{5},y=\frac{40}{5}\left][/tex]

[tex][\right x=3,y=8\left][/tex]

Therefore, the coordinates of point B would be [tex](3,8)[/tex].


Related Questions

Find f(-11/5) if f(n) = 5n + 6
A. -17
B. 5
C. -5​

Answers

The correct answer of A. B. and C. was

B. If it isn't then my calculations are wrong.

Write 21e-10 in standard form.

Answers

Answer:

you cant put this equation in standard form

Step-by-step explanation:

For his phone service, Sam pays a monthly fee of $22, and he pays an additional $0.04 per minute of use. The least he has been charged in a month is $69.32.
What are the possible numbers of minutes he has used his phone in a month?
Usem for the number of minutes, and solve your inequality for m.

Answers

The answer is 1183 minutes

How did people protest segregation during the Civil Rights Movement?


I need help

Answers

Answer:

The Civil Rights Act of 1964, which ended segregation in public places and banned employment discrimination on the basis of race, color, religion, sex or national origin, is considered one of the crowning legislative achievements of the civil rights movement

Step-by-step explanation:

Graph the linear equation ax+by=c, where a=0,b=1, and c=1.5

Answers

Use the slope-intercept form to find the slope and y-intercept.

Slope: 0

y-intercept: 1.5

When the area of a triangle is A = 26cm2

and the base is b = 8 cm, what is the height?

h = _________

Answers

Answer:

6.5 cm

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

26 = 1/2 (8) *h

26 = 4h

Divide each side by 4

26/4 = 4h/4

6.5 = h

Answer:

6.5 cm

Step-by-step explanation:

Area = ½ × base × height

26 = ½ × 8 × height

26 = 4height

height = 6.5 cm

Ross forms all two-digit whole numbers using digits 1, 2, and 3. He allows digits to repeat. Select statement(s) that are CORRECT. *

probability of both digits being the same is a likely outcome
the probability that a number includes the digit 2 only once is 5/9
first digit greater than the second digit is equally likely as the first digit less than the second digit
23 is an unlikely outcome

Answers

Answer:

Probability of both digits being the same is a likely outcome (A) and;

The first digit is greater than the second digit is equally likely as the first digit less than the second digit (C)

Step-by-step explanation:

Question:

Ross forms all two-digit whole numbers using digits 1, 2, and 3. He allows digits to repeat. Select statement(s) that are CORRECT. *

a) probability of both digits being the same is a likely outcome

b) the probability that a number includes the digit 2 only once is 5/9

c) The first digit is greater than the second digit is equally likely as the first digit less than the second digit

d) 23 is an unlikely outcome

SOLUTION

Find attached how I got the value combination.

Forming a two-digit whole number with digit 1,2 and 3 where repetition is allowed:

11, 12, 13, 21, 22, 23, 31, 32, 33

Let's check which of the options are correct.

a) Is probability of both digits being the same is a likely outcome?

From the numbers we got: 11, 22 and 33 have both digits the same.

Yes, the probability is a likely outcome

Option A is correct

b) Let the probability that a number includes the digit 2 only once = Pr( 2 only once)

Pr( 2 only once) = (digits which have number 2 once / total number)

12, 21, 23, 32

Digits which have number 2 once = 4

Total = 9

Pr( 2 only once) = 4/9

4/9 is not same as 5/9

So option B is wrong

c)The first digit is greater than the second digit = 21, 31, 32 = 3 in total

the first digit less than the second digit = 12, 13, 23 = 3 in total

Yes, they are equal in number

Option C is correct

d) 23 is a likely outcome

Option D is wrong

I don’t understand how to solve this
Please help me! I’ll give you some points.

Answers

Answer:

x=14°

Step-by-step explanation:

(6x + 2°) + (8x + 6°) + (7x + 4°) = 180°

21x + 12° = 180°

21x = 168°

x=14°

Answer:

Step-by-step explanation:

Vertically opposite angles are equal.

∠3 = ∠1

4x = x + 54

Subtract x form both sides

4x - x = x + 54 - x

3x = 54

Divide both sides by 3

3x/3 = 54/3

x = 18

∠1 = x + 54 = 18 + 54 = 72°

4) EFC is straight line

∠CFB +∠BFA +∠AFE = 180°

6x + 2 + 8x + 6 + 7x +4  = 180

6x+ 8x + 7x + 2 + 6 + 4= 180

21x + 12 = 180

21x = 180 - 12

21x = 168

x = 168/21

x = 8

A cube has surface area of 96 sq cm. What is the length of each edge of the cube?​

Answers

96/6=16
Each side has area 16 sq cm.
Each edge length is sqrt(16)=4 cm

The current student population of the Brentwood student center is 2000 the enrollment at the center increases at a rate of 4% each year to the nearest whole number what will the student population be close to in three years.

Answer step by step clearly

Answers

Answer:

2250 People

Step-by-step explanation:

P=Total population

P=2000(1+.04)^3years

P=2249.728

P=2250

Solve and graph the inequalities. HELP ASAP PLEASE 6th grade math for my little brother

Answers

Answer:

here are some notes to help

Mr. Hoffman, a science teacher, drove 10 miles to school from home in 20 minutes. He drove the 2 miles home in 30 minutes. His average velocity was ____ m/s.

Answers

In the first one he drove about 0.5 miles per second and in the second one he drove about 0.07 miles per second so it gives you about 0.285 i believe

Choose an equation that can be used to solve the problem. Adrian’s backpack has a mass of 15 kilograms. Theresa’s backpack has a mass of 8 kilograms. What is the total mass of both backpacks? *
15 - 8= 7
15 x 8= 120
15 + 8 = 23
15 + 8 + 2 = 25

Answers

The answer would be 15+8=23 because when they use the word total that would mean adding because it is saying all basically and I have zero doubts but if it is wrong I apologize.

The original dimensions of the great pyramid of Giza in Egypt were 146 meters tall and 229 meters on each side of the square base. What was the original volume of this pyramid.
A. 2,552,129
B. 1,627,121
C. 2,429,586
D. 2,337,655

Answers

Answer:

A.   2,552,129 m^3.

Step-by-step explanation:

Volume of a pyramid = 1/3 * height * area of the square base

=  1/3 * 146 * 229^2

= 2552129 m^3.

what are the ways to determine if a relation is a function

Answers

Answer: 1) Check if the inputs and outputs doesn't fail the vertical line test. 2) Check if every input has exactly on output. 3) Check if is a linear function.

Step-by-step explanation:

Which equation could be used to solve problems involving the relationships between the angles?

Answers

Answer:

see below

Step-by-step explanation:

The two angles are complementary so the sum is 90 degrees

7a+12 + 12+a = 90

Combine like terms

8a +24 = 90

Either equation would work to describe the relationship

A parking garage has a tented area with a slanted roof.

A rectangular prism and a triangular prism. The rectangular prism has a length of 40 feet, width of 15 feet, and height of 20 feet. The triangular prism has a triangular base with base 20 feet and height 20 feet. The prism has a height of 40 feet.

Dimensions of the triangular prism

Base – 20 feet by 20 feet

Height – 40 feet

Dimensions of the rectangular prism

Base – 15 feet by 40 feet

Height – 20 feet

What is the total amount of volume inside the parking garage?

ft3

Answers

Answer:

20,000 f

Step-by-step explanation:

did he work AND ES

The total amount of volume inside the parking garage which has a tented area with a slanted roof is 20000 ft³.

What is of volume of a triangular prism?

Volume of triangular prism is the amount of quantity, which is obtained in it in the 3 dimensional space. The volume of a triangular prism is base area (B) times height of it.

[tex]V=B\times h[/tex]

The volume of a rectangular prism is the product of its width, height and length.

[tex]V=w\times h\times l[/tex]

Here, (w) is the width of the base (l) is the length and (h) is the height of the rectangular prism.

A rectangular prism and a triangular prism. The rectangular prism has a length of 40 feet, width of 15 feet, and height of 20 feet.  The volume of this prism is,

[tex]V=20\times15\times40\\V=12000\rm\;ft^3[/tex]

The triangular prism has a triangular base, with base 20 feet and height 20 feet. The prism has a height of 40 feet. The volume of this prism is,

[tex]V=\dfrac{20\times20}{2}\times40\\V=8000\rm\;ft^3[/tex]

Total volume of the parking area is,

[tex]V=12000+8000\\V=20000\rm\; ft^3[/tex]

Thus, the total amount of volume inside the parking garage which has a tented area with a slanted roof is 20000 ft³.

Learn more about the volume of a triangular prism here;

https://brainly.com/question/15129289

I WILL GIVE BRAINLIEST TO FIRST GOOD ANSWER: A pizza shop has the following optional toppings: pepperoni, sausage, peppers, and onions. All pizzas come with cheese. How many different combinations of toppings are possible?

Please explain how you got it

Answers

Answer:

14

Step-by-step explanation:

Answer:

Im Sure there is 10 different combinations.

Step-by-step explanation:

*boop* i need help :P
15 divided by 6 2/3 =

A. 100/4
B. 23/4
C. 21/4
D. 100

Answers

Answer: [tex]2\frac{1}{4}[/tex]

Turn 6 2/3 into an Improper Fraction

Multiply [tex]6*3[/tex] and get 18. Now add [tex]2[/tex] and get [tex]20[/tex].

[tex]6\frac{2}{3} =\frac{20}{3}[/tex]

Do Keep Change Flip

Keep: [tex]15[/tex]

Change: ÷ into ×

Flip: 20/3 into 3/20

Your new Problem: [tex]\frac{15}{1} *\frac{3}{20}[/tex]

Multiply

[tex]\frac{15}{1} *\frac{3}{20}=\frac{45}{20}[/tex]

Simplify

[tex]\frac{45}{20} =2.25\\2.25=2\frac{1}{4}[/tex]

Answer:

[tex]2 \frac{5}{20} =2 \frac{1}{4} [/tex]

Answer C is correct.

Step-by-step explanation:

[tex]

15 \div 6 \frac{2}{ 3 } \\ \frac{15}{1} \div \frac{20}{3} \\ \frac{15}{1} \times \frac{3}{20} \\ = \frac{45}{20} \\ = 2 \frac{5}{20} = 2 \frac{1}{4} [/tex]

Bo is buying a board game that usually costs B dollars. The game is on sale, and the price has been reduced by 18%, percent.Which of the following expressions could represent how much Bo pays for the game?

Answers

Answer:

B - 18%

Step-by-step explanation:

Your school is renting an indoor water park for a school outing. The water park costs $1500 for the day.


A. How many students need to go to the water park so that each person pays $6 each?


B. Reasoning The water park can hold up to 450 people. Does the park hold enough students so that each person pays only $3:50 each?

Answers

A. 250 students need to go to the water park for them to pay 6 dollars each.

B. Yes, the park can hold enough since there would be 428 students renting for 3.50 each.

Please mark me brainliest! <3

Identify the function represented by the graph?

Answers

Answer:b

Step-by-step explanation: just common sense

Final answer:

To identify the function represented by a graph, one must analyze the slope, intercepts, and shape of the graph. The graph of a constant function is a horizontal line, while the predator-prey cycle would show an oscillating pattern. The potential energy graph in physics can display a double well pattern, while signal transduction might show a cascade over time, and motion graphs represent various types of movement.

Explanation:

Identifying the function represented by a graph involves analyzing various elements such as the shape of the graph, its slope, and intercepts, as well as any restrictions on the domain. For instance, when you come across a graph of a function that appears as a straight line, it's crucial to look at the slope and y-intercept to determine the equation of the line. If the graph is a horizontal line, then the function represents a constant value indicating that no matter the change in the independent variable x, the dependent variable y remains the same.



For analyzing a predator-prey cycle, we need to recognize the typical oscillating pattern that represents populations of predators and preys over time. When interpreting graphs showing potential energy in physics, we are often looking at a function that might show the energy levels as a function of position, with critical points determined by solving relevant equations and considering derivatives to find minima and maxima.



In the context of a biological process such as signal transduction, creating a graph would involve plotting the stages of the signaling pathway over time, which would likely result in a plot showing the cascade of events leading from the signal to the final response. When considering the graphs of the position of a moving object over time, we might see different types of curves representing different types of motion, such as uniform motion depicted by a straight line or accelerated motion depicted by a parabolic curve.

Learn more about Graph Analysis here:

https://brainly.com/question/30099251

#SPJ2

Damien purchased $43.11 worth of
coffee that sold for $23.95 per pound. How many pounds of coffee did Damien buy?

Answers

Answer:

1.8 pounds

Step-by-step explanation:

Take the total price and divide by the price per pound to determine the number of pounds

43.11/23.95 =1.8

Answer:

1

Step-by-step explanation:

He got about 1 pound :)

Which of the following expressions is equal to x2 +9?

Answers

Answer

Is (x+3) 2 becase X *2 + 9 is the similar to (x+3)2

The given expression x² + 9 is equivalent to (x+3i)(x-3i).

Hence option B is correct.

The given expression is,

x² + 9

It is equivalent to (x+3i)(x-3i).

When we expand this expression, we get,

x² - 3ix + 3ix - 9i²

Since i² is equal to -1,

Simplify the expression to x² + 9.

The answer option (A) (x+3i)(x-6i) is not equivalent to x² + 9 as it will result in a last term of -18i² instead of +9i².

Similarly, option (C) (x-3i)² is equal to x² - 6ix + 9i², which is also not equivalent to x² + 9.

Option (D) (x+3i)² will result in x² + 6ix - 9i², which is not equivalent to x² + 9 either.

Therefore, the correct answer to the given expression is,

Option (B) (x+3i)(x-3i).

To learn more about the mathematical expression visit:

brainly.com/question/1859113

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Is the line through points P(7, 6) and Q(9, 11) perpendicular to the line through points R(5, 9) and S(7, 4)? Explain.

Answers

Answer:

Step-by-step explanation:

[tex]slope~of~line~PQ=\frac{11-6}{9-7}=\frac{5}{2}\\slope~of~line~RS,~m2=\frac{4-9}{7-5}=-\frac{5}{2} \\m1 \times m2=\frac{5}{2} \times -\frac{5}{2} =-\frac{25}{4} \neq -1[/tex]

so lines are not perpendicular.

By what percent will the product of two numbers decrease if one of them is decreased by 20% and the other is decreased by 60%?

Answers

Step-by-step explanation:

The product of the original numbers: xy

The product of the altered numbers (.75x)(.5y), or 0.375xy

The product has decreased by 1 - 0.375, or 0.625, or 62.5%

Answer:

Original product:

P1 = a x b

Decreased product:

P2 = a x (100 - 20)/100 x b x (100 - 60)

    = a x b x 80/100 x 40/100

    = a x b x 8/25

=> P1/P2 = 8/25

or

P1 is decreased by: 1 - 8/25 = 17/25 = 68%

Hope this helps!

:)

Five out of seven teens said they do homework every night. What is a reasonable prediction for the number of teens out of 980 who would do homework every night?

Answers

Answer:

700 teens

Step-by-step explanation:

If five out of 7 teens do homework every night

There are 980 teens

How many out of 980 teens would do homework every night?

Firstly divide 980 teens by 7

Which is 980/7=140

Next is,

Out of 7 teens, there are 5 who do homework every night

So, multiply 140 by 5

140×5=700 teens

This means, the reasonable prediction of teens who do homework every night out of 980 is 700 teens

The predicted number of teens who would do homework every night out of 980 is approximately 700 based on the given information.

To predict the number of teens out of 980 who would do homework every night based on the given information that five out of seven teens do homework every night, we can follow these steps:
1. Calculate the proportion of teens who do homework every night:
- Proportion = 5 / 7
2. Determine the expected number of teens out of 980 who would do homework every night:
- Expected number = Proportion * 980
3. Substitute the proportion value to find the expected number:
- Expected number = (5 / 7) * 980
4. Calculate the expected number:
- Expected number = (5 * 980) / 7
5. Simplify the expression:
- Expected number = 700
6. Finally, the predicted number of teens who would do homework every night out of 980 is approximately 700 based on the given information.

I NEED HELP!!!
I will give brainliest answer.

Answers

Answer:

D

Step-by-step explanation:

Answer: D. 151 degrees.

Step-by-step explanation:

To solve this, first find the interior angle measures of the triangle. We know that it is a right triangle, so the right angle is 90 degrees, and the second angle is 61 degrees.

180 - 90 - 61 = 29 degrees.

Looking at the attached diagram - you can treat the angles surrounding s and 29 as a circle. There are 360 degrees in a circle, so the angle measures in the circle must add up to 360.

We also know that the angle directly opposite the triangle's 29 degree measure is also 29 degrees, so we can make an equation based on this information:

[tex]360 = 2(29) + 2(s)[/tex]

Solve for s:

[tex]360 = 2(29) + 2(s)\\360 = 58 + 2s\\302 = 2s\\s = 151[/tex]

S is equal to 151 degrees.

Which system of equations could be graphed to solve the equation below? log0.5x=log32 +x

Answers

Answer:

Step-by-step explanation:

The system of equation to be graphed is the following :

f(x) = Log_0.5 x

f(x) = Log_{3} (2 + x)

And the solution is the intersection point of the two graphs.

Check attachment for point of intersection.

Answer:

y1 = (Log x)/(Log 0.5)

y2 = [(Log 2)/(Log 3)] + x

Option D

Step-by-step explanation:

We are given;

Log_0.5_x = (Log_3_2) + x

To solve the equation graphically, we have to plot the graphs of these two functions and find the point of intersection of these graphs.

Using: log_a b = log b / log a

1) a = x, b=0.5

So, y1 = log0.5 x

Which gives; y1= (log x)/(log0.5)

2) a=2, b=3

So, y2 = (log_3 2) + x

So, y2 = (log 2 / log 3) +x

Hence, appropriate system is;

y1 = (Log x)/(Log 0.5)

And y2 = [(Log 2)/(Log 3)] + x

Looking at the options in the image attached, the correct solution that corresponds to our answer is Option D

20 POINTS! HELP! 20 POINTS ❗️
Which of the following pair of right triangles cannot be proven to be congruent? Select all that apply.

Answers

Answer:

1st picture:

1st case: two triangles are similar (AAA), not congruent

2nd case: two triangles are congruent (SAS)

2nd picture:

both cases satisfy: two triangles are congruent (ASA)

3rd picture:

1st case: two triangles are congruent (SAS)

2nd case: neither congruent or similar

Hope this helps!

:)

The answer to your question is in the first picture the second trig angle is congruent and in the second picture the second one is it too and in the 3 rd one the first one
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