Answer:
- The coordinates of C is (3,2)
- The coordinates of D is (11/5,14/5)
Step-by-step explanation:
Given
A(1,4) and B(6,-1)
Required
a. Point C divide AB in ratio 2:3
b. Point D divide AC in ratio 3:2
When endpoints are divided into ratios, the formula to calculate the coordinates is;
[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Solving for (a): Point C divide AB in ratio 2:3
The ratio;
[tex]m : n = 2 : 3[/tex]
For Point A;
[tex]A(x_1,y_1) = (1,4)[/tex]
For Point B;
[tex]B(x_2,y_2) = (6,-1)[/tex]
Substitute m,n,x1,x2,y1,y2 in the ratio formula given above;
[tex]C(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex]C(x,y) = (\frac{2 * 6 + 3 * 1}{3+2},\frac{2 *-1 + 3 * 4}{3+2})[/tex]
[tex]C(x,y) = (\frac{12 + 3 }{5},\frac{-2 + 12}5})[/tex]
[tex]C(x,y) = (\frac{15 }{5},\frac{10}5})[/tex]
[tex]C(x,y) = (3,2)[/tex]
The coordinates of C is (3,2)
Solving for (b): Point D divide AC in ratio 3:2
Using the same steps as (a) above;
The ratio;
[tex]m : n = 3:2[/tex]
For Point A;
[tex]A(x_1,y_1) = (1,4)[/tex]
For Point C;
[tex]C(x_2,y_2) = (3,2)[/tex]
Substitute m,n,x1,x2,y1,y2 in the folowing ratio formula;
[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
[tex]C(x,y) = (\frac{3 * 3 + 2 * 1}{2+3},\frac{3 *2 + 2 * 4}{2+3})[/tex]
[tex]D(x,y) = (\frac{9 + 2}{5},\frac{6 + 8}{5})[/tex]
[tex]D(x,y) = (\frac{11}{5},\frac{14}{5})[/tex]
The coordinates of D is (11/5,14/5)
Answer:
3,2 and 2.2,2.8
Step-by-step explanation:
got a 100 on plato
solve for x 3x+3+=12 1. 6 2. 5 3. 4 4. 3
Answer:
4.(3)
Step-by-step explanation:
3x+3 = 12
Subtract 3 to both sides.
3x = 9
Divide the left side by 3, then divide the right side by 3
x = 3
Answer:
Hi! your answer should be D. 3
Step-by-step explanation:
1. 3x+3=12
-3 -3
2. 3x=9
÷3 ÷3
3. x= 3
[So, your answer should be D. x=3]
Hope this helps!
can someone help me i cant understand with work
Answer:
Right now it would be
[tex]-40[/tex]
Since desend means down add -20 to -40
[tex]-40+(-20)=-60[/tex]
or
[tex]-40-20=-60[/tex]
Then is goes up 35, which is positive
[tex]-60+35=-25[/tex]
Therefore, the answer is -25
Hope this helps
Answer by
Fishylikeswater
Answer:
A. -25M
Step-by-step explanation:
The submarine starts at -40M underwater which then it descends ( goes down ) another -20M which added means it is now -60M underwater. It then rises 35M so you would then add -60M + 35M = -25M
Hope this helps :)
20 poinst please help i will mark u brainlestToday when Jeremy saw Mr. Winaki, the teacher said, “The amount of money in my wallet is more than $10, but less than $20. How much do I have?” Jeremy remembers talking about inequalities in math class and thinks that the answer may have something to do with that idea. In the Math Toolbox, we helped Jeremy solve Mr. Winaki ’s riddle. Now, Jeremy needs help in writing a brainteaser to stump Mr. Winaki. Your original riddle needs to be a real world problem that has an answer of more than 19 and less than 41. 1. Brainstorm Think about possible real world situations that might have an answer of more than 19 and less than 41. List three ideas for your original riddle.. Thesaurus Select three important words from the ideas you listed above. Use a thesaurus to look up synonyms of the words. Remember, Mr. Winaki is an English teacher. He will like your use of interesting new words. Record your findings in the chart below. 3. Select an idea From your list of ideas, select one about which to write a riddle. Remember, your riddle should have an answer of more than 19 and less than 41. Use one of the synonyms you found to make your writing more exciting. 4. Provide a possible answer In the Math Toolbox section of our lesson, we chose a possible solution to Mr. Winaki’s riddle. Choose a possible number that answers your riddle. 5. Writing Inequalities a. Write an inequality comparing it to 19. b. Choose the same value as a possible solution and write an inequality comparing it to 41. c. Write an inequality that shows the relationship between all three numbers? d. Represent the inequality algebraically.
Answer:
Given that “The amount of money in my wallet is more than $10, but less than $20 " can be written in inequality form as
10 < w < 20 where " w" is the amount in the wallet .
1 ) Puzzle : -
Ryan is eating cookies . His mother ask how many cookies did he have .
He said number of cookies he ate is more than 19 and less than 41 .
We can write it in equality form as 19 < x < 41 where ' x ' is number of cookies Ryan have .
2) Puzzle :-
Number of steps a child take in an hour is more than 19 and less than 41 .
Write the situation in inequality form .
19 < p < 41 where " p " is the number of steps a child take in an hour .
3) Puzzle :-
Mother said to his child : " the number of coins in your piggy bank is more than 19 and less than 41 .
19 < c < 41 where " c " is number of coins in piggy bank .
Step-by-step explanation:
is this right? someone please help :)
Answer:
it should be yes. if there are no values for A and C then yes the answer is correct.
Answer:
2a + 2c = b
Step-by-step explanation:
a = 1/2 b -c
Add c to each side
a+c = 1/2 b- c+c
a+c = 1/2 b
Multiply each side by 2
2( a+c) = 2 * 1/2 b
2a + 2c = b
which equation is represented by the graph below?
y= In x-3
y= In x-4
Y= e^x -3
Y= e^x -4
Answer:
Option (3)
Step-by-step explanation:
Given graph in this question is an exponential graph.
Parent function representing the graph is,
y = eˣ
When the parent function is shifted 4 units downwards, the new function after the translation will be,
y = eˣ - 3
Therefore, equation representing the graph is, y = eˣ - 3.
Option (3) will be the answer.
Answer:
y = e Superscript x Baseline minus 3
or the 3rd option
Step-by-step explanation:
In order for the data in the table to represent a linear
function with a rate of change of +5, what must be the
value of a?
O a = 3
O a = 8
O a = 18
O a = 33
The table to represent a linear function with a rate of change of +5
So, m = 13 + 5 = 18
a = 18
What is linear function?The slope-intercept pattern of the linear function equation. As a result, it is written as f(x) = mx + b, where m denotes the slope and b the line's y-intercept.
The graph in the table shows a linear function.
The linear function's general equation is written as y = ax+b, where a is the slope and b is a constant.
Finding the linear function's equation by using the first and third points from the table
at x = 3 ⇒ y = 13 and at x = 5 ⇒ y = 23
13 = 3a+b → (1)
23 = 5a+b → (2)
solve (1) and (2) to find a and b
So, a = 5 and b = -2
∴ y = 5x - 2
After that by substitution with x = 4 int the equation of y
∴ y = 5*4-2 = 18
m= 18
Thus, option C is correct.
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A mother is 30 years older than her son. Fifteen years ago the son was 1/3 of
his mother's age. How old is each now?
Answer: The son is 30 and the mother is 60
Step-by-step explanation:
Mother's age = m
Son's age = s
m = s + 30
m-15 = 3(s - 15)
m - 15 = 3s - 45
m = 3s - 30
(Substitution)
s + 30 = 3s - 30
2s = 60
s = 30
m = 60
Hope it helps <3
Trick question---
Just kidding I think that 15 years ago his mother was 45
he was 15 and now he is 30 and she is 60.
literally sat here thinking that 30 is ruled out, and 60 would be 20 but then she'd be too old, suddenly it clicked, if you said he'd be half her age now, it'd be to easy, because half her age now would be 30 and it'd give the answer straight away.
You or your teacher has a big percentage of the brain used. I respect.
What is the y-intercept of the line that passes through (-6,2) and (4,-2) ?
2
5
22
5
No lo a los alusta
2
5
22
5
Answer:
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
-2
5
= -0.4
θ =
arctan( ΔY ) + 360°
ΔX
= 338.19859051365°
ΔX = 4 – -6 = 10
ΔY = -2 – 2 = -4
Distance (d) = √ΔX2 + ΔY2 = √116 = 10.770329614269
Equation of the line:
y = -0.4x – 0.4
or
y =
- 2 x
5
– 2
5
When x=0, y = -0.4
When y=0, x = -1
Answer:
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
-2
5
= -0.4
θ =
arctan( ΔY ) + 360°
ΔX
= 338.19859051365°
ΔX = 4 – -6 = 10
ΔY = -2 – 2 = -4
Distance (d) = √ΔX2 + ΔY2 = √116 = 10.770329614269
Equation of the line:
y = -0.4x – 0.4
or
y =
- 2 x
5
– 2
5
When x=0, y = -0.4
When y=0, x = -1
Vicki currently earns $35.00 an hour at her job. Thanks to her hard work, her boss is going to give her a 15% raise. How much will she earn each hour after the raise?
Answer:
$40.25 per hour
Step-by-step explanation:
If you multiply 35 by 15% you get 5.25. You can either add this on, or you can multiply by 1.15 instead of .15.
FIND THE MISSING LENGTH INDICATED
Answer:
25 units.
Step-by-step explanation:
The first thing we need to do is find the hypotenuse of the triangle with side lengths 12 and 16. 12^2 + 16^2 = 144 + 256 = 400. sqrt(400) = 20. So, the hypotenuse of that triangle is 20 units.
Because the smaller length of the smaller triangle bisects the largest triangle's right angle, the two triangles are similar, with the side length 12 corresponding to the smaller side length of the larger triangle, the side length 16 corresponding to the 20 unit side, and the 20 unit hypotenuse corresponding to x.
Now that we know the triangles are similar, we can construct a proportion...
[tex]\frac{16}{20} =\frac{20}{x}[/tex]
That means that 4/5 = 20/x
1/5 = 5/x
x = 25
Hope this helps!
which is not an equation of the line going through (3, -6) and (1,2)
which table dose not represent a linear function?
Answer:
Second Graph, Top Right
Step-by-step explanation:
When the points from the top right table are graphed, they form a slight curve. This means that they are not a linear function.
Answer:
second graph top right
Step-by-step explanation:
compared to the others this graph is not linear
A parachutist's rate during a free fall reaches 198 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answer:
300 feet
Step-by-step explanation:
If we were using feet the expression would be 198x, where x is feet per second
Since they are asking in meters we need to convert feet to meters
When you do that you get 60
Now the expression is 60x
When you plug 5 into the equation it is 300
Find the Surface Area
Answer:
120 km squared.
Step-by-step explanation:
The shape shown has 5 sides: three rectangles and 2 triangles.
If you examine each triangle closely, they are 3-4-5 triangles. The area of one triangle is 3 * 4 * 1/2 = 12 * 1/2 = 12 / 2 = 6. Since there are two triangles, the total area of the triangles is 6 * 2 = 12 km squared.
The three rectangles have the same length, but their widths differ. They all have a side length of 9 km, but the largest rectangle has a width of 5 km, the medium has a width of 4 km, and the smallest has a width of 3 km.
So, the rectangles' areas added up will be (9 * 5) + (9 * 4) + (9 * 3) = 45 + 36 + 27 = 108 km squared.
And so, the total surface area is 12 km squared + 108 km squared, or 120 km squared.
Hope this helps!
Help Please. It's maths, for HegartyMaths.
STATS List below are the ages (years) of randomly selected race car drivers. Construct a 95% confidence interval estimate of the mean age of all race car drivers: ages 32, 40, 27, 36, 29, 28
Answer:
A 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].
Step-by-step explanation:
We are given below the ages (in years) of randomly selected race car drivers;
Ages: 32, 40, 27, 36, 29, 28.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean age = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{32+40+27+36+29+28}{6}[/tex] = 32 years
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 5.1 years
n = sample of car drivers = 6
[tex]\mu[/tex] = population mean age of all race car drivers
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.571 < [tex]t_5[/tex] < 2.571) = 0.95 {As the critical value of t at 5 degrees of
freedom are -2.571 & 2.571 with P = 2.5%}
P(-2.571 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.571) = 0.95
P( [tex]-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]32-2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] , [tex]32+2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] ]
= [26.65, 37.35]
Therefore, a 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].
HELP. Analyze the diagram below and complete the instructions that follow. Find the exact value of tan 0.
Answer:
Using SohCahToa we know it will be opposite over adjacent, opposite being the side across from theta and adjacent being the side next to theta, Using Toa we know it will be opposite over adjacent so the answer will be 6/2sqrt5
If they wants you to simplify more than you cant have a sqrt on the bottom so to fix this you will multiply the top and bottom by sqrt5 leaving you with 6sqrt5/ 2*5 or 6sqrt5/15
hope this helped
Answer:
C. 3^5/5
Step-by-step explanation:
Please help us with Plato: Select all the correct answers. Which vectors represent the reflection of the vector across the x-axis?
Answer:
<3, 7>
AND
[tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex]
Step-by-step explanation:
I did the plato
The vectors that represent the reflection of the vector across the x-axis are; <3, 7> and [tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex].
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.
If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
The vectors that represent the reflection of the vector across the x-axis are;
<3, 7> and [tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex].
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Figure B is a scaled copy of Figure A. What is the scale factor from Figure A to Figure B?
Answer:
1/3
Step-by-step explanation:
figure a to figure b is a reduction so we do the smaller side divided by the bigger side (use the similar sides on the figures)
5/15 = 1/3
or you could do 11/33 = 1/3
PLEASE HELP WITH THIS(INORDER FOR ME TO GIVE YOU A BRIANLIST,EXPLAIN HOW U GOT IT)(will give brainlist and thanks)(Find the perimeter)
Answer:
13x+10
Step-by-step explanation:
Answer:
7x+10 cm
Step-by-step explanation:
To find the perimeter add up all the sides
There are 5 sides
3x+5+2x+2x+5
Combine like terms
3x+2x+2x +5+5
7x+10
The perimeter is 7x+10
Please help!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer: 20ways
Step-by-step explanation:
Number of candies = 7
Number of kids = 4
Since each kid must receive at least one candy ;
Therefore number of candies left to ration is
7 - 4 = 3 candies ; among 4 kids.
To share 'n' identical object among 'r' number of individuals can be expressed in the form :
[n+(r-1)Cr-1]
n = 3 ; r = 4
[3+(4-1)C4-1] = 6C3
Recall: nCr = n! / (n-r)!r!
6C3 = 6!/(6-3)!3!
6C3 = 6!/3!3!
= (6 * 5 * 4) / (3 * 2 * 1)
= 120 / 6
= 20ways
Sara wanted to gather data about the cost of local gyms in her area. She plotted the data and determined that the average gym costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 10x + 30. Identify and interpret the y-intercept in this model.
Answer:
y-intercept is 30
Step-by-step explanation:
Given the model [tex]y = 10x + 30.[/tex] comparing this model to the equation of a straight lines we can get the y- intercept
[tex]y = 10x + 30\\\y= mx+c[/tex]
The y- intercept is 30 which is the constant factor and it describes to us about the one-time registration fee of $30.
The y-intercept in this model for the average gym costs is 30.
What is the y-intercept?In a linear equation, the y-intercept can be interpreted as the constant. It is the value that does not change with the number of months a person goes to the gym. The y-intercept can also be referred to as the fixed cost. In this question, the y-intercept is 30.
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A rectangular garden that measures 6 feet by 8 feet is roped off to form a
right triangle. What is the length of the rope?
Rope
6 ft
Answer:
10feet
Step-by-step explanation:
We solve this question, using Pythagoras Theorem to solve for the other side.
Pythagoras Theorem states that
c² = a² + b²
c = √(a² + b²)
In the question, a = 6 feet
b = 8 feet
c = length of the rope
c = √6² + 8²
c = √36 + 64
c = √100
c = 10 feet
The length of the rope is 10 feet
when you sample 3000 people is this a census or a sample?
Answer:
participants (random sampling) will determine the population to which we ... In other words, they had obtained a census rather than a sample. ... population characteristics from a relatively small representative sample of 2,000 to 3,000 people.
Answer: I'm Pretty sure its census
Step-by-step explanation: have a great day
A hobbyist is making a toy sailboat. For the triangular sail, she wants the height h (in inches)
to be twice the length of the base b (in inches). Can the area of the sail be 10 inº?

Answer:
xx
Step-by-step explanation:
Write the functions by the graphs
F(x)=
G(x)=
H(x)=
Answer:
f(x) = |x|
g(x) = |x| - 2
h(x) = |x| + 3
Step-by-step explanation:
All the functions graphed represent the absolute value functions.
Since function g(x) passes through (0, 0) and (1, 1),
Let the equation of a line passing through these points is,
y = mx + b
Slope of the line passing through these points 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{1-0}{1-0}[/tex]
m = 1
y-intercept of the line 'b' = 0
Therefore, equation of the line will be,
y = x
And the function representing the two lines (both are the mirror images) joining at the origin will be,
f(x) = |x|
When the parent function is shifted 3 units up, the new function will be
h(x) = |x| + 3
When the parent function is shifted 2 units down,
g(x) = |x| - 2
Please may someone answer it,
WORTH 81 POINTS!!!
Answer:
[tex]\boxed{V = 1436.8 cm^3}[/tex]
Step-by-step explanation:
Volume of sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 7 cm
Volume of Sphere = [tex]\frac{4}{3} (3.14)(7)^3[/tex]
V = [tex]\frac{4}{3} (3.14)(343)[/tex]
V = 4310/3
V = 1436.8 cm³
Answer:
1436.8 cm^3Solution,
Radius= 7 cm
Volume of sphere:
[tex] \frac{4}{3} \pi \: {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {7}^{3} \\ = \frac{4}{3} \times 3.14 \times 343 \\ = 1436.8 \: {cm}^{3} [/tex]
Hope this helps...
Good luck on your assignment...
What is the equation of the line through (4,5) and (0,-3)
Answer:
y = 2x - 3
Step-by-step explanation:
Slope intercept equation of a line:
y = mx + b
(0, -3) is the y-intercept, so b = -3
We have
y = mx - 3
Now we use the two points to find the slope.
slope = m = (-3 - 5)/(0 - 4) = -8/(-4) = 2
y = 2x - 3
Answer:
4,5x+-3
Step-by-step explanation:
Can someone solve this? With zeroes please. y = x^2 + 2x - 8
Answer:
X=2,-4
Step-by-step explanation:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x .
PLEASE HELP!
What is the distance from Z= (16,−15) to the x-axis?
Answer:
15 units
Step-by-step explanation:
Distance from the x-axis is measured vertically, so you would look at the second number of the coordinates, the y value. Point Z is 15 units below the x-axis.
Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.
What is the axis?
An axis in mathematics is defined as a line that is used to make or mark measurements.
Here given that,
[tex]Z= (16,-15)[/tex] which is on the x-axis.
So,
The shortest distance between the coordinate [tex](16,-15)[/tex] and [tex](16,15)[/tex].
Now, applying the distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here,
[tex](x_1,y_1)=(16,0)\\(x_2,y_2)=(16,-15)[/tex]
Substituting these values in the formula
[tex]d=\sqrt{(16-16)^2+(-15-0)^2}\\\\d=\sqrt{(0)^2+(-15)^2}\\\\d=\sqrt{0+225}\\\\d=15[/tex]
Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.
To know more about the axis
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