Answer:
The coordinates of point B = (1, -4)
Step-by-step explanation:
Complete Question
Point A is at (−3,4) and point C is at (2,−6). Find the coordinates of point B on line AC such that the ratio of AB to AC is 4:5.
Solution
Point B divides line AC into two parts
A = (-3, 4)
C = (2, -6)
AB:AC = 4:5
If (AB/AC) = (4/5)
5AB = 4AC
But AC = AB + BC
5AB = 4(AB + BC)
5AB = 4AB + 4BC
5AB - 4AB = 4BC
AB = 4BC
(AB/BC) = (4/1)
AB:BC = 4:1
Hence, point B divides line AC internally into two parts with ratio 4:1
Mathematically, if a point P(x, y) divides the coordinates (x₁, y₁) and (x₂, y₂) internally in the ratio m:n then point P(x, y) is given as
x = [(mx₂ + mx₁)/(m + n)]
y = [(my₂ + my₁)/(m + n)]
For this question,
x₂ = 2
x₁ = -3
y₂ = -6
y₁ = 4
m = 4
n = 1
Point B is then described with coordinates
x = [(4×2 + 1×-3)/(4+1)] = (5/5) = 1
y = [(4×-6 + 1×4)/(4+1)] = (-20/5) = -4
Hence, the coordinates of point B is given as
(x, y) = (1, -4)
Hope this Helps!!!
Answer:
(-3,-3)
Step-by-step explanation:
above.
Draw the line with equation y=-12x+1
Answer:
See below
Step-by-step explanation:
I attached a picture of the graph below. It has a slope of -1/2 and a y intercept of 1. Hope this helps!
Question 14 (1 point)
John is collecting vintage baseball cards and has about 25 he got from his dad. He is collecting
about 2 cards per month. Write a function, C(x), that represents how many cards John has
after x months.
N
Answer:
C(x) = 25 + 2x
Step-by-step explanation:
He already has 25 cards.
He is collecting 2 cards per month. In x months, he will have collected:
2 * x = 2x cards
That means that the number of cards he will have after x months will be the sum of the cards he already has and the cards he collects per month:
C(x) = 25 + 2x
please help , factor 6x^2-33x+15 A. 3(2x-5)(x+1) B. 3(x+1)(2x+5) C. 3(2x-1)(x+5) D. 3(x-5)(2x-1)
Answer:
D
Step-by-step explanation:
Since the end term is positive, we know the 1 and 5 must both be positive or negative. However since -33x is negative, we know 1 and 5 are both negative too
Answer:
3(2x-1 )(x-5 )
Step-by-step explanation:
6x^2-33x+15
Factor out the greatest common factor
3(2x^2 -11x +5)
Factor inside the parentheses
3(2x )(x )
We need to get to -11 so the the only factors of 5 are 1 and 5 and they have to be negative
3(2x-1 )(x-5 )
2 * -5 + -1 = -10-1 = -11
Choose the kind(s) of symmetry: point, line, plane, or none.
(A)
none
plane
point
line
it would be a Line
The line would be vertical right through the middle
can i get brainliest?
Please help there’s a picture to explain more
110
70
X=?
Answer:
Step-by-step explanation:
110 = 70 + X [ extarior angle property]
or, 110 - 70 = X
or , 40 = X
HOPE IT HELPS ...
MARK ME AS BRAINLIEST IF IT DOES SO
The standard form of the equation of a parabola is y=1/2x^2 - 4x+21. What is the vertex form of the equation?
Answer:
y=1/2*(x-4)^2+13
Step-by-step explanation:
Answer:
y=1/2*(x-4)^2+13
Step-by-step explanation:
PLEASE HELP. A Ferries wheel has a diameter of 100 ft. The center of the wheel is 60 feet off the ground. If it takes the Ferries wheel 12 seconds to make a full rotation, find the height of a rider 2 seconds after he passes position A, the right most point on the wheel.
Answer choices:
A. 103.30 ft
B. 80.34 ft
C. 74.40 ft
D. 101.96 ft
Answer:
lresaputa es la C
Step-by-step explanation:
If 28 g of cashew nuts contains 14 g of fats.
How many grams of fat are there in 42g of cashew nuts?
Answer:
21 g
Step-by-step explanation:
Use ration method
28:14 = 42:x
To find x,
(14 x 42) divided by 28, which equals 21g
what is the mean of this set {6,7,9,9,9}
Answer:
8
Step-by-step explanation:
To find the mean, or average of a data set, add all the values together, then divide by the number of values.
The data set is: 6,7,9,9,9
1. Add all the values
Add 6,7,9,9 and 9
6+7+9+9+9
40
2. Divide by the number of values
Count how many numbers are in the data set. In this case, there are 5 numbers.
Divide 40 by 5.
40/5
8
The mean of the data set is 8.
Steps:
Mean x: 8
Median x: 9
Mode: 9
Range: 3
Minimum: 6
Maximum: 9
Count: 5
Sum: 40
1: 6+7+9+9+9
2: =40
3: 40 divided by 5
4: = 8
Description:
The mean for this set is 8. We know this because when we add all the numbers = 40 then divided it by 5 = 8.
5 is the total numbers there
Please mark brainliest
Hope this helps.
Help……………………………………….
Answer:
The second option
Step-by-step explanation:
Adding n to the x inside of the parentheses moves the graph n units to the left
Answer:
5 units left. When looking at a translation of x inside of parentheses, it is the opposite of the sign. So x+5 becomes 5 to the left.
Step-by-step explanation:
Bill and Amy want to ride their bikes from their neighborhood to school which is 14.4 km away. It takes Amy 40 minutes to arrive at school. Bill arrives 20 minutes after Amy. How much faster (in km/h) is Amy than Bill for the entire trip?
Answer:
Amy is (21.6 - 14.4) 7.2 km/hr faster than Bill.
Distance = speed / time
Amy's speed
40 minutes = 40/60 = 2/3 hours
14.4 = speed / 2/3
Speed = 14.4 * 3/2 = 21.6 km/ hr
Bill speed
60 minutes = 1 hour
Speed = 14.4 km / hr.
PLEASE help, i will give brainliest<3
Please simplify then determine the value of the polynomial when n=3 and when n=2.
a) (5n^2 + 3n -4) + (-3n^2 + 4n -1)
b) (7n^2 - 5n - 2) - (-n^2 + 6n + 8)
Answer:
a. 34
b. 0
Step-by-step explanation:
you plug the n values as n
note when -n^2, you do this:
[tex]-(2)^{2}[/tex]= -4
so don't mistake it for +4
pay special attention to the signs to solve like:
+ times - is a negative!
Answer:
Simplified Expression a ) 2n^2 + 7n - 5,
Simplified Expression b ) 8n^2 - 11n - 10,
When n = 3 part a ) 34,
When n = 2 part a ) 17,
When n = 3 part b ) 29,
When n = 2 part a ) 0
Step-by-step explanation:
Consider the " simplification " process at hand;
[tex]a ) (5n^2 + 3n -4) + (-3n^2 + 4n -1),\\5n^2+3n-4-3n^2+4n-1,\\5n^2-3n^2+3n+4n-4-1,\\\\Simplified Expression = 2n^2+7n-5[/tex]
[tex]b ) (7n^2 - 5n - 2) - (-n^2 + 6n + 8),\\7n^2-5n-2+n^2-6n-8,\\\\Simplified Expression = 8n^2-11n-10[/tex]
For each part ( a and b ) I removed the ( ) and grouped like elements to receive the simplified expression;
Value of each polonomial;
[tex]a ) 2n^2 + 7n - 5,\\2 * ( 3 )^2 + 7 * ( 3 ) - 5,\\34\\\\2 * ( 2 )^2 + 7 * ( 2 ) - 5\\17[/tex]
[tex]b ) 8n^2 - 11n - 10,\\8 * ( 3 )^2 - 11 * ( 3 ) - 10,\\29\\\\8 * ( 2 )^2 - 11 * ( 2 ) - 10,\\0[/tex]
Each expression was solved through substitution and algebra.
" Simplified " Solution - See in answer above
* I hope the answer wasn't too confusing, for further information look through my response thoroughly
First gets a brainly :D
Answer:
[tex]47.25\[/tex]
Step-by-step explanation:
[tex]42 \times 1.125[/tex]
[tex]=47.25[/tex]
Answer:
$25.2
Step-by-step explanation:
What is the area of a rectangle with length (3^2)^2 meters and width of 3^2 meters?
Answer:
729m^2
Step-by-step explanation:
Area of rectangle = length x width
From the question, we know that length = 3^2^2 = 81 ( three squared is 9. Nine squared is 81)
width = 3^2 = 9.
Now for the area: length x width = 81 x 9 = 729m^2.
Please mark brainiest.
Can someone show me how to get x for both
Answer:
So since the sum of both is 13 because it shows both of the lines connected as a length of lines.
So we add them (14+x)+(x+15) = 13
14+2x+15 = 19+2x = 13
-6=2x
x=
-3
Step-by-step explanation:
. 4/18 times 2/92. 1/9 times 3/63. 12/14 times 1/84.1/7 times 5/65. 17/20 times 1/61. 4 1/4 times 3 1/22. 3 5/6 times 4 1/23. 2 1/2 times 4 7/84.3 3/5 times 2 3/85. 3 1/2 times 3 3/8Whoever can solve at least 2 from each set is awesome!
Answer:
Step-by-step explanation:
4/18×2/92
=1/9×1/23
=1/207
1/9×3/63
=1/3×1/23
=1/69
12/14×1/84
=1/14×1/7
=1/98
1/7×5/65
=1/7×1/13
=1/91
17/20×1/61
=17/1220
4 1/4 ×3 1/22
=17/4×67/22
=1,139/88
=12 83/88
3 5/6×4 1/23
=23/6×93/23
=93/6
=15 3/6
=15 1/2
2 1/2×4 7/84
=5/2×343/84
=1715/168
=10 35/168
I have answered more than 2 from each set
NEED HELP ASAP! Arianna correctly simplified an expression. When she substituted \ into the simplified expression, the value was –4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answer:
(1/6)(-10x - 4) = -4
Step-by-step explanation:
(1/6)(-3x - 24) = -4
=> -3x - 24 = -4 x 6
=> -3x - 24 = -24
=> -3x = 24 - 24
=> -3x = 0
=> x = 0 (not 2) => Incorrect option
(1/6)(-5x - 8) = -4
=> -5x - 8 = -4 x 6
=> -5x - 8 = -24
=> -5x = 8 - 24
=> -5x = -16
=> x = 16/5 (not 2) => Incorrect option
(1/6)(-10x - 4) = -4
=> -10x - 4 = -4 x 6
=> -10x - 4 = -24
=> -10x = 4 - 24
=> -10x = -20
=> x = 2 => Correct option
(1/6)(-12x - 16) = -4
=> -12x - 16 = -4 x 6
=> -12x - 16 = -24
=> -12x = 16 - 24
=> -12x = 8
=> x = -3/4 (not 2) => Incorrect option
=> Option C is correct
Hope this helps!
Answer: C. One-sixth (negative 10 x minus 4)
Step-by-step explanation: On Edgenuity!!!!!!!!!!!!!
Find the length of a. The length of the of the unknown leg is?
Answer:
10
Step-by-step explanation:
Pythagorean theorem
c² = a² + b²
26² = a² + 24²
a² = 26² - 24² = 100
a = √(100) = 10
The length of unknown leg will be a = 10 units
ConceptThe right angle triangle is given and the length of one side and length of hypotenuse are givenWe have to find the length of second sideSince the triangle given is right angle triangle we will use pythagorean theorem to find the length of third side.How to solve this problem?The steps are as follow:
The length of first side is 24 units and length of hypotenuse is 26 units and the second side is unknown which is taken as 'a' According to pythagorean theorem:(hypotenuse)^2 = (Side)^2 + (Side)^2
(26)^2 = (24)^2 + (a)^2
676 = 576 + (a)^2
(a)^2 = 676 - 576
(a)^2 = 100
a = 10 units
So the length of unknown leg will be a = 10 units
Learn more about pythagorean theorem here:
https://brainly.com/question/654982
#SPJ2
Find the y-intercept of the following equation. Simplify your answer.
y = 6x + 4
y-intercept =
Answer:
The slope is 6 and the y intercept is 4
(0,4)
Step-by-step explanation:
y = 6x + 4
This is in the form y = mx+b
where m is the slope and b is the y intercept
The slope is 6 and the y intercept is 4
(0,4)
Is -415 rational or irrational
Answer:
Rational
Step-by-step explanation:
Can convert it to a ratio (-415/1)
Answer:
Rational
Step-by-step explanation:
-415 is an integer. All integers are rational. It can be written as a fraction p/q, where p and q are integers and q is not equal to zero.
-415 can be written as [tex]-\frac{415}{1}[/tex].
Please please please answer this if you do this i will give you brain list I’ll give a thank you and I’ll rate you five star. It’s due soon so pls answer FAST!!
Answer:
b) 30^2 + b^2 = 40^2
Step-by-step explanation:
This is cuz the diagonal is the hypotenuse of the diagonal formed so it'll be c^ 2
c ^ 2 always is on the right hand side of the equation.
In this case since 40^2 is c^2 is should be on the right side of the equation.
Analyze the diagram below and complete the instructions that follow.
N
In the diagram, 212 22 22 = 23, and m41 = 609. Give the reasons that best support the following statements used to show
that m43 = 60°
1. 21 = 22 and 22 = 23; therefore, 2133
2. m 1 = 60° and 2123; therefore, 60° =m23
3. 60º = m/3; therefore, mx3 = 60°
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What is the length of the diagonal, d, of the cube shown below?
Round your answer to the nearest tenth
Answer:
103.8
Step-by-step explanation:
Length of diagonal of a cube is given by the formula:
[tex]d = side \times \sqrt{3} \\ \\ \therefore \: d = 60 \times \sqrt{3} \\ \\ \therefore \: d = 60 \times 1.73 \\ \\ \therefore \: d = 103.8 \: units[/tex]
The length of the diagonal of the cube is 103.9 units.
What is a cube?
A cube is a three dimensional figure or object which has all the side with equal length.
The length of each side of the cube = a = 60 units.
Therefore, the length of the diagonal of the cube = d = a[tex]\sqrt{3}[/tex] = 60[tex]\sqrt{3}[/tex] units = 103.9 units.
Learn more about a cube here: https://brainly.com/question/21270976
#Tag #SPJ2
If /61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang
answer in simplest radical form.
A. 5
B. 6
C. 2V15
D. 6V10
Answer:
A. 5
Step-by-step explanation:
The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.
From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:
(√61)² = (x)² + (x + 1)²
x² + x² + 2x + 1 = 61
2x² + 2x + 1 - 61 = 0
2x² + 2x -60 = 0
Dividing through by 2 gives:
x² + x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x-5)(x+6) = 0
x-5 = 0 or x+6 = 0
x = 5 or x = -6
Since the length of a side cannot be negative, x = 5 units
Answer:
The correct answer is A.
Step-by-step explanation:
X=5
The members of a basketball team need to
raise $895 for new uniforms. They already
have $351 from food sales. To raise the
remainder, they are planning a shoot-out
challenge. If 34 teams sign up, how much
must they charge per team to meet their
goal?
Answer:
$16
Step-by-step explanation:
First subtract $351 from $895 to find the dollar amount we're considering.
($895 - $351 = $544)
Then, divide the 34 teams into the $544 to yield the dollar amount each team should be charged. ($544 / 34 = $16)
A boy is playing ball in a garden surrounded by a wall 2.5 m high kicks the ball vertically up from a height of 0.4 m with a spee d of 14 m/s.For how long is the ball above the height of the wall .
Answer:
2.5 sec
Step-by-step explanation:
Height of wall = 2.5 m
initial speed of ball = 14 m/s
height from which ball is kicked = 0.4 m
we calculate the speed of the ball at the height that matches the wall first
height that matches wall = 2.5 - 0.4 = 2.1 m
using [tex]V^{2}[/tex] = [tex]U^{2}[/tex] + 2as
where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)
[tex]V^{2}[/tex] = [tex]14^{2}[/tex] + 2(-9.81 x 2.1)
[tex]V^{2}[/tex] = 196 - 41.202
[tex]V^{2}[/tex] = 154.8
v = [tex]\sqrt{154.8}[/tex] = 12.44 m/s
this is the velocity of the ball at exactly the point where the wall ends.
At the maximum height, the speed of the ball becomes zero
therefore,
u = 12.44 m/s
v = 0 m/s
a = -9.81 m/s^2
t = ?
using V = U + at
0 = 12.44 - 9.81t
-12.44 = -9.81
t = -12.44/-9.81
t = 1.27 s
the maximum height the ball reaches will be gotten with
[tex]V^{2}[/tex] = [tex]U^{2}[/tex] + 2as
a = -9.81 m/s^2
0 = [tex]14^{2}[/tex] + 2(-9.81s)
0 = 196 - 19.62s
s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.
height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m
we calculate for the time taken for the ball to travel down this height
a = 9.81 m/s^2 (positive in downwards movement)
u = 0
s = 7.49 m
using s = ut + [tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex]
7.49 = (0 x t) + [tex]\frac{1}{2}[/tex](9.81 x [tex]t^{2}[/tex] )
7.49 = 0 + 4.9[tex]t^{2}[/tex]
[tex]t^{2}[/tex] = 7.49/4.9 = 1.53
t = [tex]\sqrt{1.53}[/tex] = 1.23 sec
Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec
8y⁷÷4y⁵ what is this answer
Answer:
Step-by-step explanation:
Terms with the exponents are like terms, we can subtract the exponents from each other when we divide.
(8y^7)/(4y^5) = 2y^(7-5) = 2y^2
Answer: [tex]2y^{2}[/tex]
Step-by-step explanation:
8/4=2
[tex]y^{7} / y^{5} =y^{7-5} =y^{2}[/tex]
so the answer is 2y^2
12(3x)=12 what does x equal
Answer:
x=0.333
Step-by-step explanation:
12(3x)=12
36x=12
/36 on both sides
x=0.333
Are the following figures similar? (1 point)
Yes; the corresponding angles are congruent
No; the corresponding angles are not congruent
yes; the corresponding sides are proportional
no; the corresponding sides are not proportional
Answer:
yes the corresponding angles are congruent...
it can be wrong
Analyze the set below and answer the question that follows. (KUM) n (KUL) Which Venn diagram has shading that represents the given set?
Answer:
Choice A. The shading in the Venn Diagram shown in the first attachment represents the set [tex](K \cup M) \; \cap \; (K \cup L)[/tex].
Step-by-step explanation:
Let [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex] be sets. By the distributive law of sets, [tex]A \cup (B \cap C)[/tex] and [tex](A \cup B) \cap (A \cup C)[/tex] refer to the same set.
Apply this property to simplify the given expression:
[tex]\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}[/tex]
[tex]M \cap L[/tex] refers to the intersection between the two lower circles. The union of that intersection with set [tex]K[/tex] (the upper circle) would be the shaded region seen in choice A.
