Given:
A line passes through the points (-1, -1) and (5,8).
To find:
Which points lie on the same line?
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:
[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]
[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]
[tex]y+1=\dfrac{9}{6}(x+1)[/tex]
[tex]y+1=\dfrac{3}{2}(x+1)[/tex]
Multiply both sides by 2.
[tex]2(y+1)=3(x+1)[/tex]
[tex]2y+2=3x+3[/tex]
[tex]2y=3x+3-2[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]
So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].
Now, check each point for this equation.
Putting [tex]x=-3[/tex], we get
[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]
[tex]y=\dfrac{-9+1}{2}[/tex]
[tex]y=\dfrac{-8}{2}[/tex]
[tex]y=-4[/tex]
Similarly,
For [tex]x=9,y=15[/tex].
For [tex]x=1,y=2[/tex].
For [tex]x=4,y=6.5[/tex].
For [tex]x=3,y=5[/tex].
For [tex]x=-2,y=-2.5[/tex].
Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.
What number, divided by 3/7 , will result in a value of 2 1/3?
Evaluate the expression 2
2^5 = 32
Hope this helps! :)
Answer:
32
Step-by-step explanation:
[tex]2^{5}[/tex]
= 2 × 2 × 2 × 2 × 2
= 4 × 4 × 2
= 16 × 2
= 32
If the volume of a given cube is 729 cubic inches, what is the surface area of the
cube?
486 sq.inches
230 sq.inches
120 sq.inches
222 sq.inches
Answer:
SA = 486
Step-by-step explanation:
Its a cube. s = side length
V = [tex]s^{3}[/tex]
729 = [tex]s^{3}[/tex]
take cube root of each side : [tex]\sqrt[3]{729}[/tex] = 9
so, s = 9
Surface Area of a cube
SA = 6[tex]s^{2}[/tex]
SA = 6([tex]9^{2}[/tex])
SA = 6(81)
SA = 486
The surface area of the cube is 486 square inches. The correct option is A.
To find the surface area of a cube, we need to use the formula:
Surface Area = 6 x (side length)²
Given that the volume of the cube is 729 cubic inches, we can determine the side length of the cube using the formula for volume:
Volume = (side length)³
729 = (side length)³
Taking the cube root of both sides:
side length = ∛(729) = 9 inches
Now, we can substitute the side length into the surface area formula:
Surface Area = 6 x (9 inches)² = 6 x 81 = 486 square inches
Therefore, the surface area of the cube is 486 square inches.
To know more about the surface area of a cube follow
https://brainly.in/question/35343178
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HELPP!
The functions f(x) and g(x) are described using the following equation and table:
f(x)=-4(1.09)x
Answer:
A: The y-intercept of f(x) is equal to the x-intercept of g(x)
Step-by-step explanation:
From the equation of f(x) given, we have;
f(x) = -4(1.09)^(x)
Now,the y-Intercept will be the point where x = 0.
Thus;
f(0) = -4(1.09)^(0)
f(0) = -4
Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.
Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)
Which number line shows the solution to −4 − (−1)?
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to 4 is shown. Above this, another arrow pointing from 4 to 5 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to 4 is shown. Above this, another arrow pointing from 4 to 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 5 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
Answer:
number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow
The daily listening audience of an AM radio station is five times as large as that of its FM sister station. If 144,000 people listen to these two radio stations, how many listeners does the FM station have?
Answer:
The number of FM listereners are 24000.
Step-by-step explanation:
Let the listeners of FM are p and thus the istereners of AM are 5p.
According to the question,
p + 5 p = 144000
6 p = 144000
p = 24000
The number of FM listereners are 24000.
Find the nth term...-1,5,11,17
Answer:
23
Step-by-step explanation:
you just add 6 to every one
sin^2x + sin2x +2cox^2x = 2
Answer:
Step-by-step explanation:
[tex]sin^2 \ x + sin ^2 \ x + 2cos^ 2\ x = 2\\\\2sin^2 \ x + 2 cos^2 \ x = 2\\\\2 ( sin^2 \ x + cos^2 \ x ) = 2 \\\\2 \times 1 = 2 \\\\2 = 2 \\\\LHS = RHS \\\\Hence \ proved.[/tex]
Write the equation of a circle whose center is at (6,-7) and whose radius is 4.
Answer:
(x - 6)² + (y + 7)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (6, - 7 ) and r = 4 , then
(x - 6)² + (y - (- 7) )² = 4² , that is
(x - 6)² + (y + 7)² = 16
help me frll frll, my test is timed !!!! Which of the following scatterplots would have a trend line with a negative slope?
*y,
1
4.5
5 4
1.5
5.5
2.
4.25
3
25
5
2
3
3.75
1
3.5
3.5
1
2
3 4
5
35
425
Xy,
1
25
5
ا
1.5
3.5
4
2.
4.25
3
O
254 25
27
Answer:
i toke it on edu
Step-by-step explanation:
it is 2
Answer:
c
Step-by-step explanation:
Simplify. Your answer should contain only positive exponents.
fraction numerator 2 b squared over denominator 2 b end fraction 2b^2/2b
A. fraction numerator 3 over denominator 4 b end fraction 3/4b
B. 3 b squared 3b^2
C. b
D. 3b
Answer:
D.6b C.v B.8squared 7b<9
Which of the following biconditional statements is true?
Answer:
The answer is A :)
Step-by-step explanation:
Answer:
A whole number is even if and only if it is evenly divisible by 2
Step-by-step explanation:
BRAINLY
JannetPalos
Ambitious
808 answers
526.6K people helped
Answer:
A whole number is even if and only if it is evenly divisible by 2
Step-by-step explanation:
1. The first statement is false because product of two negative integers is positive.
Ex:
(- 2) × (- 3) = 6
2. The second statement is false because there are whole numbers which are divisible by 2 but not divisible by 4.
Ex:
6 is divisible by 2 but not divisible by 4
3. The fourth statement is false because if a whole number is divisible by 2, then, by definition, it must be an even number.
Ex:
6 is divisible by 2 and hence it is an even number
4. The third statement is true because if a whole number is divisible by 2, then, by definition, it must be an even number.
Ex:
6 is divisible by 2 and hence it is an even number
Question
Example
Step by Step
A
You can represent the measures of an angle and its complement as xºand (90-x)º.
Similarly, you can represent the measures of an angle and its supplement as x and
(180 - x )°. Use these expressions to find the measures of the angles described.
The measure of an angle increased by 68° is equal to the measure of its complement.
The measure of the angle is
and the measure of its complement is
Answer:
The measure of the angle is 11 and its complement is 79 degrees
Step-by-step explanation:
Mathematically, when two angles are complementary, the sum of the angles equal 90 degrees
so now, if the first angle is x , the second angle which is increased by 68 degrees will be x + 68
So now if we add these two, the value we will get is 90 degrees
Mathematically, we have this as;
x + x + 68 = 90
2x + 68 = 90
2x = 90-68
2x = 22
x = 22/2
x = 11
the measure of the angle is 11 and its complement will be 11 + 68 = 79
x = 4y + 3, 2x + y = -3
System of Equations
Answer:
x = -1, y = -1
Step-by-step explanation:
x = 4y + 3
2x + y = -3
We have the value of x in terms of y, so we substitute that in 2x + y = -3:
2(4y+3)+y = -3
8y+6+y = -3
9y = -9
y = -1
Now we substitute the value of y in x = 4y + 3:
x = 4(-1)+3
x = -1
Answer:
y = -1 & x = -1
Step-by-step explanation:
x = 4y + 3 .... ( 1)
2x + y = -3 ........(2)
substitute the 4y + 3 as x in the second equation
2( 4y + 3) + y = -3
simplify and solve for y
8y + 24 + y = -3
9 y + 24 = -3
9y = -3 -24
9y = -27
y = -27 / 9
y = -1
Now, substitute the value of y -1 in first equation
x = 4y + 3
solve for x
x = 4 ( - 1 ) + 3
x = -4 + 3
x = -1
which equation represents a line parallel to the y-axis?
Answer:
B. x=4
Step-by-step explanation:
I hope this helps!
Differentiate
[tex]y = 3x {}^{3} + 8x - 7[/tex]
Answer:
y=9x^2 + 8
Step-by-step explanation:
using the power rule, we will differentiate each term separately
d/dx of 3x^3 = (3)(3)x^(3-1) = 9x^2
d/dx of 8x = 8x^(1-1) = 8
d/dx of -7 = 0
combining them we get the derivative which is y = 9x^2 + 8
Answer:
9x² + 8
Step-by-step explanation:
The given function to us is ,
[tex]\implies y = 3x {}^{3} + 8x - 7[/tex]
And we need to differentiate the given function with respect to x . Taking the given function and differenciating wrt x , we have
[tex]\implies y = 3x^3 + 8x - 7 [/tex]
Recall that , the derivative of constant is 0 . Therefore ,
[tex]\implies \dfrac{dy }{dx}= \dfrac{d}{dx}(3x^3 + 8x - 7) \\\\\implies\dfrac{dy }{dx}= \dfrac{d}{dx}(3x^3)+\dfrac{d}{dx}(8x) + 0 \\\\\implies\dfrac{dy }{dx}= 3\times 3 . x^{3-1} + 8\times 1 . x^{1-1} \\\\\implies\underline{\underline{\dfrac{dy }{dx}= 9x^2+8}} [/tex]
Hence the derivative of given function is 9x² + 8 .
WILL GIVE 50 POINTS PLS RESPOND FAST!!!!
The table below shows the radius y, I’m centimeters, created by grouping algae in x days:
Time (x) 2 4 6 8
(Days)
Radius(y) 4 7 10 14
(cm)
Part A: what is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and radius of the algae. [choose the value of the correlation coefficient from 1, 0.97, 0.5, 0.2.]
Part B: what is the value of the slope of the graph of radius versus time between 6 and 8 days, and what does the slope represent?
Part C: does the data in the table represent correlation or causation? Explain your answer.
Answer:
wait whats your question
Step-by-step explanation:
m.c.m (35;50)
m.c.d (35;50)
m.c.m (116;92)
m.c.d (116;92)
Ayudaaa
9514 1404 393
Answer:
350, 5, 2668, 4
Step-by-step explanation:
a) mcm(35, 50) = 35·50/mcd(35, 50) = 35·50/5 = 350
__
b) mcd(35, 50) = 5
35 = 5·7; 50 = 5·10
__
c) mcm(116, 92) = 116·92/mcd(116, 92) = 116·92/4 = 2668
__
d) mcd(116, 92) = 4
116 = 4·29, 92 = 4·23
question is on the image.
can you do question a and b please
I'll you give the brainliest.
Answer:
a) i. 1/6
ii. 0
b) 1/6 * 60
=10
Answer:
[tex]a) 1)\frac{1}{6} \\ \\ 2)0 \\ \\b) \frac{1}{6} \times 60 = \frac{60}{6} = 10[/tex]
hope this helps you.
In the description of the following experiment, determine the experimental factor. A research team is testing a paste form of a drug to alleviate inflammation. Participants are grouped into Team A and Team B. Team A receives the paste form of the drug. Team B receives a similar paste with no active ingredients.
Answer:
The experimental factor is the drug to alleviate inflammation paste form
Step-by-step explanation:
An experimental factor is an independent variable that is being controlled by the experimenter which are the input values which the experimenter sets specifically
In the given experiment, two teams, Team A and Team B are administered different treatments (inputs)
Team A is administered the paste form of the drug being experimented
Team B is administered a similar paste with no active ingredient
Therefore, the experimental factor is the drug being administered in paste form
Sarah borrows £500 for 2 years at a rate of 15% to buy a
new laptop.
Calculate the simple interest she will pay on this loan.
Answer: 150 pounds
Step-by-step explanation:
Hallar el interés producido por un capital de /240a una tasa de interés del 30% anual prestados durante un tiempo de 2 años
Answer:
The interest for the two years is 144.
Step-by-step explanation:
Hallar the interest produced by a capital of /240 to an annual interest rate of 30% provided for a period of 2 years
Principal, P = 240
Interest, R = 30 %
Time, t = 2 years
The simple interest is given by
[tex]I = \frac{P\times R\times T}{100}\\\\I = \frac{240\times 30\times 2}{100}\\\\I = 144[/tex]
A scientist has two solutions, which she has labeled Solution A 60% and Solution B 75% Each contains salt. She knows that Solution A is salt and Solution B is salt. She wants to obtain ounces of a mixture that is salt. How many ounces of each solution should she use
Answer:
The answer is "180".
Step-by-step explanation:
Please find the complete question in the attached file.
Let's
x = ounces solution of A
y = ounces solution of B
[tex]x + y = 180 \\\\y = 180 - x\\\\0.60x + 0.85y = 0.75(180)\\\\0.60x + 0.85y = 135\\\\[/tex]
Multiply both sides of the equation by 100 to remove the decimal points.
[tex]60x + 85y = 13500\\\\60x + 85(180 - x) = 13500\\\\60x + 15300 - 85x = 13500\\\\-25x = -1800\\\\x = 72\ \ ounces\\\\y = 180 - 72 \\\\y = 108 \ \ ounces\\\\[/tex]
Pick the correct graph and equation pleasee!
Given:
Amount of flour in a bin = 30 cups
Flour required for each signature cake = [tex]1\dfrac{1}{2}[/tex] cups
To find:
The correct equation and graph for the given situation.
Solution:
Let F be the amount of flour in the bin and c be the number of signature cakes.
Flour required for each signature cake = [tex]1\dfrac{1}{2}[/tex] cups
Flour required for each signature cake = [tex]1.5[/tex] cups
Flour required for c signature cakes = [tex]1.5c[/tex] cups
Amount of flour in a bin is 30 cups and it is reduced by 1.5c cups. So, the amount of flour in the bin is:
[tex]F=30-1.5c[/tex]
At [tex]c=0[/tex], we get
[tex]F=30-1.5(0)[/tex]
[tex]F=30[/tex]
At [tex]F=0[/tex], we get
[tex]0=30-1.5c[/tex]
[tex]1.5c=30[/tex]
[tex]c=\dfrac{30}{1.5}[/tex]
[tex]c=20[/tex]
Therefore, the required equation is [tex]F=30-1.5c[/tex] and the 4th graph is correct.
Can someone please help with this problem
Answer:
f(x)=-3(x+2)^2-2
Step-by-step explanation: the the FX graph the -3 in my equation represents the decrease(for being negative) in the graph, the positive 2 represents the x axis if that number is positive the negative 3 is going to change the x axis then will end up being negative which is why the x starts off in negative 2, the last number represents the y axis if the y axis is negative 2 the y will start off at -2
2+2
f re e
points or whatever
Answer:
2+2 = 4
Step-by-step explanation:
Hope this helps.
Answer:
2 + 2 is 4 my guy
Step-by-step explanation:
thx for the points
Can someone help with both questions 19 & 20
Answer:
19.
h=0, the result is 1000×2⁰ = 1000
this is the population of bacteria the excitement started with at the very beginning.
h=-3, the result is 1000×2-³ = 1000/(2³) = 1000/8 = 125
this is a calculation 3 hours backwards from the very start of the experiment, saying that if we started the experiment 3 hours earlier, this would have had to be the starting population of the bacteria so we would arrive at the same amount of population at any given time (value of h).
20.
D 25x⁶
Step-by-step explanation:
for 19 there is not more explanation. it is all ashtray in the answer.
for 20 we see that we are dealing with a square, so ask 4 sides have the same length.
one side is 5x³.
the area of a square is simply side².
so, here (5x³)² = 25x⁶
Olivia bought 525 Euros at an exchange rate of $1.76/Euro. How many Canadian dollars did she pay for the Euros she bought?
the total amount of money for the price of one euro is equal to 1.76 [tex]\displaystyle\bf 525\cdot1.76=\underbrace{0,44\cdot 4}_{1.76}\cdot 525=2100\cdot0,44=21\cdot 44=924$\\\\Answer:She can exchange \underline{924\$ }for 525 euros[/tex]
One national survey found that 86 percent of those who were unhappily married, but who stayed with the marriage, were when reinterviewed five years later:
Comolete question is;
One national survey found that 86 percent of those who were unhappily married but who stayed with the marriage were, when re-interviewed five years later,
A) preparing to divorce
B) resigned to the situation
C) mostly "very" or "quite" happy
D) mostly "very" happy
Answer:
C) mostly "very" or "quite" happy
Step-by-step explanation:
From social psychology, we know that;
Sometimes people could be happy about something but later on as things progress they become satisfied and are happy about that same thing or person.
The same is the case here with marriage and more importantly in this research.
It says they were unhappily married but they stayed in the marriage and were interviewed 5 years after that. Thus, for them to stay that long even after being unhappy, it means that they began to become a bit happy along the line.
Thus, they would gradually become happy or mostly happy.
How long is JK?
Choose 1 answer:
A: 3
B: 2 square root 3
C: 3 square root 3
D: 6
E: 9
Answer:
C) 3 times the sq root of 3
Step-by-step explanation:
In a right angle triangle, the COS is definned as the ajacent side over the hypotenuse. So
COS 60 = JK/JL
COS 60 = JK/(6*sq root 3)
.5 = JK/(6*3**1/2)
JK = .5 *(6*3**1/2)
JK = 3*3**1/2