Answer:
21 sq. units
Step-by-step explanation:
On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula to find the location of point R?
To find the location of point R on the number line, you can use the formula for finding a point on a line segment given the endpoints and the ratio. In this case, the ratio is 3:5 and the endpoints are -14 and 2.
Explanation:To find the location of point R, you can use the formula for finding a point on a line segment given the endpoints and the ratio. In this case, the formula is:
R = Q + r(QS)
where Q is the starting point, S is the ending point, r is the ratio between Q and S, and QS is the displacement vector from Q to S. In this problem, Q is -14, S is 2, and the ratio is 3:5. So we can substitute these values into the formula and solve:
R = -14 + (3/8)(2 - (-14)) = -14 + (3/8)(16) = -14 + 6 = -8
Therefore, the location of point R is -8 on the number line.
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The location of point R is -8. The correct answer is option a. [tex]\frac{3}{3+5}(2-(-14))+(-14)[/tex]
To find the location of point R which partitions the directed line segment from Q to S in a 3:5 ratio, we use the section formula. The formula is:
[tex]R =\frac{m}{m+n}(x_2-x_1)+x_1[/tex]
Here, m = 3 and n = 5, while Q is at [tex]x_1 =[/tex] -14 and S is at [tex]x_2 =[/tex] 2.
Plugging in the values, we have:
[tex]R =\frac{3}{3+5}(2-(-14))+(-14)[/tex][tex]R = \frac{3}{8}(2+14)-14[/tex][tex]R = \frac{3}{8} (16)-14[/tex][tex]R = \frac{48}{8}-14[/tex][tex]R = 6-14[/tex]R = -8Therefore, the location of point R is at -8 on the number line and it is calculated by the expression [tex]R =\frac{3}{3+5}(2-(-14))+(-14)[/tex].
The complete question is:
On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula [tex]R =\frac{m}{m+n}(x_2-x_1)+x_1[/tex] to find the location of point R?
a. [tex](\frac{3}{3+5})(2-(-14))+(-14)[/tex]
b. [tex](\frac{3}{3+5})(-14-2)+2[/tex]
c. [tex](\frac{3}{3+5})(2-14)+14[/tex]
d. [tex](\frac{3}{3+5})(-14-2)-2[/tex]
The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972. What does the 4 represent? (1 point) The starting population of the rabbits The population of the rabbits after five years The rate the population increases The number of years that have passed
Answer: The starting population of the rabbits
Step-by-step explanation:
Given: The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972.
We know that the exponential growth function is given by :-
[tex]f(x)=Ab^x[/tex], where A is the initial amount and b is the multiplicative rate of change in time x.
As compared to the given exponential function, we have
A=4
Therefore, 4 represents the starting population of the rabbits
Eighty seven decreased by three times a number is greater than one hundred sixty five
87-3x>165
-3x> (165-85)
-3x>80
80/-3 = -26.666
check;
87-3*(-26)=165
so x < -26
A computer simulation tossed a 10-faced die 5 times. How many possible outcomes exist? 9,765,625 100,000 252 100
Answer:
Possible outcomes in tossing a 10-faced die 5 times is:
100,000
Step-by-step explanation:
A computer simulation tossed a 10-faced die 5 times.
Number of outcomes in each throw=10
Number of outcomes in 2 throws
=Number of outcomes in first throw×number of outcomes in second throw
=10×10
= 100
Hence, Number of outcomes in 5 throws
=10×10×10×10×10
=100,000
Possible outcomes in tossing a 10-faced die 5 times is:
100,000
Graph y=-1/2x^2-1. Identify the vertex of the graph. tell whether it is a minimum or maximum. (To clarify, 1/2 is a fraction *x^2)
1. (-1,0);minimum
2.(-1,0);maximum
3.(0,1);maximum
4.(0,-1);minimum
The equation y = -1/2x^2 - 1 represents a downward opening parabola with the vertex at (0, -1), making it a maximum point.
Graph: The given equation is y = -1/2x^2 - 1. This represents a downward opening parabola.
Vertex: The vertex of the parabola is at (0, -1), making it a maximum point.
Conclusion: The correct answer is option 4: (0, -1); minimum.
If a line contains the point (0, -1) and has a slope of 2, then which of the following points also lies on the line?
A. (2, 1)
B. (1, 1)
C. (0, 1)
The point that lie on the line is:
B. (1,1)
Step-by-step explanation:We are given that a line passes through the point (0,-1) and has a slope of 2.
We know that the equation of a line passing through (a,b) and having slope m is given by:
[tex]y-b=m(x-a)[/tex]
Here we have: (a,b)=(0,-1) and m=2
This means that the equation of line is:
[tex]y-(-1)=2(x-0)\\\\y+1=2x\\\\y=2x-1[/tex]
Now we will check which option is true.
A)
(2,1)
when x=2
we have:
[tex]y=2\times 2-1\\\\\\y=4-1\\\\\\y=3\neq 1[/tex]
Hence, option: A is incorrect.
B)
(1,1)
when x=1
we have:
[tex]y=2\times 1-1\\\\\\y=2-1\\\\\\y=1[/tex]
Hence, option: B is correct.
C)
(0,1)
when x=0
we have:
[tex]y=2\times 0-1\\\\\\y=0-1\\\\\\y=-1\neq 1[/tex]
Hence, option: C is incorrect.
Find the missing factor n(n-3)+2(n-3)=() (n-3)
need help solving for the midpoint between point a and point b
A is located at (-3,-5) B is located at (1,-9)
-3 + 1 = -2/2 =-1
-5 + -9 = -14/2 = -7
midpoint is (-1,-7)
From a deck of 52 cards, one card is drawn at random. Match the following subsets with their correct probabilities.
1. P(face card)
2. P(seven of hearts)
3. P(no black)
4. P(king)
5. P(diamond)
Answer:
P(face card)=3/13 P(seven of hearts)=1/52P(no black)=1/2P(king)=1/13P(diamond)=1/4Step-by-step explanation:
We know that there are a total 52 cards out of which:
There are 12 face cards ( 4 kings,4 queen and 4 jack)
There are 4 pack:
13- spades 13- club 13-heart 13-diamond.
Out of which there are 26 black cards( 13 spade and 13 club)
There are 26 red cards( 13 heart and 13 diamond)
Now , we are asked to find the probability of each of the following,
1)
P(face card)
Since there are total 12 face cards out of 52 playing cards.
Hence,
P(face card)=12/52=3/13
2)
P( seven of hearts)
As there is just 1 seven of heart out pf 52 cards.
Hence, P(seven of hearts)=1/52
3)
P(no black)
This means we are asked to find the probability of red card.
As there are 26 red card.
Hence P(no black)=26/52=1/2
4)
P(king)
As there are 4 kings out of 52 cards.
Hence, P(king)=4/52=1/13
5)
P(diamond)
As there are total 13 cards of diamond.
Hence,
P(diamond)=13/52=1/4
Two cars leave the same location at the same time but one car is heading north and the other is heading south. After 3 hours, the cars are 360 miles apart. If the car heading north is traveling 10 miles per hour slower than the car heading south, what are the two speeds of the cars?
SHOW THE EQUATION
3x +3(x-10) = 360
3x +3x-30 =360
6x-30 =360
6x=390
X = 390/6 = 65
65-10 =55
One car was driving 65 mph
The other was 55 mph
The graph below represents which system of inequalities? graph of two infinite lines that intersect at a point. One line is solid and goes through the points 0, 2, negative 2, 0 and is shaded in below the line. The other line is dashed, and goes through the points 0, 6, 3, 0 and is shaded in below the line. y < −2x + 6 y ≤ x + 2 y ≤ −2x + 6 y < x + 2 y < 2 over 3x − 2 y ≥ 2x + 2 None of the above
To solve the problem we should know about the Equation of a line and slope of a line.
The equations are (y≤ x+2) and (y< -2x+6).
Given to us
One line is solid and goes through the points (0, 2), and (-2, 0) and is shaded below the line.The other line is dashed, goes through the points (0, 6) and (3, 0), and is shaded below the line. For the first line,Given the points (0, 2), and (-2, 0), therefore,
[tex]x_2=0\\y_2=2\\x_1=-2\\y_2=0[/tex]
Substituting the values in the formula of the slope,
[tex]m=\dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
[tex]m=\dfrac{2-0}{0-(-2)} = \dfrac{2}{2} = 1[/tex]
Substitute the value of slope and a point in the formula of line,
[tex]y = mx+c\\y_2 = mx_2+c\\2 = (1)0 +c\\c = 2[/tex]
Thus, the equation of the line is y=x+2, but as given the line is solid and is shaded below the line. therefore,
y≤ x+2
For the Second line,Given the points (0, 6) and (3, 0), therefore,
[tex]x_2=0\\y_2=6\\x_1=3\\y_2=0[/tex]
Substituting the values in the formula of the slope,
[tex]m=\dfrac{(y_2-y_1)}{(x_2-x_1)}[/tex]
[tex]m=\dfrac{6-0}{0-3} = \dfrac{6}{-3} = -2[/tex]
Substitute the value of slope and a point in the formula of line,
[tex]y = mx+c\\y_2 = mx_2+c\\6 = (-2)0 +c\\c = 6[/tex]
Thus, the equation of the line is y=-2x+6, but as given the line is shaded below the line. therefore,
y< -2x+6
Hence, the equations are (y≤ x+2) and (y< -2x+6).
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10 employees in an office were absent. Of these absentees constitutes 25% of the employees, what is the total number of employees?
Bradley is returning home from a place that is 2 kilometers away. The function y = 2,000 − 90x represents Bradley's distance from home in meters, y, in relation to the number of minutes he walks, x. Which statements about this function are true?
Final answer:
The function y = 2,000 - 90x shows Bradley's distance from home decreases by 90 meters for every minute walked, starting from 2,000 meters away. The graph of this equation is a straight line with a negative slope, indicating constant speed.
Explanation:
The equation y = 2,000 - 90x represents Bradley's distance from home in meters, y, as a function of the time x in minutes that he walks. This equation is a linear function where the initial value 2,000 meters represents the distance from home at the start, and -90 meters/minute is the rate at which this distance decreases as Bradley walks home. As time increases by 1 minute, the distance from home decreases by 90 meters. This relationship shows that Bradley travels at a constant speed since the slope of the line representing the equation (which is the rate of change of distance with respect to time) is constant.
If we graph this function, we would get a straight line that starts at 2,000 meters on the y-axis when t=0 and has a negative slope of 90. Therefore, the graph shows that as time passes, Bradley gets closer to home at a steady pace. This also reflects that the total distance Bradley would walk is 2,000 meters, and the time it would take for him to return home can be found by setting the function equal to zero and solving for x.
If F(theta)=tan theta=3, find F(theta+pi)
Convert 48°36'12" to the nearest thousandth of a degree
48 degrees remains
divide minutes by 60
36/60 = 0.6
then divide seconds by 3600
12/3600=0.003 ( to nearest thousandth)
now add them all up
48 +0.6 + 0.003 = 48.603 degrees
decimal fundamentals
add 729.3 + 3.4006
What is the length of the hypotenuse of the triangle?
Answer:
length of the hypotenuse = 17 cm
Step-by-step explanation:
To find the length of the hypotenuse of any triangle we use pythagorean theorem
[tex]c^2 = a^2 + b^2[/tex]
Where c is the hypotenuse
a and b are the legs of the triangle
Given : a= 8 cm, and b= 15 cm
We find hypotenuse C
[tex]c^2 = 15^2 + 8^2[/tex]
[tex]c^2 = 225 + 64[/tex]
[tex]c^2 = 289[/tex]
Take square root on both sides
c= 17
So length of the hypotenuse = 17 cm
Please check my work!
10 POINTS!!! TO ANSWER CORRECTLY AND BRAINLIEST!!!!
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.
Prove that if m, d, and k are integers and d > 0, then (m + dk) mod d = m mod
d.
To prove that (m + dk) mod d = m mod d, we can use the definition of the modulo operation and properties of integers.
Explanation:To prove that (m + dk) mod d = m mod d, we can use the definition of the modulo operation and properties of integers. Let's assume that m and d are integers, d > 0, and k is an integer.
Start with the left-hand side: (m + dk) mod d.Using the distributive property, we can rewrite (m + dk) as m mod d + (dk mod d).Since any number mod d is less than d, (dk mod d) is equivalent to 0.Therefore, (m + dk) mod d simplifies to m mod d + 0, which is equal to m mod d.Since the left-hand side is equal to the right-hand side, we have proved that (m + dk) mod d = m mod d.Learn more about Modulo operation here:https://brainly.com/question/30264682
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Help please..........,.,,,
F a company provides 1 1/4 vacation days to its employees every month, how many vacation days does an employee get every year?
1 1/4 per month
12 months per year
1 1/4 * 12 =
5/4 * 12/1 = 60/4 = 15
they get 15 days per year
Find the probability of a couple having a baby girlgirl when their fourthfourth child is born, given that the first threethree children were all girlsall girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girlsall girls among fourfour children?
Which of the following rational functions is graphed below?
The solution is, Option A. is correct.
F(x) = 1/ (x-1)(x+4)
What is rational fraction?A rational fraction is an algebraic fraction such that both the numerator and denominator are polynomials.
Here, we have,
a graph is given .
We need to find which of the given rational functions is graphed in image.
On x-axis, 1 unit = 2 units
Clearly, we can see the graph is not defined at point x = - 4 and at x = 1.
Corresponding to x = - 4, factor is (x+4) .
Corresponding to x = 1, factor is (x-1) .
So, this graph is of the rational fraction
F(x) = 1/ (x-1)(x+4)
Hence, Option A. is correct.
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Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2-3x-3=0
Find the value of the variable and DF if D is between C and F if CD 4y -9, DF 2y-7, and CF 14.
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 13 m/s. The ball's height h (in meters) after t seconds is given by the following.
h=1+13t-5t^2
Find all values of t for which the ball's height is 8 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
For t=1.84 and t=0.76 the ball's height is 8 meters in equation h=1+13t-[tex]5t^{2}[/tex].
What is equation?An equation is a relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+ by=c. It is solved in order to find the values of variables.
How to solve equation?We have been given an equation h=1+13t-[tex]5t^{2}[/tex] and we have to find the values of t for which h=8.
So,
1+13t-[tex]5t^{2}[/tex]=8
[tex]-5t^{2}[/tex]+13t+1-8=0
[tex]-5t^{2}[/tex]+13t-7=0
Removing negative signs.
[tex]5t^{2}[/tex]-13t+7=0
We cannot solve through factorization so e use the following formula:
x=-b+-[tex]\sqrt{b^{2} -4ac}/2a[/tex]
t=(13+-[tex]\sqrt{-13^{2} -4*5*7}[/tex])/2*5
t=(13+-[tex]\sqrt{169-140}[/tex])/10
t=(13+5.38)/10, (13-5.38)/10
t=1.838, 0.762
By rounding off to nearest hundred t=1.84, 0.76.
Hence value of t for which h=8 meters are 1.84 and 0.76.
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The graph shows f(x) = 1/2 and its translation, g(x).
Which describes the translation of f(x) to g(x)?
Answer:
The translation function g(x) is given as:
[tex]g(x)=\dfrac{1}{2^x}+4[/tex]
step-by-step explanation:
The parent function is f(x) and its representation is given as:
[tex]f(x)=\dfrac{1}{2^x}[/tex]
Now the graph g*x) is obtained by translation of the graph f(x) by some units.
Now as the graph of g(x) is a shift of the graph f(x) or the graph g(x) is translated by 4 units upwards.
hence the function g(x) is represented by:
g(x)=f(x)+4.
Hence the translation function g(x) is given as:
[tex]g(x)=\dfrac{1}{2^x}+4[/tex]
You are interviewing an applicant for a sales agent position in your company. Based on the company’s record, almost every company sales agent makes a total revenue of 150x-x² pesos for selling x products in a week. If the applicant confidently assures you that he/she can easily make ₱10,000 weekly revenue, how many products should he/she sell to meet this quota?
WILL GIVE A BRAINLIEST IF THE ANSWER IS CORRECT!!! PLEASE HELP ASAP!!
Find the value of x in the expression (2a^4b^2)^x=4a^8b^4.
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5