A system of equations is simply a system that contains related equations of multiply variables
It took 5 seconds for the adults to go 20 yards and catch up to the kids
Let x represents the time of the race
The kids started 15 yards ahead, and they raced at 1 yard per second.
So, the kids' equation is represented as: [tex]\mathbf{k =15 + x}[/tex]
The adults' raced at 4 yards per second.
So, the adults' equation is represented as: [tex]\mathbf{a =4x }[/tex]
When they are side by side, we have the following equivalent equation
[tex]\mathbf{4x = 15 + x}[/tex]
Subtract x from both sides
[tex]\mathbf{3x = 15}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 5}[/tex]
It means that, it took the adults 5 seconds to catch up with the kids
Substitute 5 for x in any of the equations to calculate the distance travelled.
[tex]\mathbf{a =4 \times 5}[/tex]
[tex]\mathbf{a =20}[/tex]
It means that, the adults catch up with the kids at 20 yards
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Answer:
The adults went 123 yards and caught up to the kids in 41 seconds
Step-by-step explanation:
ixl :)
Team A beat Team B by 15 points in a football game . If a total of 35 points were scored , what was the final score of the game ?
For team A and team B
I WILL MARK YOU A BRAINLIEST
Answer:
25-10 (25 - A and 10 - B)
Step-by-step explanation:
25 - 10 equals the 15 point margin
25 plus 10 equals the 35 point score combined
Hope it helps
Simplify the expression
( 3n • 2n^3)^2
Answer:
[tex] \large\color{red}{ \tt{36n⁸}}[/tex]
Step-by-step explanation:
[tex] \large\color{lime}{ \tt{(3n×2n³)²}}[/tex]
To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.[tex] \large\color{lime}{ \tt{(3n⁴ × 2)²}}[/tex]
Multiply 3 and 2 to get 6.[tex] \large\color{lime}{ \tt{(6n⁴)²}}[/tex]
Expand (6n⁴)².[tex] \large\color{lime}{ \tt{6²(n⁴)²}}[/tex]
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.[tex] \large\color{lime}{ \tt{6²n⁸}}[/tex]
Calculate 6 to the power of 2 and get 36.[tex] \large\color{lime}{ \tt{36n⁸}}[/tex]
Hope It's Help
Of 90 gallons of water the average person uses each day, 30% is used outdoors. Mason wants to know how much water is used outdoors. How much water is used outdoors.
Answer:
The Awnser is 27 for both I did that I-ready before
Step-by-step explanation:
Answer:
27 for both blanks
Step-by-step explanation:
I just did it on iready and I got it correct
can you answer these fractions
[tex] \frac{2}{5} + \frac{3}{2} [/tex]
Due Tomorrow: Answer question 20 using steps
Answer:
angle CAB = 37
segment AC = 4.0
segment BC = 3.0
Step-by-step explanation:
angle CAB is complementary with angle ABC. 90-53=37. This is a right triangle, meaning we can use SohCohToa to find side lengths. AC = 5 * sin(53) = 4.0, and BC = 5 * cos(53) = 3.0.
how can you tell if data is continuous or discrete
For me, it helps to ask this question: Does it make sense to apply the midpoint? If it doesn't make sense, then the data is discrete. Otherwise, the data is continuous.
Here's an example:
Let's say we are counting the number of people buying a movie ticket. So the numbers we care about are positive whole numbers 1,2,3,... It doesn't make sense to apply the midpoint to the values 1 and 2 to get 1.5; you can't sell half a ticket. Therefore the variable "number of movie tickets sold" is a discrete variable. There are gaps in the data.
On the other hand, if we were measuring the weight of various coins, then this variable is continuous. It's possible to have any positive number decimal number weight (eg: 2.275 grams perhaps). It makes sense to apply the midpoint to any two weights and get some other weight. We don't have to worry about sticking to whole numbers only. Unlike before, there aren't any gaps and we consider this number set to be dense.
One way you could remember the two is to keep this in mind: If you count it, then it's likely discrete. If you can measure it, then it's continuous.
There are probably exceptions to that rule, but for the most part it holds up I think.
Write the equation of the line parallel to the line and passing through the point.
y=x+5, (8, 1)
Answer:
y=2x+9
Step-by-step explanation:
I got y-2x+9 because if you add 8-1 that equals 7 and if u do 7-5 that equals 2 so y2x and then 7 Plus 2 equals 9 so it all adds up to Y=2x+9?.
What is the equation of this graphed line?
Enter your answer in slope-intercept form
Answer:
Step-by-step explanation:
slope m = Δy/Δx = (6 - (-6)) / (2 - (-4)) = 12/6 = 2
b is the y intercept when x = 0.
b = 2
y = 2x + 2
Find the area of the square below when it is increased by a scale factor of 3
Answer:
To find the area of a square with the scale factor of 3, you multiply the side lengths by 3, so (3*L)*(3*W)= Area of your square.
Step-by-step explanation: I hope that this helps, ask questions in the comments below.(if you have any).
The area of the imagined square will be 90 units² by increased with a scale factor of 3.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
As per the imagined square with dimensions of 10 units.
Applied the scale factor 3 in the length of the square(since it has only one dimension).
10 x 3 = 30 units.
Thus, each side of the square will be 30 units in length.
Hence "By adding a scale factor of 3, the envisioned square's area will expand to 90 units²".
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In a raffle 1000 tickets are being sold, at $1 each. The first prize is $100, and there are 3 second prizes of $50 each. How much does the price of the ticket exceed the expected value
Answer:
The price of of the ticket exceeds its value by $ .75
can somebody help me plssssss
Answer:
They are equal, so =
Step-by-step explanation:
We know that one-half is .50. 3/2 is an improper fraction and when we solve to a decimal, we get 1.5.
If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population?
dPdt=200
Answer A: d cap p over d t is equal to 200
A
dPdt=200t
Answer B: d cap p over d t is equal to 200 t
B
dPdt=100t2
Answer C: d cap p over d t is equal to 100 t squared
C
dPdt=200P
Answer D: d cap p over d t is equal to 200 cap p
D
dPdt=100P2
Answer:
A. dP/dt = 200
The degree of the variable must be one for linear growth. Then the correct option is B.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
If P(t) is the size of a population at time t.
The differential equations have a linear growth in the size of the population. That means the degree of the variable must be one. And the equation of the population will be quadratic. That is given as
[tex]\rm \dfrac{dP}{dt} = 200t[/tex]
In this equation, the degree of the time (t) is one.
Thus, the correct option is B.
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describe how you know this is a proportional relanshoships
Answer:
don't see the relationship, but if it's a proportional relationship it should have the same result every time you divide the x by the y or vice versa.
Please help me please
[tex]\huge \bf༆ Answer ༄[/tex]
The translation can be can be expressed as : -
A translation
up 8 units and left 7 units[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]
how do you solve this problem lol
Guided Practice
The graph of y = 2(x + 1)2 − 4 is a translation 1 unit horizontally and 4 units vertically of the function y = 2x2. Graph this function in your notebook.
Type your answer and then click or tap Done.
The vertex of the parabola is (Fill in the blank text field 1
, Fill in the blank text field 2
( , )
Answer:
Step-by-step explanation:
hmm
The graph of a quadratic function is always a parabola. The vertex of the parabola after transformation is (-1,-4).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the two functions can be made as shown below. Therefore, the two functions are,
y=2x² → Drawn by the red line
y = 2(x + 1)² − 4 → Drawn by the blue line
Now, the vertex of a quadratic function or a parabola is the point at which the function or the parabola changes its slope, it's either the maximum of the function or the minimum of the function, depending on which side the parabola opens.
Hence, The vertex of the parabola after transformation is (-1,-4).
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Need to know this, please help
Also no links or wrong answers
HELP THIS IS DUE TOMORROW!!!!,Use a balance scale to solve the
following equation for the value of b.
17 + b = 35
Answer:
Step-by-step explanation:
just do 35-17
Answer:
Step-by-step explanation:
first find b.
To find b, subtract 17 from 35.
35 - 17 = b
35 - 17 = 18
next, add 17 and 18 to see if it equals 35.
17 + 18 = 35
so, b = 18.
Please help me ASAP please I need help
Answer:
147°
Step-by-step explanation:
Solving for x
To make a straight line the angles have to have a sum of 190. So 180°-33° would equal 147°
Answer:
x = 147°
Step-by-step explanation:
A line is 180°
180 - 33 = 147
Suppose that Y and Z are points on the number line.
If YZ=8 and Z lies at 5, where could Y be located?
If there is more than one location, separate them with commas.
Location(s) of Y :
9514 1404 393
Answer:
-3, 13
Step-by-step explanation:
8 units to the left of 5 on the number line is 5-8 = -3.
8 units to the right of 5 on the number line is 5+8 = 13.
The possible locations of Y are -3 or 13.
Write an algebraic expression for the verbal expression: "7 times the sum of a squared and b minus 4 times the sum of a squared and b".
how many ten thousand are in 1,000,000?
Answer:
100
Step-by-step explanation:
10,000 * 100 = 1,000,000
So there are 100 ten thousands in 1,000,000
Determine whether the points p1 (6,9,7), p2(9,2,0), and p3(12,-5,-6) lie on the same line
Answer:
They are not.
Step-by-step explanation:
Let's first calculate the vectors joining the first point to the second and the first to the third, they will be useful later.
[tex]\vec v_1_2 = \vec P_2 -\vec P_1 = <3; -7; -7>\\\vec v_1_3= \vec P_2 -\vec P_1 = <6; -14; -13>[/tex]
At this point we have at least three options:
Write down the line between P1 and P2 in vector form, and then see if we can fit the third point in there.
Calculate the cross product between the two, if it's non-zero the three point are not in a line.
Try to determine the plane passing for the 3 points: if we find one they are not in a line.
Option 1:
The vector form of the lne between the firs two points is [tex]<6+3t;9-7t;7-7t>[/tex]. Let's check the coordinates of the third point:
[tex]x_3:\ 6+3t= 12 \rightarrow t=2\\y_3:\ 9-7t = -5 \rightarrow t =2\\7z_3:\ 7-7t=-6 \rightarrow t = 13/7\ne 2[/tex]
So the three points are not in a line.
Option 2:
Let's calculate the cross product of the two vectors we found at the beginning.
[tex]\vec v_1_2 \times \vec v_1_3 = det \left[\begin{array}{ccc}\hat i&\hat j&\hat k\\3&-7&-7\\6&-14&-13\end{array}\right] = \hat i [-7(-13)-(-14)(-7)] - \hat j[3(-13)-6(-7)]+\hat k [3(-14)-6(-7)] = 7\hat i -3 \hat j + 0 \hat k \ne 0[/tex]
Since the result is not the null vector, the three points are not in a line.
Option 3:
Let's write the plane (in the [tex]z= ax+by+c[/tex] form that contain the three points. If the thre points are in a line, means that we can find only two of these parameters.
[tex]P1: 7= 6a+9b+c\\P2: 0= 9a+6b+c\\P3: -6= 12a-5b +c[/tex]
Since you can determine a, b and c ( I ended up with [tex]a=-\frac {10}3; b=-\frac18; c= \frac{123}8[/tex] but I probably messed something in there) the thre points are not in a line
Clare had t books. After she bought 8 more books, she had 24 books. Write and solve an equation to find the number of books Clare started with
Answer:
24-8=t
Step-by-step explanation:
I cant really explain much...
but, Hope it helps
plz mark brainiest if it does
A club with 26 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
Answer:
9,687,600
Step-by-step explanation:
27P5
= 27!/(27-5)!
= 27!/22!
= 27*26*25*24*23
= 9,687,600
Leah took her friends for a ride in her hot air balloon. The function fff models the height of the hot air balloon above the ground (in meters) as a function of time (in minutes) after takeoff.
Plot the point on the graph of fff that corresponds to when the hot air balloon landed.
Answer: point (60,0)
Step-by-step explanation: the x-intercept (60,0) shows that at 60 minuetes the balloon is 0 meter above the ground
The coordinates of the function of height and time are (210, 0) and (60, 10). The graph is attached below.
What is function?The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).
Given:
r(t) = 210 - 15t
Calculate the height after 10 minutes as shown below,
The height = 210 - 15 × 10
The height = 210 - 150
The height = 60
At time 0 the height will be,
The height = 210 - 15 × 0
The height = 210 - 0
The height = 210 meters,
Thus, the coordinates will be (210, 0) and (60, 10)
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What equation represents this sentence?
7 less than a number is 16.
7=16−n
7=n−16
7−n=16
n−7=16 100 ponits
Answer:
n - 7 = 16
Step-by-step explanation:
as it says "7 less than a number". If it was "a number less than 7" then it would be the 3rd one.
Answer: n - 7 = 16
Step-by-step explanation: i did quiz
Need help please need help
Answer:
b.y=4
c. x=6
These are the answers hope this helps
Answer:
sorry cant help
Step-by-step explanation:
how many prime numbers are multiples of 8
There are no prime numbers are multiples of 8. All the multiples of 8 are divided by 2.
What is a prime number?Prime numbers are whole numbers larger than one with only one element the number itself. Prime numbers can only be divided by the number 1 or by themselves.
All the terms that come in the table of 8 are multiples of 8.
8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are the multiples of 8. There are no prime numbers are multiples of 8.
Hence there is no prime numbers multiples of 8.
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Rachel invests $25,000 at age 25. She hopes the investment will be worth $125,000 when she turns 50. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
The rate of growth will she need to achieve her goal is 2.8%
The formula for finding the compound amount is expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
P is the amount invested = $25000
t is the time in years = 25 years
A is the amount = $125000
r is the rate in %
Substitute the given parameters into the formula to have:
[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]
Hence the rate of growth will she need to achieve her goal is 2.8%
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