From the information given above, The substitution property is used here. See further explanation below.
What is substitution property?The substituted property of equality states that one value may be substituted for another in an expression or equation and the result will be the same.
If the values of x and y are equivalent, then x and y may be substituted for one another. The property's opposite is likewise true.
For exmaple,
If x=y for any real integer x and y, then y may be replaced for x in any statement.
In the above instance, x = 2 and hence can be substituted for x in the first expression given as:
4x -3.
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Full Question:
4x-3
x=2
4(2)-3
The _____ property is used here.
In a state’s lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If t he same three numbers Are drawn in the same order, you win and collect $400. How many different selections are possible
There are 1000 different selections possible.
There are 10 digits in total from 0 to 9.
It is required to make a three digit number using 10 digits, where repetition is allowed.
So, in the three digit number, the unit place has 10 possible choices, the tens place also has 10 choices, and the hundreds place has 10 possible choices.
So, the total number of different selections of three- digit numbers can be obtained by multiplying 10 by itself three times.
Total different selection possible = Total different choices to fill the units place ×Total different choices to fill the tens place × Total different choices to fill the hundreds place
Total different selection possible = 10×10×10
= 1000
As a result there are 1000 different selections possible.
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a ski slope can be modelled by the equation of the tangent to the curve y=-0.12x^2+12 at the point where x=30
Answer:
y= -96
Step-by-step explanation:
y= -0.12x^2 +12
y= -0.12x 30^2+12
y= -96
I think the question isn't complete so I'm pretty sure I'm wrong but this is what I got :)
Some fabric shrinks when it is washed.
A piece of fabric is washed twice.
After the first wash, the area of the fabric is 75% of the area of the original piece of fabric.
After the second wash, the area of the fabric is 90% of the area of the fabric after the first
wash.
After these two washes, the area of the fabric is 2700 cm².
Calculate the area of the original piece of fabric.
After performing some mathematical operations, we know that the original area of the fabric is 4,000 cm².
What are mathematical operations?In mathematics, an operation is a function that converts zero or more input values into a discrete output value.The number of operands in the operation determines how complex it is.The four mathematical operations are functions that convert inputs that are numerical into outputs that are numerical (i.e., another number).These are addition, subtraction, multiplication, and division.So, the original area of fabric is:
The area after two washes is 2700 cm² which is 90% of the area after the 1st wash.Then:
x/100 × 90 = 270090x = 270000x = 270000/90x = 3000 cm²The area after 1st wash is 3000 cm².
Which is 75% of the original area.Then:
x/100 × 75 = 300075x = 300000x = 300000/75x = 4,000 cm²Therefore, after performing some mathematical operations, we know that the original area of the fabric is 4,000 cm².
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Using only a compass can you find points in a plane that are the same distance from points A and B
You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.
How can you use a compass to make a locus of points that are equally spaced between A and B?
Draw a straight line AB=7 cm using a ruler.Draw an arc from A using a compass, and then draw another arc that intersects the first one at the point where it crosses AB.From A to the arc, draw a straight line, then extend it to M.Measure 5 cm with a ruler and write AC on the result.We have the required triangle by joining BC.From point C, draw an arc that cuts over AC and BC. From the point where it cuts across AC and BC, draw an arc that cuts across each other. Finally, draw a line that extends from point C to the junction of the two arcs.The same holds true for A as well as O, the intersection of the two lines.Draw a circle with O as the center. This circle will serve as our incircle. Next, draw a perpendicular from O to AB. This perpendicular will serve as the radius.AN is the set of points in our locus that are equally spaced from the lines AB and AC.We must create an incircle, which is a circle inside of a triangle. We can accomplish this by creating an angle bisector from two sides; the intersection point will serve as the incentre. The center of the required circle.
The location where two points are equally distant from one another is known as the angle bisector.
Therefore,
You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.
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How to solve the equation: -2(x-2)+4=2x
Answer:
x = 2
Explanation:
Given the expression
-2(x-2)+4=2x
you are to find the value of x that will make the equation true
Open the bracket
-2x+4 + 4 = 2x
-2x + 8 = 2x
-2x - 2x = -8
-4x = -8
x = -8/-4
x = 2
Hence the solution to the equation is x = 2
Find the area of the shaded portion in the square. Show all work for full credit.
(Hint: Assume the central point of the arc is the corresponding corner.)
Non shadow part (white one) seems to be 1/4 of a circumference
So we need to find area of square minus area of 1/4 of the circumference
Square area = L^2 = 6^2 = 36
Circumference Area = (πr^2)/4 = (π*6^2)/4 = 28.27
Area of the shaded portion = 36 - 28.27 = 7.72
Write a division problem with a quotient greater than 20 less than 25? What do you guys think?
Answer:
hmmm, how about 242 divided by 11? the answer is 22 r0
Step-by-step explanation:
PLS HELP ME, I NEED HELP
Answer: A
Step-by-step explanation:
Substitute y for 0, and then find x, which is 3x<-10. divide by three, and you get x<-3.33 and A is the only one with the right x coordinate and going to the left.
Solve 2x^2-23=y when x=1
The value of y in the expression [tex]2x^{2} - 23=y[/tex] is -21.
Given System of Equations are:
[tex]2x^{2} - 23=y[/tex] .....(1)
[tex]x=1[/tex] ..........(2)
Now substituting x = 1 in in equation (1)
[tex]2x^{2} - 23 = y\\ y = 2x^{2} - 23\\ y = 2 x 1^{2} - 23\\ y = 2 x 1 - 23\\ y = 1 - 23\\ y = -21[/tex]
Hence, the value of y in the expression [tex]2x^{2} - 23=y[/tex] is -21.
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Which order pair represents point B in the graph (0, 2)(1, 0)(1, 2)(2, 1)
Notice that the point B is located two units away from the origin on the x-axis, and its one unit up fro the origin on the y-axis, thus, the point B is the ordered pair (2,1)
For the polynomial P(x) = 4x + 7x + 8 and c = 1, find P(c) by (a) direct substitution and (b) the remainder theorem
SOLUTIONS
For the polynomial P(x) = 4x^2 + 7x + 8 and c = 1
[tex]P(x)=4x^2+7x+8[/tex]where c = 1
(a) By direct substitution
[tex]\begin{gathered} P(c)=P(1) \\ P(x)=4x^2+7x+8 \\ P(1)=4(1)^2+7(1)+8=4+7+8=19 \\ P(1)=19 \end{gathered}[/tex](b) The Remainder Theorem states that when we divide a polynomial
P(x) by x - c the remainder R equals P(c)
[tex]4x^2+7x+8\div x-1[/tex]From the remainder theorem , the remainder = 19
the 90% confidence interval
Answer:
With a 90 percent confidence interval, you have a 10 percent chance of being wrong.--
Step-by-step explanation:
think it helps
have a nice night
The velocity of a drone relative to the air is modeled by v = 13i + 3j. The drone encounters wind with velocity modeled by w = −7i − 2j. Which is the true velocity vector of the drone?
From the statement of the problem, we know that:
• the velocity of the drone relative to the air is:
[tex]v=13i+3j,[/tex]• the drone encounters wind with velocity:
[tex]w=-7i-2j\text{.}[/tex]The true velocity vector of the drone is given by the sum of the velocities:
[tex]v+w=(13i+3j)+(-7i-2j)=(13-7)i+(3-2)j=6i+j.[/tex]Answer: 6i + j
What is the answer and can you answer all 3 please
For the first question, the problem is about the comparison between a graph and a function given in this case for the height of a baseball after t seconds of two players A and B.
For the second question, the problem gives a graph for player A and a function for player B
For the third question we could ask for example if the two players reach the same height at the same time how much time takes both players to reach a certain height, the maximum height of player A is bigger than player B or less than.
3. A taxi ride in a large city costs $3.50 plus $6 for each mile traveled. Write an equation to represent this
situation where d is the distance traveled.
If Brandon traveled 7.5 miles by taxi, how much was the cost, C, of his taxi ride?
Which equation represents this situation and the cost of Brandon's taxi ride?
The cost of Brandon's taxi ride is $ 4.8.
A taxi ride in a large city costs $3.50 plus $6 for each mile traveled .The 3 mile cab ride includes a basic charge as well as the cost for the distance covered.If Brandon traveled 7.5 miles by taxi, how much was the cost, C, of his taxi.
For a 6 mile trip, the cost is $4.80 which means that :
The cost of 3 miles is $4.80−$3.00=$1.80
Therefore the cost for 1 mile is $1.80÷3=$0.60
The basic fee for hiring the cab is $3.00−$1.80=$1.20
So the total cost, c for a trip of d miles will be shown below:
c=0.6d+1.2
Check:
If d=3
c=0.6(3)+1.2=3
If d=6
c=0.6(6)+1.2= 4.8
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A number line is drawn left to right with integers spaced 1 centimeter apart. An ant crawls onto the number line at +2. It then crawls 3.5 centimeters left, 4.8 centimeters right, and 7.9 centimeters left.
The ant is finally at a position -4.6 centimeters on the number line.
A number line is drawn left to right with integers spaced 1 centimeter apart.An ant crawls onto the number line at +2.This means the ant is at 2.0 on the number line.The ant then crawls 3.5 centimeters towards the left direction.This means the ant is at -1.5 on the number line now.The ant then crawls 4.8 centimeters towards the right direction.This means the ant is at 3.3 on the number line now.The ant then crawls 7.9 centimeters towards the left direction.This means the ant is at -4.6 on the number line now.To learn more about number line, visit :
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5,624 ÷ 72 using estimation
=====================================================
Explanation:
5624 is close to 5600
72 is close to 70
Therefore, 5624 ÷ 72 is close to 5600 ÷ 70 = 80
Think of it like saying 56 ÷ 7 = 8 but then we add the zeros onto each to get what is shown above.
--------
Use your calculator to find that
5624 ÷ 72 = 78.111 approximately
which isn't too far from the estimate value of 80. Our estimate is an over-estimate.
Answer: 80
Step-by-step explanation:
First change the equation to the nearest tenth,
5620 divided by 70
Now, break up the 70 into ( 10 * 7 )
So first do 5620 divided by 10
5620 divided by 10 = 562
Now if we round to the nearest tenth again we get 560
Now we can divide 560 by 7
Which comes out to 80
Last month, Carl earned $4900 after working 152 hours. What does Brian make hourly? [Round your answer to the nearest cent.
We have the following:
To know the amount earned per hour, we must divide the total value of money by the total number of hours worked, like this
[tex]\frac{4900}{152}=32.24[/tex]Which means that per hour Carl earns $ 32.24
What is the solution to the given inequality?½-½ x ²-1/O x₂ -1O xs-1O x ≥ 3O x≤ 3IntroSolve the inequality.1---X24Apply properties:AddMultiplySubtractDivideTo start over:ResetDone
Answer:
x ≤ 3
Explanation:
The given inequality is
[tex]\frac{1}{2}-\frac{1}{4}x\ge-\frac{1}{4}[/tex]To solve the inequality, we first need to subtract 1/2 from both sides
[tex]\begin{gathered} \frac{1}{2}-\frac{1}{4}x-\frac{1}{2}\ge-\frac{1}{4}-\frac{1}{2} \\ \\ -\frac{1}{4}x\ge-\frac{3}{4} \end{gathered}[/tex]Then, multiply both sides by -4. Since -4 is a negative number, the symbol of the inequality changes, so
[tex]\begin{gathered} (-4)(-\frac{1}{4}x)\leq(-4)(-\frac{3}{4}) \\ \\ x\leq3 \end{gathered}[/tex]Therefore, the answer is
x ≤ 3
Help plss
The deadline is tomorrow
The inverse and domain of the inverse of the function are attached below.
Inverse of a FunctionIn mathematics, an inverse is a function that serves to “undo” another function. That is, if y produces y, then putting y into the inverse of produces the output x. A function y that has an inverse is called invertible and the inverse is denoted by inverse of y.
The inverse of the given function is
[tex]y = (x+2)^2, y-^1(x) = \sqrt{x} - 2, -\sqrt{x} - 2[/tex]
The domain of the function is
[tex]domain= [0, \infty)[/tex]
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+ 308 - 126 =450 what number can make the equation true
answer: the number is 268
Samuel was preparing for the triathlon. He did 3 activities every morning: Ran for 30 minutes, covering 4.5 miles. Swam for 20 minutes, covering 2/3 mi. biked for 45 min, covering 9 miles. What was Samuel's average speed during his morning training?
so nobody seems to know this answer so 20 points
Samuel's average speed was 0.26 kilometers per minute during his morning training.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Given that Samuel was preparing for a triathlon. Every morning, he accomplished three things: I ran for 30 minutes and covered 4.5 miles. I swam for 20 minutes, covering around 2/3 miles. I biked for 45 minutes and 9 kilometers.
Here, we have the total distance traveled by Samuel = 4.5 + 2/3 + 9 = 14.17 kilometers
And the total time is taken by Samuel = 30 + 20 + 45 = 55 minutes
So, the average speed = distance / time
The average speed = 14.17/55
The average speed = 0.26 kilometers per minute
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How does mentat health effect aninals
Mental health affects animals as it brings about anxiety, unfriendliness and depression
Whet is mental health?Our emotional, psychological, and social well-being are all parts of our mental health. It influences our thoughts, emotions, and behaviors. It also influences our ability to manage stress, interact with others, and engage in obsessive behaviors than those found in the wild.
Having a pet as company helps reduce your anxiety. enhancing one's confidence Pets don't judge you, are unconditionally loving, and make excellent listeners. This can boost your self-confidence, particularly if you experience loneliness or miscommunication. According to science, many non-human creatures experience psychological disorders. Although it is frequent in humans, at least one mental disorder appears to have spared all other animals:
When they are abused or when they are denied what they want or need, animals frequently exhibit signs of mental illness. Perhaps this explains why captive animals appear to engage in more obsessive activities than their wild counterparts.
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How much would you need to deposit in an account now in order to have $2000 in the account in 15 years? Assume the account earns 3% simple interest. Round your answer to the nearest cent.
In three days Carter drove 2196 miles in 36 hours behind the wheel. The first day he averaged 64 mph, the second day 62 mph, and the third day 58 mph. If he drove 4 more hours on the third day than on the first day, then how many hours did he drive each day? I have x=z+4 and that's all, I need the other two equations please helpp.
Answer:
first day=10 hours, second day=12 hours, third day=14 hours
Step-by-step explanation:
64+62+58=
126+58=184
o=day 1. t=day 2. th=day 3
o+t+th=36
o+4=th
64o+62t+58th=2196
(o+t+th=36)*58
58o+58t+58th=2088
64o+62t+58th=2196
-(58o+58t+58th)=2088
6o+4t=108
o+t+th=36
o+t+o+4=36 ==> th=o+4
2o+t+4=36
2o+t=32
(2o+t=32)*3
6o+4t=108
-(6o+3t=96)
t=108-96
t=12
2o+12=32 ==> 2o+t=32
2o=20
o=10
o+4=th
10+4=14
th=14
o=10, t=12, th=14
Relative rates of growth, graphing calculator required. Not that difficult but some rules are needed. Ask me if you have any questions regarding the material. Thanks!
Given:-
[tex]f(x)=\sqrt[]{x},g(x)=\ln (x)[/tex]To find the required option, which is correct.
So we need to find the value when x tends to infinity. so to find the value we substitute infinity in place of x. so we get,
[tex]\begin{gathered} f(x)=\sqrt[]{x} \\ f(\infty)=\sqrt[]{\infty}=\infty \end{gathered}[/tex]Also we get,
[tex]g(x)=\ln (x)=\ln (\infty)=\infty[/tex]So the resulting value is infinity for both.
So the required option is The rate of growth cannot be determined.
3. In a 2-dimensional object the label is always square units and notated as units^2 i.e. square inches or in^2. What is the name and notation of a 3-dimensional object?
When we have a 3-dimensional, then the units have to by to the third power because the dimensions multiply, for example, if each dimension is in meters, then
[tex]m\times m\times m=m^3[/tex]Hence, the name of a 3-dimensional object is cubic units, and the notation is units^3.Write two angles coterminal to 5pi/7, one that’s positive and one that’s negative
As given by the question
There are given that the angle:
[tex]\frac{5\pi}{7}[/tex]Now,
To find a positive and negative coterminal angle, add and subtract 2pi to the given angle.
Then,
[tex]\begin{gathered} \frac{5\pi}{7}+2\pi=\frac{5\pi+14\pi}{7} \\ =\frac{19\pi}{7} \end{gathered}[/tex]And,
[tex]\begin{gathered} \frac{5\pi}{7}-2\pi=\frac{5\pi-14\pi}{7} \\ =\frac{-9\pi}{7} \end{gathered}[/tex]Hence, the positive and negative angles are shown below:
[tex]\frac{19\pi}{7}\text{ and -}\frac{9\pi}{7}[/tex]Michael has eight bags of mulch how many trees can he mulch if each tree requires 2/3 bags of mulch.a) 16/3, b) 3/4, c) 12, d)16
12 (option C)
Explanation:1 tree requires 2/3 bags of mulch
Let the number of trees for 8 bags of mulch = y
1 tree = 2/3 bags
y = 8 bags
Cross multiply:
8(1) = y(2/3)
[tex]\begin{gathered} 8\text{ = }\frac{2y}{3} \\ Mu\text{ltiply both sides by 3:} \\ 8(3)\text{ = 2y} \\ 24\text{ = 2y} \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by 2:} \\ \frac{24}{2\text{ }}=\frac{2y}{2} \\ y\text{ = 12 } \end{gathered}[/tex]Hence, 8 bags of mulch require 12 trees (option C)
find an equation of the line containing the two given points.Express your answer in the indicated form. points (1,2) and (3,10):standard form
Equation of the line
There are several forms to express the equation of a line.
The equation of the line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The standard form of a line is:
Ax + By = C
We are given two points (1,2) and (3,10). The point-point equation is adequate according to the data we are provided.
[tex]\begin{gathered} \displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \text{Substituting:} \\ \displaystyle y-2=\frac{10-2}{3-1}(x-1) \end{gathered}[/tex]Operating:
[tex]\begin{gathered} y-2=\frac{8}{2}(x-1)=4(x-1) \\ \\ \text{Operating:} \\ y-2=4x-4 \end{gathered}[/tex]Subtracting 4x and adding 2:
y - 4x = -4 + 2 = -2
Rearranging:
-4x + y = -2
This is the required equation in standard form
