The population after 5 years if the starting population is 3000 is 75,000.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The population after 5 years.
= n x 25
Where n is the starting population in thousands.
The expression can be considered as.
= nx²
Where x is the number of years.
Now,
n = 3000
The population after 5 years.
= 3000 x 25
= 75,000
Thus,
The population is 75,000.
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if it takes five machines five minutes to make five widgets, how long would it take 100 machines to make 100 widgets?
Answer:
5 minutes
Step-by-step explanation:
Given:
It takes five machines five minutes to make five widgets
Let's first determine how much time it takes one machine to make one widget
5 machines -> 5 widgets -> 5 minutes1 machine will take 5 times as long to make 5 widgets
1 machine -> 5 widgets-> 5 * 5 minutesTherefore for 1 machine to make 1 widget it will take 1/5th of the time
1 machine -> 1 widget -> 5 minutes
To make 100 widgets, 1 machine will take 5 x 100 minutes or 500 minutes
If we use 100 machines this time will be reduced by 100
100 machines -> 100 widgets -> 5 minutesAre the lines C and D parallel? (The figure may not be drawn to scale). Giving brainliest for whoever answers correctly
1. Yes
2.no
3. Can’t be determined
Yes the given C and D lines are parallel
How to know two lines are parallel lines?
Any two parallel lines that are crossed by a transversal can be recognized by the following characteristics.
If the corresponding angles created by any two lines are equal, then the lines are said to be parallel.If the alternate internal angles created are equal, any two lines are considered to be parallel.If the alternate outside angles created are equal, any two lines are considered to be parallel.If the consecutive interior angles on the same side of the transversal are supplementary, any two lines are said to be parallel.The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines that are always the same distance away from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.as the sum of the given angle c and d i.e. 48+132 is 180 it clearly shows that it is the Pairs of interior angles on the same side of the transversal which proves that the given lines C and D are parallel
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Below are two parallel lines with a third line intersecting them.
x =
136
The width of a sandbox is represented by x+5 The length of the sandbox is double the width. Determine an expression that would represent the area of the sandbox. To earn full credit, show your work using a method explained in the Orientation.
Answer: (x+5)(2x+10)
Step-by-step explanation: I see your comment, so try to help you fast, I am in a rush, so can't type all the work on paper yet, sorry!
Which is g(x)? In this question
The equation of the transformed function is (c) g(x) = 4(1/3x)²
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
g(x) = horizontally shrunk of f(x) by a factor 1/3 and vertical stretch by a factor of 4
The above equations implies that, we have the transformation to be:
Horizontally shrunk of f(x)Vertical stretch by a factor of 4Mathematically, this can be represented as
g(x) = 4f(1/3x)
Substitute the known values in the above equation, so, we have the following representation
g(x) = 4(1/3x)²
Hence, the transformed function si g(x) = 4(1/3x)²
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Alex made a $4000 down payment on a car. The total cost of the car was $11000. He made 40 equal monthly payments to pay the car in full. How much did Alex pay per month? Define a variable, write an equation, and solve.
Answer: Alex Paid $175 for 40 months
Step-by-step explanation:
$4000 = y-int or b
$11000 = y
40 months = x
Slope - intercept form : Y=mx+b
We are solving for m which is the slope (How much Alex Paid per month)
11000=m(40)+4000
11000=40m+4000
7000=40m
7000/40
m=175
The point (2, 90) represents the value that after 2 weeks, Paul's math average is a 90. The
point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to a 50
because he doesn't do homework and doesn't know how to log into Quizlet. What equation
represents the line of Paul's grade downfall? (5 Points)
y = -0.10x + 130
y=20x-100
y = 20x- 130
y=0.10x+90
y=-20x+90
y=-20x+130
Answer:
The equation that represents the line of Paul's grade downfall is:
y = (-20)x + 130
This equation states that for every decrease of 1 in the value of x (representing the number of weeks), the value of y (representing Paul's math average) decreases by 20.
Step-by-step explanation:
To find the equation that represents the line of Paul's grade downfall, we can use the two given points to plot the line on a coordinate plane. The point (2, 90) represents the value that after 2 weeks, Paul's math average is 90, and the point (4, 50) represents the value that after 4 weeks, Paul's grade has dropped to 50. We can plot these two points on the coordinate plane as follows:
(2, 90)
(4, 50)
To find the equation of the line that passes through these two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points, we get:
m = (50 - 90) / (4 - 2)
= -40 / 2
= -20
To find the y-intercept of the line, we can substitute the coordinates of one of the points and the slope into the slope-intercept form of the equation:
y = mx + b
Substituting the coordinates of the point (2, 90) and the slope of -20, we get:
90 = (-20)(2) + b
= -40 + b
= b - 40
Solving for b, we get:
b = 90 + 40
= 130
Omar is constructing equilateral triangle ABC. Using a compass and a straightedge, he need to copy AB to
form the other two sides of the triangle. He sets the compass width to AB and draws two arcs from A as shown.
Points A and B with identical construction marks as parts of a circle with center point A.
After plotting point C, he will draw three line segments to connect points A, B, and C. What steps should he follow to plot point C?
Without changing the compass width, draw an arc from B to intersect the other arc, and plot point C.
Without changing the compass width, draw an arc from B, and plot point C on the new arc.
Increase the compass width, draw an arc from B to intersect the other arc, and plot point C.
Increase the compass width, draw an arc from B, and plot point C on the new arc.
An equilateral triangle is a triangle that has three equal-length sides, commonly referred to as a "regular" triangle.
What is the equilateral triangle?When all three sides of a triangle are equal, the triangle is said to be equilateral. The third side is likewise equal in this unique instance of an isosceles triangle. A triangle with the sides AB, BC, and CA is equilateral.An equilateral triangle is a triangle whose three sides are all the same length, also referred to as a "regular" triangle. An isosceles triangle with three equal sides is called an equilateral triangle. It is a special case of an isosceles triangle.An equilateral triangle in geometry is a triangle whose sides are all of the same length. Since the three sides are equal, the three angles that are opposite the equal sides are also equal.Find the attachment answer
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I NEED URGENT HELP.⚠️
Find the intercepts of the line
y+1=3(x-4)
Answer:
x=13/3
Step-by-step explanation:
Find the coordinate using the subtraction method
-2x+9y=-9
-3x+5y=12
The co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).
How to co-ordinate using subtraction method?
The technique of subtracting one vector's coordinates from another vector's coordinates is known as vector subtraction.Addition is represented by travelling up the -axis and to the right on the -axis. Subtraction is represented by going left and down the -axis. Since we are travelling below, we can deduct from our coordinate point, and since we are heading rightward, we can add to it.So, the given equations are
-2x+9y=-9 ⇒ (i)
-3x+5y=12 ⇒ (ii)
(i) * 5 ⇒ -10x + 45y = -45
(ii) * 9 ⇒ -27x + 45y = 108
⇒ 17x = 153
x = 9
Now, substitute x=9 in equation (i)
-2(9) + 9y = -9
-18 + 9y = -9
9y = -9 + 18
y = 9/9
y = 1
Hence, the co-ordinates will be(x,y) by the given equation the co-ordinates (9,1).
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A roll of paper that is 3 feet wide can be cut to any length.
a. If we cut a length of 2.5 feet, what is the perimeter of the paper?
b. Complete the table with the perimeter for each given side length.
Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation
The Perimeter of the paper 11 feet and the missing data in the table is: 8, 10, 18.6, 28, 2l + 6
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is given that the length of the paper is 2.5 feet, and the breadth of the paper is 3 feet.
Using the perimeter of the rectangle:
Perimeter of the paper = 2(l+w) = 2(5.5) = 11=2(l+w)=2(5.5)=11 feet.
The missing data in the table is: 8, 10, 18.6, 28, 2l + 6
Thus, the Perimeter of the paper 11 feet and the missing data in the table is: 8, 10, 18.6, 28, 2l + 6
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In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
The score of the netball team in 5th game is 26.
What is average?A number that is calculated by adding quantities together and then dividing the total by the number of quantities is called average.
Given that, a team scored average 31 points in first four game, and then 30 points average in first five game.
Score in 4 games = 4x31 = 124
Score in 5 games = 5x30 = 150
Score in 5th game = 150-124 = 26
Hence, The score of the netball team in the 5th game is 26.
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A candle is 18 in. tall after burning for 3 hours. After 5 hours, it is 16.5 in. tall. Write a linear equation to model
the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8
hours.
a. h(t) = -0.75t + 20.25; 14.25 inches
b. h(t) = 0.75t + 15.75; 9.75 inches
c. h(t) = -0.75t + 15.75; 9.75 inches
d. h(t) = 0.75t + 20.25; 14.25 inches
Answer: To write a linear equation to model the relationship between the height h of the candle and time t, we need to find the slope and y-intercept of the line that represents this relationship.
The slope of the line is given by the rise over the run, or the change in the y-value (the height of the candle) over the change in the x-value (the time). We can calculate the slope by taking the difference in the height of the candle after 5 hours and 3 hours, and dividing it by the difference in the time:
slope = (16.5 - 18) / (5 - 3) = (-1.5) / (2) = -0.75
The y-intercept of the line is the point at which the line crosses the y-axis. This is the height of the candle when the time is 0. We can use the height of the candle after 3 hours as the y-intercept, since this is the height when the time is 3:
y-intercept = 18
We can use these values to write a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Plugging in the values we found, we get:
h(t) = -0.75t + 18
This is the linear equation that models the relationship between the height h of the candle and time t.
To predict how tall the candle will be after burning for 8 hours, we can plug in t = 8 into the equation:
h(8) = -0.75(8) + 18 = -6 + 18 = 12 inches
This means that the candle will be 12 inches tall after burning for 8 hours.
Therefore, the correct answer is (d) h(t) = 0.75t + 20.25; 14.25 inches.
To write a linear equation to model the relationship between the height of the candle and time, we can use the information given. We know that after 3 hours, the candle is 18 inches tall, and after 5 hours, it is 16.5 inches tall.
We can set up a system of linear equations to represent this information. Let's call the height of the candle h and the time t. Then we can set up the following system:
h = 18 - 3t
h = 16.5 - 5t
To solve this system, we can set the two equations equal to each other and solve for t:
18 - 3t = 16.5 - 5t
1.5 = 2t
t = 0.75
This tells us that the height of the candle decreases by 0.75 inches per hour.
Now we can use this information to predict how tall the candle will be after 8 hours. We can plug in 8 for t in the equation h = 18 - 3t to find the height of the candle:
h = 18 - 3(8)
h = 18 - 24
h = -6 inches
So the candle will be about 6 inches shorter after burning for 8 hours. This means it will be about 10.5 inches tall.
The correct option is c, h(t) = -0.75t + 15.75; 9.75 inches.
This is because we found that the height of the candle decreases by 0.75 inches per hour, which is represented by the coefficient of t in the equation. The y-intercept, 15.75, represents the initial height of the candle, which we found to be 16.5 inches.
Happy to help!
Calculate (4p +3q)² when p 2 and q = -1
Answer: read below and learn how to do it so you won’t struggle the rest of highschool college and the real world!
Step-by-step explanation:
you just plug in 2 for p and -1 for q and solve.
(4x2+3x-1)^2
4x2 =8 3x-1 =-3
(8+-3)^2
(5)^2
5x5=25
••therefore your answer is 25
it’s basic algebra. it’s not calculus:)
Pls answer and show work
The values of x and y are obtained as 12.99 and 7.5 respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
For the given triangle, the trigonometric ratios are used as follows,
Cos(30°) = x/15
=> √3/2 = x/15
=> x = 15√3/2
=> x = 15 × 0.866
= 12.99
And,
Sin(30°) = y/15
=> 1/2 = y/15
=> y = 15/2
= 7.5
Hence, for the given triangle the values of x and y are given as 12.99 and 7.5 respectively.
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HELP ME ASAP!!!!!!!!
Answer:
The lie is #3
Step-by-step explanation:
The only way to solve this is by testing each equation to see if it's true. Remember that dividing powers with the same base, in this case b, means you're just subtracting the exponents.
Substituting 5 for y in #1 gives us the equation [tex]\frac{b^9}{b^5}=b^4[/tex]. This is the same as saying [tex]b^9^-^5=b^4[/tex], which is true.
Substituting 7 for z and 2 for x in #2 gives us [tex]\frac{b^7}{b^2}=b^5[/tex]. Like we did for the first one, this is the same as [tex]b^7^-^2=b^5[/tex], which is also true.
That means that #3 is a lie, but substituting 2 for x anyway gives us [tex]\frac{b^8}{b^2}=b^8[/tex], or [tex]b^8^-^2=b^8[/tex]. This is not a true statement, and x would have to equal 0 for this to be true.
find the equation of a line passing through points (-9,8) (-18,12)
Answer: -4/9
Step-by-step explanation:
12 - 8 / -18 - (-9)
4 / -18 + 9
4 / -9
- 4/9
Please say the transformations it would take to get ABCD TO A’B’C’D’
The sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].
What is Graph transformation?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
Given is a quadrilateral ABCD and its transformed form.
The following transformations are done to obtain the transformed image -
The quadrilateral ABCD is reflected across the y - axis.The following transformation → (x - 2, y - 0) is applied to the image.Then, the image is reduced by a scale factor of [k] which is less than one.Therefore, the sequence of transformations that can generate the transformed image are the reflection of the quadrilateral across the y - axis, followed by the graph transformation (x - 2, y - 0). At the end, image is reduced by a scale factor of [k].
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The figure shows two parallel lines cut by a transversal what is the value of x
The value of.x will be 20 and the angles will each have a value of 90 degrees.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
Hence, The value of.x will be 20 and the angles will each have a value of 90 degrees.
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What is the equation of this line? Graph of a line passing through the origin and the point begin ordered pair 4 comma negative 1 end ordered pair
Answer:
y = - [tex]\frac{1}{4}[/tex] x
Step-by-step explanation:
the equation of a line passing through the origin is
y = mx ( m is the slope )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line
m = [tex]\frac{-1-0}{4-0}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x ← equation of line
I need help with this question been stuck on it for a while
The correct options are B and C, or 3x-21 and -3x21, since the inequality sign must be "flipped," or reversed, whenever you multiply or divide both sides of the inequality.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.
x≤-7
3x≥-21
-3x≤21
The correct options are B and C that is 3x≥-21 and -3x≤21 because anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.
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P, R and S are three persons with ages 26 years, 27 years and 28 years respectively. In what ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement ?
- 100 : 110 : 121
- 80 : 100 : 99
- 100 : 121 : 132
- 89 : 95 : 100
Hey!! Can anyone please tell me the answer ??
100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Let P, R and S are three persons with ages 26 years, 27 years and 28 years
We need to find the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement
x(11/10)ⁿ=y(11/10)ⁿ⁻¹=3(11/10)ⁿ⁻²
x.121/100=y.11/10=3
x/100=y/110=3/121
Hence, 100 : 110 : 121 is the ratio must they invest money at 10% per annum compounded yearly so that each gets same sum at the age of their retirement
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i need help pls and explain how it would help alot thjanks
Answer:
neither are functions
Step-by-step explanation:
For a relation to be a function each value of the input x must map to exactly one unique value in the output y
(1)
This relation is not a function since
7 → 2 and 5 → 2
Two different values of x have the same output , thus not a function
(2)
This relation is not a function since
3 → 10 and 3 → 8
Two different values of x have the same output, thus not a function
Answer:
Step-by-step explanation:
neither are functions
Adam and Eric went hiking at different times. Adam is currently 73 feet above sea level while Eric is just starting at 24 feet below sea level. What is the difference in their elevations?
Answer: The answer is 97
Step-by-step explanation:
Since Adam is above sea level, the number 73 is positive. The number 24 would be negative since it's below sea level.
73 - ( -24) = 97
To check to make sure it's right we can do this:
-24 + 97 = 73
73 - 97 = -24
A rectangular park is 110 yards long and 70 yards wide. Give the length and width of another rectangular park that has the same perimeter but a smaller area.
We shall therefore obtain a square as a result. Since each square is a rectangle, the same perimeter and smaller area will be produced by using length and breadth of 90 yards.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
Here,
original length=110 yards
original width=70 yards
perimeter=2(110+70)
=2*180
=360 yards
x+y=180
y=180-x
area=xy
A=x(180-x)
A=180x-x²
A'=180-2x
A'=0
2x=180
x=90 yards
y=90 yards
We shall so receive a square as a result. Given that each square is a rectangle, a length and width of 90 yards will result in a smaller area and the same perimeter.
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In triangle TSP, TS=SP=10 cm, TP= 12 cm. Find three heights of triangle TSP
pls answer quickly I will give brainliest to fastest answer
Answer:
Plot each graph on the same coordinate system.
TSP
TP=12cm
T
Step-by-step explanation:
23 ✓24 In a recent year, 23.1% of all registered doctors were female. If there were 55,700 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
The Total number of registered doctors will be 246753.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Let the total number of doctors be x.
Since 23.1% of all registered doctors were female. If there were 55,700 female registered doctors that year. This will be:
23.1% × x = 55700
0.231x = 55700
Divide
x = 57000 / 0.231
x =246753
The doctors are =246753.
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Which line is parallel to the line given below? y=-4/3x+1
The line which is parallel to the given line y=-4/3x+1 is y = -4/3x + 2
What is the equation of the line?
The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that the equation of the line is:
y = -4/3x + 1 ..........(1)
To find the equation of the line is parallel to the given line equation.
We know that the given equation is in the slope-intercept form
y = mx+c, where m is the slope and c, is the intercept.
Compare with given equation(1) we get
m = -4/3 and c=1
Now change the y-intercept c=1 to an intercept of c= 2
Therefore (1) becomes
y = -4/3x + 2
Hence, The equation of line y = -4/3x + 2 is the parallel line to the given equation of the line.
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Quick!
The chart shows the results of 24 spins that Suzanne made with a spinner.
Based on these results, what is the probability that Suzanne's spinner will land on France the next time?
Answer:
I was going to answer but there is no attachment.
Step-by-step explanation:
Question 1-7
Similar triangles MRC and WYC are shown where MR = 14, CR=28, WY = 6, and MW = 17.88.
What is the length of YC?
In the triangle WYC, the length of the side YC is 4.76 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know a line segment parallel to a side of a triangle divides the other two sides in the same ratio.
Given, In a ΔMRC and ΔWYC MR = 14, CR=28, WY = 6, and MW = 17.88.
Now, MR = 14 and MW = 17.88.
Therefore, (MW/MR) = 17.88/14 = 1.28.
So, If WY = 6, then WE = (1.28)(6) = 7.66.
Now, In the ΔWYC, WY = 6 and WE = 7.66.
Therefore from the Pythagoras's theorem,
WE² - WY² = YC².
YC² = (7.66)² - 6².
YC² = 22.68.
YC = 4.76.
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