If you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
The perimeter will be double of if we double the length and breadth of rectangle
→ When doubling the dimensions of a rectangle, why the area is quadruple:
We know that :
Area of rectangle = l × b
where, l is length and b is breadth
A = L × W
This means area equals length times width.
if you double the length and you double the width, the formula becomes:
A = 2 × L × 2 × W
A = 2 × 2 × L × W
A = 4 × L × W
if you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
→When doubling the dimensions of a rectangle, why the perimeter is doubles?
Let length be equal to ′l′
And breadth be equal to ′b′
Perimeter of rectangle = 2 (l + b) ____(equation i )
The perimeter if the length and breadth of the rectangle will increase by two, or will it double? So new parameters of rectangle when its length and breadth will get double on initial one.
Double length of rectangle of initial one= 2 × l=2l
Double breadth of rectangle of initial one = 2×b=2b
So the perimeter of new rectangle whose length and breadth are double of initial one are:
As we know that:
Perimeter of rectangle = 2 (l + b)
So,
Perimeter of new rectangle= 2(2l+2b), (by taking 2 common)
Perimeter of new rectangle = 2×2(l + b) ____ equation (ii)
As from equation (i) perimeter of initial rectangle is = 2(l + b)
So from equation (i) and (ii)
Perimeter of new rectangle= 2 × 2(l + b)
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
Hence, the perimeter will be double of if we double the length and breadth of rectangle.
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elsa hikes up a mountain. she hikes back down at a constant rate the table shows elsas elevation at each hour after she begins her descent
The linear equation from the given table is expressed as:
y = -1500x + 8350
How to find the equation from the table?The general form for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the equation of a line through two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
We will take the two coordinates (1, 6850) and (2, 5350)
Thus:
(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)
(y - 6850)/(x - 1) = -1500
y - 6850 = -1500x + 1500
y = -1500x + 1500 + 6850
y = -1500x + 8350
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x - 2/2 = 3x + 8/4
A. 12
B. -24
C. 16
x-2/2=3x+8/4
x-1=3x+2
-x. -x
-1=2x+2
-2. -2
-3=2x
÷2. ÷2
-3/2=x
If Rita receives $63.90 Interest for a deposit earning 6% simple interest for 150 days, what is the amountof her deposit to the
nearest dollar (zero decimal place). Use a 360-day year. Enter only the number without $ sign
Answer: 2556
Step-by-step explanation:
Let the amount of the deposit be x dollars
The amount of simple interest earned can be represented by the formula PRT/100
Where,
P is the amount of deposit
R is the annual rate of interest
T is the time in years
Therefore,
P=x
R=6
T=150/360 = 15/36 = 5/12
So,
Simple interest = x(6)(5)/1200
63.90 = 30x/1200
63.90= x/40
x= 63.90×40
x=2556
Therefore, amount deposited = 2556
PLS HELP ASAP WILL GIVE BRAINLIEST
Answer:
C
Step-by-step explanation:
None of the others are vertical angles
a is supplementary angles
b is supplementary angles
d is alternate interior angles
Prove whether each argument is valid or invalid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. If the argument is valid, then use the rules of inference to prove that the form is valid. If the argument is invalid, give values for the predicates you defined for a small domain that demonstrate the argument is invalid.
The domain for each problem is the set of students in a class.
(c)Every student who missed class got a detention.
Penelope is a student in the class.
Penelope got a detention.
Penelope missed class.
(e)Every student who missed class or got a detention did not get an A.
Penelope is a student in the class.
Penelope got an A.
Penelope did not get a detention.
(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".
Hypotheses: M(Penelope), D(Penelope)
Conclusion: M(Penelope)
Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:
From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)
From D(Penelope), we have M(Penelope)
So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".
Hypotheses: A(Penelope), ~D(Penelope)
Conclusion: ~M(Penelope)
Using modus tollens, which states that if P implies Q and Q is false, then P must be false,
we can conclude that M(Penelope) is false:
From A(Penelope) and "Every student who missed class or got a detention did not get an A",
we have ~M(Penelope) & ~D(Penelope)
From ~D(Penelope), we have ~M(Penelope)
So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
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What is the difference between 49 8/9 and 17 1/3
Answer:
49 8/9 - 17 1/3 = -5/3 or -1 2/3
a downtown building stands 4 stories tall. it is 40 feet wide and 62 feet long. the city wants to put a sidewalk all the way around the building.the sidewalk needs to be 2 feet wide and there needs to be 1 foot of space between the edge of the sidewalk and the building.which is closest to to the square footage of the sidewalk
the closest option to the square footage of the sidewalk is 460.we can get answer just by simple mathematics .
what is mathematics ?
Mathematics is a branch of study that deals with the logic of quantity, shape, and arrangement. It is the study of numbers, quantities, and shapes, as well as their relationships and properties.
In the given question,
The building is 4 stories tall, so it is 4 x 10 = 40 feet tall.
The perimeter of the building is (40 + 62) x 2 = 204 feet.
If there needs to be a 1-foot space between the building and the sidewalk, the total width of the sidewalk will be 2 + 1 + 1 = 4 feet.
Therefore, the new perimeter of the building, including the sidewalk, will be (40 + 2 + 2 + 1 + 1) x 2 + (62 + 2 + 2 + 1 + 1) x 2 = 214 feet.
So the length of the sidewalk will be 214 - 204 = 10 feet.
The width of the sidewalk will be 40 + 2 + 2 + 1 + 1 = 46 feet.
Therefore, the square footage of the sidewalk will be 46 x 10 = 460 square feet.
So, the closest option to the square footage of the sidewalk is 460.
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find the surface area of the prism
Answer: 132 cm cubed
Step-by-step explanation:
0.5*3*4*2=12
10*5=50
4*10=40
3*10=30
30+40+50+12=132 cm cubed
A car dealership sells 48 cars of the same model in one month. The average price of each car is $25,000 with a maximum variance of $3,000 due to additional options. What is the range of the total revenue that the car dealership makes for the month's sales of this car model?
Answer: A. $1,056,000 <= x <= $1,344,00
"We can always be better"
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
When this net is folded into a cube, which
edge joins with edge X?
X
F
A
E
B
D
C
When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.
Explain about the cube?A cube is a solid shape with six square faces. Each side of a square has the same side length, so all faces are the same size.
A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.
Shape Properties of Cube
It is a three-dimensional square shape It has 6 faces, 12 sides and 8 vertices All faces are square All sides are of equal length Every vertex meets three faces and three sides Sides are square All sides are of equal length Each vertex meets three faces and three sides parallel to it All angles of a cube are right anglesThus, when edge D connects with edge X, this net is folded into a cube.
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The graph of a toy car's speed y
over time x is a parabola that
shows a minimum speed of 2 m/s
after 3 seconds. After 5 seconds,
the car's speed is 3 m/s. What is
the equation in vertex form of the
parabola?
The equation in vertex form of the parabola is y=-1/30(x+23/2)²+529/120
Y axis represends the toy car's speed
X axis represents time
y=ax²+bx+c
c=0
y=ax²+bx
2=9a+3b multiplied with -5
-10 = -45a -15b........equation 1
3=25a+5b multiplied with 3
9 = 75a + 15b............equation 2
adding equation 1 and 2
9-10=75a-45a+15b-15b
30a=-1
a=-1/(30)
2=9×(-1/30)+3b
3b=2+3/10=23/10
b=23/30
y=-1/30 x²+23/30=-1/30(x²+23x+(23/2)²)+1/30 ×(529/4)
y=-1/30(x+23/2)²+529/120
Therefore, the equation in vertex form of the parabola is y=-1/30(x+23/2)²+529/120
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15 POINTS
Using Pythagoras' theorem, calculate the length
of XY.
Give your answer in centimetres (cm) to 1 d.p.
Answer:
13.27 cm
Step-by-step explanation:
I am using (xy) to mean the length of the side xy
7^2 + (xy)^2 = 15^2
49 + (xy)^2 = 225
(xy)^2 = 225-49
(xy)^2 = 176
Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm
what is 35 percent of 90
Liam has 24 yellow pencils, 15 red pencils,
and 9 blue pencils. How many pencils does
he have altogether?
Answer:
48
Step-by-step explanation:
since you are trying to find the number of pencils altogether, you add 24, 15, and 9. 24+15+9= 48
I hope this helped! :)
Identify the line of reflection,
PLEASE HELP ITS DUE IN 3 minutes!!!
Answer:
X=2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
6x^2=-3x+1 to the nearest hundredth
The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
6x² = -3x + 1
To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:
6x² + 3x - 1 = 0
Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\)
Here; a = 6, b = 3, and c = -1.
Let's substitute these values into the quadratic formula:
\(x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23\)
Therefore, the values of x are -0.73 and 0.23.
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I need to keep 20.0 mg of a drug in my system at a minimum and a Maximum of 140. mg. The half life of the drug that I put in my system is 16 hours. I have put 100.0 mg in my system by ingesting a pill. When is the earliest I should take the next 100.0 mg pill? When is the latest?
Answer:
Therefore, the earliest time to take the next pill is after 10.85 hours and the latest time is before 15.14 hours have passed.
Step-by-step explanation:
The concentration of the drug in your system after ingesting 100.0 mg can be calculated using the formula:
C = D / V
where C is the concentration, D is the dose, and V is the volume of distribution (assumed to be constant).
At the initial time, t = 0, the concentration is:
C(0) = 100.0 mg / V
After one half-life, t = 16 hours, the concentration is:
C(16) = C(0) / 2 = 50.0 mg / V
After two half-lives, t = 32 hours, the concentration is:
C(32) = C(16) / 2 = 25.0 mg / V
After three half-lives, t = 48 hours, the concentration is:
C(48) = C(32) / 2 = 12.5 mg / V
To find the earliest and latest times to take the next 100.0 mg pill, we need to calculate the concentration at those times and make sure it stays between 20.0 mg and 140.0 mg.
Let's first find the earliest time at which the concentration drops below 20.0 mg.
20.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))
Solving for x:
2^(x/16) = 50.0 / 20.0 = 2.5
x/16 = log2(2.5)
x = 16*log2(2.5) = 16*0.678 = 10.85
So the earliest time to take the next pill is after 10.85 hours.
Now let's find the latest time at which the concentration goes above 140.0 mg.
140.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))
Solving for x:
2^(x/16) = 50.0 / 140.0 = 0.3571
x/16 = log2(0.3571)
x = 16*log2(0.3571) = -15.14
So the latest time to take the next pill is before 15.14 hours have passed.
With your team, create a piecewise-defined function with at least three “pieces.” The function does not need to be a step-function with horizontal line segments, but it needs to meet the definition of a function. Make a table and a graph for your function, and write an equation for each part. Be sure to state the domain for each part, as well as the domain for the whole function.
On solving the provided question we can say that The following is the data table of the function.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here,
the provided functions that can be formed are
x -infinity < x < -10
f(x) = 2x + 10 -10 < x < 10
4X - 10 10 < x < infinty
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.
A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.
Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
The following is the data table of the function.
x y
-20 -20
-15 -15
-10 -10
-5 0
0 10
5 20
10 30
15 50
20 70
The provided functions that can be formed are
\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)
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What is the value of the equation
Answer:
304
Start with parenthesis then do multiplication, then do addition and subtraction. Just remember PEMDAS
P arenthesis
E xponents
M ultiplication
D ivsion
A ddition
S ubtraction
Hope this helps :)
solve for x, using the secant lines. 53° 189°
The measure of the arc opposite to 189° is 136°.
What are secant lines?Secant lines are lines that intersect a curve at two distinct points. They are used to approximate the slope of the curve by measuring the change in the y-coordinate of the two points divided by the change in the x-coordinate of the two points.
The measure of the angle opposite to 189° is x.
To solve for x, we can use the property of alternate interior angles.
The sides of the two secant lines that intersect outside the circle form alternate interior angles whose measures are equal.
Therefore, the two angles formed by the secant lines inside the circle must have the same measure.
Therefore, 53° + x° = 189°.
Subtracting 53° from both sides, we get x° = 136°.
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what is the value of x
The value of the variable x for the similar triangles is equal to 25
How to evaluate the value of x for the similar trianglesThe triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle
and the length DQ of the smaller triangle is similar to the length DB of the larger triangle
so;
x/(15 + x) = 40/64
64x = 40(15 + x) {cross multiplication}
64x = 600 + 40x
64x - 40x = 600 {subtract 40x from both sides}
24x = 600
x = 600/24
x = 25
Therefore, the value of the variable x for the similar triangles is equal to 25
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Solve for y: 42/10 = 21/y
Answer:
Y = 5
Step-by-step explanation:
Correct answer: y = 5
By cross multiplication, you multiply 21 × 10, which is 210. Then, you divide 210 by 42, which is 5.
When the solar system first formed, 99 percent of the gas and dust material gathered together in one spot. What did gravity form by forcing most of the gas and dust into the center of a flattened disc?(1 point)
the sun
the moons of planets
the asteroid belt
the planets
Answer:the plants formed
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ
Answer:
D
Step-by-step explanation:
They are trying to see how long it takes people to complete the writing portion of the test.
What is the slope of the line whose equation is 12=4x−6y?
Enter your answer in the box.
Yesterday, Jennifer walked several laps around a track. She made Graph 1 to describe the relationship between time and distance. Today, Jennifer alternated walking one lap and running one lap. She made Graph 2 to describe the relationship between time and distance.
Select True or False for each statement.
Graph 1. First quadrant of a coordinate plane with the X axis labeled Time and the Y axis labeled Distance. A line begins at 0, 0 and goes up and to the right. Graph 2. First quadrant of a coordinate plane with the X axis labeled Time and the Y axis labeled Distance. A graph made up of several line segments that vary in steepness begins at 0, 0 and goes up and to the right.
A
Graph 1 shows a proportional
relationship because the graph
is a line.
True False B
Graph 2 shows a proportional
relationship because the graph
passes through the origin.
True False C
Graph 2 does not show a
proportional relationship
because the graph is not a line.
True False D
Graph 1 shows a proportional
relationship because the graph
is a line that passes through the origin.
True False E
Graph 2 shows a proportional
relationship because the graph
is made up of lines.
True False F
Graph 2 shows a proportional
relationship because the graph
is increasing.
True False
The answers to the statements that have been made here are:
False falsetruetruefalsefalseHow to check for the answers.The first statement is false because the proportional relationship is not due to the fact that it is a line.The second is also false given that the graph is not proportional as it goes through the origin of the graph.True The graph in 2 does not show the proportional relationship given that it does not go by the origin.This is true. It passes through the origin.The lines contained in the graph would have to be similar first before it can show this relationship hence false.The graph is not increasing and cannot show the relationship hence false.Read more on graphs here:
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URGENT!!! If correct will mark BRANILIST
Question 1 of 10
What is happening to this graph
when the x-values are between -1 and 1?
10+
5
-10
5
10
-5
-10 +
A. It is constant.
e
B. It is decreasing.
C. It is increasing.
Step-by-step explanation:
so, please look at the graph !
it shows you the answer very clearly.
your do know what it means when it is said x = -1 or x = 1 ?
if not, please know that every function with only one input variable (argument) is usually defined as
y = g(x)
and g(x) is then an expression or a group of expressions defining the calculation of the result value (y) for a given input value (x).
and this function can then be represented by a 2- dimensional graph like this showing all valid pairs of x and y.
to represent the values of x there is a horizontal x-axis (going from left to right potentially from -infinity to +infinity).
and to represent the result values of y there is a vertical y-axis (going from down to up potentially from -infinity to +infinity).
and we are looking at the area of the crossing point of both lines, the origin with the x, y coordinates (0, 0), as this is the area of the usually most interesting behavior of the function, and where it often shows us its behavior it will have for large x far out on the chart.
so, when we say x = -1, look at this horizontal x-axis one unit to the left of the crossing with the y-axis. and now at that point look up or down on the chart where a vertical line would cross the function.
in our case (at least based on the fuzzy image) it seems that crossing will be at y = a little big bigger than 2 (above the x-axus are the positive y values, below the negative y values).
and now for x = 1.
look at the horizontal x-axis one unit to the right of the crossing with the y-axis. and now at that point look up or down on the chart where a vertical line would cross the function.
in our case it seems that crossing will be at y = between 0 and -1.
so, when we go from left to right (x=-1 to x=1), are the functional results increasing, decreasing or constant ?
what does the line do in this segment ?
it goes from upper left to lower right. also indicated by the 2 functional values we have seen : for x=-1 we got a result for y of about +2, and for x=1 we got even a negative result (a little bit below 0).
so, the right answer is, it is decreasing in that interval.
The price technology stock dropped to $9.71 today. Yesterday's price was $9.82. Find the percentage decrease.
What the meaning of statement this?
The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.
Axiom of RegularityThe set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.
The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.
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