It can be determined that a relation represented as an equation is a function if and only if for each value on x-axis, there is a corresponding value on Y-axis.
which also signifies that for each value of x , there is a value of y which exists and is real.
A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set.
Or in simple words if there is no corresponding value of y for any x, then that is not a function.
For example,
[tex]x^{2} +y^{2}[/tex]=1
when the value of x is 0 , then value of y is 1 or -1, Thus, it will not be a function.
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the distance a falling object travels towards the earth is directly proportional to the square of the time that it falls. if an orange falls 16 feet in 4 seconds, how far will it fall in 8 seconds ?
The orange will fall 64 feet in 8 seconds.
Distance:
Distance is defined as how much ground an object has covered despite its starting or ending point.
Given,
The distance a falling object travels towards the earth is directly proportional to the square of the time that it falls.
And an orange falls 16 feet in 4 seconds.
Here we need to find the how far it will fall in 8 seconds.
Based on the given details,
We know the that distance is,
D = kt²
where
k is the constant of proportionality.
To find the value of k we have to apply the given values on the equation.
=> 16 = k x (4)²
=> 16 = k x 16
=> k = 16/16
=> k = 1.
So, in 8 seconds it will fall at
=> D = 1 x (8)²
=> D = 1 x 64
=> D = 64 feet.
Therefore, the orange will fall at 64 feet in 8 seconds.
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Ben’s annual salary is £22000. He spends 15% of this on rent. How much is his rent per month
Answer:
£275
Step-by-step explanation:
To find how much Ben's rent is per month, we first have to find how much Ben spends on rent annually (every year). We can do this by multiplying his annual salary by the percentage spent on rent.
22000 · 0.15 = 3300
Now that we know Ben spends 3300 on rent a year, we can divide that amount by 12 (the number of months in a year) to find out how much his rent is per month.
3300 / 12 = 275
Solve -7+2(-4x-3)=11. Justify each step
Answer:
x=-3
Step-by-step explanation:
Let's solve your equation step-by-step.
−7+2(−4x−3)=11
Step 1: Simplify both sides of the equation.
−7+2(−4x−3)=11
−7+(2)(−4x)+(2)(−3)=11(Distribute)
−7+−8x+−6=11
(−8x)+(−7+−6)=11(Combine Like Terms)
−8x+−13=11
−8x−13=11
Step 2: Add 13 to both sides.
−8x−13+13=11+13
−8x=24
Step 3: Divide both sides by -8.
−8x
−8
=
24
−8
x=−3
Rewrite 20 − 4x^3 using a common factor.
4x(5 − x^2)
4(5 − 4x^3)
2x(10 − 2x^2)
2(10 − 2x^3)
Answer:
4x(5 − x^2)
Step-by-step explanation:
20 − 4x^3
= 4x(5 − x^2)
The equivalent expression after taking a common factor is,
⇒ 2 (10 - 2x³)
What is Mathematical expression?
The combination of numbers and variables by using sign addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression is;
⇒ 20 - 4x³
Now, Take common factor as;
⇒ 20 - 4x³ = 2 × 10 - 2 × 2x³
= 2 (10 - 2x³)
Thus, The equivalent expression after taking a common factor is,
⇒ 2 (10 - 2x³)
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Given the functions f and g, explain why you cannot find f * g.
f = { (-1,7), (1,3), (3,4), (6,8), (7,0) }
g = { (0,1), (2, -6), (4,7), (5,1), (8, -1) }
Answer:
g={(0,1), (2,-6),(4,7),(5,1), (8,1) } its korrect now
Write an compound inequality for the following graph.
The compound inequality for the graph is -5 ≤ x ≤ -1
How to write a compound inequality for the following graph?On the graph, we have the following endpoints
Endpoint 1 = -5 (closed circle)Endpoint 2 = -1 (closed circle)Also, the region between endpoints is shaded.
This means that the endpoint is a union inequality
So, we have the compound inequality to be
Endpoint 1 ≤ x ≤ Endpoint 2
This gives
-5 ≤ x ≤ -1
Hence, the compound inequality for the graph is -5 ≤ x ≤ -1
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Rearrange Vf^2=Vi^2+2aX for Vi
Making Vi the subject of formula gives the following expression: Vi = √(Vf² - 2aX).
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to make Vi the subject of formula?In this exercise, you're required to describe the steps that should be taken to rearrange and make Vi the subject of formula. Therefore, the appropriate and required steps are listed as follows:
Vf² = Vi² + 2aX
Subtracting 2aX from both sides of the equation, we have:
Vf² - 2aX = Vi² + 2aX - 2aX
Vi² = Vf² - 2aX
Taking the square root of both sides, we have:
Vi² = Vf² - 2aX
Vi = √(Vf² - 2aX)
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State the minimum monthly income and hourly wage per worker needed to cover monthly expenses for the family you used in part a. Then, explain how to calculate the hourly wage based on the monthly income and state the hourly wage. Assume that each full-time worker works four 40-hour work weeks per month, and each part-time worker works two 40-hour weeks per month.
(Please Answer with good details)
Answer:
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Step-by-step explanation:
1. Let's review the information given to answer the question correctly:
Monthly costs of a 2-adult and 3-children family in the Modesto metro area = US$ 7,846
Full-time worker = 4 weeks of 40-hour per month
Part-time worker = 2 weeks of 40-hour per month
2. Let's calculate the minimum monthly income and hourly wage per worker
Full-time worker hourly wage = Monthly costs/160
Part-time worker hourly wage = Monthly costs/80
Full-time worker hourly wage = 7,846/160
Part-time worker hourly wage = 7,846/80
Full-time worker hourly wage = US$ 49.04
Part-time worker hourly wage = US$ 98.08
Full-time worker minimum monthly income = Hourly wage * 160
Part-time worker minimum monthly income = Hourly wage * 80
Full-time worker minimum monthly income = US$ 7,846.40
Part-time worker minimum monthly income = US$ 7,846.40
Please help ASAP
What is the prime factorization of 90?
2 × 3 × 5
2 × 3 × 5
2 × 2 × 3 × 5
2 × 2 × 3 × 5
2 × 3 × 3 × 5
2 × 3 × 3 × 5
2 × 5 × 9
Answer:
the prime factorizime of 90 is this 2 × 3 × 3 × 5 or 2 × 3² ×5
rita, john, and kareem sent a total of 92 text messages during the weekend. kareem sent 4 times as many messages as rita. john sent 10 fewer messages than rita. how many messages did they each send?
Rita, John, and Kareem sent 17, 7, and 68 messages, respectively.
Use algebraic expressions to solve this problem.
Let x, y, and z be the number of messages sent by Rita, John, and Kareem, respectively.
If Rita, John, and Kareem sent a total of 92 text messages during the weekend, then:
x + y + z = 92
If Kareem sent 4 times as many messages as Rita, then:
z = 4 * x
z = 4x
If John sent 10 fewer messages than Rita, then:
y = x - 10
Evaluating z = 4x and y = x - 10 to the first equation:
x + y + z = 92
x + (x - 10) + 4x = 92
x + x - 10 + 4x = 92
6x = 92 + 10
6x = 102
x = 17
Recall that y = x - 10:
y = 17 - 10
y = 7
And z = 4x:
z = 4(17)
z = 68
If x, y, and z are the number of messages sent by Rita, John, and Kareem, respectively, then Rita, John, and Kareem sent 17, 7, and 68 messages, respectively.
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Over line TU has a midpoint at M(5,5) . Point T is at (1,8). Find the coordinates of point U.
Using the midpoint formula, the coordinates of point U are: (9, 2).
How to Apply the Midpoint Formula?The midpoint formula is: M[(x2 + x1)/2, (y2 + y1)/2]
Given the following:
Midpoint of TU is at: M(5,5)
Point T is at (1, 8), therefore, let:
M(5,5) = (x, y)
T(1, 8) = (x1, y1)
U(?, ?) = (x2, y2)
Plug in the values
M(5, 5) = [(x2 + 1)/2, (y2 + 8)/2]
5 = (x2 + 1)/2
10 = x2 + 1
10 - 1 = x2
9 = x2
x2 = 9
5 = (y2 + 8)/2
10 = y2 + 8
10 - 8 = y2
2 = y2
y2 = 2
The coordinates of point U are: (9, 2).
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solve the following 4x-1/2 = x + 7 and 3x + 2 = 2x+13/3
Answer:
a. 2.5
b. 2.333
c. 2.85
Step-by-step explanation:
A) 1. subtract -x on both sides 2. to get 3x-1/2=7
3. Add 1/2 on both sides 4. to get 3x=7.5
5. divide 3 on both sides 6. To get... x=2.5
B)1. Same process. 2. x+2=13/3
3. x=13/3-2 4. x= 2.33(repeating)
C) 1. same process. 2. 2x-x/3=3+7/4
3. 2x-x/3=4.75 4. Isolate -x/3
5.-x/3=4.75-2x 6. multiply both sides by 3
7. -x=14.25-6x 8. 5x=14.25
9. x= 2.85
* remember to distribute the 3 to each variable.
Answer:
1) 4x-1/2 = x + 7
Answer : x=5/2
2) 3x + 2 = 2x+13/3
Answer: x=7/3
Step-by-step explanation:
1) 4x-1/2 = x + 7
Solution
Let's solve your equation step-by-step.
4x−1/2=x+7
Step 1: Simplify both sides of the equation.
4x+−1/2=x+7
Step 2: Subtract x from both sides.
4x+−1/2−x=x+7−x
3x+−1/2=7
Step 3: Add 1/2 to both sides.
3x+−1/2+1/2=7+1/2
3x=15/2
Step 4: Divide both sides by 3.
3x/3=15/2/3
x=5/2
2) 3x + 2 = 2x+13/3
Solution
Let's solve your equation step-by-step.
3x+2=2x+13/3
Step 1: Subtract 2x from both sides.
3x+2−2x=2x+13/3−2x
x+2=13/3
Step 2: Subtract 2 from both sides.
x+2−2=13/3−2
x=7/3
The following figure shows the entire graph of a relationship. A coordinate plane. The x- and y-axes each scale by one. There is a vertical line graphed at x equals negative five. A coordinate plane. The x- and y-axes each scale by one. There is a vertical line graphed at x equals negative five. Does the graph represent a function? Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No
Answer:
(Choice A) A Yes
Step-by-step explanation:
What is the value of the expression that is described as “half the difference of 14 and 8”?
Answer:
I would say 6
Step-by-step explanation:
Difference is subtraction.
2 Shape 1 and Shape 2 are congruent pentagons.
Shape 1
Shape 2
Shape 2 is congruent to Shape 1 because -
A.
Shape 2 is a translation of Shape 1.
B. Shape 2 is a reflection of Shape 1.
C. Shape 2 is a rotation of Shape 1.
D. Shape 2 and Shape 1 are both pentagons.
Option B) is correct that is shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.
We know that two figures or objects are congruent if they have the same shape and size or they are the mirror image of each other.
Translation : It simply means moving. Every point should be moved in same distance and in same direction
Rotation : It means turning around a center.
Reflection : In this, the image is of the same size as the pre-image.
So according to the given figure we can see that the shape is not translated or rotated from a center but is reflected as shape 1 is the image of shape 2.
Hence shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.
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Please look at ALL of the screenshots and answer correctly! 20 points that's half of all of mine<: there will be another half with it!!!! the link to it is https://brainly.com/question/28634975?answeringSource=feedPublic%2FhomePage%2F21
Answer:
1. 13^5
2. prime
3. 8
4. 13
5. 6
Evaluate. 7+2^2⋅6+2^3−6
Over a period of 12 hours the temperature dropped 36 F. What was the average change in temperature in one hour?
a fort has enough food for 80 soliders for 60 days how long will the food lasts if 20 more solidets join after 15 days
Answer:36
Step-by-step explanation: 36 days
A fort is provided with food for 80 soldiers to last for 60 days. After 15 days, the food is sufficient for 80 soldiers for (60 – 15) days = 45 days. After 15 days, 20 additional soldiers join the fort. = 36 days.
Answer:
Step-by-step explanation:
A fort has food for 80 soldiers to last for 60 days.
Next 15 days the food is for 80 soldiers (60 – 15) days = 45 days.
Next 15 days, 20 MORE soldiers join the fort. = 36
ASNWER: 36 DAYS
Multiply (4x^2 +8)^2
Answer:
5/2 or 2.5
Step-by-step explanation
Five over two or two and 5 tenths
when w=3 , x=2 , y= -4 , z= -2
wx/2 +y
Answer:
=-1
Step-by-step explanation:
3x2/2 + -4
6/2 + -4
3 + (-4)
=-1
Answer:
-1
Step-by-step explanation:
Brackets
Indicies
Division
Multiplication
Addition
Subtraction
3 × 2/2 + -4
no brackets. no indicies.
Division
2/2 = 1
3 × 1 + -4
Multiplication
3 × 1 = 3
Addition
3 + -4 = -1
The product of two consecutive positive integers is 110. Find the value of the lesser
integer.
Which of the following shows the equation after the variables have been collected on the left and the constants have been collected on the right? −2x+13=−7x+28
−9x=15
5 x= 15
5x=41
−9x=41
Hanna's restaurant sells burrito bowls. The amount charged for a burrito bowl(b) is based on the cost for a plain taco plus an additional charge for each topping (t) as shown in the equation
B(t) = 0.25t +6
(A) If bill ordered a burrito bowl with 4 toppings how much would it cost.
(B) if Paul spent 7.50 how many toppings did he order
Answer:
The answer is 1
Step-by-step explanation:
The reason the answer is 1 its because 1 its a good number and everybody loves 1
guys help please. Enter the value for x that makes the equation 5x-2+3+-7 HELP
Step-by-step explanation:
5x-2+3-7
0=5x-9+3
0=5x-6
6=5x
x=6/5
Rectangle ABCD has coordinates of A(-5,5) B(-5,-3), C(6,-3), D(6,5). If the rectangle is dilated using a scale factor of 1.5 how long is side AD
The length of the side AD after undergoing a dilation using a scale factor of 1.5 as required in the task content is; 16.5.
What is the length of the side AD after a dilation using 1.5 scale factor?To evaluate the length of side AD prior to the transformation which involves a dilation.
The distance between two points is given by;
D = √((y2 - y1)² + (x2 x1)²)
It follows that the lengths of the pre-image can be determined as follows;
AD = √((-5-6)² + (5 -5)²)
AD = √(-11)² + 0²
AD = √121
AD = 11
Ultimately, upon undergoing a dilation using a scale factor of 1.5, the length of AD becomes; 11 × 1.5
Hence, AD = 16.5.
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Alisa drove from her house to the beach at a speed of 55 miles per hour. If it took her 1.8 hours to get to the beach, about how many miles away from the beach is Alisa's house?
Alisa's house is about 99 miles from the beach
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
With above formula, we can determine the distance of Alisa's house from the beach. Details below
How to determine the distanceThe following data were obtained from the question:
Speed = 55 miles per hourTime = 1.8 hoursDistance =?The distance of Alisa's house from the beach can be obtained as followed:
Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 55 × 1.8
Distance = 99 miles
Thus, Alisa's house is about 99 miles from the beach
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The distance between the beach and Alisa's house is 99 miles.
About how many miles away from the beach is Alisa's house?Here we need to use the general relation:
Distance = Speed*Time.
Here we know that Alisa's speed is 55 miles per hour, and she drives for 1.8 hours, then we can replace:
Speed = 55 mi/h
Time = 1.8 hours
Replacing that in the distance relation we will get:
D = (55 mi/h)*(1.8 h)= 99 mi
The distance between the beach and Alisa's house is 99 miles.
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The average rain in Annette, Alaska, in September is 0.31 inch per day. How much rain falls over the course of an average September? (September has 30 days)
Answer:
9.3
Step-by-step explanation:
If it rains 0.31 in per day and there is 30 days in September that means you need to MULTIPLY0.31
× 0.30
-----------------
0.30
9.30
-----------
9.6
help pls i don’t know this
question 3 consider a certain type of nucleus that has a decay rate constant of 0.0250 min-1. calculate the time required for the sample to decay to one-fourth of its initial value.
Answer:
since the decay rate constant of0.0 250 min.
hence the time required for the sample to decay to one forth of it's initial value is
Step-by-step explanation:
Answer:
Step-by-step explanation: