The three numbers given in the question : 21 , 72 and 62 do not have any common factor.
What do you mean by common factor ?The common factors are those that are found in both lists
Example: Factors of 12 and 30
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
Thus common factor = 1, 2, 3, 6
-------------------------------------------------------------------------------------------------------------
Given numbers : 21,72 and 62
Factors of 21 = 3 and 7
Factors of 72 = 2 and 3
Factors of 62 are 2 and 31
Thus these three numbers do not have any common factor.
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is the median of a data set is the same whether you order the set from greatest to least or least to greatest?
The value of median will be same.
Given:
The objective is to determine whether the median of a data set is same or not while ordering from greatest to least or least to greatest.
There are two possible data sets, which is even number of sets or odd number of sets.
If the number of sets (n) is even, consider two terms,
[tex]\frac{n}{2}\text{ and }\frac{n+1}{2}[/tex]Then, the average of these two numbers will gives the median of the even sets.
If the number of sets (n) is odd, the median can be calculated as,
[tex]\frac{n}{2}[/tex]Hence, the value of median will be same, even if the order of the sets are arranged greatest to least or least to greatest.
5x^2+9x+4=0 can someone help me please
Answer:
x = -4/5 or x = -1
hope this helps
10. Written as the product of two binomials, the expression (x+3)(4x-1)-(x+3)(x-9) is(1) (2x+6) (3x – 10)(3) (x+3)(3x+8)(2) (x+3)(x-10)(4) (2x+6)(3x+8)
As a product of two binomials, the expression provided in the question would now be written as follows;
[tex]undefined[/tex]Please help me asap I need assistant
Answer:
In order from left to right: Apple, Mango, Grapes, Kiwi, Banana
Step-by-step explanation:
The one furthest left is the only one that goes above 50, so it has to be apple at 55. The one next to it falls between 20 and 30, so it is going to be Mango at 25. The one next to it lies between 30 and 40, so it will be Grapes at 35. The next one falls exactly at 10, so it is Kiwi. And finally, the only one left is Banana, which is good because the bar sits at 50.
Hope this helps
Answer:
Red: Apple, Green: Mango, Blue: Grapes, Pink: Kiwi, Purple: Banana
Step-by-step explanation:
The y-axis (Number of votes) shows how many families voted for a specific fruit, using the bar graph you can connect the dots and figure out which graph is which :) Ex: Red is apple because the bar stops right between 60 and 50 showing to be halfway between the two which is 55, and apple received 55 votes.
Change the equation to standard form the state from x and y intercepts
We will have the following:
[tex]y=\frac{3}{2}x-\frac{1}{2}\Rightarrow(2)y=(\frac{3}{2}x-\frac{1}{2})(2)[/tex][tex]\Rightarrow2y=3x-1\Rightarrow3x-2y=1[/tex]So, the equation in standard form is:
[tex]3x-2y=1[/tex]And now, we determine the x & y intercepts:
x-intercept:
[tex]3x-2(0)=1\Rightarrow3x=1[/tex][tex]\Rightarrow x=\frac{1}{3}[/tex]So, the x-intercept is located at:
[tex](\frac{1}{3},0)[/tex]y-intercept:
[tex]3(0)+2y=1\Rightarrow2y=1[/tex][tex]\Rightarrow y=\frac{1}{2}[/tex]So, the y-intercept is located at:
[tex](0,\frac{1}{2})[/tex]E
B
F
D
NOTE: Angles not necessarily drawn to scale.
Answer:
75
Step-by-step explanation:
<CGE=<FGD
15=<FGD
x+<FGD=90
x+15=90
x=75
Nicole runs 7 miles in 60 minutes. At the same rate, how many miles would she run in 24 minutes?
In 24 minutes, Nicole runs the distance of 2.8 miles.
What is miles?
In mathematics, The term 'miles' is a unit of distance. It is used for the calculation of displacement measurement. It is defined as the starting point and endpoints on the graph.
According to the question, Nicole runs 7 miles in 60 minutes. Therefore, the parameters are:
Distance = 7 miles; Time = 60 minutes
Therefore, Speed = Distance/Time = 7/60 miles/minutes
Now, the time is 24 minutes and speed is 7/60 miles/minutes.
The required distance can be calculated as:
Distance = (Speed)(Time) = (7x24/60) = 28/10 = 2.8 miles
Hence, In 24 minutes, Nicole runs 2.8 miles.
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Suppose that the functions p and q are defined as follows.
p(x) = 4x-3
g(x) = -5x+5
Find the following.
(g•p) (4) =
(p•g) (4) =
Following are solutions of the functions:
(p, q)(4) = -103
(g, p)(4) = 70
What are functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
Given Data
p(x) = 4x-3
g(x) = -5x+5
g(x) = -5x +5
g(p(x)) = -5(p(x)) +5
g(p(x)) = -5(p(x)) + 5
Solving,
(g, p)(x) = -5(4x-3) +5
(g, p) (x) = -20x - 15 +5
(g, p)(x) = -20x -10
(g, p)(x) = 20(4) -10
(g, p) (x) = 80 - 10
(g, p)(4) = 70
Function,
p(x) = 4x -3
p(g(x)) = 4(g(x)) -3
(P, q)(x) = 4(-5x +5) -3
(p, q)(x) = -20x - 20 -3
(P, q)(x) = -20x -23
(p, q)(4) = -20(4) - 23
(p, q)(4) = =80-23
(p, q)(4) = -103
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Translate this sentence into an equation: 60 is the product of Mabel’s height and 4 Use the variable m to represent Mabel’s height
The statement of the question tell us that Mabel's weight times 4 equals 60, we can express this with the equation:
[tex]m\times4=60[/tex]X^2+y-9=0 test for symmetry
We have three tests of symmetry. In respect to the y-axis or in respect to the x-axis, or in respect to the origin.
For symmetry with respect to the Y-Axis, check to see if the equation is the same when we replace x with −x:
[tex]x^2+y-9=(-x)^2+y-9=0[/tex]Since the equation remains the same when we change the sign of the x variable, the equation is symmetric in respect to the y-axis.
For symmetry with respect to the X-Axis, check to see if the equation is the same when we replace y with −y:
[tex]x^2+y-9\ne x^2+(-y)-9=x^2-y-9[/tex]Since the equation does not remains the same when we change the sign of the y variable, the equation is not symmetric in respect to the x-axis.
The equation is symmetric with respect to the origin if for every point (x,y) that satisfies the equation, the point (-x, -y) also satisfies the equation.
[tex](-x)^2+(-y)-9=x^2-y-9\ne x^2+y-9[/tex]Since it doesn't satisfies this condition, the equation is not symmetric with respect to the origin.
Identify the vertical and horizontal asymptotes of the following rational function…..The rest of option D was cut off, but it says:Vertical asymptotes: x = -3 , x = 6.Horizontal asymptote at y = 0
The function is given to be:
[tex]h\mleft(x\mright)=\frac{\left(x-2\right)\left(x+3\right)\left(x-6\right)}{\left(x-4\right)\left(x+3\right)^{2}\left(x+2\right)}[/tex]Vertical Asymptotes:
The vertical asymptote of a function is the x value gotten when the denominator is equated to 0.
The denominator of the function given can be equated to 0 as shown below:
[tex](x-4)(x+3)^2(x+2)=0[/tex]Therefore, we can get the values for x using the Zero Factor Principle given to be:
[tex]\begin{gathered} If \\ ab=0, \\ \text{then} \\ a=0,b=0 \end{gathered}[/tex]Therefore, we have
[tex]\begin{gathered} x-4=0,\therefore x=4 \\ x+3=0,\therefore x=-3 \\ x+2=0,\therefore x=-2 \end{gathered}[/tex]Hence, the horizontal asymptotes are at:
[tex]x=4,x=-3,x=-2[/tex]Horizontal Asymptotes:
The horizontal asymptotes can be gotten by checking the degree of the functions that make up the numerator and denominator of the whole function. If the degree of the numerator is less than that of the denominator, then the asymptote is at y = 0.
Degree of Numerator: 3
Degree of Denominator: 4
Therefore, the horizontal asymptote is at:
[tex]y=0[/tex]ANSWER:
The correct option is OPTION B.
Solve for the value of 'x' given:5.25 = -log(x)This question will require an answer in scientific notation. For example, 0.0435 would be input as 4.35e-2Answer:
Solution
Solve for the value of 'x' given:
5.25 = -log(x)
[tex]5.25=-logx[/tex][tex]\begin{gathered} x=\frac{1}{10^{5.25}} \\ x=5.62341...e-6 \end{gathered}[/tex]dilate the figure about the given point a scale factor of 2.
1) The first thing to dilate a figure, is to know the scale factor and if it's about the origin or not.
We have k=2, as our scale factor. So the image will be twice larger (scaled) than the pre-image.
2) Since it is not about the origin but about the point, We need to count from the center of dilation (that point).
2.1) Let's locate each point of the vertex, and call them by ABCD for that pre-image, and call E the point which is going to be the center of dilation.
Counting the distances from figure ABCD to point E
Pre-image
A (7,6) ------------------ > A' ( 5 units to the left , 5 down)
B (9,6) ---------------> B' (7 to the left, 5 down)
C (6,3) -----------------> C' (4 to the left, and 2 down)
D (10,3) --------------> D' ( 8 to the left, and 2 down)
The new figure will be at
A ' ( 10 units to the left, 10 units down
B' (14 to the left, 4 down)
C' ( 8 to the left, and 4 down)
D' ( 16 to the left, and 4 down)
L
A' =(-3,-4) B' (-5,2) C' (-2, -1) D' (-6,-1)
Combine Like Terms (Basic, Decimals)May 20, 11:17:05 AM?A triangle has side lengths of (4.7u – 2.6) centimeters, (9.4u +9.1) centimeters,and (6.2v - 8.7) centimeters. Which expression represents the perimeter, incentimeters, of the triangle?20.6u - 2.50O 6.5 -2.50 + 14.1uSubmit AnswerO -2.50 + 18,5 + 2.1u0 -2.2 + 14.1u + 6.2v
Given side lengths:
(4.7u - 2.6)cm , (9.4u + 9.1)cm , (6.2v - 8.7)cm
The perimeter of a rectangle is the sum of the three sides:
[tex]\begin{gathered} (4.7u\text{ - 2.6) + (9.4u + 9.1) + (6.2v - 8.7) } \\ =\text{ 4.7u + 9.4u + 6.2v - 2.6 + 9.1 - 8.7} \\ =\text{ }14.1u\text{ + 6.2v -2.2} \\ =\text{ -2.2 + 14.1u + 6.2v} \end{gathered}[/tex]The correct answer is : -2.2 + 14.1u + 6.2v
The dosage of a cold medication is 2 mg for every 80 lb of body weight. How many milligrams of this medication are required for a person who weighs 140 lb? mg
Let x represent the amount of milligrams required for a person who weighs 140 lb.
We were told that the dosage of a cold medication is 2 mg for every 80 lb of body weight. The equations would be set up as shown below
2 = 80
x = 140
By crossmultiplying, we have
x * 80 = 2 * 140
80x = 280
We would divide both sides of th equation by 80. We have
80x/80 = 280/80
x = 3.5
Therefore, 3.5 milligrams of this medication are required for a person who weighs 140 lb
Write the equation of the line that is parallel to line m and passes through the point (4, - 5).
The slope of the line parallel to the given line will be same as that of the given line.
Let 'm' be the slope of the line,
[tex]y-b=m(x-a)[/tex]Substitute a=4 and b=-5 in the above expression.
[tex]\begin{gathered} y-(-5)=m\times(x-4) \\ y+5=mx-4m \\ y=mx-4m-5 \end{gathered}[/tex]Thus, the expression of the parallel line is y=mx-4m-5.
The mean length of 4 childrens' index finger is 8.7cm.
The mean length of 11 adults' index finger is 13.4cm.
What is the mean length (rounded to 2 DP) of these 15 people's index finger?
The mean length (rounded to 2 DP) of these 15 people's index finger is 12.15 cm.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that:
The mean length of 4 children's index fingers is 8.7cm.
The mean length of 11 adults' index fingers is 13.4cm.
The mean of 15 people = [8.7x4 + 13.4x11]/15
The mean of 15 people = [34.8 + 147.4]/15
= 182.2/15
= 12.1466 cm
= 12.15 cm
Thus, the mean length (rounded to 2 DP) of these 15 people's index fingers is 12.15 cm.
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The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 240 480 720
Create a description in words for the table.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 240-hour workout, there is 1 calorie burned, and for every 480-hour workout, there are 2 calories burned.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 240 calories burned, and for a two-hour workout, there are 480 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 240-hour workout, there is 1 calorie burned, and for every 480-hour workout, there are 2 calories burned.
Workout hours are 1 2 3
Calories Burned are 240 480 720
Option B is correct.
Given that,
The table is a proportional relationship.
Workout hours are 1 2 3
Calories Burned are 240 480 720
We can conclude from the form of the question that the quantity of calories we burn is determined by the length of time we spend practicing, making the activity (hours) the independent variable and the calories burned the dependent one. The responses C and D are automatically canceled out by this.
The table's information is all we can then depend on. The assigned hours were 1, 2, and 3, and the corresponding calories were 240, 480, and 720. Just make sure that's reflected in the response.
Therefore, Option B is correct.
The number of hours spent exercising determines the quantity of calories expended. 240 calories are expended during a one-hour workout, and 480 calories are burned after a two-hour workout.
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using this module predict when it will take to reach approximately 300 female turtles ? how many female turtles will there be in 7 years?
Answer
a) It will take 3.54 years for the turtle population to hit 300 female turtles.
b) There will be 78,125 female turtles in 7 years.
Explanation
The model has been give to us as
T(t) = 5ᵗ
where
T(t) = Female turtle population at any time t
t = time in years
First part of the question asks us to find when the turtle population will hit 300 female turtles. That is, find t when T(t) = 300
T(t) = 5ᵗ
300 = 5ᵗ
We can rewrite this as
5ᵗ = 300
We will take the natural logarithms of both sides
In 5ᵗ = In 300
t (In 5) = In 300
t (1.6094) = 5.7038
Divide both sides by 1.6094
t = (5.7038/1.6094)
t = 3.54 years = 3 years, 6.5 months
For the second part of the question, we want to calculate the number of female turtles when t = 7 years
T(t) = 5ᵗ
T(7) = 5⁷ = 78,125 female turtles
Hope this Helps!!!
Can someone please help me:
what does X equal in this linear equation?
Directions:
Graph the following linear equation
(I will give 100 points)
please hurry
X equal to 5 in this linear equation
What is linear equation ?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
0 = x - 5
x = 5
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A group of six friends ordered a pizza I wanted to arrive. There were 12 pieces of equal size 4 hours later 3/8 of pizza still remained and was going to be split evenly amongst six friends so they could finish the pizza.
Using the mathematical operations, the quantity that each of the six friends got from the 3/8 of pizza remaining after 4 hours is 0.75.
What are the mathematical operations?The mathematical operations that are used to perform basic number operations are division, multiplication, subtraction, and addition.
These basic mathematical operations can be used to compute the quantity of pizza that each friend got from the remainder.
For instance, after determining that 4.5 of the pizza is remaining, this value can be shared by 6 to get 3/4 or 0.75 for each friend.
The number of friends in the group = 6
The number of equal pieces of pizza = 12
The quantity of pizza remaining after 4 hours = 3/8 or 4.5 (12 x 3/8)
The quantity received by each friend after the equal splitting of the remainder = 0.75 (4.5/6) or 3/4 (3/8 ÷ 6).
Thus, basic mathematical operations show that each friend will get 3/4 more pizza.
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Question Completion:How much did each of the six friends get from the 3/8 remaining pizza?
The side lengths of a square are each 5p. By adding 1 to the length and subtracting 1 from the width, a rectangle is made. What is the area of the rectangle?the options are in the photo—>
we have that
1) a square
side length=5p
L=5p
W=5p
2)
adding 1 to the length ------> L=5p+1
subtracting 1 from the width ------> W=5p-1
Find out the area
A=L*W
substitute
A=(5p+1)*(5p-1)
A=25p^2-1 ----> by difference of squares
therefore
the answer is option fourthBased on the information in the diagram, which trigonometric ratio would help determine the measure of side X? What is the measure of side x to the nearest tenth 0.0 of a centimeter?
A)
[tex]undefined[/tex]write a quadratic equation in the form x^2 + bx + c =0 that has the following rootsroots {10,5}
If the roots are 10 and 5, then the equation can be expressed as:
(x - 10)(x - 5)
Distributing,
x*x - x*5 - 10*x + 10*5 =
= x² - 15x + 50
amy, becky, caroline, and dan are each trying to save $200 for a new phone. the chart shows how much each of them currently have and how much they are saving each week. show all work and explain your steps
A. How much money will Amy have in 3 weeks? Write the expression you use to solve.
B. Write an expression telling how much Amy will have in x number of weeks.
C. Who will be the first person to save $200 and how long will it take?
A) In 3 weeks, Amy will have $121.
B) An equation that shows the amount of savings Amy will have in x number of weeks is 100 + 7x.
C) Becky is the first person to save $200 in 11.5 weeks.
What is an equation?An equation is a mathematical statement that two or more mathematical expressions share equality in their values.
Equations depict the fact that two or more expressions have the same or equivalent values using the equation symbol (=).
The total amount of savings required for a new phone = $200
Amy's savings in x weeks = 100 + 7x
Becky's savings in x weeks = 85 + 10x
Caroline's savings in x weeks = 94 + 8x
Dan's savings in x weeks = 110 + 7x
Amy's savings in 3 weeks = $121 ($100 + 7(3)
Amy:If 100 + 7x = 200
7x = 100
x = 14.3
= 14.3 weeks
Becky:If 85 + 10x = 200
10x = 115
x = 11.5
= 11.5 weeks
Caroline:If 94 + 8x = 200
8x = 106
x = 13.25
= 13.25 weeks
Dan:If 110 + 7x = 200
7x = 90
x = 12.86
= 12.86 weeks
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12.3456Val measures the diameter of a ball as 14 inches. How many cubic inches of air does this ball hold, to thenearest tenth? Use 3.14 for it.The ball holds aboutcubic inches of air.
Volume of a sphere = (4/3) * Pi * r^3
Diameter = 14 inches ==> radius = diameter/2 = 14/2 = 7 ==> r = 7
[tex]V\text{ = }\frac{4}{3}\cdot\pi\cdot r^3=\frac{4}{3}\cdot3.14\cdot7^3=\frac{4}{3}\cdot3.14\cdot343=\frac{4}{3}\cdot1077.02=\frac{4308.08}{2}=2154.04[/tex]Answer:
About 2154 cubic inches
Find the distance between -4 and 2.
is it 6 or -2
Answer:
6
Step-by-step explanation:
-4 -3 -2 -1 0 1 2
In April, Mrs Ezeaku bought a bag of corn
for N2400. When she wanted to buy more in
June, she found that she could only buy 3/5
a bag for N2400. What was the percentage
increase in price from April to June
The percentage increase in price from April to June to Mrs Ezeaku, based on the cost of the bag is 66.7%
How to find the percentage increase?First, find the price of a bag in June. If 3/5 of a bag costs N2,400, then a full bag would be:
= Cost of proportion / Proportion of bag
= 2, 400 / (3 / 5)
= N4, 000
The percentage increase from April to June is:
= ( Price in June - Price in April) / Price in April x 100%
= ( 4, 000 - 2, 400) / 2, 400 x 100%
= 1, 600 / 2, 400 x 100%
= 66.7%
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Patrick bought his recliner on sale for 3x + 1 dollars. To replace his recliner now, it would cost Patrick 5x - 3 dollars. Write an expression that represents the difference in the price of the replacement recliner and the original recliner?
The expression for the difference the price of the original recliner and the replacement recliner will be;
⇒ (2x - 4)
What is mathematical expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Original price of the recliner = (3x + 1) dollars.
Replacement price of the recliner = (5x - 3) dollars.
Now,
The difference of the price of the original recliner and the replacement recliner will be calculated as;
⇒ Replacement recliner - Original recliner
⇒ (5x - 3) - (3x + 1)
⇒ 5x - 3 - 3x - 1
⇒ 2x - 4
Therefore, The expression for the difference the price of the original recliner and the replacement recliner will be;
⇒ (2x - 4)
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Find the area of a rectangle whose length and breadth are 3x²y² and 5xy2 respectively.
Answer:
A = 15x³[tex]y^{4}[/tex]
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × breadth
= 3x²y² × 5xy²
= 3 × 5 × x² × x ×y² × y²
= 15 × x³ × [tex]y^{4}[/tex]
= 15x³[tex]y^{4}[/tex]
