After 6 seconds, the drone and the football will be at the same height.
To solve this problemWe must make the football and drone's heights equal, then use a timer to find a solution.
The drone's height can be calculated as h_drone(t) = 4t
Where
t is the time in seconds 4t is the drone's height in metersSetting the heights equal to each other:
[tex]-2t^2 + 16t = 4t[/tex]
Simplifying the equation:
[tex]-2t^2 + 16t - 4t = 0-2t^2+ 12t = 0[/tex]
Factoring out common terms:
-2t(t - 6) = 0
Setting each factor equal to zero:
-2t = 0 or t - 6 = 0
To find t, use the formula -2t = 0 t = 0 (This is a representation of the kickoff timing for the football.)
For t - 6 = 0, t = 6 (This indicates the moment the football and drone will be at the same height.)
Therefore, after 6 seconds, the drone and the football will be at the same height.
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Find the area and circumference of the following.
(a) A circle of radius 7 cm Take π = 22/7
Answer:
A = 154 cm² , C = 44 cm
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
given r = 7 , then
A = [tex]\frac{22}{7}[/tex] × 7²
= [tex]\frac{22}{7}[/tex] × 49
= 22 × 7
= 154 cm²
the circumference (C) of a circle is calculated as
C = 2πr
= 2 × [tex]\frac{22}{7}[/tex] × 7
= 2 × 22
= 44 cm
PLEASE HELP SOLVE X AND Y
GIVING 100 POINTS
The value of x in the line is 0.5 units and the value of y is 1.7 units.
How to solve variables in a line segment?The length of the lines are indicated on the diagram. The line below is bisected into two equal halves.
Therefore, let's find the value of x in the line segments.
5x + 8 = 21x
5x - 21x = -8
-16x = -8
divide both sides of the equation by -16
x = -8 / -16
x = 1 / 2
Therefore, let's find the value of y in the line segments.
20y - 2 = 17y + 3
20y - 17y = 3 + 2
3y = 5
divide both sides of the equation by 3
y = 5 / 3
y = 5 / 3 = 1.66666666667 = 1.7
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How many solutions does -3=2x²-8x+8 have
Answer:
no real solutions
Step-by-step explanation:
the easiest method would be to graph the equation and see how many intersection points with the x-axis there are; that represents the number of solutions
when we graph the equation we first want to add 3 to each side of the equation to get the following:
y = 2x²-8x+11
what we see is that the parabola does not intersect the x-axis at all; therefore, there are no 'real' roots or solutions
Answer:
Step-by-step explanation:
x =(4-√24)/4=1-1/2√ 6 = -0.225.
A bag contains 7 red marbles, 6 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be red?
The likelihood that all three marbles selected will be red is 0.0588 to the nearest 1000th.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
Total number of marbles=7+6+5
=18
the probability, to the nearest 1000th, that all three marbles drawn will be red,
=(7/18)*(7/18)*(7/18)
=0.0588
The probability, to the nearest 1000th, that all three marbles drawn will be red is 0.0588.
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Solve these simultaneous equations.
y=x
y=x²-6
Answer:
solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1
Step-by-step explanation:
To solve these simultaneous equations, we need to find the values of x and y that satisfy both equations.
Given:
y = x
y = x² - 6
We can substitute the first equation into the second:
x = x² - 6
we can subtract x from both sides to get:
0 = x² - 7x + 6
Then we can factor it:
(x-6)(x-1) = 0
Therefore x = 6 or x = 1
So the solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1
There are two solutions, (6,6) and (1,1)
What is the additive inverse of 4 (- 4?
The additive inverse of 4 is -4. This means that when 4 is paired with -4, the two numbers cancel each other out and the result is 0.
The additive inverse of a number is the opposite of that number. For example, the additive inverse of 4 is -4. This means that when two numbers are added together and one of them is 4 and the other is -4, the result will be 0. This is because the two numbers cancel each other out. The same is true for any number and its additive inverse. For example, 8 and -8 added together will also result in 0. Additive inverses are an important part of algebra and can be used to solve equations. By understanding the concept of additive inverses, you can easily manipulate equations and solve for unknowns. This is due to the fact that when two numbers are added together and one of them is the additive inverse of the other, the result will always be 0.
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How do you write a function from a table of values?
To write a function from a table of values, you can use the data in the table to determine the pattern or relationship between the input (x) and output (y) values. Once you have identified this pattern or relationship, you can use mathematical notation to express it as a function in the form of y = f(x).
Give an example of the function from a table of values.For example, if you have a table of values that shows a linear relationship between x and y, you can use the slope-intercept form of a linear equation (y = mx + b) to write the function. You can use the values in the table to find the slope (m) and the y-intercept (b) and then plug them into the equation to get the function.
You may also use the interpolation method to estimate a function from a table of values with a non-linear relation.
It's helpful to plot the data points on a graph to help identify the pattern or relationship, and to check that the function you've written correctly represents the data in the table.
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Complete question is: How do you write a function from a table of values?
What is the best method to apply in solving the equation x² 9?
The best method to apply in solving the given equation x² = 9 is the factorization method.
Factorisation is defined as the breaking or deterioration of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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Andrew is paid 4$ per hour for the first 30 hours he works each week. he makes 5$ per hour for each hour he works over 30 hours per week. in other words, total wages= fixed wages for 30 hours + additional wages at 5$ per hour.
Part A
Write a function that gives Andrews total wages when he works more than 30 hours. use the variables w for wages and h for hours.
Answer: For the first 30 hours, Andrew will earn 4 (30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5 (h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is
Step-by-step explanation: For the first 30 hours, Andrew will earn 4(30) = $120. For each additional hour beyond 30 that Andrew works, he will earn 5(h - 30). Therefore, the function that gives Andrew's total wages when he works more than 30 hours is:
w = 120 + 5(h - 30).
So, if he works 35 hours, he will earn:
120 + 5(35 - 30) = 120 + 5(5) = 120 + 25 = $145.
If he works 42 hours, he will earn:
120 + 5(42 - 30) = 120 + 5(12) = 120 + 60 = $180.
I hope this helps!
which pair of expressions are equivalent.
a) 3(x+ 2) and 3x + 2
b) 4d+ 2e and 8d +e
c) f+f+f+g and 3fg
d) b+b+ 3c and 2b +3c
Answer:
d) b+b+3c and 2b+3c
Step-by-step explanation:
b+b=2b
2b+3c=2b+3c
The height of a kicked ball can be modeled by the quadratic function h = - 0 .01x^2 + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet. Approximately how far does the ball travel horizontally by the time it hits the ground?
The horizontal distance covered by the ball is 119.5 ft.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the height of a kicked ball can be modeled by the quadratic function h = - 0 .01x² + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet.
The horizontal distance covered by the ball will be calculated as,
h = - 0 .01x² + 1.18x + 2
Equate h to zero and solve for the distance x,
- 0.01x² + 1.18x + 2 = 0
Use the quadratic formula,
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x = \dfrac{-1.18\om\sqrt{(1.18^2)-(4\times(-0.01)\times2}}{2\times-0.01}[/tex]
[tex]x=\dfrac{-1.18\pm\sqrt{1.4+0.08}}{-0.02}[/tex]
x = ( -1.18 - 1.21 ) / 0.02
x = 119.5 ft
The horizontal distance will be 119.5 ft.
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Is the triangle with sides 25 cm 5 cm and 24 cm a right triangle?
The triangle with sides 25cm, 5cm and 24cm is not a right triangle.
Now, According to the question:
Let us assume that :
ABC is a right triangle,
A = 25cm
B = 5 cm
C = 24 cm
We have to find if the given sides of a triangle form a right triangle.
By using Pythagoras theorem for a right triangle,
[tex]A^2 = B^2+C^2[/tex]
[tex](25)^2 = (5)^2 + (24)^2[/tex]
LHS:[tex](5)^2 + (24)^2[/tex]
= 25 + 576
= 601
RHS:[tex](25)^2[/tex]
= 625
LHS ≠ RHS
Since, the Pythagorean theorem does not apply, the given sides do not form a right triangle.
Therefore, the triangle with sides 25cm, 5cm and 24cm is not a right triangle.
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How to restore stuff
We can see here that in order to restore stuff, here are some steps to take:
Research the item: Learn as much as you can about the item you want to restore, including its age, materials, and any history or sentimental value.Assess the damage: Determine the extent of the damage and what needs to be done to restore the item.Gather materials: Collect all the necessary materials, such as paint, glue, and any tools you may need.What is restoration?Restoration is the process of returning an object or structure to its original condition or a close approximation of it. This can include cleaning, repairing, and/or preserving items such as furniture, antiques, artwork, historic buildings, and more.
The goal of restoration is to preserve the integrity of the item and maintain its historical or sentimental value. This process can include various techniques such as carpentry, metalworking, painting, and conservation.
To still restore a stuff,
Clean the item: Use a gentle cleaner to remove any dirt or grime from the item.Repair any damage: Use glue or other adhesives to fix any broken part.Learn more about restoration on https://brainly.com/question/2843805
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How do you dilate a linear function?
If the parent graph is made steeper or less steep (y = ½ x), the transformation is called a dilation.
And if the parent graph is changed so that it falls to the right instead of rising to the right (y = -x), the transformation is called a reflection.
If x is replaced by x/A in a formula and A>1, then the effect on the graph is to expand it by a factor of A in the x-direction (away from the y-axis). If A is between 0 and 1 then the effect on the graph is to contract by a factor of 1/A (towards the y-axis). We use the word "dilate'' to mean expand or contract.
f y is replaced by y/B in a formula and B>0, then the effect on the graph is to dilate it by a factor of B in the vertical direction. As before, this is an expansion or contraction depending on whether B is larger or smaller than one. Note that if we have a function y=f(x), replacing y by y/B is equivalent to multiplying the function on the right by B: y=Bf(x). The effect on the graph is to expand the picture away from the x-axis by a factor of B if B>1, to contract it toward the x-axis by a factor of 1/B if 0<B<1, and to dilate by |B| and then flip about the x-axis if B is negative.
When dilating a line, check if the center is on the line. If the center lines on the line, the line remains the same.
The line whose equation is y = x + 3 is dilated by a scale factor of 2 centered at the origin. Write the equation of the line after the dilation.
M= 1 , b =3
0=0 +3
0 ≠ 3
center not on line
(0 ,3)→(0 ,6) d2 y intercept
(1 ,4)→(2 ,8) d2 y intercept
y = mx + b
y =x +6
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What is the percent of increase from 5 to 7?
The percentage increse in value from 5 to 7 is 40 %
What is Percentage ?A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
The initial value is 5
Final value = 7
Increse in value 7-5 = 2
Percentage increse is [tex]\frac{2}{5}* 100 = 40 \ \% \\[/tex]
The percentage increse in value from 5 to 7 is 40 %
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What is the additive inverse of 924?
The Additive Inverse of 924 is -924
⇒ The number that, when added to 924, will result in a sum of zero is the additive inverse of 924. The formula to solve the issue where x is the additive inverse of 924 is as follows:
924 + x = 0
⇒ When we solve the preceding equation for x, we obtain x = -924. As a result, the answer to the question "What is the additive inverse of 924?" is -924.
∴Therefore Additive Inverse of 924 = -924
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The point of intersection of angle bisectors of a triangle is called .
A . circumcentre
B. incentre
C. orthocentre
D. centroid
The point of intersection of a triangle's angle bisectors is known as the incentre.
What exactly is an incentre?The incentre is the point where the triangle's three angle bisectors meet at a single point. For more understanding, draw a triangle. Name each angle with A, B, and C. Place P in the triangle's center. The point that connects A to P, B to P, and C to P is the angle bisector of a triangle. Point P is the intersection of all of the lines mentioned above. The explanation leads us to the conclusion that the incenter is the center of the triangle pointed out by P.Then, what is the explanation of the other options?The point of intersection where the three perpendicular bisectors meet or intersect is called the circumcenter.The point of intersection where the three triangle’s altitudes meet or intersect is called the orthocentre. The point of intersection where the triangle’s three median values meet or intersect is called the centroid. The letter G is usually used to denote the centroid.Learn more about incentre in triangle:
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Anna and julia each take a bycicle trip. Anna ride 20 mile in 1 1/3 hour. Julia ride 246 mile in 16 hour. Which rider ha the lower unit rate? by how much?
Julia has lower rate than anna by 0.375 miles/ hour
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit. Let us understand this using some examples:
40 miles/2 hours = 20 miles/hour, Unit rate is 20 miles per hour
160 words/4 minutes = 40 words/minutes, Unit rate is 40 minute per minute
To compare the unit rate of the two riders, we need to determine the number of miles per hour for each of them.
For Anna, the unit rate is 20 miles / 1 1/3 hour = 15 miles/hour.
For Julia, the unit rate is 246 miles / 16 hours = 15.375 miles/hour.
So, Julia has a lower unit rate than Anna by 0.375 miles/hour.
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Greg’s parents bought a $350.00 savings bond when he was born. When he turns 3030, the bond’s value will have increased 125%. How much will the savings bond be worth on Greg’s thirtieth birthday?
Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
What is the percentage?In mathematics, a quantity or ratio known as A% stands for a percentage of 100.
There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.
To represent percentages, the symbol "%" is typically written after the number.
So, we know that:
The bond is $350.
The return is 125% when Greg turns 30.
Then, the amount after she turns 30 will be as follows:
350/100 * 125
437.5
Bonds value: 437.5 + 350 = $787.5
Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
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How do you convert a base 2 number to base-3?
The most common way to convert a base-2 number to base-3 number is to convert a base-2 number to decimal or base-10 number first then convert base-10 number to base-3 number. You actually can directly convert it to base-3 number, but it is more complicated to do.
How to convert it base-2 number to decimal and decimal to base-3 number?There is two ways to convert base-2 number to decimal or base-10 number, using positional notation methods and doubling methods. Positional notation methods are done as follow:
First, list every digit of base-2 number in a row. Ex : 101101. The list will be 1 - 0 - 1 - 1 - 0 - 1Second, multiply each digit in a row start from the right from zero then continue with +1 for the next-left of the number. Lets continue the calculation from step 1 as follow:1 - 0 - 1 - 1 - 0 - 1
2⁵ 2⁴ 2³ 2² 2¹ 2⁰
Last, summarize all the result in step 2. Let use the previous example, the calculation will be : 2⁵ + 2⁴ + 2³ + 2² + 2¹ + 2⁰ = 45₁₀After we get base 10, then convert base-10 number to base-3 number like this:
Divide the decimal by 3 until we cant divide the number with 3 anymore.The remainder of the division will be put as a base-number 3. To write the result, start writing from the last remainder to the first reminder. Example: The result of 72₁₀ will be 2200₃. See the attached picture.Learn more about base number here
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The sides of a triangle are as follows. The second side of a triangle is twice the length of the first side. The third side of the triangle is half of the second side. If the perimeter of the triangle is 36 units, what is the measure of all the sides? Write and solve an equation.
Jean Junction i elling jean at 15% off the regular price the regular price i $25 per pair what i the dicount amount
The discount amount is $3.75 ($25 x 15% = $3.75).
1.Calculate the discount: Regular price x discount percentage = discount amount
2. Plug in the values: $25 x 15% = $3.75
3.The discount amount is $3.75.
The discount amount can be calculated by taking the regular price and multiplying it by the discount percentage. For example, if the regular price is $25, and the discount percentage is 15%, the discount amount can be calculated by multiplying the regular price by the discount percentage ($25 x 15% = $3.75). Therefore, the discount amount is $3.75. This calculation can be used to calculate the discount amount for any given regular price and discount percentage.
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What is the range of the given function?
((-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7))
A (x/x = -5, -4,-2,0,2)
B (uly = -9,-3,0,5, 7)
C lr=-9, -5,-4.-3,-2.0,2,5,7
D g1g=-9,-5,-4,-3,-2,0,2,5,7
Answer: B (-9, -3, 0, 5, 7)
Step-by-step explanation:
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts.
The points that the cooking group leader did label are (0,15) and (30,0). Thus, the correct answer is C.
As your first step, find the function that best represents x and y:
x is the number of 8-ounce jars x.y is the number of 16-ounce jars.Hence, the function is:
8x + 16y = 240The group leader labeled (0,15) on the y-axis, which means that when the number of small jars is 0, the group can use 15 large jars. This means that 15 large jars can hold 240 oz of spaghetti sauce, which is true since:
8x + 16y = 240(15x0) + (16x15) = 2400 + 16 x 15 = 24015 x 15 = 240The group leader also labeled (30,0) on the x-axis, which means that when the number of large jars is 0, the group can use 30 small jars. This means that 30 small jars can hold 240 oz of spaghetti sauce, which is true since:
8x + 16y = 240(8x30) + (16x0) = 2408 x 30 + 0 = 2408 x 30 = 240The function that represents this line is 8x + 16y = 240, where x is the number of small jars and y is the number of large jars. The line passes through (0,15) and (30,0) as the two intercepts.
This question should be written as:
A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts. Which points did the group leader label?
A. (0,8) and (16,0) B. (0,30) and (15,0) C. (0,15) and (30,0) D. (0,16) and (8,0)The correct answer is C.
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I need help This is hard
To calculate the percent change in David's water intake from Tuesday to Wednesday, we can use the following formula:
percent change = (new value - old value) / old value * 100
In this case, the old value is the number of cups of water David drank on Tuesday (16 cups) and the new value is the number of cups of water he drank on Wednesday (12 cups).
Plugging these values into the formula:
percent change = (12 - 16) / 16 * 100 = -25%
So David's water intake decreased by 25% from Tuesday to Wednesday.
_______________
The original amount in the problem is the amount of water David drank on Tuesday, which is 16 cups.
It was given in the problem as the base value to calculate the percent change in David's water intake from Tuesday to Wednesday.
_____________
The change in David's water intake in this problem is the difference between the amount of water he drank on Tuesday and the amount of water he drank on Wednesday.
On Tuesday, he drank 16 cups of water, and on Wednesday, he drank 12 cups of water.
So the change in David's water intake is:
16 cups - 12 cups = 4 cups
David drank 4 cups less water on Wednesday than on Tuesday.
Step-by-step explanation:
The original amount is 16 cups.
The new amount is 12 cups.
The amount of change is the difference of the two:
16 - 12 = 4 cups.Percent change is the change from the original amount:
4/16*100% = 25%This is a drop or decrease in percent.
at a football game, a vender sold a combined totalf of 248 sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and hot dogs sold.
Answer:
Number of soda = 186
Number of hot dog= 62
Step-by-step explanation:
Let us take number of sodas as x and number of hot dogs as y
Then
x + y = 248 [Equation 1]
and
3y = x
Hence,
3y -x = 0 [Equation 2]
By adding [Equation 1 & 2]
(+x -x) 3y + y = 248 + 0
4y = 248
4 4
y = 62
Substitute y= 62 in [Equation 1] to get
x + y = 248
x + 62 = 248
x = 248 - 62
x = 186
Earth approximately 33x 107 miles from the sun. Saturn is approximately 8.87 x 108 miles from the sun. About how much farther is S
from the sun than Earth is?-
OA 794x107 miles
OB 724x10 miles
0 43×10 miles
OD 4.3x10 miles
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What is prime multiple of 10?
A multiple of 10 cannot be equals to a prime number. Multiple of 10 is always equals to a composite number.
As given in the question,
Multiple of a given number 10 are equals to :
10 , 20 , 30, 40, 50, ........, so on.
Prime number are those numbers which have only two factors one and the number itself.
Number 10 itself is not a prime number.
Factors of 10 are equals to :
1, 2, 5, 10
More than two factors.
All the Multiples of 10 cannot be a prime number as they have more than two factors.
Multiple of 10 represents the composite number.
Therefore, multiple of 10 cannot be equals to a prime number they are composite number.
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Question
Which statement describes the relationships between x and y in these two equations?
y = 10x
y = x + 10
In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
y = 10x, we can say that the algebraic equation represents "the value of y is twice the value of x.
Also, for the equation y = x + 10, we can say "the value of y is two more than the value of x.
Hence, In y = 10x the value of y is twice the value of x, and in y = x + 10 the value of y is 10 more than the value of x.
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When writing a piecewise function from a graph how do you determine the domain of each rule?
When writing a piecewise function from a graph, the domain of each rule is determined by the x-values of the graph.
A piecewise function is a function that is defined by different rules for different ranges of the input (x-values). Each rule corresponds to a different interval of the domain.
To determine the domain of each rule when writing a piecewise function from a graph, you can use the following steps:
Identify the intervals of the x-axis where the graph changes behavior.
Write the domain of the function for each interval.
Write the rule for each interval of the domain.
For example, if a graph has a behavior change at x = 1, x = 3, and x = 5, then the domain of the function can be written as:
f(x) = {
y1, x < 1
y2, 1 ≤ x < 3
y3, 3 ≤ x < 5
y4, x ≥ 5
}
The domain for each rule is the interval of x-values between the changes in behavior. In this example, the first rule applies to x values less than 1, the second rule applies to x values between 1 and 3, the third rule applies to x values between 3 and 5, and the fourth rule applies to x values greater than or equal to 5.
Here, note that when writing a piecewise function, it is important to make sure that there are no gaps or overlaps in the domain of the function and that the x-values where the graph changes behavior are included in the domain of at least one of the rules.
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