When first differences are the same it's a linear equation. First differences are equal to the slope, m. General equation is f(x) = mx + b
To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function.
How can one locate an equation?
determine a line's equation from two points:
Using the slope formula, determine the slopeTo find the y-intercept (b), use the slope and one of the points.You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx +b)To learn more about f(x) = mx + b refer to:
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IIIO GEOMETRYVolume of a sphereThe radius, R, of a sphere is 6.2 m. Calculate the sphere's volume, V.Use the value 3.14 for n, and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The formula for calculating the volume of a sphere is expressed as
Volume = 4/3 x pi x radius^3
From the information given,
pi = 3.14
radius = 6.2
By substituting these values into the formula, we have
Volume = 4/3 x 3.14 x 6.2^3
Volume = 997.7999
Rounding to the nearest tenth,
Volume = 997.8 m^3
Find the maximum value of the quadratic function.
Answer:
-49.
Step-by-step explanation:
Convert to vertex form:
f(x) = -7x^2 - 14x - 56
= -7(x^2 + 2x + 8)
= -7 [(x + 1)^2 - 1 + 8)
= 7(x + 1)^2 - 49
- so the maximum value is -49.
What does it multiply too
0.88
X 1.2
Answer:
1.056
Step-by-step explanation:
My number is a multiple of 4. My number has 8 factors, including 2 and 3. My number is less than 30. My number is
Answer:
24
Step-by-step explanation:
mutiples of fours under 30 leave 7 possible numbers
but the only number w 8 factors under 30 is 24
(if you're too lazy to read all of the below im about to say then because it is divisible by 2,3,4 and less than 30 the number is 2 x 3 x 4 = 24)
First, we exclude 0 cause it has more than 8 factors (literally)
Since 2 and 3 are 2 of the number's factors, it must be divisible by 6.
Therefore, we have 4 options : 6,12,18,24 (30 does not count)
Since it is divisible by 4, we are left with 2 : 12 and 24.
(here's something extra which is how to identify the number of factors a number has, not necessary in this case cause we can just count, but it's useful anyways)
We do the prime factorization of that number :
For example : 120
The prime factorization of 120 is 2^3 x 3 x 5.
Now, we take the index number of every single one of the prime numbers in the factorization, add each of them by 1 and multiply them
So, the index number of 2 is 3, 3 is 1 and 5 is 1 (2^3 x 3^1 x 5^1)
-> 120 has (3+1)(1+1)(1+1) = 16 (factors).
Applying it to this case, only 24 would work, as :
24 = 3 x 2^3
So, it has (3+1)(1+1) = 8 (factors), just as it says.
Suppose that 19 inches of wire costs 76 cents.
At the same rate, how many inches of wire can be bought for 64 cents?
Answer: 16 inches
Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.
Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents
Solve the inequality r divided by negative 3.2 is greater than or equal to 7.6 for r.
r ≥ −24.32
r ≤ −24.32
r ≥ 2.375
r ≤ −2.375
Answer:
r ≤ -24.32
Step-by-step explanation:
r/-3.2 > 7.6
r /-3.2 × 3.2 > 7.6 × -3.2
r ≤ -24.32
Answer: r ≤ −24.32
Step-by-step explanation:
The inequality you provided is:
r/-3.2 >= 7.6
To solve for r, we can multiply both sides of the inequality by -3.2 to get:
r <= -24.32
Therefore, r is less than or equal to -24.32.
I hope this helps! Let me know if you have any other questions.
At a particular restaurant, each pizza roll has 55 calories and each mini hotdog has 70 calories. A combination meal with pizza rolls and mini hotdogs is shown to have 910 total calories and 12 more pizza rolls than mini hotdogs. Determine the number of pizza rolls in the combination meal and the number of mini hotdogs in the combination meal.
There are 14 pizza rolls in the combination meal and 2 mini hotdogs in the combination meal.
In the above question, it is given that
At a particular restaurant,
Number of calories in Pizza roll = 55 calories
Number of calories in mini hotdogs = 70 calories
A combination meal with pizza rolls and mini hotdogs is shown to have total = 910 calories
We need to find , the number of pizza rolls and number of mini hotdogs in the combination meal
Let the number of mini hot dogs be x
Then number of pizza roll be x+12 ( given )
The following equation is generated from the given information as
55( x + 12) + 70x = 910
55x + 70x + 660 = 910
125x = 910 - 660
Then, number of hotdogs are x = 2
and, number of pizza rolls = x + 12 = 2+12 = 14
Hence, there are 14 pizza rolls in the combination meal and 2 mini hotdogs in the combination meal
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Explain and correct the error in this calculation
-Picture below-
The error calculated is 2/5×3/8 = 3/20
What is error?An estimate or approximation of a true value and an error are two different things.
An error is defined as a mistake or a state of being incorrect. If you add 2+2 and get 5, that is an error. When a mistake causes you to believe the wrong conclusion about a collusion and you stick with it, that is an example of error.
Given
2/5×3/8 = 3/10
which is not possible, because 2×4 = 8 and the numerator and denominator is divided by 2 at the same time.
1/5×3/4 = 3/20
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Fill in the blank. Using the number line below, the plotted number is
when rounded to the nearest thousand.
Answer:2000 will be the nearest thousand.
Step-by-step explanation:
If f(x) = 1/5x - 11, what is f(−12)?
PLS HELP
Circle A has a diameter of 9 cm. Circle B has a radius of 6 cm.
a.) Which circle has the larger circumference? A or B?
b.) About how many centimeters larger is it?
cm larger
(NO PICTURE INCLUDED) (DONT ASK FOR PIC)
The circle that has the larger circumference is circle B. The difference in the circumference is 9.42 cm.
Which circle has the bigger circumference?A circle is a bounded object in which points from the center is equidistant to the circumference. The circumference of a circle is the perimeter of the circle. The diameter of a circle is a straight line that touches two opposite points on the circumference of a circle and also passes through the center. Radius is half the diameter of a circle.
The circumference of a circle = 2πr
Where:
π = pi = 22/7 r = radius = diameter / 2Circumference of Circle A = 22/7 x 2 x (9/2) = 28.29 cm
Circumference of Circle B = 22/7 x 2 x 6 = 37.71 cm
Difference in circumference = 37.71 - 28.29 = 9.42 cm
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Beth wanted to go to the school dance but we only had 25$ people to spend . If the ticket costs 5$, how many cookies could Beth buy at the dance if each cookie costs 1.25
The variables all have the same identity for all conceivable values. A conditional equation can only be true in particular situations where the values of the variables match. A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies
Explain about Equation?The classification of various types of functions can be done using four primary categories. depending on a factor Onto function, one-to-one relationship, many-to-one relationship, and into function are all examples of relationships between function.
A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.
Equations' true strength is in their ability to explain numerous aspects of the world in a highly accurate manner. (This is why, if one can be found, an equation's solution can be helpful.)
Hence, A linear equation is an identity if solving it results in a true assertion, such as 0 = 0. The answer is 16 cookies
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i need helppppppppp plsssssssssssssssss
Answer:
Step-by-step explanation:
A!
Answer: Function A is faster by 1 meter per second.
Step-by-step explanation:
The first function has a greater speed because by taking the meters per second, you get 14 meters per second. Meanwhile, function B has only 13 meters per second, therefore function A is faster by 1 meter per second.
Problem 1
(3x - 4y = 0
(4x - 5y = k
Consider the following system of equations:
where k is a constant real number. Solve the system for (x, y) in terms of k. Do not replace
the constant k with a numerical value. Give your solution as an ordered pair in terms of k.
[For example: If you solve the system and obtain x = 2k and y = 5k + 1, then you would
write your solution as (2k, 5k + 1).]
The ordered pair is [4k , 3k]
In first equation, 3x - 4y = 0
∴ 3x = 4y
x = 4y/3. ----1
Placing the value of x in second equation:
4x - 5y = k
4[4y/3] - 5y = k
16y/3 - 5y = k
[tex]\frac{16y - 15y}{3}[/tex] = k
16y - 15y = 3k
y = 3k
Replacing the value of y in eq. 1, we get
x = 4k
∴ The ordered pair is [4k , 3k]
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Given: AABC, mzC = 90°
m2A = 30°, BC = 16
Find: AB and AC
Help fast
The most appropriate choice for trigonometry will be given by -
AB = 32
AC = [tex]16\sqrt{3}[/tex]
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin\theta,[/tex] [tex]cos\theta[/tex], [tex]tan\theta[/tex], [tex]cot\theta[/tex], [tex]sec\theta[/tex], [tex]cosec\theta[/tex]
[tex]sin\theta=\frac{perpendicular}{hypotenuse}\\\\cos\theta=\frac{base}{hypotenuse}\\\\tan\theta=\frac{perpendicular}{base}\\\\cot\theta=\frac{base}{perpendicular}\\\\sec\theta=\frac{hypotenuse}{base}\\\\cosec\theta=\frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The figure has been attached here.
Since this is a right angled triangle, trigonometry can be applied here,
Since ∠C = 90°, AB is the hypotenuse of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex] as the side opposite to 90° angle is the hypotenuse.
Let BC be the base of [tex]\DeltaABC[/tex][tex]\Delta ABC[/tex]
BC = 16
m∠B = 180 - (90 + 30)
= 180 - 120
= 60°
cos 60 = [tex]\frac{BC}{AB}[/tex]
[tex]\frac{1}{2} = \frac{16}{AB}\\AB = 16\times 2\\AB = 32[/tex]
sin 60 = [tex]\frac{AC}{AB}[/tex]
[tex]\frac{\sqrt{3}}{2} = \frac{AC}{32}\\\\AC = 32 \times \frac{\sqrt{3}}{2}\\\\AC = 16\sqrt{3}[/tex]
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how can proportional relaships help solve problems
Answer:
tldr: we can set up constant proportions: [tex]\frac{a \text{ units}_1}{b \text{ units}_2} = \frac{c\text{ units}_1}{d\text{ units}_2}[/tex] to solve for values.
Step-by-step explanation:
Proportional Relationships can help in certain situations where values scale proportionally.
For example let's say I take 10 minutes to do 3 pages of work.
I can solve for how long it takes me to do each page: [tex]\frac{3\text{ pages}}{10 \text{ minutes}}[/tex]
Now in real life this isn't going to be constant, because after a certain amount of time humans get tired, and to be this consistent across many minutes is very unrealistic.
But assuming humans don't get tired and it's completely consistent, we can assume this proportion of: [tex]\frac{\text{pages}}{\text{minutes}}[/tex] should be constant, which it represents the amount of pages we do per minute.
This is useful because know this value is equal to [tex]\frac{3\text{ pages}}{10 \text{ minutes}}[/tex] in one scenario, I know this is equal in all scenarios.
So I can set up a proportion as such: [tex]\frac{3\text{ pages}}{10 \text{ minutes}} = \frac{x \text{ pages}}{y \text{ minutes}}[/tex]
to solve for how many pages I can do in "y" minutes, or how many minutes it takes to do "x" pages.
when the product of 6 and 8 became 48, what must be done to write that in scientific notation ?
By definition, Scientific notation has the following form:
[tex]a\cdot10^n[/tex]Where the coefficient "a" is a number from 1 to 10, but not including 10 and the exponent "n" is an Integer. The base will be always 10.
When you write a number in Scientific notation, the decimal point must be after the first digit of the coefficient.
In this case, you have:
[tex]6\cdot8=48[/tex]So, in order to write that product in Scientific notation, you must move the decimal point one space to the left. This must be represented in the exponent. If you move it just one space, to the left, then the exponent will be 1 and will be positive.
Therefore, you get that this is:
[tex]=4.8\cdot10^1[/tex]Therefore, you can determine that the answer is:
[tex]4.8\cdot10^1[/tex]Please help me with this question
Answer:
its A
Step-by-step explanation
i took this test
A ribbon is 3 4/5 feet long. Each hair tie needs
2/5 feet. How many hair ties can you make?
A ribbon is 3 4/5 feet long. Each hair tie needs 2/5 feet. Number of hair ties is 6
What is meant by fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction, Next, multiply the two numerators. Then, multiply the two denominators.
No of hair ties = 6
How to find number of hair ties :
Length of the ribbon = 3 4/5 feet
Length of each hair tie needed = 2/5 feet
To find how many ties , divide the total length of ribbon by 2/5
That is = [tex]\frac{3 (4/5)}{2/5}[/tex]
= 6 You can make 6 no. of hair tie from 3 4/5 feet ribbon.
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In a scale diagram, 0.15 inch represents 150 feet. How many inches represent 2.5 feet?
Answer:
.0025 inches
Step-by-step explanation:
[tex] \frac{.15}{150} = \frac{x}{2.5} [/tex]
[tex]150x = 3.75[/tex]
[tex]x = .0025[/tex]
suppose the scores of students on an exam are normally distributed with a mean of 573 and a standard deviation of 72. then approximately 99.7% of the exam scores lie between the integers and , and the mean is halfway between these two integers.
The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between that is it will lie in the range.
We are given that the scores are normally distributed.
The mean of the data is 573.
The standard deviation of this data is 72.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
So,
We can write,
μ = 573
σ = 72
Then, the given expression is,
( μ - 3σ < x < μ +3σ ) = 99.7%
So,
μ - 3σ = 573 - 3*72
μ - 3σ = 573-216
μ - 3σ = 357
μ +3σ = 573 + 3*72
μ + 3σ = 573+216
μ + 3σ = 789
Hence, the mean is halfway between these two integers are = 357 and 789
Empirical rule states that for a normally distributed data that
about 68% data lies between μ + 1σ that is one standard deviation from mean.
about 95% data lies between μ + 2σ that is one standard deviation from mean.
about 99.7% data lies between μ + 3σ that is one standard deviation from mean.
Therefore,
The mean is halfway between these two integers are = 357 and 789, then the 99.7% of data will lie between that is it will lie in the range.
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5. Solve the system using substitution.
{4x + 5y = 7
{
{y= 3x + 9
What variable in the top equation will you substitute the bottom equation into? (x or
y)
6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation? (This is what it looks like BEFORE you simplify it.)
7. Using the equation you came up with for question 6, what does it look like simplified?
8. What is the solution to the equations from question 5?
Answer:
x= -2, y= 3
Step-by-step explanation:
5. Solve the system using substitution.
4x + 5y = 7
y= 3x + 9
What variable in the top equation will you substitute the bottom equation into? y
6. Using the information from question 5, what does the top equation look like after you substitute from the bottom equation into the top equation?
4x + 5(3x+9) = 7
7. Using the equation you came up with for question 6, what does it look like simplified?
4x+5(3x+9) = 7, distribute 5 over the sum in parenthesis
4x+15x+45 = 7, subtract 45 from both sides of the equation
4x+15x+45-45 = 7-45, combine like terms
19x = -38, divide both sides by 19
x = -2
8. What is the solution to the equations from question 5?
y= 3x+9, substitute x for -2
y = 3(-2) +9
y = -6+9
y = 3
The solution for the system of equations
4x + 5y = 7
y= 3x + 9
is x= -2, y= 3
This means that the point (-2, 3) is the intersection of line 4x+5y=7 and line y=3x+9 and that point belongs to both lines.
Answer:
Below in bold.
Step-by-step explanation:
5. 4x + 5y = 7
y= 3x + 9
Substitute for y from the top equation.
5y = -4x + 7
y = (-4x + 7)/5
Substituting:
(-4x + 7)/5 = 3x + 9
6. Substituting from bottom equation, we get:
4x + 5(3x + 9) = 7
7. Simplifying the above:
4x + 15x + 45= 7
19x = -38
8. Solving equations from part 5:
(-4x + 7)/5 = 3x + 9
-4x + 7 = 15x + 45
-38 = 19x
x = -2.
Now substitute x = -2 into y = 3x + 9
y = 3(-2) + 9
= 3.
Solution is x = -2, y = 33
Solve the linear system using the elimination method. Type youranswer as an ordered pair in the form (#,#). 2x + 5y = 8-10x – 9y = -72
1 ) Let's solve this Linear System with the elimination method
Choose the x, as the first variable to be eliminated
2x + 5y = 8 Multiply by 5 the whole equation
-10x – 9y = -72
Adding both equations:
10x +25y=40
-10x -9y=-72
----------------------
0 16y=-32 Dividing both equations by 16
y=-2
2) Plugging into the simplest equation within that Linear System:
2x +5(-2) = 8
2x -10 = 8 Adding 10 to both sides
2x = 18 Dividing both sides by 2
x=9
3) So the answer is the pair (9,-2)
find five soultion linear eqation x+y=3
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.
What are Equations?Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. The given equation is x + y = 3Let the value of x = 0,then,0 + y = 3⇒ y = 3One of the solutions for x + y =3, is (0,3)Similarly, If x = 1,then,1 + y =3⇒ y = 3 - 1 = 2One of the solutions for x + y =3, is (1,2)If x = 2,then,2 + y = 3⇒ y = 3 - 2 = 1One of the solutions for x + y =3, is (2,1)If x = 3, then,3 + y = 3⇒ y = 3 - 3 = 0One of the solutions for x + y =3, is (3,0)If x = 4,then, 4 + y = 3⇒ y = 3 - 4 = -1One of the solutions for x + y =3, is (4, -1)Hence, five solutions of the equation x + y = 3, are:(0,3), (1,2), (2,1), (3,0) and (4, -1).Mathematical variables are used in even the most fundamental and straightforward algebraic equations. There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.To learn more about Equations, refer to:
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The five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).
What are Equations?Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.
A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.
What is the linear equation's general form?Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.
Let the value of
x = 0,
then,
0 + y = 3
⇒
y = 3
One of the solutions
for x + y =3, is =(0,3)
Similarly, If x = 1,
then,
1 + y =3 ⇒ y = 3 - 1 = 2
One of the solutions for x + y =3, is
(1,2)
If x = 2,
then,
2 + y = 3
⇒ y = 3 - 2 = 1
One of the solutions for x + y =3, is
(2,1)
If x = 3, then,
3 + y = 3
⇒ y = 3 - 3 = 0
One of the solutions for x + y =3, is
(3,0)
If x = 4,
then,
4 + y = 3
⇒ y = 3 - 4 = -1
One of the solutions for x + y =3, is
(4, -1)
Hence,
five
solutions of the equation x + y = 3, are:
(0,3), (1,2), (2,1), (3,0) and (4, -1).
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The equation7y =хrepresents:neitherinverse variationdirect variation
The equation is:
[tex]y=\frac{7}{x}[/tex]If x grows then y is going to reduce, and if y gets smaller, then t grows. this means that is an inverse variation
when a number is added to 18 the answer is the same as 59 mins 20. what is the number?
Algebra 2 help
Ccfggggggggyytttt
The solution to the quadratic equation -3 = 4x² + 9x using quadratic formula is; x = (-9 + √33)/8 or (-9 - √33)/8
How to use the quadratic formula?The general form of any quadratic equation is written as;
ax² + bx + c = 0
The quadratic formula that is used to solve this is given by;
x = [-b ± √(b² - 4ac)]/(2a)
Now, we are given the quadratic equation as;
-3 = 4x² + 9x
It can be written as;
4x² + 9x + 3 = 0
Thus, using quadratic formula we have;
x = [-9 ± √(9² - (4 * 4 * 3))]/(2 * 4)
x = [-9 ± √(81 - 48)]/8
x = (-9 ± √33)/8
x = (-9 + √33)/8 or (-9 - √33)/8
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given r(x)= 11/(x-4)^2 which repress the domain restriction on r(x) and the corresponding inverse function?
A function that "undoes" another function is referred to as an inverse in mathematics. To put it another way, if f(x) yields y, then y introduced into the inverse of f yields x. A function that can be inverted has an inverse, which is denoted by the symbol f1. The solution is: x>4;r-1(x)=4-(root of (11/x)
Explain about the inverse function?Something that is opposite or reversal in nature or quality. The inverse of "if A then B" is "if not-A then not-B" — compare contrapositive. 2: a proposition or theorem constructed by opposing both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem.
reciprocal, inverse multiplicative. (Mathematics) One of two numbers whose product is 1: the multiplicative inverse of 7 is 1/7, while the reciprocal of 2/3 is 3/2. type: antagonism, oppositeness. the connection between seemingly opposing parties.
If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function. The term "f inverse" is widely used to refer to this particular inverse function, which is singular.
The solution is: x>4;r-1(x)=4-(root of (11/x)
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what is(7x10^-6) (5x10^-6) in scientific notation?
Answer:
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive. So 3.5 times 10 to the power of -11
The table contains data on the number of people visiting a historical landmark over a period of one week.
From the data provided, we can consider the following function as a good approximation:
[tex]y=2.57+49.29x-3.86x^2[/tex]Therefore:
The answer is:
a quadratic function with a negative value of a
