A linear equation is any equation that results in a straight line, as each value is a fixed number from the previous.
In a non-linear equation, a variable is being raised to a power, which results in a curved line.
Answer:
b. y^2 = x^2 + 3 not a linear equation
Step-by-step explanation:
Linear equations are equations in which the variable is in the first degree, or only to the first power.
a. y = x + 6 Nothing above the first power
b. y^2 = x^2 + 3 X and y are to the second power
c. x = 5 Only to the first power
d. 2x = 3y Only to the first power
A cell phone company collected data if texting speed in words per minute according to time in minutes. explain why a scatter plot is used to represent the data, including the purpose of scatter plots
Answer:
Scatter plots resembles line graphs in that they are plotted on the x and y axis. The are used because they show how much one variable is affected by another.
Scatter diagrams are important since in statistics they can show the extent of correlation, if any, between the values of observed quantities or a behavior.
Answer:
A scatter plot is defined as a diagram which uses Cartesian coordinates to display values about two variables, one indepedent, the other one dependent.
This diagrams are used in statistics to display information about surveys to a certain sample in a population. The purpose of a scatter plot is to shows if the variables are related, that is, if they have any type of linear correlation between them. If they have linear correlation, then the data is represented by a line.
Now, in this case, the independent variable is time in minutes and the dependent variable is texting. Basically, with this data, the company will be able to stablish the relation between words written in a certain time, that is, the speed of texting actually.
With a scatter plot, they would find the relation that forms the speed of texting. It could be "the more time, more text is written", or "the less time, more text is written".
If we need to establish a possible relation, the most logical would be "the more time, more word are texted".
What equation is a quadratic model for the data set? X 4, 10, 13, 17, 8, 12, 6 y 20, 86, 174, 274, 72, 135, 44
Answer:
Option C is correct.
[tex]y = 0.9673x^2-0.8475x + 10.4334[/tex] is an quadratic model equation for the data set
Step-by-step explanation:
To find the equation of the quadratic model for the given data set:
x y
4 20
10 86
13 174
17 274
8 72
12 135
6 44
We begin by entering the data into a graphing utility and displaying the scatter plot, as shown below in the figure. In the scatter plot, you can see that the data appears to follow a parabolic pattern.Using the feature of a graphing utility, you can find the quadratic model as shown below.Therefore, the quadratic model for the given data is given by;
[tex]y = 0.9673x^2-0.8475x + 10.4334[/tex]
What is the smallest possible slope for y=x^3 -3x^2 +5x -1
let's find its first derivative for "y"
[tex]\bf y=x^3-3x^2+5x-1\implies \cfrac{dy}{dx}=3x^2-6x+5[/tex]
now, we can run the quadratic formula on that derivative, and it turns out we end up with a negative radicand and therefore an imaginary/complex solution, which is a way to say there are no solutions for it, so the quadratic never touches the x-axis.
so hmmm what is the smallest value it goes down to, for the derivative, before it goes right back up?
well, for that we can simply check her vertex location.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ \cfrac{dy}{dx}=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-6}x\stackrel{\stackrel{c}{\downarrow }}{+5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{(-6)}{2(3)}~~,~~5-\cfrac{(-6)^2}{4(3)} \right)\implies \left( 1~~,5-\cfrac{36}{12} \right) \\\\\\ (1~,~5-3)\implies (\stackrel{x}{1}~,~\stackrel{y}{2})[/tex]
so, "y" or dy/dx goes as low as 2 before going back up, and that happens when x = 1.
Check the picture below.
Step-by-step explanation:
We need to find minimum slope for y = x³ -3x² +5x -1
Slope is derivative of y
[tex]\texttt{Slope,}\frac{dy}{dx}=3x^2-6x+5[/tex]
Now we need to find minimum of 3x² -6x +5
At minimum derivative of 3x² -6x +5 is zero
That is
6x - 6 = 0
x = 1
So the slope is minimum at x = 1
At x = 1,
Slope = 3 x 1² -6 x 1 +5 = 2
Minimum slope possible for x³ -3x² +5x -1 is 2
write a point-slope equation for the line that passes through the point (1,6) and is parallel to the line given by y=5x+25 do not use parenthesis on the y side
Answer:
[tex]y-6=5(x-1)[/tex]
Step-by-step explanation:
To make the line parallel, it has to have the same slope as the other. Because it is in slope-intercept form, we can see that the slope of the line is 5.
Now we have all of the numbers we need for point-slope form. The point-slope form looks like this:
[tex]y-y_{1}=m(x-x_{1})[/tex]
So when we input our values for the variables, the equation is:
[tex]y-6=5(x-1)[/tex]
Slope-intercept form:
y = mx + b
"m" is the slope, "b" is the y-intercept (relevant later)
Point-slope form:
y - y₁ = m(x - x₁) "m" is the slope
For lines to be parallel, their slopes have to be the SAME
The given line's slope is 5, so the parallel line's slope is also 5.
So you know:
m = 5
(x₁ , y₁) = (1 , 6)
Now you can plug this in:
y - y₁ = m(x - x₁)
y - 6 = 5(x - 1)
Mr. Logan needs to buy snacks for his daughter's soccer team. He decides to buy crackers and granola bars at a local grocery store. The price of the crackers is $9 for 3 boxes, and the price of the granola bars is $6 for 3 boxes. Mr. Logan ends up buying $20 worth of crackers and granola bars. Which equation represents the relationship between the number of boxes of crackers, x, and the number of boxes of granola bars, y, that Mr. Logan bought at the grocery store?
Answer:x=4 and y=4
Step-by-step explanation: if you divide 9 by 3 it would be 3 and 6 divided by 3 would be 2 so if you multiply 2 by 4 and 3 by 4 and you add them together it will equal 20
Answer: [tex]3x+2y=20[/tex]
Step-by-step explanation:
Let x be the number of boxes of crackers and y be the number of boxes of granola bars that Mr. Logan bought at the grocery store.
Given : The price of the crackers is $9 for 3 boxes, and the price of the granola bars is $6 for 3 boxes.
i.e. price of one box of crackers = $9 ÷3 = $3
Price of one box of granola bars=$6÷3 = $2
Mr. Logan ends up buying $20 worth of crackers and granola bars.
i.e. (Cost of each box of crackers) x + (Cost of each box of granola bars) y
i.e. [tex]3x+2y=20[/tex]
Hence, the equation represents the relationship between the number of boxes of crackers, x, and the number of boxes of granola bars, y, that Mr. Logan bought at the grocery store :
[tex]3x+2y=20[/tex]
Which decimal is between 0.6 and 0.7
Answer:
0.65
Step-by-step explanation:
0.6 is short for 0.60
0.7 is short for o.7
0.61,0.62,063,0.64,0.65,0.66,0.67,0.68,0.69,0.70
0.65 is in the middle
Answer: The answer is 0.65
Step-by-step explanation:
A large cheese pizza costs $18. Each topping you add on cost $1.50 How much would it cost to get a large cheese pizza with c toppings added? Write your answer as an expression.
which of the following is true for the graph of the quadratic function f(x)=3(x+2)(×-2)
Answer:
A
Step-by-step explanation:
given y = 3(x + 2)(x - 2) = 3(x² - 4) = 3x² - 12
for the y- intercept let x = 0
f(0) = - 12 → y-intercept is the point (0, - 12) → True
for x-intercepts let y = 0
3(x + 2)(x - 2) = 0
x + 2 = 0 ⇒ x = - 2
x - 2 = 0 ⇒ x = 2
x- intercepts are (- 2, 0) and (2, 0) → not (0, - 12)
since f(x) = 3x² - 12 is symmetric about the y-axis
the vertex is at (0, - 12 ) → not (- 2, 2)
Your friend factors the expression 48x-16. Is your friend correct? Explain your reasoning.
Answer:
16(3x - 1)
Step-by-step explanation:
the greatest common factor of 48 and 16 is 16, hence
48x - 16 = 16(3x - 1)
Final answer:
After factoring out the greatest common factor of 16 from the expression 48x-16, the correct factored form is 16(3x - 1). The friend's factorization is correct if this result was obtained, demonstrating the universal application of mathematical rules.
Explanation:
To evaluate if your friend factored the expression 48x-16 correctly, we look for the greatest common factor that both terms in the expression share. Both 48x and 16 are divisible by 16. Factoring out the greatest common factor of 16, we get:
16(3x - 1)
This is the factored form of the expression 48x-16, which shows that your friend is correct if they arrived at this result. This method is an application of the distributive property, which states that a(b + c) = ab + ac. In this case, we take out a '16' from both terms, which is the inverse process - factoring.
Moreover, the principles that apply to factoring expressions are the same regardless of location or time, demonstrating the universality of mathematical rules. Whether we are factoring polynomials or checking arithmetic, using the correct rule and applying it properly is essential.
The slope of the line passing through the points (7, 5) and (21, 15) is ???
Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point ???
Answer:
(21,5)
Step-by-step explanation:
To find the slope that passes through the points (7,5) and (21,15) , we use the formula
m = (y2-y1)/ (x2-x1)
= (15-5)/(21-7)
= 10/14
=5/7
We want a slope that is 1/3 this slope so we will multiply by 1/3
5/7 * 1/3= 5/21
We know the slope and one point (0,0) we can use the same formula to figure out x and y
m = (y2-y1)/ (x2-x1)
5/21 = (y2-0)/ (x2-0)
Let the tops be equal and the bottoms be equal
5 = y2-0
5 =y2
and the bottoms
21 = x2-0
21= x2
We have the point
(21,5)
Answer:
here you go
View the picture for your answer!
have a wonderful day :))
Find the area of 9.5 and 4.1
Answer:
38.94
Step-by-step explanation:
To find the area, multiply the length times the width. In this case 9.5 times 4.1.
I'll Mark Brainliest!!!!!!!!!!
Real estate values in a town are increasing at a rate of 9% per year.
Mr. Townsend purchased a building for $375,000 in 2010.
How much can he expect to sell the building for in 2020, assuming this trend continues?
Enter your answer in the box.
Round to the nearest whole dollar.
$
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
2020 -2010 = 10 YEARS
375,000 X .09 = 33,750 2011 VALUE 33750 + 375000 = 408,750
408750 X .09 = 36787.50 2012 VALUE 445537.50
445537.50 X .09 = 40,098.38 2013 VALUE 485635.88
485635.88 X .09 = 43707.23 2014 VALUE 529343.11
529343.11 X .09 = 47640.88 2015 VALUE 576983.99
576989.99 X .09 = 51928.56 2016 VALUE 628918.55
628918.55 X .09 = 56602.67 2017 VALUE 685521.22
685521.22 X .09 = 61696.91 2018 VALUE 747218.13
747218.13 X .09 = 67249.63 2019 VALUE 814467.76
814467.76 X .09 = 73,302.10 2020 VALUE $887,769.86
Rounded to the nearest dollar: $887,770.00
40 people adopted a manatee 30th foundation this year 30% more people adopted how many more people adopted a manatee this year
Answer:
12
Step-by-step explanation:
Change the percentage into a decimal
30% = 30/100 = 0.30
Multiply 40 with 0.30
40 x 0.30 = 12
12 more people adopted, making 52 in all.
~
Answer:
52
Step-by-step explanation:
30% more means the original 100% plus 30% more of the original 40
That's 130% = 130/100 = 1.3
"of" means x, so it's 40 x 1.3 = 52 people
Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%. She earned $1,696.50 in interest. How long (in years) was the money invested?
Answer:
5 years.
Step-by-step explanation:
She earns $339.3 per year on interest rate. So I divided 1,696.50 by 339.3 to get the amount of ears.
Lina invested for 5 years.
What is simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.The formula to calculate simple interest is Prt, where P is the principle amount, r is the rate and t is the time in years.How to know how long (in years) was the money invested?According to the problem,
Lina invested $7,800 in a mutual fund at a simple interest rate of 4.35%.She earned $1,696.50 in interest.So, we can say $ 1,696.50 is the interest
∴ Prt = 1696.50
⇒ (7800)(4.35/100)t = 1696.50
⇒ t = 5
∴ Line invested for 5 years.
Find more about "Simple Interest" here: https://brainly.com/question/25793394
#SPJ2
Determine the domain and range. Please help!!
The domain is the set of all numbers. The range is also the set of all real numbers.
Why is this the case? Because the line extends forever in both directions along the x and y axis. We can plug in any x value and solve for y, or vice versa, and we don't have any restrictions for the input or output.
-----------------------
To write "the set of all real numbers" in interval notation, you would write [tex](-\infty, \infty)[/tex]
This is the interval from negative infinity to positive infinity, spanning the entire real number line.
Evaluate the expression a/b for a=24 and b=4
Answer:
a/b =6
Step-by-step explanation:
We want to evaluate a/b
a=24, b=4
Substitute these values into the expression
a/b =24/4
= 6
Final answer:
When evaluating the expression a/b with a=24 and b=4, the result is 6, as you simply divide 24 by 4.
Explanation:
The expression to evaluate is a/b, where a=24 and b=4.
To calculate this, simply divide the value of a by the value of b:
Step-by-step calculation:
Insert the known values into the expression: a/b = 24/4.
Divide 24 by 4 to get the result.
24 divided by 4 equals 6.
Therefore, if a=24 and b=4, the value of a/b is 6.
how much will the interest be for a $500 loan at 6% interest for one year
Answer:
300 dollars of interest
Step-by-step explanation:
5000 (0.06)
300
Answer:
$30
Step-by-step explanation:
You are being asked to figure out simple interest, I think.
Givens
i = ?P = 500r = 6%t = 1 yearFormula
i = P*r*t
Solution
i = 500*6%*16% = 6/100 = 0.06i = 500 * 0.06 * 1i = 30Edit
You want this to be done using a % proportion. Is that correct from what I read in the comments after the question (which I didn't see -- sorry).
6/100 = x/500 That's the proportion. Cross multiply6 * 500 = 100*x Multiply the numbers on the left3000 = 100 x Divide both sides by 1003000/100 = 100x/100 Do the division30 = xSo it comes to the same thing.
If a muffin calls for 1 and 3/4 cups of sugar, how many cups of sugar will be needed if only 1/4 of the recipe is being made?
Answer: 7/16 or .4375
Step-by-step explanation: 1/4 of 1 is 1/4. 1/4 of 3/4 is .1875 which also equals 3/16. Add 1/4 and 3/16 to get 7/16 cups of sugar or 0.4375. Hope this helps!
solve for h
A=1/2 bh
Answer:
2A /b = h
Step-by-step explanation:
A=1/2 bh
We want to isolate h
First we multiply by 2
2A = 2 * 1/2 bh
2A = bh
Then we divide by b to isolate h
2A /b = bh/b
2A /b = h
What is the nth term of the geometric sequence 4, 8, 16, 32, ... ?
Answer:
tn = a*2^(n - 1)
Step-by-step explanation:
a = 4
r = 2
tn= a*2^(n-1)
Try it
t3 = 4*2^(3 -1) Combine the power
t3 = 4 * 2^2 Find 2^2
t3 = 4 * 4 Multiply
t3 = 16 Answer for t3
Answer:
2^(n+1)
Step-by-step explanation:
You don't even need to use algebraic methods or the formula for this; it's just common sense. 4=2^2, 8=2^3, 16=2^4.
4 is the term 1
8 is term 2
2=term # (1) + 1 for 4
3 = term # (2) + 1 for 8
And so on
So it is 2 to the power of (term # + 1)
How many solutions exist for the given equation?
(x + 12) = 4x – 1
zero
one
two
infinitely many
The number of solutions exist for the given equation (x + 12) = 4x – 1
is one.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given that;
The equation=(x + 12) = 4x – 1
Now,
We can simplify the given equation as follows:
x + 12 = 4x - 1
Adding 1 to both sides:
x + 13 = 4x
Subtracting x from both sides:
13 = 3x
Dividing both sides by 3:
x = 13/3
Therefore, by solving equation answer will be one.
Learn more about solving equations here:
https://brainly.com/question/13072448
#SPJ7
you have one penny 1 nickel 1 dime and 1 quarter you select two coins at random. what is the probability that you will have exactly $0.15?
Answer:
the probability of getting the exact coins that make $0.15 is 33.3% (1/3)
Step-by-step explanation:
Calvin goes shopping over the weekend and buys a new pair of shoes,a T-Shirt, a pair of sunglasses, and a hat that costs $9. The shoes are twice as much as the shirt, and the sunglasses are half as much as the shirt. The total cost of his purchase is $65. How much does each cost?
Let the costs of shoes, t-shirt, and glasses be represented by s, t, g, respectively. The problem statement tells us these relationships:
... s = 2t
... g = t/2
... s +t +g +9 = 65 . . . . . the $9 cost of the hat is added into the total
_____
Solution
Substituting for s and g, we have ...
... 2t +t +t/2 +9 = 65
... (3 1/2)t = 56 . . . . . collect terms
... t = 56/3.5 = 16 . . . . divide by the coefficient of t
The shoes are 2t, so $32.
The t-shirt is t, so $16.
The sunglasses are t/2, so $8.
The hat is $9.
The sum of two consecutive whole numbers is 57. What is the value of the greater of the two numbers
[tex]n,\ n+1-\text{ two consecutive whole numbers}\\57-\text{the sum}\\\\n+n+1=57\qquad\text{subtract 1 from both sides}\\2n=56\qquad\text{divide both sides by 2}\\n=28\\\\n+1=28+1=29\\\\Answer:\ \boxed{\text{The greater of the two numbers is 29}}[/tex]
The two consecutive whole numbers that sum to 57 are 28 and 29. The solution was achieved by setting up an equation and solving for x which represents the smaller number. The greater number is 29.
Explanation:The sum of two consecutive whole numbers is 57 pertains to a simple arithmetic problem. If two consecutive numbers sum to 57, we can set up an equation to solve for the numbers. Let's call the smaller number 'x'. This means the next number would be 'x + 1' since it's consecutive, or next in line. The equation for your problem would then be x + (x + 1) = 57. Simplifying the equation gives us 2x + 1 = 57, and then subtracts 1 from both sides to get 2x = 56.
The last step is to divide both sides by 2, which gives us: x = 28. So, the smaller number is 28 and the greater number is 29.
Learn more about consecutive whole numbers here:https://brainly.com/question/123052
#SPJ3
In geometry the four sides of a square are all the same length. One side measures (3x+4) and the perimeter of the square is 76. Find the value of X. Hint: First set up an equation to help you solve for X
Answer:
Step-by-step explanation:
We can set up an equation:
4(3x+4)=76
We can distribute the left side and get:
12x+16=76
Subtract 16 from both sides:
12x=60
Divide 12 from both sides:
x=5
Check:
4(3*5+4)
4(15+4)
4(18)
76
So x=5
Use the diagram to find the measurement of each of the angles
Answer:
1. ∠LOQ = 80°
2. ∠LRQ = 40°
3. ∠LBQ = 40°
Step-by-step explanation:
The measure of a central angle (angle that goes to the center of the circle) is EQUAL to the ARC from which it is intercepted. The measure of the angle that is on opposite side, on the circumference, of the circle is HALF of the ARC from which it is intercepted.It is given that ARC QL has a measure of 80.
Central angle from ARC QL (with same measure) are angle LOQ only.Opposite angles (half of measure of ARC QL) from ARC QL (on opposite side on circumference) are angles LRQ and LBQ.1.
m∠LOQ: ∠LOQ is the central angle from ARC QL so it has SAME MEASURE.
∠LOQ = 80°
2.
m∠LRQ: ∠LRQ is the opposite angle from ARC QL so it is HALF of ARC QL.
∠LRQ = [tex]\frac{1}{2}(80)=40[/tex]
∠LRQ = 40°
3.
m∠LBQ: ∠LBQ is also another opposite angle from ARC QL so it is HALF of ARC QL as well.
∠LBQ = [tex]\frac{1}{2}(80)=40[/tex]
∠LBQ = 40°
solve the system of equations. -5x + 8y =0
Answer:
Step-by-step explanation:
helloooooo heres the answer...X=8/5
you get this by moving your Y variable to the left by adding its opposite (-8y) to both sides.
then you should be left with -5x=-8y when in this step divide both steps by -5, which will get you 8/5 hence the answer X=8/5
QUESTION WORTH 30 POINTS!
Answer:
changing by one
Step-by-step explanation:
Find the area of an equilateral triangle whose perimeter is 15 units.
Answer:
The area is 1/2×3×3= 4.5
Step-by-step explanation:
What is the x-intercept of the line with the equation 1/3x+y=-15
The x-intercept is for y = 0.
substitute y = 0 to the equation of the function:
[tex]\dfrac{1}{3}x+y=-15\\\\\dfrac{1}{3}x+0=-15\\\\\dfrac{1}{3}x=-15\qquad\text{multiply both sides by 3}\\\\\boxed{x=-45}[/tex]
Answer: x-intercept = -45 → (-45, 0).Answer:
(-45,0)
Step-by-step explanation:
I took the test