Yes, solutions, roots, x-intercepts, and zeros are the same thing.
What is a quadratic equation?
The general quadratic equation is given by:
a*x^2 + b*x + c = 0
So the solutions are the values of x such that the above thing is zero.
On another hand, a parabola or a quadratic function is given by:
a*x^2 + b*x + c = y
The roots, zeros, or x-intercepts (these represent the same thing) are given by:
a*x^2 + b*x + c = 0
Zero or Root means that when you evaluate the function in that value the outcome is zero.X-intercept means that for that value of x, the function intercepts the x-axis, so the function is equal to zero.So these are the values of x such that the function becomes equal to zero, so these are exactly the same thing as the solutions of a quadratic equation.
Concluding, yes, solutions, roots, x-intercepts, and zeros are the same thing.
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Dr. Gilmore's research group tagged and released 800 squirrels for a study of a local park. Later, they trapped 430 squirrels, 43 of which had tags.
To the nearest whole number, what is the best estimate for the squirrel population?
Using proportions, it is found that the best estimate for the squirrel population is of 8000.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 43 squirrels out of 430 had tags. Considering that in the entire population, 800 are tagged, and we want to find the total population, the rule of three is given by:
43 tagged - 430 squirrels
800 tagged - x squirrels
Applying cross multiplication:
[tex]43x = 430 \times 800[/tex]
[tex]x = \frac{430 \times 800}{43}[/tex]
[tex]x = 8000[/tex]
The best estimate for the squirrel population is of 8000.
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what is it and why?
Answer:
C
Step-by-step explanation:
the solution to a system of equations given graphically is at the point of intersection of the 2 lines.
the lines here are parallel and never intersect. Thus there is no solution
The men walked down the streets to the mine with their heads bent close to their chests. In groups of five or six they scurried on. It was impossible to recognize individuals from the small gaps between their caps, pulled down over their eyes, and the tightly bound scarves tied tightly over the bottom half of their faces
Is the inference true or false? The weather was cold, windy, and rainy.
Please select the best answer from the choices provided
T
F
The cost of a business is the amount of money spent to start the business and keep it in operation. The revenue is the amouunt of
money the business earns from the sale of goods or services.
An online business called Muffins A-plenty started on January 1 of a recent year. The lines in the graph represent the cost function and
the revenue function of the first six months that Muffins A-plenty has been in operation.
Part A
Write equations to represent the cost function and the revenue function for this business,
Parts
The profit of a business equals revenue minus cost. First write an equation that represents the profit function for Muffins replenty using
the functions for cost and revenue, Then, predict the profit after 10 months of operation, found your answer to the nearest dollar. Provide
valid mathematical reasoning and calculations to support your answer,
The profit function of the business is the difference between the revenue and the cost functions
The equations of the cost and the revenue functions are: [tex]y = \frac 43x[/tex] and [tex]y = 0.5x + 3.5[/tex]The profit function is [tex]y = \frac 56x - 3.5[/tex]The profit after 10 months of operation is 29/6Part A: The equations to represent the functionsFor the revenue function, we have the following points
(x,y) = (0,0) and (6,8.0)
Since the line passes through the origin, the equation of the line would be:
[tex]y = \frac{y_1}{x_1} * x[/tex]
So, we have:
[tex]y = \frac{8.0}{6} * x[/tex]
[tex]y = \frac 43x[/tex]
For the cost function, we have the following points
(x,y) = (0,3.5) and (9,36) for x > 5
The equation of the line would be:
[tex]y = \frac{y_1-y_2}{x_1-x_2} * (x - x_1) + y_1[/tex]
So, we have:
[tex]y = \frac{6.5-3.5}{6-0} * (x - 0) + 3.5[/tex]
[tex]y = 0.5x + 3.5[/tex]
Hence, the equations of the cost and the revenue functions are: [tex]y = 0.5x + 3.5[/tex] and [tex]y = \frac 43x[/tex]
Part B: The profit functionThis is calculated as:
Profit = Revenue - Cost
So, we have:
[tex]y = \frac 43x - 0.5x - 3.5[/tex]
Evaluate the difference
[tex]y = \frac 56x - 3.5[/tex]
Part C: The profit after 10 months of operationSubstitute 10 for x in [tex]y = \frac 56x - 3.5[/tex]
[tex]y = \frac 56 * 10 - 3.5[/tex]
[tex]y = \frac {50}6 - 3.5[/tex]
Evaluate the difference
[tex]y = \frac {50-21}6[/tex]
[tex]y = \frac {29}6[/tex]
Hence, the profit after 10 months of operation is 29/6
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How many times greater is the value of 3 in 300 than the value of the 3 in 30
Answer:
ten times I hope I'm right
Step-by-step explanation:
3 × 100 = 300
3 × 10 = 30
sense 3 is what is being talked about, 3 in the 300 is 100 times and 3 in 30 is 10 times.
100 is 10 times 10
10 × 10 = 100
value is the total
how many times greater is the total of the 3 in both numbers
3 in 300 is 10 times the 3 in 30
hope this helps
Solve
6÷2(1+2)
Please tell me the answer
Answer:
9
Step-by-step explanation:
Follow the order of operations:
ParenthesesExponentMultiplication and DivisionAddition and SubtractionGiven expression: 6 ÷ 2(1 + 2)
Carry out the operation inside the parentheses first:
⇒ 6 ÷ 2(3)
⇒ 6 ÷ 2 × 3
Now multiply/divide by going left to right:
⇒ 3 × 3 = 9
Solution:
To solve this problem, we will need to use the "BODMAS".
Solving the expression:
[tex]\bullet \ \ 6 \div 2(1 + 2)[/tex]
First, simplify the expression inside the brackets.
[tex]\bullet \rightarrow 6 \div 2(3) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ex\text{Bracket addition}][/tex]
Now, 2(3) can also be written as 2 × 3, as 2(3) and 2 × 3 are equivalent.
[tex]\bullet \rightarrow 6 \div 2 \times 3[/tex]
According to the BODMAS, division first.
[tex]\bullet \rightarrow 3 \times 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ex\text{Division}][/tex]
According to the BODMAS, multiplication next.
[tex]\bullet \rightarrow \boxed{\bold{9}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\tex\text{Multiplication}][/tex]
Thus, the solution to 6 ÷ 2(1 + 2) is 9.
slope- intercept form: y= -4/3x + 2
what is the standard form?
Answer:
4x-3y=-6
Step-by-step explanation:
90 POINTS!!
Haley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week and her brother is spending $15 each week. After how many weeks will their savings account have the same amount of money in them?
Answer:
3 weeks
Step-by-step explanation:
Set the equations. Let "amount of weeks" be signified by the variable, x.
First, note that Haley starts with $155, and saves $10 each week:
10x + 155
Next, note that her brother has $230 saved and spends $15 each week:
230 - 15x.
Set the two equations equal to each other:
10x + 155 = 230 - 15x
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 155 and add 15x to both sides of the equation:
10x (+15x) + 155 (-155) = 230 (-155) - 15x (+15x)
10x + 15x = 230 - 155
25x = 75
Next, divide 25 from both sides of the equation:
(25x)/25 = (75)/25
x = 75/25 = 3
3 weeks is your answer.
~
Paisley has a bag of 16 marbles that are green, orange, and yellow. If there are 8 green marbles, how many marbles have to yellow in order for P(yellow) = 1⁄4?
Answer:
4
Step-by-step explanation:
16 marbles take away 8 green ones which is equivalent to ½, u will have 8 marbles left or ½, so to get ¼ youll have to halve 8 to get 4.
Please answer!! a b c or d?
Answer:
The reflection of a horizontal line has the same result as a rotation of 90 degrees clockwise.
Answer: Choice B
270 degree rotation clockwise
=======================================================
Explanation:
Notice that 270+90 = 360
Going 90 degrees in one direction is the same as going 270 degrees in the other direction because the two combine to a full 360 degree rotation.
Check out the image below for an example. In the example, the point P starts at (0,5). Doing either rotation mentioned will get us to (-5,0).
28+56t+28w to identify the equivalent expressions.
Choose 2 answers:
Answer:
28(1 + 2t + w)
Step-by-step explanation:
This polynomial can be factored by factoring out 28.
28 + 56t + 28w = 28(1 + 2t + w)
A city's population is currently 467,500. If the population doubles every 42 years, what will the population be 168 years from now?
If the population doubles every 42 years then the population will be after 168 years from now, 7,498,000
What are exponential functions?An exponential function is a mathematical function which we write as a
f(x) = aˣ, where a is constant and x is variable term. The most commonly used exponential function is eˣ , where e is constant having value 2.7182
We can use exponential growth:
If the population doubles every 42 years, the population after t years can be modeled as:
P = 467,500 x 2^(t/42)
where P is the population after t years and 467,500 is the current population.
To find the population 168 years from now, we can plug in t = 168:
P = 467,500 x 2^(168/42)
= 467,500 x 2⁴
= 467,500 x 16
= 7,498,000
So, the population of the city 168 years from now is approximately 7,498,000.
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9) y + 3 = -(x + 5)
5
A) x + y = 5
C) x - y = 5
B) 2x + 5y = 0
D) 8x – 5 y=-25
Answer:
y+3=-(x+5)5
y+3=-5x-25
y+3+5x+25=0
y+5x+28=0
50 POINTS (8th Grade Math)
Two basic math problems, answer correctly.
Trolling is not tolerated and will result to a report!
Correct answers only!
Answer: 1st; (-5, 1)
2nd;(-3, 1)
I’m pretty sure this is it, I’ve done questions like this for a while now, I think I got it right, sorry if I didn’t I tried my best.
Make and test a conjecture about the given quantity.
18. The product of two negative even integers
19. The sum of two negative odd integers
20. The sum of two even integers and two odd integers
21. When you return from a run, your
friend states, “If you ran 1 mile, then
you ran 5280 feet." Your friend then
asks if you can write the statement as
a biconditional statement. Write the
biconditional statement and decide
whether it is true.
Answer:
18. The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Decide whether statement is true: So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
Step-by-step explanation:
18. The product of two negative even integers.
Let the integers be -2m and -2n, m and n are positive integers
Product in (-2m) × (-2n) = 4mn = 2(2mn)
= 2p, p = 2mn
The conjecture is: The product of two negative even integers is an even integer.
Testing: Let integers be -4 and -6. [Two negative even integers]
Then (-4) × (-6) = 24 [Even integer]
19. The sum of two negative odd integers.
Let the integers be -(2m + 1) and -(2n + 1), m and n are positive integers
Then -(2m + 1) + [-(2n + 1)] = -2m - 1 - 2n - 1
= -2m - 2n - 2
= -2(+m + 2 + 1)
= -2p, p = m + n + 1
The conjecture is: Sum of two negative odd integers is a negative even integer.
Testing: Let the two negative odd integers be -3 and -7.
Then -3 + (-7) = -10 is a negative even integer
20. The sum of two even integers and two odd integers.
Let the integers be 2m, 2n, 2p + 1, 2q + 1 (m, n, p, q are positive integers)
Then, 2m + 2n + 2p + 1 + 2q + 1 = 2(m + n + p + q + 1)
= 2r, r = m + n + p + q + 1
The conjecture is: Sum of two even integers and two odd integers is an even integer.
Testing: Let integers be 4, 12, 13, 17 (Two even integers and two odd integers)
Then 4 + 12 + 13 + 17 = 46 (Even integer)
21. Let p: You ran 1 mile
Let q: You 5280 feet
The statement is: p------->q [If you ran 1 mile, then you ran 5280 feet]
Since 1 mile = 5280 feet
So if p is True then q is also True.
Hence p------->q is True. So the given statement is True.
help me pls!!! ASAPPPP this assignment is missing and I'm not even halfway through...
Answer:
5y + 25
Step-by-step explanation:
You simply multiple everything inside by the outside
y x 5
5 x 5
giving you 5y + 25
Find an equation for the line that passes through the points (-5, -5) and (3, 5)
Answer:
5x-4y+5=0.
Step-by-step explanation:
1) if the point A(-5;-5) and B(3;5), the formula is:
[tex]\frac{x-X_A}{X_B-X_A} =\frac{y-Y_A}{Y_B-Y_A}[/tex]
2) according to the formula above:
[tex]\frac{x+5}{3+5} =\frac{y+5}{5+5}; \ = > \ \frac{x+5}{4}=\frac{y+5}{5};[/tex]
or 5x-4y+5=0.
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
?
?
17 yd
11 yd
9 yd
(4 yd
15 yd
Answer:
The missing length would be 6
Step-by-step explanation:
The owner of a bike shop would like to analyze the sales data to determine if the business is growing, declining, or remaining flat. The owner has the following data: Sales Revenue Last Year =$125,000 Sales Revenue Current Year = $150, 000 What is the Sales Growth?.
The sales growth of the business of owner of a bike shop is $25000 and this business is growing.
What is sales growth?Sales growth is the amount of by which a business is growing. Sales growth is the difference of sales revenue of current year and the sales revenue of last year.
The owner of a bike shop would like to analyze the sales data to determine if the business is growing, declining, or remaining flat. The owner has the following data:
Sales Revenue Last Year =$125,000
Sales Revenue Current Year = $150, 000
As, the sales growth is the difference of sales revenue of current year and the sales revenue of last year. Thus, the sales growth of the business is,
[tex]\rm SG=150000-125000\\SG=25000[/tex]
Hence, the sales growth of the business of owner of a bike shop is $25000 and this business is growing.
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Au cours d'une année, le prix de l'essence à la pompe augmente de 4% puis de 6% et enfin baissé de 10%. Quel est le taux d'évolution du prix de l'essence cette année?
Answer:
[tex] \\black{ \rule{1pt}{900000pt}} \
[/tex][tex]
In four years time Evie will be three times older than she was two years ago, How old will she be in one year
Answer: Evie will be 6 years old in one year.
2 years ago, Evie was 3 years old. Now, she is 5. 4 years after 5 would make her 9. 3*3=9
If In four years time Evie will be three times older than she was two years ago, then in one year's time Evie will be 6
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
In four years time Evie will be three times older than she was two years ago,
Let the age of Evie be x in one year.
By the given information we formulate a equation.
In four years time means we have to add 4 to the present age, x+4.
three times older than she was two years ago can be written as 3(x-2)
Now,
In four years time Evie will be three times older than she was two years ago
x + 4 = 3(x − 2)
Apply distributive property on RHS side
x+4=3x-6
x-3x=-6-4
-2x=-10
x=5
Therefore in one year's time Evie will be x+1 =6, 6 years old.
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What is the circumference of a circle with a radius of 84 inches? (Use 3.14 for Pi.)
Answer:
238.76
Step-by-step explanation:
I believe
Answer:
C≈527.79in
Solution
C=2πr=2·π·84≈527.78757in
i need to find the x and the y
Answer: X=1 Y=-5
Step-by-step explanation:
−9x+2y+−2y=−19+−2y(Add -2y to both sides)
−9x=−2y−19 (Divide by 9 on both sides)
x= 2/9y+19/9 now Substitute 5(2/9y+19/9)+4y=-15=
46/9+95/9=-15 (simplify both sides)
46/9+95/9+-95/9=-15+-95/9 (Add (-95)/9 to both sides) =
46/9y=-230/9 (now divide both sides by 46/9) than equals
y=-5
for X we plug in -5 like this: X=2/9(-5)+19/9 now just evaluate than simplify both sides which equals: 1
If the area of a triangle whose base measures 3 cm is 6 sq.cm, then its height is
O 4 cm
O 2 cm
O 6 cm
O 5 cm
Answer:
then the height would be 2 because 3*2=6
Step-by-step explanation:
Answer:
4 cm
Step-by-step explanation:
area of triangle is: area = (base*height)/2.
since the area is 6 m^2, and base is 3 cm,
6 m^2 = (3 m*height)/2
12m^2 = 3 m*height
height = 4 m
5. A chef prepared 48,462 plates of shrimp. There were 96 shrimp on each plate. How many
shrimp did the chef prepare?
Answer:
4,652,352
Step-by-step explanation:
Plates of shrimp prepared = 48,462
No. of shrimps in each plate = 96
No. of shrimps in total = 48,462 x 96
= 4,652,352
What is EC? please help me I will mark you as brainliest!
Step-by-step explanation:
DB/EC = AD/BE
5/EC = 4/12
5 = 4/12 EC
5×12/4 = EC
15 = EC
EC = 15
help with math homework please! [ image attached + 15 point award ]
Answer:
40°
Step-by-step explanation:
As we have,
[tex]\rm\hookrightarrow[/tex]The Sum of all sides of a triangle is 180°
Now,
[tex]\rm\hookrightarrow 79+x+52+x+73=180\\\\\rm\hookrightarrow x=180-79-52-73\\\\\rm\hookrightarrow x=-12[/tex]
Again, finding the measure of ∡A by putting the value of x.
[tex]\rm\hookrightarrow x+52\\\\\rm\hookrightarrow -12+52\\\\\rm\hookrightarrow 40[/tex]
help me) 2y+x+3x-y
Simplify this expression by combining like terms
YALL PLEASE HELP ME
IDC ABOUT THE POINTS
Which ratio shows all circles are similar
Radius:area
Diameter: circumference
Area; circumference radius
Diameter:
Answer:
Diameter: Circumference
Step-by-step explanation:
Because this is Pi, which is the same for any circle.
Instructions: Rewrite the equation in Slope-Intercept Form.
Answer:
y=−2/5x+2
Step-by-step explanation:
^