Graph the equation y=-x^2-12x-35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex
Answers
Please check the image attached aside with the graph of the quadratic equation.
How to graph a quadratic equation by matching three pointsIn this problem we have a quadratic equation, of which we should plot the graph by matching five points. We can make use of its vertex, two roots, y-intercept and other point. First, determine the vertex of the quadratic function:
- x² - 12 · x - (35 + y) = 0
x² + 12 · x + (35 + y) = 0
12² - 4 · 1 · (35 + y) = 0
144 - 4 · (35 + y) = 0
144 - 140 - 4 · y = 0
4 · y = 4
y = 1
- x² - 12 · x = 36
x² + 12 · x + 36 = 0
(x + 6)² = 0
x = - 6
The vertex of the quadratic equation is (x, y) = (- 6, 1).
Second, calculate the roots of the quadratic equation:
- x² - 12 · x - 35 = 0
x² + 12 · x + 35 = 0
(x + 5) · (x + 7) = 0
The roots of the quadratic equation are (x, y) = (- 5, 0) and (x, y) = (- 7, 0).
Third, determine the y-intercept of the quadratic equation:
y = - 0² - 12 · 0 - 35
y = - 35
The y-intercept of the quadratic equation is (x, y) = (0, - 35).
And fourth, find another point by evaluating the quadratic equation:
y = - 1² - 12 · 1 - 35
y = - 48
The remaining point is (x, y) = (1, - 48).
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Related Questions
Factor.
1. 9a²-18a
2. 16a³b³ +32a¹b
3. x2+x^ + xử
4. 3x5 + 4x4 - 5x²
5. 2x³-X
Please Help
Answers
The below mentioned are the factors of given equations
Factorization:
In mathematics, factorization or factoring is the method of expressing a quantity or another numerical component as a product of many factors, typically small or easier components of the same kind.
In the case of integers, ancient Greek mathematicians were the first to consider factorization. They demonstrated the fundamental theorem of arithmetic, which states that any positive integer can be taken account into a prime number product , which cannot be factored into integers greater than 1. Furthermore, this factorization is unique until the order of the factors is changed.
1)[tex]9a^{2}-18a=9a(a-2)[/tex]
2)[tex]16a^{3}b^{3} +32ab=16ab((ab)^{2} +2)[/tex]
3) inappropriate question
4)[tex]3x^{5} +4x^{4} -5x^{2} =x^{2} (3x^{3} +4x^{2} -5)[/tex]
5)[tex]2x^{3} -x=2(x-1)(x+1)[/tex]
Therefore,The above mentioned are the factors of the given questions.
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Rent for the month $ 1,150 monthly take-home salary $ 2,685 spending for food $ 595 cash in checking account $ 550 savings account balance $ 1,990 balance of educational loan $ 2,760 current value of automobile $ 9,800 telephone bill paid for month $ 115 credit card balance $ 285 loan payment $ 180 auto insurance $ 330 household possessions $ 4,400 video equipment $ 2,600 payment for electricity $ 140 lunches/parking at work $ 230 donations $ 260 personal computer $ 1,700 value of stock investment $ 1,110 clothing purchase $ 160 restaurant spending $ 180
Answers
$22,150 is the total assets .
What is total assets?
A person or entity's total assets are all of their possessions combined. Assets are things with economic value that an owner uses over time to reap benefits. These assets are often listed in the accounting records and can be seen on the company's balance sheet if the owner is a business.Total asset = Saving account balance + current value of automobile + video equipment + personal computer + cash in checking account + household possessions + value of stock investment
= $1990 + $9800 + $2600 + $1700 + $550 + $4400 + $ 1110
= $22,150
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Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) I'd say rational number. If p and q are integers, then -(p/a) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
Answers
Given that p and q are integers,
then find out -(p/q) = (-p)/q = p/(-q)
with real world example.
First of all we have know about Integers
a whole number, a number that is not a fraction.
and secondly Rational numbers
A rational number is any number that can be expressed in the form p/q where 'q' is not equal to zero. The quotient of the rational number p/q is nothing but the result that we get when we divide 'p' by 'q'.
For real world contexts we put some value at the place of p and q.
let p=1
q=2
-(1/2) = (-1/2) =(1/-2)
by evaluate it we get ...
-1/2=-1/2=-1/2
Rules for Negative rational numbers
If the rational number takes the form -(p/q), then either p or q takes the negative value. It means that -(p/q) = (-p)/q = p/(-q).If numerator and denominator are of opposite signs.All are less than 0.Hence If p and q are integers, then -(p/a) = (-p)/q = p/(-q).
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if 3^n is a factor of 100!, what is the largest possible value of n
Answers
The largest possible value of n is approximately equal to 331.
What is the largest possible value of the integer n behind a power equation?
In this problem we find a factorial number as the result of a power with a base of 3. First, we need to estimate the maximum possible value of n (as a real number) by using logarithm properties:
3ⁿ = 100!
3ⁿ = 1 · 2 · 3 · ... · 99 · 100
㏒₃ 3ⁿ = ㏒₃ (1 · 2 · 3 · ... · 99 · 100)
n · ㏒₃ 3 = ㏒₃ 1 + ㏒₃ 2 + ㏒₃ 3 + ... + ㏒₃ 99 + ㏒₃ 100
n ≈ 331.090
Second, find the maximum possible integer n related to 100! is found by truncating the result found in the previous section. Hence, the largest possible value of n is approximately equal to 331.
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6-6x=7x-9x-18 the value of x
Answers
Answer:
X = 6
Step-by-step explanation:
6-6X = 7X -9X -18 Combine 7x -9x
6 - 6x = -2x -18 Add 6x to both sides of the equation
6 = 4x - 18 Add 18 to both sides of the equation
24 = 4x Divide both sides by 4
6 = x
Check:
6-6X = 7X -9X -18
6 - 6(6) = 7(6) -9(6) -18
6 - 36 = 42 - 54 -18
-30 = 1-12-18
-30 =-30
Marco's monthly budget is $3550. What is the total amount of money Marco spends monthly on his house payment?
Answers
Cuantos múltiplos de 9 hay entre 60 y 100
Answers
Answer: 5 multiples of 9
Step-by-step explanation:
First take the difference between 100 and 60.
100-60=40
Then divide the difference by 9.
40/9=4.44
4.44 rounded up is 5 ==> 5 multiples of 9
Primero toma la diferencia entre 100 y 60.
100-60=40
Luego divide la diferencia entre 9.
40/9=4,44
4.44 redondeado es 5 ==> 5 múltiplos de 9
Answer:
5
Step-by-step explanation:
9*7 = 63
9*8 = 72
9*9 = 81
9*10 = 90
9*11 = 99
Hay 5 múltiplos de 9 entre los números 60 y 100
Write the equation for the horizontal line that contains point G(4, 8).
Oy=8
O x = 8
O x = 4
O y = 4
Answers
Answer:
y = 8
Step-by-step explanation:
A horizontal line will have the form y = k where k is a constant and determines the distance from the x axis. All points on this line will have a constant y value for all x values
Since the line passes through (4,8) we have y = 8 as the equation for the line
if 52-4x=28, then x=6
Answers
-4*6(x) = -24 so it’s correct but if that’s not the answer try, -24x=24 so it would equal X=-1
E. Sketch the graph of the following functions. Make a table of values.
Answers
The table for each function is presented below and its graphs are attached in this answer.
Function 1
x 3x-5
-2 -11
-1 -8
0 -5
1 -2
2 1
Function 2
x -x+3
-2 5
-1 4
0 3
1 2
2 1
Function 3
x x²-2x+1
-2 9
-1 4
0 1
1 0
2 1
Function 4
x -3x²+1
-2 -11
-1 -2
0 1
1 -2
2 -11
Linear Function
An equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=7x+2. Where:
a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex] .
b= the constant term that represents the y-intercept.
For solving this question, you should plot the points from the given equation and after that draw a line.
What is a Quadratic Function?The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
Function 1First column represents the value of x and the second column represents the value of the function for each value of x
x 3x-5
-2 -11
-1 -8
0 -5
1 -2
2 1
See the figure graph1.
Function 2First column represents the value of x and the second column represents the value of the function for each value of x
x -x+3
-2 5
-1 4
0 3
1 2
2 1
See the figure graph2.
Function 3First column represents the value of x and the second column represents the value of the function for each value of x
x x²-2x+1
-2 9
-1 4
0 1
1 0
2 1
See the figure graph3.
Function 4First column represents the value of x and the second column represents the value of the function for each value of x
x -3x²+1
-2 -11
-1 -2
0 1
1 -2
2 -11
See the figure graph4.
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Please help dont be like last guy if you do help i will give you extra points
Answers
The quotient of 455 ÷ 36 is 12 with a remainder of 23.
How to calculate the value?It should be noted that the subtraction of 360 from 455 will be 95.
Then after that 72 is subtracted from 95 and this will be 23.
Therefore, the quotient is 12 with a remainder of 23.
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A bakery sells hot chocolate in small cups and large cups. The prices are shown on the sign.
Hot Chocolate Prices
Small.........
(8 fluid ounces)
Large.......
(12 fluid ounces)
$2.99 each
%
$3.99 each
The bakery sold 64 cups of hot chocolate today. The ratio of small cups to large cups sold today was 5 to 3.
What percentage of money earned from the hot chocolate sales today was from the sale of large cups? Round the ans
whole percentage. Enter the answer in the box.
Answers
The percentage of money earned from the sale of hot chocolate is 44%.
How much is earned from the sale of hot chocolate?
Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).
Number of large cups bought = (3/8) x 64 = 24
Number of small cups bought = (5/8) x 64 = 40
Total revenue from selling large cups = 24 x 3.99 = $95.76
Total revenue from selling small cups = 40 x 2.99 = $119.60
Total profit = $119.60 + $95.76 = 215.36
Percentage earned from the sale of large cups = (95.76 / 215.36) x 100 = 44%
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For each chore Faith does, her mom gives her $5.50. The equation y=5.5x can be used to represnt this situation. What is the constant of proportioality? What does the constant of proportianality represent in the context of the probelm?
Answers
The constant of proportionality for y = 5.5x will be 5.5.
What is defined as the constant of proportionality?The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, rate constant, unit rate, continuous of variation, and even the rate of change.A directly proportional relationship relation is shown below.
y ∝ x
where
∝ = the proportionality symbol
The variables that are related are y and x. Therefore,
y = kx
where
k is the proportionality constant.
For each chore Faith does, her mom gives her $5.50, which is shown by;
Using y = kx, the equations y = 5.5x can be designed as a directly proportional relationship.
As a result, k = 5.5 has been the proportionality constant.
The proportionality constant for y = 5.5x is 5.5.
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210 sticks of gum each stick sold for 50 cents how much money did i make
Answers
210 x .50 = $105
HELPP I AM STUCK IN THIS PROBLEM AND NEED IT BY TMR!!
Answers
Answer: 100 scores
Step-by-step explanation:
Let the number of points on your fifth test be x
Hence,
[tex]\displaystyle\\\frac{59+80+65+96+x}{5}=80\\[/tex]
Multiply both parts of the equation by 5:
300+x=80*5
300+x-300=400-300
x=100
What is 7[2.5 + 3(12 - 7)] and can you please show me how to do it
Answers
Answer: 122.5
Step-by-step explanation:
First, you have to do the distributive property for all numbers. In order to do that, you must first combine like terms.
Combining like terms are numbers that are in the parenthesis that don't have an exponent, variable, etc. In this case, you would combine 12 and -7 since they are in the same parenthesis case. 12-7 would be 5. Now, you have 7[2.5] + 3(5)]
Next, you use PEMDAS which means multiplication (parenthesis) is next which means you multiply 3 and 5. 3x5 - 15.
After that, you combine like terms again with the 2.5 and the 15 since the 15 is now out of the parenthesis. 2.5 + 15 = 17.5
Finally, you take the 7 and multiply that by 17.5 now that you have those 2 numbers left and they are in the brackets. 17.5x7 is 122.5!
However, if there is a variable to solve for, then the answer would be none/no solution because both sides are not equal.
A+company+packed+8+dark+chocolates+in+a+box+of+32+assorted+chocolates.+which+of+these+does+not+represent+inferential+statistics?+a.)+25%+of+the+chocol
Answers
Answer:
it is 3
Step-by-step explanation:
beacuse i did it
Mr.chong has some money to buy tins of paint. if he buys 18 tins of paint. he will need another $80. if he buys 10 tins of paint, he will have $32 left.
Answers
Amount of one tin of paint is $14 and the total amount Mr. Chong have is $172.
Let amount of one tin of paint = x
Let the total amount Mr. Chong having = y
On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,
18x = y + 80
On rearranging this equation can be written as,
18x - y = 80 equation 1
On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,
10x = y - 32
On rearranging this equation can be written as,
-10x + y = 32 equation 2
On adding equation 1 and equation 2, we get
18x - y -10x + y = 80 + 32
8x = 112
x = (112/8) = 14
On substituting x = 14 in equation 2 , we get
-140 + y = 32
y = 172
So, amount of one tin of paint is $14 and the total amount Mr. Chong have is $172.
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what is the approximate value of this square root? 162‾‾‾‾√ enter your answer, rounded to the nearest tenth, in the box.
Answers
Answer:
If what youre asking is √162, then the answer is 9√2
Step-by-step explanation:
Answer: 12.73
type it in your calculator if you can
What is the solution to |14|-|-14|
Answers
Answer: The solution to |14|-|-14| is 0
Answer:
The answer is 0
Step-by-step explanation:
absolute value of 14 and -14 is 14 and 14 minus 14 equals 0
Suppose a particle is moving along the x-axis so that it’s position at time t is given by the formula:
s(t)=2t^2 -t + 3t^1/3
Find the particle’s velocity and acceleration at time, t=1.
Answers
Answer: It should be 4
Step-by-step explanation:
Just plug in 1 for t, t=1
(solve each system by graphing. Check your solution) questions 11 and 13
Answers
Answer: 10. (2,4) 11. (4,9) 13. (2,-2) 14. (1,2)
Step-by-step explanation:
Just plugged em into desmos & double checked
Answer: 11. (4,0) 13. (2,-2)
Step-by-step explanation:
11.
[tex]\displaystyle\\\left \{ {{y=\frac{1}{2} x+7 } \atop {y=\frac{3}{2}x+3 }} \right. \\\\y=\frac{1}{2}x+7[/tex]
x | 0 | 4 |
y | 7 | 9 |
[tex]\displaystyle\\y=\frac{3}{2}x+3\\[/tex]
x | 0 | 2 |
y | 3 | 6 |
13.
[tex]\displaystyle\\\left \{ {{y=x-4} \atop {y=-x}} \right. \\\\y=x-4[/tex]
x | 0 | 4 |
y | -4 | 0 |
[tex]y=-x[/tex]
x | 0 | 4 |
y | 0 | -4 |
what is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)? (1 point) y − 5
Answers
y - 11 = -3 ( x + 2) is the equation in point-slope form of the line .
What is slope ?
The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").Given points : (0, 5) and (−2, 11)
Slope of the line passing through given points
[tex]m = \frac{y_{2}- y_{1} }{x_{2} - x_{1} } = \frac{11 - 5}{-2 - 0} = \frac{6}{-3} = -3[/tex]
Thus, slope of line passing through given points m=-3
We know that the equation of a line passing through points ( x₀ , y₀) with slope 'm' is ( y - y₀ ) = m(x - x₀)
Thus, equation of a line passing through (−2, 11) with slope m=-3 will be
( y - 11 ) = -3 ( x - (-2))
y - 11 = -3 ( x + 2)
Hence, the equation of line is y - 11 = -3 ( x + 2).
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give the type of triangle that has these angles
27 degrees
63 degrees
91 degrees
Answers
63 degrees = acute triangle
91 degrees = obtuse triangle
An angle is acute when it’s less than 90
And it’s obtuse when it’s greater than 90
I hope this helps!
respond to the following in a minimum of 175 of your own words: how would you explain the differences between the trapezoidal rule and simpson's rule to a first-year student majoring in math? what do these rules solve? what are the error limits of each method? under what circumstances would you use one method instead of the other?
Answers
The differences between the trapezoidal rule and simpson's rule is -
The trapezoidal rule and Simpson's method, the latter a set of formulas of varying complexity, are both Newton-Cotes formulas, that are used to examine and model complex curves.
What is trapezoidal rule?The trapezoidal rule is just an integration rule that divides a curve into small trapezoids to calculate the area under it. A area under the curve is calculated by adding the areas of all the small trapezoids.
Follow the steps below to use the trapezoidal rule to determine the area under given curve, y = f. (x).
Step 1: Write down the total number of sub-intervals, "n," as well as the intervals "a" and "b."Step 2: Use the formula to determine the width of the sub-interval, h (or) x = (b - a)/n.Step 3: Use the obtained values to calculate this same approximate area of a given curve, ba f(x)dx Tn = (x/2) [f(x0) + 2 f(x1) + 2 f(x2) +....+ 2 f(n-1) + f(n)], where xi = a + ixWhat is Simpson's method?Simpson's rule is used to approximate the area beneath the graph of the function f to determine the value of the a definite integral (such that, of the form b∫ₐ f(x) dx.
Simpson's 1/3 rule provides a more precise approximation. Here are the steps for using Simpson's rule to approximate the integral ba f(x) dx.
Step 1: Figure out the values of 'a' & 'b' from interval [a, b], as well as the value of 'n,' which represents the number of subintervals.Step 2: Determine the width of every subinterval using the formula h = (b - a)/n.Step 3: Using the interval width 'h,' divide this same interval [a, b] [x₀, x₁], [x₁, x₂], [x₂, x₃], ..., [xn-2, xn-1], [xn-1, xn] into 'n' subintervals.Step 4: In Simpson's rule formula, substitute all of these values and simplify. b∫ₐ f(x) dx ≈ (h/3) [f(x0)+4 f(x1)+2 f(x2)+ ... +2 f(xn-2)+4 f(xn-1)+f(xn)].Thus, sometimes we cannot solve an integral using any integration technique, and other times we don't have a particular function to integrate. Simpson's rule aids in approximating the significance of the definite integral in such cases.
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what is 39/80 as a decimal
Answers
Answer:0.4875.
Step-by-step explanation:
Answer:
0.48750
explanation:
If 0.25 cm represents 5 feet on a blueprint, what is the actual length of a room that is 8.5 inches long?
Answers
In proportion , 13 ft is the actual length of a room.
What in mathematics is a proportion?
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
0.25 inches 8.5 inches
---------------- = --------------
5 ft x ft
Using cross products
0.25x = 8.5 * 5
Divide each side by 0.25
0.25x/0.25 = 8.5 * 5/0.25
x = 13
x = 13 ft
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Can someone please answer this. I need it today
-19 + 16 + (-42)
Answers
Answer:
-45
Step-by-step explanation:
math
-19 + 16 = -3
-3 + (-42) = -45
zoe walks from her house to a bus stop that is 460 yards away. as zoe's distance from her house increases from 50 yards to 210 yards, her distance from the bus stop varies from incorrect yards to 250 correct yards.
Answers
Adrianna's distance from her house increases from 60 yards to 180 yards, her distance from the bus stop varies from 340 yards to 220 yards.
What is the straightforward meaning of distance?
The distance or length between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour.Adrianna walks from her house to a bus stop that is 400 yards away.
as Adrianna walks to the bus stop the distance between Adrianna and bus stop will b decreasing .
Further As Adrianna's distance from her house is 60 yards then she is 400 -60 = 340 yards away from bus stop
Also As Adrianna's distance from her house is 180 yards then she is 400 -180 = 220 yards away from bus stop .
As Adrianna's distance from her house increases from 60 yards to 180 yards, her distance from the bus stop varies from 340 yards to 220 yards.
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The branch of statistical studies called descriptive statistics summarizes important aspects of a data set. True or false?.
Answers
Yes, The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Here,
We have to find the statement,
''The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.'' is true or not.
What is Descriptive statistics?
Descriptive statistics is a means of describing features of a data set by generating summaries about data samples.
Now,
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Because : Descriptive statistics refers to the summary of important aspects of a data set.
Hence, The statement ''The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.'' is true.
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