Which is the graph of the function f(x) = x2 + 2x – 6? Mark this and return
Answers
Focus: ( -1, -27/4 )
Axis of Symmetry: x = -1
Directrix: y = -29/4
X | Y
———
-3| -3
-2| -6
-1 | -7
0 | -6
1 | -3
The graph of the function f(x) = x² + 2x − 6 is an upward-opening parabola with the vertex at (-1, -7) and a y-intercept at (0, -6). There are no asymptotes for this quadratic function.
Explanation:To find the graph of the function f(x) = x² + 2x − 6, we need to look at the characteristics of this quadratic equation. This is a parabola that opens upward because the coefficient of x² is positive. We can find the vertex of this parabola by using the formula -b/2a for the x-coordinate of the vertex.
Here, a = 1 and b = 2. Applying the formula, we get the x-coordinate of the vertex as -b/2a = -2/(2×1) = -1. Now, we plug this value back into the function to get the y-coordinate of the vertex: f(-1) = (-1)² + 2(-1) − 6 = 1 - 2 - 6 = -7. Therefore, the vertex of the parabola is at (-1, -7). The parabola will intersect the y-axis when x = 0, which gives us the y-intercept f(0) = -6. No asymptotes are present in this quadratic function.
The graph of f(x) is symmetrical about the line x = -1 and has a y-intercept at (0, -6). The vertex at (-1, -7) is the lowest point on the graph since the parabola opens upwards. Thus, we are looking for a graph with these characteristics to represent the function f(x) = x² + 2x − 6.
Related Questions
determine whether each equation is a linear equation. write yes or no. if yes, write the equation in standard form. if the answer is no, circle the part that makes it no
1. y = 4 - 2x
Answers
the equation in standard form is;
2x + y = 4
hope this helped, God bless!
The given equation y = 4 - 2x is a linear equation, however, it is not in standard form. The standard form is 2x + y = 4.
Explanation:The equation y = 4 - 2x is indeed a linear equation. A linear equation is an equation that represents a straight line when graphed. It generally has the form 'y = mx + b' where 'm' represents the slope of the line, and 'b' represents the y-intercept. Here, 'm' is -2 and 'b' is 4.
However, it is not currently in standard form. The standard form of a linear equation is 'Ax + By = C', where A, B, and C are integers, and A and B are not both zero. To write the equation in standard form, we can re-arrange it as 2x + y = 4.
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if it takes Joan one and a half hours to watch a movie, how many films can he watch in ten and a half hours
Answers
steps:
10 1/2 divided by 1 1/2
How many radians are contained in a central angle that is 2/3 of a circle?
Answers
The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The central angle that is 2/3 of a circle will be given as,
⇒ 2π × (2 / 3)
Simplify the expression, then we have
⇒ 2π × (2 / 3)
⇒ 4π / 3 radian
The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.
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Every 3 days Marco fills up his car with gas. Every 8 days he washes his car. On what day will Marco fill his car with gas and wash it?
Answers
A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?
A) 8 mm^3
B) 27 mm^3
C) 7.2 mm^3
D) 12 mm^3
Answers
Sam gets $1000 dollars per month. She has to spend $20 a day on transportation, she also needs to buy groceries each week and have $30 extra spending money per week. How much money should be spent on food per day?
Answers
1,000 ÷ 30 = $33.33/day. This is her daily budget.
Transportation cost = $20/day.
Spending money/day = $30/week ÷ 7days/week = 4.28 /day
Daily Budget:
33.33 = transport + spending money + groceries
33.33 = 20 + 4.28 + groceries Subtract 24.28 from each side:
9.05 = groceries
$9.05 per day should be spent on groceries, assuming she doesn't want to save any of her income.
Find 14/15−1/3 . Write your answer as a fraction in simplest form.
Answers
~PutarPotato
Suppose that one worker can produce 15 cookies, two workers can produce 35 cookies together, and three workers can produce 60 cookies together. what is the average product of the first two workers?
Answers
Prove that if b is a square matrix then b+b^t is symmetric
Answers
[tex](\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top[/tex]
and so [tex]\mathbf B+\mathbf B^\top[/tex] is indeed symmetric.
Marika Perez’s gross biweekly pay is $2,768. Her earnings to date for the year total $80,272. What amount is deducted from her pay for Social Security taxes if the rate is 6.2%? What amount is deducted for Medicare, which is taxed at 1.45%?
Answers
Answer:
The deduction for social Security tax is $4976.86 and the deduction for Medicare tax is $1163.94 .
Step-by-step explanation:
Marika Perez’s gross biweekly pay is $2,768. Her earnings to date for the year total $80,272.
What amount is deducted from her pay for Social Security taxes if the rate is 6.2%?
[tex]0.062\times80272=4976.86[/tex] dollars
What amount is deducted for Medicare, which is taxed at 1.45%?
[tex]0.0145\times80272=1163.94[/tex] dollars
What is the remainder obtained by dividing x7 x5 1 by the generator polynomial x3 1?
Answers
The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]
Given:
The generator polynomial is [tex]{x^3} + 1.[/tex]
The polynomial is [tex]{x^7} + {x^5} + 1[/tex]
Explanation:
There are two methods of dividing the two polynomials.
(1). Synthetic division
(2). Long division method
The fraction can be expressed as,
[tex]{\text{Fraction}}= \dfrac{{{x^7} + {x^5} + 1}}{{{x^3} + 1}}[/tex]
The denominator of the fraction is [tex]{x^3} + 1[/tex] and the numerator of the fraction is [tex]{x^7} + {x^5} + 1.[/tex]
Divide [tex]{x^7} + {x^5} + 1[/tex] by [tex]{x^3} + 1[/tex] to obtain the remainder and the quotient of the polynomial.
The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]
Kindly refer the image attached below.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Long division method
Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree, cubic polynomial, quadratic equation.
Final answer:
To find the remainder of the polynomial division of x^7 + x^5 + 1 by x^3 + 1, one would perform polynomial long division or synthetic division, continuing until the degree of the remainder is less than the divisor.
Explanation:
The student is asking how to find the remainder of a polynomial division. Specifically, they want to know the remainder when dividing x^7 + x^5 + 1 by the polynomial x^3 + 1. To solve this, one would typically use long division of polynomials or synthetic division. The process is similar to long division with numbers. We would start by looking at the highest degree terms of both polynomials and divide them, then multiply the divisor by the result and subtract from the dividend. Repeat this process until the degree of the remainder is less than the degree of the divisor. Since finding the remainder requires us to consider terms up to x^2, we are essentially looking for the result of division that does not perfectly divide, similar to how 7 divided by 3 leaves a remainder.
the sum of the measures of the three of a angles of triangle is 180. In a triangle, the measures of three angles are x,x-5 and x+23. What is the measure of each angle
Answers
x + x-5 + x +23 = 180
combine like terms:
3x +18 = 180
subtract 18 from each side:
3x = 162
divide both sides by 3
x = 162 / 3 = 54
Angle x = 54 degrees
Angle x-5 = 54-5 = 49 degrees
Angle x +23 = 54 +23 = 77 degrees
Line M passes through the points (–5, 9) and (–1, 9).
Answers
Let me tell you why, first the y intercepts are not changing, the x intercepts are just changing which means that the line will be horizontal. You can also prove this by actually graphing the points and connecting the dots.
Two, a horizontal line always has a slope of zero, slope is rise over run, when rise = 0, no matter what the run is the slope will be zero.
For example 0/9 = 0, 0/1 = 0.
A machine laying underground cable can place 125 meters of cable in 5 minutes
Answers
So, 25 meters of cable can be placed in 1 minute.
The ratios are:
125:5 = 25:1
Another way to write the ratio is:
125/5 = 25/1
I hope this helps:)
The machine lays cable at a rate of 25 meters per minute. This is calculated by dividing 125 meters by 5 minutes.
To determine how quickly the machine can lay underground cable, we need to calculate the rate of cable it places per minute. We start by noting that the machine can lay 125 meters of cable in 5 minutes.
We calculate the rate as follows:
Divide the total length of cable by the total time: 125 meters / 5 minutes = 25 meters per minute.This means the machine lays cable at a rate of 25 meters per minute.
Complete Question: A machine laying underground cable can place 125 meters of cable in 5 minutes. What is the rate per minute?
What is another way to write 46
Answers
Final answer:
The number 46 can be written as 'forty-six', 'XLVI' in Roman numerals, '101110' in binary, '56' in octal, '2E' in hexadecimal, a sum or product of other numbers, or in scientific notation as 4.6 x 10ⁱ.
Explanation:
There are several ways to write the number 46 in mathematics. One alternative way to express the number is by using words, such as 'forty-six'. Another method is to use Roman numerals, which would be 'XLVI'. Additionally, 46 can be represented in other numerical bases; for example, in binary, it is '101110', in octal, it is '56', and in hexadecimal, it is '2E'. If we dive into mathematics, 46 can also be written as a sum of other numbers, such as 23 + 23, or a product of primes, which for 46 is 2 x 23. Lastly, 46 can be expressed in scientific notation as 4.6 x 10±, though this form is more commonly used for very large or very small numbers.
Which fraction is equivalent to 4 over negative 9?
A.) -4 over 9
B) 4 over 9
C) -4 over -9
D) 9 over 4
Answers
Answer:
A) -4 over 9
Step-by-step explanation:
We have the fraction [tex]\frac{4}{-9}[/tex] the equivalent of this fraction is [tex]\frac{-4}{9}[/tex]
[tex]\frac{4}{-9}= \frac{-4}{9} =-\frac{4}{9}[/tex]
Both fractions are the same and equivalent, the negative sign makes the whole fraction negative regardless of whether it is in the numerator or denominator.
Jackson earned $60 and put 1 5 of those earnings into his savings account. How much did he put into his savings account?
Answers
Answer:
12
Step-by-step explanation:
=1x60
5x1
=60
5
12
Barbara D’Angelo’s bank granted her a single-payment loan of $1,000 for 100 days at 12% ordinary interest. What is the amount of ordinary interest owed?
Answers
I=prt
I interest owed?
P principle 1000
R interest rate 0.12
T time 100days/360days
360 days in a year which ordinary interest means
I=1,000×0.12×(100÷360)
I=33.33. ..Answer
Hope it helps!
Ms. Winter makes homemade bath soaps and bottles of lotion. In her inventory, she had 48 bath soaps and 64 bottles of lotion. She wants to use all of her inventory to make as many gift baskets as she can use using the same number of bath soaps and the same number of lotion bottles in each gift basket. She will be able to make at most ? gift baskets. Each basket will contain ? bath soaps and ? bottles of lotion.
Answers
The trick here is to determine which common factors 48 and 64 have.
Factors of 48 are 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Factors of 64 are 2, 4, 8, 16.
Note that the common factors are 2, 4, 8 and 16.
Also note that there are a total of 48+64 bottles, all of which must be used.
Since there are more bottles of Lotion than there are bottles of Soap,
the number of Lotion bottles in each basket will be greater than the number of Soap bottles in that basket. S and L together equal 48+64 = 112.
We want to maximize the number of baskets that can be created. Call this number N.
N(S+L) = 112. Because there are more Lotion bottles than there are Soap bottles, S = (48/64)L, or S = 3L/4
Imagine that N baskets are created. Each basket will contain L bottles of Lotion and 3L/4 bottles of Soap.
L and S must both be integers, so that we're dealing only in whole, full bottles of lotion and soap.
Let's make a table here:
N L S=3L/4 Total # of bottles of S and L
16 4 3 16(4+3) =112
This was my first guess! We could make 16 baskets, each containing
4 bottles of lotion and 3 bottles of soap.
Try again:
N L S=3L/4 Total # of bottles of S and L
16 4 3 16(4+3) =112
12 8 6 12(8+6) = 168 (this doesn't work since
there are only 112 bottles, total.
The constraints here are as follows:
1) S is always (3/4) of L: S = 3L/4, and both S and L must be integers.
2) N(S+L) must equal 112.
There's probably an algebraic solution to this problem. You might want to think about this and see whether you can create and solve a system of linear equations that produces the same optimal results:
"16 baskets containing 8 bottles of lotion and 6 bottles of soap"
satisfies the requirement that S = 3L/4, and also the requirement that N(S+L)=112.
Officer Brimberry wrote 8 tickets for traffic violations last week, but only 5 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answers
(8-5)/(8)
3/8=0.375
*100 to get percentage
0.375*100=37.5% decrease
Answer:
The percent decrease is [tex]37.5\%[/tex]
Step-by-step explanation:
we know that
[tex]8\ tickets[/tex] ------> represent the [tex]100\%[/tex]
so
by proportion
Find the percent decrease
[tex]\frac{100}{8}\frac{\%}{tickets} =\frac{x}{(8-5)}\frac{\%}{tickets} \\ \\x=100*(8-5)/8\\ \\x=100*3/8\\ \\x=37.5\%[/tex]
A pizza parlor has 8 different toppings and 3 different cheeses to choose from on the menu. How many pizza combinations are possible if each pizza has 1 topping and 1 cheese
Answers
Final answer:
To find the number of pizza combinations available using 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, one multiplies the number of topping choices by the number of cheese choices, giving 8 x 3 = 24 possible combinations.
Explanation:
Calculating Pizza Combinations
When calculating the number of possible pizza combinations with 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, we use basic counting principles. Each pizza can be thought of as a combination of one topping and one cheese. Since these choices are independent, we multiply the number of options for toppings by the number of options for cheeses to find the total combination possibilities. This results in 8 toppings multiplied by 3 cheeses, giving 24 possible combinations.
The formula used is straightforward: Number of combinations = Number of toppings × Number of cheeses.
Pizza Combination Calculation Example
For instance, if you were at a pizza parlor where you could choose from pepperoni, mushrooms, onions, and 5 other toppings, along with mozzarella, cheddar, and one other cheese, you could create 24 unique pizzas. Just pick one topping and one cheese, and that's your combination.
Last year Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pick up what was his average cost per month for phone service and garbage pick up?
Answers
So 98.4 / 12 = 8.2 and next part 79.2 / 12 = 6.6
Mr. Henderson spent $8.2 a month for phone service and $6.6 for garbage pick up.
A = (97.40 + 79.20)/2
You finish.
Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation? (1 point) 1/8 mile per hour, 1/8 hour per mile, 1 mile per hour, 8 hours per mile
Answers
miles / hr = 96/12 = 8 miles per hr
hr / mile = 12/96 = 1/8 hr per mile <==
Answer:
I believe the answer is 1/8 hour per mile
Step-by-step:
I don't know. I just believe that that is the most reasonable answer to this question and I have this question as well, it might seem hard it's really not.
Each box holds 10 cartons of milk.there are 300 cartons of milk.how many boxes are there?
Answers
The answer is 30 boxes
An animal park has 120 gazelles. If the population increase 5% in on year, how many gazelles will the park have next year?
Answers
The number of gazelles will the park have next year will be 126 if An animal park has 120 gazelles. If the population increase 5% in on year.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
An animal park has 120 gazelles. If the population increase 5% in on year,
= 5% of 120
= 6
= 6 + 120
= 126
Thus, the number of gazelles will the park have next year will be 126 if An animal park has 120 gazelles. If the population increase 5% in on year.
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Which product represents the fraction of the circle that is shaded?
A. 3/4 x 1/2
B. 2/3 x 3/4
C. 1/4 x 3/4
D 3/4 x 3/4
Answers
Answer:
D 3/4 × 3/4
Step-by-step explanation:
The part of the circle that is black is 1/4 of the circle. The remaining 3/4 is divided by the dashed lines into 4 equal parts, so each of those parts is 1/4 of 3/4 of the circle. 3 of the parts are shaded blue, so those represent ...
... 3/4 × 3/4 . . . of the circle
The correct product that represents the fraction of the shaded circle is D. 3/4 x 3/4.
Explanation:The correct answer is D. 3/4 x 3/4.
The fraction represents the shaded part of the circle. We can determine the shaded area of the circle by multiplying the fraction of the radius by the fraction of the circumference that is shaded. In this case, 3/4 x 3/4 would yield a product that represents the fraction of the circle that is shaded.
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Which of the following is an example of a proper fraction?
A. 7⁄6
B. 4⁄3
C. 3⁄4
D. 4⁄4
Answers
Hope this helps!
if 45 grams of a drug are contained in 200 mL how many grams are contained in 80 ml
Answers
45/200g have 1ml
0.225g have 1ml
0.225*80 have 80 ml
18 g have 80ml
A rectangular room is 22 meters longer than it is wide, and its perimeter is 1616 meters. find the dimension of the room.
Answers
1616 meters= 2 (L+w) substitute for L
1616m+ 2(w+22m+w) divide each side by 2
808m= 2w+22m subtract 22m from each side
786m=2w divide each side by 2
393m=w Anwer: The width is 393 meters
L=w+22m=393m+22m=415m Answer: The length is 415 meters
In his bookstore Toby places 21 books on shelves with 7 books on each shelf how many shelves does Toby need