Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain.
a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens upward.
c. Because a < 0, the parabola opens downward.
d. Because a > 0, the parabola opens upward.
Answers
When a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards and from the given equation a < 0 that is why the graph of the quadratic equation is a parabola that opens downward.
Given :
Quadratic Function --- [tex]y = -x^2-10x + 1[/tex]
The graph of the quadratic equation is in the shape of the parabola. The generalized quadratic equation is given by:
[tex]ax^2 + bx +c = 0[/tex]
Now, compare the given equation ([tex]y = -x^2-10x + 1[/tex]) with the generalized quadratic equation which is given above.
[tex]a = -2[/tex]
b = -10
c = 1
According to the rules of the graph, when a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards.
Therefore, the correct option is c).
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Related Questions
What is the equation of the circle whose center and radius are given.
center ( 7, -3), radius = 7
Answers
The equation for a circle is
[tex](x - h)^{2} + ( y - k)^{2} = r^{2} [/tex]
(h,k) is the center
r is the radius
Put in the values you know
[tex](x - 7)^{2} + ( y + 3)^{2} = 7^{2}[/tex]
Simplify
[tex](x - 7)^{2} + ( y + 3)^{2} = 49[/tex]
The equation is [tex](x - 7)^{2} + ( y + 3)^{2} = 49[/tex]
Hope this helps!
Plug in the numbers; center is (h, k) and radius is r.
(x - 7)² + (y - -3) = 7²
Simplify to:
(x - 7)² + (y + 3) = 49
A residual plot is shown. Which statements are true about the residual plot and the equation for the line of best fit for the data? Check all that apply.
The equation for the line of best fit is not a good approximation for the data because the points have a curved pattern.
The equation for the line of best fit is a good approximation for the data because the points are random, having no pattern.
The residual plot has a linear pattern.
The points of the residual plot are spread evenly above and below the x-axis.
The residual plot has the pattern of a curve.
The equation for the line of best fit is not a good approximation for the data because the points have a linear pattern
Only right answers, please. This is important for my grade.
Answers
Answer:
answer is 1 & 3 on edg
Step-by-step explanation:
Write a single algebraic rule for the series of transformations: a reflection about the x-axis, a rotation of 90 degrees clockwise, and a translation of 4 units right and 2 units down.
Answers
(x,y) → (x,-y)
A rotation of 90 degrees clockwise
(x,-y) → (-y,-x)
Translating 4 units right and 2 units down
(x,-y) → (-y + 4,-x - 2)
Therefore your answer is (x,y) → (-y + 4,-x - 2)
2x + 4y = 12 converted into slope intercept form (y=mx+b)??
Answers
To convert 2x + 4y = 12 into slope-intercept form, we must put it into y = mx + b form, where m represents the slope of the line and b is the y intercept of the equation. To begin, we should subtract 2x from both sides so that we can get the variable y alone on the left side of the equation.
2x + 4y = 12
4y = -2x + 12
Next, because there cannot be a coefficient on the variable y in this form, we must divide both sides of the equation by 4.
y = -2/4x + 3
Because 2 and 4 are both divisible by 2, we can divide both the numerator and the denominator by 2 to further simplify the equation.
y = -1/2x + 3
Therefore, the answer is y = -1/2x + 3.
Hope this helps!
To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), you subtract 2x from both sides and then divide by 4 to isolate y, resulting in y = -1/2x + 3, where the slope (m) is -1/2 and the y-intercept (b) is 3.
Explanation:To convert the equation 2x + 4y = 12 into slope-intercept form (y=mx+b), we need to solve for y. Here's how you can do it step by step:
Begin with the original equation: 2x + 4y = 12.Subtract 2x from both sides to isolate the y-term: 4y = -2x + 12.Divide each term by 4 to solve for y: y = -½x + 3.Now the equation is in slope-intercept form where m (the slope) is -1/2 and b (the y-intercept) is 3. The slope m is defined as the rise over the run of the straight line, and the y-intercept b is the point where the line crosses the vertical axis, which in this case is when x=0 and y=3.
Find the value of the lesser root of x^2-6x+8=0
Answers
[tex]x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} a=1, b=-6, c=8 [/tex]
[tex]x= \frac{6+/- \sqrt{36-4*1*8} }{2*1} x=(6+/- \sqrt{36-32} )/2 x=(6+/-2)/2 x_{1} =4, x_{2}=2[/tex]
Answer:
The value of lesser root is:
x=2
Step-by-step explanation:
We are given a quadratic equation in terms of variable " x " as:
[tex]x^2-6x+8=0[/tex]
We know that for any quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
The roots of x are calculated as:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
a=1 , b=-6 and c=8
Hence, on solving for roots:
[tex]x=\dfrac{-(-6)\pm \sqrt{(-6)^2-4\times 1\times 8}}{2\times 1}\\\\\\x=\dfrac{6\pm \sqrt{36-32}}{2}\\\\\\x=\dfrac{6\pm \sqrt{4}}{2}\\\\\\x=\dfrac{6\pm 2}{2}[/tex]
Hence, we have:
[tex]x=\dfrac{6+2}{2}\ or\ x=\dfrac{6-2}{2}\\\\x=\dfrac{8}{2}\ or\ x=\dfrac{4}{2}\\\\\\x=4\ or\ x=2[/tex]
Hence, the value of lesser root is:
x=2
After the data was recorded, Mary gives her latest book a rating of 1 star. How will this new rating affect the mean rating of her books? The mean book rating will not change.
Answers
What is the solution set of (x - 2)(x - 3) = 2?
a. {1, 4}
b. {2, 3}
c. {4, 5}
Answers
Remove the brackets. Use Foil
F: x^2
O: -3x
I: -2x
L:(-2)(-3) = 6
What you have now is
x^2 - 3x - 2x + 6 = 2
Step Two
Combine like terms.
x^2 - 5x + 6 = 2
Step Three
Subtract 2 from both sides.
x^2 - 5x + 6 - 2 = 0
x^2 - 5x + 4 = 0
Step 4
Factor
(x - 4)(x - 1) = 0
Step 5
Find the zeros.
x - 4 = 0
x = 4
x -1 = 0
x = 1
Solution Set
(1,4)
Can someone help me please?
Write the equation for finding the nth term of the sequence. 18, 14, 10
Answers
The formula for the [tex] n^{th} [/tex] term of an arithmetic sequence is [tex] a_{n} =a_{1}+(n-1)d[/tex] and in your case [tex] a_{n} =18+(n-1)(-4)=18-4n+4=22-4n[/tex].
If arc AXC = 235°, what is m∠ABC?
a. 117.5°
b. 60°
c. 55°
d. 125°
Answers
Please mark brainlist
Answer:
The correct option is c.
Step-by-step explanation:
Given information: The measure of arc AXC is 235°. Let the center of the circle be O.
The sum of all disjoint arcs is 360°. So,
[tex]Arc(AXC)+Arc(AC)=360^{\circ}[/tex]
[tex]235^{\circ}+Arc(AC)=360^{\circ}[/tex]
[tex]Arc(AC)=360^{\circ}-235^{\circ}[/tex]
[tex]Arc(AC)=125^{\circ}[/tex]
[tex]\angle AOC=125^{\circ}[/tex]
The measure of arc AC is 125°.
Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.
[tex]\angle AOC+\angle ABC=180^{\circ}[/tex]
[tex]125^{\circ}+\angle ABC=180^{\circ}[/tex]
[tex]\angle ABC=180^{\circ}-125^{\circ}[/tex]
[tex]\angle ABC=55^{\circ}[/tex]
The measure of angle ABC is 55°. Therefore the correct option is c.
The diagram shows the locations of John and Mark in relationship to the top of a tall building labeled A.
A) Describe < 4 as it relates to the situation
B) Describe < 3 as it relates to the situation
Answers
a]
∠4 is the angle of elevation as seen by Mark from his location. It is the angle between the horizontal and the line from the object to the observer's eyes.
b]
∠3 is the angle of depression and it is congruent to the angle 5, which is the angle of elevation as seen by John from his location.
Let d(t) =6t^2 be the distance function, find the average velocity from (4, 4.1)
Answers
average v = 4.86 / 0.1 = 48.6
Thomas bought a new backpack that was 30% off the original price. The sale resulted in a $15 discount. What was the original price of the backpack?
a.) $45
b.)$50
c.)$65
d.)$70
Answers
1% = $15 ÷ 30 = $0.50
100% = $0.50 x 100 = $50
Answer: $50 (Answer B)
Final answer:
To calculate the original price of Thomas's backpack, we set up an equation with the information that a 30% discount resulted in a $15 savings, which, when solved, indicates the original price was $50. The correct option is b.)$50
Explanation:
Thomas bought a new backpack at a 30% discount, which saved him $15. To find the original price, we can set up an equation to solve for the original price. Let's denote the original price as 'P'. The equation would therefore be 0.30 * P = $15, meaning 30% of the original price is equal to the $15 discount he received.
First, divide both sides of the equation by 0.30 to isolate 'P':
P = $15 / 0.30
P = $50
Hence, Thomas's backpack originally cost $50 before the discount was applied. Therefore, the correct answer is b.) $50.
In order to conduct a certain experiment, four students are randomly selected from a class of 20. how many different groups of four stdents are possible
Answers
i am assuming this is correct this is how i learned just take all numbers in equation and multiply by each other
A card is drawn randomly from a standard deck of cards. you win $10 if the card is a spade or an ace. what is the probability that you will win the game?
Answers
These two events are not mutually exclusive; this means they can happen at the same time. For two events that are not mutually exclusive,
P(A or B) = P(A) + P(B) - P(A and B)
This gives us
P(spades or Ace) = P(spades) + P(Ace) - P(spades and Ace)
There are 13 spades out of 52 cards.
There are 4 aces out of 52 cards.
There is 1 card that is a spade and an ace out of 52 cards.
13/52 + 4/52 - 1/52 = 16/52 = 4/13
You are selling cookies for your organization. One box of cookies is sold for $3. Thirty percent of the sale price goes to the bakery to pay for the cookies. The rest of the sale price is split evenly between the regional headquarters for your organization, and your local chapter. How much does your local chapter earn for each box of cookies that are sold? How many boxes of cookies do you have to sell to earn $100 for your local chapter?
Answers
(1/2)×($3 - 0.30×$3) = (1/2)×$3×0.70 = $1.05 for each box of cookies
B) If the number you must sell to earn $100 is represented by n, then you have
$1.05×n = $100
n = 100/1.05 ≈ 95.24
To earn $100 for your local chapter, you must sell 96 boxes of cookies.
If you round off 23 to nearest ten.what is the answer
Answers
The amounts of 8 charitable contributions are $100, $80, $250, $100, $500, $1000, $100, and $150.
The mean, median, and mode of the amounts are given below. mean = $285 median = $125 mode = $100
Which value describes the amount received most often?
Answers
I am wondering if the answer to this question is Table B. At x = 1, f'(x) = 1/2. At x = 2, f'(x) = 3. Does this mean that, between 1 and 2, the slope should be greater than 1/2 and less than 3? (e.g. graph B)?
Answers
=========================================================
f ' (1) is shown to be positive
f ' (2) is shown to be positive as well
There are no critical values between x = 1 and x = 2, so f ' (x) is positive on the interval 1 < x < 2, so f(x) is increasing on this interval
All of this points to either choice A or choice B
--------------------------------
Similarly,
f ' (3) is negative
f ' (4) is negative
so f ' (x) is negative where 3 < x < 4 due to no other critical values being between x = 3 and x = 4
Based on these facts alone, the answer is either choice B or choice D
But we know that it can't be choice D as we determined it was between A and B. This rules out choice D
So all that's left is choice B
The equation of a circle is (x−2)2+(y−16)2=169 .
What is the circle's radius?
Enter your answer in the box.
units
Answers
The radius of the circle with the equation (x−2)^2+(y−16)^2=169 is 13 units.
The equation of the circle provided is (x−2)2+(y−16)2=169. In the standard form of a circle's equation, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, we see that 169 represents r2. Hence, to find the radius of the circle, we take the square root of 169.
The radius r is calculated as r = √169 = 13 units. Therefore, the circle's radius is 13 units.
What is the number six million, thirty thousand, expressed in scientific notation? 6.03 × 10^6
6.3 × 10^5
6.3 × 10^6
6.03 × 10^4
Answers
6.3 * 10^6 = 6,300,000
Hope this helps!
So, your answer is: B) 6.3 x 10^6
An equation of the line passing through (6,−3) having slope −35 is
Answers
Now we plug in the point given and solve for b.
- 3 = - 35(6) + b
- 3 = - 210 + b
207 = b
So your equation is:
y = - 35x + 207
The first term of an arithmetic sequence is -5 , and the twelfth term is 1.7 .find the common difference
Answers
a12 = 1.7
a12 = a+(n-1)d
1.7 = -5+(12-1)d
1.7+5 = 11d
6.7/11 = d
0.60 = d
Help please!!! I would appreciate it.
Answers
Explanation:
In this case you need to find the area under the curve, which would essentially be the probability of a value in the sample space.
Now the range given is from 60 to 80; it contains the mini-triangle.
The area of the triangle = (1/2)*base*height
Since base = 80 - 60 = 20
Height = 0.025 - 0 = 0.025 (see in the graph)
Therefore
The area of the triangle = 1/4 = 0.25 which is essentially be the probability.
In percentage form, it is 25% (Option D)
What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?
Answers
Final answer:
The total amount on a $6,500 investment at a 6% annual interest rate compounded yearly for 25 years is approximately $28,353.25, with the interest earned being about $21,853.25.
Explanation:
To calculate the total amount and the amount of interest earned on $6,500 at 6% for 25 years, we need to identify whether the interest is compounded annually, monthly, or if it's simple interest. Since the type of interest isn't specified, we'll assume it's compounded annually, which is common in savings accounts. The formula for compound interest is:
A = P(1 + r/n)nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($6,500)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested or borrowed for, in years (25 years)
For this example, since the interest is compounded annually, n = 1. First, convert the interest rate from a percentage to a decimal by dividing by 100: 6% / 100 = 0.06. Now, plug the values into the formula:
A = $6,500(1 + 0.06/1)1*25
A = $6,500(1 + 0.06)25
A = $6,500(1.06)25
Calculating this out, A, which is the total future amount, comes out to:
A = $28,353.25 approximately
To find out the total interest earned, subtract the principal from the final amount:
Total interest = A - P
Total interest = $28,353.25 - $6,500
Total interest = $21,853.25 approximately
The total amount is about $28,353.25 and the amount of interest earned is about $21,853.25.
Which of the following is the best linear approximation for f(x) = cos(x) near x= π/2
Answers
f(x) ≈ f(a) + f'(a)(x-a)
Evaluating f at π/2
f(π/2) = cos(π/2) = 0
Since f(x) = cos(x), differentiating gets us
f'(x) = -sin(x)
f'(π/2) = -sin(π/2) = -1
So the local liner approximation is
f(x) ≈ 0+ -1(x-π/2)
f(x) ≈ -x+π/2
The answer to this question is -x+π/2
The best linear approximation for f(x) = cos(x) near x = π/2 is L(x) = π/2 - x. This conclusion is reached by finding the slope of the tangent line to the function at x = π/2 (which is the cosine derivative at this point), and then applying the formula for linear approximation.
Explanation:The linear approximation of a function at a certain point is the line tangent to the function at that point. In this case, we want the linear approximation for f(x) = cos(x) near x = π/2. The slope of the tangent line at a point is equal to the derivative of the function at that point, and the cosine derivative is -sin(x). So at x = π/2, the slope is -sin(π/2) = -1.
Now, we use the formula for the linear approximation, which is L(x) = f(a) + f'(a)(x-a). In this case, a is π/2, so we get L(x) = cos(π/2) - 1(x - π/2). Since cos(π/2)=0, the best linear approximation is L(x) = 0 - 1(x - π/2) = π/2 - x.
Note:We use the
cosine derivative
to find the slope of the tangent line and the
linear approximation formula
to find the equation of the line. We also assume a
small-angle approximation
since we are close to x = π/2.
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whats the equation of the line that passes through (3,8) and (6,0)
Answers
WHERE M IS SLOPE
SO
EQUATION OF LINE IS Y-0={(8-0)/(3-6)}[X-6]
¶¶ Y= (-8/3)(X-6)
HERE YOU GO---- {3Y+8X-48=0}
HOPE THIS IS HELPFUL
To begin this problem, we need to use the two points that we are given to find the slope of the line. Slope is defined as the change in y values divided by the change in x values, or rise/run, and is represented by the variable m.
m = (y1-y2)/(x1-x2) = (8-0)/(3-6) = 8/(-3) = -8/3
Now, we can use the slope and one of the points from our given values to create an equation of the line in point-slope form.
y = m(x-h) + k, where a point on the line is (h,k)
y = -8/3(x - 3) + 8
Now, we can distribute our slope and simplify through addition.
y = -8/3x + 8 + 8
y = -8/3x + 16
Therefore, your answer is y = -8/3x + 16.
Hope this helps!
On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?
A.119 yards
B.101 yards
C.10,201 yards
D.1,980 yards
Answers
99ft
A ------------------------- B
| |
20 ft | |
| |
C -------------------------- D
The question is asking you to solve for the diagonal line between points C and B. If you imagine a line there, you actually have the rectangle split into two triangles. So if you have triangle ABC, side CB would be the longest line, or the hypotenuse. That means you can use the Pythagorean Theorem to solve the problem.
A^2 + B^2 = C^2
99^2 + 20^2 = C^2
9,801 + 400 = C^2
10,201 = C^2
Now you solve for the square root of 10,201 to get C.
sqr (10,201) = C
C = 101 yards
Complete the steps in order to write the inverse of f(x) = x + 5 1. = x + 5 2. = y + 5 3. = y 4. = x – 5
Answers
f(x) = x + 5
1. y = x + 5
Switch places from x and y.
2. x = y + 5
Subtract 5.
3. x - 5 = y
Switch sides.
4. y = x – 5
Now we've found our answer.
~ Hope this helps you!
The inverse of the given function y =x+5 is y =x-5.
The given function is:
y =x+5
What is an invertible function?
A function is invertible only if each input has a unique output and each element of the codomain should be mapped.
Step1: check function is invertible i.e. bijective i.e. one-one and onto or not
f(x₁)=x₁+5
f(x₂) = x₂+5
f(x₁) = f(x₂)
x₁+5 =x₁+5
x₁=x₂
So, the function is one-one or injective.
For onto range and codomain should be same.
Step 2: interchange x and y
x=y+5
Step3: bring 5 to the left side of the equation.
x-5 = y
Step4: write in y=f(x) form
y = x-5
Therefore, the inverse of the given function y =x+5 is y =x-5.
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Use the guess-and-check method to solve the equation: 6(x + 3) + 1 = 31
Answers
A square sheet of paper is folded diagonally. What is the length of LN?
A) 10 in.
B) 20 in.
C) 10√2
D) 5√4
Answers
Length of side of the paper is 10 in
LN is the diagonal of the square
Answer:
C) 10√2 in
Explanation:
A square has 4 equal sides. This means that all four sides of the square are equal to 10 in.
Now, folding a square diagonally will lead to the formation of two congruent right-angled triangles (check the attachment).
We need to get the length of LN which is the hypotenuse of the right-angled triangle.
This means that we can apply the Pythagorean theorem:
(hypotenuse)² = (side1)² + (side2)²
(LN)² = (10)² + (10)²
(LN)² = 200
LN = √200
LN = 10√2 in
Hope this helps :)