what quadratic has a graph with x-intercepts 6 and -6?
a)y=x^2-6
b)y=x^2-36
c)y=x^2+36
d)y=x^2-12x+36
Answers
y=x²-36----> (x+6)*(x-6)
the x-intercepts are
x=6
x=-6
therefore
the answer is
the option
b)y=x^2-36
see the attached figure
Related Questions
Bob can type 2 letters in 4 hours while Bill can do it in 6. How many hours would it take them, working together, to type six letters?
Answers
r1 = 2/4 = 1/2 letter / hour
The production rate of Bill is given by:
r2 = 2/6 = 1/3 letter / hour
Thus, the production rate of both is:
r1 + r2 = 1/2 + 1/3 = 5/6 letter / hour
Then, the production of 6 letters is given by:
rate * time = letters
(5/6) t = 6
t = (6/5) 6
t = 36/5 = 7 1/5 hours = 7hr 12 min
Answer:
it would take them, working together, to type six letters about:
7hr 12 min
Answer:
It would take them 7.2 hours.
What are the factors of x^2-64
Answers
a^2 - b^2 = a^2 - b^2
so
x^2-64
=x^2 - 8^2
= (x + 8)(x - 8)
The factors of x^2 - 64 are (x - 8) and (x + 8), derived by recognizing the expression as a difference of squares and applying the formula a^2 - b^2 = (a - b)(a + b).
Explanation:The question asks about the factors of x^2-64. This expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b). In this case, x^2 is a^2, and 64 is b^2, with b being 8 since 82 = 64. Applying the formula, we get:
x^2 - 64 = (x - 8)(x + 8)
This shows that the factors of x^2-64 are (x - 8) and (x + 8). This process of factoring by recognizing patterns, especially the difference of squares, is a useful algebraic skill when simplifying expressions or solving equations.
If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?
4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC
Answers
The ratio of similar sides to triangles should be equal AC/XC=BC/YC BC=BY+YC BC=4+7=11
AC/10=11/7 or 7/11=10/AC the ratio above should be used for calculation of AC
Answer:
The correct option is 4.
Step-by-step explanation:
In triangle ABC and XYC,
[tex]\angle BAC=\angle YXC=60^{\circ}[/tex] (Given)
[tex]\angle BCA=\angle YCX[/tex] (Reflexive Property)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle XYC[/tex]
The corresponding sides of similar triangles are proportional.
Since triangle ABC and XYC, therefore
[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]
[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]
[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]
[tex]\frac{10}{AC}=\frac{7}{11}[/tex]
Therefore option 4 is correct.
n circle A shown below, m Arc BC is 61° and m Arc EF is 76°: Points B, C, E, F lie on Circle A. Lines BE and CF pass through point D creating angle EDF. Measure of arc BC is 61 degrees and What is m∠FDE?
Answers
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
So the answer is 68.5°
Answer:
The correct answer is 68.5°
The calculated result of the angle FDE is 68.5°. Whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.
m<FDE = 1/2( Arc BC + Arc 76)
m<FDE = 1/2 (61° + 76°)
m<FDE = 137/2 = 68.5°
Give Brainliest if you please
What is the measure of the angle?
Answers
Measure of the angle=65°+90°=155°
We can conclude that the measure of the bigger angle in the picture is 155°
So the angle is 90 degrees + 65 degrees = 155 degrees
The fourth one is the answer
What is the area of a regular hexagon with a side length of 12 cm
Answers
More exactly would be 374.12.
Hope this helps!
Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to S10. Round to the nearest hundredth.
Answers
[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}\\\\S_{10}=4\cdot \dfrac{(-\frac{1}{2})^{10}-1}{-\frac{1}{2}-1}=4\cdot \dfrac{(\frac{1}{1024}-1)}{(-\frac{3}{2})}\\\\=\dfrac{8}{3}\cdot \dfrac{1023}{1024}=\dfrac{341}{128}[/tex]
The sum is approximately 2.66.
Am I correct in thinking that the answer to this derivative problem is B?
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Answers
dy/dx = x(1+y)
dy/(1+y) = x dx .... separate variables
int[dy/(1+y)] = int[x dx] ... apply integral to both sides
ln(1+y) = (1/2)x^2+C ... see note below
1+y = e^{(1/2)x^2+C}
1+y = e^C*e^{(1/2)x^2}
1+y = Ce^{(1/2)x^2}
y = Ce^{(1/2)x^2}-1
Answer is actually choice C (not choice B)
note: we would use absolute value bars for the natural log on the left side, but because y > -1, this means 1+y > 0. So there's no need to worry about if 1+y is negative
-----------------------------------------------------
Checking the answer:
y = Ce^{(1/2)x^2}-1
dy/dx = d/dx[ Ce^{(1/2)x^2}-1 ]
dy/dx = d/dx[(1/2)x^2]*Ce^{(1/2)x^2}
dy/dx = (1/2)*2x*Ce^{(1/2)x^2}
dy/dx = x*Ce^{(1/2)x^2} ... we get some messy expression
x*(1+y) = x*(1+Ce^{(1/2)x^2}-1)
x*(1+y) = x*Ce^{(1/2)x^2} .... we get the same messy expression as before
So this shows that dy/dx = x*(1+y) is a true equation for y > -1 and y = Ce^{(1/2)x^2}-1, which confirms the right answer.
Wai recorded the length of each wire needed for a science project. What is the total length of wire needed?
Answers
we know that
the attached figure is a frequency table
Multiply each number of Length by its frequency
The product is the total amount for that value
Add the products
so
(1/8)*1+(1/4)*1+(1/2)*3+(3/4)*8+(1)*4+1 3/8*(2)
1 3/8----> 11/8
=(1/8)*1+(1/4)*1+(1/2)*3+(3/4)*8+(1)*4+11/8*(2)
=(1/8)+(1/4)+(3/2)+(6)+(4)+11/4
=(1+2+12+48+32+22)/8
=117/8-----> 14.625-----> 14 5/8 ft
the answer is
14.625 ft or 14 5/8 ft
Answer:
14 5/8
Step-by-step explanation:
multiply each number by it's frequency the product is the total value .
New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 inches tall. the scale of the model to the actual statue is 1:232. what is the height of the actual statue to the nearest foot?
Answers
Quick need the answer!
Answers
please help asap 50 pts
Answers
Your answer should be C.
[tex]The\; vertex\; is\; at\; 19,361\; so\; your\; answer\;is\;c![/tex]
Q: what is the complete factorization of the polynomial below x^3+4x^2-x-4?
A. (x+1)(x-1)(x+4)
B. (x-1)(x-1)(x-4)
C. (x+1)(x-1)(x-4)
D. (x-1)(x-1)(x+4)
Answers
The solution is Option A.
The factorized form of the polynomial equation A = x³ + 4x² - x - 4 is given by B = ( x + 1 ) ( x - 1 ) ( x + 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the factorized equation be represented as = B
Now , let the equation be A
The value of A is given by A = x³ + 4x² - x - 4
On simplifying the equation , we get
A = x³ + 4x² - x - 4
Taking x² as the common term in the first two terms of the equation ,
A = x² ( x + 4 ) - x - 4
The equation can be further simplified as
A = x² ( x + 4 ) - ( x + 4 )
Taking ( x + 4 ) as the common term in the first two terms of the equation ,
A = ( x² - 1 ) ( x + 4 )
Now , ( x² - 1 ) can be simplified as ( x + 1 ) ( x - 1 )
So , the value of B is
B = ( x + 1 ) ( x - 1 ) ( x + 4 )
Therefore , the value of B is ( x + 1 ) ( x - 1 ) ( x + 4 )
Hence , the factorized equation is ( x + 1 ) ( x - 1 ) ( x + 4 )
To learn more about equations click :
https://brainly.com/question/19297665
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I am first going to try finding the tangent line at this point:
Take the derivative:
dy/dx = (3x^2 - e^x)/2y
Solve using (0, 1)
dy/dx = (0 - 1)/6 = -1/6
I believe that -1/6 is the slope of the tangent line, so the slope of the normal line should be +6, right?
Answers
[tex]e^x-x^3+y^2=10[/tex]
[tex]y^2=x^3-e^x+10[/tex]
Take the derivative of both sides.
[tex]2y \dfrac{dy}{dx} = 3x^2-e^x [/tex]
[tex]\dfrac{dy}{dx}= \dfrac{3x^2-e^x}{2y}[/tex]
Plug in (0, 3) and you get -1/6.
The derivative of a function at a certain point is the slope of the tangent of that point.
This is because the derivative is supposed to represent the rate of change for the function, and the slope of a line represents a constant rate of change. The rate of change of a function at a certain point is constant, so a line can be used to represent it. This line is the tangent line.
It is a property of perpendicular lines to have slopes that are negative reciprocals of another. The negative reciprocal of -1/6 is 6, so you are correct.
The slope of the normal is 6.
Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?
Answers
One half life 500 mg to 500/2 = 250 mg
One half life 250 mg to 250/2 = 125 mg
Etc .......
Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Explanation:To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.
Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.
So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:
1000mg / 62.5mg = 16.
Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:
16 x 6 = 96.
Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
A bag contains 5 5 green marbles, 10 10 yellow marbles, 4 4 red marbles. two marbles are drawn without replacement which means that once the first marble is selected it is not put bag into the bag. it is not replaced. what is the probability of drawing a green marble then a red marble?
Answers
Number of green marbles = 5
Number of red marbles = 4
P(Green, then red) = (4/19)(5/18) = 5/28
Answer: 5/28
The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit
Answers
To calculate the area, multiply 15 and 6, then divide the product by 2.
15 × 6 = 90
90 ÷ 2 = 45
The area of this triangle is 45.
A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease
A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?
Answers
[tex]P(X) = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of success we want
p = probability of success
Therefore, since the problem tells you that X is the number of subjects who test positive for the disease, you will have:
[tex]P(X) = \frac{30!}{0!(30-0)!} 0.02^{0} (1-0.02)^{30-0} [/tex]
= 1 · 1 · 0.98³⁰
= 0.5455
Hence, the probability of none of the 30 subjects testing positive to the desease is 54.55%
B) In a binomial distribution, the mean is given by the formula:
μ = n · p
= 30 · 0.02
= 0.6
And the standard deviation is given by the formula:
σ = √[n·p·(1-p)]
= √[30·0.02·0.98]
= √0.588
= 0.77
Hence, the mean is 0.6 and the standard deviation is 0.77
C) This test is not very viable: 30 subjects are a sample too small compared to the population (millions of people who need to be tested), the probability of finding that all the 30 subjects are healty is only a little bit over 50%, the standard deviation is too high compared to the mean, and 2% of false positive is a percentage too high to consider the test viable.
The dot product of u with itself is 12. what is the magnitude of u?
Answers
we know it's dot product is 12, thus
[tex]\bf \ \textless \ a,b\ \textgreater \ \cdot \ \textless \ a,b\ \textgreater \ \implies (a\cdot a)+(b\cdot b)\implies \boxed{a^2+b^2=12}\\\\ -------------------------------\\\\ ||\ \textless \ a,b\ \textgreater \ ||=\sqrt{a^2+b^2}\implies \sqrt{\boxed{12}}[/tex]
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
jen is thinking of a number. the product of this number and 3.4 is 176.8. find jens number.
Answers
The product of the number and 3.4 is 176.8, so we can write the equation as:
3.4x = 176.8
Dividing by 3.4 on both sides, we get:
x = 52
Thus, Jen is thinking of 52 as his number
Let the unknown number equal X. We are given that the product of X and 3.4 is equal to 176.8. The term "product" implies the use of multiplication. With this knowledge, we can represent the problem using the following formula:
3.4x = 176.8
Now divide both sides of the equation by 3.4:
x = 52
We have now proven that Jen is thinking of the number 52.
I hope this helps!
Write the expression 5x+4x^2(2x+7)-6x^2-9x as a polynomial in standard form
Answers
5x + 8x³ + 28x² - 6x² - 9x
8x³ + 22x² - 4x
This can be simplified to:
2x(4x² + 11x - 2)
I don't know which of those answers you are looking for.
Answer:
8x^3 + 22x^2 - 4x
Step-by-step explanation:
5x+4x^2(2x+7)-6x^2-9x
Open the bracket
5x + 8x^3 + 28x^2 - 6x^2 - 9x
= 8x^3 + 28x^2 - 6x^2 - 9x + 5x
= 8x^3 + 22x^2 - 4x
In standard form, the polynomial 5x+4x^2(2x+7)-6x^2-9x is 8x^3 + 22x^2 - 4x
A group of 12 people attend a meeting. Every pair of people shook hands with each other. How many handshakes were there?
Answers
So there will be 11+10+9+8+7+6+5+4+3+2+1=66 handshakes.
Hope this helped!
Find the area of the rectangle below (3x-2) (4x-7)
Answers
-> 12x^2-21x-8x+14
= 12x^2 - 29x + 14
So the area of the rectangle would be 12x^2 - 29x + 14.
Hope this helps. If you have any questions, place it in the comment section below.
If and only if this assumption is correct, then the area is L * W, or
(3x-2)(4x-7) = 12x^2 -13x + 14.
Find the surface area of each right regular pyramid. a pentagonal pyramid with base sides 1.5 meters, base area 3.9 m2, and slant height 4 meters
Answers
since the base area is 3.9 m2, we could just add that to the total at the end.
since the base edge is 1.5 m and the height is 4m, we could find the area of the face by doing (1.5 times 4)/2 which would give us 3m2.
Since there are 5 faces(pentagonal), we would multiply 3 times 5, and would get 15m total for all the triangle faces.
so to get the total surface area, you would add 15 + 3.9 (which was the base area) and get 18.9m2....
....;);) hope this helps
A museum charges a school $200 to hold a trip + $2 entrance fee per person. The students must share the total cost of the trip equally include the entrance feee for 8 teachers. What is the function Y(x) that gives that gives the cost per X person attending the trip?
Answers
This is because 16 needs to be added to the base amount since the teachers cost is automatically added in.
Which represents a quadratic functionWhich represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3
Answers
Answer:
[tex]f(x) = -7x^2 -x +2[/tex] represents a quadratic function.
Step-by-step explanation:
A polynomial of degree two is called quadratic function,
Also, degree of polynomial is the highest power of its monomial ( individual term with non zero coefficient ),
Since, [tex]f(x) = 2x^3 + 2x^2 -4[/tex] has degree 3,
⇒ [tex]f(x) = 2x^3 + 2x^2 -4[/tex] is not a quadratic function,
[tex]f(x) = -7x^2 -x +2[/tex] has degree 2,
⇒ [tex]f(x) = -7x^2 -x +2[/tex] is a quadratic function,
[tex]f(x) = -3x+2[/tex] has degree 1,
⇒ [tex]f(x) = -3x+2[/tex] is not a quadratic function,
[tex]f(x) = 0x^2 + 3x -3[/tex] has degree 1,
⇒ [tex]f(x) = 0x^2 + 3x -3[/tex] is not a quadratic function,
Mind helping someone out?
I've kinda been stuck on this problem and it's my last math problem for the day.
Answers
The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form? Show your work.
8 square units
20 square units
24 square units
28 square units
Answers
we know that
surface area=area A +area B+area C+area D+area E+area F
area A=area F
area B=area area D
area C=area E
so
surface area=[2*1]+[4*2]+[4*1]+[4*2]+[4*1]+[2*1]----> 28 units²
the answer is
28 units²
Answer:
the answer is d:)
Step-by-step explanation:
i took the quiz on edge and got 100:D
Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.
Answers
A correlation can be called association when it can be ascertained that the result in one variable is as a result of the result of the other variable. Though correlation is a condition for causation, but correlation does not imply causation.
Therefore, given that there were a strong correlation between the variables n and p, the true statement is "n may cause p".
what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)
Answers
Answer:
[tex](30\sqrt{3}-21\sqrt{6})[/tex]
Step-by-step explanation:
We have to find the product of the expressions.
[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]
= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)
= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]
= [tex]15\sqrt{12}-21\sqrt{6}[/tex]
= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]
= [tex]30\sqrt{3}-21\sqrt{6}[/tex]
= [tex](30\sqrt{3}-21\sqrt{6})[/tex]