Answer:
(0.4, -57.9)
Step-by-step explanation:
y = 3x³ + 12x² - 10x - 56
dy/dx = 9x² + 24x - 10 = 0
x = [-24 +/- sqrt(24² - 4(9)(-10))]/(2×9)
x = -3.033006505, 0.3663398379
d²y/dx² = 18x + 24
For minima, d²y/dx² > 0 which is at x = 0.3663398379
y = 3(0.3663398379)³ + 12(0.3663398379)² - 10(0.3663398379) - 56
y = -57.90544608
What is the complete factorization of x2 + 2x − 63? A. (x + 21)(x − 3) B. (x − 9)(x + 7) C. (x + 9)(x − 7) D. (x − 21)(x + 3)
Answer:
(x + 9)(x - 7)
Step-by-step explanation:
We want to factorize [tex]x^2 + 2x - 63[/tex]
We need to find two numbers such that their product is -63 and they add up to +2. The two numbers are +9 and -7:
[tex]x^2 + 9x - 7x - 63\\\\= x(x + 9) -7(x +9)\\\\ = (x +9)(x -7)[/tex]
The complete factorization is (x + 9)(x - 7)
The factored form of the expression x² + 2x - 63 is (x + 9)(x - 7).
What is the factored form of the expression?Given the expression in the question:
x² + 2x - 63
To determine the complete factorization of the quadratic expression x² + 2x - 63, we aim to break it down into its simplest factors.
This is achieved through factoring, a process of identifying the expressions that, when multiplied, result in the original quadratic expression.
x² + 2x - 63
Now, find a pair of integers whose sum equals 2,
and whose product equals -63.
We use integers 9 and -7.
Next, rewrite the quadratic expression using these factors:
(x + 9)(x - 7)
Therefore, the complete factorization of x² + 2x - 63 is (x + 9)(x - 7).
Option C) (x + 9)(x - 7) is the correct answer.
Learn more about factorization here: brainly.com/question/20293447
#SPJ6
Write the composite number for each prime factorization. You may wish to use a calculator.
5) 22 x 3 x 52
6) 2x32x7
7) 33 x 5
8) 2 x 53
Only one of those is actually a prime factorization. Demand better from your teacher. Anyway, I think they're just asking us to take out the calculator and enter the multiplication into it.
5) 22 isn't prime, neither is 52. Answer: 3432
6) 32 isn't prime. Answer: 448
7) 33 isn't prime. Answer: 165
8) Finally a real prime factorization. Answer: 106
x - x equals ?............
Answer:
0
Step-by-step explanation:
if x stade for any number like 5 then it will be 5-5=0
hope this helps you out need more help ask me
A bag contains yellow marbles and blue marbles, 23 in total. The number of yellow marbles is 7 less than 2 times the number of blue marbles. How many yellow marbles are there? Please help its due really soon!
Answer:
b=10, a=13
Step-by-step explanation:
let s number of yellow = a
number of blue = b
we have
a+b =23
2b - a = 7
->a+b +2b -a = 23+7
-> 3b = 30
->b = 10
->a = 13
What is the nth term to this sequence 18,16,14,12
What is the nth term to this sequence 18,16,14,12 ?
Answer: 4
Explanation:
1. 18
2. 16
3. 14
4. 14
5. 12
6. 10
7. 8
8. 6
9. 4
Answer:
Hey!
The nth term for your sequence is -2!
Step-by-step explanation:
18 - 2 = 16
16 - 2 =14
And so on! (the nth term of a sequence is basically the differences between the different terms!)
HOPE THIS HELPS!!
I need help with this question please.
Answer:
work is shown and pictured
15 POINTS + BRAINLIEST
true or false box plot questions
Answer:
b is false, idk about a the median is the middle line its 70 in this case
Answer:
a. true
b. false
Step-by-step explanation:
a. 2 parts of diagram are 50% and that's 62 - 70
b. median height is 70 in
Suppose x varies inversely with y and y varies inversely with z. How does x vary with z? Justify your answer algebraically
Answer:
x varies inversly inversly with z,
so it Maries linearly.
x to y and then to a can be expressed as
x = m/y
y = n/z
so we can say
x = m/(n/z) = m/n * z
m & n could be any constant numbers, like 5 or 3.7
Here is an example where both are just one:
x = 1/y
y = 1/z
so we can say
x = 1/(1/z) = 1/1 * z
(would really, really appreciate the brainliest)
What is the probability that I will choose a cat owner and a bird owner. Please help. Thanks
Answer:
The probability is 1/36.
Step-by-step explanation:
2/3 are dog owners
1/6 are cat owners
1/6 are bird owners
If you choose two owners, there is a 1/6 chance that you will choose a cat owner and a 1/6 chance you will choose a bird owner. Each of these are independent, so you simply multiply 1/6 by 1/6.
1/6 * 1/6= 1/36
Solve for b.
-3b = 9 - 4b
B=
Answer:
b=9
Step-by-step explanation:
move the 4b over to the other side by adding it to both sides
[tex]-3b(+4b)=9-4b(+4b)[/tex]
[tex]1b=9[/tex]
How do you simplify [tex]\frac{\sqrt{2} +\sqrt{6} }{\sqrt{8} + \sqrt{6} }[/tex]?
The trick is to exploit the difference of squares formula,
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:
[tex](\sqrt8+\sqrt6)(\sqrt8-\sqrt6)=(\sqrt8)^2-(\sqrt6)^2=8-6=2[/tex]
Whatever you do to the denominator, you have to do to the numerator too. So
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}{(\sqrt8+\sqrt6)(\sqrt8-\sqrt6)}=\dfrac{(\sqrt2+\sqrt6)(\sqrt8-\sqrt6)}2[/tex]
Expand the numerator:
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{2\cdot8}+\sqrt{6\cdot8}-\sqrt{2\cdot6}-(\sqrt6)^2[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=\sqrt{16}+\sqrt{48}-\sqrt{12}-6[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=4+\sqrt{48}-\sqrt{12}-6[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(\sqrt4-1)[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6)=-2+\sqrt{12}(2-1)[/tex]
[tex](\sqrt2+\sqrt6)(\sqrt8-\sqrt6}=-2-\sqrt{12}[/tex]
So we have
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+\sqrt{12}}2[/tex]
But √12 = √(3•4) = 2√3, so
[tex]\dfrac{\sqrt2+\sqrt6}{\sqrt8+\sqrt6}=-\dfrac{2+2\sqrt3}2=\boxed{-1-\sqrt3}[/tex]
Let x be a positive integer. If (-3)ºx (-3)* = (-3)14,
what is x?
Answer:
[tex]-3^{\circ \:}x\left(-3\right)=\left(-3\right)\cdot \:14 : x = \frac{840}{180^{\circ \:}}[/tex]
Decimal Form:
[tex]x = -267.38030...[/tex]
Step-by-step explanation:
[tex]-3^{\circ \:}x\left(-3\right)=\left(-3\right)\cdot \:14[/tex]
Remove Parentheses: [tex](-a) = -a[/tex]
[tex]-3^{\circ \:}x\left(-3\right)=-3\cdot \:14[/tex]
Multiply the numbers: [tex]3 * 14 = 42[/tex]
[tex]-3^{\circ \:}x\left(-3\right)=-42[/tex]
Divide both sides by: [tex]-3^{\circ \:}\left(-3\right)[/tex]
[tex]\frac{-3^{\circ \:}x\left(-3\right)}{-3^{\circ \:}\left(-3\right)}=\frac{-42}{-3^{\circ \:}\left(-3\right)}[/tex]
Simplify:
[tex]x=-\frac{840}{180^{\circ \:}}[/tex]
Hope I helped. If so, may I get brainliest and a thanks?
Thank you, have a good day! =)
Which expression can be used to convert 22 Australian dollars to US dollars
Answer: 22 AUD x 1.2USD / 1AUD
Step-by-step explanation: The expression would be like this: 22 Australian dollars/1.2 (value of Australian dollars to US dollars) = X US dollars/1 We would get the value of x by multiplying 1 to 22 then divide it by 1.2 and we would get the US conversion from it. We could also put the expression 22=1.2x directly and we would get the US conversion from it.
Write this number in scientific notation.
0.0000071=
Answer:
7,1 × 10-⁶
Step-by-step explanation:
Once you move the comma 1 time by right (,) you have -1, so by moving it six times, you have 7,1 × 10-⁶
How do I do Radicals?
Answer:
For online calculators you can type sqrt() or just sqrt and it will do it for you
Answer:
See belowStep-by-step explanation:
To simplify radicals that are not perfect squares, we need a new method.
Example: [tex]\sqrt{27}[/tex]
27 is not a perfect square square the square root cannot be used.
[tex]\sqrt{27} = 5.19615242271[/tex]
To solve this, we need to break down the radical into simpler parts.
[tex]\sqrt{27} = \sqrt{3} * \sqrt{9}[/tex]
[tex]\sqrt{9} = 3[/tex]
[tex]\sqrt{3}[/tex] cannot be simplified
[tex]\sqrt{27}[/tex] = 3[tex]\sqrt{3}[/tex]
Good luck on your test!
I'm always happy to help :)
What value of z makes the following equation true?
−3z+3=35
Answer:
-10 2/3Step-by-step explanation:
Given
−3z+3=35Solving for z:
-3z = 35 - 3-3z = 32z = 32/-3z = -10 2/3Ms. Donaldson earns $19.20 per hour for the first 40 hours she works in a week. She earns 1 1/2 times that amount per hour for each hour she works beyond 40 hours in a week. Last week Ms. Donaldson worked 45.5 hours. a) How much money did she earn last week? b) A health insurance payment of $34.75 was deducted from Ms. Donaldson's earnings for the week. After the insurance deduction, payroll taxes equal to 32% of the balance were deducted. What was the amount that Ms. Donaldson received?
Answer:
a) $926.40
b) $606.32
Step-by-step explanation:
a)
If she worked a total of 45.5 hours, she will receive $19.20 per hour in the first 40 hours and 1.5 * $19.20 for the exceeding 5.5 hours, so her earnings is:
19.2 * 40 + 1.5 * 5.5 * 19.2 = $926.40
b)
The deduction is $34.75, so the remaining will be:
926.40 - 34.75 = $891.65
Then, after this deduction, the taxes is 32% of the remaining, so:
891.65 - 0.32 * 891.65 = $606.32
She received $606.32
Create your own equation
Answer:
45+20=65
21+33=54
90+10=100
100+30= 130
Step-by-step explanation:
45+20=65
Doesn't belong as it has an odd numbered answer where as all the others have even answers
HOPE THIS HELPS
correct expression equivalent to 9-(3-6x)
Answer:
6 + 6x
Step-by-step explanation:
9 - (3-6x) = 9 - 3 - (-6x)
= (9-3) +6x
= 6 + 6x
1) expand the bracket
2) group like terms together
3) simplify to form expression
A Lua reflete parte da luz solar que nela incide. Admite que: a luz refletida pela Lua demora 1,28 segundos a chegar à Terra; entre a Lua e a Terra, a luz percorre 300 000 000 de metros em cada segundo; o trajeto da luz é retilíneo. Determina a distância da Lua à Terra. Apresenta o resultado em metros, escrito em notação científica. Mostra como chegaste à tua resposta.
Answer:
3.84 * 10^8 meters
Step-by-step explanation:
As the speed of light is 300,000,000 meters/second and the time that the light takes to go from the moon to the Earth is 1.28 seconds, we can find the distance using the formula:
Distance = speed * time
So we have that:
Distance = 300,000,000 * 1.28 = 384,000,000 meters
In cientific notation, we need the first number to be in the interval from 1 to 10, so we have 3.84, and we have to multiply by 10^8 to reach our result, so we have:
Distance = 3.84 * 10^8 meters
Paul has 27 pet cats. 14 of them are short-haired. 11 of them are kittens. 5 of them are long haired adult cats. How many of them are short haired kittens?
6.The base of an isosceles triangle is 6 cm and its perimeter is 16 cm. Length of each of the equal sides is
Answer:
erm
Step-by-step explanation:
The sides will be:
6cm
6cm
4cm
Answer:
In isosceles triangle two sides are equal . Let the length be x .hence perimeter can be given as x + x + 6 . Therefore 2x + 6 = 16 . And 2x = 10 .and hence x =5 . So the length of each side is 5 cm
Step-by-step explanation:
how are u supposed to find the area only with the circumference?
Answer:
We can find the radius from circumference and then area
Circumference(C) = 2πr
r = C/2π
r = 20/2π
r = 10/π
Area = πr²
Area = π × 10/π × 10/π
Area = 100/π
Area = 100/3.14
Area = 10000/314 = 31.84 cm² (approx)
Area = 32 cm² (Rounding to nearest whole number)
Answer:
32 m²
Step-by-step explanation:
We need to work out the area of the flower garden when we are given the circumference. First we need to know the formula's for area of circle and circumference of circle which are
→ Area of a circle = π × r² where 'r' is the radius
→ Circumference of a circle = 2 × π × r where 'r' is the radius
So we need to form an equation with the circumference of a circle formula and work out the radius in order to find the area so,
In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided by 2 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.
2 × π × r = 20
→ Substitute 3.14 for π
2 × 3.14 × r = 20
→ Simplify
6.28 × r = 20
→ Divide both sides by 6.28 to isolate 'r'
r = 3.18471338
So now we now the radius of the circle we can substitute the radius into the area of circle formula
Area = π × r²
→ Substitute 3.14 for π and r for 3.18471338
Area = 3.14 × 3.18471338²
Area = 31.847133842
To the nearest whole number your answer is 32 m²
Label each point on the number line with the correct value. Click each dot on the image to select an answer. Choices
Answer:
You might need to repost or edit this question - there are no choices or picture.
Answer:
There are no choices.
Step-by-step explanation:
If 5 adult movie tickets cost $25, how much do 11 tickets cost?
Answer:
$55
Step-by-step explanation:
5 tickets = $25
1 ticket = $5 (divide by 5 on both sides)
multiply by 11
11 tickets = 5 ×11
11 tickets = $55
Given find M for MON
Answer:
∠ MON = 15°
Step-by-step explanation:
∠ LOM + ∠ MON = ∠ LON, substitute values
9x + 44 + 6x + 3 = 77, that is
15x + 47 = 77 ( subtract 47 from both sides )
15x = 30 ( divide both sides by 15 )
x = 2
Thus
∠ MON = 6x + 3 = 6(2) + 3 = 12 + 3 = 15°
The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive. Which function best models the data?
A) y = 9,958(0.972)^x
B) y = 0.972(9,958)^x
C) y = 9,219x– 150
D) y = –150x + 9,219
Answer:a
Step-by-step explanation:
Answer:
It is A, y = 9,958(0.972)x
Step-by-step explanation:
Can anybody help me solve this? You must solve for X first.
(Click in picture for full image)
Answer:
45 degrees
Step-by-step explanation:
angle QRS is same as (2x + 3) because it is an isosceles triangle
so, 90 + (2x+3) + (2x+3) =180 degrees
2x+3 +2x+3=180-90
2x+2x +3+3=90
4x+6=90
4x=90-6
4x=84
x=84/4
x=21
substitute x=21 in (2x+3)
2*21+3=45
PLEASE HELP!!
Which of the following is statements is TRUE about the figure.
A. △ABC~ △DFE by AA Similarity Theorem
B. △ABC~ △DFE by ASA Similarity Theorem
C. △ABC~ △DFE by SSS Similarity Theorem
D. △ABC~ △DFE by SAS Similarity Theorem
E. There is not enough information provided
Answer:C
Step-by-step explanation:There is definitely enough info.
And there are no angles so it has to be SSS~ (It's dilated by 1.5 by the way)
Given that events A and B are independent with P(A)=0.24P(A)=0.24 and P(B|A)=0.85P(B∣A)=0.85, determine the value of P(B)P(B), rounding to the nearest thousandth, if necessary.
Answer:
P(B) = 0.85
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
[tex]P(A) = 0.24, P(B|A) = 0.85[/tex]
These events are independent.
This means that [tex]P(A \cap B) = P(A)*P(B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B|A) = \frac{P(A)*P(B)}{P(A)}[/tex]
[tex]P(B|A) = P(B)[/tex]
So
[tex]P(B) = 0.85[/tex]