Answer:
f(x) = (x + 2)(x - 5)(x - 6)
Step-by-step explanation:
given the zeros of f(x) are x = a, x= b and x = c, then the factors are
(x - a), (x - b) and (x - c)
The function is then the product of the factors
f(x) = (x - a)(x - b)(x - c)
Here zeros are x = - 2, x = 5 and x = 6, thus the factors are
(x + 2), (x - 5) and (x - 6), so
f(x) = (x + 2)(x - 5)(x - 6) ← in factored form
Final answer:
To create a polynomial with zeros at -2, 5, and 6, the factored form is (x + 2)(x - 5)(x - 6).
Explanation:
To write a polynomial function in factored form with zeros at −2, 5, and 6, we start by creating factors based on these zeros. Each zero corresponds to a factor of the polynomial where the variable x is set equal to the zero value. Therefore, the factors would be (x + 2), (x - 5), and (x - 6). We then multiply these factors together to get the polynomial.
The factored form of the polynomial is then (x + 2)(x - 5)(x - 6). If you wanted to write this polynomial in standard form, you would expand the factors to get x³ - 9x² + 4x + 60.
Subtract: (2x3+7x2−4)−(2x2+4x−10)
To subtract the given expressions, first, simplify each expression separately by combining like terms. Then subtract the second expression from the first expression by distributing a negative sign and adding it to the first expression.
Explanation:To subtract the given expressions, (2x^3+7x^2-4) - (2x^2+4x-10), we need to simplify each expression separately and then subtract them. First, combine like terms within each expression. Then, subtract the terms of the second expression from the first expression. This can be done by distributing a negative sign to each term in the second expression and then adding it to the first expression.
So, (2x^3+7x^2-4) - (2x^2+4x-10) = 2x^3+7x^2-4 - 2x^2-4x+10.
Combining like terms, we get 2x^3+(7x^2-2x^2)+(-4-4x)+(10). Simplifying further, we have 2x^3 + 5x^2 - 4x + 6. Therefore, the result of the subtraction is 2x^3 + 5x^2 - 4x + 6.
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who has fulton virtual
Answer:
no i don't sry
Step-by-step explanation:
Fulton Virtual provides competency based, personalized middle and high school learning options for FCS students throughout the district. This page is where students request and access Fulton Virtual courses. Parents can access the Fulton Virtual parent portal here too.
Simplify the following expression log(x^4)-log(x^3)
Answer:
log x
Step-by-step explanation:
Using the rule of logarithms
• log [tex]x^{n}[/tex] ⇔ n log x
Hence
log [tex]x^{4}[/tex] - log x³
= 4 log x - 3 log x
=log x
The value of logx⁴ - logx³ will be logx.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
If you want to write 1 in logarithm then it will be log(base).
The first method →
Given,
⇒ logx⁴ - logx³
By log property that loga7 = 7loga
⇒ 4logx - 3 logx
⇒ logx
The second method →
This question can also be solved by another log property that
logm - logn = log(m/n)
Since given,
logx⁴ - logx³ = log(x⁴/x³) = logx
Hence, The value of logx⁴ - logx³ will be logx.
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2. Simplify
(1) 41
5a 2a
(u)
4x-4
*+2x-3
a-5b
2a+b
(iii)
2
5
Answer:
Can you take a pic of the problem if you can't type it out?
Step-by-step explanation:
Answer:
3/10a
Step-by-step explanation:
4/5a - 1/2a
4 × 2a - 1 × 5a/5a × 2a
8a - 5a/10a²
3a/10a²
3/10a
-TheUnknownScientist
Choose a number line to model the following situation:
Pedro deposited $35 in his savings account, then withdrew $50.
Answer: Number 4.
Since Pedro deposited $35, the line would start at 0 and go up to positive 35. However, Pedro then withdrew $50- which is more than he has in his account, so he would have $-15, which means he'd owe a fee.
Good luck,
LaciaMelodii :)
Answer:
d). or the 4th choice
Step-by-step explanation:
hope this helped!!
if the diameter of a circle is 50 yards ,the radius is
If the diameter of a circle is 50 yards the radius must be 25 yards.
This is because the radius is always half the diameter of the circle. Since we know the diameter is 50 yards, half of 50 is 25 so the radius must be 25 yards.
Have a great day!
The radius of the circle is 25 yards.
What is a Circle ?A circle is a round shaped figure which has all its points in one plane and the distance between all the points on its circumference to the center of the circle is equal .
It is given that
Diameter of a circle is 50 yards.
Radius of a circle = Diameter of circle / 2
Radius of the circle = 50/2 = 25 yards
Therefore the radius of the circle is 25 yards.
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4. With an eccentricity of 0.25, Pluto's orbit is the most eccentric in the
solar system. The length of the minor axis of its orbit is approximately
10,000,000,000 km. Find the distance between Pluto and the sun at
perihelion and aphelion (perihelion is the point where it is closest to the
sun, and aphelion is the point where it is furthest from the sun.) Round
your answers to the nearest kilometer.
aphelion
At aphelion, the distance between Pluto and the sun is approximately 8,000,000,000 km.
Explanation:The distance between Pluto and the sun at aphelion can be calculated using the formula:
Distance at aphelion = length of the minor axis / (1 + eccentricity).
Plugging in the given values, we get:
Distance at aphelion = 10,000,000,000 km / (1 + 0.25).
Calculating the result gives us a distance of approximately 8,000,000,000 km.
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Weights of Andrews cats are 8 pounds, 15 pounds, 18 pounds, 15 pounds, and 12 pounds. Which statements are true about the weights of Andrews cats? Select the four that apply.
A. The mean is 13.6 pounds
B. The median is 16 pounds
C. The range is 10 pounds
D. The mode is 15 pounds
E. The mean is greater than the median
F. The median and the mode are the same
Answer:
a,b,d,f
Step-by-step explanation:
Please Help!!
Use Euler’s formula to write in exponential form.
Answer:
C, [tex]4e^{i(7\pi/4)}[/tex]
Step-by-step explanation:
To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:
[tex]e^{ix}=\cos{x}+i\sin{x}[/tex]
Given the complex number [tex]2\sqrt{2}-2i\sqrt{2}[/tex], we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.
One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression [tex]2(\sqrt{2}-i\sqrt{2})[/tex]
Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression [tex]4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right)[/tex] , and now we have something to work with.
Looking back at Euler's formula [tex]e^{ix}=\cos{x}+i\sin{x}[/tex], we can map our expression inside the parentheses to the one on the right side of the formula, giving us [tex]\cos{x}=\frac{\sqrt2}{2}[/tex] and [tex]\sin{x}=-\frac{\sqrt2}{2}[/tex], or equivalently:
[tex]\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x[/tex]
At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so [tex]x=\frac{7\pi}{4}[/tex], and we can finally replace our expression in parentheses with its exponential equivalent:
[tex]4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}[/tex]
Which is c on the multiple choice section.
What is the mean of the set of data?
6, 7, 10, 12, 12, 13
6
7
10
11
Answer:
10
Step-by-step explanation:
Mean is all the given numbers in the set added together then divided by the total amount of numbers
6+7+10+12+12+13= 60
60÷6=10
Answer:10
Step-by-step explanation: Mean is all the given numbers in the set added together ,then divided by the total amount of numbers
6+7+10+12+12+13= 60
60÷6=10
4y^2 - 37 = 27, what is the positive value of y?
Answer:
y = 4Step-by-step explanation:
[tex]4y^2-37=27\qquad\text{add 37 to both sides}\\\\4y^2=64\qquad\text{divide both sides by 4}\\\\y^2=16\to y=\pm\sqrt{16}\\\\y=-4\ or\ y=4[/tex]
To solve for 'y' in the equation 4y^2 - 37 = 27, you isolate y^2, take the positive square root, and find that the positive value of y is y = 4.
Explanation:To find the positive value of 'y' from the equation 4y^2 - 37 = 27, we first need to isolate y. Starting with 4y^2 - 37 = 27, add 37 to both sides to get 4y^2 = 64. Divide both sides by 4 to isolate y^2, leading to y^2 = 16. Finally, take the square root of both sides. Remember that the square root of a number gives both positive and negative solutions. However, because the question asks for the positive value, we ignore the negative root. Thus, the positive value of y is y = 4.
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please help me i dont get it at all
y = 218.2. The lenght of side y by trigonometry is 218.2.
In order to solve this problem we are going to use the angles and sides of a right triangle and its relation by expressions that we call trigonometric ratios.
In the image we can see that the lenght of the opposite leg is 141 , we do not know the lenght of the adjacent leg y and the hypotenuse x. The key to solve this problem is to use trigonometric ratios and the equation tan θ = sin θ/cos θ = opposite leg/adyacent leg = 141/y
Clear for y for the equation tan θ = sin θ/cos θ = 141/y, we obtain:
y = arctan θ (141)
y = arctan (43°)(141) = 218.2
I need help with this question
ANSWER
Option D
EXPLANATION
The given function is
[tex]y = \sqrt{16x - 32} - 3[/tex]
We factor 16 under the radical.
[tex]y = \sqrt{16(x - 2)} - 3[/tex]
[tex]y = \sqrt{16} \times \sqrt{(x - 2)} - 3[/tex]
[tex]y = 4 \sqrt{x - 2} - 3[/tex]
This is the graph of
[tex]y = 4\sqrt{x } [/tex]
translated 2 units right and 3 units down.
The last option is the correct choice.
Which inequality represents the
following situation times 5 less
than a number is no more than 27?
[tex]\frac{3}{5}(x - 5) \leq 27[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: Option D
The inequality that represents the situation is:
[tex]\frac{3}{5}(x-5)\leq 27[/tex]
following situation
Step-by-step explanation:
Suppose an unknown number X.
That number minus 5 is:
[tex]x-5[/tex]
Now, [tex]\frac{3}{5}[/tex] times the unknown number minus 5 is:
[tex]\frac{3}{5}(x-5)[/tex]
We know that all this expression is not greater than 27.
Then we use the symbol "less or equal than" ([tex]\leq[/tex]) to represent the situation
[tex]\frac{3}{5}(x-5)\leq 27[/tex]
I really need help with this!!
Answer:
Step-by-step explanation:
10 contain both chocolate and caramel
There are 18 candies.
3 don't contain either chocolate or caramel
12 contain chocolate.
There are 18 - 12 - 3 that are not accounted for. So we have 3 that are not mentioned. Those 3 must contain just caramel.
So it should be filled out like this
contain caramel Do not contain Caramel
10 2
3 3
The Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits. Suppose your chosen number is 3079 .
(a) What is the probability that the winning number matches your number exactly?
(Enter your answer rounded to four decimal places.)
=
(b) What is the probability that the winning number has the same digits as your number in any order?
(Enter your answer rounded to four decimal places.)
Answer:
a) P(a)= 0.0001
b) P(b)= 0.0024
Step-by-step explanation:
Given:
Chosen number = 3079
Possible numbers that have chance of winning from 0000 to 9999= 10,000
Winning condition= if made choice matches the winning digits
Now
a)What is the probability that the winning number matches your number exactly?
From 0000 to 9999, only one time can the number 3079 can be the winning number, so
P(a)= 1/10000
= 0.0001
b)What is the probability that the winning number has the same digits as your number in any order?
Winning numbers from 0000 to 10000 that have same digits as 3079 are
4 x 3 x 2 x 1 = 24 ways
Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:
0379
0397
0973
0937
0793
0739
3079
3097
3970
3907
3790
3709
7039
7093
7930
7903
7390
7309
9073
9037
9370
9307
9730
9703
P(b)= 24/10000
=0.0024 !
Which expression represents the number of ways that a president and vice president can be chosen out of a group of 15 people?
Answer: The answer is 15 * 14
Step-by-step explanation:
You start with 15 people to choose from to select a president, so you have 15. After removing one person 15-1,=14 you have fourteen people to choose from, to select a vice president. This gives you 15*14.
The expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.
What is Permutation?Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
[tex]^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
The number of people that are available for the post of the president is 15, while the number of people that are available for the post of vice-president after the president is selected is 14. Therefore,
Number of ways in which president and vice-president can be selected
= ¹⁵P₂
= 15 × 14
Hence, the expression that can be used to represent the number of ways that a president and a vice-president can be chosen out of a group of 15 people is 15×14 or ¹⁵P₂.
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Solve the equation for x square root x-8+2=7
Square root x=13
x=169
Hope you get it!
To solve the equation x^2√x-8+2=7, follow these steps: combine like terms, square both sides, simplify, take the cube root, and simplify again to find x = 3.
Explanation:To solve the equation x2√x-8+2=7, we need to isolate the variable x. Here are the steps:
Combine like terms: x2√x = 3.Square both sides of the equation to eliminate the square root: (x2√x)2 = 32.Simplify: x3 = 9.Take the cube root of both sides: (∛x3) = (∛9).Simplify: x = 3.Therefore, the solution to the equation is x = 3.
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what does 6v+2-4=-3 equal?
Answer: v = [tex]-\frac{1}{6}[/tex]
6v + 2 - 4 = -3 Combine like terms
6v - 2 = -3 Add 2 to both sides
6v = -1 Divide both sides by 6
v = [tex]-\frac{1}{6}[/tex] Answer!
The price of a watch was increased by 20% to 198. What was the price before the increase?
To find the original price before the increase, divide the new price by 1 + the percent of increase.
198 / 1.20 = 165
The original price was $165
The price before the increase was $ 165
What is percentage?Percentage can be said as a part of a whole expressed in hundredths .
How to know what was the price of the watch before the increase?Let the price of the watch be $ x
According to the problem,
The price of a watch was increased by 20% to $ 198.So, we can write x + 20x/100 = 198
⇒ 6x/5 = 198
⇒ x = 165
∴ The price before the increase was $ 165
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Suppose you deal three cards from a regular deck of 52 cards. What is the probability that they will all be jacks?
Answer:
Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]
Step-by-step explanation:
We are given that we deal with three cards from a regular deck of 52 cards.
We are to find the probability of getting all three Jacks.
There are a total of 4 jacks in a regular deck of 52 cards.
Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]
Example: 1, 6, 2, 3
Proportion is 1:2=3:6
25) 3, 6, 7, 14
Proportion is _________________
26) 2, 6, 5, 15
Proportion is _________________
27) 7, 2, 14, 4
Proportion is _________________
28) 2, 2, 1, 4
Proportion is _________________
29) 10, 5, 8, 4
Proportion is _________________
30) 3, 12, 8, 2
Proportion is _________________
25) proportion is 3:6=7:14
26) proportion is 2:6=5:15
27) proportion is 2:4=7:14
28) proportion is 1:2=2:4
29) proportion is 4:8=5:10
30) proportion is 2:8=3:12
What is the value of x?
Answer: Whats the whole question?
Step-by-step explanation:
what are the solutions of tye quadratic equation below 3x²-x=11
Answer:
Step-by-step explanation:đáp án a
∆=b²-4ac= 1² - 4*3*(-11)=133
=>√∆=√133
X=(-b±√∆)/2a
X=(-(-1)±√133)/2*6
X=(1±√133)/6
Solve the equation for x.
the square root of the quantity x minus 6 end quantity plus 3 equals 10
A. x=1
B. x=13
C. x=43
D. x=55
ANSWER
D. x=55
EXPLANATION
The given radical equation is
[tex] \sqrt{x - 6} + 3 = 10[/tex]
Add -3 to both sides
[tex] \sqrt{x - 6} = 10 - 3[/tex]
[tex] \sqrt{x - 6} =7[/tex]
Square both sides.
[tex] { (\sqrt{x - 6})}^{2} = {7}^{2} [/tex]
[tex]x - 6 = 49[/tex]
Solve for x to get:
[tex]x = 49 + 6 = 55[/tex]
Factored form of 5(q-9)+c(q-9)
Answer:
(q-9) (5+c)
Step-by-step explanation:
Factor out the common factor. In this case, q-9.
5(q-9) + c(q-9)
(q-9) (5+c)
You sell an automobile part for $9.98, which includes a $.40 sales tax. The article cost you $8.75.
What percentage markup are you charging (to the nearest tenth)?
Answer:
9.5%
Step-by-step explanation:
Buying price of the part= $ 8.75
Selling price of the part= $ 9.98
sale tax= $0.40
Selling price before sale tax= $9.98-$ 0.40 = $ 9.58
Make-up amount charged= $9.58- $8.75 = $ 0.83
As a percentage= (0.83/ 8.75) ×100
=9.5%
Can someone help me solve the blanks PLEASE
Step-by-step explanation:
You need to remember that
[tex] log( \frac{a}{b} ) = log(a) - log(b) [/tex]
and
[tex] log(ab) = log(a) + log(b) [/tex]
then the solution is
[tex] log( \frac{r}{st} ) = log(r) - log(st) \\ = log(r) - ( log(s) + log(t) ) \\ = log(r) - log(s) - log(t) [/tex]
Solve for x
2(x+1)=8
Provide step by step instructions
Step-by-step explanation:
2 * (x + 1) = 8 | :2
x + 1 = 4 | -1
x = 3
Answer:
x = 3
Step-by-step explanation:
2 ( x + 1 ) = 8
⇒ Expand brackets
2 x + 2 = 8
⇒ Minus 2 from both sides
2 x = 6
⇒ Divide by 2 from both sides to isolate x
x = 3
(1) 1 UU
15. Line segment RW has endpoints R(4, 5) and W6, 20). Point P is
on RW such that RP:PW is 2:3. What are the coordinates of point P?
(1) (2,9) (2) (0, 11) (3) (2, 14) (4) (10,2)
14
Answer:
P = (4.8, 11)
Step-by-step explanation:
P = 3R + 2W
RP + PW
= 3(4,5) + 2(6,20)
2 + 3
= (12,15) + (12,40)
5
= (24,55) = (4.8, 11)
5
Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is
on RW such that RP: PW is 2:3. the coordinates of point P would be (0, 11).
What is the coordinate of the point which divides a line segment in a specified ratio?Suppose that there is a line segment {AB} such that a point P(x,y) lying on that line segment{AB} divides the line segment {AB} in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
the coordinate of A is (x_1, y_1)
and the coordinate of B is (x_2, y_2)
Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is
on RW such that RP: PW is 2:3.
[tex](x,y) = \left( \dfrac{2(6) + 3(-4)}{2+3} , \dfrac{2(20) + 3(5)}{2+3} \right)\\\\(x,y) = \left( \dfrac{12- 12}{5} , \dfrac{40+15}{5} \right)\\\\(x,y) = \left( \dfrac{0}{5} , \dfrac{55}{5} \right)\\\\(x,y) = (0, 11)[/tex]
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