Answer:
x(x - 2)(x + 5)x = 0, x = 2, x = -5Step-by-step explanation:
x^3 + 3x^2 - 10x
~Factor
x(x - 2)(x + 5)
Solve for the zero.
x(x - 2)(x + 5) = 0
We know that; x = 0, x - 2 = 0, and x + 5 = 0
x = 0
x - 2 = 0
x = 2
x + 5 = 0
x = -5
Best of Luck!
Here we are provided with an polynomial of degree 3 and we have to factorise it first and then we have to compute it's zeroes.
Given Polynomial:
x³ + 3x² - 10xTaking common x from all the 3 terms,
➝ x(x² + 3x - 10)
Factorising through Middle term factorisation,
➝ x(x² + 5x - 2x - 10)
➝ x{x(x + 5) - 2(x + 5)}
➝ x(x - 2)(x + 5)
Hence, Factorised !!
Now equating to 0 to find the zeroes of the poly.
➝ x(x - 2)(x + 5) = 0
That means,
x = 0x - 2 = 0x + 5 = 0So, the zeroes of the polynomial is 0, 2 or -5
And we are done....
Carry On Learning [tex]![/tex]
I have 7 hundreds blocks, 5 tens blocks, and 8 ones blocks. I use my blocks to model two 3-digit number. What could my two number be?
758
(if you don't have to use all the blocks)
757
750
708
754 etc
Two balls are placed in a box according to the following process: 1. A fair coin is tossed. A white ball is placed in the box if a head occurs, otherwise a red ball is placed in the box. 2. The fair coin is tossed again. A red ball is placed in the box if a tail occurs, otherwise a white ball is placed in the box. Balls are drawn from the box three times in succession (always with replacing the drawn ball back in the box). On all three occasions a red ball is drawn from the box. There are two pieces of information available: the process by which balls are placed in the box and the 3 observations of a ball drawn from the box. Making use of all relevant available information, what is the probability that both balls in the box are red
Answer:
The probability that both balls in the box are red given that all three occasions a red ball is drawn from the box is [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Let RRR be the event in which red Balls are drawn from the box three times in succession
Let rr be the event that two red balls are placed in a box
Let rw be the event the first red ball was placed and then white ball was placed
Let wr be the event the first white ball was placed and then red ball was placed
Let ww be the event that two white balls are placed in a box
Now we know that :
[tex]P(rr)=P(rw)=P(wr)=P(ww)=\frac{1}{4}[/tex]
Probability of getting red Balls three times in succession given that both are placed red balls in box:
[tex]P(RRR|rr)=1[/tex]
Probability of getting red Balls three times in succession given that one ball is red and another is white in a box
[tex]P(RRR|wr)=P(RRR|rw)=\frac{1}{2^3}=\frac{1}{8}[/tex]
Probability of getting red Balls three times in succession given that both are placed white balls in box:
[tex]P(RRR|ww)=0[/tex]
Now we are supposed to find the probability that both balls in the box are red given that all three occasions a red ball is drawn from the box i.e. P(rr|RRR)
So, we will use bayes theorem
[tex]P(rr|RRR)=\frac{P(RRR|rr) P(rr)}{P(RRR|rr) P(rr)+P(RRR|rw) P(rw)+P(RRR|wr) P(wr)+P(RRR|ww) P(ww)}\\P(rr|RRR)=\frac{1 \times \frac{1}{4}}{1 \times \frac{1}{4}+\frac{1}{8} \times \frac{1}{4}+\frac{1}{8} \times \frac{1}{4}+0 \times \frac{1}{4}}\\\\P(rr|RRR)=\frac{\frac{1}{4}}{\frac{5}{16}}\\\\P(rr|RRR)=\frac{4}{5}[/tex]
Hence the probability that both balls in the box are red given that all three occasions a red ball is drawn from the box is [tex]\frac{4}{5}[/tex]
please help me with this
Answer:
y-5=3/4(x-6)
Step-by-step explanation:
The picture you posted is a bit unclear and difficult to look at, but that's alright.
This is a simple question if you understand that the point slope for equation is: y-y1 = m(x-x1).
m is the slope and (x1,y1) is a point on the graph.
So, if you input the point (6,5) on the graph, it works.
You can double check with the other equations to see that they are all wrong!
In which number is the digit 5 one hundred times larger than it is in the number 253
Answer:
The 5 would be in the Thousands place
Step-by-step explanation:
Hope this helps any
Determine whether the pair of triangles is congruent.
Choose the correct answer below.
Congruent
Not congruent
Answer:
not congruent
Step-by-step explanation:
congruent is just a fancy way of saying the same in geometry. so to check if its congruent, see if all side lengths correspond to another side length on the other triangle. they do not, so they can't be congruent
hope this helped :)
what percent of 20 is 18?
Answer:
90%
Step-by-step explanation:
A fraction consists of two numbers and a fraction bar:
18/20
The number above the bar is the numerator: 18
The number below the bar is the denominator: 20
Divide the numerator by the denominator to get fraction's value:
Val = 18 ÷ 20
Do you know the tricks to multiplying variables?
Answer:
yes I know how to to multiple variables.
the selling price of a product is $20 and the markup is $4 What percentage of the selling price does the markup represent
Answer:
20%
Step-by-step explanation:
The ratio of 20 to 4 can be simplified to 5:1, by switching it around, we get 1/5. 1/5 as a percentage can be expressed as 20%
Answer:
20%
Step-by-step explanation:
Given the following question:
20% of 20
To find the answer we will use the formula to calculate percentages.
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times20}{100}[/tex]
[tex]20\times20=400[/tex]
[tex]400\div100=4[/tex]
[tex]=4[/tex]
20% of 20 is 4, which means your answer is "20%."
Hope this helps.
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 29 feet more
than the length of the shortest side. Find the dimensions if the perimeter is 141 feet.
What is the length of the shortest side?
The length of the shortest side is
(1)
What is the length of the second side?
The length of the second side is
(2)
What is the length of the third side?
The length of the third side is
(3)
Answer:
Step-by-step explanation:
8y8yy89y99u98u89y7t8y7i6u7i9jo
Which is a unit rate 15 miles per gallon
Answer:
60/4
Step-by-step explanation:
Hope this helps.
Need help not sure if I got this right???????????
How do you do this question?
This series diverges by the limit test (some books may call it the nth term test).
Recall the limit test is the idea if the sequence doesn't converge to 0, then the series diverges.
In this case, the sequence converges to n/(7n) = 1/7 since all we are about are the leading terms when n gets very large.
After some very large n value, we're effectively adding on 1/7 or very close to it, each time. The infinite sum does not approach a fixed value. It keeps growing forever.
Find the area of the sector. Round your answer to nearest tenth.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =90 \end{cases}\implies \begin{array}{llll} A=\cfrac{(90)\pi (20)^2}{360}\implies A=100\pi \\\\\\ A\approx 314.2 \end{array}[/tex]
Use the volume formula to find the volume of the prism.
A. 21 cubic units B. 42 cubic units C. 27 cubic units D. 9 cubic units
Answer:
D Because
Step-by-step explanation:
1/2 +1/2 is 1 so 1+1+3+4 is 9
HOPE THIS HELP! :)
Which of the following is true?
A |−5| < 4
B |−4| < |−5|
C |−5| < |4|
D |−4| < −5
B is true
Step-by-step explanation:
because no number with them to lines can be a negative
The speed of a tidal wave, s, in hundreds of miles per hour can be modeled by the equation, [tex]s=\sqrt{t} -2t+6[/tex] , where t represents the time from its origin in hours. The graph of the tidal wave is shown.
Using it's concept, it is found that the domain of the function regarding the speed of the tidal wave is explained by:
[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.
What is the domain of a function?It is the set that contains all possible input values for the function. In a graph, it is given by the x-values, that is, the horizontal axis values.
In this graph, the horizontal axis assumes values between 0 and 4, which is the time after the wave, and considering that the wave cannot be less than zero. Hence, the correct option is:
[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.
More can be learned about the domain of a function at https://brainly.com/question/25897115
Solve
8x + 12x = 180 what does x equal?
Answer:
8x + 12x = 180
x=9
Step-by-step explanation:
Answer:
x = 9
Step-by-step explanation:
8x + 12x = 180
20x = 180
x = 180/20
x = 9
Please mark me the brainliest!?!
The ratio of the side length of a square perimeter is always 1 to 4 peter drew a sqaure with a perimeter of 28 inches
Answer:
7
Step-by-step explanation:
Please help with this one
Answer:
The first answer is D
the second answer is B
Step-by-step explanation:
The reason why the first answer is D is because in the problem it says at least twice as many seniors is travelling compared to the juniors and D is the only one that shows at least twice than as many juniors and it also it true in the equation 230>2y+x
The reason why the second answer is B is because both of the lines touch at the points (-2,1) which is the same points as B
A tree is 26.4 feet tall. What is its height in meters? Use the following conversion: 1 meter is 3.3 feet.
Answer:
8.047 meters hope this helps and google as the converter if you need it
Answer:
8 meters
Step-by-step explanation:
26.4 / 3.3 = 8 meters
(5,-5) (6,-6) (7,-7) (8,-8) what is the slope
Answer:
i think its straight line
Let f(x) = logx
What is the average rate of change of f(x) from 4 to 6?
Round to the nearest hundredth.
(a.) 0.09
(b.) 0.18
(c.) 0.20
(d.) 0.41
(a.) 0.09
equation:
f(x) = log(x)
rate of change:
[tex]\sf \rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\sf \rightarrow \sf \dfrac{log(4) -log(6)}{4-6}[/tex]
[tex]\sf \rightarrow 0.088[/tex]
[tex]\sf \rightarrow 0.09[/tex]
Answer:
[tex]A.\: 0.09[/tex]
Step-by-step explanation:
Rate of Change is: [tex]\frac{y{_1-y{_2} } }{x_2-x_1}[/tex]
[tex]\frac{log(4)-log (6)}{4-6}[/tex]
[tex]0.088[/tex]
[tex]0.09[/tex]
maths I need help asap it's about sequence and functions good rewards!
Answer:
a₄ = 50
Step-by-step explanation:
work back from the seventh term a₇ using the reverse of the term to term rule , that is
divide by 2 then subtract 3
a₇ = 442
a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218
a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106
a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50
Answer:
[tex]a_{4}=50[/tex]
Step-by-step explanation:
[tex]a_{4} = 50[/tex]
a₇ = 442
a₆ = 442 ÷ 2 - 3 = 221 - 3 = 218
a₅ = 218 ÷ 2 - 3 = 109 - 3 = 106
a₄ = 106 ÷ 2 - 3 = 53 - 3 = 50
these numbers form an addition and subtraction fact family 8,3,11 choose the fact family formed by these numbers the choices are a 8+3=11 11-3=8 b 8-3=5 11-3=8 11+8=19 11+3=14 c 11-8=3 11-3=8 11+3=14 c 11-8=3 11-3=8 11+3=14 11+8=19 d 3+8=11 8+3=11 11-8=3 11-3=8 is it abc or d what is the answer
Answer: A
Step-by-step explanation:
The mass of a carbon-12 atom is 1.99\times 10^{-23}1.99×10
−23
grams. The mass of a neutron is 1.68\times 10^{-24}1.68×10
−24
grams. How many times greater is the mass of a carbon-12 atom than the mass of a neutron? Write your answer in standard notation, rounding to the nearest tenth.
Answer:
If the mass of one electron is 9.11 x 10-28 g, and you are looking for the mass of a mole of electrons, you need to understand Avogadro's number. One mole is 6.02 x 1023 particles. So you will have to multiply (6.02 x 1023) x (9.11 x 10-28 g) to get your answer of 5.48 x 10-4 grams (answer rounded to significant figures)
Step-by-step explanation:
1.2 x 10¹ times greater is the mass of a carbon-12 atom than the mass of a neutron
What is Division?A division is a process of splitting a specific amount into equal parts.
To find the ratio of the mass of a carbon-12 atom to the mass of a neutron, we can divide the mass of carbon-12 by the mass of a neutron:
(1.99×10⁻²³ grams) / (1.68×10⁻²⁴ grams)
= 11.8 grams
This means the mass of a carbon-12 atom is 11.8 times greater than the mass of a neutron. Written in standard notation and rounded to the nearest tenth, the answer is 1.2 x 10¹
Hence, 1.2 x 10¹ times greater is the mass of a carbon-12 atom than the mass of a neutron
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
Factor 48e+180 using greatest common factor
What is the value of the expression?
(7 2/3−4 8/9)+(5 2/3−2 1/2)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
5 17/18
Step-by-step explanation:
Your calculator can help with this.
__
The integer parts of the mixed numbers can be dealt with separately. The fractional parts are added and subtracted using a common denominator. Here, that denominator is the least common multiple (LCM) of 2, 3, and 9, so is 18.
((7 2/3) -(4 8/9)) +((5 2/3)) -(2 1/2))
= (7 2/3) +(5 2/3) -((4 8/9) +(2 1/2))
= 12 4/3 -(6 +8/9 +1/2)
= 13 6/18 -(6 +16/18 +9/18)
= 13 6/18 -(6 +25/18) = 13 6/18 -(7 7/18)
= (13 -7) +(6/18 -7/18)
= 6 -1/18
= 5 17/18
__
Additional comment
Doing the math in the manner shown above means you can mostly do it without a calculator. If you like, you can convert all of the numbers to improper fractions, then add those. This often requires a calculator.
= (138/18 -88/18) +(102/18 -45/18)
= 50/18 +57/18
= 107/18 = 5 17/18
The following histogram shows the relative frequencies of the hieight recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches
The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches
(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work
Answer:
0.22268
Step-by-step explanation:
z-score is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work
At least means equal to or greater than 67 inches
z = 67 - 64.97/2.66
z = 0.76316
P-value from Z-Table:
P(x<67) = 0.77732
P(x>67) = 1 - P(x<67) = 0.22268
The probability that the selected woman will have a height of at least 67 inches is 0.22268
Which of the following would be appropriate to measure in centimeters
Answer:
c
Step-by-step explanation:
The average amount of time to finish this quiz is 26 minutes with a standard deviation of 1.2 minutes. What is the probability that you will finish this quiz in 23.84 minutes or less? Write your answer as a percentage with 2 decimals.
Answer:
What is the probability that you will finish this quiz in 23.84 minutes or less?
0.03593
Write your answer as a percentage with 2 decimals
= 3.59%
Step-by-step explanation:
The z score formula is given as:
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Mean = 26 minutes
Standard deviation = 1.2 minutes.
The probability that you will finish this quiz in 23.84 minutes or less(≤) is calculated as:
z = (x-μ)/σ
z = 23.84 - 26/1.2
z = -1.8
Probability value from Z-Table:
P(x ≤ 23.84) = 0.03593
Converting to percentage
0.03593 × 100
= 3.593
Approximately to 2 decimal places = 3.59%