3x² - 14x + 8 = 0
Δ = (-14)² - 4*3*8 = 196 - 96 = 100 = 10²
2 solutions
x' = (14 + 10) / (2*3) = 24 : 6 = 4
x" = (14 - 10) / (2*3) =4/6 = 2/3
3 (x - 4) (x - 2/3) = 0
361,354,347, ...
Find the 47th term.
This is an arithmetic sequence with a common difference given by d= -7
I will start by defining my first term as u⁰=361
Now we have to think, if u⁰ is my 1st term than my 47th term would be u⁴⁶ not u⁴⁷ since i start counting from 0 and not 1.
Using the relation that describes the implicit relation of an arithmetic sequence, i can say:
u(n)=u⁰+nd where n is any number
u⁴⁶=u⁰+46d
u⁴⁶=361+46(-7)
u⁴⁶=361-322
u⁴⁶=39
Answer:
39.
Step-by-step explanation:
This is an arithmetic sequence with common difference -7
47th term = a + d(n - 1)
= 361 - 7(47-1)
= 39.
A person metabolic rate is the rate at which the body consumes energy. Metabolic is important in studies of weight gain, dieting, and exercises. Here are the metabolic rates of 7 men who took part in study of dieting. (Unites are calories per 24 hours).Find the Variance & stranded deviation. 1666 1362 1614 1460 1867 1439
Answer:
mean= 1588 and Standard deviation=190.99
Step-by-step explanation:
Identify the vertex
y=x^2-2x-3
Answer:
The vertex is located at (1,-4)
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
We have the following quadratic equation and we need to express it in vertex form. Thus, we need to complete the squares:
[tex]y=x^2-2x-3[/tex]
Adding and subtracting 1:
[tex]y=x^2-2x+1-3-1[/tex]
The first three terms are the square of a binomial:
[tex]y=(x-1)^2-4[/tex]
Comparing to the vertex form of a quadratic equation, the vertex is at (1,-4).
The vertex is located at (1,-4)
If you bought 100 shares of Starbucks stock for $45 a share two years ago and it is
now worth $65. How much would you make if you sold it now?
O $200
O $2,200
O None of the Above
O $2,000
[tex]x+0.08+3.21\leq 60[/tex]
*How far can a train travel in 45 minutes if it is traveling at 80 miles per hour?
Answer:
53 miles
Step-by-step explanation:
80 miles per hour
x miles per 45 minutes
So, we know that an hour is 60 minutes so lets change the hour to that.
80 miles per 60 minutes
x miles per 45 minutes
Now, we do cross-multiplication:
[tex]\frac{x}{45}[/tex] [tex]\frac{80}{60}[/tex]
So, we multiply 80 by 45 which is 3200. Then, we divide 3200 by 60 which is 53.3. So, the train travels 53.3 miles in 45 minutes.
But to round it, it would be 53 miles.
Hope this helps
The number of miles traveled by train in 45 minutes will be 60 miles.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The speed of the train is 80 miles per hour. Then the number of miles in 45 minutes is calculated as,
80 = D / (45 / 60)
D = 80 x 45 / 60
D = 60 miles
The number of miles traveled by train in 45 minutes will be 60 miles.
More about the speed link is given below.
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question is attached thanks
[tex]\\ \sf\longmapsto12x+7=10(x+1)-3[/tex]
[tex]\\ \sf\longmapsto 12x+7=10x+10-3[/tex]
[tex]\\ \sf\longmapsto 12x+7=10x+7[/tex]
[tex]\\ \sf\longmapsto 12x=10x[/tex]
[tex]\\ \sf\longmapsto x=10/12=5/6[/tex]
We need natural number
put 0[tex]\\ \sf\longmapsto 12(0)=10(0)[/tex]
Yes 0 is a solution
All negatives must be included in your final answer:
ie. if the question asks for the whole number portion, numerator, or denominator of the answer and it has a negative, you must include that negative.
Be sure to reduce all fractions fully and convert improper fractions to mixed numbers before stating your final answer
Answer:
im pretty sure that the answer is 2/3
Step-by-step explanation:
questions are in the pictures
Answer:
True
I hope this helps!
Find the midpoint (-8,6), (5,-7)
Answer:
Hello
Midpoint of (-8,6) and (5,-7)
P(a,b)=(x1+x2/2),(y1+y2/2)
=(-8+5/2),(6+-7/2)
=(-3/2),(-1/2)
Midpoint of (-8,6) and (5,-7) is (-3/2),(-1/2)
Hope it helps you.....
Slove for x
Show all work
Answer:
x=15
Step-by-step explanation:
[tex]18^2=12(x+12)\\\\324=12(x+12)\\\\323=12x+144\\\\\cfrac{180}{12} =\cfrac{12x}{12} \\\\x=15[/tex]
~
Nhat is the slope of the line whose equation is y-4=(x-2)?
A. - 5/2
B. - 2/5
C. 2/5
D. 5/2
See picture for math work and answer.
Write in standard form
0.0000684
What is 9.513 times 5.7 equal?
Answer: 54.2241
Step-by-step explanation:
You multiply 9.513 by 5.3 which gives you an answer of 54.2241. (Hope this helped)
What is the first step in solving the equation 2/3x+1/3x+2=5
NEED HELP ASAP
DUE BY 3!!!!!
Answer:
190
Step-by-step explanation:
Select the statement that describes this expression: 5 x (3 + 4) − 4.
5 times the sum of 3 and 4, then subtract 4
5 times 3 plus 4 minus 4
5 more than the sum of 3 and 4, and then subtract 4
5 times 3 plus the difference of 3 and 4
Answer:
A) 5 times the sum of 3 and 4, then subtract 4
Compact l x-2 l - l x-3 l
I need fast
Thank you !
P/s : l x l is absolute value
Answer:
You can't solve this without a specific value of x.
Step-by-step explanation:
Well, all that the absolute value sign means, is that you work in them like parenthesis, but when you "open them up" no matter what, the result will be positive.
So, | x - 2 | - | x - 3 | is just a showing you that you are going to have a positive answer for x - 2, and you are going to have a positive answer for x - 3.
Now, since we don't have a specific value for x, just to simplify this even more, lets just quickly substitute x = 1, just for a reference, so:
| 1 - 2 | - | 1 - 3 | = | -1 | - | -2 |
= 1 - 2
= -1
Ok, so we got that, now we can go back to the original problem. Since we really don't have a specific value for x, we can't really simplify this any further. Maybe if you had a specific value or placeholder for x, then you would be able to solve this.
Which is the graph of y = sqrt x-3
Answer:
The second option
Step-by-step explanation:
The square root of a function could be smaller than 3, so the function could evaluate to less than 0, but the other 3 don't have any points smaller than 0. Therefore, the only possible option is the 2nd one.
Also, if you try to evaluate it in x = 0, which is sqrt(0)-3 = -3, the only option that satisfies that would be the second one.
I hope this helped.
The second option is the graph of y = √x-3.
Here, we have,
The square root of a function could be smaller than 3,
so the function could evaluate to less than 0, but the other 3 don't have any points smaller than 0.
Therefore, the only possible option is the 2nd one.
The graph of y = √(x) - 3 represents a square root function that is shifted vertically downward by 3 units.
The square root function itself is a curve that starts at the point (0, 0) and gradually increases as x increases.
By subtracting 3 from the square root function, the entire graph is shifted downward by 3 units.
This means that the new y-values of the graph are 3 units less than the corresponding y-values of the square root function.
Also, if you try to evaluate it in x = 0, which is √(0)-3 = -3,
the only option that satisfies that would be the second one.
To learn more on graph click:
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order least from greatest -50 44 -3 1.5
Answer:
-50, -31.5, 44 I think
Step-by-step explanation:
The order from least to greatest is:
-50, -3, 1.5, 44
When the negative value increases ( from -1 to -2 ), the value in general decreases. Negative values have a lower value than non-negative numbers.
What is the answer to -3-8g+4g-6
Your friend claims that because you can find the distance from a point to a line, you should be able to find the distance between any two lines. Is your friend correct? Explain your reasoning.
Using the Binomial distribution,
If n=10 and p=0.4, find P(x=5)
Answer:
P(x=5)=0.2
Step-by-step explanation:
Binomial Distribution
Consider a random event that has only two possible outcomes. Call p to the probability that the event has a 'successful' outcome, and q to the 'unsuccessful' outcome.
It's clear that p+q=1, or q=1-p.
Now repeat the random event n times. We want to calculate the probability of getting x successful outcomes. This can be done with the following formula:
[tex]\displaystyle P_{x} = {n \choose x} p^{x} q^{n-x}[/tex]
Where
[tex]\displaystyle {n \choose x}[/tex]
Is the number of combinations:
[tex]\displaystyle {n \choose x} =_nC_x=\frac{n !}{x ! (n-x) !}[/tex]
Calculate the probability for n=10, p=0.4, x=5. It follows that q=1-p=0.6:
[tex]\displaystyle P_{5} = {10 \choose 5}\cdot 0.4^{5}\cdot 0.6^{10-5}[/tex]
[tex]\displaystyle P_{5} = 252\cdot 0.4^{5}\cdot 0.6^{5}[/tex]
[tex]P_{5} = 0.2[/tex]
P(x=5)=0.2
Please help fast I rlly need the help rn I need to finish this
Answer:
30 in³
Step-by-step explanation:
surface area = 2(2 * 5 + 5 * u + 2 * u) = 62
2(10 + 5u + 2u) = 62
2(10 + 7u) = 62
10 + 7u = 62/2 = 31
7u = 31 - 10 = 21
so u = 21/7 = 3 in
Volume = 2 * 5 * 3 = 30 in³
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA POINTS** !! DONT SKIP :((
Someone help I don’t understand
Answer:
a)C
b)E
Step-by-step explanation:
a) You have to pick a vowel. There are three vowels and a total of 6 letters so it is 3/6 so the answer is C
b) Picking a card that is not T. None of the 6 letters are T so the probablity of picking a card with no T is 1. So the answer is E.
If a = [1,2,3] and b = [1, 3, –2], find the angle between a and b.
Answer:
85.9°
Step-by-step explanation:
angle = [tex]\arccos\frac{a\cdot b}{|a| |b|} = \arccos\frac{1+6-6}{{\sqrt{1+4+9}}\sqrt{1+9+4}}\\=\arccos\frac{1}{14}=85.9 degrees[/tex]
What is the volume of the
rectangular prism shown
below?
Answer:
C. 216 m^2
Step-by-step explanation:
The formula for the volume of a right solid is area of the base multiplied by the height. Following this formula, we multiply the given area of the base (27 m^2) by the height (8 m) to get 216 m^2, which is option C.
According to the equation, how much would a person earn who works 40 hours?
What if the person got a $50 bonus and also worked some hours? How would this change the graph?
What if the person got a $2 per hour rate? How would this change the graph of the line?
What is slope? Write a conclusion about the ratio and slope.
The slope of the graph is $15 per hour. The linear function is given by y = 15x
What is a linear function?A linear function is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the y intercept
The graph passes through the point (1, 15) and (8, 120) is:
y - 15 = [(120 - 15)/(8 - 1)(x - 1)
y = 15x
For 20 hours; y = 15(20) = $300
If the person got a $50 bonus and also worked some hours, the graph would change because the y intercept would be 50.
If the person got a $2 per hour rate, the graph would change because the slope would be 2.
The slope of the graph is $15 per hour.
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Rachel invests $6,500 into a 5-year CD. The interest rate is 4.2% and is compounded semi-annually. How much will she have in her account at the end of the 5 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=6500\left(1+\frac{0.042}{2}\right)^{2\cdot 5}\implies A=6500(1.021)^{10}\implies A\approx 8001.49[/tex]