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Answer:
x = 2 or x = 9
Step-by-step explanation:
To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).
2(3) +4(3(x -3)) = (x +4)(x -3)
6 +12x -36 = x² +x -12
x² -11x +18 = 0
Using the quadratic formula to find the solutions, we have ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]
The solutions are x=2 and x=9.
What value of x makes the equation 3x +7=22
Answer:
x = 5
Step-by-step explanation:
Your goal is to isolate x
3x + 7 = 22
Subtract 7 from both sides and you are left with
3x = 15
In order to isolate x divide both sides by 3
x = 5
Given the coordinates of two points on a line, explain two methods to determine the slope of the line.
Answer:
Step-by-step explanation:
1. Use the slope formula (y2 - y1 / x2 - x1)
2. Use the graph. Take two points and count the rise over the run.
Can you please help me
Answer:
you will type your answers and send
Answer:
Step-by-step explanation:
⅔-2/5 = 4/15
How many solutions will each system of linear equation have?
Answer:
The top system of equations has one solution, the middle system has infinitely many, and the bottom system has no solution.
Step-by-step explanation:
We can immediately see the top system has one solution because the two equations have different slopes.
For the middle system, we can rearrange terms and multiply by 3 to get that the equations are the same line, so there are infinitely many solutions.
Finally, we can move the -2x to the other side in the first equation of the bottom system to get 2x+y=5. But it also equals -7 from the second equation! This is impossible, so there are no solutions to the bottom system.
Use the method of cylindrical shells to write out an integral formula for the volume of the solid generated by rotating the region bounded by the curve y = 2x - x^2 and the line y = x about the y-axis.
Answer:
The answer is "[tex]\frac{5\pi}{6}[/tex]"
Step-by-step explanation:
Please find the graph file.
[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]
In the figure, L1 || L2. 2x=174º. Find Za+Zb.
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Answer:
12°
Step-by-step explanation:
We assume you mean ...
∠x = 174°
Angle a is supplementary to angle x, so is ...
∠a = 180° -174° = 6°
Angle b is a vertical angle with respect to angle 'a', so is the same measure.
∠a +∠b = 6° +6° = 12°
I’m so confused. Need the help
1.621 kN
Step-by-step explanation:
Let the centerline of the canal be the x-axis. Because the forces exerted by the horses are symmetric to the centerline, only the x-components of these forces contribute to the resultant force on the barge, i.e., the y-components cancel out. Each x-component is equal to [tex]F_x = 839\cos 15[/tex] = 810.4 N. Therefore, the resultant force on the barge is twice this:
[tex]F_{net} = 2(839\:\text{N})\cos 15 = 1620.8\:\text{N}[/tex]
[tex]= 1.621\:\text{kN}[/tex]
please answer all the questions and get 15 pts
Answer:
Here you go
Ans is in pictures.
Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
Do 8 plz find OS thanks
Answer:
OS = 10
Step-by-step explanation:
We can use a ratio to solve
QP PR
----- = ------
QO OS
14 7
----- = -------
14+6 OS
14 7
----- = -------
20 OS
Using cross products
14 * OS = 7*20
14 OS = 140
Divide by 14
OS = 140/14
OS = 10
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
a family has two children. what is the probability that both are girls, given that at least one is a boy
Answer: The probability would be zero
Step-by-step explanation:
There are two children and one is a boy, so the probability of both being girls is a zero
Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).
1. g(x) = f(x + 1)
2. g(x) = f(x) - 2
Please help i also need to graph
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Answer:
left 1 unitdown 2 unitsStep-by-step explanation:
The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.
1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)
__
2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)
Find the value of x in each case:
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Answer:
x = 36
Step-by-step explanation:
The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...
(180 -2x) +x +(180 -4x) = 180
180 = 5x . . . . . . add 5x-180 to both sides
36 = x . . . . . . . divide by 5
__
Additional comment
This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27
Answer:
3 e^t/2 + 4 = 27
e^t/2 = 23 / 3
Taking natural log of both sides
t/2 = ln 23/3 = ln 7.667 = 2.037
t = 4.074
Check:
3 e^4.074/2 + 4 = 27
27 = 27
I don't get this question i need some help please!!!
Answer:
2 sqrt(2) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/4
4 sin 45 = x
4 ( sqrt(2)/2) =x
2 sqrt(2) = x
Answer: D
Use sine to find the x-value:
[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?
measure horizontally
measure vertically
measure depth..
Help please, thanks
Answer: B. X It passes the vertical line test :)
Step-by-step explanation:
The weight of bags of fertilizer is normally distributed with a mean of 50 pounds and standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh:
a. Between 45 and 55 pounds?
b. At least 56 pounds?
c. At most 49 pound?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Normal Distribution:
[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]
For point a:
[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]
[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]
For point b:
[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]
For point c:
To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]
[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]
When the function f(x) = 4(2)x is changed to f(x) = 4(2)x − 13, what is the effect? (5 points)
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. The x-intercept is 13 spaces higher.
c. The y-intercept is 13 spaces lower.
d. All input values are moved 13 spaces to the left.
Answer:
C
If x = o then f(0) = 4(2) * 0 = 0
If f(x) = 4(2) 0 - 13
then f(x) = -13 at x = 0
Answer:
it will indeed be c
Step-by-step explanation:
deesnuts
At a concession stand; three hot dogs and two hamburgers cost $9.75; two hot dogs and three hamburgers cost $10.25. Find the cost of one hot dog and the cost of one hamburger.
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Answer:
hot dog: $1.75hamburger: $2.25Step-by-step explanation:
Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...
3x +2y -9.75 = 0
2x +3y -10.25 = 0
We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:
3, 2, -9.75, 3
2, 3, -10.25, 2
Now, we can form differences of cross-products in adjacent pairs of columns:
d1 = (3)(3) -(2)(2) = 9 -4 = 5
d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75
d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25
Then the solutions are found from ...
1/d1 = x/d2 = y/d3
x = d2/d1 = 8.75/5 = 1.75
y = d3/d1 = 11.25/5 = 2.25
The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.
_____
Additional comment
This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.
For a given pair of columns with coefficients ...
a b
c d
The cross-product we form is ad -cb.
Please help! Identify the recursive formula for the sequence 20, 28, 36, 44, . . . .
Answers below in picture:
Option A
Answered by GauthMath if you like please click thanks and comment thanks
By examining past tournaments, it's possible to calculate the probability that a school wins their first game in the national college basketball tournament. Each school's rank going into the tournament is a strong indicator of their likelihood of winning their first game.
Find the linear regression equation that models this data.
The linear regression model which models the data is :
y = -6.41053X + 103.83509
Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )
Using technology :
• Enter the data into the columns provided ;
The regression equation obtained for the data is : y = -6.41053X + 103.83509
Where ;
Slope = -6.41053
Intercept = 103.83509
X = Rank
y = probability percentage
Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.
Learn more on linear regression : https://brainly.com/question/12164389
Question 8 of 53
How much would $700 be worth after 8 years, if it were invested at 5%
interest compounded continuously? (Use the formula below and round your
answer to the nearest cent.)
A(t) = P•e^rt
A. $5887.12
B. $1044.28
C. $6432.11
D. $38,218.71
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Answer:
B. $1044.28
Step-by-step explanation:
Putting the given numbers into the given formula, we have ...
A(8) = $700•e^(0.05•8) ≈ $1044.28
Use the unit circle to find tan 60°.
a. square root 3/3
c. 2 square root 3/3
b. square root 3/2
d. square root 3
Please select the best answer from the choices provided
A
B
C
D
the answer is d ( square root 3 )
tan = oposite / adjacent
tan 60° = √3 / 1
= √3
Computers from a certain manufacturer have a mean lifetime of 62 months, with a standard deviation of 12 months. The distribution of lifetimes is not assumed to be symmetric. Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers
Answer:
Between 38 and 86 months.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean of 62, standard deviation of 12.
Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers?
Within 2 standard deviations of the mean, so:
62 - 2*12 = 38
62 + 2*12 = 86
Between 38 and 86 months.
1/2 of 12=1/4 of?
1/3 of 90=2/3of?
Answer:
24 and 45
Step-by-step explanation:
Okay, now that I can answer this question with the right answers:
The easy way to do this is to first solve the left hand side of the equation.
1/2 of 12 is the same as 12/2 = 6.
So 6 = 1/4 * x
To solve for that unknown x, just multiply both sides by 4 to cancel out the fraction:
6*4 = 4* 1/4*x
24 = x
For the other equation, do the same thing:
1/3 * 90 = 90/3 = 30
30 = 2/3*x
30*3 = 3* 2/3 *x
90 = 2x
90/2 = 2x/2
45 = x
Given the number 2376.458 rounded to the following place values: 1) Rounded to the nearest hundred, 2) Rounded to the nearest whole unit, 3) Rounded to the nearest hundredth,
Answer:
1)2400
is the result of rounding 2376.458 to the nearest 100.
2) 2376
is the result of rounding 2376.458 to the nearest integer.
3)2376.46
is the result of rounding 2376.458 to the nearest 0.01
I hope this is right and it helps !!!!!!!!!!!!!!!!
Answer:
1(2400)
2(2376)
3(2376.46)
Step-by-step explanation:
it's just your fraction skills
