Answer:
[tex]x-2y=-12[/tex]
Step-by-step explanation:
Hi there!
1) Determine the equation of the line in slope-intercept form
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
Plug in the slope [tex]\frac{1}{2}[/tex]
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (6,9) and solve for b
[tex]9=\frac{1}{2}(6)+b\\9=3+b[/tex]
Subtract 3 from both sides
[tex]9-3=3+b-3\\6=b[/tex]
Plug 6 back into [tex]y=\frac{1}{2}x+b[/tex]
[tex]y=\frac{1}{2}x+6[/tex]
2) Rearrange the equation into standard form
Standard form: [tex]Ax+By=C[/tex] where A, B and C are integers and A is typically positive
[tex]y=\frac{1}{2}x+6[/tex]
Multiply both sides by 2 to remove the fraction
[tex]2y=1x+12\\2y=x+12[/tex]
Subtract x from both sides to isolate 12 as C
[tex]2y-x=x+12-x\\2y-x=12\\-x+2y=12[/tex]
Multiply both sides by -1 to make A positive
[tex]x-2y=-12[/tex]
I hope this helps!
Consider the following quadratic equation. y = x2 – 8x + 4 Which of the following statements about the equation are true? The graph of the equation has a minimum. When y = 0, the solutions of the equation are a = 4 + 2V3 o When y = 0, the solutions of the equation are r x = 8 + 2V2. o The extreme value of the graph is at (4,-12). The extreme value of the graph is at (8,-4). U The graph of the equation has a maximum. Submit
Answer:
The graph of the equation has a minimum.
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
The extreme value of the graph is (4,-12).
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
y = x2 – 8x + 4
Quadratic equation with [tex]a = 1, b = -8, c = 4[/tex]
a is positive, so it's graph has a minimum.
Solutions when y = 0
[tex]\Delta = b^2-4ac = 8^2 - 4(1)(4) = 64 - 16 = 48[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{48}}{2} = \frac{8 + 4\sqrt{3}}{2} = 4 + 2\sqrt{3}[/tex]
[tex]x_{2} = \frac{-(8) - \sqrt{48}}{2} = \frac{8 - 4\sqrt{3}}{2} = 4 - 2\sqrt{3}[/tex]
When y = 0, the solutions are [tex]4 \pm 2\sqrt{3}[/tex]
Extreme value:
The vertex. So
[tex]x_{v} = -\frac{-8}{2} = 4[/tex]
[tex]y_{v} = -\frac{48}{4} = -12[/tex]
The extreme value of the graph is (4,-12).
On the first day of training, Aretha holds a plank position for 30 seconds. She increases her time by 20% each day. What is the first day on which Aretha holds a plank for over a minute? Show your work
Answer:
5 th day
Step-by-step explanation:
Given :
1st day :
Time = 30 seconds
Time increases by 20% each day :
2nd day = 20% * 30 = (1.20 * 30) = 36 seconds
3rd day = 1.20 * 36 = 43.2 seconds
4th day = 1.20 * 43.2 = 51.84 seconds
5th day = 1.20 * 51.84 = 62.208
First day Aretha hold a plank for over 1 minute is the 5th day
Pythagorean theorem
Answer:
hello
Step-by-step explanation:
a²+b²=c²
16²+b²=65²
256+b²=4225
b²=4225-256
b²=3969
[tex]b = \sqrt{3969}[/tex]
b=63
b=63 mi
have a nice day
Answer:
b = 63
Step-by-step explanation:
In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.
c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)
c = 65 , a = 16 b = ?
65² = 16² + b²
4225 = 256 + b²
4225 - 256 = b²
b² = 3969
b = [tex]\sqrt{3969}[/tex]
b = 63
check
c² = 16 ² + 63²
= 256 + 3969
= 4225
c = √4225
c = 65
1.
If the measures of three angles of a quadrilateral
are 30, 70, and 110, find the measure of the fourth
angle.
Answer:
150
Step-by-step explanation:
The sum of the angles of a quadrilateral are 360. Let x be the unknown angle
30+70+110+x = 360
Combine like terms
210 +x = 360
Subtract 210 from each side
210+x-210 = 360-210
x = 150
Answer:
The measures of the fourth angle is 150 .
Step-by-step explanation:
Given :-The measures of three angles of quadrilateral are 30 , 70 and 110.
To find :-Find the measures of fourth angle.
Solution :-Let, the measures of fourth angle be x.
We know that sum angles of quadrilateral are 360 .
30 + 70 + 110 + x = 360
combine like terms
210 + x = 360
subtract 210 from 360.
x = 360 - 210
x = 150
Therefore, the fourth angle of quadrilateral is 150.
write an equation of the line below
Gavin was thinking of a number. Gavin doubles it and adds 6.6 to get an answer of 9. Form an equation with
x
from the information.
Answer:
(9-6.6)÷2=x
Step-by-step explanation:
Do it in reverse from 9 all the way to x.
Answer:
(9-6.6)÷2=x
Step-by-step explanation: since you had 9 as the answer, start there. Then subtract 6.6. You then divide that number by 2 to get x
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
A line goes through the points (1, -19), (-4,1), (0, -15), (2, -23). What is the slope and y-
intercept of the line
Answer:
Step-by-step explanation:
The y-intercept is super easy. The y-intercept exists when x = 0; therefore, the point given where x = 0 is found in (0, -15). That means that the y-intercept is -15. Easy enough. Now, the slope.
Since all these points are on the same line, using any 2 of them in the slope formula will get us the slope. I picked the first 2 points (1, -19) and (-4, 1):
[tex]m=\frac{1-(-19)}{-4-1}=\frac{1+19}{-5}=\frac{20}{-5}= -4[/tex]
The y-intercept is -15 and the slope is -4
I’ve been staring at this problem for 10 minutes and still have no idea
9514 1404 393
Answer:
B. (-∞, 1) ∪ (1, 2]
Step-by-step explanation:
When you are looking for answers to domain questions, you are looking for values of the variable(s) that make the function undefined. Here, there is a square root involved, and the rational function has a denominator that might be zero.
The function is only defined for square roots of non-negative numbers. That is ...
2-x ≥ 0 ⇒ x ≤ 2
The rational function is only defined for non-zero denominators, so ...
x-1 ≠ 0
x ≠ 1
__
So, you're looking for a domain description that includes all numbers less than or equal to 2, and excludes x=1. The attached number line shows a graph of this.
The domain divides into two parts: all numbers less than 1, and those numbers between 1 and 2 (including 2). This will be the union ...
(-∞, 1) ∪ (1, 2]
Which statement is true about the function f(x) = negative StartRoot x EndRoot?
Answer:
It has the same domain and range as the function f(x) = StartRoot x EndRoot. It has the same range but not the same domain as the function f(x) = StartRoot x EndRoot. It has the same domain and range as the function f(x) = negative StartRoot negative x EndRoot.
Step-by-step explanation:
Express 0.1 as a percent.
A company that manufactures vehicle trailers estimates that the monthly profit for selling its midsize trailer is represented by function p, where t is the number of trailers sold. p(t)= -25t^3+625t^2-2500t Use the key features of function p to complete these statements. The company makes a profit when it sells _____trailers. The maximum profit of approximately $____ occurs when it sells approximately____ trailers.
Answer:
The answer is below
Step-by-step explanation:
The profit equation is given by:
p(t)= -25t³+625t²-2500t
The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:
p'(t) = -75t² + 1250t - 2500
-75t² + 1250t - 2500 = 0
t = 2.3 and t = 14.3
Therefore t = 3 trailers and t = 15 trailers
p(15) = -25(15³) + 625(15²) - 2500(15) = 18750
Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.
Answer:
See below
Step-by-step explanation:
Since t is number of trailers, the domain includes only those values greater than 0.
On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.
On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.
So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.
Find the volume of the prism.
With composte solids, all you have to do is find the volume of each and then add them together
Answer:
1760 cm³
Step-by-step explanation:
Volume For top "trapezoidal" prism : (14 * 4)/2 * 20 = 28 * 20 = 560
Volume for bottom rectangular prism = 6 x 10 x 20 = 60 x 20 = 1200
1200 + 560 = 1760 cm³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
The probability that a person has blue eyes is 16%. Three unrelated people are selected at random. a. Find the probability that all three have blue eyes b. Find the probability that none of the three have blue eyes c. Find the probability that one of the three has blue eyes
Answer:
Step-by-step explanation:
All three have blue eyes.
P(1 has blue eyes) = 16/100 = 4/25
P(3 have blue eyes) = 4/25 * 4/25 * 4/25
P(3 have blue eyes ) = 64/15625
If you need the decimal answer, it is .004096
No one has blue eyes out of three
The probability for this is very large.
P(no blues) = 1 - 64/15625
P(no blues) = 15561/15625
If you need the decimal answer, it is 0.996
One has blue eyes (the other two do not).
P(1 has blue eyes) = 16/100 * 84/100*84/100
P(1 has blue eyes) = 112896/1000000
P(1 has blue eyes) = 0.112896
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)
Answer:
0.42ft/mn
Step-by-step explanation:
we have the following information to answer this question
dv/dt = 40 feet
height = 11 ft
volume = 1/3πr²h
= 1/3π(h/2)²h
= 1/3πh³/4
= πh³/12
dv/dt = π3h²/12
= πh²/4
dh/dt = 4/πh²dv/dt
= 4(40)÷22/7(11)²
= 160/380.29
= 0.42 ft/min
The height of the pile is therefore increasing by 0.42ft/min at a height of 11 feets
Use trigonometric identities to verify each expression is equal. sin(x)/1-cos(x)-cot(x)=csc(x)
Answer:
See Below.
Step-by-step explanation:
We want to verify the identity:
[tex]\displaystyle \frac{\sin x}{1 - \cos x} - \cot x = \csc x[/tex]
We can multiply the fraction by 1 + cos(x):
[tex]\displaystyle \frac{\sin x(1+\cos x)}{(1 - \cos x)(1+\cos x)} - \cot x = \csc x[/tex]
Difference of Two Squares:
[tex]\displaystyle \frac{\sin x(1+\cos x)}{1-\cos^2 x} - \cot x = \csc x[/tex]
From the Pythagorean Theorem, we know that sin²(x) + cos²(x) = 1. Rearranging, we acquire that sin²(x) = 1 - cos²(x). Substitute:
[tex]\displaystyle \frac{\sin x(1+\cos x)}{\sin^2 x} - \cot x = \csc x[/tex]
Cancel:
[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\cot x = \csc x[/tex]
Let cot(x) = cos(x) / sin(x):
[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\frac{\cos x}{\sin x} = \csc x[/tex]
Combine Fractions:
[tex]\displaystyle \frac{ 1 + \cos x - \cos x}{\sin x}= \csc x[/tex]
Thus:
[tex]\displaystyle \frac{1}{\sin x}=\csc x = \csc x[/tex]
Hence proven.
Prob and stats question help
Answer:
It is C
Step-by-step explanation:
Trust me, i got it right
Answer:
C
Step-by-step explanation:
have a great rest of your day!! btw Ill view ur profile!! :)
A company's sales force makes 400 sales calls, with + 0.25 probability that a sale will be made on a call. What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made? Enter your answer as a decimal value, rounded to 4 decimal places.
Answer:
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.
This means that [tex]n = 400, p = 0.25[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]
What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?
Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.
X = 74.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -2.94[/tex]
[tex]Z = -2.94[/tex] has a p-value of 0.0016
X = 55.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -5.14[/tex]
[tex]Z = -5.14[/tex] has a p-value of 0
0.0016 - 0 = 0.0016
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Approximately 70% of U.S. adults had at least one pet as a child. We randomly survey 60 U. S. adults. We are interested in the number that had at least one pet as a child. The probability that at least 3 adults had at least one pet as a child means:
A. P(X=0)+P(X=1)+P(X=2)+P(X=3)
B. P(X=0)+P(X=1)+P(X=2)
C. P(X=4)+P(X=5)+P(X=6)+ ...
D. P(X=3)+P(X=4)+P(X=5)+ ...
Answer:
D. P(X=3)+P(X=4)+P(X=5)+ ...
Step-by-step explanation:
Given
[tex]n =60[/tex]
[tex]pr = 70\%[/tex] -- proportion of adults with pet
Required
Represent at least 3 adult with pet as a probability
At least 3 means 3 or more than.
So, the probability is represented as:
[tex]P(x \ge 3) = P(3) + P(4) + P(5) + ........[/tex]
Hence;
(d) is correct
write a rational number between root2 and root3
Answer:
prational number between root2
HELPPP PLSSSSSSSSSSS
Answer:
45 + m<DBC = 180
Step-by-step explanation:
m<ABD + m<DBC = 180
45 + m<DBC = 180
WILL GIVE BRAINLIEST (Right angle) Trigonometry
please help!
Answer:
<A = 41.4°
Step-by-step explanation:
Recall, SOH CAH TOA
Reference angle = <A
Hypotenuse length = 8
Adjacent length = 6
Since Hypotenuse and Adjacent are involved, we would apply CAH, which is:
Cos A = Adj/Hyp
Plug in the values
Cos A = 6/8
Cos A = 0.75
[tex] A = Cos^{-1}(0.75) [/tex]
A = 41.4096221° ≈ 41.4° (nearest tenth)
At the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 cheeses
Answer:
Diego can choose the 15 items in 128 different ways.
Step-by-step explanation:
Since at the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads, and he wants to use the Express Lane, so he can only buy 15 items, to determine how many ways can he choose which 15 items to buy if he wants all 6 cheeses the following calculation must be performed:
4 x 4 x 8 = X
16 x 8 = X
128 = X
Therefore, Diego can choose the 15 items in 128 different ways.
Suppose we want to choose 5 objects,without replacement from 16 distinct objects
Answer:
4368 ways
Step-by-step explanation:
We want to choose 5 objects,without replacement from 16 distinct objects.
We can use combination in this case. The formula for the combination is given by :
[tex]_{n}C_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have, n = 16 and r = 5
So,
[tex]_{16}C_5=\dfrac{16!}{5!(16-5)!}\\\\_{16}C_5=\dfrac{16!}{5!11!}\\\\=4368[/tex]
So, there are 4368 ways in which we want to choose 5 objects,without replacement from 16 distinct objects.
Find the median of the following data 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7
Answer:
11
Step-by-step explanation:
first, sort the numbers from lowest to highest.
5,5,6,7,8,9,10,*10,12*,14,15,17,18,18,18,20
the median is the number in the middle of the data
average if you need to (10+12 and divide by 2)
Split 294x306, which identity is used to solve it?
Answer:
identity :- ( a + b ) ( a - b ) = a² - b ²
Answer :- 89,694
Step-by-step explanation:
Given : 294 × 306
split 294 × 306
294 × 306 = ( 300 - 6 ) × ( 300 + 6 )
Using Identity, ( a + b ) ( a - b ) = a² - b ² :
= ( 300 )² - ( 6 )²
= 90000 - 36
= 89,964
Hence, 294 × 306 = 89,694
Find the height of the cylinder. Round your answer to the nearest whole number.
Volume
= 113 m 3
Answer:
C
Step-by-step explanation:
3² * pi * 4 = 113
113 / pi / 3²
gives you 4
this time the radius was squared correctly XD
Answer:
C. 4m
Step-by-step explanation:
Work backwards from the formula of volume cylinder:
Formula = πr²h
113 = 3.14 * 9 * h
113/9 = 3.14 * h
12. 6 = 3.14 / h
4 = h
h = 4
Check:
Volume = 3.14*9*4
Volume = 3.14 * 36
volume = 113.04 ≈ 113
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which of the following expressions could be used to represent "three less than half a number"?
• 1/2 - 3n
• 3 - 1/2n
• 3n - 1/2
• 1/2n - 3
Answer:
the answer is
[tex]3 - \frac{1}{2}n [/tex]
A fair six-sided die is rolled 54 times. Theoretically, how many times should a roll of "5" occur?
-14
-9
There is no way to tell
-5
Answer:
9 times
Step-by-step explanation:
P("5") = 1/6
n("5") = 1/6 × 54 = 9
Answer:
9
Step-by-step explanation:
(the number of different possible outcomes) 1/6 * 54 = 9
Hope that this helps!
Find the work done by the gas for the given volume and pressure. Assume that the pressure is inversely proportional to the volume. (See Example 6.) A quantity of gas with an initial volume of 2 cubic feet and a pressure of 1000 pounds per square foot expands to a volume of 3 cubic feet. (Round your answer to two decimal places.)
810.93
Step-by-step explanation:Let the pressure be given by P and the volume be V.
Since pressure is inversely proportional to volume, we can write;
P ∝ [tex]\frac{1}{V}[/tex]
=> P = [tex]\frac{c}{V}[/tex] -------------(i)
Where;
c = constant of proportionality.
When the volume of the gas is 2 cubic feet, pressure is 1000 pounds per square foot.
V = 2 ft³
P = 1000lb/ft²
Substitute these values into equation (i) as follows;
1000 = [tex]\frac{c}{2}[/tex]
=> c = 2 x 1000
=> c = 2000 lbft
Substituting this value of c back into equation (i) gives
P = [tex]\frac{2000}{V}[/tex]
This is the general equation for the relation between the pressure and the volume of the given gas.
To calculate the work done W by the gas, we use the formula
[tex]W = \int\limits^{V_1}_{V_0} {P} \, dV[/tex]
Where;
V₁ = final volume of the gas = 3ft³
V₀ = initial volume of the gas = 2ft³
Substitute P = [tex]\frac{2000}{V}[/tex], V₁ = 3ft³ and V₀ = 2ft³
[tex]W = \int\limits^{3}_{2} {\frac{2000}{V} } \, dV[/tex]
Integrate
W = 2000ln[V]³₂
W = 2000(In[3] - ln[2])
W = 2000(0.405465108)
W = 810.93016
W = 810.93 [to 2 decimal places]
Therefore, the work done by the gas for the given pressure and volume is 810.93