First, we need to find the line equation of the given graph. In our to do it, we can choose 2 points along the line, for instance,
\(\begin{gathered} (x_1,y_1)=(-1,-2) \\ (x_2,y_2)=(0,2) \end{gathered}\)Then, the slope is given by
\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-(-2)}{0-(-1)}=\frac{4}{1}=4 \end{gathered}\)And we can note that the y-intercept is y=2. Thefore, the line equation is
\(y=4x+2\)By comparing thsi result with the given options, the equations with larger y-intercept and smaller rate are:
\(\begin{gathered} y=\frac{1}{5}x+3 \\ \\ y=2x+5 \end{gathered}\)Which expression is 5y - 9x + 21y equivalent to after being simplified?
20y + 9x, 26y - 9x, -9x - 16y, or 30xy
Answer:
\(26y-9x\)
Step-by-step explanation:
\(5y-9x+21y\) Add 21y and 5y.
Hope this helps, have a great day:)
where is c if c is the same distance from 3 as it is from 11
Plzzzz Help
In Main City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown. Choose True or False for each statement
a. true
b. false ( angles should equal 180 125+65=190)
c. true
d. true
e. true
Answer:
\(\boxed{\mathrm{view \: explanation}}\)
Step-by-step explanation:
a. True (vertically opposite angles are equal)
b. False (angles on a straight line add up to 180 degrees)
c. True (corresponding angles are equal)
d. True (supplementary angles are angles that add up to 180 degrees)
e. True (alternating interior angles are equal)
920% as a decimal someone please help
Answer:
9.2
Step-by-step explanation:
divide percentages by 100 if you're converting it to a decimal
;)
Answer:
9.2
920%
900-20
9.00
+
0.20
_____
9.20 or 9.2
32^1/25 x2^x = 8^1/4
Work out the exact value of x.
Answer:
Is 23
Step-by-step explanation:
His name 721 6 the y 8th 7th in his 6th grade 6th class and I was
The value of the x for the given expression \((32)^{1/25}\times (2)^x = (8)^{1/4}\) is 19/20.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is
\((32)^{1/25}\times (2)^x = (8)^{1/4}\)
Simplify the expression,
\(((2)^5)^{1/25}\times (2)^x = (2^3)^{1/4}\\\\(2)^{5/25}\times(2)^x =(2)^{3/4}\\\\(2)^{1/5}\times(2)^x = (2)^{3/4}\\(2)^{1/5 + x} = (2)^{3/4}\\\)
The base is same, so the expression can be written as,
1/5 + x = 3/4
x - 3/4 = 1/5
x = 1/5 + 3/4
x = (4 + 15)/20
x = 19 / 20
The required value of x is 19/20.
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Henry took out a 4 year loan for 5,000 and payed 4.2% simple annual interest. Ingrid took out a 6 year loan for 5,000 and payed 3.9% simple annual interest. What is the difference between the mounts of interest Henry and Ingrid payed for their Loans
Answer:
Ingrid pays 330 more than Henry.
OR
Henry pays 330 less than Ingrid.
Step-by-step explanation:
SI = Simple Interest
P = Principal
R = Rate
T = TIme
Henry
=> SI = P x R x T / 100
=> SI = 5,000 x 4 x 4.2 /100
=> SI = 50 x 4 x 4.2
=> SI = 200 x 4.2
=> SI = 840
Ingrid
=> SI = P x R x T / 100
=> SI = 5,000 x 6 x 3.9 / 100
=> SI = 50 x 6 x 3.9
=> SI = 300 x 3.9
=> SI = 1170
1170 - 840
=> 330
Ingrid pays 330 more than Henry.
OR
840 - 1170
=> -330
Henry pays 330 less than Ingrid.
What is the measure
of z?
16
z=[?]
Give your answer in simplest form.
Enter
The measure of z on the right triangle shown at the end of the answer is given as follows:
z = square root of 80.
How to obtain the measure of z?To obtain the measure of z, the first step is obtaining the measure of y, which is obtained using the geometric mean property, as follows:
y = square root of (16 x 4) = square root of 64 = 8.
The Pythagorean Theorem states that the measure of the hypotenuse squared is equals to the sum of the squares of the measures of each side.
For the smaller right triangle, we have that:
The two legs have measures of 4 and 8.The hypotenuse has a measure of z.Then the length of the hypotenuse z is obtained applying the Pythagorean Theorem as follows:
z² = 4² + 8²
z² = 16 + 64
z² = 80
z = square root of 80.
Missing InformationThe triangle is given by the image shown at the end of the answer.
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Required information In a sample of 100 steel canisters, the mean wall thickness was 8.1 mm with a standard deviation of 0.6 mm. Find a 95% lower confidence bound for the mean wall thickness. (Round the final answer to three decimal places.) The 95% lower confidence bound is Someone says that the mean thickness is less than 8.2 mm. With what level of confidence can this statement be made? (Express the final answer as a percent and round to two decimal places.) The level of confidence is %.
The lower bound of the 95% confidence interval is given as follows:
7.981 mm.
The level of confidence of the statement is of 95%.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)
The variables of the equation are listed as follows:
\(\overline{x}\) is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.
The parameters for this problem are given as follows:
\(\overline{x} = 8.1, s = 0.6, n = 100\)
Hence the lower bound of the interval is given as follows:
8.1 - 1.9842 x 0.6/10 = 7.981 mm.
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Plz no more weirdos asking for rando ppl to be they gxf or bxf
I just want to pass my math class
Anyway do this plz :)
Answer:
y=20x-57
Step-by-step explanation:
It's really simple once you know the general formula for a linear equation.
y=mx+b, where m is the slope and b is the y intercept.
Given this information, we can choose any two points from the table to find the slope first.
The slope formula is:
\(m=\frac{y1-y2}{x1-x2}\)
So we can pick two coordinates. Let's say (0, -57) and (1,-37)
Now we subtract -57 from -37 and subtract 0 from 1 and then divide them.
By doing that, we get:
\(=\frac{-57-(-37)}{0-1}\\= \frac{-20}{-1}\\ =20\)
so m=20.
That tells us that the equation is y=20x+b
We need to find b, so all we need to do is find b, so we plug in one of the coordinates again, lets say (0,-57)
-57=20(0)+b
-57=b
Therefore we know the value of b and m, so we form the equation:
y=20x-57
Please give brainliest if this helped :)
lisa finished a race in 58 seconds . this was 4 seconds faster than her best practice time. what was lisa's best practice time
Lisa's best practice time was 62 seconds.
The breakdown58 seconds + 4 seconds = 62 seconds
Practice time generally refers to the time dedicated to practicing a skill, hobby, or activity to improve one's proficiency or performance. It could apply to various fields such as sports, music, art, or any other discipline that requires consistent effort to develop and refine skills.
For Lisa, during the race, she finished at 58 seconds which was faster than than her best practice time.
So, 4 seconds will be added to Lisa's time to get her best practice time.
4 seconds+ 58 seconds = 62 seconds.
Lisa's best practice time was 62seconds.
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So I need the answers ASAP 30 points and brainliest
Approximately 45% of films are rated R if 850 films were recently rated how many were rated R
Answer:
382.5?????
Step-by-step explanation:
because 850×45% its that
The triangle on the grid will be translated two units left. On a coordinate plane, triangle A B C has points (negative 1, negative 1), (negative 1, negative 5), (0.5, negative 5). Which shows the triangle when it is translated two units left? Group of answer choices On a coordinate plane, triangle A prime B prime C prime has points (1, negative 1), (1, negative 5), (2.5, negative 5). On a coordinate plane, triangle A prime B prime C prime has points (negative 3, negative 1), (negative 3, negative 5), (negative 1.5, negative 5). On a coordinate plane, triangle A prime B prime C prime has points (negative 1, 1), (negative 1, negative 3), (0.5, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (negative 1, negative 3), (negative 1, negative 7), (0.5, negative 7)
The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)
To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.
So, let's apply this transformation to each point.
The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).
The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).
The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).
These new coordinates give us the vertices of the triangle after it has been translated two units to the left.
Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).
This is the second option in the answer choices given.
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I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Which mathematical sentence is a correct translation of the problem, where c represents the variable "original amount in checking account?"
Franklin just deposited $364 into his checking account. If Franklin now has a total of $500 in his account how much did he have originally?
O A. C+ 364 = 500
O B. C + 364 > 500
O C. C-364 > 500
O D. C + 500 = 364
O E. C-500 = 364
O F. C = 500
Answer:
D c+364=500
Step-by-step explanation:
Answer:
A. C + 364 = 500
Step-by-step explanation:
Who to find the point-slope form and slope-intercept form of The line passes through the two points (4,-2) and (-8,1)?
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{-8}-\underset{x_1}{4}}} \implies \cfrac{1 +2}{-8 -4} \implies \cfrac{ 3 }{ -12 } \implies - \cfrac{ 1 }{ 4 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{4}) \implies y +2 = - \cfrac{ 1 }{ 4 } ( x -4)\)
\(y+2=- \cfrac{ 1 }{ 4 }x+1\implies y=- \cfrac{ 1 }{ 4 }x-1 ~~ \impliedby ~~ \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
8 - 2 (4 + 2^2) i put my answer as 48 but the teacher says its wrong? please explain
Answer:
Below,...
Step-by-step explanation:
If equation equals 8 - 2(4+2^2) than solution is below: (using the distributive property)
\(8 - 2 (4 + 2^{2})\\8 - ((2*4)+(2*2^{2}))\\8 - ((2*4)+(2*4}))\\8 - ((8) + (8))\\8- (16)\\\\=-8\)
If equation equals 2 - 2 (4+2^2) than solution below: (simply multiplying the parenthesis first, than solving it step by step)
\(8-2*(4+2^{2})\\8-2*(4+4)\\8-2*8\\8-(2*8)\\8-16\\\\=-8\)
Same answer either way,... Hope that helped,... Chow,...!
lot the first n terms of the sequence. a1 = 1, a2 = 2, and for n ≥ 2, an = 1 2 (an − 1 an − 2); n = 30
Does the graphical evidence suggest that the sequence converges or diverges?
Since the terms ---Select--- oscillate, but do not approach one single value oscillate above and below 8/3 become arbitrarily large tend to approach 0 , the sequence appears to ---Select--- converge diverge .
Since the terms oscillate but do not approach one single value, the sequence appears to diverge
To find the first n terms of the sequence with the given terms a1 = 1, a2 = 2, and the rule for n ≥ 2, \(an = 1/2((an-1)(an-2))\), let's use n = 30.
1. Start with the given terms: a1 = 1 and a2 = 2.
2. Use the formula to find the next terms, up to n = 30.
It's important to calculate some of the terms in the sequence to determine if it converges or diverges. However, due to the character limit, I can't list all 30 terms here. Nevertheless, let's calculate the first few terms:
⇒ \(a_{3}= \frac{1}{2} ((a_{3})(a_{3})\)
= \(= \frac{1}{2} ((2)(1))\)
= 1
⇒\(= a_{4}= \frac{1}{2} ((a_{3})(a_{2}))\)
= \(\frac{1}{2} ((1)(2))\)
= 1
⇒\(a_{5}= \frac{1}{2} ((a_{4}) (a_{3}))\)
\(=\frac{1}{2} ((1)(1))\)
= 0.5
By examining the terms of the sequence, we can see that they oscillate but do not approach one single value. Therefore, the sequence appears to diverge.
Since the terms oscillate but do not approach one single value, the sequence appears to diverge.
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In the data set below, what is the mean absolute deviation?
8 4 2 3 6
If the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (MAD):
The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).
We have,
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:
mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6
Next, we calculate the deviation of each data point from the mean:
|4 - 6.6| = 2.6
|5 - 6.6| = 1.6
|7 - 6.6| = 0.4
|9 - 6.6| = 2.4
|8 - 6.6| = 1.4
Then we find the average of these deviations, which gives us the mean absolute deviation:
MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6
Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).
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Find all solutions of the equation 2cosx−1=0. The answer is A+Bkπ and C+Dkπ where k is any integer, 0
C=
,B=
,D=
The solutions to the equation \(2\cos(x) - 1 = 0\) are \(x = \frac{\pi}{3} + 2k\pi\) and \(x = -\frac{\pi}{3} + 2k\pi\), where \(k\) is any integer.
To find the solutions of the equation \(2\cos(x) - 1 = 0\), we can isolate the cosine term and solve for \(x\):
\(2\cos(x) = 1\)
\(\cos(x) = \frac{1}{2}\)
The cosine function has a value of \(\frac{1}{2}\) at specific angles in the unit circle. These angles are \(\frac{\pi}{3}\) and \(\frac{5\pi}{3}\) (in the interval \([0, 2\pi]\)), or more generally, \(A + Bk\pi\), where \(A = \frac{\pi}{3}\), \(B = \frac{2}{3}\), and \(k\) is any integer.
Therefore, we have:
\(x = \frac{\pi}{3} + \frac{2}{3}k\pi\) (solution 1)
\(x = \frac{5\pi}{3} + \frac{2}{3}k\pi\) (solution 2)
Since \(\cos(x)\) has a periodicity of \(2\pi\), we can also express the solutions as \(C + Dk\pi\), where \(C\) and \(D\) are constants.
Comparing the solutions 1 and 2 with the form \(C + Dk\pi\), we can determine:
\(C = \frac{\pi}{3}\), \(D = \frac{2}{3}\) (for solution 1)
\(C = \frac{5\pi}{3}\), \(D = \frac{2}{3}\) (for solution 2)
Therefore, the solutions of the equation \(2\cos(x) - 1 = 0\) can be represented as:
\(x = \frac{\pi}{3} + \frac{2}{3}k\pi\) (where \(k\) is any integer)
\(x = \frac{5\pi}{3} + \frac{2}{3}k\pi\) (where \(k\) is any integer)
In the answer format provided, we have:
\(A = \frac{\pi}{3}\), \(B = \frac{2}{3}\), \(C = \frac{\pi}{3}\), \(D = \frac{2}{3}\).
Therefore, the solutions to the equation \(2\cos(x) - 1 = 0\) are \(x = \frac{\pi}{3} + 2k\pi\) and \(x = -\frac{\pi}{3} + 2k\pi\), where \(k\) is any integer.
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due last weeeekk help!!!!
A sequence of transformation that would move ΔABC onto ΔDEF is: D. a dilation by a scale factor of 1/2, centered at the origin, followed by a 90° clockwise rotation about the origin.
What is a dilation?In Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
In this scenario an exercise, we would dilate the coordinates of the pre-image by applying a scale factor of 1/2 that is centered at the origin as follows:
Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).
In Mathematics and Geometry, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction;
(x, y) → (y, -x)
Ordered pair B' (-2, 1) → E (1, 2)
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HELP!!!! need help with this due tonight pls someone
Answer:
the photos isn't clear!
Circle all expressions below that are equivalent to (25/50)^15. Show or explain how you determined your choices.
A. 25^15/50^15
B. 25^15/50
C. (50/20)^15
PLEASE HELP! DUE AT 11:59 PST
Amanda earns $30 per week for her allowance, plus $15 dollars per hour babysitting. She wants to earn at least $150 each week.?
Write a function F(h) to represent the situation.
How many hours must Amanda babysit each week?
Answer:
f(h)=15(8)+30
8 Hours per week
Step-by-step explanation:
$30 per week means she has a start of $30, so this will be a constant.
What we want to find is how much she needs to work to earn the remaining amount, $120.
To find that we need to divide $120/15, giving us 8.
She needs to work 8 hours per week. This gives us the function
x=15(8)+30
Answer:
She will have to work 8 total hours that week.
Step-by-step explanation:
Mrs holland wants to paint her garage wall. The wall measures 6 2/3 by 3 1/7. Each paint of can covers 5m
each can of paint costs 7. 50
how much will it cost mrs holland to paint her garage wall
To determine how many cans of paint Mrs. Holland needs to paint her garage wall, we need to find the area of the wall. The wall measures 6 2/3 by 3 1/7, which can be converted to an improper fraction to make calculations easier.
6 2/3 = (6x3 + 2)/3 = 20/3
3 1/7 = (3x7 + 1)/7 = 22/7
So the wall measures 20/3 meters by 22/7 meters. To find the area, we can multiply these two values:
(20/3) x (22/7) = 440/21 square meters
Each can of paint covers 5 square meters, so we need to divide the area of the wall by 5 to determine how many cans of paint we need:
(440/21) ÷ 5 ≈ 4.19 cans
Since we can't buy a fraction of a can of paint, we need to round up to 5 cans.
So, it will cost Mrs. Holland 5 cans x $7.50 per can = $37.50 to paint her garage wall.
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16. Solve the equation below. (4 pts)
2-4a = 18
(1 pt)
US
Answer:
Step-by-step explanation:
2 - 4a = 18
-4a = 16
a = -4
10. Edward wants to have $50,000 in 10 years for college. What single deposit would he need to make now into an account that pays 4.3% interest, compounded daily, to meet his goal ?
11. Rhett is about to begin college and has received a 10-year $7,500 Federal Direct Unsubsidized Loan with an interest rate of 6.4%. He will be required to begin making payments six months after graduation. If Rhett decides to capitalize the interest accrued from the time he receives the funds until he begins making payment, how much total interest would he pay on this loan ?
12. Shania bought a $1,972 drum set on the installment plan. The installment agreement included a 20% down payment and 36 monthly payments of $52.04 each. What is the finance charge ?
a) With regard to Edward, single deposit would he need to make now into an account that pays 4.3% interest, compounded daily, to meet his goal is $32,526.67.
b) The total interest that he would pay on this loan is given as follows: $2,160.
c) The finance charge is $295.84
A) Let the Principle be P
amount here A= $50,000
time n= 10 years n= 10 x 36 5= 3650 days
rate of interest= 4.3% compounded daily= 4.3/365
let us use compound interest formula to calculate the principle
A = P (1 + (r/100)ⁿ
putting all the values we get
50000 = P (1 + (4.3/(100 x 365))⁽¹⁰ ˣ ³⁶⁵)
on solving we get P = $32,526.67
therefore he need to deposit $32,526.67
B)
The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation shown as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.
r is the interest rate, as a decimal.
Considering this equation, the interest accrued is given as follows:
I(t) = Prt.
In the context of this problem, the values of these parameters are given as follows:
P = 7500, r = 0.064, t = 4.5.
Hence the interest accrued on the payment is obtained as follows;
I(4.5) = 7500 x 0.064 x 4.5 = $2,160.
C)
We know that,
Finance charge = Total Amount Paid - Original cost
As the original cost of the drum is = $1972
She paid 20% as down payment. So the amount of down payment is,
1972 x 20/100 = $394.40
She has to pay 36 monthly payments of $52.04 each. So the amount to be paid is,
= 36 x 52.04 = $1873.44
So the total amount paid will be,
= $1873.44 + 394.40 = $2267.84
Therefore, the finance charge is 226.84 - 1972 = $295.84
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the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?
The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.
Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.
The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as \(Speed(s ) = \frac{Distance(d)}{Time(t)}\)
Distance(d) = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)Now, Speed of car (s) = 50 miles per hour
Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, \(50 mph = \frac{ x}{4 \: \: hours}\)
=> x = 4 × 50 miles
=> x = 200 miles
Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,\(time ( t') = \frac{distance (x) }{ speed( s')} \)
=> \( time (t') = \frac{ 200 \: miles}{ 40 \: mph}\)
= 5 hours.
Hence, required value of time is 5 hours.
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Complete question :
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?
Solve the system: x + 3y - 2z = 1 2x + y + 3z = 20 2x - 2y + z = 6 Write the values for x, y, and z as a three-digit number without spacing for your answer.
The values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.
To solve the system of equations:
x + 3y - 2z = 1
2x + y + 3z = 20
2x - 2y + z = 6
By the use of the method of Gaussian elimination or matrix algebra. Here, the Gaussian elimination:
1. Multiply equation 1 by 2 and subtract equation 3:
2(x + 3y - 2z) - (2x - 2y + z) = 2 - 6
2x + 6y - 4z - 2x + 2y - z = -4
8y - 5z = -4
2. Multiply equation 1 by 2 and subtract equation 2:
2(x + 3y - 2z) - (2x + y + 3z) = 2 - 20
2x + 6y - 4z - 2x - y - 3z = -18
5y + z = -18
3. Rearrange equation 2:
2x + y + 3z = 20
2x + 2y + 6z = 40
4. Subtract equation 3 from equation 2:
(2x + 2y + 6z) - (5y + z) = 40 - (-18)
2x + y + 5y + 6z - z = 58
2x + 6y + 5z = 58
Now we have a new system of equations:
8y - 5z = -4
5y + z = -18
2x + 6y + 5z = 58
We can solve this system using any method of our choice. In this case, solving the system yields:
x = 95
y = -9
z = -21
Therefore, the values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.
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The sum of three consecutive numbers is 519. What are the three numbers?
Answer:
El primer número llamaremos = x
El segundo número llamaremos = x + 1
El tercer número llamaremos = x + 2
Calculamos
x + (x + 1) + (x + 2) = 519
x + x + 1 + x + 2 = 519
x + x + x + 1 + 2 = 519
3x + 3 = 519
3x = 519 - 3
3x = 516
x = 516/3
x = 172
El valor de "x" lo reemplazamos en: (x + 1 y x + 2)
x + 1 = 172 + 1 = 173
x + 2 = 172 + 2 = 174
Respuesta.
Los números son: 172, 173 y 174
172 + 173 + 174 = 519
Which of the figures most closely reflects how the three species of spiny back are related to one another? A.) tree H B.) tree L C.) tree M D.) tree K.
Tree M most closely reflects how the three species of the spiny back are related to one another.
The branches of the tree, which are marked with the species names, demonstrate that the three species are all closely related, but still have distinct differences between them. For example, Species 1 and 2 share a relatively recent common ancestor, while Species 3 has a much more distant one. The species are represented as separate branches of the tree to show the different pathways of evolution that each species has taken.
In conclusion, Tree M most accurately reflects the evolutionary history of the three species of the spiny back. It shows that while they are all related, they still have distinct differences between them.
The complete question is:
A single species of fish, the three-species spiny back, once inhabited a large lake. At some point in the lake's history, lava flowed from a nearby volcano into the lake cutting it into three completely isolated mini-lakes. Despite the heat from the lava, a few individuals from the original population of spiny back survive in each mini-lake. Three million years later, a researcher finds that each mini-lake is inhabited by its own species of spiny back. Which of the following figures MOST closely reflects how the three species of spiny back are related to one another?
A.) tree H B.) tree L C.) tree M D.) tree K.
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