Answer:
[tex]ax^5+ by^5=241[/tex]
Step-by-step explanation:
Given:
[tex]ax + by = 1[/tex][tex]ax^2+ by^2 = 11[/tex][tex]ax^3+ by^3 = 25[/tex][tex]ax^4+ by^4 = 83[/tex]We can re-write the left sides of the given equations as follows:
[tex]ax^2+ by^2=(ax+by)(x+y)-xy(a+b)[/tex]
[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]
[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]
Therefore, following this pattern:
[tex]ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]
Use the given values and the expanded expressions to create 2 equations to help find the values of (x+y) and xy:
Equation 1
[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]
[tex]\implies 25=11(x+y)-xy(1)[/tex]
[tex]\implies 25=11(x+y)-xy[/tex]
Equation 2
[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]
[tex]\implies 83=25(x+y)-xy(11)[/tex]
[tex]\implies 83=25(x+y)-11xy[/tex]
Multiply Equation 1 by 11:
[tex]\implies 275=121(x+y)-11xy[/tex]
Then subtract Equation 2 from this to eliminate 11xy and find the value of (x+y):
[tex]\implies 192=96(x+y)[/tex]
[tex]\implies (x+y)=2[/tex]
Multiply Equation 1 by 25:
[tex]\implies 625=275(x+y)-25xy[/tex]
Multiply Equation 2 by 11:
[tex]\implies 913=275(x+y)-121xy[/tex]
Subtract the 2nd from the 1st to eliminate 275(x+y) and find the value of xy:
[tex]\implies 288=-96xy[/tex]
[tex]\implies xy=-3[/tex]
Therefore, we now have:
[tex]ax^4+ by^4 = 83[/tex][tex]ax^3+ by^3 = 25[/tex][tex](x+y)=2[/tex][tex]xy=-3[/tex]Substitute these into the equation for ax⁵ + by⁵ and solve:
[tex]\implies ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]
[tex]\implies ax^5+ by^5=(83)(2)-(-3)(25)[/tex]
[tex]\implies ax^5+ by^5=166+75[/tex]
[tex]\implies ax^5+ by^5=241[/tex]
Yuson must complete 15 hours of community sevice. She does 3 hours each day. Which linear equation represents the hours Yuson still has to work after x days?
A. Y=3x + 15
B. Y= -3x - 15
C. Y= -3x + 15
D. Y= 3x - 15
Answer:
C) y = -3x + 15
Step-by-step explanation:
Let's start with the hours required, 15. For each day worked we can subtract 3 hours. X days would mean 3x hours. Subtract that from the goal of 15 hours:
15 - 3x
The time remaining, y, is given by the equation 15 - 3x.
Rearrange the equation to match the format in the options,
y = 15 - 3x
y = -3x + 15
Option C
The base of a triangular prism is a right triangle with a base of 6 inches, a height of 8 inches, and a third side length of 10 inches. the height of the prism is 14 inches. find the surface area of the prism.
The surface area of the rectangular prism with the dimensions that are stated is: 384 in.²
What is the Surface Area of a Triangular Prism?Surface area = perimeter of base × height of prism + 2(base area)
= (s1 + s2 + s3)L + 2(1/2bh)
Given the following:
side of base (s1) = 6 in.side of base (s2) = 8 in.side of base (s3) = 10 in.Length of prism (L) = 14 in.Triangular base length (b) = 6 in.h = 8 in.Surface area = (6 + 8 + 10)14 + 2(1/2 × 6 × 8)
Surface area = 384 in.²
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The following cone has a height of 12 cm and a slant height of 16 cm. A right angle is formed between the height and radius of the cone
what is the length of the radius
Step-by-step explanation:
[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]
[tex] \sf Height_{\blue{cone}}=12 \: cm [/tex][tex] \sf Slant \: height_{\blue{cone}}=16\: cm [/tex][tex]\pink{\large{\underline{\underline{\sf To \: find:-}}}}[/tex]
[tex] \sf Radius_{\blue{cone}}=? [/tex][tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]
We know that,
[tex]\underline{\boxed{\sf (Radius)^2= (Slant height)^2-(height)^2}}[/tex]
[tex] \sf (Radius)^2 = (16)^2-(12)^2[/tex]
[tex] \sf (Radius)^2 = 256-144=112[/tex]
[tex] \longmapsto \sf Radius = \sqrt{112}≈10.6\:cm[/tex]
Q: Sam challenges Tom to a race. If Sam can run 6 meters per second and Tom can run at 7 meters per
second. After a minute and a half how far apart will they be?
Answer:
90 meters
Step-by-step explanation:
so, what we know is that there are 90 seconds in one minute and a half.
Sam can run 6 meters per second. which means after 90 seconds, he should have run 540 meters.
Tom can run 7 meters per second. This means after 90 seconds, he should have run 630 meters.
630-540 = 90
give brainliest please!
hope this helps :)
This table shows input and output values for a linear function f(x)
What is the difference of outputs for any two inputs that are three values apart.
Express your answer as a decimal.
The answer is 0.75 because I took the test and that's what the answer was :)
Write the equation of the line that passes through the points (-3,3) and (4, -1).
put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line,
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{4 +3} \implies \cfrac{ -4 }{ 7 }[/tex]
[tex]\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}{3}=\stackrel{m}{-\cfrac{4}{7}}(x-\stackrel{x_1}{(-3)})\implies y-3=-\cfrac{4}{7}(x+3)[/tex]
Explain step by step how you find the product of 6x^2y^5 and 3x^2 - 8x + 2xy^2 + 4y^3
The final product is 18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸
What is a product ?
The product is result obtained when a number or an expression is multiplied by the other number.
The product of the given expression
6x²y⁵ and 3x²-8x+2xy²+4y³
6x²y⁵ (3x²-8x+2xy²+4y³)
Step 1 : To multiply each term in the bracket with the other expression
out of the bracket
6*3*x²*y⁵*x² - 6*8*x²*y⁵ +6x²y⁵ *2*x*y² + 6*4*x²y⁵ *y³
Step 2 : The like variables will be solved
18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸
This is the final product
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the ratio of Â, B and C in triangle ABC is 2:3:4. calculate the size of each angle
Answer:
40°, 60°, 80°
Step-by-step explanation:
sum the parts of the ratio , 2 + 3 + 4 = 9 parts
the sum of the 3 angles in a triangle = 180° , then
180° ÷ 9 = 20° ← value of 1 part of the ratio , then
2 parts = 2 × 20° - 40° = ∠ A
3 parts = 3 × 20° = 60° = ∠ B
4 parts = 4 × 20° = 80° = ∠ C
Calculate the area of the following composite figure. (Please i need help with this)
The area of the composite shape in the diagram given is: 100 square inches.
How to Find the Area of a Composite Figure?Area of a composite figure = sum of the areas of the shapes that make up the figure.
Area of the composite shape = 2(area of triangle) = 2(1/2bh)
Area of the composite shape = 2(1/2×10×10)
Area of the composite shape = 100 square inches.
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Find the area and volume of a 11 inch cube (pls write do the equation in steps)
Answer:
1331 inches cubed
Step-by-step explanation:
V=LHW
since it is a cube, the length, height, and width will all be the same; 11 inches. You have to multiply 11 by 11 by 11, which equals 1331.
Hope this helped!
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.4 meters thick.
Let y represent the ice sheet's thickness (in meters) after x weeks.
Complete the equation for the relationship between the thickness and number of weeks.
y=_____
The equation for the relationship between the thickness and number of weeks is y = 3.8 - 0.2x
How to write equation?Ice lost per week = 0.2 metersIce remaining after 7 weeks = 2.4 metersNumber of weeks = xRelationship between the thickness and number of weeks = yIce lost at 7 weeks = 7(0.2) = 1.4 meters
Total thickness of ice before loss = Ice remaining after 7 weeks + Ice lost at 7 weeks
= 2.4 + 1.4
= 3.8 meters
The equation:
y = Total thickness of ice before loss - (Ice lost per week × Number of weeks)
= 3.8 - (0.2 × x)
y = 3.8 - 0.2x
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One day Maria spends 6/20 of the day asleep. Calculate in hours and minutes the amount of time she spends asleep.
Answer:
7 hours and 12 minutes
Step-by-step explanation:
there are 24 hours in a day, so multiply 6/20 by 24 to find the number of hours:
6*24/20 = 36/5 = 7 1/5 hours
we now know maria sleeps for 7 whole hours
next, there are 60 minutes in an hour, so multiply 1/5 by 60 to get 12 minutes
the perimeter of a rectangle is 20 cm and it's area is 24cm^2 find the length and breath of the rectangle
Answer:
length = 6cm , breadth = 4cm
Step-by-step explanation:
Let's assume length = l
breadth = b
Given perimeter of a rectangle = 20 cm
2(l+b) = 20
l+b = 20/2
l+b = 10
l = 10 - b____(1)
Given area of rectangle = 24 cm²
l×b = 24____(2)
(1) in (2) => l × b = 24
(10-b) × b = 24
10b - b² = 24
10b = 24 + b²
0 = b² - 10b + 24
b² - 10b + 24 = 0
b² + 6b + 4b + 24 = 0
b(b+6) +4(b+6) = 0
(b+4)(b+6) = 0
b+4 = 0. &. b+6 = 0
b = -4. b = -6
breadth must be less than length and it should be positive
So b = 4 cm
b=4 in (1)
(1)=> l = 10 - b
l = 10 - 4
l = 6
True or false? The graph represents a function
Answer:
true
Step-by-step explanation:
The statement is true because every graph associated a unique x-value for each y - value
What is the x and y intercept of y=1/3x-2, y=12-6x, and y=3x-7? Please show work!
Answer:
y = 1/3x - 2:
y - intercept: - 2x - intercept: 6y = 12 - 6x:
y - intercept: 12x - intercept: 2y = 3x - 7:
y - intercept: -7x - intercept: 7/3Step-by-step explanation:
Hello!
Slope Intercept FormThe slope-intercept form of a line is [tex]y = mx + b[/tex]
y = output, ordinatem = slopex = input, abscissab = y-intercepty = 1/3x - 2The y-intercept is the "b" value of the line, given as -2.
To find the x-intercept, we simply replace the y-value with 0:
0 = 1/3x - 22 = 1/3x6 = xy - intercept: - 2
x - intercept: 6
____________________________________________________
y = 12 - 6x
You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.
Solving for the x-intercept (remember, replace y with 0):
0 = -6x + 12-12 = -6x2 = xy - intercept: 12
x - intercept: 2
____________________________________________________
y = 3x - 7Simply take the "b" value, -7, to find the y-intercept of -7.
Solve for the x-intercept:
0 = 3x - 77 = 3xx = 7/3y - intercept: -7
x - intercept: 7/3
Additional Note:
You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.
The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.
A flower pot hangs from a brace. △MNQ and △MNP form the brace what is the value of x?
The value of x from the given triangle formed by the pot hanging from a brace is; x = 50°
How to find the missing angle in a triangle?
We are given from the diagram that;
∠NMP = 110° and ∠NPM = 30°
Sum of angles in a triangle is 180°.
Thus;
∠MNP = 180 - (110 + 30)
∠MNP = 40°
Thus;
x = 90 - 40
x = 50°
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14 friends go out for dinner and the bill for food and drink comes to £130. The friends decided to add a 5% tip on the top of this total. If they divide this expense equally between them, How much does each friend pay?
The amount each friend does pay is £9.75
How to calculate the pay of each friend using fractions and arithmetic operations?We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.
From the given information:
The 5% of 130 = £6.5Total amount paid = £130 + £6.5 = £136.5Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]
The cost of each friend = £9.75
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help please and I'll mark you brainiest.
The probability will include:
P(A and 1) = 1/24P(C and 2) = 1/12.P(B and 3) = 1/12.P(A and 4) = 1/12How to calculate the probability?The probability of P(A and 1) will be:
= 1/4 × 1/6
= 1/24
The probability of P(C and 2) will be:
= 1/4 × 2/6
= 1/12
The probability of P(B and 3) will be:
= 2/4 × 1/6
= 1/12
The probability of P(A and 4) will be:
= 1/4 × 2/6
= 1/12
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A population of beavers decreases exponentially at a rate of 7.5% per year. What is the equivalent monthly rate to the nearest hundredth of a percent
Answer:
0.65%
Step-by-step explanation:
i took the test
Solve for x in the equation x squared 4 x minus 4 = 8.
Answer:
±2√3
Step-by-step explanation:
Equation :
x² -4 = 8
x² -12 = 0
Using the quadratic formula then simplifying gives you :
±2√3
I know this lacks explanation but please brainliest
Answer:
x=2 or -6
Step-by-step explanation:
×^2+4×-4=8
8 will enter inside and become -8
x^2+4x-4-8=0
x^2+4x-12
(x^2+6x)(-2x-12)
x(x+6)-2(x+6)
(x-2)(x+6)
x=2 or x=-6
Please help! Giving brainlist!
If y=2x-1 is changed to y = x+ 2,
how would the graph of the new
function compare with the first one in terms of steepness and shift?
The graph of the function y = x+2 is steeper than the graph y = 2x-1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given functions are:-
y=2x-1y = x+2The graph of the functions is attached with the answer below. In the graph, we can see that the slope of the graph y = x+2 is steeper than the graph of y = 2x - 1.
The two graphs intersect at the point ( 3,5 ) so it is the solution of the two linear equations.
Hence the graph of the function y = x+2 is steeper than the graph y = 2x-1.
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I need help
30 POINTS!!!!
Answer:
A. Upward
B. (-2, -1)
C. X= -3, -1 ||| Y= 3
D. X=-2
Step-by-step explanation:
Please help and thanks
Choose the correct answer
2x>12x and 7x<14
Answer:
C - x < -6 and x < 2
Step-by-step explanation:
2x ">" -12 and 7x < 14. with negative numbers, the bigger the number the less it is. -12 < -6 because negative numbers work the opposite way that positive numbers do. I hope this helps you!!!!
True or False?
A square can be similar to a triangle since a square is composed of two triangles.
When Ronald goes to BIG Burgers, he orders a sandwich and a side order. For the
Answer:
true is the answer not hard question
Solve for x
−5(-3x-3)+5x+4=-1
If f (x) = StartRoot one-half x minus 10 EndRoot + 3, which inequality can be used to find the domain of f(x)?
StartRoot one-half x EndRoot greater-than-or-equal-to 0
One-half x greater-than-or-equal-to 0
One-half x minus 10 greater-than-or-equal-to 0
StartRoot one-half x minus 10 EndRoot + 3 greater-than-or-equal-to 0
The inequality that represents the domain of the function is [tex]\frac 12x - 10 \ge 0[/tex]
How to determine the domain?The function is given as:
[tex]f(x) = \sqrt{\frac 12x - 10} + 3[/tex]
Set the radicand greater than or equal to 0
[tex]\frac 12x - 10 \ge 0[/tex]
Multiply through by 2
x - 20 ≥ 0
Add 20 to both sides
x ≥ 20
Hence, the domain of the function is x ≥ 20
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Evaluate 5(x - 1) - 2 when x = 3
Answer:
8
Step-by-step explanation:
Given algebraic expression:
5(x - 1) - 2
To:
Evaluate this expression using x = 3
Solution:
5(x - 1) - 2Evaluate by plugging x = 3 to this expression:
5(3-1)-2Simplify using PEMDAS.
5(2)-210-28We can conclude:
By evaluating x = 3 to the given expression,the answer will be 8.
PLEASE HELP ASAP
What is the missing statement for the sixth step in the proof below?
Answer:
C
Step-by-step explanation:
The last reasoning is the side angle side theorem. In the whole proof, there is no mention of an angle. So the answer has to involve prooving that the angle in between the two sides that have been proven similar is the same in both traingles. This is best accomplished by statement C.
Which list correctly orders A, B, and C from least to greatest when A=171, B = -6, and C=1-51?
A, B, C
B, C, A
C, B, A
A, C, B