Answer:
y = 1
Step-by-step explanation:
Substitute -10 for x so the equation would be y=2/5-10-3
that would then be y=4-3
which would equal 1
Find the h.c.f of {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2}x 3 +y 3 andx 2 −xy+y 2
Factorize the sum of cubes:
[tex]x^3 + y^3 = (x+y) (x^2 - xy + y^2)[/tex]
so [tex]x^2-xy+y^2[/tex] is a factor of [tex]x^3+y^3[/tex]. Then the HCF is [tex]\boxed{x^2 - xy + y^2}[/tex].
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k > 0. Are Rectangle 1 and Rectangle 2 similar? Why or why not? Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1. Write a paragraph proof to show that the area of Rectangle 2 is times the area of Rectangle 1. Answer:
Yes, the two rectangles are similar, because rectangle 2 is a dilation of rectangle 1.
Are the two rectangles similar?
We know that rectangle 1 has dimensions L and W.
And rectangle 2 is made by multiplying the dimensions of rectangle 1 by a factor k > 0.
Then, rectangle 2 is just a dilation of rectangle 1, this means that in fact, the two rectangles are similar by definition.
Then:
Dimensions of rectangle 1:
Length = LWidth = W.Perimeter = 2*(W + L)Area = W*LFor rectangle 2:
Length = k*LWidth = k*WPerimeter = 2*(k*L + k*W) = k*(2*(L + W))Area = (k*L)*(k*W) = k²(L*W)Above we can see that the perimeter of rectangle 2 is k times the perimeter of rectangle 1, and the area of rectangle 2 is k squared times the area of the rectangle 1.
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A bike shop offers three kinds of cycles—tricycles, bicycles, and unicycles. Together, the cycles in the shop have a total of 98 wheels and 46 seats. (Tricycles have 3 wheels, bicycles have 2 wheels, and unicycles have 1 wheel. All cycles have 1 seat.) There are twice as many bicycles as tricycles. How many of each type of cycle are in the shop?
Answer:
There are 13 tricycles, 26 bicycles, and 7 unicycles.
Step-by-step explanation:
Let t=the number of tricycles, b=the number of bicycles, and u=the number of unicycles.
Equation to find the number of wheels:
3t+2b+u=98
This can be found because we know that each tricycle has 3 wheels, so we multiply the number of tricycles by 3. This can be done with bicycles and unicycles as well.
Equation to find the number of seats:
t+b+u=46
We know that there are two times as many bicycles as there are tricycles, this can be represented by the equation b=2t.
We can plug this into our number to wheels equation to get:
3t+2(2t)+u=98
3t+4t+u=98
7t+u=98
u=-7t+98
We can also put this into out number of seats equation to get:
t+2t+u=46
3t+u=46
u=-3t+46
Set the equations equal to each other to get:
-7t+98=-3t+46
-4t+98=46
-4t=-52
t=13
b=2t
b=2(13)
b=26
b+t+u=46
26+13+u=46
39+u=46
u=7
There are 13 tricycles, 26 bicycles, and 7 unicycles.
Solve this recurrence relation together with the initial condition given. an = 2an−1 for n ≥ 1, a0 = 3
The solution of the recurrence relation is [tex]a_n=3.2^n[/tex]
For given question,
We have been given a recurrence relation [tex]a_n = 2a_{n-1}[/tex] for n ≥ 1
and an initial condition [tex]a_0=3[/tex]
Let [tex]a_n[/tex] = m², [tex]a_{n-1}[/tex] = m and [tex]a_{n-2}[/tex] = 1
So from given recurrence relation we get an characteristic equation,
⇒ m² = 2m
⇒ m² - 2m = 0 .........( Subtract 2m from each side)
⇒ m(m - 2) = 0 .........(Factorize)
⇒ m = 0 or m - 2 = 0
⇒ m = 0 or m = 2
We know that the solution of the recurrence relation is then of the form
[tex]a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n[/tex] where [tex]m_1,m_2[/tex] are the roots of the characteristic equation.
Let, [tex]m_1[/tex] = 0 and [tex]m_2[/tex] = 2
From above roots,
[tex]\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n[/tex]
For n = 0,
[tex]\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2[/tex]
But [tex]a_0=3[/tex]
This means [tex]\alpha_2=3[/tex]
so, the solution of the recurrence relation would be [tex]a_n=3.2^n[/tex]
Therefore, the solution of the recurrence relation is [tex]a_n=3.2^n[/tex]
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Given the following vectors in component form:
r = ⟨2, 3⟩
s = ⟨5, –3⟩
t = ⟨–8, 6⟩
Check all expressions whose sum represents the same vector as (r + s) + t.
LeftAngleBracket 0, 7 RightAngleBracket + LeftAngleBracket negative 8, 6
RightAngleBracket LeftAngleBracket 7, 0 RightAngleBracket + LeftAngleBracket negative 8, 6 RightAngleBracket LeftAngleBracket 2, 3 RightAngleBracket + LeftAngleBracket negative 3, 3 RightAngleBracket LeftAngleBracket 2, 3 RightAngleBracket + LeftAngleBracket 3, negative 3 RightAngleBracket LeftAngleBracket negative 6, 9 RightAngleBracket + LeftAngleBracket 5, negative 3 RightAngleBracket
All expressions whose sum represents the same vector as (r + s) + t. is Option b,c,e
What are the expressions that equals (r + s) + t. ?Where
r= (2,3)
s= (5,-3)
t= (-8,6)
Generally, the equation for statement is mathematically given as
(7,0)+(-8,6) ,(2,3)+(-3,3) and (-6,9)+(5,-3) are equal to (r+s)+t
Therefore
x=(2,3)+(5,-3)
x=(7,0)
Now we can calculate (r+s)+t as
(7,0)+(-8,6)
(7-8,0+6)
(-1,6)
For (b)
x=(7,0)+(-8,6)
x=(-1,6)
in this scenario x expressions is equal to (r+s)+t
For (c)
x=(2,3)+(-3,3,)
x=(-1,6)
in this scenario x expressions is equal to (r+s)+t
For (e)
[tex]x=(-6,9)+(5,-3)[/tex]
x=(-1,6)
in this scenario x expressions is equal to (r+s)+t
In conclusion, all expressions whose sum represents the same vector as (r + s) + t. is b,c,e
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Someone help me pls and thank you
Answer:
4,11
Step-by-step explanation:
11-4=7
11*4=44
To find the actual integers, factor 44 and experiment with each pair of factors, an example being 2 and 22.
2*22=44
However, if you subtract 2 from 22, you get 20, not 7.
22-2-20
make x the subject. show work!
Answer:
[tex]x = \frac{b}{6a} - c[/tex]
Step-by-step explanation:
Steps are as below:
(I will refer A as 'a' and B as 'b')
[tex]a = \frac{b}{c + x} - 5a \\ a + 5a = \frac{b}{c + x} \\ 6a = \frac{b}{c + x} \\ 6a(c + x) = b \\ 6ac + 6ax = b \\ 6ac = b - 6ax \\ b - 6ax = 6ac \\ - 6ax = 6ac - b \\ 6ax = - (6ac - b) \\ 6ax = b - 6ac \\ x = \frac{b - 6ac}{6a} \\ x = \frac{b}{6a} - \frac{6ac}{6a} \\ x = \frac{b}{6a} - c[/tex]
PLEASE HELP CORRECT ANSWER ONLY PLS
Answer:
y = -1x + 5
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = -1x + 5
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-2x+5
Step-by-step explanation:
For every increase in x, y decreases by 2
so the slope is -2
You can solve for the y-intercept by going backward, 1-1=0, 3+2=5
the y-intercept is (0,5)
Using the slope intercept equation format, the answer is y-2x+5
HELP NEEDED ASAP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!
Consider function h.
What is the range of function h?
Answer: (-[tex]\infty[/tex], [tex]\infty[/tex])
Step-by-step explanation:
The following graph is a graph with a slant asymptote, which is an asymptote that isn't horizontal or vertical (i.e. doesn't have a slope of 0 or [tex]\infty[/tex]).
To review, an asymptote is a line that the graph of a function approaches, but will never touch. Normally, a horizontal asymptote would limit the range as the graph can never cross a certain y-value.
However, there is no such y-value that must not be crossed in a slant asymptote; therefore, there is not limitation to the range. The range would be all real numbers.
Hence, the range of function h is (-[tex]\infty[/tex], [tex]\infty[/tex]).
A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66? If x represents the number of 13 cent stamps and y the 18 cent stamps, which system represents the problem?
Answer:
18 stamps of 13 cent
24 stamps of 18 cent
Step-by-step explanation:
we have to solve the following system:
x + y = 42 equation (1)
13x + 18y = 666 equation (2)
(1) ⇒ y = 42 - x
We substitute y by 42 - x in equation (2) :
13x + 18(42 - x) = 666
⇔ 13x + 756 - 18x = 666
⇔ -5x + 756 = 666
⇔ -5x = 666 - 756
⇔ -5x = -90
⇔ x = 18
…………………………
Then
y = 42 - x
= 42 - 18
= 24
The top of the John Hancock Building is a rectangle whose length is 60 ft more than the width. The perimeter is 520 feet. What is the length?
Group of answer choices
a. L = 160 ft
b. L = 40 ft
c. L = 100 ft
d. L = 80 ft
Answer:
160 ft
Step-by-step explanation:
We have
2(length + width)= perimeter
than,
let, width =x
now,
2(x+60+x) = 520
or, 2x+60 = 260
or, 2x = 200
or, x = 100
so length is 100+60 = 160
Help with this question please.
Answer:
Step-by-step explanation:
Which of these tables represents a function
The table that represents a function is:
C. YWhat is a Function?A function is an expression that represents the relationship between two variables. The variables in this case are the dependent and independent variables.
To identify a function, you need to note that no variable of x should be equal to y.
The formular is represented this way: y = f(x). The table that satisfies this condition is the Y table.
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The student body of 135 students wants to elect two representatives combination or permutation
The method to use is Combination
What is combination?Combination is a way or method of selecting items from a collection without a defined order or manner.
The formula for finding Combination is given as;
Combination = n!/ r!(n -r)!
n = 135
r = 2
Combination = 135!/ 2!(135 - 2)!
Thus, the method to use is Combination
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An allergy medication is successful in treating 60% of all patients who use it. The medication is given to 200 patients. Let X
The mean is μ=140.
The standard deviation is σ = 6.4807.
The probability that X (number of successful treatments) is 128 or less is 0.0322.
What is normal distribution curve?In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.
According to the question,
An allergy medication is successful in treating 70%
The medication is given to 200 patients.
Thus,
The random variable X is a binomial random variable with n = 200 (there were 200 patients).
The probability that a medication is successful in treating a randomly selected patient is 0.7.
p = 0.7 (the medication was successful in 70% cases).
Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.
[tex]\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}[/tex]
Substitute values of 'n' and 'p' to get the result,
[tex]\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}[/tex]
Thus, the mean is obtained as 140.
The standard deviation is 6.4807.
Step 2: find P(X≤128)
As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.
[tex]$n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$[/tex]
[tex]\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}[/tex]
Therefore, the probability that X is 128 or less. is 0.0322.
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The complete question is-
An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.
please can someone tell me how to get the answer
The number of three-digit number you can make is 8
How to determine the number of digits?The usable digits are given as:
4 and 9
Since the two digits can be repeated, then we have
First = 2
Second = 2
Third = 2
So, we have:
Total = 2 * 2 * 2
Evaluate
Total = 8
Hence, the number of three-digit number you can make is 8
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Find the measure of each interior angle of a regular octagon. (A regular polygon is one that has all the same sides and angles). [1]
The interior angle of a regular octagon is 135 degrees.
What is an octagon?An octagon is a polygon that has 8 sides. Therefore, a regular octagon is a octagon with all it sides and angles equal to each other.
Therefore, the sum of angles in an octagon is each interior angle multiply by the number of sides.
Therefore,
n = number of sides = 8
Hence,
interior angle = (n - 2)180 / n
interior angle = (8 - 2)180 / 8
interior angle = 6 × 180 / 8
interior angle = 1080 / 8 = 135°
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A line passes through the points (-1,-1) and (5,8) which points lie on the same line?
Answer: all points [tex](x,y)[/tex] that satisfy [tex]y=\frac{3}{2}x+\frac{1}{2}[/tex]
Step-by-step explanation:
The slope of the line is
[tex]\frac{-1-8}{-1-5}=\frac{-9}{-6}=\frac{3}{2}[/tex]
So, substituting into point-slope form, the equation is
[tex]y+1=\frac{3}{2}(x+1)\\\\y+1=\frac{3}{2}x+\frac{3}{2}\\\\y=\frac{3}{2}x+\frac{1}{2}[/tex]
Therefore, all points [tex](x,y)[/tex] that satisfy [tex]y=\frac{3}{2}x+\frac{1}{2}[/tex] will lie on the same line.
Help me solve this image please!!!
Based on the information, Christian would have $5525.5 of an annuity.
How to calculate the annuity?According to the given information, the number of coffees per week is 3 then, per month is 3x4 = 12
Each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54
Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133
n = number of payments = 8 x 12 = 96
We can use the formula for finding the future value as below
FV = C x [ ( 1 + r )n-1 ] / ( r )
FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)
= 54 x [ (1.13609 - 1)] / (0.00133)
= 54 x 0.13609 / (0.00133)
= 54 x 102.3233
= 5525.5
Therefore Christian would have $5525.5 of the annuity.
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Suppose you start with a full tank of gas (17 gallons) in your truck. After driving 3 hours, you now have 3 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing
Step-by-step explanation:
in 3 hours the truck used 17 - 3 = 14 gallons.
that means it used
14 gallons / 3 hours = 14/3 gallons / hour
and that means it is using
14/3 × x gallons in x hours
y = 17 - (14/3 × x)
the gas left in the tank is decreasing by 14/3 gallons per hour.
Which equation shows an example of the associative property of addition? (–7 i) 7i = –7 (i 7i) (–7 i) 7i = 7i (–7i i) 7i × (–7i i) = (7i – 7i) (7i × i) (–7i i) 0 = (–7i i)
The equation which shows the associative property of addition is; (–7 + i) +7i = –7 (i +7i).
What is the associative property of addition?Associative property of addition postulates that Changing the grouping of addends does not change the sum of the numbers. As an instance, ( 5 + 3 ) + 4 = 5 + ( 3 + 4 )
Consequently, the equation which shows the associative property of addition is; (–7 + i) +7i = –7 (i +7i)
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Ryan is cleaning out his room. his sister gives him 4 boxes of books to put with the 3 books he already had. when he finishes cleaning he discovers he now has 35 books on his shelves. how many books were in each box?
Answer:
8 books per box.
Step-by-step explanation:
One must assume that the books are evenly distributed among the boxes. Ryan has 3 books already and adds 4 boxes to reach a total of 35 books:
3 books + 4 boxes = 35 books
4 boxes = 35 books-3 books
4 boxes = 32 books
1 box = 8 books
There are 8 books per box.
40 boys and 28 girls stand in a circle, hand in hand, all facing inwards. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl
Answer:
28-18=10
Step-by-step explanation:
10 boys give their left hand
hope it helps
sry if im wrong
There are 10 boys who give their left hand to a girl in the given scenario.
In a circle, the total number of students is equal to the sum of the number of boys and girls.
Therefore, in this case, there are 40 boys + 28 girls = 68 students in total.
Since exactly 18 boys give their right hand to a girl, there are 18 boys who are connected to girls in a clockwise direction. As the remaining boys are connected in a counterclockwise direction, the number of boys giving their left hand to a girl can be determined by subtracting 18 from the total number of girls.
Thus, the number of boys giving their left hand to a girl is 28 - 18 = 10 boys.
Therefore, there are 10 boys who give their left hand to a girl in the given scenario.
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Which of the following rational functions is graphed below?
--10
10-
-10
O A. F(X) = x+1
10
Answer: D
Step-by-step explanation:
There are vertical asymptotes at [tex]x=\pm 1[/tex].
This eliminates everything except for D.
The graph is of the rational function f(x) = 1 / (x-1)(x + 1) Hence, Option D. is correct.
What is rational function?A rational function is an algebraic fraction such that both the numerator and denominator are polynomials.
Here, we have been given the graph.
We have to find which of the given rational functions is graphed in image.
On x-axis, 1 unit = 2 units
Clearly, we can see the graph is not defined at point x = - 4 and at x = 1.
Corresponding to x = - 4, factor is (x+4) and Corresponding to x = 1, factor is (x-1) .
So, this graph is of the rational function
f(x) = 1 / (x-1)(x + 1)
Hence, Option D. is correct
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Rank--from first to last--the following steps for finding the bottleneck and capacity in a process with rework.
Steps for finding the bottleneck and capacity in a process with rework:
atevaluateevaluate---What is the bottleneck and capacity in a process with a rework?In production and project management, a bottleneck is a process in a chain of processes whose restricted capacity reduces the capacity of the entire chain. A bottleneck causes production stalls, supply overstock, customer pressure, and low employee morale.To evaluate a reworked process, a weighted average processing time must be calculated. Because the processing time for rework differs from the initial processing time, a weighted average processing time must be computed. The resource's capacity is divided by its weighted average processing time.Steps for determining the bottleneck and capacity in a reworked process:atevaluateevaluate---Therefore, steps for finding the bottleneck and capacity in a process with rework:
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PLEASE IM BEGGING U so hard to understand T_T
Answer:
[tex]b^{2} +7b+7[/tex] with remainder 1
Help me pleaseeeeeeeeeeeeeeeeeeeee
Answer:
a = 16.52 cmb = 23.85 cm=========================
Given AB = 22 cmm∠A = 42°m∠B = 75°To findSide length of a and bSolutionThe law of sines is:
a/sin A = b/sin B = c/sin CStep 1Find the value of ∠C using the angle sum theorem:
m∠A + m∠B + m∠C = 180°42° + 75° + C = 180°117° + C = 180°C = 180° - 117°C = 63°Step 2Find side a:
Note, the sides of a triangle are marked as:
a = BC, b = AC, c = AB (opposite to respective angle).Use two pairs with one unknown:
a/sin A = c/sin CSubstitute values and solve for a:
a/ sin 42° = 22/sin 63°a = 22*sin 42°/sin 63°a = 16.52 cm (rounded)Step 3Find side b, similar to finding side a:
b/ sin 75° = 22/sin 63°b = 22*sin 75°/sin 63°b = 23.85 cm (rounded)Answer:
a = 16.5 cm (nearest tenth)
b = 23.8 cm (nearest tenth)
Step-by-step explanation:
Definition
A, B and C are the angles and a, b and c are the sides opposite the angles.
From inspection of the triangle:
A = 42°B = 75°c = 22 cmInterior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42° + 75° + C = 180°
⇒ C = 180° - 117°
⇒ C = 63°
To find the missing side lengths a and b, use the Sine Rule:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Substitute the given values into the Sine Rule formula:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
Finding side a:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=\dfrac{22\sin 42^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=16.52162239...[/tex]
Therefore, side a is 16.5 cm (nearest tenth).
Finding side b:
[tex]\implies \sf \dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=\dfrac{22\sin 75^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=23.84984577...[/tex]
Therefore, side b is 23.8 cm (nearest tenth).
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The Table Shows a proportional relationship between x and y for each Value of x and y match it to the correct unit rate y/x in its simplest form
The correct proportions are given as follows:
x = 3, y = 27: 9/1.x = 9, y = 81: 9/1.x = 21, y = 126: 6/1.x = 14, y = 84: 6/1.x = 12, y = 36: 3/1.x = 15, y = 45: 3/1.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportions for this problem are given dividing y by x, hence:
x = 3, y = 27: 27/3 = 9, hence 9/1 has to be marked.x = 9, y = 81: 81/9 = 9, hence 9/1 has to be marked.x = 21, y = 126: 126/6 = 6, hence 6/1 has to be marked.x = 14, y = 84: 84/14 = 6, hence 6/1 has to be marked.x = 12, y = 36: 36/12 = 3, hence 3/1 has to be marked.x = 15, y = 45: 45/15 = 3, hence 3/1 has to be marked.More can be learned about proportions at https://brainly.com/question/24372153
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What is the surface area of pyramid with a square base of 5km and slant of 4.7km
The surface area of pyramid is 47km^2
A regular pyramid has a base that is a regular polygon and a vertex that is above the center of the polygon.
A pyramid is named after the shape of its base. A rectangular pyramid has a rectangle base. A triangular pyramid has a triangle base.
Given that the base of the pyramid is 5 km and the slant height is 4.7km
We need to find the surface area of pyramid
We know that
The lateral surface of pyramid = 4 *(1/2* length of base * slant height)
= 2*5*4.7
=47km^2
Hence the surface area of the pyramid is 47km^2
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