What is the solution to the system of equations below?
y = two-fifths x minus 3 and x = –10

Answer:

[tex]b^{2} +7b+7[/tex] with remainder 1

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].

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]

Answer:

Step-by-step explanation:

The number of three-digit number you can make is 8

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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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.

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.

The table that represents a function is:

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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Answer:

y = -1x + 5

Step-by-step explanation:

y = mx + c

y = gradient(x intercept) + y intercept

y = -1x + 5

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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The correct proportions are given as follows:

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:

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Answer:

=========================

The law of sines is:

Find the value of ∠C using the angle sum theorem:

Find side a:

Note, the sides of a triangle are marked as:

Use two pairs with one unknown:

Substitute values and solve for a:

Find side b, similar to finding side a:

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:

Interior 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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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

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.

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.

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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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

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.

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]).

Steps for finding the bottleneck and capacity in a process with rework:

Therefore, steps for finding the bottleneck and capacity in a process with rework:

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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.

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.

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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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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The method to use 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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The interior angle of a regular octagon is 135 degrees.

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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All expressions whose sum represents the same vector as (r + s) + t. is Option b,c,e

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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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

The equation which shows the associative property of addition is; (–7 + i) +7i = –7 (i +7i).

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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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

Based on the information, Christian would have $5525.5 of an 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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Yes, the two rectangles are similar, because rectangle 2 is a dilation of rectangle 1.

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:

For rectangle 2:

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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