the given point is on the graph of y=​f(x). Find a point on the graph of y=​g(x).
​g(x)=​f(x−​1)+​3; ​(6​,15​)

Answer:

Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...

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Answer: The two positive numbers that satisfy the given requirements are 25 and 50.

Step-by-step explanation:

Let's call the two positive numbers x and y. We want to maximize their product while satisfying the condition that "the sum of the first and twice the second is 100", or mathematically:

x + 2y = 100

We can use algebra to solve for one of the variables in terms of the other:

x = 100 - 2y

Now we want to maximize the product xy:

xy = x(100 - 2y) = 100x - 2xy

Substituting x = 100 - 2y:

xy = (100 - 2y)y = 100y - 2y^2

To find the maximum value of this expression, we can take the derivative with respect to y and set it equal to zero:

d(xy)/dy = 100 - 4y = 0

Solving for y gives:

y = 25

Substituting y = 25 into the equation x + 2y = 100, we get:

x + 2(25) = 100

x = 50

Therefore, the two positive numbers that satisfy the given requirements are x = 50 and y = 25, and their product is:

xy = 50(25) = 1250

Answer:

D

Step-by-step explanation:

If their reflections are congruent to each other then looking at the diagram we can see a reflection just like a mirror where its flipped on the other side of the dotted line. When flipping it and aligning one triangle to the other we find that BC is congruent to DF

(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:

mean = n x mean time = 50 x 5 = 250 minutes

variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9

The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:

te = n x mean time / (1 - p1 x p2)

where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:

σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:

Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.

(d) The variability class of the squared coefficients of variation can be determined as follows:

C0² (Part a): (0.6)^2 = 0.36 (low variability)

C0² (Part b): (0.6)^2 = 0.36 (low variability)

Ce² (Part c): (0.026)^2 = 0.000676 (low variability)

(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.

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Answer:

61°

Step-by-step explanation:

∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.

Answer:

{y,x}={-1,1}

to leave and take

The difference of the medians as a multiple of the interquartile range is 0.5,So the correct answer is option (A) 0.5.

The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in numerical order.

For example, consider the data set {3, 5, 2, 6, 1, 4}. When the values are ordered from smallest to largest, we get {1, 2, 3, 4, 5, 6}. The median in this case is the middle value, which is 3.

We can first find the medians and interquartile ranges of the two dot plots.

For Mr. Wilson's class:

Median = 12

Q1 = 10

Q3 = 14

IQR = Q3 - Q1 = 14 - 10 = 4

For Mr. Watson's class:

Median = 10

Q1 = 8

Q3 = 12

IQR = Q3 - Q1 = 12 - 8 = 4

The difference of the medians is |12 - 10| = 2. Therefore, the difference of the medians as a multiple of the interquartile range is:

$$\frac{2}{4} = \boxed{0.5}$$

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4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569

Answer:

?

Step-by-step explanation:

Answer: 2 meters

Step-by-step explanation:

The length of one train car is 80 millimeters. Therefore, the length of the entire train is:

25 cars × 80 mm per car = 2000 mm

To convert millimeters to meters, we need to divide by 1000:

2000 mm ÷ 1000 = 2 meters

Therefore, Venell's model train is 2 meters long.

The correct option for this question is (d) "No, none of the sides are parallel."

why it is and what is a Quadrilateral?

To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.

We can find the slopes of the line segments CD and EF as follows:

slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)

slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3

Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.

Alternatively, we can also find the slopes of the line segments CF and DE as follows:

slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5

slope of DE = (8 - 5) / (3 - (-8)) = 3/11

Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.

Therefore, the answer is option (d) "No, none of the sides are parallel."

A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.

There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.

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Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.

calculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.

Change in temperature on Monday from High to low

=15-10=5°F

Change in temperature on Tuesday from High to low

=8-(-4)=12°F

Change in temperature on Wednesday from High to low

=-2-(-5)=3°F

Change in temperature on Thursday from High to low

=-3-(-7)=4°F

Change in temperature on Friday from High to low

=-1-(-12)=11° F

Days when change in temperature more than 10° F are Tuesday and Friday.

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The Complete question is attached below:

The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)

where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.

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Complete question:

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by

A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'

B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---

C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°

D. ΔY = f(x₁ +Xq, X2, Xk).

The expressiοn 5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³). Thus, οptiοn (c) 5x3 is the cοrrect respοnse.

The cοefficients (the numbers in frοnt οf the variables) οf the expressiοn 5x(x²) can be multiplied, and the expοnents οf the variables can be added, tο determine the prοduct.

The first cοefficient we have is 5 times 1, giving us 5. Sο, using the secοnd x², we have x tο the pοwer οf 2 multiplied by x tο the pοwer οf 1 (frοm the first x). Expοnents are added when variables with the same base are multiplied. Sο, x¹ multiplied by x² results in x³.

Cοmbining all οf the parts, the phrase becοmes:

5x(x²) is equal tο 5 * x¹ * x² (5 * x³ = 5x³).

Thus, οptiοn (c) 5x³ is the cοrrect respοnse.

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a) The first four nonzero terms of the power series for f(x) about x=0 are

e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!

The general term of the power series is (-2)^n (2x)^(2n) / (2n)!

b) The interval of convergence of the power series is (-∞, ∞).

c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder

|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!

a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula

f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ

where fⁿ(0) denotes the nth derivative of f evaluated at x=0.

In this case, we have

f(x) = e^6(-2x^2)

fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)

So, we can write the power series as

f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)

= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)

To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula

f(0) = e^6

f'(0) = 0

f''(0) = 24

f'''(0) = 0

So, the first four nonzero terms of the power series are:

e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!

The general term of the power series is

(-2)^n (2x)^(2n) / (2n)!

b) To find the interval of convergence of the power series, we can use the ratio test

lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|

= lim [n→∞] |-4x^2/(2n+1)(2n+2)|

= lim [n→∞] 4x^2/(2n+1)(2n+2)

Since this limit depends on the value of x, we need to consider two cases

i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.

ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value

|4x^2/(2n+1)(2n+2)| < 1

This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).

c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series

|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!

where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].

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a. The slope of AB is  [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. The mid-point of Diagonal AC is  [tex](0, -1/2)[/tex]

A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.

a.

Slope is given by

[tex]A = (-2, 3) and B = (-5, 0)[/tex]

[tex]m = 1[/tex]

[tex]B = (-5, 0) and C = (2, -4)[/tex]

[tex]m = -4/7[/tex]

Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex]  .

b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.

c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y

Thus, Diagonal  [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]

Midpoint  [tex]= ((-2 + 2), (3 + -4))[/tex]

[tex]= ((0), (-1))[/tex]

Now divide them by 2

[tex]= ((0/2), (-1/2))[/tex]

[tex]= (0, -1/2)[/tex]

Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]

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Step-by-step explanation:

There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:

P = 2

Q = 5

R = 1

S = 8

T = 9

U = 9

With these values, we have:

PQR = 251

STU = 156

And the sum of PQR and STU is indeed 407.

A quadratic function in standard form that passes through the points [tex](-8,0), (-5,-3), and (-2,0)[/tex] is equals to the [tex]f(x) = (1/3)( x^{2} + 10x + 16)[/tex].

f(x) = ax2 + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

In other terms, you have a quadratic equation if a times the squares of the expression after b plus b twice that same equation not square plus c equals 0.

[tex]f(x) = ax^{2} + bx + c ----(1)[/tex]

is determined by three points and must be [tex]a[/tex] not equal [tex]0[/tex]. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs [tex](-8,0), (-5,-3)[/tex], and [tex](-2,0)[/tex] and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point[tex]( -8,0), x = -8, y = f(x) = 0[/tex] in equation [tex](1)[/tex],

[tex]= > 0 = a(-8)^{2} + b(-8) + c[/tex]

[tex]= > 64a - 8b + c = 0 -------(2)[/tex]

Similarly, for second point [tex]( -5,-3) , f(x) = -3, x = -5[/tex]

[tex]= > - 3 = a(-5)^{2} + (-5)b + c[/tex]

[tex]= > 25a - 5b + c = -3 --(3)[/tex]

Continue for third point [tex](-2,0)[/tex]

[tex]= > 0 = a(-2)^{2} + b(-2) + c[/tex]

[tex]= > 4a -2b + c = 0 --(4)[/tex]

So, we have three equations and three values to determine.

Subtract equation [tex](4)[/tex] from [tex](2)[/tex]

[tex]= > 64 a - 8b + c - 4a + 2b -c = 0[/tex]

[tex]= > 60a - 6b = 0[/tex]

[tex]= > 10a - b = 0 --(5)[/tex]

subtract equation [tex](4)[/tex] from [tex](3)[/tex]

[tex]= > 21a - 3b = -3 --(6)[/tex]

from equation (4) and (5),

[tex]= > 3( 10a - b) - 21a + 3b = -(- 3)[/tex]

[tex]= > 30a - 3b - 21a + 3b = 3[/tex]

[tex]= > 9a = 3[/tex]

[tex]= > a = 1/3[/tex]

from [tex](5)[/tex] , [tex]b = 10a = 10/3[/tex]

from [tex](4)[/tex], [tex]c = 2b - 4a = 20/3 - 4/3 = 16/3[/tex]

So,[tex]f(x)= (1/3)( x^{2} + 10x + 16)[/tex]

Hence, required values are [tex]1/3, 10/3,[/tex] and [tex]16/3[/tex].

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Answer:

-------------------------------------

Given 3 points of a quadratic function and two of them lie on the x-axis:

These two points are representing the roots of the function. With known roots we can show the function in the factor form:

Substitute the roots into the equation and use the third point with coordinates x = - 5, f(x) = - 3, find the value of a:

This gives us the function in the factor form:

Convert this into standard form of f(x) = ax² + bx + c:

If a₁ = 5 and an 5an-1 then The value οf a₄ is 625.

An arithmetic sequence is a sequence οf numbers in which each term after the first is fοund by adding a fixed cοnstant number, called the cοmmοn difference, tο the preceding term. Fοr example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a cοmmοn difference οf 3, since each term after the first is fοund by adding 3 tο the preceding term.

The nth term οf an arithmetic sequence can be fοund using the fοrmula:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, and d is the cοmmοn difference. The sum οf the first n terms οf an arithmetic sequence can be fοund using the fοrmula:

Sn = n/2 (a1 + an)

We are given that a₁ = 5, and that the nth term is 5 times the (n-1)th term. We can use this infοrmatiοn tο find the value οf a₄ as fοllοws:

a₂ = 5a₁ = 5(5) = 25

a₃ = 5a₂ = 5(25) = 125

a₄ = 5a₃ = 5(125) = 625

Therefore, the value of a₄ is 625.

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The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.

An employee who earned $20,000 will contribute $260 to the welfare fund.

To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.

The first $1000 will have a contribution rate of 4%.

Contribution for the first $1000 = 4% of $1000 = $40.

The next $1000 will have a contribution rate of 3%.

Contribution for the next $1000 = 3% of $1000 = $30.

The next $1000 will have a contribution rate of 2%.

Contribution for the next $1000 = 2% of $1000 = $20.

The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.

Contribution for the remaining amount = 1% of $17,000 = $170.

Now, let's sum up the contributions for each tier:

$40 + $30 + $20 + $170 = $260.

Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.

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We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm​, here is a guide:

A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.

Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.

Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.

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The experimental probability that at least one of the first three customers that walks into the store will make a purchase is 60%.

It is determined by counting the number of times an event occurs in a given experiment and dividing the total number of trials by the number of successful outcomes.

The experimental probability that at least one of the first three customers that walks into the store will make a purchase is calculated by dividing the total number of customers who make a purchase by the total number of customers who enter the store.

In this case, there are 3 trials and 2 customers who make a purchase.

The experimental probability is 3 by 5 which is the total number of trials.

Thus, the experimental probability

=3/5

= 60%.

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Answer:

Answer: C. f(x) = 2x²+x+6

Answer:

To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.

F1 × F2 can be expanded using the distributive property:

F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3

= 36y^2 + 12y - 54y - 18

= 36y^2 - 42y - 18

Now we can subtract F3 from the result:

F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)

= 36y^2 - 42y - 18 + y + 8

= 36y^2 - 41y - 10

Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.

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Sin 30 =3/x

1/2=3/x

x=6

The concept of Euclidean geometry is the study of geometrical shapes (plane and solid) and figures based on different theorems and axioms.

The concept of Euclidean geometry as required to be discussed is basically introduced for flat surfaces or plane surfaces. The postulates of the Euclidean geometry are as follows!

1 : A straight line may be drawn from any one point to any other point.

2 :A terminated line can be produced indefinitely.

3 : A circle can be drawn with any centre and any radius.

4 : All right angles are equal to one another (Congruent).

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Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.

What is equation ?

An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.

Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.

Let's call the length in inches "i" and the length in centimeters "c".

We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:

1 inch = 2.45 centimeters

To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:

c = 2.45i

This is the equation Kingsley can use to convert any given length in inches to centimeters.

Alternatively, we can rearrange this equation to solve for i:

c = 2.45i

Divide both sides by 2.45:

c/2.45 = i

So the equation for converting from centimeters to inches is:

i = c/2.45

Therefore,  since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.

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The system of equation is now written as:

y = −2x−8

y = x+ 1

First, we will plotting two system of  equations on the same axis, and then we'll explore the different factors to consider when plotting two linear inequalities on the same axis. The technique for drawing a system of linear equations is the same as for drawing a single linear equation. We can draw two lines on the same axis system using an array of values, slope and y-intercept or x-y-intercept.

Now,

these using slope-intercept form on the same set of axes. Remember that slope-intercept form looks like

y = mx+ b,  so we will want to solve both equations for y.

First, solve for y in 2x+y=−8

2x+ y = −8

OR, y = −2x− 8

Second, solve for y in

x− y = −1

Or, y = x+1

The system is now written as

y = -2x - 8

y = x + 1

Now you can plot the two equations using their slope and intercept on the same set of axes as shown in the figure below. Note that these charts have one thing in common. It is their intersection, the point that lies on the two lines. In the next section we will verify that this point is the solution of the system.

Complete Question:

Graph each system of equations. Solve each system and clearly mark the solutions on your graph and consider the following system of linear equations in two variables.

                            2x+ y = −8 and x− y = −1

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The actual intake of carbohydrates is 138% as compare to recommended intake.

Recommended intake of carbohydrates or any other nutrient are,

Based on the information provided,

Consumed 159 grams of carbohydrates,

Recommended intake is between 115 and 166 grams.

Calculate the percentage of actual intake compared to the recommended intake, use the following formula,

Percentage = (Actual Intake / Recommended Intake) x 100%

Substituting the values in the formula we have,

⇒Percentage = (159 / 115) x 100%

⇒Percentage ≈ 138.3%

Therefore,  the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.

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Answer:

The answer is brand B

Step-by-step explanation:

You divide $14.88 by 24 which equals 68 cents per item.

Then brand B is 60 cents per item which is the better buy!