I need help on this question

Plot two points of each equation

Equation 1 Equation 2

3x - 2y = 10 9x + 4y = - 50

x y x y

0 -5 0 12.5

10/3 0 -50/9 0

Graph

The coordinates of another point are (4, 6).

We are given the coordinates of two points. The two points are (0, 4) and (2, 5). A straight line passes through the two given points.

We will find the equation of the straight line using the formula given below :

(y - y1) = [(y2 - y1)/(x2 - x1)](x - x1)

(y - 4) = [(5 - 4)/(2 - 0)](x - 0)

(y - 4) = (1/2)x

y = (1/2)x + 4

We have to find another point on the line. Let us choose a value for the x-coordinate equal to 4. The y-coordinate can be calculated as given below :

y = (1/2)4 + 4

y = 2 + 4

y = 6

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Correct option is A, The temperature started at 78°F and decreased by 6°F. Then the temperature decreased by 5°F.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign, One such equation is 3x - 2 = 5 + x.

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Length: 18 in.

Width: 6 in.

We can use “x” as the width in this scenario. If the width is x, then the length is 3x, since length is three times the width. The perimeter would be length + length + width + width. Since the perimeter is 48, we could say that:

x + x + 3x + 3x = 48

Which simplifies to 8x=48

If you divide by 8 on both sides, you get

X=6. Then you Can plug 6 back into your x width and 3x length.

(See attached image) hope this helped!

Hello!

Let's set up some variables:

Let's consider the relationship between the length and the width:

              [tex]\hookrightarrow L=3W[/tex]

The perimeter of the rectangle is equal to 48 and 2W + 2L

  [tex]\hookrightarrow 2L + 2W = 48[/tex]

Let's replace the 'L' in terms of 'W' and solve:

    [tex]2(3W) + 2W = 48\\6W + 2W=48\\8W = 48\\W = 6[/tex]

Since L = 3W

  [tex]\hookrightarrow L = 3W = 3*6 = 18[/tex]

Answer:

Hope that helps!

Answer:

Equations:
Cost equation C(x) = 100 + 5x
Sales equation S(x) = 15x

Graph provided

Solution at breakeven point i.e. where sales = costs is at x = 10 lbs

Step-by-step explanation:

Total cost = $100 capital cost of equipment + production cost of $5 per pound of soap

Cost equation C(x) = 100 + 5x  where x is the number of pounds of soaps produced

Sales Equation S(x) = 15x where x is the number of pounds of soap sold

The break-even quantity (in lbs) of soap to be sold to pay for equipment is when both equations are equal to each other

100 + 5x = 15x
==> 15x = 100 + 5x
==> 15x - 5x = 100   (subtract 5x on both sides)

==> 10x = 100

==> x = 10 lbs of soap

At this quantity, Sales and Costs are evened out

Answer: k=-2

Step-by-step explanation:

[tex]\displaystyle\\3 x^2+x+k=\\\\3x^2+3x-2x+k=\\\\3x(x+1)-2(x-\frac{k}{2}) \\\\Hence,\\\\x-\frac{k}{2} =x+1\\\\-\frac{k}{2} =1\\[/tex]

Multiply both parts of the equation by -2:

[tex]\displaystyle\\-\frac{k}{2}(-2) =1(-2)\\\\k=-2[/tex]

The calculated area's maximum percentage relative error is approximately 1.33%.

we know that:

Area of the circular disc is given by A = πr²

consider A = πr²

Differentiate both sides with respect to r, we get

dA/dr = 2πr

⇒ dA = 2πr dr

calculate area:

A = πr²

A = π(30)²

A = 900π

A = 2826 cm²

Because of an error in measurement, the radius might actually be as big as 30+0.2 cm

= 30.2 cm

If r is increased from 30 by an amount Δr = dr = 0.2

Then the actual change in the calculated area would be :

ΔA = A(30+Δr)-A(30)

ΔA = A(30.2)-A(30)

ΔA = (30.2)²π -  900π

ΔA = 912.04π - 900π

= 12.04π cm²

So we estimated the maximum error in calculated area as 12.04π cm²

≅ 37.8 cm²

The maximum relative error in calculated area is:

ΔA/A= dA/A = 12.04π/900π

= 0.013

= 1.33 %

The maximum % relative error in calculated area is about 1.33%.

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Ed earned $112 for 8 hours of

work.

At this rate, how much will he

earn for 40 hours of work?

For 40 hours of work = (112 x 40) /8 = $ 560

The shortest possible length that Zara's fence could be is 12 feet long.

The fence panels Zara uses are 6 feet long each and the fence panels that Chester uses is each 4 feet long.

The multiple of the number 6: 6, 12, 18, 24

The multiple of the number 4: 4, 8, 12, 16, 20, 24

The numbers 6 and 4 have the same multiple 12, 24. The least common multiple of them is 12.

So Zara's fence has the shortest length is 12 feet, because Zara and Chester have the same length fence as Zara uses fence panels that are each 6 feet long. Chester uses are 4 feet long.

The shortest length of Zara's fence is 12 feet.

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Answer:fact

Step-by-step explanation:Opiians have a persianal veiw sush as "the cows should sleep in the shed" while facts are absolute "the cows sleep in the shed"

Answer:

[tex](\frac{15}{2},6)[/tex]

Step-by-step explanation:

Hey, Grace! Pleasure to meet you.

To solve this problem, I would strongly suggest for you to use the midpoint formula.

I have attached an image below of the formula used for plugging in values.

Confused? Let me show you! :)

M means midpoint by the way...

M = [tex](\frac{8+7}{2},\frac{10+2}{2}) = (\frac{15}{2} ,6)[/tex]

There you go! Let me know if you have any questions, and best of luck with the rest of your assignment.

Hello, you just missed one multiplicity which has a root at

[tex]x = 2[/tex]

The detailed solution is given below. Good luck!

Answer:

f(x) = 2(x - 2)²(x + 1)(x - 1)

Step-by-step explanation:

a polynomial of the 4th degree has as highest exponent for terms in x : 4

your previous attempt only gets you to x³ terms, so to a polynomial of 3rd degree.

you made the following mistakes :

you used the factor for the root (zero) at x = 2 only once, although it has a multiplicity 2 (that means it has to be used twice : the same zero solution appears twice) :

e.g. (x - 2)²

you used the same factor for the root at -1 and at +1.

no, they are different, of course, as -1 and +1 are different.

e.g.

(x + 1)(x - 1)

you miscalculated the factor to fulfill also the last criteria to have a y- intercept at (0, -8), y = f(0) = -8.

so, the equation is

f(x) = 2(x - 2)²(x + 1)(x - 1)

why ?

when x = 0, all terms are eliminated except for the last one that is the multiplication of all constant integers of the factors. and to get -8 in such a multiplication, we have already 3 negative factors (that will create a negative result), and any other factor needs to be positive to keep that negative result.

as -2, -2 (due to the ² factor we have it twice in the calculation), +1 and -1 are necessary for the roots (giving us -4 as result), we need an initial integer factor to now create the needed -8 result (2 × -4 = -8) :

2 × -2 × -2 × +1 × -1

By evaluating the given linear equation, we will see that the missing values in the table are:

Here we have a table that relates the inputs, x, with the outputs, y, of the linear equation:

y = 2x + 1

To find the missing values we need to evaluate the linear equation in the given inputs, a is the value that we get when x = -2, evaluating in that we get:

a = 2*(-2) + 1

a = -4 + 1

a = -3

The value of b is what we get when x = 0.

b = 2*0 + 1

b = 1

The value of c is what we get when x = 1.

c = 2*1 + 1

c = 3

The value of d is what we get when x = 2.

d = 2*2 + 1

d = 4 + 1

d = 5

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The equation in function notation is: f(x) = 3x + 9.

Slope of the line = 3

Y-intercept = 9

X-intercept is: -3.

In function notation, the equation can be written as .f(x) = mx + b, where:

Given the equation, -3x + y = 9, rewrite in function notation as:

-3x + y + 3x = 3x + 9

y = 3x + 9

f(x) = 3x + 9

Slope of the line is, m = 3.

The y-intercept of the equation is, b = 9.

To find the x-intercept, substitute y = 0 into y = 3x + 9:

0 = 3x + 9

-3x = 9 [subtraction property of equality]

-3x/-3 = 9/-3 [division property of equality]

x = -3

The x-intercept is: -3.

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the person is able to name .441 more songs

Step-by-step explanation:

The shortest distance to reach the starting point by Dolores is 2.7 kilometres.

The shortest distance will be the line directly connecting the two points. This will form the right angled triangle and hence can directly be calculated. We will be calculating hypotenuse from Pythagoras theorem.

Distance² = 2.2² + 1.5²

Taking square on Right Hand Side

Distance² = 4.84 + 2.25

Performing addition on Right Hand Side of the equation

Distance² = 7.09

Taking square root on Right Hand Side

Distance = ✓7.09

Distance = 2.7 kilometres

Thus, the shortest distance back to the starting point is 2.7 kilometres.

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Answer:

$88

Step-by-step explanation:

Sarah will take 90 minutes to reach her school from her house if she continues to walk with her friend without increasing speed.

According to the question,

We have the following details:

Sarah leaves her house at 6:25 a.m.

She meets her friend at 6:45 a.m.

So, we have:

The time taken by Sarah to meet her friend after 1 mile = (6:45 - 6:25) minutes

The time take by Sarah to meet her friend after 1 mile = 20 minutes

Now, we can find Sarah's speed.

We know that the formula of speed is as follows:

Speed = distance/time

Speed = 1/20 mile/min

Now, the distance of her school from her house is 4.5 mile.

So, we have:

Time taken = distance/speed

Time taken = 4.5/(1/20) min

Time taken = 4.5*20 min

Time taken = 90 minutes

Hence, the time taken by Sarah to reach her school from her house is 90 minutes.

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The distance between the Bumper Boats and the Parachute Plunge is given by:

15 units.

Suppose that we have two points with coordinates given yb [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following rule:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse representing the distance between them.

In the context of this problem, the coordinates of the Bumper Boats and of the Parachute Plunge are given as follows:

Hence the distance between these two points is given as follows:

[tex]D = \sqrt{(6 - (-6))^2+(11 - 2)^2}[/tex]

D = sqrt(12² + 9²)

D = 15 units.

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Answer: its 225

Step-by-step explanation: you should try it and find out. / I did  

Placing these functions from slowest asymptotic growth to fastest asymptotic growth. f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).The exponents we got.

Given that,

Placing these functions from slowest asymptotic growth to fastest asymptotic growth,

Come to question,

f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).

(ln ln ln n) < (ln n + 2021) < ([tex]n^{lg n}[/tex] ) < ((n/lg n)⁸) < (n⁸ - n⁶ + n⁴ - n² + 1) < (n²⁰²¹) < ([tex]32^{n/5}[/tex]) < (3³ⁿ) < ([tex]16^{lgn}[/tex]) < ( 2021 ∛n)

Let's understand, lg n < n < exponential. on the basis of it,

f₇(n) comes first, it will be smaller than f₄(n), because ln n is > ln ln ln n.

f₄(n) comes second, it will be smaller than f₀(n), because O(n) functions are larger than O(log n).

f₀(n) comes third, it will be smaller than f₃(n), because O(n⁸) functions are larger than O([tex]n^{log n}[/tex]).

f₃(n) comes fourth, it will be smaller than f₅(n), because (n⁸ - n⁶ + n⁴ - n² + 1) will give more larger value than ((n/lg n)⁸), these both functions are O(n⁸).

f₅(n) comes fifth, it will be smaller than f₉(n), because n⁸< n²⁰²¹.

f₉(n) comes sixth,  it will be smaller than f₂(n), because n²⁰²¹ is O(n), whereas [tex]32^{n/5}[/tex] = 2n is exponential, and exponential are larger than O(n).

f₂(n) comes seventh, it will be smaller than f₆(n), because 2n < 3³ⁿ, both are exponential (2 < 3).

f₆(n) comes eight, it will be smaller than f₁(n), because 3³ⁿ < [tex]16^{logn}[/tex], both are exponential (3 < 16).

f₁(n) comes ninth, it will be smaller than f₈(n), because [tex]16^{logn}[/tex] < 2021 ∛n, both are exponential (16 < 2021).

Complete question:  Place these functions in order from slowest asymptotic growth to fastest asymptotic

growth. Justify the claimed order for each pair of consecutive functions that appear in your ordered

list. For instance, if you claim that

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The value of [x] in the figure given is 54.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.

Given are two parallel lines.

The two lines are parallel and are intersected by a transversal. Assume

that  -

∠1 = (x +3)°

∠2 = (2x - 61)°

Now, the angle at the vertically opposite position with respect to ∠2 will have same measurements. Let's call this ∠3 = (2x - 61)°.

Now, ∠3 and ∠1 are alternate interior angles and their measures will be equal. So, we can write -

∠1 = ∠3

x + 3 = 2x - 61

3 + 61 = 2x - x

x = 64

The value of [x] is 54

Therefore, the value of [x] in the figure given is 54.

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A linear function with the same y-intercept as the one that is represented by the graph is: table 1.

In Mathematics, the slope of any linear function can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

At points (-3, -4) and (-1, 2) from table 1, the slope of the line would be calculated as follows:

Slope, m = (2 + 4)/(-1 + 3)

Slope, m = 6/2

Slope, m = 3.

Note: The y-intercept of the line shown on the graph is equal to 5 because the x-value is zero (0) at this point.

By using point (-3, -4), the y-intercept of this line would be calculated by using the slope-intercept form:

y = mx + b

Where:

Making y-intercept (b) the subject of formula, we have:

y-intercept, b = y - mx

y-intercept, b = -4 - 3(-3)

y-intercept, b = -4 - (-9)

y-intercept, b = -4 + 9

y-intercept, b = 5.

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Complete Question:

Which linear function has the same y-intercept as the one that is represented by the graph?

Complete the missing terms in the arithmetic sequence shown here: 2, ,4.5, 7, 9.5, 12?

It should be noted that an arithmetic sequence has a first term and common difference.

In this case, a = first term = 2

a + 2d = 3rd term = 7

Since a + 2d = 7

2 + 2d = 7

2d = 7 - 2

2d = 5

Divide

d = 5/2 = 2.5

The common difference is 5

The second term will be:

= a + d

= 2 + 2.5

= 4.5

The 4th term will be:

= a + 3d

= 2 + 3(2.5)

= 2 + 7.5

= 9.5

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Percentages are essentially fractions where the denominator is 100. To show that a number is a percent,  the full price of the ticket is 293.75.

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.

The cost of the ticket Arno buys is $43.68.

The discount she got for the original cost of ticket is 16%.

We need to find the original cost of the ticket.

We need to convert the percentage to a decimal number.

by dividing 16 with 100 we get the decimal value.

16%=16/100=0.16

Now, to find the original or full price of ticket, we need to multiply zero point one six with x equal to forty three point six eight.

0.16×x=43.68

Divide both sides by 0.16

x=293.75

Hence the full price of the ticket is 293.75.

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Answer: 121 im pretty sure

Step-by-step explanation: 21175 divided by 175

The quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.

Dividend = Divisor x Quotient + Remainder

For the given question,

The number -34 is to be divided by 6.

In this, dividend is -34 and divisor is 6.

Now while dividing the number comes should be less than -34.

Thus, -34 divided by 6 gives quotient as -36 and remainder as 2.

Where,  the remainder r has to satisfy 0≤r<6, and in particular cannot be negative.

Therefore, the quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.

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