!!25 Points!!Solve using augmented matrices. Show your work
x+y=1
3x-y=7

the person is able to name .441 more songs

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 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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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

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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To answer this question, we need to remember the next theorem:The

We have that the hypotenuse is the largest side of a right triangle. In this case, it is equal to (5 + 20) = 25 units.

The leg of the right triangle we need to find is m, and we know that the projection of m on the hypotenuse is 5 units.

Theref

Answer:

1.7^28/1.6^21 the second option.

Step-by-step explanation:

Answer:

x > 56

Step-by-step explanation:

x/8 - 13 > -6

x/8 > 7

x > 56

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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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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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?

Answer: 121 im pretty sure

Step-by-step explanation: 21175 divided by 175

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

194 grams

EXPLANATION

We have that the half life of the uranium is 2 years.

This means that it will take 2 years for the uranium to decay to half of its original value.

The formula for exponential decay is:

where y = the value after the decay

a = initial value

b = rate of decay.

t = number of years

First, we have to find b.

We have that 776 grams of uranium will decay to half its amount (388 grams) in 2 years. This means that:

Therefore, after 4 years (t = 4), the amount of uranium left will be:

That is the amount of uranium that will be left after 4 years.

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:

3rd option

Step-by-step explanation:

In the 3rd option, two sides from each triangle in the large triangle are compared.

Answer:

1575

Step-by-step explanation:

Comment

You are just asked to figure out the commission. The rule is to place 100 underneath what is given as the %. In effect, % = x / 100 in decimal form. In this case x = 2.5

So the % is 2.5/100 = 0.025 as a decimal

So commission is 63000 * 0.025 = $1575 commission

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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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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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

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:

[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.

Step-by-step explanation:

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

The first table represents a linear function.

A linear function is one that changes at a constant rate. Any linear function has an increase or decrease that is constant. The slope of the line, denoted by the letter m in the equation y = mx + b, is this constant rate of change.

Given are the tables with values of x and y.

In a table of linear functions, the ratio of the difference in y values to the difference in x values is consistently constant.

The first table is given as:

x y

1 3

2 7

3 11

4 15

Only table 1 in the provided tables represents a linear function.

This is because the equivalent values of y change by 4 when the value of x changes by 1.

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Answer:

See below

Step-by-step explanation:

1   note the other angle at d = 62   ( isosceles triangle)

2  x = 180 - 62 - 62 -25

Answer:

x = 31°

Step-by-step explanation:

since AB = BD then Δ ABD is isosceles with base angles congruent, so

∠ ADB = ∠ BAD = 62°

the sum of the 3 angle in Δ ABD = 180° , so

∠ ABD = 180° - 62° - 62° = 180° - 124° = 56°

∠ ABD and ∠ CBD are a linear pair and sum to 180° , so

56° + ∠ CBD = 180° ( subtract 56° from both sides )

∠ CBD = 124°

the 3 angles in Δ CBD sum to 180° , then

x + 124° + 25° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

The function is -|x+3|. The range is (-∞,0].

Given that,

The function is -|x+3|

We must determine the function's range.

A function's domain and range are its constituent parts. The domain of a function is the set of all possible input values, whereas the range of a function is its potential output. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B.

The function is -|x+3|

The domain is (-∞,∞)

The range is (-∞,0]

Therefore, the range is (-∞,0].

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Answer:

$88

Step-by-step explanation: