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The system of equations has one solution (-1, 1)

From the question, we are to graph the given system of equations.

The given system of equation is

y + 2x = −1

3y − x = 4

The graph of the given system of equations is shown below.

From the graph, we can observe that the solution to the given system of equation is given by two lines that intersect at the point (-1, 1).

Hence, the system of equations has one solution (-1, 1)

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I think the answer is A. The first one

Answer:

A. 2-liter bottle;$1.40

Step-by-step explanation:

We have to find out which option has the higher cost per liter. To do this we must find out how much each option would be if it was a liter.

1st set up each equation
2-liter = $2.80 we can divide by 2 on both sides of the equal sign and we get 1 liter = $1.40.
6(1/2) liter bottles = $3.90 this becomes 3 liters = $3.90 then we divide by 3 on both sides of the equal sign and we get $1.30

2nd we compare
$1.40(2 liter bottle) > $1.30 (6 1/2 liter bottles)

Answer:

18x2 -24 x + 8

Step-by-step explanation:

( f o g) (x) = f ( g(x) ) = f( 3x-2) = 2( 3x-2)2 = 2( 9x2 - 12x + 4) = 18x2 -24 x + 8

a) The preparation of a traditional income statement for Carbon Company is as follows:

Carbon Company

Sales revenue                         $600,000

Costs:

Materials               $ 101,300

Energy                       21,590

Setups                      24,360

Purchasing              26,200

Customer service   20,200

Long-term labor     29,400

Administrative        30,700     $253,750

Operating Income                  $346,250

b) The preparation of an activity-based income statement for Carbon Company is as follows:

Carbon Company

Sales revenue                                                                     $600,000

                   Resources supplied    Unused Resources   Used Resources

Materials               $ 101,300                     $ 2,300              $99,000

Energy                       21,590                         2,210                  19,380

Setups                      24,360                                0                 24,360

Purchasing              26,200                         7,800                  18,400

Customer service   20,200                         9,700                 10,500

Long-term labor     29,400                         4,650                 24,750

Administrative        30,700                         5,950                 24,750        

Total                   $253,750                      $32,610              $221,140

Operating Income                                                            $378,860

                          Unused Resources Capacity     Cost Driver Volume

Resources used

Materials                        $ 2,300                                 9,000 pounds

Energy                               2,210                        380 machine-hours

Setups                                     0                                         87 setups

Purchasing                      7,800                         80 purchase orders

Customer service           9,700                                         70 returns

Long-term labor              4,650                              330 labor-hours

Administrative                5,950                              450 labor-hours

Materials $ 101,300

Energy 21,590

Setups 24,360

Purchasing 26,200

Customer service 20,200

Long-term labor 29,400

Administrative 30,700

Sales revenue  $600,000

                   Resources supplied       Unused Resources   Used Resources

Materials               $ 101,300                         $ 2,300              $99,000

Energy                       21,590                             2,210                  19,380

Setups                      24,360                                    0                 24,360

Purchasing              26,200                             7,800                  18,400

Customer service   20,200                             9,700                 10,500

Long-term labor     29,400                             4,650                 24,750

Administrative        30,700                             5,950                 24,750        

Total                   $253,750                          $32,610              $221,140

Thus, the traditional income statement for Carbon Company shows an operating income of $346,250, while the activity-based income statement shows an operating income of $378,860.

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Answer:

The intervals represent the domain, or the values on the horizontal axis.

When x ≤ -3, the graph should form a straight line at y = 3. Because the interval includes x = -3, the rightmost part of the line should be capped with a closed dot. The line should continue for infinity to the left.

When -3 < x < 4, the graph should form a line with the equation (2x + 1). Because the interval does not include the endpoints, the endpoints should have open dots.

When x ≥ 4, the graph should form a straight line at y = -4. Because the interval includes x = 4, the leftmost endpoint should be a closed dot. The right of the line should continue for infinity.

**The included graph does not take the endpoints into account

Answer:

See attached for graph.

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases}3 & \textsf{if }x\leq -3\\2x+1 & \textsf{if }-3 < x < 4 \\ -2 & \textsf{if } x\geq 4 \end{cases}[/tex]

Therefore, the function has three definitions:

[tex]f(x)=3 \quad \textsf{when x is less than or equal to 3}[/tex]

[tex]f(x)=2x+1 \quad \textsf{when x is more than -3 and less than 4}[/tex]

[tex]f(x)=-2 \quad \textsf{when x is more than or equal to 4}[/tex]

When graphing piecewise functions:

First piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies f(-3)=3 \implies (-3,3)[/tex]

Place a closed circle at (-3, 3).

As this piece of the function is f(x) = 3 for any value of x that is less than or equal to -3, draw a horizontal straight line to the left from the closed circle.  Add an arrow at the end.

Second piece of function

Substitute the endpoints of the interval into the corresponding function:

[tex]\implies f(-3)=2(-3)+1=-5 \implies (-3,-5)[/tex]

[tex]\implies f(4)=2(4)+1=9 \implies (4,9)[/tex]

Place an open circle at (-3, -5) and (4, 9).

Join the points with a straight line.

Third piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies f(4)=-2 \implies (4,-2)[/tex]

Place a closed circle at (4, -2).

As this piece of the function is f(x) = -2 for any value of x that is more than or equal to 4, draw a horizontal straight line to the right from the closed circle.  Add an arrow at the end.

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In order to compare and contrast the steps of two different constructions using a compass, we simply take a note of the different steps followed in both the constructions.

How to compare and contrast the steps?

For both the constructions, observe the corresponding steps steps that have been performed in order.

Then, note down what similarity you find while constructing the two different constructions in the first step.

Once you know the the similarities, you can further trace down the differences in the procedure of the two constructions by observing the first step. This is how you can compare and contrast the first step of two different constructions using a compass.

This process can be followed for all the steps for comparing and contrasting two different constructions.

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By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.

Herein we have a complex number in rectangular form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The root formula is introduced below:

[tex]z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n}\right) +i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for k ∈ {0, 1, ..., n - 1}      (1)

Where n is the grade of the complex root.

The magnitude and direction of the complex number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:

k = 0

z₁ = 2.997 + i 4.002

k = 1

z₂ = - 4.964 + i 0.595

k = 2

z₃ = 1.967 - i 4.597

By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.

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The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).

The component form of a vector is known to be depicted as < x, y >.

Note that:

x  - tells the distance or how far to the right or left, a vector is known or seen to be going.

y -  tells the distance or how far to  the upper part or downward a vector is known or seen to be going.

From the question and looking at the image attached, we were able to obtain (-4,4) and (2, 0)

So:

⇒  (-4,4)  --------(-4+6)(4-4)-------(2,0)

⇒ (6,-4)

Hence, The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).

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Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of [tex]a^{2}[/tex] + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

[tex]3x^{2}[/tex] - 2 = -5x
[tex]3x^{2}[/tex] + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

The probability that exactly 3 of the chosen sandwiches are turkey is; 0.004

We are given;

Total number of sandwiches = 15

Number of sandwiches that were turkey = 6

Now, she selects 6 of the sandwiches and we want to find the probability that exactly 3 are turkey.

Now, number of ways of selecting 6 sandwiches is; 15C6

Number of ways of selecting 3 turkey's out of the 6 chosen is; 6C3

Thus, the probability that exactly 3 of the chosen sandwiches are turkey is; 6C3/15C6 = 20/5005 = 0.004

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1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

1) The following trigonometric formulae are used to derive the half-angle formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a half angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a half angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a half angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in rectangular form to polar form are obtained by trigonometric functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in polar form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in rectangular form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the linear function y = 5 · x - 8, we proceed to use the following substitution formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

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Answer:

D

Step-by-step explanation:

Widrawal is - 30

Deposit is +30

-30+30 = 0

the statement is false, as there no exist a value of t such that cos(t) > 1.

Here we have the statement:

"There are values of t so that the equation cos(t) = 5/3"

Now, remember that the range of the sine and cosine equations is given by:

R: -1 ≤ y ≤ 1

And 5/3, the value in the statement, is larger than 1, which is the maximum in the range.

Then the statement is false, as there no exist a value of t such that cos(t) > 1.

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Answer:

144

Step-by-step explanation:

24*6

Because this month she saved 6 times as MUCH money compared to last month

Answer:

Step-by-step explanation:

Equivalent polar coordinates will have the same modulus and some multiple of 360° added to the argument, or the opposite modulus and some odd multiple of 180° added to the argument.

  a∠b° = a∠(b+360n)° = -a∠(b +180 +360n)°

Equivalents will be ...

  (2, (-60 +360n)°) = (2, 300°)

  (-2, (-60 +180 +360n)°) = (-2, -240°) = (-2, 120°)

Equivalents will be ...

  (-2, (240 +360n)°) = (-2, -120°)

  (2, (240 +180 +360n)°) = (2, -300°) = (2, 60°)

The values of X and Y are 30 and 11 respectively

The figure that represents the complete question is added as an attachment

The given parameters are:

DH = X +3

HF  = 3Y

GH = 2X -5

HE = 5Y

From the attached parallelogram, we have:

DH = HF

GH = HE

Substitute the known values in the above equation

X + 3 = 3Y

2X - 5 = 5Y

Make X the subject in X + 3 = 3Y

X = 3Y - 3

Substitute X = 3Y - 3 in 2X - 5 = 5Y

2(3Y - 3) - 5 = 5Y

Expand

6Y - 6 - 5 = 5Y

Evaluate the like terms

Y = 11

Substitute Y = 11 in X = 3Y - 3

X = 3*11 - 3

Evaluate

X = 30

Hence, the values of X and Y are 30 and 11 respectively

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The statement that correctly compares the water bills for the two neighborhoods based on the histogram given is that the range of water bills on Pine Road is higher than the range of water bills on Front Street.

It should be noted that a histogram means a graph that shows the frequency of the numerical data using rectangles.

In this case, the statement that correctly compares the water bills for the two neighborhoods based on the histogram given is that the range of water bills on Pine Road is higher than the range of water bills on Front Street. This was the difference between the highest and lowest number.

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Answer: More homes on Pine Road had water bills above $200 than on Front Street.

Step-by-step explanation: edge 2023

Answer:

1,920 watts per circuit

Step-by-step explanation:

To find the load for 1 circuit (per circuit) we can divide 28,800 watts by 15 circuits

28800/15 = 1,920 watts per circuit

Answer:

calcium =1x40=40

chlorine=2x35=70

40+70=110

ca=40/110×100=36.36

when we approximate it become 36.4

thanks

the correct option is:

"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

A circle is defined as the set of equidistant points to a given point which is the center of the circle.

That distance to the center is called the radius.

Here, the center is at the point (0, 0), also called the origin, so if the distance between the point A and the origin, then point A lies on top of the circle P.

From that, we conclude that the correct option is:

"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

That is the only proof that we can (and should) use to prove that a point lies on a circle.

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Answer:

The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."

Step-by-step explanation:

I did the test

Step-by-step explanation:

shown above but I need words so

If a data set contains three points, and two of the residuals are -10 and 20, the third residual is 10 (option B).

A residual is the difference between the observed value and the estimated value of the quantity of interest.

The residual of a data points should normally sum up to zero (0). This means the following applies:

-10 + 20 + x = 0

x = 10

Therefore, if data set contains three points, and two of the residuals are -10 and 20, the third residual is 10.

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Answer:

1.60

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

[tex]\sqrt{(5-2)^2 +(-2-2)^2}=5[/tex]

The estimated income statement for the month shows a loss of $840000.

The estimated income statement for the month will be:

Sales = $25,600,000

Less: Cost of goods sold

Direct materials (320000 × 15) = $4,800,000

Direct labor (320000 × 17) = $5,440,000

Variable costing (320000 × 15) = $11,200,000

Fixed manufacturing cost = $1,530,000

Total cost of goods sold = $22970000

Gross profit = $25,600,000 - $22970000 = $2,630,000

Gross profit = $2,630,000

Less:

Variable selling and administrative expense = $3200000

Fixed selling and administrative = $270000

Loss from operations = $840000

Therefore, the estimated income statement for the month shows a loss of $840000.

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Using a calculator, the critical value for the t-distribution with a confidence level c=0.80 and sample size n=29 is of Tc = 1.3125.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level c=0.80 and sample size n=29 is of Tc = 1.3125.

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The time taken for Company B to clear the parcel of land alone is 14.25 hours

1/8 = 1/x + 1/(x + 4)

1/8 = (x+4)+ (x) / (x)(x+4)

1/8 = (x+4+x) / (x² + 4x)

1/8 = 2x+4 / (x² + 4x)

cross product

1(x² + 4x) = 8(2x + 4)

x² + 4x = 16x + 32

x² + 4x - 16x - 32 = 0

x² - 12x - 32 = 0

Using quadratic formula

x = 14.25 or -2.25

The time taken for Company B to clear the parcel of land alone can only be positive,

Therefore, it is 14.25 hours

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Using the t-distribution, it is found that since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.

At the null hypothesis, it is tested if the average is not less than 25, that is:

[tex]H_0: \mu \geq 25[/tex]

At the alternative hypothesis, it is tested if the average is less than 25, that is:

[tex]H_1: \mu < 25[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

Considering the situation described, the values of the parameters are given as follows:

[tex]\overline{x} = 24.97, \mu = 25, s = 2.16, n = 10[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{24.97 - 25}{\frac{2.16}{\sqrt{10}}}[/tex]

t = -0.04

Using a t-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with 10 - 1 = 9 df and t = -0.04, the p-value is of 0.4844.

Since the p-value is greater than 0.01, there is no evidence that the new machine should be rejected at the 0.01 significance level.

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the problem want us to find:

 [tex]\hookrightarrow \text {Slope-intercept form}[/tex]

What is the slope-intercept form:

 [tex]\hookrightarrow \text {it is when the function has the y-variable isolated by itself to one side}\\\hookrightarrow \text{and everything else to the other side}[/tex]

Let's apply our knowledge:

  [tex]2x =3y-5\\-3y=-5-2x\\y=\frac{2}{3} x+\frac{5}{3}[/tex]

Answer:[tex]y=\frac{2}{3} x+\frac{5}{3}[/tex]

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Answer: 184

(I am not sure if I have misunderstood the question, but the final answer I got was 184, which wasn't any one of the choices. I was wrong in understanding, please let me know and I will modify my answer)

Step-by-step explanation:

Given expression

6 (4 + 2)² - 32

Simplify values in the parenthesis

6 (6)² - 32

Simplify exponents

6 × 36 - 32

Simplify multiplication

216 - 32

Simplify subtraction

[tex]\Large\boxed{184}[/tex]

Hope this helps!! :)

Please let me know if you have any questions