Choose the correct graph of the given system of equations. y − 2x = −1 x + 3y = 4 graph of two lines, one with a positive slope and one with a negative slope, that intersect at the point negative 1, 1 with text on graph that reads One Solution negative 1, 1 graph of two lines that intersect at the point 1, 1 with text on graph that reads One Solution 1, 1 graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions

Answer:

See below

Step-by-step explanation:

For the second step, [tex]\angle T\cong\angle R[/tex] by Alternate Interior Angles. The rest of the steps appear to be correct.

Part: $1.92 (the discount amount)

Percent: 30% (the discount percentage)

Base: The original price of the item before the discount and sale, which we can calculate as follows:

Let x be the original price of the item.

The discount of $1.92 represents 30% of the original price, so we can write:

0.30x = 1.92

Solving for x, we get:

x = 1.92 / 0.30

x = 6.40

Therefore, the base is $6.40 (the original price of the item before the discount and sale).

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It is false that for a population of scores, the sum of the deviation scores is equal to expected value.

The sum of deviation scores is not equal to the expected value (EX) of a population of scores. The expected value represents the average value that we expect to obtain if we were to repeatedly sample from the population.

The sum of deviation scores is the sum of the differences between each score and the mean of the population. It provides information about the total variability in the data. While both concepts are related to the distribution of scores, they serve different purposes and are calculated differently.

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To find a pair of values that make the linear equation 14x - y = -14 a true statement, we can choose any value for x and calculate the corresponding value of y.

Let's choose x = 2:

14(2) - y = -14

28 - y = -14

Now, we can solve for y:

-y = -14 - 28

-y = -42

Dividing both sides by -1 (to isolate y):

y = 42

Therefore, the pair of values (x, y) that make the equation true is (2, 42).

Answer:

Option D

Step-by-step explanation:

       (-5, -2)   ;   x₁ = -5  & y₁ = -2

        (5 , 4)    ;   x₂ = 5   & y₂ = 4

Plugin the points in the below mentioned formula and find the slope.

  [tex]\boxed{\bf slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

             [tex]\sf = \dfrac{4-[-2]}{5-[-5]}\\\\\\=\dfrac{4+2}{5+5}\\\\=\dfrac{6}{10}\\\\=\dfrac{3}{5}[/tex]

Equation of slope-intercept form: y =mx + b

Here, m is the slope and b is the y-intercept.

     [tex]\sf y = \dfrac{3}{5}x + b[/tex]

  The line is passing through (5, 4). So, substitute the points in the equation and find the y-intercept.

           [tex]4 =\dfrac{3}{5}*5 + b\\\\\\4=3+b\\\\[/tex]

      4 - 3 = b

            b = 1

Slope intercept form of the equation:

            [tex]\sf y = \dfrac{3}{5}x + 1[/tex]

Answer:

[tex]\frac{8}{x}[/tex]

Step-by-step explanation:

what is the sum 3/x+9+5/x-9

[tex]\frac{3}{x} + 9 + \frac{5}{x} - 9 =[/tex]     (add [tex]\frac{3}{x}[/tex] and [tex]\frac{5}{x}[/tex])

[tex]\frac{8}{x} + 9 - 9 =[/tex]            (solve 9 - 9 = 0)

[tex]\frac{8}{x}[/tex]                           ( your answer)

Answer:

(x,y)=(2,0)

Step-by-step explanation:

Multiply top equation by 4 and bottom equation by 5

-5y = 10 - 5x --> -20y = 40 - 20x

-2y = 8 - 4x --> -10y = 40 - 20x

Subtract both equations

-10y = 0

y = 0

Substitute y=0 into one of the original equations to find x

-5y = 10 - 5x

-5(0) = 10 - 5x

0 = 10 - 5x

5x = 10

x = 2

Therefore, the solution is (x,y)=(2,0)

Step-by-step explanation:

P odd = spin of 1 or 3

P greater than 3  = spin of 4  

   three spins out of 4 possible spins   =  3/4

Answer: 38.4 + 216 = 254.4

Step-by-step explanation: The volume of the block at the top is 38.4 and the volume of the block at the bottom is 216 so add them together to make 254.4

Hope it helped :D

The probability of hitting the black circle as required is closer to 0 than. it is to 1.

The probability of hitting the white portion of the target as required is closer to 1 than it is to 0.

It follows from the task content that the probability of hitting the circle is dependent on the area of the black circle and the square shaped target.

Since the area of the square is; 9² = 81.

The area of the black circle is; π(1.5)² = 7.07.

Since the area of the black circle is less than half the area of the square; it follows that the the probability are as stated in the answer section above.

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Answer:

  C.  KL = 10.14

Step-by-step explanation:

You want the length of segment KL in ∆JKL given it is similar to ∆XYZ with lengths JK=11.31, XY=8.7, YZ=7.8.

Corresponding sides of similar triangles are proportional. It can be useful to identify corresponding sides and their given measures:

  JK = 11.31, XY = 8.7

  KL = ?, YZ = 7.8

This lets us write the proportion ...

  KL/JK = YZ/XY

  KL/11.31 = 7.8/8.7 . . . . . . . . . . use given values

  KL = 11.31(7.8/8.7) = 10.14 . . . multiply by 11.31

The measurement of KL is 10.14 untis.

__

Additional comment

You have to go by the sequence of vertices in the similarity statement, not the appearance of the figure. One triangle is rotated from the other in the figure, so that parallel sides are not corresponding sides.

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Answer:

the answer is 5 the probability of each colors is 5

In both cases considered below, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.

Let's consider a nonempty subset X ⊆ ℕ.

To prove that X has an ∈-minimal element, we can follow the given hint: pick an arbitrary n ∈ X and look at the intersection of X with the set {0, 1, 2, ..., n}.

Let's denote this intersection as Y = X ∩ {0, 1, 2, ..., n}.

We can observe the following:

Y is a nonempty subset of ℕ: Since X is nonempty, and we are intersecting it with a nonempty set {0, 1, 2, ..., n}, the resulting set Y = X ∩ {0, 1, 2, ..., n} will also be nonempty.

Y is a finite subset of ℕ: The set {0, 1, 2, ..., n} is finite, and the intersection of any two finite sets is also finite. Therefore, Y is a finite subset of ℕ.

Since Y is a nonempty and finite subset of ℕ, it must have a minimal element with respect to the element hood relation ∈.

Let's denote this minimal element as m, where m ∈ Y.

Now, we need to show that m is an ∈-minimal element of X, i.e., for any x ∈ X, either x = m or m ∉ x.

Consider an arbitrary element x ∈ X. We know that x ∈ Y because Y is defined as the intersection of X with {0, 1, 2, ..., n}. Since m is the minimal element of Y, we have two cases:

Case 1: If x = m, then we have x = m, satisfying the condition.

Case 2: If x ≠ m, then x ∈ Y implies that x ∉ {0, 1, 2, ..., n} \ {m}. In other words, x ∉ {0, 1, 2, ..., n} or x = m. But x ≠ m, so x ∉ {0, 1, 2, ..., n} must hold. Since x ∉ {0, 1, 2, ..., n}, we can conclude that m ∉ x.

In both cases, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.

Since we picked an arbitrary n ∈ X and showed that X ∩ {0, 1, 2, ..., n} has an ∈-minimal element, we have demonstrated that every nonempty subset X ⊆ ℕ has an ∈-minimal element.

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[tex] \sf \large \frac{3x + 4}{x + 2} + \frac{ {x}^{2} + 2x}{2x + 4} [/tex]

[tex] \sf \large \frac{3x + 4}{x + 2} + \frac{ x(x + 2)}{2(x + 2)} [/tex]

[tex] \sf \large \frac{3x + 4}{x + 2} + \frac{ x \cancel{(x + 2)}}{2 \cancel{(x + 2)}} [/tex]

[tex] \sf \large \frac{3x + 4}{x + 2} + \frac{ x}{2} [/tex]

[tex] \sf \large \frac{2(3x + 4) + x(x + 2)}{2(x + 2)} [/tex]

[tex] \sf \large \frac{6x + 8 + {x}^{2} + 2x}{2x + 4} [/tex]

[tex] \sf \large \frac{ {x}^{2} + 8x + 8}{2x + 4} [/tex]

y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

The equation y= -2 -4x in the form of slope intercept form y=mx+b is y=-4x-2.

Where m represents the slope and y intercept is -2.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The negative reciprocal of -4 is 1/4.

Therefore, the slope of the perpendicular line is 1/4.

The perpendicular line is y=1/4x-2.

We know that the parallel lines have same slope.

y=-4x+3

Hence, y=1/4x-2 is a perpendicular line and y=-4x+3 is a parallel line.

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To rewrite equation [tex]x^2 + 5x + 6[/tex] as[tex]x^2 + rx + sx + 6[/tex], we need to choose suitable values for r and s that satisfy r + s = 5.

To rewrite the quadratic expression[tex]x^2 + 5x + 6[/tex] as equivalent to[tex]x^2 + rx + sx + 6[/tex] , we need to find the values of r and s that satisfy the equation.

Let's start by expanding [tex]x^2 + rx + sx + 6:[/tex]

[tex]x^2 + rx + sx + 6 = x^2 + (r + s)x + 6[/tex]

We can see that the coefficient of x in the original expression is 5, and in the rewritten expression, it is (r + s). Therefore, we want to find values for r and s such that r + s = 5.

Next, we need to consider the constant term. In the original expression, the constant term is 6, and in the rewritten expression, it is also 6. Therefore, we want r, s, and 6 to satisfy the equation.

Since r + s = 5, we can solve for one variable in terms of the other. For example, if we choose r = 3, then s = 2 to satisfy the equation. Alternatively, we could choose r = 4 and s = 1, or any other combination that adds up to 5.

So, rewriting [tex]x^2 + 5x + 6[/tex] as [tex]x^2 + rx + sx + 6[/tex]can be achieved by choosing suitable values for r and s that satisfy r + s = 5.

For example, if we choose r = 3 and s = 2, the equivalent expression would be [tex]x^2 + 3x + 2x + 6.[/tex]

In summary, to rewrite[tex]x^2 + 5x + 6[/tex]as [tex]x^2 + rx + sx + 6[/tex], we need to choose suitable values for r and s that satisfy r + s = 5.

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Answer:

1 2/3

Step-by-step explanation:

If the company has budgeted 6 2/3 hours to complete a project, and 1/4 of that time is spent on research, we can find the amount of time spent on research as follows:

Total time for the project = 6 2/3 hours

Time spent on research = (1/4) * (6 2/3) hours

We can simplify 6 2/3 to an improper fraction as follows:

6 2/3 = (6 x 3 + 2) / 3 = 20/3

Substituting this value into the equation above, we get:

Time spent on research = (1/4) * (20/3) hours

Multiplying the fractions, we get:

Time spent on research = 5/3 hours

We can convert this improper fraction to a mixed number as follows:

5/3 = 1 2/3

Therefore, the company plans to spend 1 2/3 hours on research.

Answer:

[tex]\mathrm{23cm,19.81cm^2}[/tex]

Step-by-step explanation:

[tex]\mathrm{Solution:}\\\mathrm{Let\ a=5cm,\ b=8cm\ and\ c=10cm}\\\mathrm{Let\ "P"\ denote\ the\ perimeter\ and\ "A"\ denote\ the\ area\ of\ the\ triangle.}\\\mathrm{Then,\ P=a+b+c=5+8+10=23cm}\\\mathrm{Also,\ Semiperimeter(s)=\frac{P}{2}=\frac{23}{2}=11.5}\\[/tex]

[tex]\mathrm{Now,}\\\mathrm{Area\ of\ triangle=\sqrt{s(s-a)(s-b)(s-c)}}\\\mathrm{=\sqrt{11.5(11.5-5)(11.5-8)(11.5-10)}}\\\mathrm{=\sqrt{11.5\times 6.5\times 3.5\times 1.5}}\\\mathrm{=19.81cm^2}\\\mathrm{So,\ the\ perimeter\ of \ the\ triangle\ is\ 23cm\ and\ area\ is\ 19.81cm^2.}[/tex]

Adding the two cases together, we get a total of 360 + 720 = 1080 six-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 once, such that the number is divisible by its unit digit.

To find the number of 6-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 once, such that the 6-digit number is divisible by its unit digit, we can consider the following cases:

Case 1: The unit digit is 2, 4, or 6

In this case, the unit digit is already divisible by itself. We have 3 choices for the unit digit. For the remaining 5 digits, we have 5 choices for the first digit, 4 choices for the second digit, 3 choices for the third digit, 2 choices for the fourth digit, and 1 choice for the fifth digit. Therefore, the total number of 6-digit numbers is 3 * 5 * 4 * 3 * 2 * 1 = 360.

Case 2: The unit digit is 1, 3, or 5

In this case, the unit digit is not divisible by itself. We have 3 choices for the unit digit. For the remaining 5 digits, we have 5 choices for the first digit, 4 choices for the second digit, 3 choices for the third digit, 2 choices for the fourth digit, and 1 choice for the fifth digit. However, for the sixth digit, it cannot be the same as the unit digit since the number needs to be divisible by the unit digit. Therefore, we have 2 choices for the sixth digit. Hence, the total number of 6-digit numbers is 3 * 5 * 4 * 3 * 2 * 2 = 720.

Adding the two cases together, we get a total of 360 + 720 = 1080 six-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 once, such that the number is divisible by its unit digit.\

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Answer: 40 is the arithmetic mean

Step-by-step explanation:

The final simplified form of the equation using BEDMAS​ is:

76 + (55555co)/12 + TO + 47

To simplify the equation using the order of operations (BEDMAS), we'll follow these steps:

-12 - 11 - 10 - 9 - 8 - 7 + 6 + 5 + (co ÷ 12) × 55555 + 11 + 10 + 9 - 2 - 1 - TO - 9 - 10 - 11 + "12 × (4 ÷ 4) + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Let's simplify this step by step:

-12 - 11 - 10 - 9 - 8 - 7 = -57

-57 + 6 + 5 = -46

co ÷ 12 = co/12

co/12 × 55555 = (55555co)/12

(55555co)/12 + 11 + 10 + 9 = (55555co)/12 + 30

-2 - 1 = -3

TO - 9 - 10 - 11 = TO - 30

"12 × (4 ÷ 4) = 12

12 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 80

Now we can simplify the entire equation:

-46 + (55555co)/12 + 30 - 3 + TO - 30 + 80

To further simplify the equation:

46 + (55555co)/12 + 30 - 3 + TO - 30 + 80

Let's simplify the expression:

46 + (55555co)/12 + 30 - 3 + TO - 30 + 80

= 76 + (55555co)/12 + TO + 47

The final simplified form of the equation is:

76 + (55555co)/12 + TO + 47

Simplifying further depends on the value or expression assigned to "co" and "TO." Without specific values or expressions, we cannot provide a final simplified form of the equation.

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The surface area of the rectangular cuboid is S = 426 feet²

Given data ,

Let the surface area of the cuboid be S

Let the length of the rectangular cuboid be L = 12 feet

Let the width of the rectangular cuboid be W = 9 feet

Let the height of the rectangular cuboid be H = 5 feet

Now , The total surface area of the cuboid is given by the formula

Surface Area = 2 ( LH + LW + HW )

So, S = 2 ( 12 x 5 + 12 x 9 + 5 x 9 )

S = 2 ( 60 + 108 + 45 )

S = 2 x 213

S = 426 feet²

Hence , the surface area is S = 426 feet²

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The correct sum of numbers from 1 to n is 100.

We have,

Let's assume the correct sum of numbers from 1 to n is S.

According to the problem,

Juan made a mistake and added one of the numbers twice.

Let's call this number x.

The wrong sum that Juan obtained is 100.

The correct sum, S, can be expressed as the sum of numbers from 1 to n excluding the number x, plus the number x itself:

S = (1 + 2 + 3 + ... + (x-1) + (x+1) + ... + n) + x.

Since Juan added x twice, the wrong sum can be expressed as the sum of numbers from 1 to n without excluding any number: 100 = 1 + 2 + 3 + ... + (x-1) + x + (x+1) + ... + n.

We can subtract the correct sum equation (step 4) from the wrong sum equation (step 5) to find the value of x:

100 - S = (1 + 2 + 3 + ... + (x-1) + x + (x+1) + ... + n) - ((1 + 2 + 3 + ... + (x-1) + (x+1) + ... + n) + x).

Simplifying further, we get: 100 - S = x - x = 0.

From step 6, we see that 100 - S = 0, which means S = 100.

Therefore,

The correct sum of numbers from 1 to n is 100.

In conclusion, the correct sum of the numbers from 1 to n is 100.

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The complete question:

Juan wants to find the sum of the numbers from 1 to n, but in doing so he makes a mistake and adds one of these numbers twice, obtaining the wrong result 100.

The correct answer is option (C): 0.487

If the typical duration for a customer to receive their food in a dining establishment is 15 minutes, it is possible to utilize the exponential function to estimate the likelihood of obtaining the meal within the initial 10 minutes.

The probability density function (PDF) that characterizes the exponential distribution is expressed as f(x) = (1/µ) * e^(-x/µ), where µ denotes the mean or average value.

The average duration in this scenario is 15 minutes, denoted as µ. Our goal is to determine the probability of X falling between the limits of a and b, where a is set at 0 and b is set at 10.

To calculate this probability, we need to integrate the PDF from a to b:

P(0 ≤ X ≤ 10) = ∫[tex][0 to 10] (1/15) * e^(-x/15) dx[/tex]

Integrating this expression gives us:

P(0 ≤ X ≤ 10) = [tex][-e^(-x/15)] from 0 to 10[/tex]

Plugging in the values, we get:

P(0 ≤ X ≤ 10) = [tex][-e^(-10/15)] - [-e^(0/15)][/tex]

Simplifying further:

P(0 ≤ X ≤ 10) = [tex]-e^(-2/3) + 1[/tex]

Using a calculator, we can evaluate this expression:

P(0 ≤ X ≤ 10) ≈ 0.487

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To find the image of point Q after applying the given translation rule, we need to apply the rule to the coordinates of point Q(-2, 6).

Using the translation rule (x, y) → (x + 4, y - 5), we can apply the rule to the coordinates of point Q:

Q' = (-2 + 4, 6 - 5)

= (2, 1)

Therefore, the image of point Q after the translation is Q'(2, 1).

Answer:

The answers are

Emperor Penguin and Artatic wolf

Multiplying 0.79 by √2 yields an irrational answer.

To determine which number produces an irrational answer when multiplied by 0.79, we need to identify a number that, when multiplied by 0.79, results in a non-terminating and non-repeating decimal.

If the result of multiplying a number by 0.79 is a rational number, it would have a terminating or repeating decimal representation. However, if the result is an irrational number, it would have a non-repeating and non-terminating decimal representation.

To find such a number, we can look for an irrational number, such as the square root of a non-perfect square. Let's consider √2.

When we multiply 0.79 by √2, the result is:

0.79 * √2 ≈ 1.1141...

The decimal representation of this product does not terminate or repeat, indicating that it is an irrational number. Therefore, multiplying 0.79 by √2 produces an irrational answer.

In summary, multiplying 0.79 by √2 yields an irrational answer.

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Answer: C. not buying any phone

Hello!

16 - (2.5 + 4.25) = 9.25

The geometric sequence is:

[tex]\boxed{15,9,\frac{27}{5},\frac{81}{25}, \frac{243}{125} }[/tex]

A geometric sequence, or geometric progression, is a sequence of numbers where each successive number is the product of the previous number and some constant  [tex]\text{r}[/tex].

Now,

We need to find the 2nd, 3rd and 4th term of the geometric sequence. To find these terms, we need to know the common difference. The common difference can be determined using the formula,

Where [tex]\text{a}_1=15[/tex] and [tex]\text{a}_5=\frac{243}{125}[/tex]

For [tex]\text{n}=5[/tex], we have,

[tex]\dfrac{243}{125}=15(\text{r})^4[/tex]

Simplifying, we have,

[tex]\sf r= \dfrac{3}{5}[/tex]

Thus, the common difference is [tex]\sf r= \frac{3}{5}[/tex]

Now, we shall find the 2nd, 3rd and 4th terms by substituting [tex]\sf n=2,3,4[/tex] in the formula [tex]\text{a}_{\text{n}}=\text{a}_1(\text{r})^{\text{n}-1}[/tex]

For [tex]\sf n=2[/tex]

[tex]\text{a}_2=15\huge \text(\dfrac{3}{5}\huge \text)^1[/tex]

   [tex]=\bold{{9}}[/tex]

Thus, the 2nd term of the sequence is 9

For [tex]\sf n=3[/tex], we have,

[tex]\text{a}_3=15\huge \text(\dfrac{3}{5}\huge \text)^2[/tex]

[tex]=15\huge \text(\dfrac{9}{25}\huge \text)[/tex]

[tex]\bold{=\dfrac{27}{5}}[/tex]

Thus, the 3rd term of the sequence is [tex]\bold{{\frac{27}{5}}}}[/tex]

For [tex]\sf n=4[/tex], we have,

[tex]\text{a}_4=15\huge \text(\dfrac{3}{5}\huge \text)^3[/tex]

[tex]=15\huge \text(\dfrac{27}{25}\huge \text)[/tex]

[tex]\bold{=\dfrac{81}{25}}[/tex]

Thus, the 4th term of the sequence is [tex]\bold{\frac{81}{25}}[/tex]

Therefore, the geometric sequence is:

[tex]\boxed{\bold{15,9,\frac{27}{5},\frac{81}{25}, \frac{243}{125}}}[/tex]

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