Choose the graph that matches the following system of equations: 5x + 2y = 2 3x − 3y = 18 a A line includes points 0 comma 6 and 2 comma 4. A line includes points 0 comma 2 and negative 2 comma 7. b A line includes points 0 comma 1 and 2 comma negative 4. A line includes points negative 1 comma negative 7 and 0 comma negative 6. c A line includes points 0 comma 1 and 1 comma negative 4. A line includes points 2 comma negative 4 and 0 comma negative 6. d A line includes points 0 comma 6 and 1 comma 3. A line includes points 0 comma 1 and 1 comma 6.

Answer:

Một trục số đi từ âm 6 đến dương 6. Các điểm ở âm 6, âm 2, 5.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

14.9

Step-by-step explanation:

Hope this helps!

The equation to complete the square for x² + 3x = 6 is 3/2 (option a)

To complete the square for the equation x² + 3x = 6, we need to add a specific number to both sides of the equation. The number we need to add is half of the coefficient of x, squared. In other words, we need to find (b/2)², where b is the coefficient of x.

In this equation, b is 3, so (b/2)² is (3/2)², which simplifies to 9/4. Therefore, to complete the square, we need to add 9/4 to both sides of the equation:

x² + 3x + 9/4 = 6 + 9/4

Now, we can rewrite the left side of the equation as a perfect square:

(x + 3/2)² = 33/4

Finally, we can solve for x by taking the square root of both sides of the equation:

x + 3/2 = ± √(33/4)

x = -3/2 ± √(33/4)

Therefore, the answer to the question is a) 3/2.

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Answer:

The largest angle in the triangle is the measure of 90° (answer choice D).

Step-by-step explanation:

We are given that there are three angles in a triangle:

We know that a triangle's interior angles will sum to be 180 degrees. With this information, we can create an equation in which we add all three values together and set the sum of them equal to 180 and solve for x.

Our equation will be combining the above three angles and setting them equal to 180.

To set up our equation, let's first add the three angle values together.

\(\text{x + (x + 10) + (x + 50)}\)

Then, we will set this value equal to 180 since the angles will add up to equal this amount.

\(\text{x + (x + 10) + (x + 50) = 180}\)

Now, we need to use simplifying techniques in order to be able to solve for x on both sides of the equation. Let's start by collecting our constants on the left side of the equation.

We first can identify our constants.

These numbers are not our variable, or x, so therefore these are our constants. This is the easiest way to identify them.

The signs on both are addition, which means the integers are positive. Therefore, when combining them, we will add them together.

\(\text{10 + 50 = 60}\)

Now, we need to rewrite our equation. We no longer have a 10 or a 50, so we can do the following:

Therefore, our new equation will reflect these changes:

\(\text{x + x + (x + 60) = 180}\)

Now, we just need to combine our variables.

Our new rewritten equation will reflect the above changes.

\(\text{3x + 60 = 180}\)

Now, we need to follow the steps to solve a two-step algebraic equation. These steps vary based on the equation, but we want to isolate our x term on either side of the equation (conventionally, we choose the left side) and our constant term on the opposing side.

In order to do this, we need to subtract the 60 from the left side of the equation to leave the x by itself. In order to do this, we also need to subtract 60 from 180. The rule in algebra states that the actions performed on one side of the equation must also be reflected on the opposing side of the equation.

Therefore, by subtracting 60 from the left side, we also subtract 60 from the right side.

\(\text{3x + 60 - 60 = 180 - 60}\\\\\text{3x = 120}\)

Now that we have the x term isolated, we need to take note that we have a coefficient. This means that we need to isolate the x entirely. We are going to do this by dividing both sides of the equation by 3.

\(\frac{3x}{3} = \frac{120}{3}\\\\\text{x = 40}\)

Now, we have solved for our x term. However, we are not done. We still need to find the measures of the angles, which is easily done by substituting our value for x (40) into the three expressions.

For our first expression:

\(\text{x = 40}\)

For our second expression:

\(\text{40 + 10 = 50}\)

For our third expression:

\(\text{40 + 50 = 90}\)

Now, to answer the final question, we need to find the measure of the largest angle.

Our three angle measures as determined above are:

We can see that 90 is the largest number in the set, so our answer is 90°, or answer choice D.

Step-by-step explanation:

x + x + 10 + x + 50 = 180°

3x + 60 = 180°

3x = 120

x = 40

Angles are 40° , 50° , 90°

Here, The largest Angle is 90°

The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

Answer:

0.1 == -0.1

1/7 == -1/7

10 == -10

-7 == 7

Step-by-step explanation:

I took the test

The opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The numbers are:

0.005, 12, 0, -2

As we know, from the definition of the number, a number is a mathematical entity that can be used to count, measure, or name things.

The opposite of any number can be obtained by changing the sign of the number.

The opposite of the number 0.005 is -0.005

The opposite of the number 12 is -12

The opposite of the number 0 is 0

The opposite of the number -2 is 2

Thus, the opposite of the numbers 0.005, 12, 0, -2 are -0.005, -12, 0, 2 after changing the sign of the number.

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To find the sum of the first 11 terms in a geometric series with a first term of -2 and a common ratio of 5, we can use the formula for the sum of a geometric series.

The sum of the first 11 terms in a geometric series can be calculated using the formula for the sum of a geometric series. In this case, the first term is -2 and the common ratio is 5. The formula for the sum of the first n terms of a geometric series is S_n = a(1 - r^n) / (1 - r), where S_n represents the sum, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the given values, we have S_11 = -2(1 - 5^11) / (1 - 5). Simplifying the expression gives us S_11 = -2(-4,882,812) / (-4), which further simplifies to S_11 = 9,765,624.

Therefore, the sum of the first 11 terms in the geometric series is 9,765,624. This represents the cumulative total obtained by adding -2, 10, -50, 250, and so on, for a total of 11 terms, where each term is obtained by multiplying the previous term by the common ratio of 5.

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Step-by-step explanation:

f(x) = x + 3 for x >= -2.

Hence f(-2) = (-2) + 3 = 1.

So you're given two ifs. If x is less than -2, use the top equation. If x is equal to or greater than 2, use the bottom equation.

Since x = -2, use the bottom equation.

\(f(x)=x+3\\f(-2)=-2+3\\f(-2)=1\)

Your answer is f(-2) = 1.

The way in which the graph of 2y − x = 1 compare with the graph of 3y − x = 1 is that: A. the graph of 2y − x = 1 has a steeper slope than the graph of 3y − x = 1.

In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

For the graph of 2y − x = 1, the slope is given by:

2y − x = 1

2y = x + 1

y = x/2 + 1/2  

Slope, m₁ = 1/2 or 0.5.

For the graph of 3y − x = 1, the slope is given by:

3y − x = 1

3y = x + 1

y = x/3 + 1/3

Slope, m₂ = 1/3 or 0.3.

Therefore, m₁ > m₂ (steeper slope).

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Answer:

3 ; 1 minute ;75%

Step-by-step explanation:

Given :

Service time = 15 seconds = 15/60 = 0.25 minute per customer

μ = number of customers per minute = 1/0.25 = 4

Arrival rate, λ= 3 persons per minute

L = λ ÷ (μ - λ)

L = 3 ÷ (4 - 3)

L = 3 ÷ 1

L = 3

b) How long would you expect it to take to get a cup of coffee?

L / arrival rate (λ)

3 / 3

= 1 minute

c) What percentage of time is the urn being used?

Utilization rate = λ/ μ

= 3 / 4

= 0.75 = 0.75 * 100% = 75%

Answer:

f (1) = 1/ 2(1) + 3

= 1/2 + 3

= 1/5

Answer:

4.

A= S²

A= 13²

A= 169

p= 4s

p= 4× 13

p= 52

5.

A= L×W

A= 21× 5

A= 105

p= 2(L+W)

P= 2(21+5)

P= 2(26)

P= 52

6.

A = L×W

A= 15× 9

A = 135

p=2(L+W)

P= 2( 15 + 9)

P= 2(24)

p = 48

Don't forget to put in the units

The answer to this problem is 9.

-6+(-3)-(-18)

Since (+)(-)=(-) and (-)(-)=(+),

-6-3+18

-9+18

9

Answer:

9

Step-by-step explanation:

-6 + -3 - (-18)

-6 - 3 + 18

-9 + 18

9

- (-) = +

+ (+) = +

- (+) = -

+ (-) = -

Answer:

Step-by-step explanation:

Based on similar triangle;

14/49 = x+5/9x+1

Cross multiply

49(x+5) = 14(9x+1)

49x + 245 = 126x + 14

49x - 126x = 14 - 245

-77x = -231

x = -231/-77

x = 3

Hence the value of x is 3

Answer:

sorry I don't speak alien

Answer:

z = 4/3 or 1 1/3

Step-by-step explanation:

z−4/9−1/3=5/9

Change 1/3 to have a denominator of 9

1/3 *3/3 = 3/9

z−4/9−3/9=5/9

Combine like terms

z -7/9 = 5/9

Add 7/9 to each side

z-7/9+7/9 = 5/9+7/9

z = 12/9

z=4/3

or as a mixed number

z = 1 1/3

The function for the value of the motorcycle after x years are;

y = 8000 - 500x

y = -500x + 8000

A function is a relationship between inputs where each input is related to exactly one output.

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have given that new motorcycle has a value of $8,000. Every year its value decreases by $500.

Now, we have y = amount of the motorcycle

x = number of years

The function for the value of the motorcycle after x years.

y = 8000 - 500x

y = -500x + 8000

Thus,

y = 8000 - 500x

y = -500x + 8000

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Answer:

\(x<\frac{y+8}{4}\)

​​  \(x\geq \frac{y}{4} -1\)

Step-by-step explanation:

no the answers aren't the same

To find the solution of the compound inequality x − 2 > 4 or 5x ≥ 35, we need to solve each inequality separately and then combine their solutions using the OR operator.

Solving x − 2 > 4, we add 2 to both sides to get x > 6.
Solving 5x ≥ 35, we divide both sides by 5 to get x ≥ 7.

The solution of the compound inequality x − 2 > 4 or 5x ≥ 35 is the set of all values of x that satisfy at least one of the inequalities, which is x > 6 or x ≥ 7.

To graph this solution, we draw a number line and mark the points 6 and 7 with open circles (because they are not included in the solution). Then we shade the region to the right of 6 and/or to the right of 7, as shown below:

<---o---o=========>
6   7

The open circles indicate that 6 and 7 are not included in the solution, because x can be any value greater than 6 or any value greater than or equal to 7, but not both at the same time.

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the problem is x > 6 or x ≥ 7. To explain this solution, we need to solve each inequality separately and then combine the results.

First, we solve x − 2 > 4 by adding 2 to both sides to get x > 6.

Next, we solve 5x ≥ 35 by dividing both sides by 5 to get x ≥ 7.

To combine the results, we take the union of the two solutions, which gives us x > 6 or x ≥ 7. This means that any value of x that is greater than 6 or equal to 7 will satisfy the original compound inequality.

The graph that represents this solution is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

the solution to the compound inequality x − 2 > 4 or 5x ≥ 35 is x > 6 or x ≥ 7, and the graph that represents it is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

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The sentence is true. A median of a triangle connects the midpoint of one side of the triangle to the midpoint of another side of the triangle.

To understand this, let's break it down step by step:
1. A triangle has three sides.
2. A median of a triangle is a line segment that connects a vertex (corner) of the triangle to the midpoint of the opposite side.
3. So, if we take one side of the triangle and find its midpoint, and then take another side of the triangle and find its midpoint, the median will connect these two midpoints.

For example, let's say we have a triangle ABC. The midpoint of side AB is M, and the midpoint of side AC is N. The median connecting these two midpoints will be the line segment MN.

In summary, the statement is true. A median of a triangle connects the midpoint of one side of the triangle to the midpoint of another side of the triangle.

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Rate of the given base $23,500 and the portion $6227.50 is equal to 26.5 percent ( nearest tenth ).

As given in the question,

Given base of the required rate is equal to $23,500

Portion of the given base used is equal to $6227.50

Formula to calculate the rate percent is given by :

Rate percent = [(Portion of the given base used) / ( Base) ] × 100

Substitute the value in the formula we get,

⇒ Rate percent = ( 6227.50 / 23,500 ) × 100

⇒ Rate percent = 26.5%

Therefore, rate percent of the given base and the portion used is equal to 26.5%.

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The commission of the agent is 196000

From the question, we have the following parameters that can be used in our computation:

Commission percentage = 7%

Earnings = 2.8 million

Using the above as a guide, we have the following:

Commission = 7% * Earnings

Substitute the known values in the above equation, so, we have the following representation

Commission = 7% * 2.8 million

Evaluate

Commission = 196000

Hence, the commission is $196000

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Starting Times (Waves):
- Wave 1
- Wave 2
- Wave 3

Starting Areas (Corrals):
- Wave 1 Corral A
- Wave 1 Corral B
- Wave 1 Corral C
- Wave 1 Corral D
- Wave 1 Corral E
- Wave 2 Corral A
- Wave 2 Corral B
- Wave 2 Corral C
- Wave 2 Corral D
- Wave 2 Corral E
- Wave 3 Corral A
- Wave 3 Corral B
- Wave 3 Corral C
- Wave 3 Corral D
- Wave 3 Corral E

Possible Combinations:
- Wave 1 Corral A
- Wave 1 Corral B
- Wave 1 Corral C
- Wave 1 Corral D
- Wave 1 Corral E
- Wave 2 Corral A
- Wave 2 Corral B
- Wave 2 Corral C
- Wave 2 Corral D
- Wave 2 Corral E
- Wave 3 Corral A
- Wave 3 Corral B
- Wave 3 Corral C
- Wave 3 Corral D
- Wave 3 Corral E

To create a tree diagram for the waves and corrals, follow these steps:

1. Begin by drawing three branches representing the three scattered starting times or "waves" - label them Wave 1, Wave 2, and Wave 3.
2. From the end of each wave branch, draw five branches representing the "corrals" within each wave.
3. Label the corrals under Wave 1 as Corral 1A, Corral 1B, Corral 1C, Corral 1D, and Corral 1E.
4. Label the corrals under Wave 2 as Corral 2A, Corral 2B, Corral 2C, Corral 2D, and Corral 2E.
5. Label the corrals under Wave 3 as Corral 3A, Corral 3B, Corral 3C, Corral 3D, and Corral 3E.

Now, you have a tree diagram that shows the possible waves and corrals runners could be assigned to in the marathon.

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The function f(x) = x-2 is not continuous at x 2 but its limit as x → 2 exists .

Given,

Function: f(x) = x-2

Now to check the continuity of function:

A real function f(x) is said to be continuous at a point 'a' of its domain if limits exist at the point 'a' and equals to f(a) .

Check,

f(2) = 0

at less than 2

f(x)< 0

at greater than 2

f(x)> 0

Hence the function is not continuous at x=2 .

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The value of mean is 59.8 and the variance of the sampling distribution is 1440.46

Given,

In the question:

The distance X is measured in miles and the sampling distribution of X is given by;

X :-      0        10    50     100

P(X) : - 1 /12    1/6   1/3    5/12

Calculate the mean and variance of this sampling distribution.

Now, According to the question:

The variance of a random variable provides an idea of the dispersion of the random variable with respect to its hope. It is then defined as shown in the image.

Then you first calculate E [x] and E [\(x^{2}\)], and then be able to calculate the variance.

E[x] = 0 × 1/12 + 10 × 1/6 + 50 × 1/3 + 100 × 5/12

E[x] = 1.6 + 16.6 + 41.6

Mean/ E[X] = 59.8

So E[X]²= 59.8² = 3576.04

On the other hand

E[\(x^{2}\)] = \(0^2\) × 1/12 + \(10^2\) × 1/6 + \(50^2\) × 1/3 + \(100^2\) × 5/12

E[\(x^{2}\)] = 0 + 16.6 + 833.3 + 4166.6

E[\(x^{2}\)]  = 5016.5

Then the variance will be:

Var[x]=  E[\(x^{2}\)]  - E[X]²

Var[x] =  5016.5 - 3576.04

Var[x] = 1440.46

Hence, The value of mean is 59.8 and the variance of the sampling distribution is 1440.46

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Answer:

(3, 1250 )

Step-by-step explanation:

Given x = 3, then

y = 10 × 5³ = 10 × 125 = 1250

Answer:

5+4c=25

Step-by-step explanation:

Answer:

5 + 4c = 25

Step-by-step explanation:

The 5 dollars spent on paper is separate from the price of all the candy, so you will add that to the total of the candy.You bought 4 pieces of candy, you that value can be changed.You spent a total of 25 dollars.We have all the info to set up an equation:

5 + 4c = 25

p.s: i have a piece of candy?

Answer:

Calculus in baseball. In baseball, calculus can be used to optimize the pitcher’s throw to achieve maximum efficiency. Also, calculus can be used to calculate the projectile motion of baseball’s trajectory and to predict if runners can make it to the next base on time given their running speed and the speed of a hit ball.

Step-by-step explanation:

The unite rate of the kendra's bike ride is found as 3 blocks / min.

The given question is-

Unit rate = number of blocks/ total time

Unit rate = 30 / 10

Unit rate = 3 blocks / min

Thus, the unit rate of the kendra's bike ride is found as 3 blocks / min.

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Answer:

dad

Step-by-step explanation: