What conclusion can you draw about a nonzero real number if its absolute value is equal to itsopposite?

Answer:

\(y = 16\frac{2}{3} x + 100\) or \(y = \frac{50}{3} + 100\)

Step-by-step explanation:

The equation of a line is \(y = mx + b\), with \(m\) being the slope and \(b\) being the y-intercept.

We can see on the graph that the y-intercept, where the line crosses or touches the y-axis, is 100. So, our new equation is \(y = mx + 100\).

Now we have to find the slope. Let's pick a point that's clearly on the graph. Perhaps (3, 150). And then we'll take the y-intercept point for convenience, (0, 100).

Then, we'll use \(\frac{y_{2} - y_{1}}{x_{2} - x_{1} }\) to find the slope.

Let's substitute in our points.

\(\frac{150-100}{3-0}\)

Simplify.

\(\frac{50}{3}\)

Now, we can leave the slope like that or turn it into a mixed number. As a mixed number, your slope is \(16\frac{2}{3}\).

We'll put that in our equation for a line and...bam!

\(y = 16\frac{2}{3} x + 100\) or \(y = \frac{50}{3} + 100\)

Answer:

9=11

Step-by-step explanation:

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

Explanation

Step 1

group similar terms

Step 2

Add similar terms

Answer:

One number is 29, and the other one 45

Step-by-step explanation:

Solve this problem by creating two equations that represents the statements, and solve for the unknowns using substitution:

Let's say that one of the numbers is X , and the other one Y, and assume that Y is larger than X, so when we do their difference we get the 16 units they mention in the problem:

Y - X = 16

The info on the  product of the two numbers will give us our second equation:

X * Y = 1305

Now use the first equation to substitute Y with 16 + X, in the second equation:

X (16 + X) = 1305

16 X + X^2 = 1305

X^2 + 16 X - 1305 = 0

Now use the quadratic formula to solve for X, and we get two possible answers: X = -45 or X = 29

So, since we are looking for whole numbers, we discard the negative answer, and keep X = 29

Then, the value of the other number "Y" is = 29 + 16 = 45

Answer:

Step-by-step explanation:(-4, -1) --> (4, -1). Translating two units to the right means adding two units to the x-coordinate: (4, -1) --> (6, -1). This is our final point

Answer: Choice A) \(\boldsymbol{x \le -3} \textbf{ or } \boldsymbol{x \ge 9}\)

===================================================

Explanation:

Let's solve the first inequality mentioned.

To do so, divide both sides by 6.

\(6x \le -18\\\\6x/6 \le -18/6\\\\x \le -3\)

The inequality sign stays the same the entire time. It only flips if we divided both sides by a negative number.

Through similar steps, this is how we'd solve the second inequality given:

\(9x \ge 81\\\\9x/9 \ge 81/9\\\\x \ge 9\)

So overall \(\boldsymbol{x \le -3} \ \textbf{ or } \ \boldsymbol{x \ge 9}\)

The key word "or" is important. If it was "and", then we'd have no solutions because no such number is both smaller than -3 and also larger than 9 at the same time.

The graph of this on the number line will involve closed circles at -3 and 9. Then we shade anything that is not between those closed circles.

Answer:

x ≤ -3 or x ≥ 9

Step-by-step explanation:

Hello!

We can solve for x in both inequalities that are given.

The answer is the first option: x ≤ -3 or x ≥ 9.

Tip:
If you have an inequality with a negative coefficient, such as -3x ≤ 6, when dividing a number by a negative number, you have to flip the inequality.

The correct expression which is not a rational expression,

⇒ (x+3)(2x-1) / (x+3)

We have to given that;

All the expressions are,

⇒ (x+3)(2x-1) / (x+3)

⇒ (3x²+3x) / (4x+5)

⇒ (3x+4√x-7) / (2x+2)

⇒ (2x²-3x³+5) / 5x

Since, A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Hence, We can simplify all the expressions as,

⇒ (x+3)(2x-1) / (x+3)

⇒ (2x - 1)

Hence, It is not a rational expression.

⇒ (3x²+3x) / (4x+5)

⇒ 3x (x + 1) / (4x + 5)

Hence, It is a rational expression.

⇒ (3x+4√x-7) / (2x+2)

⇒ (3x + 4√x - 7) / 2 (x + 1)

Hence, It is a rational expression.

⇒ (2x²-3x³+5) / 5x

Hence, It is a rational expression.

Thus, The correct expression which is not a rational expression,

⇒ (x+3)(2x-1) / (x+3)

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Answer:

30 kg of dough

Step-by-step explanation:

you have to figure out how much dough he made in an hour. so divide the total hours by to the amount of dough. you then multiple the total hours by the amount of dough per hour.

27/9=3

3*10= 30

Answer:

253009

Step-by-step explanation:

503^2=253009

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

Step-by-step explanation:

answer is 9.66

Answer:

x = 4

Step-by-step explanation:

x - 6 = 2x - 10

-2x     -2x

-x - 6 = -10

    +6    +6

----------------

-x = -4

÷-1   ÷-1

------------

x = 4

I hope this helps!

Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

\(\bf{2y+4y=6-3y}\)

\(\bf{6y=6-3y}\)

Add 3y to each side

\(\bf{6y+3y=6}\)

Combine like terms

\(\bf{9y=6}\)

Divide each side by 9

\(\bf{y=\dfrac{6}{9}}\)

\(\bf{y=\dfrac{2}{3}}\)

Hence, the answer is 2/3.

A quadrilateral is a figure having four sides and four angles. The six types of quadrilaterals are rectangle, square, parallelogram, rhombus, kite and trapezoid.

According to the question,

We have to name six types of quadrilaterals by first defining a quadrilateral.

A quadrilateral is a figure where it has four sides and four angles. These sides and angles may sometimes be equal to each other and sometimes may be not. However, in all quadrilaterals, the sum of all four angles is 360°.

Six types of quadrilateral are rectangle (opposite sides of rectangle are equal), square (all sides are equal and each angle is a right angle), parallelogram (opposite sides are parallel and equal), rhombus, kite and trapezoid.

Hence, a quadrilateral is a figure having four sides and four angles. The six types of quadrilaterals are rectangle, square, parallelogram, rhombus, kite and trapezoid.

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Answer:

see image...

the (x-h) shifts the curve left right (east west)

and the +k at the end shifts it up/down (north/south)

Step-by-step explanation:

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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The 5th term of the arithmetic series is  1179/ 19.

The 10th term of the arithmetic series , S is 66.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

66 = a + 9d

The sum of the first 20 terms of S is 1290.

Therefore,

Sₙ = n / 2 (2a + (n - 1)d)

1290 = 10(2a + 19d)

1290 = 20a + 190d

combine the equation

66 = a + 9d

1290 = 20a + 190d

Hence,

a = 66 - 9d

1290 = 20(66 - 9d) + 190d

1290 = 1320 - 180 + 190d

1290 - 1320 + 180 = 190d

190d = 150

d = 150 / 190

d = 15 / 19

Hence,

a = 66 - 9(15  /19)

a = 66 - 135 / 19

a = 1254 - 135/ 19

a = 1119 / 19

Hence, let's find the fifth term.

a₅ = a + 4d

a₅ = 1119 / 19 + 4(15 / 19)

a₅ = 1119 / 19 + 60 / 19

Therefore,

a₅ =  1179/ 19

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Answer:

im sorry if not but i think its 7.24

Step-by-step explanation:

Answer:

USE SOCRACTIC IT WOULD REALLY HELP

Answer: Mean: 4.625 Median: 6

Step-by-step explanation:

Answer:

True

Step-by-Step

When the x was 2, the y was 11.

When the x was 4, the y was 19.

So for every two on the x side, the y side adds 8.

So yes, there's a pattern AKA, this a proportional table.

Hope this helped! :)

Answer:

  57 cm²

Step-by-step explanation:

You have a composite figure and you want to find its area.

There are several ways you can decompose the given figure. Three of them are shown in the attachments. The missing dimensions are found by realizing that the sum of the right-side dimensions is equal to the left-side dimension, and the sum of the bottom-side dimensions is equal to the top dimension.

Extending the vertical boundary line divides the figure into a left rectangle that is 7 cm high and 7 cm wide, and a right rectangle that is 2 cm high and 4 cm wide. This is shown in the first attachment.

The area of each rectangle is the product of its height and width, and the total area is the sum of these:

  Area = (height)×(width) . . . . . area formula for one rectangle

  Area = (7 cm)(7 cm) +(2 cm)(4 cm) = 49 cm² +8 cm² = 57 cm²

Extending the horizontal boundary line divides the figure into a top rectangle 2 cm high and 11 cm wide, and a bottom rectangle 5 cm high and 7 cm wide. This is shown in the second attachment. The total area is ...

  Area = (2 cm)(11 cm) +(5 cm)(7 cm) = 22 cm² +35 cm² = 57 cm²

A line can be drawn corner-to-corner to divide the figure into two trapezoids. This is shown in the third attachment.

The upper right trapezoid has bases 11 cm and 4 cm, and height 2 cm.

The lower left trapezoid has bases 7 cm and 5 cm, and height 7 cm.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

Then the total area is ...

  Area = 1/2(11 cm +4 cm)(2 cm) +1/2(7 cm +5 cm)(7 cm) = 15 cm² +42 cm²

  Area = 57 cm²

The rectangle that encloses the entire figure is 7 cm high and 11 cm wide, so has an area of ...

  A = HW = (7 cm)(11 cm) = 77 cm²

From that area, the lower right corner space is cut out. It has dimensions 5 cm high by 4 cm wide, so an area of (5 cm)(4 cm) = 20 cm².

The area of the figure itself is the difference between the area of the bounding rectangle and the area of the cut-out space at lower right:

  Area = 77 cm² -20 cm² = 57 cm²

The area of the figure in the picture is 57 cm².

Answer:

We can write 36 as a product of prime factors: 36 = 2² × 3². The expression 2² × 3² is said to be the prime factorization of 36.

Step-by-step explanation:

From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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1) to obtain the value of x, we must equate AC and BD based on the diagonal properties of a rectangle. Note that a rectangle's diagonal divides it into two congruent right triangles.

A rectangle's diagonals are all the same length. A square is a quadrilateral whose diagonals bisect each other, intersect at right angles, and are congruent.

Thus,

Since BD = AC

2x + 19 = 5x - 2

To solve the equation 2x + 19 = 5x - 2, we need to isolate x on one side of the equation.

First, we can simplify both sides by combining like terms. Subtracting 2x from both sides gives:

19 = 3x - 2

Next, we can isolate x by adding 2 to both sides:

21 = 3x

Finally, we can solve for x by dividing both sides by 3:

x = 7

Therefore, the solution to the equation 2x + 19 = 5x - 2 is x = 7

b) The Properties of Parallel Lines Intersected by a Transverse Postulate states that when a transversal intersects two parallel lines, the corresponding angles are congruent, the alternate interior angles are congruent, and the same-side interior angles are supplementary. This means that

∠LMN + ∠MNK = 180°

Thus,

115 +  ∠MNK = 180

∠MNK = 180 - 115

∠MNK = 65°

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Answer:

I think the answer is 45/4 i'm so sorry if the answer is wrong

Step-by-step explanation:

Answer:

11 1/4

Step-by-step explanation:

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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