Consider the graphs of the following lines.
3x - 5y = 2
3x + 5y = -2
Find the slope m of each line.
3x - 5y = 2
m₁ =
3x + 5y = -2
m2 =
8.6A.
4

The domain of the relation include the following: A. {1, 2, 3, 6}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain:

Domain = {1, 2, 3, 6}.

In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {1, 2, 3, 6}.

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Answer:

h(2)=12

Step-by-step explanation:

Given:

h(x)=4x+4

Find:

h(2)

Substitute 2 into x.

[tex]h(2)=4(2)+4[/tex]

Solve:

[tex]h(2)=12[/tex]

Answer:

  (c)  3

Step-by-step explanation:

You want the y-value of the solution to the equations ...

We are interested in the value of y, so it can be useful to eliminate x from the equation(s). The x² term appears in both, so it is convenient to subtract the first equation from the second.

  (x² +y²) -(x² -y) = (9) -(-3)

  y² +y = 12

  y² +y -12 = 0 . . . . . . subtract 12

  (y +4)(y -3) = 0 . . . . . factor

  y = -4 or +3 . . . . . . . . values that make the factors zero

Solving the first equation for y, we find ...

  x² +3 = y . . . . . . . add y+3

We know that x² cannot be negative, so this tells us the values of y will be ...

  y ≥ 3

Of the two solutions we found above, the value -4 is extraneous (not in the domain of y).

The y-coordinate of the solution is 3, choice C.

__

Additional comment

The solution is the point of intersection of the two curves shown in the attachment. The y-coordinate of that point is 3.

<95141404393>

The given sample space could represent a win and loss game by flipping a coin twice, where win represent the outcome head and loss represent the outcome tail.

A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.

The subset of the sample space are events.

Given sample space is S = {WW, WL, LW, LL}

This can be interpreted as the outcomes in a random experiment, which has only two possibilities, either win or loss.

Suppose that we flip a coin two times.

Possible outcomes are,

HH : head appears twice

HT : head appears at first and tail appears second

TH : tail appears first and then head appears

TT : tail appears twice

Let the outcome head represent the win and tail represent the loss.

Possible outcomes are then WW, WL, LW, LL.

Hence the given sample space can be a possible outcomes of flipping a coin twice.

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Answer:

(4) on a graph, the solution of a system of equations is the point where the lines intersect.

(5) a system of linear equations includes at least two linear equations.

(6) the solution of a system of linear equations is any values of the variables that satisfy both equations at the same time.

Answer:

lower right option

Step-by-step explanation:

using the properties of logarithms

• loga + logb ⇔ log(ab)

• loga - logb ⇔ log ([tex]\frac{a}{b}[/tex] )

• log[tex]x^{n}[/tex] = nlogx

• lne = 1

given

a[tex]e^{bt}[/tex] = c ( take ln of both sides )

ln a[tex]e^{bt}[/tex] = lnc

lna + ln[tex]e^{bt}[/tex] = lnc

lna + bt lne = lnc ( subtract lna from both sides )

bt = lnc - lna

bt = ln ([tex]\frac{c}{a}[/tex] ) ← divide both sides by b

t = [tex]\frac{ln(\frac{c}{a}) }{b}[/tex]

The correct option is C. The IQR is the best measure of variability, and it equals 4.

The IQR (interquartile range), a measure of variability that depicts the range of the middle 50% of the data, is used in box plots. It is determined as the gap between the first and third quartiles (Q1 and Q3) (Q1). Since the box in this instance spans the numbers 17 to 21 on the number line, Q1 equals 17 and Q3 equals 21. IQR = Q3 - Q1 = 21 - 17 = 4 as a result.

The difference between the dataset's maximum and minimum values is represented by the range, another measure of variability. As a result of its sensitivity to extreme values, it is less reliable than the IQR. Although the range in this instance is equal to 27 - 10 = 17, it could not correctly reflect the variety of the data.

Therefore, the IQR is the most appropriate measure of variability for this data, and its value is 4.

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In  linear equation, 60m  is the height of flagpole c .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Height/ Shadow

Shadow of the pole = 12 m

Height of the pole = x m

Tim's shadow = Height of the pole - Tim's distance

12 m - 10 m =  2 m

Tim's height = 2 m

Hence:

x/12 = 2/10

Cross Multiply

2x = 12 × 10

x = 120/2

x = 60 m

Approximately = 60m

Hence, the height of the flagpole = 60m

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In the Metric System , each millimeter increment is equal to the 1/10 or 0.1 of a centimeter .

The Metric System is defined as a standardized system of measurements which is used in many countries around the world.

In the Metric System, there are different units of length, which include  millimeters (mm) and centimeters (cm).

we know that , 1 centimeter is equivalent to 10 millimeters. This means that each millimeter increment is equal to 0.1 of a centimeter.

For Example, if we measure a length of 50 millimeters, we can convert it to centimeters by dividing 50 by 10, which gives you a length of 5 centimeters.

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The given question is incomplete , the complete question is

In the metric system each millimeter increment is equal to ____ of a centimeter .

Answer:

Answer: 67

18+5x2^3-7+16

18+5x8-7+16

18+40-7+16

67

Answer:

35 :)

Step-by-step explanation:

Answer:

35

7x5=35

You need to know your multiples.

7, 14, 21, 28, 35, 42, 49, 56, and so on.......

Answer: corn 806,736

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

A union is the graph of a compound inequality that contains "or," meaning the solution is a solution of either inequality, but not necessarily both. The union represents all values that satisfy at least one of the inequalities in the compound inequality. The solution is shown as the shaded region on the graph that represents the union of the solutions of the individual inequalities.

For the given right triangle, the value of z is approximately 16.155 cm.

To find the value of z in a right triangle with sides 6 cm and 15 cm, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (z) is equal to the sum of the squares of the lengths of the other two sides (6 cm and 15 cm).

So we can write the equation:

z^2 = 6^2 + 15^2

Simplifying the equation:

z^2 = 36 + 225

Adding the numbers on the right side of the equation:

z^2 = 261

Taking the square root of both sides of the equation:

z = √261

Approximating the square root:

z ≈ 16.155

Therefore, the value of z is approximately 16.155 cm.

Note: The question is incomplete. The complete question probably is: Find the value of z (hypotenuse) if the other dimensions are 6cm, 15cm and right angle in triangle.

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The solution to the inequality is a coordinate of (-1.8, 0.6)

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

y> -2x - 3

Y <4/3x +3

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, the shaded area has a coordinate of (-1.8, 0.6)

Hence, the solution is (-1.8, 0.6)

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Answer:

Yes it is a right triangle

Step-by-step explanation:

These side lengths correspond to a Pythagorean triple, specifically 8-15-17, which is a set of three positive integers that satisfies the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, also known as the hypotenuse.

In this triangle, 32^2 + 60^2 = 8^2 + 15^2 = 17^2, which confirms that it is indeed a right triangle.

Answer:

$3692

Step-by-step explanation:

100-21=79

=> 0.79

12000 × 0.79^5 = $3692

Answer:

81

Step-by-step explanation:

Answer:871

Step-by-step explanation:If he drove 603 miles in 9 hours, he drove 67 miles per hour. So in 13 hours he will drive 67x13, which is 871.

Answer:

Step-by-step explanation:

David would drive 871 miles. This is because 603 ÷ 9 = 67.

So, you'd have to multiply 67 times 13. Because 67 is the average mph.

Answer:

Step-by-step explanation:

square root of 100 is 10 and the only point that is on 10 is f so f = 10 or square root of 100

square root of 80 equals about 8.9 and the only point on 8.9 d so d is equal to square root of 80

3 * pi is about 9.4 and the only option left is e so e = 3 * pi

The area of this figure with radius 20.8 ft include the following: D. 432.64π ft² ≈ 1358.5 ft².

Mathematically, the area of a circle can be calculated by using this mathematical expression:

Area = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = π × 20.8²

Area of circle = 432.64π square feet.

Area of circle = 1358.5 square feet.

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62 kilograms was found to be equal to approximately 136.7 pounds using conversion formula.

To convert kilograms to pounds, the following formula is used:

Pounds = Kilograms x 2.20462

Plugging in 62 kilograms, we get:

Pounds = 62 x 2.20462

Pounds ≈ 136.7

Therefore, 62 kilograms is approximately equal to 136.7 pounds.

The pound (symbol: lb) is defined as exactly 0.45359237 kilograms, or approximately 16 ounces. There are also different types of pounds, such as the avoirdupois pound (used for general purposes) and the troy pound (used for precious metals).

The kilogram (symbol: kg) is used to measure the mass of an object or substance. For example, it can be used to measure your own body weight, the weight of a bag of groceries, or the mass of a planet. The prefix "kilo-" means "one thousand", so a kilogram is equal to 1,000 grams.

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1429 cubic centimeters is the  volume of contents the chef will be able to fill the bowl.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that Chef uses a bowl shape which has radius of 8cm to prepare her avocado lime sauce.

We have to find the volume of contents the chef will be able to fill the bowl with using her estimation upto 2/3.

Firstly let us find volume of bowl.

Volume=4/3πr³

=4/3×3.14×(8)³

=2143.5

To find the amount of contents the chef can fill the bowl with, we need to multiply this volume by 2/3,

So 2143.5×2/3

1429.04 cubic centimeters.

Hence,  the chef will be able to fill the bowl with about 1429 cubic centimeters of avocado lime sauce.

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1) values are 15, 16 and 17

2) Drawn in the graph (2)

3)  [tex]x \geq 6[/tex] and graph (3)

Question 6)  [tex]m > 4[/tex] and graph (6)

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

1)

As per the given data:

Values are: 12, 13, 14, 15, 16, 17

Given inequality:

[tex]\frac{x}{5} \geq 3\\= x \geq 5\times3\\= x \geq 15[/tex]

The values of [tex]x[/tex] greater than or equal to 15 out of the given values are:

15, 16 and 17

15, 16, 17 are the solutions of the given equality.

2)

Given inequality:

[tex]x < 8[/tex]

For making the graph, first draw the point [tex]x=8[/tex]

The region to the left of the point [tex]x=8[/tex] will represent the graph as shown in the diagram.

3)

Given inequality:

[tex]x-5\geq 1[/tex]

= [tex]x \geq 1 + 5[/tex]

=  [tex]x \geq 6[/tex]

For making the graph, first draw the point [tex]x=6[/tex]

The region to the right and including the point  [tex]x=6[/tex] will represent the graph as shown in the diagram.

6)

Given inequality:

[tex]6m > 24[/tex]

= [tex]m > \frac{24}{6}[/tex]

= [tex]m > 4[/tex]

For making the graph, first the plot the point m = 4.

The region to the right of the point m = 4 will represent the graph as shown in the diagram.

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The value of angle L, x and angle M is 55°, 35 and 60° respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

From the triangle:

∠OLM + ∠MLN = 180° (sum of angles in a straight line)

125 + ∠MLN = 180°

∠MLN = 55°

Also:

∠MLN + ∠MNL + ∠LMN = 180 (sum of angle in a triangle)

substituting:

55 + (2x - 10) + 65 = 180

2x + 110 = 180

2x = 70

x = 35°

∠LMN = 2x - 10 = 2(35) - 10 = 60°

The value of angle M is 60°

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The acceleration of the car is not constant but is increasing steadily, starting at 10 km/h, decreasing to 5 km/h, and then remaining constant at 5 km/h.

To find the acceleration of the car, we need to use the formula:

acceleration = (final velocity - initial velocity) / time

Let's calculate the acceleration for each interval of time:

For the first interval, the initial velocity is 35 km/h and the final velocity is 45 km/h. The question says the speed increases each second.

Therefore, the acceleration is:

acceleration = (45 - 35) / 1 = 10 km/h

For the second interval, the initial velocity is 40 km/h and the final velocity is 45 km/h. Again, the acceleration is:

acceleration = (45 - 40) / 1 = 5 km/h

For the third interval, the initial velocity is 45 km/h and the final velocity is 50 km/h. The acceleration is:

acceleration = (50 - 45) / 1 = 5 km/h

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Answer:

x=5, y=51

Step-by-step explanation:

y = x + 46

y = 7x + 16   substitute equation 1 into equation 2 to get an expression all in terms of x, then solve for x

7x + 16 = x + 46

6x = 30

x = 30/6 = 5     substitute this into either equation and solve for y

y = 5 + 46 = 51

For the polygon the individual value of the interior angles.

a) 15 sides is 145°

b) 20 sides is 108°

c) 3 sides is 60°

d) 4 sides is 90°

e) 100 sides is 18°

A regular polygon is one where all sides are the same length and all interior angles are the same. The number of sides of a regular polygon can affect the value of its interior angles.

a) 15 sides: The sum of the interior angles of a regular polygon with 15 sides is equal to 2180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2180 / 15 = 145 degrees per angle.

b) 20 sides: The sum of the interior angles of a regular polygon with 20 sides is equal to 2160 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2160 / 20 = 108 degrees per angle.

c) 3 sides: The sum of the interior angles of a regular polygon with 3 sides is equal to 180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 180 / 3 = 60 degrees per angle.

d) 4 sides: The sum of the interior angles of a regular polygon with 4 sides is equal to 360 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 360 / 4 = 90 degrees per angle.

e) 100 sides: The sum of the interior angles of a regular polygon with 100 sides is equal to 1800 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 1800 / 100 = 18 degrees per angle.

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Expression for actual length and actual width of the concrete patio are

30x inches and 30y inches respectively.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given,

A blueprint of a concrete patio has a scale of 2 inches=5 feet.

2 inches = 60 inches

scale factor = 60/2 = 30

Let length of the patio on the blue print is x inches

width of the patio on the blue print is y inches

then actual length of the 30x inches

actual width of the patio = 30y inches

Hence, 30x inches is actual length and 30y inches is actual width of the concrete patio.

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