The table shows data for a random sample of 20 students out of middle school. Use the sample to draw an inference about each measure. Explain your reasoning.
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Graph the two lines
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
Answer:
For Equation 1:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6For Equation 2:
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4Step-by-step explanation:
We are given two lines - one is an equation and one is an inequality.
Neither are in slope-intercept form (y = mx + b), so we need to make these adjustments.
Slope-intercept form has two key parts to the equation: m, which is the slope of the line and b, which is the y-intercept of the line.
Equation 1
[tex]\displaystyle2x+3y=18\\\\3y = -2x + 18\\\\y = -\frac{2}{3}x+6[/tex]
With this, we can now determine the domain, range, slope, and y-intercepts for this line.
For Equation 1, because our equation is in slope-intercept form, we can find the slope and the y-intercept.
Our equation is [tex]y=-\frac{2}{3}x+6[/tex]. Therefore, our m is [tex]-\frac{2}{3}[/tex] and our b is 6.
Because the equation is linear, there is no instance in which the line will not meet an x- or y-value. Therefore, our domain and range is all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6Equation 2
[tex]\displaystyle3x-4y>16\\\\-4y>-3x+16\\\\y < \frac{3}{4}x-4[/tex]
Now that we have solved the inequality, we can determine our slope, the domain, and the range of the function.
We can use the same tactic as before - m is our slope and b is our y-intercept. Therefore, [tex]\frac{3}{4}[/tex] is our slope and -4 is our y-intercept.
Because the inequality represents a line, our domain is all real numbers, or [tex]\mathbb{R}[/tex]. If we were to plug in any number for x, y would be true for that value. Therefore, our range is also all real numbers, or [tex]\mathbb{R}[/tex].
Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4please help! determine whether the number is closest to 0, or 1. explain why. (a. 10/9) (b. 9/16) (c. 2/15) theyre not answer choices.
What is the volume of a cube with an edge length of 3.2 meters? Enter your answer, as a decimal, in the box.
Mike says that 3/3 of his fraction model is shaded blue. Ryan says that 6/6 of the same model is shaded blue. Are the two fractions equivalent?
A standard coffee mug has a capacity of 16 fluid ounces. If Annie needs to fill 12 mugs mugs with coffee, how many quarts of coffee does she need?
what is the value of x if
6x +4=4x-2
Find the distance between the points (2, 3) and (2, 8).
A) 2
B) 5
C) 10
D) 15
The value of the distance between the points (2, 3) and (2, 8) is,
⇒ d = 5 units
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
To find the distance between the points (2, 3) and (2, 8).
Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Thus, The value of the distance between the points (2, 3) and (2, 8) is,
⇒ d = √(2 - 2)² + (8 - 3)²
⇒ d = √5²
⇒ d = 5 units
Thus, The value of the distance between the points (2, 3) and (2, 8) is,
⇒ d = 5 units
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find the difference (-ab+9a-1)-(5ab-3)
Evan's mother used 1/3 pound of beef, 1/2 pound of shrimp, and 3 pounds of pasta to make dinner for 4 people.
Use this information to answer ALL FOUR PARTS below.
Question:
Part A:
Each person will receive an equal share of beef with none left over. What is the amount, in pounds, of each serving of beef?
Part B:
Each person will receive an equal share of shrimp with none left over. What is the amount, in pounds, of each serving of shrimp?
Part C:
Each person will receive an equal share of pasta with none left over. What fraction represents the amount, in pounds, of each serving of pasta?
Part D:
Evan only ate 1/2 of the pasta that he received. What is the amount, in pounds, of pasta did Evan eat? Explain how you got this answer step-by-step using math vocabulary.
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate
The store donates __ basketballs
I need to know the answer
Gcf of 28x3 and 16x2y2
The greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex] is the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
To find the greatest common factor (GCF) of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
, we need to identify the common factors between the two expressions.
The prime factorization of is [tex]2.2.7.x.x.x.[/tex]
The prime factorization of [tex]16x^{2} y^{2}[/tex] is [tex]2.2.2.2.x.x.y.y.[/tex]
Now, let's identify the common factors:
Both expressions have [tex]2.2.x.x[/tex] in common.
So, the greatest common factor (GCF) of and [tex]16x^{2} y^{2}[/tex] is [tex]4x^{2}[/tex] .
COMPLETE QUESTION:
Circle the GCF of [tex]28x^{3}[/tex] and [tex]16x^{2} y^{2}[/tex]
[tex]28x^{3}[/tex]: [tex]2.2.7[/tex].*•*•*
[tex]16x^{2} y^{2}[/tex]:[tex]2.2.2.2.x.x.y.y[/tex]
1) Given that lines L and M are parallel, which of the statements is true? A) ∠ DEF ≅ ∠ EBC B) ∠ ABC ≅ ∠ DEF C) ∠ ABC ≅ ∠ EBC D) ∠ BEF ≅ ∠ ABC
a jope rope is 9 feet long how long is the jump rope in yards
Hot air is less dense than cool air, so hot air will rise above cool air. Increasing the air temperature inside a hot air balloon makes it lighter than the surrounding air, so the balloon can lift up. The density of hot air is about 0.25 kg/m^3 less than that of cool air, which means a cubic meter of hot air can lift about 0.25 kg. What is the minimum volume of hot air needed to lift a hot air balloon carrying 800 kg?
The minimum volume of hot air needed to lift a hot air balloon carrying 800 kg is 3200 m³.
Explanation:The minimum volume of hot air needed to lift a hot air balloon carrying 800 kg can be calculated by using the density difference between hot air and cool air. Given that the density of hot air is about 0.25 kg/m³ less than that of cool air, we can calculate the volume of hot air needed.
Let V be the volume of hot air needed. The weight of the hot air balloon is equal to the weight of the cool air displaced by the hot air balloon. So we can set up the equation 800 kg = ((V + 1) - V) x 0.25 kg/m³, where 1 represents the volume of the hot air balloon itself.
Simplifying the equation, we have 800 kg = 0.25 kg/m x 1 m³, which gives us V = 800/0.25 = 3200 m³. Therefore, the minimum volume of hot air needed to lift the hot air balloon carrying 800 kg is 3200 m³.
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2 - 4x = 14 A) -4 B) -3 C) 0 D) 3 Eliminate
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What is the trigonometric ratio for sin C ?
Enter your answer, as a simplified fraction, in the boxes.
Answer:
The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
Step-by-step explanation:
Given : A right triangle ABC with ∠B = 90° and AC = 82 and BC = 80
We have to find the value of [tex]\sin C[/tex]
Since, Sine is defined as the ratio of perpendicular to its hypotenuse.
Mathematically written as [tex]\sin\theta=\frac{Perpendicular}{Hypotenuse}[/tex]
For the given triangle ABC, we have
Using Pythagoras theorem, For a right angled triangle, sum of square of base and perpendicular is equal to the square to its hypotenuse.
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Substitute, we get,
[tex](82)^2-(80)^2=(AB)^2\\\\ 6724-6400=(AB)^2\\\\ 324=(AB)^2\\\\ \Rightarrow AB =18[/tex]
[tex]\theta=C[/tex]
So, perpendicular = AB and Hypotenuse = AC
[tex]\sin C=\frac{AB}{AC}[/tex]
[tex]\sin C=\frac{18}{82}=\frac{9}{41}[/tex]
Thus, The trigonometric ratio for [tex]\sin C[/tex] is [tex]\frac{9}{41}[/tex]
What is the answer to 3(t-7)=6t
The area of a rectangle playgrond is 78 square meters. If the length of the playground is 13 meters, what is its width?
Answer:
6 meters.
Step-by-step explanation:
Let w represent width of the rectangle.
We have been given that the area of a rectangle playground is 78 square meters. The length of the playground is 13 meters.
We know that area of a rectangle is width times length of rectangle. We can represent our given information in an equation as:
[tex]\text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
[tex]78\text{ m}^2=13\text{ m}\times \text{Width}[/tex]
[tex]13\text{ m}\times \text{Width}=78\text{ m}^2[/tex]
[tex]\frac{13\text{ m}\times \text{Width}}{13\text{ m}}=\frac{78\text{ m}^2}{13\text{ m}}[/tex]
[tex]\text{Width}=6\text{ m}[/tex]
Therefore, the width of the rectangle is 6 meters.
Find the discriminant of the quadratic $3x^2 - 7x + 6.$
Answer:
Discriminant of the quadratic is-23
Step-by-step explanation:
The given quadratic function is [tex]3x^2-7x+6[/tex]
Comparing with the expression [tex]ax^2+bx+c[/tex]
a = 3, b = -7, c = 6
The discriminant of the quadratic is given by [tex]D=b^2-4ac[/tex]
Substituting the known values, discriminant of the quadratic is
[tex]D=(-7)^2-4(3)(6)\\\\D=49-72\\\\D=-23[/tex]
Therefore, discriminant of the quadratic is-23
Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if necessary.
Answer:
Time of driving of Maria = 1.8 hours
Step-by-step explanation:
Let a be time drove by Carlos and b be the time drove by Maria.
Carlos and Maria drove a total of 233 miles in 4.4 hours.
Total time = 4.4 hours
a + b = 4.4 ------------------eqn 1
Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the remainder of the trip and averaged 50 miles per hour.
Speed of Carlos = 55 miles per hour
Speed of Maria = 50 miles per hour
Total distance = 233 miles
That is
55 a + 50 b = 233----------------------eqn 2
eqn 1 x 50
50 a + 50 b = 220---------------------------eqn 3
eqn 3 - eqn 2
55 a + 50 b - 50 a - 50 b = 233 - 220
5a = 13
a = 2.6
Substituting in eqn 1
2.6 + b = 4.4
b = 1.8
Time of driving of Maria = 1.8 hours
A candy wrapping robot can wrap 434 pieces of candy in five minutes. How many pieces of candy can it wrap in any number of minutes
which expression is equivalent to 20-4x/4
a. 5-x
b. 5-4x
c. 20-x
d. 80-16x
The expression (20-4x)/4 equals 5 - x.
Given is an expression (20-4x)/4 we need to find an equivalent expression to it,
A mathematical expression or equation that is equivalent to another expression or equation is one that has the same value or meaning.
In other words, if two phrases yield the same result or depict the same mathematical relationship, they are deemed equal.
So,
By multiplying each word in the brackets by 4, it is possible to simplify the formula (20-4x)/4.
This results in:
(20/4) - (4x/4)
Simplifying even more
5 - x
Therefore, the expression (20-4x)/4 equals 5 - x.
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a photograph measuring 4 inches wide and 5 inches long is enlarge to make a wall mural. If the mural is 120 inches wide, how long is the mural?
|-2x+6|=-8 absolute value equations
Picture is attached need help fast thanks
A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle? increased by a factor of 8 increased by a factor of 4 increased by a factor of 16 increased by a factor of 12
Answer:
Increased by a factor of 4
Step-by-step explanation:
the fish tank in Paul's bedroom has a pump that will recirculate 75 gallons of water in 1/4 of an hour. Find the unit rate in gallons per hour.
a. 5 gallons per hour
b. 18.75 gallons per hour
c. 300 gallons per hour
d. 187.5 gallons per hour
Greyson's mom used 4 out of 12 eggs to make pancakes. Then she used 3 out of 12 eggs to make cupcakes. What fraction of a dozen eggs did she used in all? ( Hint: 1 dozen = 12)
Well . . .
4 out of 12 eggs makes the fraction 4/12 for pancakes.
3 out of 12 eggs makes the fraction 3/12 for cupcakes.
4/12 + 3/12 + 7/12
If you don’t know how to do it here you go judging by how easy the question is -
Only add the numerator (top) and keep the denominator (bottom) the same.
Hope this helps :)