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
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.
A cube-shaped bin has an edge length of 34 yard.
What is the volume of the container?
Answer:
[tex]V=\frac{27}{64}yd^3[/tex]
Step-by-step explanation:
The edge length of the cube shaped bin is [tex]\frac{3}{4}\text{ yards}[/tex]
Hence, [tex]s=\frac{3}{4}\text{ yards}[/tex]
The volume of the cube is given by
[tex]V=s^3[/tex]
Plugging the value of s, we get
[tex]V=(\frac{3}{4})^3[/tex]
This can be further simplified as
[tex]V=\frac{3\times3\times3}{4\times4\times4}\\\\V=\frac{27}{64}[/tex]
Hence, the volume of the container is 27/64 cubic yards.
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 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 table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
$0.50
$0.67
$1.07
$1.50
Book sold Profit f(x)
(X)
100 ║ $50.00
250 ║ $275.00
300 ║ $350.00
350 ║ $425.00
answer is A-$0.50
You are given a table
[tex]\begin{array}{cc}\text{Number of books sold} & \text{Profit}\\100 & \$50\\250 & \$275\\300 & \$350\\350 & \$450\end{array}[/tex]
The rate of change for the function represented in the table can be calculated using the formula
[tex]\dfrac{y_{i+1}-y_i}{x_{i+1}-x_i},[/tex]
where i=1,2,3.
1. When i=1,
[tex]\dfrac{y_2-y_2}{x_2-x_1}=\dfrac{275-50}{250-100}=\dfrac{225}{150}=1.5[/tex]
2. When i=2,
[tex]\dfrac{y_3-y_2}{x_3-x_2}=\dfrac{350-275}{300-250}=\dfrac{75}{50}=1.5[/tex]
3. When i=3,
[tex]\dfrac{y_4-y_3}{x_4-x_3}=\dfrac{425-350}{350-300}=\dfrac{75}{50}=1.5[/tex]
Then the rate of change is $1.5
Answer: correct choice is D.
The rate of change for the function is [tex]\$ 1.5[/tex]
The rate of change for the function is calculate by the formula
[tex]\frac{y_{n+1}-y_n}{x_{n+1}-x_n}[/tex]
Where [tex]n=1,2,3[/tex].
A) when [tex]n=1[/tex]
[tex]\frac{y_{1+1}-y_1}{x_{1+1}-x_1}=\frac{y_{2}-y_2}{x_{2}-x_2}[/tex]
[tex]\dfrac{275-50}{250-100}=\dfrac{225}{100}[/tex]
Hence Rate of change when [tex]n=1[/tex] is [tex]1.5[/tex]
B)when [tex]n=2[/tex]
[tex]\frac{y_{2+1}-y_2}{x_{2+1}-x_2}=\frac{y_{3}-y_2}{x_{3}-x_2}[/tex]
[tex]\dfrac{350-275}{300-250}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=2[/tex] is [tex]1.5[/tex]
C) when [tex]n=3[/tex]
[tex]\frac{y_{3+1}-y_3}{x_{3+1}-x_3}=\frac{y_{4}-y_3}{x_{4}-x_3}[/tex]
[tex]\dfrac{425-350}{350-300}=\dfrac{75}{50}[/tex]
Hence Rate of change when [tex]n=3[/tex] is [tex]1.5[/tex]
So the rate of change for function represented in the table is same for different value of [tex]n[/tex] i.e, [tex]\$ 1.5[/tex].
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please 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 value of x if
6x +4=4x-2
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
Alexander found the means-to-MAD ratio of two data sets to be 3.4
What can he conclude about the distributions?
A.
They are similar.
B.
They are somewhat similar.
C.
They are different.
D.
They are identical.
Answer: the answer is c
Step-by-step explanation:
Jennifer bought a thousand inch roll of ribbon for $21.00. If she cuts the ribbon into 75 equal hair ribbons, how much did she spend per ribbon?
Which property justifies the fact that 5(x-2) is equivalent to 5x-10
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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A campground consists of 5 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 4 yd. The area of the campground, including the beach, is 950 sq yd. What is the width of one campsite?
A. 14.35 yd
B. 13.93 yd
C. 11.93 yd
To find the width of one campsite, we subtract the area of the beach from the total area and divide by 5 (the number of campsites). We set up a quadratic equation and solve for the width, finding that it is approximately 13.93 yd.
Explanation:The student's question is about finding the width of one campsite in a linear arrangement of five campsites along a beach. Given that the area of the campground, including the beach, is 950 sq yd and the distance from the edge of a campsite to the water is 4 yd, we can set up an equation to find the total width of the five campsites. The total width of the campsites will be the total area minus the area of the beach, divided by the length of the campsites (which is 5 times the width of one campsite).
Let's call the width of one campsite 'w'. The area of the beach is 5w * 4 yd, since it extends the entire length of the campsites and is 4 yd wide. Therefore, the area of just the campsites is 950 sq yd - 5w * 4 yd. Since we have five campsites, all of equal width, the total width of the campsites is 5w. So we can set up the following equation:
950 - 5w * 4 = 5w2
Now solve for w:
950 - 20w = 5w25w2 + 20w - 950 = 0Using the quadratic formula, we find that w is approximately 13.93 yd, so the correct answer is B. 13.93 ydB. 13.93 yd. The approximate width of one campsite is 13.81 yards.
Explanation:To find the width of one campsite, we need to divide the area of the campground by the number of campsites. The given area of the campground is 950 sq yd, and there are 5 campsites. So, the area of one campsite is 950 sq yd / 5 = 190 sq yd. Since the campsite is square, the width and length are equal. Let's assume the width of one campsite is 'x' yards. Then the equation becomes x^2 = 190. By taking the square root of both sides, we get x = √190 ≈ 13.81 yards. Therefore, the approximate width of one campsite is 13.81 yards.
The westside bakery uses 440 pounds of flour to make 1,000 loaves of bread.Each loaf contains the same amount of flour.How many pounds of flour are used in each loaf of bread
Final answer:
Each loaf of bread from the Westside bakery contains 0.44 pounds of flour.
Explanation:
To determine the amount of flour used in each loaf of bread, we need to divide the total amount of flour used by the number of loaves produced. In this case, the bakery uses 440 pounds of flour to make 1,000 loaves of bread. So, to find out the amount of flour used in each loaf, we divide 440 by 1,000.
440 ÷ 1,000 = 0.44 pounds of flour
Therefore, each loaf of bread contains 0.44 pounds of flour.
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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What fraction of a batch of trail mix consists of peanuts
The fraction of a batch of trail mix consisting of peanuts is 43/6.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Number of cups for peanuts = 2(2/3)
Total number of cups in the trial mix.
= 2(2/3) + 3/4 + 2(1/2) + 1(1/4)
= 8/3 + 3/4 + 5/2 + 5/4
= (32 + 9 + 30 + 15)/12
= 86/12
= 43/6
= 7(1/6)
Thus,
The fraction of peanuts is 43/6.
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Which statements about the opposite of −12 are true?
Select each correct answer.
A. −12 and its opposite are on located on the same side of zero on a number line
B. The opposite of −12 is -1/12
C.−12and its opposite are located the same distance from zero on a number line.
D.The opposite of the opposite of −12 is −12
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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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
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]
can you help me..Pls work it out
find the difference (-ab+9a-1)-(5ab-3)
Amy and Ebony are shopping. Amy has $77. Together, Amy and Ebony have less than $172. If x represents the amount of money Ebony has, which of the following inequalities represents this information?
A.) $77 + x > $172
B.) $172 + x < $77
C.) $77 + x < $172
D.) x - $77 < $172
What is the answer to 3(t-7)=6t
What's the formula for finding the surface area of a prism and the formula for the surface area of a triangular prism??
Answer:
i) The general formula to find the surface area of a prism = ph + 2B
ii) The area of the triangular prism = ph + 2([tex]\frac{1}{2} bh[/tex])
Step-by-step explanation:
A prism is a three-dimensional figure. The surface area of a figure is the sum of all the areas of its sides.
For example, rectangular prism has 6 sides, to find the surface of rectangular prism, we need to find the area of each side and add them together to get the surface area.
So, the general formula to find the surface area of a prism = ph + 2B, where "p" is the perimeter of the base, "h" is the height of the prism and B is the area of the base.
Now let's find the area of triangular prism.
In the triangular prism, there are two triangles and three rectangles.
Area of a triangle = [tex]\frac{1}{2} bh[/tex]
So, the area of the triangular prism = ph + 2([tex]\frac{1}{2} bh[/tex])
I need to know the answer
Which number produces a rational number when added to 1/2?
Adding any rational number to 1/2 results in another rational number, because rational numbers can always be expressed as fractions with integers as numerators and denominators, making addition straightforward by finding a common denominator.
Any number that can be expressed as a fraction where both the numerator and denominator are integers (excluding zero as the denominator) will produce a rational number when added to 1/2. For example, adding 1/2 to 3 (which is the same as 3/1) will yield 3 1/2 or 7/2, still a rational number. By definition, rational numbers include integers, finite decimals, and repeating or terminating decimals, as they can all be represented as fractions.
Understanding Rational Numbers:
To solve the more difficult problem, one might need to find common denominators when working with more complex fractions. For instance, adding 1/2 to 2/3 requires a common denominator: 3/6 + 4/6 = 7/6. The key point here is that when you add any rational number to another rational number (like 1/2), the result will be rational because you can find a common denominator and then add the numerators, keeping that same common denominator.
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 :)
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
What is the upper quartile of the data represented in the following box-and-whisker plot?
8
12
16
20
Answer:
Step-by-step explanation:
12