Find the 5th partial sum of the arithmetic sequence an=2n–3.
Use the zero product property to find the solutions to the equation 6x^2-5x=56
6x² -5x -56 = 0 . . . . . subtract the constant
(3x +8)(2x -7) = 0 . . . .factor*
The zero product property says the product will be zero only when one (or both) of the factors is zero.
First Factor
... 3x +8 = 0
... x + 8/3 = 0 . . . . divide by the coefficient of x
... x = -8/3 . . . . . . subtract 8/3
Second Factor
... 2x -7 = 0 . . . . . . set the factor to zero
... x -7/2 = 0 . . . . . divide by the coefficient of x
... x = 7/2 . . . . . . . add 7/2
_____
*Comment on factoring
There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.
... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)
Answer:
B. x = -8/3, or x= 7/2
Step-by-step explanation:
A circle is divided into parts. Which sum could represent the angle measures that make up the circle?
A circle is always going to be 360°.
The graph below shows the solution to a system of inequalities
Which of the following inequalities is modeled by the graph?
A. x + 4y ≥ 15; y ≥ 0
B.x − 4y ≥ 15; y ≥ 0
C.x + 4y ≤ 15; y ≥ 0
D.−x − 4y ≥ 15; y ≥ 0
A light bulb consumers 1800 watt-hours per day. How long does it take to consume 9450 watt-hours?
To find out how long it takes for a light bulb to consume 9450 watt-hours, when it uses 1800 watt-hours per day, divide 9450 watt-hours by 1800 watt-hours per day, which equals 5.25 days.
Explanation:The question involves calculating how long it takes for a light bulb to consume a certain amount of energy (9450 watt-hours) given its daily consumption rate (1800 watt-hours per day).
To find the duration, you simply divide the total energy by the daily consumption rate:
Total energy to be consumed = 9450 watt-hours
Daily energy consumption = 1800 watt-hours per day
Duration = Total energy ÷ Daily energy consumption
Duration = 9450 watt-hours ÷ 1800 watt-hours/day = 5.25 days
Therefore, it will take 5.25 days for the light bulb to consume 9450 watt-hours of energy.
Click on ALL the values for n that make this inequality true. There maybe more than one answer.
[tex]120 \geq 10n + 20[/tex]
Possible Answers:
You can divide by 10 and subtract 2.
12 ≥ n + 2 . . . . . . divide by 10
10 ≥ n . . . . . . . . . subtract 2
The values that will make the inequality true are those that are 10 or less, including 0 and all negative numbers.
Find the first five non-zero terms of taylor series centered at x=3x=3 for the function below. f(x)=6x−x2−−−−−−√ f(x)=6x−x2
Which logarithmic equation is equivalent to 3^2 = 9?
Answer:
[tex]log_3(9)=2[/tex]
Step-by-step explanation:
[tex]3^2 = 9[/tex]
Logarithmic form is the reverse of exponential form
To convert exponential form in to log form we use a rule
[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]
WE apply the same rule in our exponential equation to convert it into log form
[tex]3^2 = 9[/tex]
The base of exponent is the base of log
[tex]log_3(9)=2[/tex]
In △ABC, AB = 7 and AC = 17. Find m∠B to the nearest degree
68
38
21
87
Answer:
The m∠B is 68°
Step-by-step explanation:
Given the right angled triangle ABC in which right angled is at A.
AB = 7 units and AC = 17 units
we have to find the measure of ∠B.
By trigonometric ratios,
[tex]cot \angle B=\frac{AB}{AC}[/tex]
[tex]cot \angle=\frac{7}{17}[/tex]
[tex]\angle B=cot^{-1}(\frac{7}{17})[/tex]
[tex]\angle B=67.619864948\sim 68^{\circ}[/tex]
Hence, the m∠B is 68°
Option 1 is correct
Let j and k stand for two different rational numbers. If ∣j∣>∣k∣, then what else must be true?
A) j is farther from 0 than k is. B) j is less than k. C) On a number line, j is to the right of k.
D) the opposite of j is less than the opposite of k
A is the correct answer trust me
Answer:
A) j is farther from 0 than k is
Step-by-step explanation:
margaret purchased a doormat measuring 1/2 yard by 2/3 yard for her back door step. If the step is 1/4 square yard, will the mat fit? explain
Final answer:
The doormat measuring 1/2 yard by 2/3 yard will not fit on a step that is 1/4 square yard because the doormat's area, 1/3 square yard, is larger than the step's area.
Explanation:
The question "Will a doormat measuring 1/2 yard by 2/3 yard fit on a step that is 1/4 square yard?" involves understanding of measuring areas in yards and comparing the area of the doormat with that of the step. First, we calculate the area of the doormat by multiplying its length and width (1/2 yard * 2/3 yard = 1/3 square yard).
Next, we compare the area of the doormat, which is 1/3 square yard, to the area of the step, which is 1/4 square yard. Since 1/3 square yard is larger than 1/4 square yard, the doormat will not fit perfectly on the step as it is too big.
Write, and show on a number line, the set of all the numbers that are:
greater than (−3) and less than 3.
The city transportation commission surveys a random sample of licensed drivers, asking the question, "Do you favor increasing the number of bus routes within the city limits?" Which shows how bias might have affected the results of the survey? A. The question is biased in favor of bus riders. B. The question is biased against bus riders. C. Surveying only licensed drivers creates a bias against people who don't have driver's licenses. D. Since the survey used random sampling, it is unlikely to be biased.
How many x intercepts appear on the graph of this polynomial function? F(x)=x^4-5^2.
1 x intercept
2 x intercepts
3 x intercepts
4 x intercepts
How to find A? help please and thanks
A punch recipe requires 4/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?
an automobile radiator contains 20 L of antifreeze and water. this mixture is 20% antifreeze. how much of this mixture should be drained and replaced with pure antifreeze so that the mixture will be 50% antifreeze.
Final answer:
To make a 20L mixture 50% antifreeze, 7.5L of the mixture should be drained and replaced with pure antifreeze. This calculation is based on the original 20% antifreeze concentration and the goal of reaching a 50% concentration without changing the total volume.
Explanation:
The question asks how much of a 20L mixture, which is 20% antifreeze, needs to be drained and replaced with pure antifreeze so the mixture will be 50% antifreeze. To solve this, first calculate the current amount of antifreeze in the mixture: 20L * 20% = 4L. Let's say x liters are drained and replaced with pure antifreeze. The volume of the solution does not change, the remaining 20L. After replacement, the quantity of antifreeze is (4 - 0.2x + x) liters (since we subtract the antifreeze drained, which is 20% of x, and add back x liters of pure antifreeze), and we require this to be 50% of the total, which is 10L (50% of 20L).
Setting up the equation: 4 - 0.2x + x = 10. Simplifying gives 0.8x = 6, so x = 7.5. Therefore, 7.5L of the mixture should be drained and replaced with pure antifreeze to achieve a 50% concentration.
Finn imagines 1 more row of nines to find the total area of 9 * 9 rectangle. explain how this could help him solve 9 * 9
Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners? S = {FGI, GFI, IFG} S = {FGI, FIG, GFI, GIF} S = {FGI, FIG, GFI, GIF, IFG, IGF} S = {FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF}
The sample space or sets showing the possible orders of the other three runners is S = {FGI, FIG, GFI, GIF, IFG, IGF}.
What are Sets?Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.
Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team.
Haley is the first runner in the relay. The other runners can run in any order.
The sample space or sets showing the possible orders of the other three runners will be
S = {FGI, FIG, GFI, GIF, IFG, IGF}
Thus, the correct option is C.
More about the sets link is given below.
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A container shape as a rectangular prism can hold 840 wooden cube blocks with edge lengths of 1/2 feet. What is the volume of the container?
The figures shows the show the dimension of a tennis court and a basketball court given in term of the width x in feet.
Which model shows the correct factorization of x2 + 2x - 8
The correct answer is D.
I just took the test.
How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number. The large tire has a diameter of 60 inches. The small tire has a radius of 9 inches.
For the large tire with a diameter of 60 inches, it would make 38 rotations after traveling 600 feet. The small tire with a radius of 9 inches would make 127 rotations in the same distance.
Explanation:First, let's convert the feet into inches since the tire measurements are given in inches. There are 12 inches in a foot, so 600 feet is equal to 7200 inches. Now, we need to determine the circumference of each tire, which we can find using the formula for the circumference of a circle which is 2πr (twice the product of pi and the radius).
For the large tire, the diameter is 60 inches, so the radius (r) is half the diameter, which is 30 inches. Thus, the circumference of the large tire would be 2π*30, which is about 188.5 inches. The large tire would therefore make about 7200/188.5 = 38 rotations.
The small tire has a radius (r) of 9 inches, so its circumference is 2π*9, which is about 56.55 inches. The small tire would hence make about 7200/56.55 = 127 rotations.
Please note that the numbers are rounded off to the nearest whole number as requested.
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The large tire makes approximately 38 rotations, and the small tire makes approximately 128 rotations when each travels a distance of 600 feet.
Explanation:To find the number of rotations a tire makes, you first need to know the circumference of the tire, which represents the distance the tire would cover in one full rotation. The circumference of a circle (or tire, in this case) is calculated as 2πr, where r is the radius of the circle.
For the large tire with a diameter of 60 inches (which makes the radius 30 inches because the radius is half the diameter): The circumference is 2π × 30 = 188.5 inches. Convert this to feet because the distance given is in feet. So, 188.5 inches is about 15.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 15.7 feet = approximately 38 rotations.
For the small tire with a radius of 9 inches: The circumference is 2π × 9 = 56.5 inches, which is about 4.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 4.7 feet = approximately 128 rotations.
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which method could be used to factor 4x^2-50
The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.
The given quadratic expression [tex]\(4x^2 - 50\)[/tex] can be factored using the difference of squares method.
The difference of squares formula is[tex]\(a^2 - b^2 = (a + b)(a - b)\).[/tex]
In this case, a = 2x and [tex]\(b = \sqrt{50}\).[/tex]
1. Identify the expression as a difference of squares: [tex]\(4x^2 - 50 = (2x)^2 - (\sqrt{50})^2\).[/tex]
2. Apply the difference of squares formula:[tex]\(4x^2 - 50 = (2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]
3. Further simplify by factoring out 2: [tex]\(4x^2 - 50 = 2(2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]
The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.
Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept.
The Choices are
F(x)=2x^2-4x-3
G(x)= -x^2+x+1
H(x)= -2x^2+3x-1
M(x)=x^2-9
N(x)= -3x^2+7
Out of the options provided, only G(x) = -x^2 + x + 1 fits the conditions asked in the question. It is a quadratic function that opens downward, has a vertex that is a maximum, and a positive y-intercept.
Explanation:The key features of a quadratic function are determined by its equation: f(x) = ax2 + bx + c. The sign of 'a' determines whether the function opens up or down. If 'a' is positive, the graph opens up, and if 'a' is negative, it opens down. The vertex of a quadratic function is given by the formula (-b/2a , f(-b/2a)). If 'a' is negative, this vertex will be a maximum. The y-intercept of the function is the value of 'c' in the quadratic equation. According to the conditions provided, we can classify the given functions.
f(x) = 2x2 - 4x - 3 opens upward and has a negative y-intercept; it’s not in the selection.G(x) = -x2 + x + 1 opens downward, has a maximum vertex, and a positive y-intercept. It fits the conditions.H(x) = -2x2 + 3x - 1 opens downward and has a maximum vertex, but has a negative y-intercept, so it’s not in the selection.M(x) = x2 - 9 opens upward and has a negative y-intercept; it’s not in the classification.N(x) = -3x2 +7 opens downward and has a maximum vertex, but it does not mention whether there is a positive y-intercept; so it’s unclear.
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Patricia pays $1.19 each to download songs to her MP3 players. If n is the number of downloaded songs, which equation represents the cost C in dollar?
Each term in a binomial expansion has degree n; therefore, the product of the exponents of each term is n.
true
or
false
Answer:
False
Step-by-step explanation:
In any binomial expansion of the form
[tex](x+a)^n = \Sigma_0^n nCr x^{n-r} a^{r}[/tex]
We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n
Hence product of exponents of each term cannot be n.
The given statement is false.
Only the sum of the exponents of each term in a binomial expansion has degree n
what is community property and associative property
Final answer:
The associative property in mathematics states that the way in which numbers are grouped or associated does not affect the result of the operation. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership.
Explanation:
The associative property is a property in mathematics that states that the way in which numbers are grouped or associated does not affect the result of the operation. For example, for addition, the associative property states that (a + b) + c = a + (b + c). This property holds true for addition and multiplication, but not for subtraction and division.
Community property, on the other hand, is a concept in the field of law, specifically property law. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership. It is most commonly associated with community property states in the United States.
Using the tables found in the textbook, determine the difference between the monthly payments on a $120,000 home at 6½% and at 8% for 25 years.
Answer:115.20
Step-by-step explanation:
How many ways can Hannah give three of her eight T-shirts to her younger sister?