Answer:
−(x−1)(x+9)=0
And..
3x2−6x=0
Step-by-step explanation:
Final answer:
The two equations most appropriately solved by using the zero product property are −(x−1)(x+9)=0 and 3x²−6x=0, as they can be directly factored into a product of terms equaling zero.
Explanation:
The question involves finding which two equations would be most appropriately solved by using the zero product property. The zero product property states that if the product of two numbers is zero, then at least one of the multiplicands must be zero. Therefore, equations that can be factored into a product of terms equaling zero can be solved using this property.
−(x−1)(x+9)=0: This equation is already in a factored form and directly applies the zero product property. Set each factor equal to zero and solve for x: x−1=0 or x+9=0, which gives x = 1 or x = −9.3x²−6x=0: This equation can be factored as 3x(x−2)=0. By applying the zero product property, set 3x=0 and x−2=0, solving for x gives x = 0 or x = 2.The other options, 4x² = 13 and 0.25x²+0.8x−8=0, are not immediately in a form that uses the zero product property without further manipulation or do not directly apply to this property.
Find the equation of the line with the given properties: slope of 2, contains the point ( 4, -3).
Answer:
y = 2x - 11
Step-by-step explanation:
We are given that a line has a slope of 2 and passes through the point (4, -3).
As the question doesn't specify, we can write the equation of the line in any format.
There are 3 ways to write the equation of the line. They are:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0 and a cannot be negative. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Although while all of these choices are valid, let's write the equation in slope-intercept form, as that is the most common way to write the equation of the line.
As we are already given the slope of the line, we can immediately plug it into the equation as m.
Replace m with 2.
y = 2x + b
Now we need to find b.
As the line contains the point (4, -3), we can use its values to help solve for b.
Substitute 4 as x and -3 as y.
-3 = 2(4) + b
Multiply.
-3 = 8 + b
Subtract 8 from both sides.
-11 = b
Substitute -11 as b in the equation.
y = 2x - 11
Topic: finding the equation of the line
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On Monday, Amie rides her bike from home to school. After school, she bikes to work. After work, she bikes home. Based on the information in the diagram below, about how many miles does Amie bike on Monday?
The answer is D: 13.1 miles
In 1987 the average price of gasoline was $0.94. Today the price of gas is about $3.00. What is the percent increase from 1987 to today? (explain the problem please)
Answer:
-219.1% decrease
Step-by-step explanation:
.94-3.00=-2.06
-2.06/.94=-2.191
-2.191*100=-219.1 decrease
What are the approximate solutions of 4x2 + 3 = −12x to the nearest hundredth?
x ≈ −3.23 and x ≈ 0.23
x ≈ −2.72 and x ≈ −0.28
x ≈ 0.28 and x ≈ 2.72
x ≈ −0.23 and x ≈ 3.23
Help me ASAP
THANKS
IF YOU DON’T KNOW THE ANSWER DON’T ANSWER! RANDOM ANSWERS WILL BE MODERATED!
Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?
A) f has a relative minimum at x = 1.5
B) f has relative maximum at x = -1.5
C) f is decreasing on the interval from x = 1 to x = 2
D) none of these are true
https://seminole.flvs.net/webdav/assessment_images/educator_apcalcab_v14/08_01_04.gif
The only statement that is true as regards the graph of f ′(x) is;
C: f is decreasing on the interval from x = 1 to x = 2
We are told that the graph of f ′(x) has x-intercepts at x = –3, x = 1 and x = 2.Now, f'(x) is simply the derivative of f(x) and the derivative of f(x) is defined as the slope.
Since x-intercepts of the derivative are at x = –3, x = 1 and x = 2. It means that the values of x that will make the slope to be zero are x = –3, x = 1 and x = 2.Now, the minimum for the derivative graph usually happens when the the graph goes from negative to positive. This means that the graph is decreasing when the x-intercepts of the slope is positiveIn contrast the graph is increasing when the x-intercepts of the slope is negative.
Let us look at the options;
Option A; This is not correct because the derivative has to be zero at minimum point. Option B; This is not also correct because the derivative has to be zero at maximum point.Option C; This is correct because slope is positive when the graph is decreasing and from x = 1 to x = 2 is positive interval.Read more about graph of derivative of a function at; https://brainly.com/question/2284808
A customer buys 3 bottles of water for ninety-nine cents each seven percent tax on each bottle what is the total bill
What does it mean if a statistic is resistant? choose the correct answer below.
a. extreme values (very large or small) relative to the data do not affect its value substantially.
b. changing particular data values affects its value substantially.
c. an estimate of its value is extremely close to its actual value.
d. extreme values (very large or small) relative to the data affect its value substantially?
A statistic is said to be resistant if it isn't significantly affected by outliers or extreme values in the data. It remains relatively stable when extreme values are added or removed from the dataset.
Explanation:In statistics, when a statistic is described as resistant, it is typically referring to its ability not to be affected by outliers or extreme values (very large or small) in a dataset. In other words, a resistant statistic is relatively stable and does not change dramatically if an extreme value is added to, or removed from, the dataset. So, the correct answer is: a. extreme values (very large or small) relative to the data do not affect its value substantially.
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Just a quick math question.
When converting 18 quarts into gallons, I would have to divide by 4 to get the answer which is 4.5, but why am I dividing by 4? Where did 4 come from?
The table gives the probability distribution of the number of books sold in a day at a bookstore. What is the probability of 16 or more books being sold on a given day?
number of books sold in a day
0-5
6-10
11-15
16-20
21-25
probability
0.110
0.206
0.464
0.201
?
The probability of 16 or more books being sold on a given day is 0.22 or 22%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
The table gives the probability distribution of the number of books sold in a day at a bookstore.
The missing probability will be
We know that the sum of all the outcomes must be one.
0.110 + 0.206 + 0.464 + 0.201 + x = 1
On solving, we have
x = 0.019
The number of books sold in a day Probability
0-5 0.110
6-10 0.206
11-15 0.464
16-20 0.201
20-25 0.019
The probability of 16 or more books being sold on a given day will be
[tex]\rm P(x \geq 16) = 0.201 + 0.019 = 0.22[/tex]
The probability of 16 or more books being sold on a given day is 0.22 or 22%.
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Anton must pay a co-pay of $30 for an office visit. His insurance company will then pay 85% of the cost of the visit. How much will Anton pay for an office visit that costs $270? (Points : 1) $36.00 $40.50 $56.00 $70.50
Given:
Anton must pay a co-pay of $30 for an office visit.
His insurance company will then pay 85% of the cost of the visit.
Office visit costs $270
Solution:
[tex] co-pay \; =\; \$30 [/tex]
[tex] Insurance \; Company \; pay = 85\% \; of\; 270 = \frac{85}{100} \cdot 270 = \frac{22950}{100}=\$ 22950\\ \\ Anton \; Pay\; remaining \; of\; what\; Insurance\; Company\; pay.\\ \\ So, \; Anton \; Pay = \$270 - \$229.50=\$40.5\\ \\ [/tex]
Conclusion:
Anton totally Pay = Remaining amount for office visit + Co-pay for office visit
[tex] Anton \; pay \; for\; an \; office \; visit \; that\; costs \; \$270\; = \; \$30 \; + \; \$40.5\; =\; \$70.5 [/tex]
Add the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).
The answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fraction is 1 1/5 = 6/5
The reciprocal of the above fraction = 5/6
= 1.25 - 1 3/4 + 5/6
= 1.25 - 7/4 + 5/6
= 1.25 - 11/12
= 4/12
= 1/3
Thus, the answer would be 1/3 after adding the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (−1 3/4 ).
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Raina's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Raina $4.40 per pound, and type B coffee costs $5.80 per pound. This month, Raina made 171 pounds of the blend, for a total cost of $856.00 . How many pounds of type A coffee did she use?
i just tried to solve this everyway i know possible when you get the answer lmk please.
At a local department store, pants have been reduced to $26. this price is at 68.4% of the original price for pants. given this, what was the original price of the pants?
-r+8(-5r-2) what is the equivalent expression
-41r+16
Answer:
Step-by-step explanation:
If a 16 in. by 24 in. window has a wooden frame 3 inches wide surrounding it, what is the total area of the window and frame?
Answer:
The CORRECT answer is 660 sq inches
Step-by-step explanation:
What is the domain of the relation graphed below? GET 50 POINTS!
Answer:
Domain is the set of x values
so domain is {-5 , -4 , -3 , 1 , 2 , 5}
Compute the requested average. Tim Worker receives the following income monthly from a second job. Jan. Feb. Mar. Apr. May June $200 $150 $250 $260 $285 $380 What is his average pay? (To the nearest hundredth.)
254.17255.37257.83259.85
What is the smallest integer greater than -1/2 .
Which values are solutions to the inequality below?
Check all that apply.
√x ≤ 11
a) 121
b) 120
c) 111
d) -10
e) 122
f) no solutions
The values that are solutions to the inequality √x ≤ 11 are 121, 120, and 111.
Explanation:To find the values that are solutions to the inequality √x ≤ 11, we first need to square both sides of the inequality. This gives us x ≤ 121. So any value of x that is less than or equal to 121 will be a solution.
Now let's check each option:
a) 121: 121 is equal to 121, so it is a solution.b) 120: 120 is less than 121, so it is a solution.c) 111: 111 is less than 121, so it is a solution.d) -10: Negative numbers do not have real square roots, so -10 is not a solution.e) 122: 122 is greater than 121, so it is not a solution.f) no solutions: This option is not a valid solution.In summary, the values that are solutions to the inequality √x ≤ 11 are: 121, 120, and 111.
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Group of kids rode horses to canyon. 20 eyes 30 legs between them. How many horses
Final answer:
To solve this problem, we set up equations based on the total number of eyes and legs. By solving the system, we find that the group consists of 5 horses.
Explanation:
The question asks us to solve a problem involving a group of kids and horses by using the given information about the total number of eyes and legs. Since humans have two eyes and two legs, and horses have two eyes and four legs, we can set up a system of equations to find the solution.
Let's denote the number of kids as 'k' and the number of horses as 'h'. Since each human and horse has two eyes, the total number of eyes is given by the equation: 2k + 2h = 20. Similarly, the total number of legs is given by the equation: 2k + 4h = 30. Solving these equations will give us the number of kids and horses in the group.
Solving for 'k' from the first equation gives us k = 10 - h. Substituting this into the second equation gives us 2(10 - h) + 4h = 30. Simplifying this equation results in 20 - 2h + 4h = 30, which further simplifies to 2h = 10, and thus h = 5. Therefore, there are 5 horses in the group.
Which of the following equations is of a parabola with a vertex at (0, 3)?
y = (x - 3) ^2
y = (x + 3) ^2
y = x ^2 - 3
y = x^ 2 + 3
The General Equation of Parabola having vertex at (0,0) and Focus(a,0) and (0,a) is
[tex]y^{2}= 4ax[/tex] or [tex]x^2 =4ay[/tex]
Now ,the Given equation of parabola having vertex at (0,3) is
x^2=y-3
It is 3 unit above y axis. So the parabola will open in the upward direction.
Out of all the options provided which are
1.y = (x - 3) ^2
2.y = (x + 3) ^2
3.y = x ^2 - 3
4.y = x^ 2 + 3
Option 4. y = x^ 2 + 3 is correct.
Answer:
y = x^ 2 + 3
Step-by-step explanation:
Write a proportion to find how many points xx a student needs to score on a test worth 80 points to get a test score of 80%.
Answer:cross multiply to solve
100x = 50*78
x = 50*78/100
x = 39 points needed to score a 78%
Step-by-step explanation:hope this helps:D
Here are four decimal numbers: 0.98, 0.3, 0.26, 0.627 order from smallest to largest.
A classic counting problem is to determine the number of different ways that the letters of "personnel""personnel" can be arranged. find that number.
The number of different ways in which the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
Further explanation:
A permutation is an arrangement of objects in their order in which we find number of ways that can occur in a period of time.
If all the letters are different then the number of arrangement can be written as follows:
[tex]\boxed{\begin{aligned}P(n)&=n!\\&=n\cdot (n-1)\cdot (n-2)...2\cdot 1\end{aligned}}[/tex]
The number of different permutation can be calculated as follows:
[tex]\boxed{p(n)=\dfrac{n(n-1)(n-2)...2\cdot 1}{n_{1}!\cdot n_{2}!}}[/tex]
Here, [tex]n_{1}[/tex] and [tex]n_{2}[/tex] are the different kind of object such that [tex]n_{1}+n_{2}+n_{3}+\cdot \cdot+n_{k}=n[/tex].
Given:
The given word is “PERSONNEL”.
Calculation:
Step 1:
First consider that all the letters are different i.e, repetition of letter is allowed.
The given word “PERSONNEL” has [tex]9[/tex] letters.
Therefore, the number of ways for arranging nine letters can be calculated as follows:
[tex]\begin{aligned}P(9)&=9\cdot (9-1)\cdot (9-2)\cdot \cdot 2\cdot 1\\&=9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot3 \cdot 2\cdot 1\\&=362,880\end{aligned}[/tex]
Therefore, the different arrangements of the given word is [tex]362,880[/tex].
Step 2:
Since, the letter N and E is repeated two times in given word “PERSONNEL” then the half of the arrangement is repeated of these two letters.
Use the formula for finding the number of distinguishable permutation. It can be calculated as follows:
[tex]\begin{aligned}\text{Number of permutation}&=\dfrac{362880}{2!\cdot 2!}\\&=\drac{362880}{4}\\&=90,720\end{aligned}[/tex]
The number of different ways that the letter of “PERSONNEL” can be arranged is [tex]90,720[/tex].
Thus, the number of different ways that the letter of “PERSONNEL” can be arranged is [tex]\boxed{\bf 90,720}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Permutation
Keywords: Permutation, combination, personnel, counting, arrangement, different ways, order, letters, different ways, repetition, arranged objects, distinguishable permutation, counting problem.
The number of different ways to arrange the letters of 'personnel' is calculated using combinatorics and permutation formulas, resulting in 151,200 unique arrangements.
To find the number of different ways to arrange the letters of the word "personnel", we must use the principles of combinatorics and permutations.
The word 'personnel' consists of 9 letters with repetitions: there are three E's, two N's, one P, one S, one O, and one L. To count the number of unique arrangements, we start with the total factorial of all letters, which is 9!, but then we need to account for repeated letters by dividing by the factorials of the frequency of each repeating letter.
This results in the following permutation formula:
N! / (n1!)n2!...nk!
Where N is the total number of letters, and n1, n2, ..., nk are the number of times each unique letter is repeated.
So for 'personnel': 9! / (3!)(2!) = 151,200
There are therefore 151,200 unique ways to arrange the letters in 'personnel'.
there were 13,426 eligible voters for a certain election. On election day 8,206 people cast their vote. What was the percent of voter turn-out?
Final answer:
The percent of voter turnout in this election was 61.1%.
Explanation:
Voter turnout refers to the percentage of eligible voters who cast a ballot in an election.
To calculate the percent of voter turn-out, you need to divide the number of people who cast their vote by the total number of eligible voters, then multiply by 100 to get the percentage.
Number of people who cast their vote: 8,206
Total number of eligible voters: 13,426
To calculate the percent of voter turnout we use the following formula:
Divide the number of people who voted by the number of eligible voters.
Multiply the result by 100 to get a percentage.
= (8,206 / 13,426) × 100
= 0.611 × 100
= 61.1%
Therefore, the percent of voter turnout in this election was 61.1%.
Find two numbers their sum is −7 and their difference is 14
PLZ HELP FAST
A circle is divided into 18 equal parts how many degrees is the angel measure for part?
A merchant uses the rule: selling price equals cost + 10% of cost. This is a function. Why?
Answer:
y=x+0.10
Step-by-step explanation:
The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels an shared the cost equally. How much did each person pay?
Answer:
$3.40
Step-by-step explanation:
To find out the amount each person paid, let's find the total cost of the pretzels first.
6 pretzels ----- $5.10
1 pretzel ----- $5.10 ÷6= $0.85
8 pretzels ----- 8($0.85)= $6.80
The total cost of 8 pretzels is thus $6.80.
Since the total cost was shared equally amongst two people, each person paid half of the total cost.
Amount each person paid
= $6.80 ÷2
= $3.40
By taking a quotient between the total cost and the number of people, we can see that each one pays $3.40
How much did each person pay?We know that the price of 6 pretzels is $5.10, then the price for each pretzel is given by the quotient:
$5.10/6 = $0.85
We know that Simon and Sofia bought 8 pretzels, so they pay:
P = 8*$0.85 = $6.80
And they divide that evenly between the two, so we can take the quotient:
p = $6.80/2 = $3.40
That is the amount that each person pays.
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