The possible rational roots for the equation 3x⁴ + 2x² - 12 = 0 are ±1, ±2, ±3, ±4, ±6, ±12, ±1/3, ±2/3, ±4/3, ±2, ±4, and ±12/3. To find the possible rational roots of the equation 3x⁴ + 2x² - 12 = 0 using the Rational Root Theorem, we need to look at the factors of the constant term (in this case, -12) and the factors of the leading coefficient (in this case, 3).
The factors of 3 are ±1 and ±3, and the factors of 12 are ±1, ±2, ±3, ±4, ±6, and ±12.
To determine the possible rational roots, we use the fractions of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Combining the factors, the possible rational roots are: ±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±12/1, ±1/3, ±2/3, ±4/3, ±6/3, ±12/3.
Simplifying the fractions, the possible rational roots are: ±1, ±2, ±3, ±4, ±6, ±12, ±1/3, ±2/3, ±4/3, ±2, ±4, and ±12/3.
Therefore, the possible rational roots for the equation 3x⁴ + 2x² - 12 = 0 are ±1, ±2, ±3, ±4, ±6, ±12, ±1/3, ±2/3, ±4/3, ±2, ±4, and ±12/3.
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what is the solution for the equation 4x -10 equals 2x
x=5
x=4
x=1
x=1.67
Answer:
x=5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers.
Samantha and Mia are 13 km apart from each other.
What is Pythagorean ?A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.
Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.
Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.
A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.
Hypotenuse of the triangle, which measures distance between the females
the Pythagorean theorem,
H² = P² + B²
H² = 7² + 11²
H² = 49 + 121
H = √170
H = 13.038
H = 13km
Between them, there is a 13 kilometer distance.
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Mr. Mudd gives each of his children $2000 to invest as part of a friendly family competition. The competition will last 10 years. The rules of the competition are simple. Each child can split up his or her $2000 into as many separate investments as they please. The children are encouraged to do their research on types of investments. The initial investments made may not be changed at any point during the 10 years; no money may be added and no money may be moved. Whichever child has made the most money after 10 years will be awarded an additional $10,000. Child Performance of investments over the course of the competition Albert $1000 earned 1.2% annual interest compounded monthly $500 lost 2% over the course of the 10 years $500 grew compounded continuously at rate of 0.8% annually Marie $1500 earned 1.4% annual interest compounded quarterly $500 gained 4% over the course of 10 years Hans $2000 grew compounded continuously at rate of 0.9% annually Max $1000 decreased in value exponentially at a rate of 0.5% annually $1000 earned 1.8% annual interest compounded biannually (twice a year) 1. What is the balance of Albert’s $2000 after 10 years? 2. What is the balance of Marie’s $2000 after 10 years? 3. What is the balance of Hans’ $2000 after 10 years? 4. What is the balance of Max’s $2000 after 10 years? 5. Who is $10,000 richer at the end of the competition?
Answer:
Step-by-step explanation:
Albert:
$1000 earned 1.2% annual interest compounded monthly
= 1000 (1+.001)120
(periodic interest = .012/12 ,n is periods = 10yr x 12 mos)
$500 lost 2% over the course of the 10 years
= 500 (.98)
$500 grew compounded continuously at rate of 0.8% annually
= 500 e^008(10) 10 years interest .008 (in decimal form)
Add these three to see how Albert did with his investments
The balance of Albert is $2159.07; the balance of Marie is $2244.99, the balance of Hans is $2188.35, and the balance of Max is $2147.40. Marie is $10,000 richer at the end of the competition.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To determine the balance of Albert’s $2000 after 10 years :
If the amount of $1000 at 1.2 % compounded monthly,
A = P(1 +r/n)ⁿ n = 10 years
here P = $1000 and r = 1.2
A = 1000(1 + 0.001)¹²⁰
A = $1127.43
If Albert $500 losing 2%
So 0.98 × 500 = $490
If $500 compounded continuously at 0.8%
So A = P\(e^{rt}\)
A = 500\(e^{0.008\times 10}\)
A = 541.6
So the balance of Albert’s $2000 after 10 years :
Total balance = 1127.43 + 490.00+ 541.64 = $2159.07
To determine the balance of Marie’s $2000 after 10 years:
If 1500 at 1.4 % compounded quarterly,
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
If $500 Marie’s gaining 4 %
So 1.04 × 500 = $520.00
So the balance of Marie’s $2000 after 10 years
Total balance = 1724.99 + 520.00 = $2244.99
To determine the balance of Hans’ $2000 after 10 years:
If $2000 compounded continuously at 0.9%
So A = 2000\(e^{0.009\times 10}\)
A = $2188.3
To determine the balance of Max’s $2000 after 10 years :
If $1000 decreasing exponentially at 0.5 % annually
So A = 1000(1 - 0.005)¹⁰= $951.11
If $1000 at 1.8 % compounded bi-annually
So A = 1000(1 + 0.009)²⁰ = $1196.29
So the balance of Max’s $2000 after 10 years
Total balance = 951.11 + 1196.29 = $2147.40
Therefore, Marie is $10,000 richer at the end of the competition.
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Consider this function.
f(x)=2x-2Which graph represents the inverse of function ?
>
у
54
sX
5
4
+
3+
3-
2
N
2
2
2
3
4
-2
3
-1
-1
-2 +
-2+
-37
-3
Answer:
the first graph
Step-by-step explanation:
the inverse function is(x+2)/2
therefore,2 points on the graph are
(0,1),(-2,0)
Question 3 (1 point)
Writes an equation that can be used to show the relationship between the side lengths of the
triangle based on the Pythagorean Theorem.
261 cm²
O a
Ob
Oc
Od
19 cm
19 cm
Question 3 of 5 | Page 3 of 5
x² +261 = 19
x + 261 = 19
x² +261² = 19²
x² +261 = 19²
On solving the provided question, An expression that finds the sum of x and y => X + Y
What is an expression?a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples - 2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥
We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value.
An expression that finds the sum of x and y -
=> X + Y
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Una tienda virtual ofreció el 15% de descuento el dia de su aniversario.ese dia Jorge compro una lavadora que regularmente cuesta 1350000.cuanto ahorro en la compra
Answer:
unooooooooooooooooooooooooooooooooooooooooooo
Step-by-step explanation:
Subjects who participate in a study of patients with inflammatory bowel disease are described as the:a. accessible population. b. element. c. sample. d. target population.
The target population is the population of interest that researchers aim to generalize their findings to.
The correct answer is c. sample.
In a research study, the population of interest is often too large or too difficult to access entirely. Therefore, researchers select a representative subset of the population to study, which is called a sample. In this case, patients with inflammatory bowel disease are the population of interest, and those who participate in the study are the sample.
The accessible population refers to the portion of the population that is accessible to the researcher. For example, if a researcher is studying the prevalence of a disease in a certain region, the accessible population would be the individuals living in that region.
An element refers to a single member of the population or sample.
The target population is the population of interest that researchers aim to generalize their findings to.
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The ounces of soda consumed by an adult next month are an example of a discrete random variable.
a. True
b. False
The ounces of soda consumed by an adult next month are examples of a discrete random variable, False
A discrete random variable are known as counts. This is because it takes on only a countable number of distinct values. This means a random variable can only be considered to be discrete if it can take on values that are countable in an interval, otherwise it can be continuous.
Now on the question of ounces of soda consumed by an adult next month is considered not to be discrete random variable. This is because ounces of soda or volume of soda consumed are countless and infinite in number.
Hence, the statement that says ounces of soda consumed by an adult next month are an example of a discrete random variable is False.
Choice b(False) is correct.
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I need help with this
a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).
To solve:
12 - 4x = 15 - 3x
12 = 15 + x
-3 = x
Therefore, x is equal to -3.
b) To find the value of AB, plug in the value of x found in part a).
12 - 4x
12 - 4(-3)
12 - (-12)
12 + 12 = 24
Thus, segment AB is equal to 24.
c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.
15 - 3x
15 - 3(-3)
15 - (-9)
15 + 9 = 24
Thus, segment DE is also equal to 24.
We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.
I hope this helps!
Select the correct answer from each drop-down menu.
Consider the function f(x) = (1/2)^x
Graph shows an exponential function plotted on a coordinate plane. A curve enters quadrant 2 at (minus 2, 4), falls through (minus 1, 2), (0, 1), and intersects X-axis at infinite in quadrant 1.
Function f has a domain of
and a range of
. The function
as x increases.
Function f has a domain of all real numbers and a range of y > 0. The function approaches y = 0 as x increases.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
The horizontal section of any graph is typically used for the representation of all domain values. Additionally, all domain values are both read and written by starting from smaller numerical values to larger numerical values, which means from the left of a graph to the right of the coordinate axis.
By critically observing the graph shown in the image attached above, we can logically deduce the following domain and range:
Domain = [-∞, ∞] or all real numbers.
Range = [1, ∞] or y > 0.
In conclusion, the end behavior of this exponential function \(f(x)=(\frac{1}{2} )^x\) is that as x increases, the exponential function approaches y = 0.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Hot Spot is a California lottery game. Players pick 1 to 10 Spots (sets of numbers, each from 1 to 80) that they want to play per draw. For example, if you select a 4 Spot, you play four numbers. The lottery draws 20 numbers, each from 1 to 80. Your prize is based on how many of the numbers you picked 27% match one of those selected by the lottery. The odds of winning depend on the number of Spots you choose to play. For example, the overall odds of winning some prize in 4 Spot is approximately 0.256.
You decide to play the 4 Spot game and buy 5 tickets. Let X be the number of tickets that win some prize. 6452 Location 18277 of 68468 32°F Mostly cloudy 6:10 3/14 the location of the mean on your histogram.
a. Xhas a binomial distribution. What are n and p?
b. What are the possible values that x can take?
c, Find the probability of each value of X. Draw a probability histogram for the distribution of X. (See Figure 14.2 on page 331 for an example of a probability histogram.)
d. What are the mean and standard deviation of this distribution? Mark the location of the mean on your histogram
Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and 0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.
a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.
b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)
Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,
P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228
P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392
P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269
P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093
P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016
P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011
d) The mean and standard deviation of the distribution is given by:
mean = n*p = 5*0.256 = 1.28
standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995
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1x+2x = what?
Will mark brainiest whatever that mean
Answer:
3x
Step-by-step explanation:
Answer:
3x
Step-by-step explanation:
1+2=3
so 1X+2x=3x
simplify
4w^5(-9w^3-9w-9)
please help!
Answer:
- 36\(w^{8}\) - 36\(w^{6}\) - 36\(w^{5}\)
Step-by-step explanation:
Using the rule of exponents
\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\) , then
4\(w^{5}\) (- 9w³ - 9w - 9) ← distribute parenthesis by 4\(w^{5}\)
= - 36\(w^{(5+3)}\) - 36\(w^{(5+1)}\) - 36\(w^{5}\)
= - 36\(w^{8}\) - 36\(w^{6}\) - 36\(w^{5}\)
Answer:
\( = > 4 {w}^{5} ( - 9 {w}^{3} - 9w - 9) \\ \: \: \: \: = > - 36w {}^{5 + 3} - 36 {}^{5 + 1} - 36 {}^{5} \\ = > - 36 w{}^{8} - {36w}^{6} - 36w {}^{5} \)
What are all the values that a standard deviation s can possibly take?.
The values that a standard deviation s can possibly take are all non-negative real numbers
How to determine the values
The standard deviation of a distribution is the square root of the variance.
The standard deviation is represented by the following formula:
\(\sigma = \sqrt{\sigma^2\)
For the above formula to have a usable value, then the following must be true
\(\sigma^2 \ge 0\) ---- i.e. the variance must be at least 0.
So, we have:
\(\sigma \ge \sqrt{0\)
Evaluate the square root
\(\sigma \ge 0\)
Hence, the values that a standard deviation s can possibly take are all non-negative real numbers
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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
Answer:
6 < x < 26
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , then
16 - 10 < x < 16 + 10 , that is
6 < x < 26
The manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots. What is the probability of a customer buying carrots? 1.4 percent 5.0 percent 10.0 percent 11.4 percent
Answer:
The probability of a customer buying carrots is 5 percent.
Step-by-step explanation:
Given that the grocery store manager reports that there is a 12% chance that the consumer will buy apples during their stay in the store, a 5% chance that they will buy apples and carrots, and a 17% chance that they will buy apples. or carrots, to determine the chances that this consumer buys only carrots we must make the following reasoning:
-Since there is a 12% probability of buying apples, and 17% of buying apples or carrots, the difference between the two should be the probability of people buying carrots only: that probability would be 5%, which in turn it is the percentage of chances that the consumer buys both vegetables.
Therefore, the chances of a consumer buying carrots at the store is 5%.
Answer:
C. 10.0 percent
Step-by-step explanation:
P(A) = 0.12
P(A\cap C)=0.05
P(A\cup C)=0.17=P(A)+P(C)-P(A\cap C)
0.17=0.12+P(C)-0.05
P(C)=0.17-0.12+0.05=0.10
PLEASE HELP!!!!!
Which statement is true about a dot plot?
A.
A dot plot shows the median of a data set.
B.
A dot plot shows the first quartile, but not the second quartile of any given data set.
C.
A dot plot shows the frequency of the individual values of any given data set.
D.
A dot plot shows the frequency of an interval of values of any given data set.
E.
A dot plot gives information about the average of any given data set.
Answer:
C.
A dot plot shows the frequency of the individual values of any given data set.
Step-by-step explanation:
Which situation relates to the graph
A) an ice cream shop sells one scoops of ice cream for two dollars of each additional scoop cost one dollar
B) an ice cream shop sells two scoops of ice cream for two dollars in each additional scoop cost one dollar
C) an ice cream shop sells two scoops of ice cream for three dollars in each additional scoop cost one dollar
D) an ice cream shop sells to scoops ice cream for three dollars each additional scoop cost three dollars
PLEASE HELP ME
Answer:
C.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
it is trust me
Item 3 Martin is a chef and a caterer. When catering an event, he plans the amount of food to be prepared based on the number of people he needs to serve. The equation y = 7x represents the number of ounces of chicken required to serve x people. The equation y = 5x represents the number of ounces of fish required to serve x people. What is true of the comparison of the two graphs?
Answer:
The line representing the number of ounces of chicken required to serve x people is steeper than the line representing the number of ounces of fish required to serve x people.
Step-by-step explanation:
I took the test
Comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x people
Recall:
The linear equation of a proportional graph is represented as y = mx, where m is the slope or gradient.The larger the value of the slope, the steeper the slope of the graph.Given the following:
Graph representing the number of ounces of chicken required to serve x people: y = 7x
The slope is 7.
Graph representing the number of ounces of fish required to serve x people: y = 5x.
The slope is 5.
Therefore, comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x peopleLearn more about slopes on:
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EASY POINTS!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
\(2x^{2}\)+\(7x\)+3
A man walks 5m due south and then 12m due East. Find his distance from the starting point.
Answer: 13 m
Step-by-step explanation:
distance from starting point = root{(5)^2 + (12)^2 }
=root{ 25 + 144}
= 13
Answer:
13 mStep-by-step explanation:
Between south direction and east direction we have right angle, so we can use Pythagorean theorem:
a² + b² = c²
a = 5 m
b = 12 m
c = the distance
\(5^2+12^2=c^2\\\\c^2=25+144\\\\c^2=169\\\\c=\sqrt{169}=13\,m\)
CAN SOMEONE PLEASE HELP ME I'M STUCK. PLEASE
I don't understand and know how to solve it.
Answer:
7/10
Step-by-step explanation:
red + green = 50 + 20 = 70 marbles
Total marbles = 50 + 30 + 20 = 100 marbles
P(red or green) = 70/100
P(red or green) = 7/10
From the top of a cliff 168 m above the water, the angle of depression of a boat on the water is 25°. How far is the boat from the foot of the cliff? Please answer!! Asap I need help!!
The distance of the boat from the foot of the cliff is 360 metres.
How to find the distance of the boat?From the top of a cliff 168 m above the water, the angle of depression of a boat on the water is 25°.
The distance of the boat from the foot of the cliff can be calculated as follows:
The situation forms a right angle triangle.
Using trigonometric ratios,
tan 25 = opposite /adjacent
opposite side = 168 m
adjacent side = distance of the boat from the foot of the cliff
Hence,
tan 25 = 168 / a
a = 168 / tan 25
a = 168 / 0.46630765815
a = 360.277671148
a = 360 metres
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What is the degree of 5xpower2+6xpower2+7ypower2
Answer:
7
Step-by-step explanation:
Explanation:
6x5+5x4−3x2+x7
Please help! will give brainliest!
Given right triangle ABC with altitude BD drawn from vertex B to hypotenuse AC, find the lengths of AD, BD, and CD.
Keep as improper fraction
Answer:
AD = 3
BD = 10
CD = 17
Step-by-step explanation:
The requires side lengths are:
\(AD = \frac{49}{25}\)
\(BD = \frac{168}{25}\)
\(CD = \frac{576}{25}\)
Considering triangle BDC, we have:
\(BC^2 = BD^2 +CD^2\)
This gives
\(24^2 = BD^2 +(25 - AD)^2\)
\(576 = BD^2 +(25 - AD)^2\) --------- (1)
Considering triangle ABD, we have:
\(7^2 = BD^2 + AD^2\)
\(49 = BD^2 + AD^2\) ---- (2)
Subtract (2) from (1)
\(576 - 49 = BD^2 -BD^2 +(25 - AD)^2 - AD^2\)
\(527 = (25 - AD)^2 - AD^2\)
Expand
\(527 = 625 - 50AD + AD^2 - AD^2\)
\(527 = 625 - 50AD\)
Collect like terms
\(50AD = 625 - 527\)
\(50AD = 98\)
Divide both sides by 50
\(AD = \frac{98}{50}\)
Reduce fraction
\(AD = \frac{49}{25}\)
Recall that:
\(49 = BD^2 + AD^2\)
So, we have:
\(49 = BD^2 + (49/25)^2\)
\(49 = BD^2 + 2401/625\)
Collect like terms
\(BD^2 = 49 - 2401/625\)
Take LCM
\(BD^2 = \frac{625 *49 - 2401}{625 }\)
\(BD^2 = \frac{28224}{625}\)
Take the square roots of both sides
\(BD = \frac{168}{25}\)
Also, we have:
\(CD = 25 - AD\)
This gives
\(CD = 25 - \frac{49}{25}\)
Take LCM
\(CD = \frac{625 - 49}{25}\)
\(CD = \frac{576}{25}\)
Hence, the requires side lengths are:
\(AD = \frac{49}{25}\)
\(BD = \frac{168}{25}\)
\(CD = \frac{576}{25}\)
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Question 15 The Six Sigma DMAIC approach is the best way to attack all problems and should be employed whenever possible, O True O False Next Previous
False. The Six Sigma DMAIC approach is best suited for number of problems and issues that require a systematic approach and have measurable results. It should not be employed for all problems as some may require a different approach.
The Six Sigma DMAIC (Define, Measure, Analyze, Improve, Control) approach is a systematic process that is used to identify and eliminate defects in processes, products, or services. This approach is best suited for problems and issues that have a structured approach, measurable results, and an opportunity for improvement. However, it should not be employed for all problems as some may require a different approach such as root-cause analysis or process mapping. Additionally, some number of problems may require creative solutions that cannot be addressed using the DMAIC approach. In these cases, alternative approaches such as brainstorming or design thinking should be employed.
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Determine the equation of the line that passes through the (8,-27) and is parallel to the line y = - 3x - 1
The equation parallel to the given equation, and passing through the given point is
y = -3x - 3
Explanation:Given the line:
y = -3x - 1 ................................................(1)
The slope of this equation is -3
A line parallel to this line has the same slope as this, but a different y-intercept.
Let the parallel line be
y = -3x + b ..............................................(2)
To find the unknown b, we use the given point (8, -27), i.e x = 8, y = -27 into equation (2) and solve for b
-27 = -3(8) + b
-27 = -24 + b
b = -27 + 24
= -3
Substitute the value of b into (2), we have
y = -3x - 3
can anyone solve this
Answer:
1 in 1191
Step-by-step explanation:
because if 9 tickets have been given away you would have to subtract that from the 1200 which is 1191
Guys i need help i don’t want a link tho i just want a direct answer
Answer:
1.25 gallons/week i think
Step-by-step explanation:
carrie and joel plan to sell apple pies at the county fair for $6 each. the ingredients they used cost $3.75 per pie. they rent an oven for $54 to keep the pies hot throughout the day. how many pies must carrie and joel sell in order to break even?
Answer:
24 pies
Step-by-step explanation:
Let x represent the number of pies and set up an equation:
6x = 3.75x + 54
Solve for x:
6x = 3.75x + 54
2.25x = 54
x = 24
So, Carrie and Joel have to sell 24 pies to break even