Answer:
Step-by-step explanation:
hello
[tex]y^2-4y+6= (y+1)^2-2y-1-4y+6=(y+1)^2-6y+5=(y+1)^2-6(y+1)+11[/tex]
so
[tex]\dfrac{y^2-4y+6}{y+1}=y+1-6+\dfrac{11}{y+1}=y-5+\dfrac{11}{y+1}[/tex]
hope this helps
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate. Round your answer to the nearest thousandth.
n1 = 677 n2 = 3377
x1 = 172 x2 = 654
Answer:
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Step-by-step explanation:
Given first sample size n₁ = 677
First sample proportion
[tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]
Given second sample size n₂ = 3377
second sample proportion
[tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]
Null Hypothesis : H₀ : p₁ = p₂.
Alternative Hypothesis : H₁ : p₁ ≠ p₂.
Test statistic
[tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]
where
[tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]
P = 0.2036
Q = 1 - P = 1 - 0.2036 = 0.7964
[tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]
Z = 3.775
Critical value ∝=0.05
Z- value = 1.96
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.
90 34 41106 84 5355 48 4175 49 9792 73 7480 94 10256 83
Required:
Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals).
Answer:
[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]
[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]
Step-by-step explanation:
Information given
90 34 41 106 84 53 55 48 41 75 49 97 92 73 74 80 94 102 56 83
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
[tex]\bar X=71.35[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=22.48 represent the sample standard deviation
n=20 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=20-1=19[/tex]
Since the Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.093[/tex]
And replacing we got:
[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]
[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]
Select the correct answer from each drop-down menu. Month____ Balance ($) January 45 February 10 March -15 April -35 May -5 The table shows the balance in David’s bank account for the first five months of the year. David’s balance was highest in ____ , and his debt was highest in _____
Answer:
end
January
April
1st blank might also be (account)
Answer:
January and April
Step-by-step explanation:
A residential complex has left for the recreation area a circular-shaped extension of 40 m radius. In this space, a basketball court 30 m long by 15 m wide will be built. Also, a trapezoid-shaped park will be left in the sand, 6 m with a larger base, 4 m with a lower base and 3.5 m in height. What is the area left in the circular zone, after building the basketball court and the sand park? NOTE: remember the value of π = 3.14
Answer:
Step-by-step explanation:
Area of the circular zone = [tex]\pi[/tex]r^2
= 3.14 × 40^2 = 3.14 × 1600 = 5024 m^2
Area of the basketball court = l × b
= 30 × 15 = 450 m^2
Area of the trapezium shaped park = ( 6 + 4 ) 3.5 / 2
= 35/2 = 17.5 m^2
∴ Area left in the circular zone = Area of the circular zone - ( Area of the basketball court + Area of the trapezium shaped park )
= 5024 - ( 450 + 17.5 )
= 5024 - 467.5
= 4556.5 m^2
hope this helps
plz mark it as brainliest!!!!!!!
A plane flies 240 miles due north, then 320 miles due west. How
many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)
Answer: The distance of the shortest route of return is 400
Step-by-step explanation:
The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
BC² = 320² + 240²
BC² = 160000
BC = √160000
BC = 400
Need help please guysssssss
Answer:
C
Step-by-step explanation:
3x+2-x>8
2x+2>8
2x>8-2
2x>6
x>3
Answer:
C
Step-by-step explanation:
An urn contains 25 red marbles, 27 blue marbles, and 36 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble?
Answer:
25/88
Step-by-step explanation:
25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles
P(red) = number of red/total
= 25/88
Answer:
Dear user,
Answer to your query is provided below
Probability of choosing a red marble is 0.28 or (25/88)
Step-by-step explanation:
Total number of marbles = 88
Number of red marbles = 25
Probability = 25/88
A man starts walking from home and walks 3 miles at north of west, then 5 miles at west of south, then 4 miles at north of east. If he walked straight home, how far would he have to the walk, and in what direction
Answer:
Step-by-step explanation:
We shall find the solution of this problem with the help of vector notation of i , j , which show east and north direction .
The first displacement can be represented by the following
D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j
The second displacement can be represented by the following
D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j
The third displacement can be represented by the following
D₃ = 4 cos 45 i + 4 sin45 j = 4 /√2 i + 4 /√2 j
Total displacement D =
D₁ +D₂ + D₃
= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j
= - 4 / √2 i + 2 / √2 j
D = - 2.8288 i + 1.414 j
Magnitude of D
= √ ( 2.8288² + 1.414² )
= 3.16 miles
For direction we calculate angle with X axis
Tanθ = 1.414 / 2.8288
θ = 26 °
As x is negative and Y is positive ,
the direction will be north of west .
the number 312 lies between the perfect cubes what are they
Answer:
216-343
Step-by-step explanation:
the number 312 lies between 125 and 330
Surface area of a cylinder: S = 2ar+2arh , solve for h.
Answer:
[tex]h = \frac{s - 2ar}{2ar} \\ [/tex]
Step-by-step explanation:
[tex]s = 2ar + 2arh \\ s - 2ar = 2arh \\ \frac{s - 2ar}{2ar} = \frac{2arh}{2ar} \\ h = \frac{s - 2ar}{2ar} [/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
Renee is making a scale diagram of her MP3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the MP3 player is 4 centimeters, and the width is 7 centimeters. This is , and the scale factor is .
Answer:
2
Step-by-step explanation:
Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]
So,
Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2
So,
The scale factor is 2
Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
Answer:
The lowest score eligible for an award is 92.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 82.2, \sigma = 5[/tex]
If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 82.2}{5}[/tex]
[tex]X - 82.2 = 5*1.96[/tex]
[tex]X = 92[/tex]
The lowest score eligible for an award is 92.
18 + 5k / 3
I need help asap please cuz my mom asked me to solve this in 2min
#aisanmoms #SOS
Answer:
Nothing can be further done to this equation. It has been simplified all the way.
Laura is stuck in aisle six at the supermarket trying to decide which jar of peanut butter to buy.
She can buy a 16-ounce jar for $2.59 or a 24-ounce jar for $3.29. Which jar has a lower unit price,
per ounce?
Answer: 24 ounce jar
Step-by-step explanation:
Unit price of 16 ounce jar
= 2.59 / 16
= 0.161875
Unit price of 24 ounce jar
= 3.29 / 24
= 0.137083
How many parallel and perpendicular lines, are there in a trapezium?
Answer:
US
0 parallel linesoptionally, one or two (opposite) angles may be 90°World
2 parallel linesoptionally, one line perpendicular to the two parallel linesStep-by-step explanation:
It depends on where you are. A "trapezium" outside the US is the same as a "trapezoid" in the US, and vice versa.
A trapezium (World; trapezoid in the US) is characterized by exactly one pair of parallel lines. One of the lines that are not parallel may be perpendicular to the parallel lines, but that will only be true for the specific case of a "right" trapezium.
__
A trapezium (US; trapezoid in the World) is characterized by no parallel lines. It may have one angle or opposite angles that are right angles (one or two sets of perpendicular lines), but neither diagonal may bisect the other.
In the US, "trapezium" is rarely used. The term "quadrilateral" is generally applied to a 4-sided figure with no sides parallel.
Sekkrit help!!!!! If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.
Answer:
The value of a is 0.
Step-by-step explanation:
Given that (x+1) is a factor to a function, it means that when x = -1 is substitute into the function, you will get a 0 value. So you have to substitute the value of x into the function and make it 0, to find a :
[tex]p(x) = a {x}^{2} + x + 1[/tex]
[tex]let \: p( - 1) = 0 \\ let \: x = -1[/tex]
[tex]p( - 1) = a {( - 1)}^{2} + ( - 1) + 1[/tex]
[tex]0 = a - 1 + 1[/tex]
[tex]a = 0[/tex]
Answer:
a=0Solution,
To find a,
We should know that,
Factor of polynomial gives root of polynomial like:x-a if a factor of p(X) then p(a)=0 at X=a
So,
X+1=0
X=0-1
X=-1
put x=-1 into p(X) it gives zero.
[tex]p( - 1) = 0 \\ a {( - 1)}^{2} + ( - 1) + 1 = 0 \\ a(1) - 1 + 1 = 0 \\ a = 0[/tex]
hope this helps....
Good luck on your assignment....
A graduate student majoring in linguistics is interested in studying the number of students in her college who are bilingual. Of the 1,320 students at the college, 466 of them are bilingual. If the graduate student conducts a study and samples 50 students at the college, use a calculator to determine the probability that 17 or fewer of them are bilingual.
The result will be the probability that 17 or fewer out of the 50 sampled students are bilingual.
To determine the probability that 17 or fewer out of 50 sampled students are bilingual, we can use the binomial probability formula. Let's calculate it step by step:
First, we need to determine the probability of an individual student being bilingual. We can do this by dividing the number of bilingual students by the total number of students:
P(bilingual) = 466 / 1320
Next, we'll use this probability to calculate the probability of having 17 or fewer bilingual students out of a sample of 50. We'll sum up the probabilities for having 0, 1, 2, ..., 17 bilingual students using the binomial probability formula:
P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)
Where:
P(X = k) = (nCk) * (P(bilingual))^k * (1 - P(bilingual))^(n - k)
n = Sample size = 50
k = Number of bilingual students (0, 1, 2, ..., 17)
Now, let's use a calculator to compute these probabilities. Assuming you have access to a scientific calculator, you can follow these steps:
Convert the probability of an individual being bilingual to decimal form: P(bilingual) = 466 / 1320 = 0.353
Calculate the cumulative probabilities for having 0 to 17 bilingual students:
P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)
Using the binomial probability formula, we'll substitute the values:
P(X ≤ 17) = (50C0) * (0.353)^0 * (1 - 0.353)^(50 - 0) + (50C1) * (0.353)^1 * (1 - 0.353)^(50 - 1) + ... + (50C17) * (0.353)^17 * (1 - 0.353)^(50 - 17)
Evaluate this expression using your calculator to get the final probability. Make sure to use the combination (nCr) function on your calculator to calculate the binomial coefficients.
for such more question on probability
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Using the central limit theorem, the probability that 17 or fewer of them are bilingual.
The following information is given in the question:
Population size N = 1320
Number of bilingual students = 466
Sample size n = 50
number of bilingual students in the sample = 17
Population proportion:
[tex]P =\frac{466}{1320}[/tex]
P =0.3530
Q= 1-3530
Q = 0.647
Sample proportion:
[tex]p = \frac{17}{50}[/tex]
p = 0.34
q = 1-0.34
q = 0.66
Since,
[tex]X \sim B(n, p)[/tex]
E(x) = np and var(x) = npq
Here, the sample size (50) is large and the probability p is small.
So we can use the central limit theorem, which says that for large n and small p :
[tex]X \sim (nP, nPQ)[/tex]
Where, P =0.3530
nP = 50 x 0.3530 = 17.65
and nPQ = 50x0.3530x0.647 = 11.41
Now, we want to calculate P(X≤17)
[tex]P(X\leq 17) = P(\frac{x-nP}{\sqrt{nPQ}}\leq \frac{17-17.65}{\sqrt{11.41}})[/tex]
[tex]P(X\leq 17) = P(z}\leq \frac{-0.65}{3.78}})[/tex]
[tex]P(X\leq 17) = P(z}\leq -0.172)[/tex]
[tex]P(X\leq 17) = P(z}\geq 0.172)[/tex]
[tex]P(X\leq 17) =1- P(z}\leq 0.172)[/tex]
[tex]P(X\leq 17) =1-0.56[/tex]
[tex]P(X\leq 17) =0.44[/tex]
Hence, the probability that 17 or fewer of the students are bilingual is 0.44.
Learn more about central limit theorem here:
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Which expression is equivalent to negative 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4?
Answer:
-4*4^7
Step-by-step explanation:
Answer:
-65536
Step-by-step explanation:
I do not think I understand the question but -4*4*4*4*4*4*4*4=-65536
I think there may be missing information like if the question is multiple choice.
Hope that helps
find the quotient of (5+4i)/(6+8i) ans express in simplest forms
Answer:
Your correct answer is 31/50 + -4/25 i
Step-by-step explanation:
5+4i/6+8i = 31/50 + -4/25 i
(Geometry) PLEASE HELP ASAP
Answer:
CD=72x=7please see the attached picture for full solution
Hope it helps
Good luck on your assignment
A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and a sample standard deviation of 0.34 second. This sample data is used as a pilot study, and now the investigator would like to design a new study to construct a 99% confidence interval with width 0.1. What is the necessary sample size
Answer:
[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]
So the answer for this case would be n=308 rounded up to the nearest integer
Step-by-step explanation:
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.1/2 =0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution since the sample size is large enough to assume the estimation of the standard deviation as the population deviation. The critical value for this case is [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]
So the answer for this case would be n=308 rounded up to the nearest integer
Which equation is the inverse of y = x2 + 16? y = x2 – 16 y = plus-or-minus StartRoot x EndRoot minus 16 y = plus-or-minus StartRoot x minus 16 EndRoot y = x2 – 4
Answer:
[tex]\pm \sqrt{x-16}[/tex] is the inverse of [tex]y = x^2 + 16[/tex]
Step-by-step explanation:
Given that:
[tex]y = x^2 + 16[/tex]
Let us proceed step by step to calculate the inverse:
Step 1: Put [tex]y = f(x)[/tex]
[tex]f(x) = y=x^2 + 16[/tex]
Step 2: Interchange [tex]x[/tex] and [tex]y[/tex]:
[tex]x = y^2 + 16[/tex]
Step 3: Solve the equation to find the value of [tex]y[/tex]:
[tex]y^2 =x- 16\\\Rightarrow y =\pm \sqrt{x- 16}[/tex]
Step 4: Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:
[tex]\Rightarrow y =f^{-1}(x)=\pm \sqrt{x- 16}[/tex]
So, the inverse of [tex]y = x^2 + 16[/tex] is [tex]\pm \sqrt{x- 16}[/tex].
The equation which is the inverse of y = x2 + 16 is; f-¹ = y = ±√(x -16)
To evaluate the inverse of the function, y = x2 + 16.
We must first make x the subject of the formula and swap x and y as follows;
x = ±√(y - 16)y = ±√(x - 16)Therefore, the inverse function is;
f-¹ = y = ±√(x -16)Read more on inverse function:
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Find the scale ratio for the map described below.
1 mm (map)equals500 m (actual)
The scale ratio is 1 to
nothing.
Answer:
The answer is nothing duh
Step-by-step explanation:
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2 + 9.8t + 1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
Answer:
Step-by-step explanation:
max can be found by the formula:
t=-b/2a
t=-9.8/2*(-4.9)
t=-9.8/-9.8
t=1
1 sec
to find maximum height obtained we find the vertex:
plug in 1 for t and simply solve:
h(t)= -4.9t^2 + 9.8t + 1
h(t)= -4.9*1^2 + 9.8*1 + 1
h(t)= -4.9*1 + 9.8 + 1
h(t)= -4.9 + 10.8
h(t)= 5.9
height is 5.9
Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $180 monthly payment, 6.25% interest, 11 years
Answer:
The future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
Consider the provided information:
It is provided that monthly payment is $175, interest is 7% and time is 11 years.
The formula for the future value of the annuity due is:
Now, substitute P = 175, r = 0.07 and t = 11 in above formula.
Hence, the future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=55,
x=33,
p=0.55
p(3)=_________
Answer:
P(33) = 0.0826
Step-by-step explanation:
The binomial distribution in this case has parameters n=55 and p=0.55.
The probability that k successes happen with these parameters can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]
We have to calculate the probability fo X=33 succesess.
This can be calculated using the formula above as:
[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]
What is the solution to this equation? 4x+x-15+3-8x=13
Answer:
x = -25/3
Step-by-step explanation:
The equation simplifies to -3x - 25 = 0, so
-3x = 25 =>
x = -25/3
Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that employees in the United States must be paid time-and-a-half (1.5 times the normal hourly rate) for each hour worked over 40 hours per week
Answer:
see below for the table valuesUS labor cost: $115275 per yearStep-by-step explanation:
The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...
(6 days/week)($1.10/day) = $6.60/week
The three laborers working 50 weeks/year will have a labor cost of ...
(3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year
__
In the US, the labor charge per person per week is ...
(14 hr/day)(6 day/week) = 84 hr/week
That's 40 hours of straight pay and 44 hours of overtime pay, or ...
7.25(40 +1.5(44)) = 7.25(106) = 768.50
For 150 person-weeks per year, the total US labor charge is ...
($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year
__
The materials cost for a year is ...
($50/rug)(12 rugs/year) = $600/year
__
The revenue is ...
($2000/rug)(12 rugs/year) = $24,000/year
Profit is the difference between revenue and the total of costs:
profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia
__
So, the table gets filled as follows:
(labor, material, fixed cost, revenue, profit)
Mongolian-made
($990, $600, $10000, $24000, $12410)
US-made
($115275, $600, $10000, $24000, -$101,875)
The US labor cost would be $115,275.
_____
Comment
For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.
PLEASE ANSWER!!!!!!!! Which system of equations does this graph represent? Linear graph and parabola. They intersect at 2, negative 1 and negative 3, 4 (1 point)
A. y = x2 − 5 y = −x + 1
B. y = x2 − 5 y = −x − 1
C. y = x2 + 5 y = −x + 1
D. y = x2 + 5 y = −x − 1
Answer:
Option (A)
Step-by-step explanation:
For equation of the line,
Let the equation is, y = mx + b
Slope 'm' of the line passing through two points (-3, 4) and (2, -1),
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4+1}{-3-2}[/tex]
= -1
y-intercept of this line, b = 1
Now we substitute these values in the equation,
y = -x + 1
Let the equation of the parabola is,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola,
Since vertex of the given parabola is (0, -5),
then the equation will be,
y = a(x - 0)²- 5
y = ax² - 5
Since a point (2, -1) lies on this parabola,
-1 = a(2)² - 5
5 - 1 = 4a
a = 1
Equation of the parabola will be,
y = x² - 5
Therefore, Option (A) will be the answer.
wich of the following properties was used for 3(x+2)=3x+6
Answer:
you will want to have a good understanding of these properties to make the problems in ... Here, the same problem is worked by grouping 5 and 6 first, 5 + 6 = 11. ... “three times the variable x” can be written in a number of ways: 3x, 3(x), or 3 · x. ... Use the distributive property to evaluate the expression 5(2x – 3) when x = 2.
y
The distributive property tells us that if were given an expression such as 3(x + 2), we can multiply the 3 by both the x and the 2 to get 3x + 6.