Answer:
x- coordinate = 5
Step-by-step explanation:
Given a parabola in standard form , f(x) = ax² + bx + c ( a ≠ 0 ) , then
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = x² - 10x + 3 ← is in standard form
with a = 1 , b = - 10 , then x- coordinate of vertex is
x = - [tex]\frac{-10}{2}[/tex] = 5
You randomly select one card from a 52-card deck. Find the probability of selecting the 9 of spades or the 3 of clubs.
The probabilitiy is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
2/52=1/26
Step-by-step explanation:
A professor wondered if there was a difference in the proportion of students who dropped math classes between females and males. The professor randomly selected 20 math classes around campus and recorded the gender of the individual and whether or not a student enrolled in the class at the beginning of the term dropped the class at some point during the term. Assuming all conditions are satisfied, which of the following tests should the researcher use? Choose the correct answer below.
a) Chi-square goodness of fit test
b) two-sample z-test for proportions C
c) paired t-test
d) one-sample z-test for proportions
e) two-sample t-test
Answer:
b) two-sample z-test for proportions
Step-by-step explanation:
The most appropriate test to use for the research hypothesis stated above is the two sample z-test for proportions, this is because, the experiment has two independent groups (male and female) with the result of each group not affecting the result of the other. The experiment clearly stses that, it is to estimate the difference in proportion, hence, it is a test of proportions rather than mean. Also when performing, a two sample tests of proportion, the Z distribution is used.
A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
11 meters
Step-by-step explanation:
First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).
The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is
(√3/4)((11-4x)/3)²
= (√3/4)(11/3 - 4x/3)²
= (√3/4)(121/9 - 88x/9 + 16x²/9)
= (16√3/36)x² - (88√3/36)x + (121√3/36)
The total area is then
(16√3/36)x² - (88√3/36)x + (121√3/36) + x²
= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)
Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)
When x=0, each side of the triangle is 11/3 meters long and its area is
(√3/4)a² ≈ 5.82
When x=2.75, each side of the square is 2.75 meters long and its area is
2.75² = 7.5625
Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 11 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (11 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (11 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(11 - x)/3 = 0
2x/4 - (√3/6)(11 - x) = 0
2x / 4 = (√3/6)(11 - x)
√3x = 11 - x
√3x + x = 11
x (√3 + 1) = 11
x = 11 / (1.732 + 1)
x = 11/2.732
x = 4
Thus,
The length of the square must be 4 m in order to maximize the total area.
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A bank wishes to estimate the mean balances owed by customers holding Mastercard. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
A. 76
B. 85
C. 86
D. 77
Answer:
D. 77
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation is estimated to be $300
This means that [tex]\sigma = 300[/tex]
If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
This is n for which M = 80. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]80 = 2.327\frac{300}{\sqrt{n}}[/tex]
[tex]80\sqrt{n} = 2.327*300[/tex]
[tex]\sqrt{n} = \frac{2.327*300}{80}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*300}{80})^2[/tex]
[tex]n = 76.15[/tex]
Rounding up:
77 cardholders should be sampled, and the correct answer is given by option d.
Find the missing side. Round your answer to the nearest tenth
Answer:
14.7
Step-by-step explanation:
tan(73)=48/x
or, x=48/tan(73)
or, x=14.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
ive gotten it wrong like 4 times n i cannot figure it out pls help
Answer:
x = 74.74 m
Step-by-step explanation:
you need simple trigonometry to solve it
cosine of an angle is the ratio of the adjacent side to the hypotenuse
cos(42.2) is about 0.74
so X / Hypotenuse = 0.74
we know hypotenuse is 101 m
X / 101 = 0.74
x = 74.74 m
hope this helped!
plzzzzz helllllllppppppp worth 25 points
Answer:
Step-by-step explanation:
Let's fill that in with what the variables are "worth":
(3)(-3)+2(-2) and simplify to
-9 + (-4) which, when you add those 2 negatives, gives you
-13, choice B.
Answer:
[tex]x = 3 \\ y = - 3 \\ z = - 2 \\ xy + 2z = 3 \times - 3 + 2 \times - 2 \\ = - 9 - 4 \\ = - 13 \\ thank \: you[/tex]
The SAT and ACT college entrance exams are taken by thousands of students each year. The scores on the exam for any one year produce a histogram that looks very much like a normal curve. Thus, we can say that the scores are approximately normally distributed. In recent years, the SAT mathematics scores have averaged around 480 with standard deviation of 100. The ACT mathematics scores have averaged around 18 with a standard deviation of 6.
a. An engineering school sets 550 as the minimum SAT math score for new students. What percent of students would score less than 550 in a typical year?
b. What would the engineering school set as comparable standard on the ACT math test?
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
Answer:
a) 75.8% of students would score less than 550 in a typical year.
b) The comparable standard would be a minimum ACT score of 22.2.
c) 0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Question a:
SAT, so mean of 480 and standard deviation of 100, that is, [tex]\mu = 480, \sigma = 100[/tex]
The proportion is the p-value of Z when X = 550. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{550 - 480}{100}[/tex]
[tex]Z = 0.7[/tex]
[tex]Z = 0.7[/tex] has a p-value of 0.758.
0.758*100% = 75.8%
75.8% of students would score less than 550 in a typical year.
b. What would the engineering school set as comparable standard on the ACT math test?
ACT, with a mean of 18 and a standard deviation of 6, so [tex]\mu = 18, \sigma = 6[/tex]
The comparable score is X when Z = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.7 = \frac{X - 18}{6}[/tex]
[tex]X - 18 = 0.7*6[/tex]
[tex]X = 22.2[/tex]
The comparable standard would be a minimum ACT score of 22.2.
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
This is 1 subtracted by the p-value of Z when X = 700, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 480}{100}[/tex]
[tex]Z = 2.2[/tex]
[tex]Z = 2.2[/tex] has a p-value of 0.9861.
1 - 0.9861 = 0.0139
0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
The triangles are similar, find y
Answer:
y = 3.6
x = 3.5
Step-by-step explanation:
The triangles are similar.
[tex]\frac{3}{2.4} = \frac{x}{2.8} = \frac{4.5}{y}[/tex]
Find y:
[tex]\frac{4.5}{y} = \frac{5}{4}[/tex]
[tex]4.5 * 4 = 5y => 18 = 5y => y = 3.6[/tex]
Find x:
[tex]\frac{x}{2.8} = \frac{5}{4}[/tex]
[tex]2.8 * 5 = 4x => 14 = 4x => x = 3.5[/tex]
How many sides does a regular polygon have if each interior angle measures 178°?
The number of sides of a regular polygon with an interior angle [tex]\[{178^ \circ }\][/tex] is 180.
What is the regular polygon?
A polygon is regular when all angles are equal and all sides are equal.
A regular polygon has if each interior angle.
Interior angle of given polygon =178
An exterior angle of polygon =180 −178 =2
The sum of exterior angles of any polygon is 360
Number of sides of a regular polygon
[tex]=\frac{360}{2}[/tex]
[tex]=180[/tex]
Therefore, The number of sides of a regular polygon is 180.
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The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. Which of the following correctly labels the population?
1–1020
01–1020
001–1020
0001–1020
I think its (B), 01-1020.
Answer:
Should be (B)
01-1020
ED2021
The correct label for the population is 1 - 1020,
Option A is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a number of population given.
Each items has an equal probability of being chosen.
We have,
The population in this case refers to the entire group of interest, which is the entire student body of the school.
The total number of students is 1,020.
The population is usually labeled with a range or interval that includes all the possible values of the variable of interest.
In this case, the variable of interest is whether or not a student has an opinion on parking.
The correct label for the population is 1-1020, as this range includes all possible student identification numbers at the school.
The other options (01-1020, 001-1020, and 0001-1020) are not correct because they suggest that there are leading zeros in the student identification numbers, which is not usually the case.
Thus,
The correct label for the population is 1-1020,
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This answer was confusing for sure
Answer: lol ez
B.
Step-by-step explanation: XD
Answer:
D
Step-by-step explanation:
The general formula for the sine or cosine function is
y = A*Sin(Bx + C) + D
C = 0 in this case
B = pi / 3
The period is given by the formula
P = 2 * pi / B
P = 2 * pi//pi/3
The 2 pis cancel and you are left with 2*3 = 6
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5x − 6y = 4 10x − 12y = 8 one and only one solution infinitely many solutions no solution Correct: Your answer is correct. Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answer:
same line infinite solutions
Step-by-step explanation:
5x − 6y = 4
10x − 12y = 8
10x − 12y = 8
10x − 12y = 8
0 = 0
same line infinite solutions
consider the differential equation x3y ''' + 8x2y '' + 9xy ' − 9y = 0; x, x−3, x−3 ln(x), (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x, x−3, x−3 ln(x)) = ≠ 0 for 0 < x < [infinity].
Verifying that a given expression is a solution to the equation is just a matter of plugging in the expression and its derivatives, and making sure that the given expressions are indeed linearly independent.
For example, if y = x, then y' = 1 and the other derivatives vanish. So the DE after substitution reduces to
9x - 9x = 0
which is true for all 0 < x < ∞.
To check for linear independence, you compute the Wronskian, which, judging by what you wrote, you've already done...
3. You buy butter for $3 a pound. One portion of onion compote requires 2 oz of butter. How much does the butter for one portion cost?
Answer:
The butter for one portion cost $ 0.375.
Step-by-step explanation:
Given that you buy butter for $ 3 a pound, and one portion of onion compote requires 2 oz of butter, to determine how much does the butter for one portion cost, the following calculation must be performed:
2 oz = 0.125 lb
1 = 3
0.125 = X
3 x 0.125 = X
0.375 = X
Therefore, the butter for one portion cost $ 0.375.
need help with math plz thanks
Answer:
0
Step-by-step explanation:
[tex]f(x)=2x-4\\f(2)=2(2)-4\\f(2)=4-4\\f(2)=0[/tex]
Answer:
0
Step-by-step explanation:
If f(x) = 2x - 4
Then f(2) = 2(2) -4
f(2) = 4 - 4
= 0
Use the substitution method to solve this system.
y = 2x+4
3x+y = 9
Answer:
x = 1; y=6
Step-by-step explanation:
y = 2x +4
3x + y = 9
Substitute 2x+4 for y in 3x+y = 9
3x + y = 9
3x + 2x+4 = 9
5x + 4 = 9
5x = 9-4
5x = 5
5x/5 = 5/5
x = 1
Substitute 1 for x in y = 2x +4
2(1) + 4
2 + 4
= 6
Answered by Gauthmath
A survey asked 25 students about their favorite sport. A frequency table of their responses is below.
Basketball, 4; football, 7; lacrosse, 3; soccer, 8; volleyball, 3.
Which of the following is the correct relative frequency table for the students’ favorite sport?
Answer: The second one
Step-by-step explanation:
response/25=x/100 and then you solve for x
A percentage is a way to describe a part of a whole. The correct table is B.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the number of students who play different sports as,
Basketball = 4
Football = 7
Lacrosse = 3
Soccer = 8
Volleyball = 3
Now, the percentage of students for each sport can be written as,
Basketball = 4/25 = 0.16
Football = 7/25 = 0.28
Lacrosse = 3/25 = 0.12
Soccer = 8/25 = 0.32
Volleyball = 3/25 = 0.12
Hence, the correct table is B.
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the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
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Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
A number plus 16 times its reciprocal equals 8. Find all possible values for the number.
Answer:
4
Step-by-step explanation:
[tex]n+16\frac{1}{n} = 8\\\\n^2+16=8n\\n^2 -8n+16=0\\[/tex]Factorizing we get the answer 4
If f(x)=-4x-5 and g(x)=3-x whats is g(-4)+f(1)
Answer: -2
Step-by-step explanation:
g(-4) = 3 - (-4) = 3 + 4 = 7f(1) = -4(1) - 5 = -4 - 5 = -9g(-4) + f(1) = 7 + (-9) = 7 - 9 = -2
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used
Answer:
Cluster Sampling
Step-by-step explanation:
Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.
Thank you for all the help guys
Answer:
a is the right answer thanks(A) A small business ships homemade candies to anywhere in the world. Suppose a random sample of 16 orders is selected and each is weighed. The sample mean was found to be 410 grams and the sample standard deviation was 40 grams. Find the 90% confidence interval for the mean weight of shipped homemade candies. (Round your final answers to the nearest hundredth)
(B) When 500 college students are randomly selected and surveyed; it is found that 155 own a car. Find a 90% confidence interval for the true proportion of all college students who own a car.
(Round your final answers to the nearest hundredth)
(C) Interpret the results (the interval) you got in (A) and (B)
The correct answer to the given question is "[tex]\bold{392.47\ < \mu <\ 427.53}[/tex],[tex]\bold{0.28 \ < P <\ 0.34}[/tex], and for Interpret results go to the C part.
Following are the solution to the given parts:
A)
[tex]\to \bold{(n) = 16}[/tex]
[tex]\to \bold{(\bar{X}) = 410}[/tex]
[tex]\to \bold{(\sigma) = 40}[/tex]
In the given question, we calculate [tex]90\%[/tex] of the confidence interval for the mean weight of shipped homemade candies that can be calculated as follows:
[tex]\to \bold{\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{S}{\sqrt{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}\\\\\to \bold{(\alpha) = 1 - 0.90 = 0.10}\\\\ \to \bold{\frac{\alpha}{2} = \frac{0.10}{2} = 0.05}\\\\ \to \bold{(df) = n-1 = 16-1 = 15}\\\\[/tex]
Using the t table we calculate [tex]t_{ \frac{\alpha}{2}} = 1.753[/tex] When [tex]90\%[/tex] of the confidence interval:
[tex]\to \bold{410 \pm 1.753 \times \frac{40}{\sqrt{16}}}\\\\ \to \bold{410 \pm 17.53\\\\ \to392.47 < \mu < 427.53}[/tex]
So [tex]90\%[/tex] confidence interval for the mean weight of shipped homemade candies is between [tex]392.47\ \ and\ \ 427.53[/tex].
B)
[tex]\to \bold{(n) = 500}[/tex]
[tex]\to \bold{(X) = 155}[/tex]
[tex]\to \bold{(p') = \frac{X}{n} = \frac{155}{500} = 0.31}[/tex]
Here we need to calculate [tex]90\%[/tex] confidence interval for the true proportion of all college students who own a car which can be calculated as
[tex]\to \bold{p' \pm Z_{\frac{\alpha}{2}} \times \sqrt{\frac{p'(1-p')}{n}}}[/tex]
[tex]\to \bold{C.I= 0.90}[/tex]
[tex]\to\bold{ (\alpha) = 0.10}[/tex]
[tex]\to\bold{ \frac{\alpha}{2} = 0.05}[/tex]
Using the Z-table we found [tex]\bold{Z_{\frac{\alpha}{2}} = 1.645}[/tex]
therefore [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is
[tex]\to \bold{0.31 \pm 1.645\times \sqrt{\frac{0.31\times (1-0.31)}{500}}}\\\\ \to \bold{0.31 \pm 0.034}\\\\ \to \bold{0.276 < p < 0.344}[/tex]
So [tex]90\%[/tex] the confidence interval for the genuine proportion of college students who possess a car is between [tex]0.28 \ and\ 0.34.[/tex]
C)
In question A, We are [tex]90\%[/tex] certain that the weight of supplied homemade candies is between 392.47 grams and 427.53 grams.In question B, We are [tex]90\%[/tex] positive that the true percentage of college students who possess a car is between 0.28 and 0.34.Learn more about confidence intervals:
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write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
FH ≈ 6.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )
8 × sin49° = FH , then
FH ≈ 6.0 ( to the nearest tenth )
Answer:
6
Step-by-step explanation:
sin = opposite/hypotenuse
opposite = sin * hypotenuse
sin (49) = 0,75471
opposite = 0,75471 * 8 = 6,037677 = 6
A population proportion is 0.57. Suppose a random sample of 657 items is sampled randomly from this population.
a. What is the probability that the sample proportion is greater than 0.58?
b. What is the probability that the sample proportion is between 0.54 and 0.60?
c. What is the probability that the sample proportion is greater than 0.56?
d. What is the probability that the sample proportion is between 0.53 and 0.55?
e. What is the probability that the sample proportion is less than 0.48?
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
Answer:
d) Asking questions to make sure they understand what's being said
Step-by-step explanation:
Asking questions is important for learning and clears up any confusion.
The midpoint of has coordinates of (4, -9). The endpoint A has coordinates (-3, -5). What are the coordinates of B?
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Answer:
(11, -13)
Step-by-step explanation:
If midpoint M is halfway between A and B:
M = (A +B)/2
Then B is ...
B = 2M -A
B = 2(4, -9) -(-3, -5) = (8+3, -18+5)
B = (11, -13)
Answer:
Use the midpoint formula:
[tex]midpoint=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]
Endpoint A = (x₁, y₁) = (-3, -5)Endpoint B = (x₂, y₂)Midpoint = (4, -9)Substitute in the values:
[tex](4, -9)=(\frac{-3+x_{2}}{2} +\frac{-5+y_{2}}{2} )[/tex]
[tex]4=\frac{-3+x_{2}}{2} \\4(2)=-3+x_{2}\\8+3=x_{2}\\x_{2}=11[/tex] [tex]-9=\frac{-5+y_{2}}{2} \\(-9)(2)=-5+y_{2}\\-18+5=y_{2}\\y_{2}=-13[/tex]
Therefore, Point B = (11, -13)
If a system including the quadratic equation representing the parabola and a linear equation has no solution, which linear equation could be the second equation in the system? A. 1/2x=y+4 B. 2x-y=0 C.y=6 D.y=2x+6
9514 1404 393
Answer:
D. y=2x+6
Step-by-step explanation:
The line cannot intersect the parabola if it has a y-intercept greater than 5 and a suitable slope. The only sensible answer choice is ...
y = 2x +6
Answer:
D. y = 2x + 6.
Step-by-step explanation:
The required equation would not intersect the parabola at any point.
The only one to fit that is D.
please can anyone help me with this question what is the probability of the spinner landing on an even number.
