Describe the complement of a given event77% of a persons credit card purchases are $50 a more
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sets
[tex]77\%\text{ of a person's credit card purchases are \$50 and more}[/tex]STEP 2: find the complement
The complement will be the percentage that cannot purchase $50 and more.
Since percentages equal 100, therefore the complement will be:
[tex]100\%-77\%=23\%[/tex]Hence, the answer in % is given as 23
Related Questions
The value of an industrial embroidery machine is decreasing according to the function defined byV(t) = 10,890(3)–0.21where tis the number of years since the machine was purchased. What does the y-intercept represent?OA. the value of the machine after 3 yearsB.the amount of time it takes for the value of the machine to reach zeroOC.the original value of the machineODthe rate at which the value of the machine depreciates21 Edimentum All rights reserved
Answers
Solution
We have the following expression:
[tex]V(t)=10890(3)^{-0.2t}[/tex]for this case the y intercept is given when t=0 so we have:
[tex]V(0)=10890(3)^{-0.2\cdot0}=10890[/tex]And this value represent the following:
C. the original value of the machine
Since thats the starting value without depreciation
Jakia is a member of the Usaah club at rshs for the 2020-2021 school year she works at a local fast food restaurant after school and on weekends. She saving for the college tour schedule for December 2021 . Jakia saved 20 in June ,25 in july,30 in August, and plans to continue this pattern each mouth how much money will jakia save in November 2021
Answers
November savings = 45
Explanation:
Amount saved in June = 20
Amount saved in July = 25
Amount saved in August = 30
From the above, there is an increament of 5 as the month increases:
30-25 = 25-20 = 5
September = August savings + increament
September saving = 30 + 5 = 35
October = September savings + increament
October = 35 + 5 = 40
November = October savings + increament
November savings = 40 + 5
November savings = 45
2. Find the coordinates of P so that P partitions AB in the ratio 5.1 with A(2, 4) and B(8, 10).
Answers
Answer:
The coordinates of P is;
[tex]P=(7,9)[/tex]Explanation:
We want to find the coordinate of P such that P partitions AB in the ratio 5:1.
Given the coordinates of A and B as;
[tex]\begin{gathered} A(2,4) \\ B(8,10) \end{gathered}[/tex]Let (x,y) represent the coordinates of point P;
[tex]\begin{gathered} \frac{x-2}{8-x}=\frac{5}{1} \\ x-2=5(8-x) \\ x-2=40-5x \\ x+5x=40+2 \\ 6x=42 \\ x=\frac{42}{6} \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{y-4}{10-y}=\frac{5}{1} \\ y-4=5(10-y) \\ y-4=50-5y \\ y+5y=50+4 \\ 6y=54 \\ y=\frac{54}{6} \\ y=9 \end{gathered}[/tex]Therefore, the coordinates of P is;
[tex]P=(7,9)[/tex]Helen has a 4 kilometer-head start on París how long will it take París to catch Helen if helen travels at 6 kilometers per hour and París traveled at 8 km per hour
Answers
Assume "h" = number of hours traveled
Helen's speed = 6km per hour and is 4km advanced than Paris
Paris' speed = 8km per hour
Therefore, we can form the following equations:
a. Helen's distance traveled = 4km + 6km (h) = 4 + 6h
b. Paris' distance traveled = 8km (h) = 8h
For us to determine how long will Paris be able to catch Helen, we'll have to assume they have traveled the same distance. In this case:
Helen's distance traveled = Paris' distance traveled
[tex]\begin{gathered} 4+6h=8h \\ \text{Subtrach 6h on both sides of the equation.} \\ 4+6h-6h=8h-6h \\ 4=2h \\ \text{Divide two on both sides.} \\ \frac{4}{2}=\frac{2h}{2} \\ 2=h \end{gathered}[/tex]Therefore, it will take 2 hours for Paris to catch up with Helen which is at 16km.
Mavis says that -7/9 * 6 is less than 7/9 * (-6) explain whether or not maybe this is correct
Answers
EXPLANATION
-7/9*6 is the same number that 7/9*(-6) because by the property of the products ---> the order of symbols doesn't change the solution : -a*b= a*-b
What is the equation of the line that passes through the point ( − 8 , − 3 ) that is parallel to the line 5 x − 8 y = − 40 ? Write the equation in slope-intercept form.
Answers
The outdoor temperature was 8° at midnight the temperature declined 5° during each of the next three hours. What was the temperature at 3 AM?
Answers
After performing mathematical operations, we can conclude that the temperature at 3:00 am would be 3°.
What do we mean by mathematical operations?Any mathematical operation that converts zero or more discrete input values into discrete output values is known as a discrete operation.The number of operands affects how complicated the operation is.Functions that convert numerical inputs into numerical outputs are the four mathematical operations (i.e., another number).These are addition, subtraction, multiplication, and division.So, the temperature at 3:00 am:
The temperature at midnight is 8°.Temperature falls by 5° in the next 3 hours.Then, the temperature at 3:00 am can be calculated as:
8 - 5 = 3°Therefore, after performing mathematical operations, we can conclude that the temperature at 3:00 am would be 3°.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
Answers
The equations that have the same solutions as 2.3p – 10.1 = 6.5p – 4 – 0.01p are as follows:
2.3p – 10.1 = 6.49p - 4230p - 1010 = 650p - 400 - pHow to find same solution equation?Systems of equations that have the same solution are called equivalent systems.
Therefore, the equation that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p can be calculated as follows:
Hence, let's find the solution of this :
2.3p – 10.1 = 6.5p – 4 – 0.01p
Simplifying the above equation by collecting like terms gives;
2.3p – 10.1 = 6.5p – 4 – 0.01p
2.3p – 10.1 = 6.5p – 0.01p - 4
Therefore, one of the equivalent solution is as follows:
2.3p – 10.1 = 6.49p - 4
Both sides of an equation will remain equal, when both sides are
multiplied by the same value.
Therefore, let's multiply both sides by 100,
2.3p – 10.1 = 6.5p – 4 – 0.01p
100(2.3p – 10.1) = 100(6.5p – 4 – 0.01p)
230p - 1010 = 650p - 400 - p
Therefore, another equivalent solution is 230p - 1010 = 650p - 400 - p
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A 99% confidence interval for the mean of a population is such that:A. There is a 99% chance that it contains the standard deviation of the populationB. There is a 99% chance that it contains the mean of the populationC. There is a 99% chance that it contains all the values in the population.D. It contains 99% of the values in the population
Answers
Step 1
It means that there is a 99% chance that the interval you have calculated from your data (a random sample of some kind) covers the true value of what you are using that data to learn about.
This means that there is a 99% chance it contains all the values in the population
Answer;
[tex]Option\text{ C}[/tex]How do you write 4,260 in scientific notation?x 10Submit
Answers
4.26 × 10³
Explanation:To write 4260 in scientific notation, we would move the point from right to left starting at 0 to the place in between 4 and 2
The number of movement = 3
[tex]4260\text{ = 4.260}\times10^{n\text{ umber of movement}}[/tex][tex]\begin{gathered} 4260\text{ = 4.260}\times10^3 \\ =\text{ 4.26}\times10^3 \end{gathered}[/tex]Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?
Responses
3.5 meters
3.5 meters
45meters
7 meters
Answers
The distance he would've covered is 32.02m if he ran through a straight line.
What is Pythagoras's Theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
[tex]x^2 = y^2 + z^2\\[/tex]
Let's substitute the values into the equation and solve.
[tex]x^2 = 20^2 + 25^2\\x = 32.02m[/tex]
Jimmy would've jogged 32.02m if he ran through a straight line.
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The equation y = 10x represents the liters of water a baseball team drinks each practice. This equation shows that after three practices, the team will have consumed 30 liters of water.
Determine the constant of proportionality.
Answers
if equation y = 10x represents the liters of water a baseball team drinks each practice. This equation shows that after three practices, the team will have consumed 30 liters of water. Then 1/10 is constant of proportionality
What is Equation?
Two or more expressions with an Equal sign is called as Equation.
The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
The equation is y=10x
x 1 2 3 4 5
y 10 20 30 40 50
This represents the liters of water a baseball team drinks each practice.
It is given that After three practices, the team will have consumed 30 liters of water.
1/10, 2/20,3/30..
1/10 is the constant of proportionality.
Hence 1/10 is the constant of proportionality for equation y=10x.
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HELP ASAP 30 POINTS 9TH GRADE MATH. WILL GIVE BRAINIEST IF CORRECT
Solve.
Question 1.
-4x + 17 ≥ 9.
Question 2.
| 5 + z | + 3 = 10.
Question 3.
Match to the correct one
5y + 2 = 5y + 8. 1. All real numbers
2 (y + 4) = 2y + 8. 2. No solutions
5y + 2 = 2y + 8 3. Infinity many solutions.
Question 4.
Solve for x.
x - 4 ≥ 5. SHOW YOUR WORK.
question 5.
solve for x.
12x = 4 (2x -3) - 12.
SHOW YOUR WORK.
Question 7.
Solve for x
3(x + 2) = 3x + 2
Answers
Answer:
Question 1: x≤2
Question 2: z=2 or z=−12
Question 3: in the image above
Question 4: x≥9
Question 5: x = -6
Question 7: There are no solutions.
Step-by-step explanation:
Question 1
−4x+17≥9
Step 1: Subtract 17 from both sides.
−4x+17−17≥9−17
−4x≥−8
Step 2: Divide both sides by -4.
−4x
−4
≥
−8
−4
x≤2
------------------------------------
Question 2.
| 5 + z | + 3 = 10.
|5+z|+3=10
|z+5|+3=10
Step 1: Add -3 to both sides.
|z+5|+3+−3=10+−3
|z+5|=7
Step 2: Solve Absolute Value.
|z+5|=7
We know eitherz+5=7orz+5=−7
z+5=7(Possibility 1)
z+5−5=7−5(Subtract 5 from both sides)
z=2
z+5=−7(Possibility 2)
z+5−5=−7−5(Subtract 5 from both sides)
z=−12
------------------------------------
Question 3.
5y+2=5y+8
Step 1: Subtract 5y from both sides.
5y+2−5y=5y+8−5y
2=8
Step 2: Subtract 2 from both sides.
2−2=8−2
0=6
There are no solutions.
2(y+4)=2y+8
Step 1: Simplify both sides of the equation.
2(y+4)=2y+8
(2)(y)+(2)(4)=2y+8(Distribute)
2y+8=2y+8
Step 2: Subtract 2y from both sides.
2y+8−2y=2y+8−2y
8=8
Step 3: Subtract 8 from both sides.
8−8=8−8
0=0
All real numbers
5y+2=2y+8
Step 1: Subtract 2y from both sides.
5y+2−2y=2y+8−2y
3y+2=8
Step 2: Subtract 2 from both sides.
3y+2−2=8−2
3y=6
Step 3: Divide both sides by 3.
3y/3 = 6/3
y=2
This has a solution, check your question
------------------------------------
Question 4
x−4≥5
Step 1: Add 4 to both sides.
x−4+4≥5+4
x≥9
------------------------------------
Question 5
12x=4(2x−3)−12
Step 1: Simplify both sides of the equation.
12x=4(2x−3)−12
12x=(4)(2x)+(4)(−3)+−12(Distribute)
12x=8x+−12+−12
12x=(8x)+(−12+−12)(Combine Like Terms)
12x=8x+−24
12x=8x−24
Step 2: Subtract 8x from both sides.
12x−8x=8x−24−8x
4x=−24
Step 3: Divide both sides by 4.
4x/4 = −24/4
x=−6
------------------------------------
Question 6
3(x+2)=3x+2
Step 1: Simplify both sides of the equation.
3(x+2)=3x+2
(3)(x)+(3)(2)=3x+2(Distribute)
3x+6=3x+2
Step 2: Subtract 3x from both sides.
3x+6−3x=3x+2−3x
6=2
Step 3: Subtract 6 from both sides.
6−6=2−6
0=−4
There are no solutions.
Line A has a slope of −3 . Line B has a slope of 4. Line C has a slope of 2.
Which line is closest to being horizontal?
Line A
Line B
Line C
I don't know.
Answers
Line C is closest to being horizontal.
Given,
Line A has a slope of −3.
Line B has a slope of 4.
Line C has a slope of 2.
To find the which line is closest to being horizontal?
Now, According to the question:
Slope of line A (m1) = -3
Slope of line B (m2) = 4
Slope of line C (m3) = 2
Slope of horizontal line = 0
Closest to being horizontal is given by l m l
For line A = l-3 l = 3
For line B = l4l = 4
For line C = l2l = 2
As 2 is smaller it is closest to horizontal
Hence, Line C is closest to being horizontal.
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Use technology to find points and then graph the line y=-3(x-1)-4,y=−3(x−1)−4, following the instructions below.
Answers
Given the equation;
[tex]y=-3(x-1)-4[/tex]We asked to find some points and plot the graph.
Explanation
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Therefore, when x =0
[tex]\begin{gathered} y=-3(0-1)-4 \\ y=3-4 \\ y=-1 \end{gathered}[/tex]When x =1
[tex]\begin{gathered} y=-3(1-1)-4 \\ y=-4 \end{gathered}[/tex]Therefore, the graph of the equation can be seen below.
Find the rational function which represents the graph. If you could help with both sections that would be amazing
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given points on the graph
[tex]\begin{gathered} \text{ Points are given in the form of }(x,y) \\ \therefore\text{ points are:} \\ (x_1,y_1)=(2,0) \\ (x_2,y_2)=(0,-2) \end{gathered}[/tex]STEP 2: Write the slope-intercept form of the equation of a line
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}[/tex]STEP 3: Write the formula to get the equation of a line using two given points
[tex](y-y_1)=m(x-x_1)[/tex]STEP 4: We use the given points to get the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]STEP 5: Substitute the given points into the formula in step 4 to get the slope
[tex]m=\frac{-2-0}{0-2}=\frac{-2}{-2}=1[/tex]STEP 6: Since we have a slope and two points, we use the formula in step 3 to get the function that represents the line
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ U\sin g\text{ point }(2,0) \\ (y-0)=1(x-2) \\ y=1(x-2) \\ y=x-2 \end{gathered}[/tex]STEP 7: We get the rational function of the line using the given hole
[tex]\begin{gathered} \text{hole}=(5,3) \\ \text{equation of line }\Rightarrow y=x-2 \\ \\ To\text{ get the rational function, we write the function of each coordinate that makes it undefined} \\ (5,3)\Rightarrow x=5\Rightarrow x-5 \\ (5,3)\Rightarrow y=3\Rightarrow y-3 \\ We\text{ divide the equation of the line in step 6 by the expressions above} \\ \text{Hence, the rational function is given as:} \\ \frac{y}{y-3}=\frac{x-2}{x-5} \end{gathered}[/tex]Hence, the rational function representing the line with the given hole is:
[tex]\frac{y}{y-3}=\frac{x-2}{x-5}[/tex]GIVING 200 POINTS 2 QUESTIONS WILL GIVE BRAINLYEST
Answers
Answer:
Question 1 = 18.5 6618.375 / 357.75 = 18.5
Question 3 = 1542 m^2
Quetion 4 = 560 inch ^ 3
Step-by-step explanation:
Question 1 = 18.5 6618.375 / 357.75 = 18.5
Question 3 = 26214 / 17 = 1542. Since dividing m^3 you get m^2.
Question 4 = 560 inch ^ 3 10*14*4
Answer:
Question 1 = 18.5 6618.375 / 357.75 = 18.5Question 3 = 1542 m^2Quetion 4 = 560 inch ^ 3Step-by-step explanation:Question 1 = 18.5 6618.375 / 357.75 = 18.5Question 3 = 26214 / 17 = 1542. Since dividing m^3 you get m^2. Question 4 = 560 inch ^ 3 10*14*4
Step-by-step explanation:
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 259.1 and a standard deviation of 68.2. (All units are 1000 cells/µl.) Using the empirical
rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 54.5 and 463.77
b. What is the approximate percentage of women with platelet counts between 122.7 and 395.5?
a. Approximately % of women in this group have platelet counts within 3 standard deviations of the mean, or between 54.5 and 463.7
(Type an integer or a decimal. Do not round.)
PLEASE HELP ASAP
Answers
Using the Empirical Rule, it is found that:
a. Approximately 99.7% of women in this group have platelet counts within 3 standard deviations of the mean, or between 54.5 and 463.7.
b. Approximately 95% of women in this group have platelet counts between 122.7 and 395.5.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of 68%.The percentage of scores within two standard deviations of the mean of the distribution is of 95%.The percentage of scores within three standard deviations of the mean off the distribution is of 99.7%.Hence for item a the percentage is of 99.7%, as the measures are within 3 standard deviations of the mean.
In item b, the measures are within two standard deviations of the mean, as:
259.1 - 2 x 68.2 = 122.7.259.1 + 2 x 68.2 = 395.5.Hence the percentage is of 95.5%.
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5. Jenny has $65 in her checking account. She bought 9 equally priced DVDs and paid with acheck. Her new account balance is $32. How much was each DVD?
Answers
This implies that, the money spent on the 9 equally priced DVDs is:
[tex]\text{Money Spent on the 9 equally priced DVDs= 65 -32 =\$3}3[/tex]Therefore, the amount spent on each DVD is:
[tex]\frac{33}{9}=\text{ \$3.67}[/tex]Hence, each DVD costs $3.67
Find the area and the circumference of a circle with diameter 8cmUse 3.14 for n , and do not round your answer
Answers
ANSWER:
Circumference of the circle is 25.12 centimeters
Area of the circle is 50.24 square centimeters
STEP-BY-STEP EXPLANATION:
We have that the formula for the circumference and the area are the following:
[tex]\begin{gathered} c=2\cdot\pi\cdot r \\ A=\pi\cdot r^2 \end{gathered}[/tex]The radius is equivalent to half the diameter, therefore, we replace:
[tex]\begin{gathered} r=\frac{d}{2}=\frac{8}{2}=4 \\ \text{ replacing} \\ c=2\cdot3.14\cdot4=25.12\text{ cm} \\ A=3.14\cdot4^2=50.24cm^2 \end{gathered}[/tex]the circumference of the circle is 25.12 cm and the area is equal to 50.24 square centimeters
I need help with this question! I worked it out however my answer is not an answer choice.
Answers
The given expression is:
[tex]undefined[/tex]1) Drag and drop the numbers to place them in increasing order.
-1.6
0.6
- 1/6
3/7
2) Drag and drop the numbers to place them in increasing order.
-1.3
1.4
-0.6
0.7
Answers
The most appropriate choice for ascending order and descending order will be given by -
1) Numbers in increasing order are -1.6, [tex]-\frac{1}{6}[/tex], [tex]\frac{3}{7}[/tex], 0.6
2) Numbers in increasing order = -1.3, -0.6, 0,7, 1.4
What is ascending order and descending order?
Ascending order is the method of arranging of set of numbers from their lowest value to their highest value.
Descending order is the method of arranging of set of numbers from their highest value to their lowest value.
Here,
1)
[tex]-\frac{1}{6} = -0.167[/tex]
[tex]\frac{3}{7} = 0.429[/tex]
Numbers in increasing order are -1.6, -0.167, 0.429, 0.6
Numbers in increasing order are -1.6, [tex]-\frac{1}{6}[/tex], [tex]\frac{3}{7}[/tex], 0.6
2)
Numbers in increasing order = -1.3, -0.6, 0,7, 1.4
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help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answers
By using the graph of the given function, the value of x such that f(x) = -3 is -2.
What is a graph?A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the x-intercept of any graph simply refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).
By critically observing the graph which models the data of this function, we can reasonably and logically deduce that the value of x when the function, f(x) = -3 is is equal to -2.
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Kavin made the 10 number cardsshown below.444N11997Gavin shuffled the cards and thenflipped them over so his friend Rickcould not see the numbers. If Rickrandomly chose one of the cards, hewas more likely to choose a card witha 4 than a card withA an odd numberB a prime numberC another even numberD an odd number less than 7
Answers
We have a total of 10 cards.
From these 10 cards, three cards are number 4, so the probability of choosing a number 4 is P = 3/10.
Calculating the probability for each option, we have:
A. Odd number
There are 6 odd numbers among the cards, so the probability is P = 6/10
B. Prime number
There are 3 prime numbers among the cards, so the probability is P = 3/10
C. Another even number
There are 4 even numbers among the cards, so the probability is P = 4/10
D. An odd number less than 7.
There are 3 odd numbers less than 7, so the probability is P = 3/10
The bigger probability is for an odd number, therefore the correct option is A.
−|a+b|/2−c when a = 1 3/5 , b = −2 , and c = −7
Answers
Answer: the answer should be -2/25
Step-by-step explanation:
I took the test.
Parents plan to ship some items to their child who is attending college out of town. Thestudent definitely needs towels, which weigh 9 pounds. The cost is $45 to ship up to 15pounds.a. Write and solve an inequality that represents how many pounds the parents can add tothe shipment without having to pay additional shipping costs
Answers
Answer
The inequality equation is
(9 + x) ≤ 15
The solution is
x ≤ 6 pounds
The number of pounds that the parents can add to the shipment without having to pay additional shipping costs is less than or equal to 6 pounds.
Step-by-step Explanation
The question wants us to write and solve an inequality that represents how many pounds the parents can add to the shipment without having to pay additional shipping costs.
The towels needed by the student already weigh 9 pounds.
The maximum weight of shipment that is allowable for a payment of $45 is 15 pounds.
Let the additional weight that the parents can add to the shipment without having to pay additional shipping costs be x.
Since the maximum weight allowable is 15 pounds, the 9 pounds already on ground plus the additional x pounds must not exceed 15 pounds. That is, that total weight must always be less than or equal to 15 pounds.
Mathematically,
(9 + x) ≤ 15
This is the inequality equation. We can now solve this
(9 + x) ≤ 15
Subtract 9 from both sides
(9 + x) - 9 ≤ 15 - 9
9 + x - 9 ≤ 6
x ≤ 6
Hence, the number of pounds that the parents can add to the shipment without having to pay additional shipping costs is less than or equal to 6 pounds.
Hope this Helps!!!
Plot the given parabola on the axes. Plot the roots, the vertex and two other points.
Answers
Solution
Step 1:
The first two points are the roots of the parabola.
To get the roots of the parabola, equate y = 0
[tex]\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7)-5(x + 7) = 0} \\ (x\text{ + 7)(x - 5) = 0} \\ x\text{ = -7 , x = 5} \\ \text{The parabola intercept x-axis at (-7, 0) and (5 , 0)} \end{gathered}[/tex]Step 2:
Find the y-intercept.
To find the y-intercept, plug x = 0
[tex]\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ y=0^2\text{ + 2}\times0\text{ - 35} \\ y\text{ = -35} \\ y-\text{intercept is (0 , -35)} \end{gathered}[/tex]Step 3:
Find the vertex
[tex]\begin{gathered} \text{The vertex is (}\frac{-b}{2a}\text{ , y)} \\ b\text{ = 2, a = 1} \\ x\text{ = }\frac{-b}{2a} \\ x\text{ = }\frac{-2}{2\times1} \\ x\text{ = }\frac{-2}{2} \\ x\text{ = -1} \\ y=(-1)^2\text{ + 2(-1) - 35} \\ y\text{ = 1 - 2 - 35} \\ y\text{ = -36} \\ \text{Vertex = (-1, -36)} \end{gathered}[/tex]Final answer
All the five points are:
Roots (x-intercept) = (-7, 0) , (5 , 0)
y-intercept = (0, -35)
vertex = (-1, -36)
Other point = (-5, -20)
Use the four-step procedure for solving the following variation problem.The height that a ball bounces varies directly as the height from which it was dropped. A tennis ball dropped from 17 inches bounces 11.9 inches. From what height was the tennis ball dropped if it bounces 42 inches?The tennis ball needs to be dropped from the height of ?that it bounces 42 inches.(Type an integer or a decimal.)
Answers
If we drop a ball from 60 inches height it bounces 42 iches.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
The height that a ball bounces varies directly as the height from which it was dropped.
A tennis ball dropped from 17 inches bounces 11.9 inches.
We need to find from which height if we drop a ball bounces 42 iches.
Let us consider x as the unknown height
Let us form a equation by the given data
17/11.9=x/42
Apply cross multiplication
17×42=11.9x
714=11.9x
Divide both sides by 11.9
60=x
Hence if we drop a ball from 60 inches height it bounces 42 inches.
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If line q has a slope of -3, what is the slope of any line perpendicular to q?
Answers
The slope of the perpendicular line is equal to -3.
What is the slope of a line?
A line's slope provides information on the steepness and direction of the line. By determining the difference seen between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of either a straight line through them. The letter "m" is frequently used to denote slope.Two lines must have a slope product of -1 in order to be perpendicular to one another.Given that,
the slope of line q, m= -3
the slope of any line perpendicular to given line q=1/m
1/-3
=-3
The slope of the perpendicular line is equal to -3.
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Find the equation for the tangent to the curve of f at the point:f(x) = (3x+1)² , x = -1
Answers
The eqaution of the tangent at the point x = -1 is:
[tex]y=-12x-8[/tex]To solve this, first, we need to find the value of y when x = -1:
[tex]f(-1)=(3\cdot(-1)+1)^2=(-3+1)^2=(-2)^2=4[/tex]Then we want to find the equation of the tangent at the point (-1, 4)
The next step is to find the derivative of the equation, because the derivative thell us the slope of the tangent line at a certain point:
[tex]\begin{gathered} f(x)=(3x+1)^2 \\ f^{\prime}(x)=2(3x+1)\cdot3=6(3x+1)=18x+6 \\ \\ f^{\prime}(x)=18x+6 \end{gathered}[/tex]Now that we have the derivative, let's calculate the slope of the tangent like in the point (-1, 4). To do this, we evaluate the derivative in x = -1:
[tex]f^{\prime}(-1)=18\cdot(-1)+6=-18+6=-12[/tex]The slope of the tangent line is -12.
Now we have all the necessary things to construct the equation of a line: we have the slope (-12) and a point (-1, 4).
The slope-point form of a line is:
[tex]\begin{gathered} y=m(x-x_0)+y_0 \\ \end{gathered}[/tex]Where m is the slope and x0, y0 are the x and y coordinates of a point
Then:
[tex]\begin{gathered} \begin{cases}m=-12 \\ x_0=-1 \\ y_0=4\end{cases} \\ y=-12(x-(-1))+4=-12\mleft(x+1\mright)+4=-12x-12+4=-12x-8 \end{gathered}[/tex]And that's the equation of the line y = -12x - 8
