The maximum area istype your answer...ft in length by type your answer...ft in width
Answers
The measurements are
1. 4unit by 4 unit
2. 6 unit by 2 unit
3. 5 units by 3 units
4. 1 units by 7 units
To arrange the area from the largest to the smallest we have to compute the area of the measurements.
[tex]\begin{gathered} \text{area = lw} \\ \text{area}=\text{ 4}\times4=16units^2 \\ \text{area}=\text{ 6}\times2=12units^2 \\ \text{area}=\text{ 5}\times3=15units^2 \\ \text{area}=\text{ 1}\times7=7units^2 \end{gathered}[/tex]The arrangement from highest to smallest is represented as follows
4units by 4 units
5 units by 3 units
6 units by 2 units
1 unit by 7 units
Related Questions
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]Find the exact value of sin 120° in simplest form with a rationaldenominator.
Answers
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.
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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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
An industrial machine made 1,629 cans of diet sodas and 6 times as many
regular sodas over the course of 46 minutes. The regular sodas were then
placed into 3 shipping boxes with each shipping box containing the same
number of sodas. How many regular sodas were in each shipping box.
Answers
Each of the shipping boxes contains 2172 cans of regular soda.
Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion.
The industrial machine made a total of 1629 cans of diet soda which is 6 times as much regular soda in 46 minutes.
Then, the total number of regular sodas made will be:
R = 4 × Total number of diet soda
R = 4 × 1629 cans
R = 6516 cans
The regular sodas were packed in 3 shipping boxes with each having the same number of soda cans.
Therefore, the number of cans of regular sodas in each box will be:
N = 6516/3
N = 2172 cans
There are 2172 cans of regular sodas in each shipping box.
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On a recent test, Mark got 6 questions out of 40 wrong. Which answer best describes the percent of questions he got correct?
Answers
answer 85%
Step-by-step explanation:
6-40=34
100 divide by 40
2.5 times 34
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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This hutch is made up of two rectangular prisms. 1 7 ft 2 ft 2 127 ft 22 ft 4 ft What is the total volume of this hutch, in cubic feet?
Answers
Answer
40 cubic feet
Step-by-step explanation
The volume of a rectangular prism is calculated as follows:
[tex]V=whl[/tex]where w is the width, h is the height and l is the length of the prism.
The hutch is made up of two rectangular prisms, one with a width of 1 1/3 ft, a height of 2 1/2 ft, and a length of 4 ft. The other one has a width of 2 2/3 ft, a height of 2 1/2 ft, and a length of 4 ft.
To calculate the volume of the hutch, first, we need to calculate the volume of each prism, and then add them.
The volume of the smaller prism is:
[tex]\begin{gathered} V_1=1\frac{1}{3}\cdot2\frac{1}{2}\cdot4 \\ V_1=13\frac{1}{3}\text{ cubic feet} \end{gathered}[/tex]The volume of the bigger prism is:
[tex]\begin{gathered} V_2=2\frac{2}{3}\cdot2\frac{1}{2}\cdot4 \\ V_2=26\frac{2}{3}\text{ cubic feet} \end{gathered}[/tex]Finally, the volume of the hutch is:
[tex]V_1+V_2=13\frac{1}{3}+26\frac{2}{3}=40\text{ cubic feet}[/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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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.
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
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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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]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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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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use a calculator.15. Select all the numbers that are solutions to the equation x2 = 15. (2 pt)A. 225B. 225C. 7.5D. 715E. -V15
Answers
√15, and -√15
1) Considering the equation below, let's solve it:
[tex]\begin{gathered} x^2=15 \\ \sqrt[]{x^2}=\sqrt[]{15} \\ x=\sqrt[]{15},\text{ -}\sqrt[]{15} \end{gathered}[/tex]2) So the answer is √15, and -√15
Since (√15)² = 15 and (-√15)²=15
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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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:
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]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.
Write the equation below in standard form. Show work. 8/3y = 5/6x - 2
Answers
To write the equation in standard form:
Step 1. Multiply the expression by 6
[tex]\begin{gathered} (\frac{8}{3}y=\frac{5}{6}x-2)\cdot6 \\ 16y=5x-12 \end{gathered}[/tex]Step 2. Clear the independent term
[tex]\begin{gathered} 16y=5x-12 \\ 16y-5x=-12 \end{gathered}[/tex]The equation in standard form is 16y-5x=-12
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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what is the area of a parallelogram with a side of 11 8 and 10
Answers
The area of the parallelogram with dimensions 11.8 units and 10 units is 118 square units
How to find the area of a parallelogramParallelogram is a general term that refers to quadrilaterals with the opposite sides parallel to each order
Area refers to the space covered by an object or extent covered
Hence to find the pace covered by the parallelogram which is the area of the parallelogram we multiply the both sides as follows
let the length, L = 11.8 units and width, w = 10 units
Area of parallelogram = L * w
= 11.8 * 10
= 118 square units
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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.
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!!!
−|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.
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)
factor this polynomial completely[tex] {x}^{2} - 8x + 16[/tex]
Answers
Solution.
[tex]\begin{gathered} Given \\ x^2-8x+16 \\ =x^2-4x-4x+16 \\ =x(x-4)-4(x-4) \\ =(x-4)(x-4) \end{gathered}[/tex]The answer is (x-4)(x-4)
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
