The area of Circle B could be about 300 in², about 900 in², or about 2,700 in² depending on its radius.
To determine which one is correct, you would need to know the radius or diameter of the circle.
Use the formula for the area of a circle, which is
A = πr²,
where A is the area and
r is the radius.
If you have the radius, plug it into the formula and calculate the area.
Compare the calculated area to the options provided (300 in², 900 in², or 2,700 in²)
to determine which one is closest to the area of Circle B.
Without more information about Circle B's radius or diameter, it is impossible to determine the exact area from the
options given.
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The polling results show the ratio of votes for candidate A to candidate B
15 18
25 30
35 42
45 ?
at this rate, if candidate A received 45 votes did candidate B receive
ANSWERS: A.54 B.56 C.60 D.90
Answer:
54
Step-by-step explanation:
if you look at the ratios between the values of A and B. you will see that the successive values of A increase by 10 while B increase by 12
Therefore for A
35 + 10 = 45
for B
42 + 12 = 54
"Zola sold 540 eggs. If these are 36% of the total eggs. Then how many are not sold?
Answer: 960 eggs are not sold.
Step-by-step explanation:
Let t be the number of total eggs.
36%(t) = 540
0.36(t) = 540
t = 1500
1500 - 540 = 960
PLEASE SHOW WORK!!!!!!!!!
The monthly percent decrease in average weekly crate production from Month A to Month B is 40%.
How is a % determined? What is a percentage?A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for it. Percentages are frequently used to represent change or growth over time and to compare two values. Finding the proportion of the quantity you are interested in to the total is necessary before you can compute a percentage. The percentage is then calculated by multiplying the ratio by 100.
For Month A the production is:
2000 + 3000 + 2000 + 3000 = 10,000
Thus, average weekly production is:
A = 10,000 / 4
A = 2500
For month B we have:
2000 + 1000 + 3000 + 0 = 6000
Average weekly crate production is:
= 6000 / 4
= 1500
The percentage decrease is given by:
percent decrease = [(original value - new value) / original value] x 100%
= [(2500 - 1500) / 2500] x 100%
= 40%
Therefore, the monthly percent decrease in average weekly crate production from Month A to Month B is 40%.
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4.02 Lesson check ! (5)
The given sequence is not an arithmetic sequence. Option B is correct.
Determining the common difference of a sequenceGiven the sequence below
-2, -8, -32, -128
The nth term of an arithmetic sequence is given as Tn = a + (n-1)d
The common difference is the difference between the preceding and the succeeding term.
First term = -2
Second term = -8
Common difference = -8 -(-2) = -6
d= -32 + 8 = -24
Since the values are not equal, hence the sequence is not an arithmetic sequence.
Hence the common difference of the sequence is 8
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The net below represents a container. A net consisting of three same-sized rectangles and two small triangles, one on each end of the center rectangle. Part A What solid figure does it show? Triangular prism Rectangular prism Triangular pyramid Rectangular pyramid Part B How many vertices does the container have? Enter your answer in the box. vertices
Answer:
b
d
. ._-_-_-__---_--_--_----___-_--------_--------------------------__-_______--_-__-________---_-_--___-----__--
Find the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2).Use the linear approximation to estimate the value of ????(0.9,−1.9)f(0.9,−1.9) =
The linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is (x,y)≈6.4−4(x−1)−6(y+2). Using this linear approximation, we can estimate the value of (0.9,−1.9) to be approximately 6.1.
To explain further, linear approximation is a method used to approximate a function with a linear equation near a given point. We use linear approximation to estimate the value of a function at a certain point without actually having to evaluate it.
First, we find the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2). We do this by finding the derivative of ????(x,y) with respect to x and y and substituting the coordinates of the given point.
Taking the partial derivative of ????(x,y) with respect to x, we get ????x(x,y)=4x−4 and substituting x = 1 and y = -2, we get ????x(1,−2)=−4.
Similarly, taking the partial derivative of ????(x,y) with respect to y, we get ????y(x,y)=−6y−6 and substituting x = 1 and y = -2, we get ????y(1,−2)=18.
Therefore, the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is ????(x,y)≈6.4−4(x−1)−6(y+2).
Using this linear approximation, we can estimate the value of ????(0.9,−1.9) to be approximately 6.1. We do this by substituting x = 0.9 and y = -1.9 in the linear approximation, which gives us ????(0.9,−1.9)≈6.1.
Hence, the value of ????(0.9,−1.9) is estimated to be approximately 6.1 using the linear approximation of the function ????(x,y)=18−2x2−3y2 at the point (1, -2).
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Lauri spent 4% of x hours at her part time job. What is x if 4% of x is about 32 hours? Explain how you estimated and which property of equality you used to find it x. Please don't answer random stuff. Any spam or irrelevant answers will be reported
Lauri spent 4% of 800 hours at her part time job, which is about 32 hours. The property of equality was used to solve for x.
To estimate x, we can use the property of equality. This property states that if two equations are equal, then the two sides of the equation are equal. Therefore, if we know that 4% of x is about 32 hours, we can set up an equation and solve for x. The equation is 4% of x = 32 hours. We can convert 4% to a decimal by dividing 4 by 100, which gives us 0.04. This can then be rewritten as 0.04x = 32 hours. To solve for x, we can divide both sides by 0.04. This gives us x = 800 hours. This means that if Lauri spends 4% of x hours at her part time job, then x must be 800 hours.
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a line segment is drawn between (6,4) and (8,3). Find its gradient, midpoint and length.
Answer:
Gradient of the line segment:
The gradient of a line segment is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:
m = (3 - 4) / (8 - 6) = -1/2
Therefore, the gradient of the line segment is -1/2.
Midpoint of the line segment:
The midpoint of a line segment is given by the formula:
((x1 + x2) / 2, (y1 + y2) / 2)
In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:
((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)
Therefore, the midpoint of the line segment is (7, 3.5).
Length of the line segment:
The length of a line segment is given by the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:
d = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(2^2 + (-1)^2) = sqrt(5)
Therefore, the length of the line segment is sqrt(5).
Answer:
To find the gradient of the line segment, we use the formula:
gradient = (change in y) / (change in x)
So, gradient = (3 - 4) / (8 - 6) = -1/2
To find the midpoint of the line segment, we use the formula:
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
So, midpoint = ((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)
To find the length of the line segment, we use the distance formula:
length = sqrt((x2 - x1)^2 + (y2 - y1)^2)
So, length = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(5)
Therefore, the gradient of the line segment is -1/2, the midpoint is (7, 3.5), and the length is sqrt(5).
Prove:
△BEC≅△DEA\triangle BEC \cong \triangle DEA
△BEC≅△DEA
We meet the SAS requirement for congruence because the two triangles share two congruent sides as well as the included angle.
To prove that △BEC≅△DEA, we can use the Side-Angle-Side (SAS) congruence theorem.
First, we can see that BE=ED, as both are radii of the same circle.
Secondly, angle BEC and angle DEA are both 90 degrees, as they are inscribed angles that subtend the same arc BD.
Lastly, we can see that EC=EA, as they are both radii of the same circle.
Therefore, we have the two triangles sharing two congruent sides and the included angle, satisfying the SAS criterion for congruence. Hence, we can conclude that △BEC≅△DEA.
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Please help NOW ASAP
What is a credit score?
Question 28 options:
It is a number that helps lenders assess how well you manage your financial obligations in the past.
It is a number that tells you how many credit cards you have open.
It is a number that tells you how much you owe.
It is a number that grades you on your use of credit cards.
Answer:
Step-by-step explanation:
A credit score is a number that helps lenders assess how well you manage your financial obligations in the past.
I hope this helps.
Write the perimeter of the triangle as a simplified polynomial. Then factor the polynomial.
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
1. different ratios that can be formed from the original ratio
ratio
2. a comparison of two quantities or numbers
tape diagram
3. a comparison of one part of a whole to another part of the same whole
part-to-whole ratio
4. a comparison of a part and its whole
associated ratios
5. a drawing that looks like a section of tape and demonstrates a relationship between quantities
part-to-part ratio
PLEASE HELP ASAP P L E A S EEEE
1. If the οriginal ratiο is 2:3, we can fοrm different ratiοs by:
Multiplying bοth the numeratοr and denοminatοr by the same number, such as 2:3 x 2 = 4:6 οr 2:3 x 3 = 6:9
Dividing bοth the numeratοr and denοminatοr by the same number, such as 2:3 ÷ 2 = 1:1.5 οr 2:3 ÷ 3 = 0.67:1
Examples οf ratiο, tape diagram, part-tο-whοle ratiο, assοciated ratiοs, part-tο-part ratiο?Any ratiο that is equivalent tο the οriginal ratiο can be fοrmed in this way
2. Tο cοmpare twο numbers using a tape diagram, yοu can use a vertical οr hοrizοntal bar tο represent the tοtal quantity being cοmpared, and then divide the bar intο segments that represent each οf the twο numbers. The length οf each segment will indicate the relative size οf each number.
3. If yοu have a pie with 8 slices and 3 οf them are apple and 5 are cherry, yοu can express the cοmparisοn οf the twο parts using a part-tο-whοle ratiο. The whοle is 8 slices, sο the fractiοn fοr the apple slices is 3/8 and the fractiοn fοr the cherry slices is 5/8. Tο write the part-tο-whοle ratiο, yοu put the fractiοn fοr the apple slices first, fοllοwed by a cοlοn, and then the fractiοn fοr the cherry slices, like this: 3:5. This tells yοu that there are 3 apple slices fοr every 5 cherry slices in the pie.
4. Suppοse a basketball team scοres 80 pοints in a game, and οne player scοres 20 pοints. Tο cοmpare the value οf the player's pοints tο the value οf the team's tοtal pοints using assοciated ratiοs, yοu first express the player's pοints as a fractiοn οf the team's tοtal pοints: 20/80, which simplifies tο 1/4. Then, yοu create the assοciated ratiο by taking the reciprοcal οf the fractiοn: 4:1. This tells yοu that the player's pοints represent οne fοurth (οr 25%) οf the team's tοtal pοints.
5. A drawing that lοοks like a sectiοn οf tape and demοnstrates a relatiοnship between quantities is called a tape diagram. Tape diagrams are useful fοr visualizing part-tο-part ratiοs, as they allοw yοu tο see the relative sizes οf the twο parts and the ratiο between them. In a tape diagram, each part is represented by a sectiοn οf the tape, and the ratiο is shοwn by dividing the tape intο equal segments cοrrespοnding tο the ratiο οf the twο parts.
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enid jogs on a treadmill for exercise. each time she finishes jogging, the treadmill will report the number of calories she burned. enid claims that the distance she jogs and the number of calories she burns are in a proportional relationship. data from her last four jogs are shown.
Yes, Enid is correct that the distance she jogs and the number of calories she burns are in a proportional relationship. This means that as the distance she jogs increases, the number of calories she burns also increases at a constant rate.
To see this proportional relationship, we can look at the data from her last four jogs on the treadmill. Let's say that the distance she jogged is represented by x and the number of calories she burned is represented by y.
If we divide the number of calories she burned (y) by the distance she jogged (x), we should get the same constant rate for each of her four jogs.
For example, if she jogged 2 miles and burned 200 calories, the constant rate would be 200/2 = 100. If she jogged 4 miles and burned 400 calories, the constant rate would also be 400/4 = 100.
This shows that there is a proportional relationship between the distance she jogs and the number of calories she burns on the treadmill. The constant rate in this case is 100, which means that for every 1 mile she jogs, she burns 100 calories.
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(10 points) Consider the following data from a sample of n=7 . x: 168 178 176 174 178 174 172 y: 50 57 55 55 58 54 53 The y-intercept of the least squares line is -72.1818181818182. Compute the slope of the least squares line and enter the equation of the least squares line below. (As always, if you round, make sure you do so correctly, only round your final answer, and keep at least three decimal places.) The least squares line is y=
The equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.
(10 points) Consider the following data from a sample of n=7 . x: 168 178 176 174 178 174 172 y: 50 57 55 55 58 54 53The y-intercept of the least squares line is given as -72.1818181818182. We have to calculate the slope of the least squares line and input the equation of the least squares line. The given data is shown below:X: 168 178 176 174 178 174 172Y: 50 57 55 55 58 54 53We know that y-intercept of the least squares line is given by b = ybar - m * xbarwhere xbar = (1/n) * ∑x and ybar = (1/n) * ∑y. Now, to calculate the slope of the least squares line, we need to calculate the value of the numerator of the following equation:Slope, m = [(n∑xy) - (∑x∑y)] / [(n∑x^2) - (∑x)^2]Here, ∑x and ∑y are the summations of x and y values, respectively. ∑xy is the sum of the products of each x and y value, and ∑x^2 is the sum of each x value squared. So, let's calculate all of these values for the given data.We have, n = 7∑x = 1202∑y = 382∑x^2 = 213468∑xy = 71848Now, substituting these values in the formula of slope, we have:Slope, m = [(7 * 71848) - (1202 * 382)] / [(7 * 213468) - (1202)^2] = 3.6000630680907Therefore, the slope of the least squares line is 3.600. Now, we can use the slope and the y-intercept to find the equation of the least squares line. Therefore, the equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.
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Ross has a rectangular garden in his backyard. He measures one side of the garden as 30 feet and diagonal as 33 feet. What is the length of the other side of his garden? Round to the nearest tenth of a foot
Thus, the length of the other side of Ross's garden is 18 feet.
Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
To find the length of the other side of Ross's garden, we can use the Pythagorean theorem.
In this case, let's assume the length of the other side of Ross's garden x.
We can set up the following equation:
x² + 30² = 33²
Solving for x, we get:
x² = 33² - 30²
x² = 1089 - 900
x² = 289
x = √289
x = 17.
Thus, the length of the other side of Ross's garden is 18 feet.
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Form an equation in u and show it simplifies to 2u^2-20u+36=0
(u - 5 + (7))(u - 5 - (7)) = 0 is the equation we created in u that simplifies to 2u2 - 20u + 36 = 0.
What exactly are equations, and what varieties exist?The two forms of equations are identity equations and conditional equations. The variables all have the same identity for all conceivable values.
Creating an equation in u that can be solved for 2u² - 20u + 36 = 0
It indicates that the following are the solutions for x for a quadratic equation of the form ax² + bx + c = 0:
x = (-b±√(b²-4ac))/2a
By dividing both sides by 2, we can rewrite the equation 2u2 - 20u + 36 = 0 as follows:
u² - 10u + 18 = 0
u = (-(-10) ± √((-10)² - 4(1)(18))) / 2(1)
Simplifying this expression, we get:
u = (10 ± √(100 - 72)) / 2
u = (10 ± √(28)) / 2
u = (10 ± 2√(7)) / 2
u = 5 ± √(7)
A quadratic equation with roots r1 and r2 can be expressed as: This allows us to merge the two solutions into a single equation.
(x - r1)(x - r2) = 0
By substituting in the two answers we discovered for u, we obtain:
(u - 5 + √(7))(u - 5 - √(7)) = 0
Extending this phrase results in:
u² - 10u + 18 = 0
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An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $1300 and her stock in Company B was worth $4820. The stock in Company A has decreased 22% since last year and the stock in Company B has decreased 25%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
The investor's stock balance has decreased by a total of [tex]24.36[/tex]%.
Do investors count as owners?You aren't a property owner; you are a lending investor. You have invested in ownership if you purchase stock in a corporation. Your proportionate part of the company's profits will be deducted from the return you get. The original investment sum will continue to be correlated to the overall worth of the business.
What becoming an investor entails?The investors is someone or something that makes investments in other persons or groups with the intention of profiting to them in the future. On principle, everyone who invests money for something qualifies as an investor.
The decrease in stock A,
[tex]= 1300 * 22[/tex]%
[tex]= 286[/tex]
Decrease in stock B,
[tex]= 4820 * 25[/tex]%
[tex]= 1205[/tex]
Total decrease [tex]= 286+1205[/tex]
[tex]= 1491[/tex]
Total percentage decrease,
[tex]= (1491 / (1300 + 4820) ) * 100[/tex]%
[tex]= 1491 / 6120 * 100[/tex]%
[tex]= 24.36[/tex]%
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words from a written text the person can remember after five minutes with the text.
The words from a written text that a person can remember after five minutes with the text are known as short-term memory.
Short-term memory refers to the storage of information for a brief period of time, usually a few seconds to a few minutes. It is a type of memory that is involved in the conscious processing of information and is responsible for holding information in mind for immediate use.
The capacity of short-term memory is limited and varies from person to person. Generally, it can hold about 7 pieces of information or less, and can only hold it for a short period of time. This is why it is important to transfer important information from short-term memory to long-term memory through a process called encoding.
To improve short-term memory, one can use techniques such as repetition, chunking, visualization, and association. By doing this, it is possible to hold more information in short-term memory for a longer period of time.
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Solve the linear equation x-9=\frac{3}{5}xx−9=
5
3
x (Please put your answer as a decimal. )
The solution to the equation is x = 22.5.
To solve the equation x-9 = (3/5)x, we can first simplify the right-hand side by multiplying both sides by 5 to get rid of the fraction:
5(x-9) = 3x
An equation is a mathematical statement that indicates the equality of two expressions. Equations typically contain variables, which are represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equals sign are called the left-hand side and right-hand side of the equation.
Expanding the left-hand side, we get
5x - 45 = 3x
Next, we can simplify by subtracting 3x from both sides:
2x - 45 = 0
Adding 45 to both sides, we get:
2x = 45
Finally, dividing both sides by 2, we get:
x = 22.5
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Ryan made strawberry jam and raspberry jam. He made enough strawberry jam to fill 1/8 of a jar. If he made 1/3 as much raspberry jam as strawberry jam, how many jars will the raspberry jam fill?
Write your answer as a fraction or as a whole or mixed number.
_______ jars
The number of jars of raspberry jam filled is required.
The number of jars of raspberry jam is 1/24
Fraction:
A fraction represents a part of a whole, or more generally, any number of equal parts. In common English, a fraction describes the number of parts of a certain size, such as half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator that appears above (or before a slash, such as 1⁄2) a line, and a non-zero denominator that appears. Multipliers and denominators are also used in less common fractions, including complex, complex, and mixed fractions.
According to the Question:
The number of jars of strawberry jam is 1/8 jars.
The number of jars of raspberry jam is half of the number of jars of strawberry jam.
So,
1/8 × 1/3
= 1/24
The number of jars of raspberry jam is 1/24.
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[tex]\frac{4}{7} +\frac{3}{4} +\frac{1}{8}[/tex]
I need help!! Please, I'll give brainliest!
Answer:
429
Step-by-step explanation:
For what values of c does the quadratic equation [tex]x^2-2x+c=0[/tex] have:
a. no real roots
b. two roots of the same sign
c. one root equal to zero and one negative root
d. two roots of opposite signs
Answer:
Step-by-step explanation:
a: in the quadratic formula, no real roots would mean b^2 - 4ac<0 because of the discriminant. b^2 is 4, so all 4c has to satisfy is that it’s greater than 4. Solving, c>1
b: casework:
Both are negative: This is impossible because square roots are always positive, so at least one would always be positive.
Both are positive: sqrt(4-4c)<2. 0<c<=1.
c. I’m not entirely sure of what you mean, but when c=0, 0 is a root of the quadratic equation, but the other root is positive 2, so no value?
d. sqrt(4-4c)>2. Another possibility is that the same thing is less than -2, but square roots are always positive. This remains true for c<0.
Example 22: Find angle a, b and c ? a bº Co 106⁰ 35
According to the figure the value of a b and c is
a = 39
b = 141
c = 39
How to find the anglesThe angles are solved using the concept of sum of angles in a triangle is equal to 180 degrees
Solving for a
a + 106 + 35 = 180
a + 106 + 35 = 180
a + 141 = 180
Next, we can isolate a by subtracting 141 from both sides:
a + 141 - 141 = 180 - 141
a = 39
a = c = 39 corresponding angles
b + c = 180 degrees (linear pair theorem)
b + 39 = 180
b + 39 - 39 = 180 - 39
b = 141
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Based on the amount of unsatisfied customers. What would be the cost of Software C?
If the cost of customer acquisition is $50 and the cost of customer retention is $30, then the cost of Software C would be $80,000. This is because 10,000 customers x ($50 acquisition cost + $30 retention cost) = $80,000.
What is acquisition cost?Acquisition cost is the cost associated with obtaining an asset or resource. It includes the purchase price, transportation costs, installation costs, taxes, and any other associated costs.
The cost of Software C can be determined by calculating the total cost of lost customers due to software issues. To do this, companies typically look to the customer lifetime value (CLV) of each customer. CLV is the total revenue generated by a customer over the course of their relationship with the company. By multiplying the CLV by the number of unsatisfied customers, companies can get a good idea of what the cost of Software C is.
For example, if a company has 10,000 customers and their CLV is $100, then the cost of Software C would be $1,000,000. This is because 10,000 customers x $100 CLV = $1,000,000.
The cost of Software C can also be determined by looking at the cost of customer acquisition and retention.
In addition to the cost of lost customers, companies must also factor in the cost of fixing the software issue. This cost can vary depending on the complexity of the issue and the size of the company. Companies should also consider the cost of lost productivity due to the software issue, as well as any other costs associated with the issue.
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Answer:
54665655
Step-by-step explanation:
The following figure is made of 3 triangles and 1 rectangle.
4
2
B
Figure
Triangle A
Triangle B
Rectangle C
Triangle D
Whole figure
A
2
4
T
6
2C 2D
H
2
Find the area of each part of the figure and the whole figure.
Area (square units)
19
1
I
Answer:
Shape Area (units^2)
A 20
B 2
C 4
D 6
Total = 32
Step-by-step explanation:
See the attached worksheet. These calculations assume that the "6" is the length of the line segment as marked. Using the expressions for areas or traingles and rectangles, as noted, each area is calculated and the sum is 32 units^2.
Use this common denominator to find equivalent fractions for 1 2/3 and 3/4 if 1 2/3=1 and 3/4=
The required equivalent fractions for 1 10/15 and 9/12.
Given, two mixed fractions 1 2/3 and 3/4, determine equivalent fractions using 15 as the common denominator.
Simplification:
The process in mathematics of manipulating and interpreting functions to make a function or expression simpler or easier to understand is called simplification, and the process is called simplification.
1. Simplify fractions by canceling all common factors of the numerator and denominator and writing the fraction in its lowest/simplest form.
2. Simplify mathematical expressions by grouping and combining similar terms. This makes expressions easy to understand and solve.
According to the Question:
Here,
First
= 1 2/3
= 1+ 2 / 3
= 1 + 2 × 5 / 3 × 5
= 1 + 10 / 15
Again,
Second,
= 3 / 4
= 3 × 3 / 4 × 3
= 9/12
Thus, the required equivalent fractions for 1 10/15 and 9/12.
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Find all the missing side lengths and angle measures of each triangle.
Answer:
Step-by-step explanation:
<ATC+90+60=180
<ATC=30
we know that,
if 30-------x
60--------[tex]x\sqrt{3}[/tex]
90---------2x
so, x\sqrt{3}=10
x=10/sqrt{3}
Martin throws a ball straight up in the air. The
equation h(t) = −16t2 + 40t + 5 gives the height
of the ball, in feet, t seconds after Martin releases
it.
How many seconds before the ball Martin threw
hits the ground?
2.62 seconds before the ball Martin threw hits the ground.
Define quadratic equationThe definition of a quadratic as a second-degree polynomial equation demands that at least one squared component must be included. These are also known as quadratic equations.
Let t be the time in seconds
h(t) be he height of the ball, in feet
we have
h(t) = −16t² + 40t + 5
we know that
When the ball hits the ground, the height is equal to zero
so
−16t² + 40t + 5=0
The equation solving formula for a quadratic equation of the type
at²+bt+c=0
is equal to
t=(-b±√(b²-4ac))/2a
in this problem we have
−16t² + 40t + 5=0
so
a=-16
b=40
c=5
substitute in the formula:
t = (-40±√(40²-4×40×5))/2×-16
t = (-40±√(1600-800))/-32
t=2.62sec
therefore, 2.62 seconds before the ball Martin threw
hits the ground.
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Prove the following:
Let l be a line, let P be an external point, and let F be the foot of the perpendicular from P to l. If R is any point on l that is different from F, then PR > PF.
The proof that line segment PR is greater than the line segment PF is shown below
Proving that the length PR is greater than PFGiven that
P is an external pointF is the foot from P to the lineThe above statements mean that we have a right triangle PFR such that
PF is the length of one of the legs.PR is the length of the hypotenuse.FR is the length of the other leg.In a right triangle, the longest side is the hypotenuse
This means that
PR is greater than PF
This proves that if R is any point on line l that is different from F, then PR > PF.
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The basketball player releases another shot from (13,0) and makes the shot the shot also passes through (10,1. 4)
(a) Yes, the player makes the shot; (b) A quadratic function in standard form that models the path of the shot is: [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]
(a) We need to find the x-int to see if he makes the shot at (3,0).
so, first we factor!
[tex]y=-\frac{1}{20} (x-6)(x-3)[/tex]
0 = (x - 6) = (6, 0)
0 = (x - 3) = (3, 0)
This shows that the player makes the shot.
(b) x- int = (13, 0) and (3, 0)
random point = (10, 1.4)
f(x) = a(x - 13) (x - 3)
1.4 = a(10 - 13) (10 - 3)
1.4 = a(-3) (7)
[tex]\frac{1.4}{-21} = \frac{-21a}{-21}[/tex]
a = 0.06 ≈ [tex]\frac{-3}{50}[/tex]
the Quadratic function is [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]
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Full Question:
A professional basketball player's shot is modeled by the function shown, where x and y are measured in feet.
a. Does the player make the shot?
b. The basketball player releases another shot from the point (13,0) and makes the shot. The shot also passes through the point (10, 1.4). Write a quadratic function in standard form that models the path of the shot.