Answers
Using the discriminant of a quadratic function, it is found that:
6. The range of values is of c ≤ 1/16.
8. The range of values of k is: -9 < k < -1.
10. The discriminant is never negative, hence the function has real roots for all values of k.
Discriminant of a quadratic functionA quadratic function is modeled as follows:
y = ax² + bx + c.
The discriminant of the function is given as follows:
Δ = b² - 4ac
For item 6, the function is given as follows:
y = 2x² - 3x + (2c + 1).
The coefficients are given as follows:
a = 2, b = -3, c = 2c + 1.
The function is positive for all values of x if it has at most one real root, hence:
Δ ≥ 0
(-3)² - 4(2)(2c + 1) ≥ 0
9 - 16c - 8 ≥ 0
1 - 16c ≥ 0
16c ≤ 1
c ≤ 1/16
For item 8, the function is given as follows:
y = kx² - (k - 3)x - 1 = 0.
The coefficients are given as follows:
a = k, b = -k - 3, c = -1.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(-k - 3)² - 4(k)(-1) < 0
k² + 6x + 9 + 4k < 0
k² + 10k + 9 < 0
Hence the range is:
-9 < k < -1.
For item 10, the function is given as follows:
y = kx² + (k - 2)x - 2 = 0.
The coefficients are given as follows:
a = k, b = k - 2, c = -2.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(k - 2)² - 4(k)(-2) < 0
k² - 4k + 4 + 8k < 0
k² + 4k + 4 < 0
(k + 2)² < 0.
(k + 2)² is always positive, hence the function will always have real roots.
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Answer
Discriminant of a quadratic functio
A quadratic function is modeled as follows:
y = ax² + bx + c.
The discriminant of the function is given as follows:
Δ = b² - 4ac
For item 6, the function is given as follows:
y = 2x² - 3x + (2c + 1).
The coefficients are given as follows:
a = 2, b = -3, c = 2c + 1.
The fnction is positive for all values of x if it has at most one real root, hence:Δ ≥ 0
(-3)² - 4(2)(2c + 1) ≥ 0
9 - 16c - 8 ≥ 0
1 - 16c ≥ 0
16c ≤ 1
c ≤ 1/16
For item 8, the function is given as follows:
y = kx² - (k - 3)x - 1 = 0.
The coefficients are given as follows:
a = k, b = -k - 3, c = -1.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(-k - 3)² - 4(k)(-1) < 0
k² + 6x + 9 + 4k < 0
k² + 10k + 9 < 0
Hence the range is:
-9 < k < -1.
For item 10, the function is given as follows:
y = kx² + (k - 2)x - 2 = 0.
The coefficients are given as follows:
a = k, b = k - 2, c = -2.
It has no real roots if:
Δ < 0
b² - 4ac < 0
(k - 2)² - 4(k)(-2) < 0
k² - 4k + 4 + 8k < 0
k² + 4k + 4 < 0
(k + 2)² < 0.
(k + 2)² is always positive, hence the function will always have real roots.
Step-by-step explanation:
Related Questions
What is the distance between the points (−3, −5) and (−3, −7)?
Answers
The distance between the points (−3, −5) and (−3, −7) is 2 units.
How to use distance formula?The distance formula gives the shortest distance between two points in a two-dimensional plane.
The distance formula is a useful tool for calculating the distance between two points.
Therefore,
d = √(x₂ - x₁)²+(y₂ - y₁)²
Let's find the distance between the points (−3, −5) and (−3, −7).
Hence,
x₁ = -3
x₂ = -3
y₁ = -5
y₂ = -7
d = √(-3 + 3)² + (-7 + 5)²
d = √(-2)²
d = √4
d = 2
Therefore, the distance between the point is 2 units.
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Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Mei Mei can use while staying within her budget.
Answers
Answer:
Step-by-step explanation:
Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Mei Mei can use while staying within her budget.
The
inequality
for the required
condition
will be 46+5x<70 as she want to keep the
bill
under $70 according to question. Also she can buy 5 gg that is number of
gigabytes
in a month.
What is inequality?
An
inequality
in mathematics is a relationship that makes a non-equal
comparison
between two numbers or other
mathematical
expressions. It is most commonly used to compare the
sizes
of two numbers on a
number
line.
How to solve the inequality?
To solve an inequality, follow these steps: Remove fractions by
multiplying
all terms by the fractions' least common
denominator
.
Simplify
the
inequality
by combining like terms on each side.
Subtract
or add
amounts
to get the unknown on one side and the numbers on the other.
according to the question,
$46 is the fix cost that she has to pay.
$5 is the cost of gg she buys that is variable.
let us assume that x gigabytes she can buy in a month.
$70 is the maximum bill amount she want.
so the inequality would be,
46+5x<70
5x<70-46
5x<26
x<26/5
x<5.2
so, she can
buy
5 gg at
maximum
in a month with the inequality 46+5x<70 for the given conditions.
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[tex] {3x}^{4} {y}^{ - 2} x {2x}^{ - 1} {y}^{2} [/tex]whats the answer
Answers
Multiply the numbers and combine exponents with the same base.
Juan is investing his money. He thinks that he should make $12 for every $100 he invests. How much does he expect to make in an investment of $4200?
Answers
We have to estimate how much he expects to make investing $4200 if he should make $12 for every $100.
We can apply the rule of three as:
[tex]\begin{gathered} 100-->12 \\ 4200-->x=4200*\frac{12}{100} \\ x=4200*0.12 \\ x=504 \end{gathered}[/tex]Answer: he expects to make $504.
hlp
A jacket costs $50.50 more than a pair of sneakers. If the total cost of both items is $200.00, find the cost of each
Answers
The total cost of a Jacket is $124.75 and the cost of pair of sneaker is $74.75.
Let us say that the cost of the pair of sneakers is X dollars.
According to the given situation,
Cost of One jacket is 50 dollars more than the cost of a pair of sneakers.
Cost of one jacket = $(50 + X).
Total cost of one jacket and one pair of sneakers is $200.
Total cost of jacket and sneakers = $200
We get,
X + (X+50.5) = 200
2X + 50.5 = 200
The above equation that we have got is linear equation in one variable because it has degree 1 and one 1 variable.
Further solving the equation,
2X + 50.5 = 200
2X = 149.5
X = 74.75
So, the cost of one pair of sneakers is $74.75
Cost of One jacket is $(X + 50.5).
Cost of one jacket = $124.75.
So, one jacket costs $124.75 and sneakers cost $74.75.
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Assume boat license plates have two numbers, followed by three letters, followed by two numbers. Letters and numbers can repeat multiple times in the same license plate. For example, possible license plates are 12ABC40 and 55EEE55. How many different license plates are possible?
Answers
Answer:
175,760,000
Step-by-step explanation:
This is the counting principle.
There are 7 positions. Multiply the number of possible characters in each position.
_ × _ × _ × _ × _ × _ × _
The numbers are from 0 to 9, so there are 10 of them.
There are 26 letters in the English alphabet.
10 × 10 × 26 × 26 × 26 × 10 × 10
Answer: 175,760,000
Find the selling price of a $249.50 cell phone with a 30% markup. Round to the nearest cent when necessary.$74.85$72.22$324.35$174.65
Answers
Answer:
$324.35
Explanation:
Given a $249.50 cell phone with a 30% markup, to determine the selling price of the cell phone we need to first calculate 30% of $249.50 as seen below;
[tex]\frac{30}{100}\times249.5=0.3\times249.5=74.85[/tex]We'll now add $74.85 to $249.50 to finally get the selling price of the cell phone;
[tex]74.85+249.5=324.35[/tex]Therefore, the selling price of the cell phone is $324.35.
The length of a rectangle is 1 units more than the width. The area of the rectangle is 72 units. What is the length, in units, of the rectangle?
Answers
Type the correct answer in the box. The area of the figure is (BLANK) square units.
Answers
Given:
Find: Area of the figure.
Sol:
The area of Triangle ABH is:
Area
[tex]\text{ Area=}\frac{1}{2}\times\text{ Base}\times\text{ height}[/tex]In triangle is:
Base = (9-3)
Height = 8
So Area of ABH is:
[tex]\begin{gathered} \text{ Area=}\frac{1}{2}\times6\times8 \\ \\ =24 \end{gathered}[/tex]Area of rectangle BDFH so,
[tex]\text{ Area=Length}\times\text{ width}[/tex]Width = 8
[tex]undefined[/tex]your dinner bill was $21.00 if you leave a 15% tip, how much will the tip be?
Answers
Solution:
Given:
The dinner bill = $21.00
The tip = 15% of the bill
Hence,
[tex]\begin{gathered} =15\text{ \% of \$21} \\ =\frac{15}{100}\times21 \\ =\frac{315}{100} \\ =\text{ \$3.15} \end{gathered}[/tex]Therefore, the tip will be $3.15
help meeeeeee pleaseee !!!!
Answers
Answer:
See below
Step-by-step explanation:
Use points given in hint to find slope, m = (2000 -1000) /( 6- 8) = -500
then y = - 500x + b sub i oneof the points to calculate b = 5000
so y = - 500x + 5000
if x = 7.5
y = -500(7.5) + 5000 = 1250 dollars
Scott paid $13.24 for a 3.41 pound bag of shrimp at one store. The following week, he paid $18.99 for a 4.96 pound bag at another store. Find the unit price for each bag. Then state which bag is better buy based off the unit price. Round your answers to the nearest cent.
Answers
Solution:
Scott paid;
$13.24 for 3.41-pound bag of shrimp
This means,
[tex]\begin{gathered} \text{ \$13.24=3.41pound} \\ 3.41\text{pound}=13.24 \\ \text{The unit price means the price of 1pound.} \\ 1\text{pound=}\frac{13.24}{3.41} \\ \text{Unit price= \$3.88 to the nearest tenth} \end{gathered}[/tex]$18.99 for 4.96-pound bag of shrimp
This means,
[tex]\begin{gathered} \text{ \$18.99=4.96pound} \\ 4.96\text{pound}=18.99 \\ \text{The unit price means the price of 1pound.} \\ 1\text{pound=}\frac{18.99}{4.96} \\ \text{Unit price= \$3.83 to the nearest tenth} \end{gathered}[/tex]Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.
Thus, the 4.96-pound is a better buy.
Twelve less than seven times a number is sixteen. Find the number.
Answers
Answer:
4
Step-by-step explanation:
put in equation form
7x - 12 = 16
solve for x
7x = 28
x = 4
Write the ratio statement as a fraction and reduced to the lowest term if possible
Answers
We must write the ratio 7 to 15 and reduce it to the lowest term if possible.
The ratio is:
[tex]\frac{7}{15}.[/tex]Because 15 is not divisible by 7, we conclude that the ratio is already in its lowest form.
Answer[tex]\frac{7}{15}[/tex]Which statement explains how you could use coordinate geometry to prove the diagonals of a quadrilateral are perpendicular?
Answers
To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.
What is coordinate geometry?
The science of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry).
Finding the difference between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
m=(rise/run) = (y2-y1)/(x2-x1)
(x1,y1) = coordinates of the line's first point
(x2,y2) = coordinates of the line's second point
To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.
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PLS HELP ME WITH THIS
you need to use the y=mx+b
Answers
Hello!
What is a slope-intercept form:
y = mx + b
m: slope[tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1--3}{1-0} =\dfrac{4}{1} =4[/tex]
b: y-intercept or point that has an x-coordinate value of 0==> thus is -3
So our equation is [tex]y=4x-3[/tex]
Hope that helps!
I need help with this practice problem The subject is complex numbers and vectors
Answers
we have the expression
[tex]12\sqrt{2}cis(\frac{7pi}{6})\colon3\sqrt{3}cis(\frac{pi}{4})[/tex]therefore
[tex]12\sqrt{2}c\imaginaryI s(\frac{7p\imaginaryI}{6})\operatorname{\colon}3\sqrt{3}c\imaginaryI s(\frac{p\imaginaryI}{4})=\frac{12\sqrt{2}}{3\sqrt{3}}cis(\frac{7pi}{6}-\frac{pi}{4})=4\sqrt{\frac{2}{3}}cis(\frac{11pi}{12})[/tex]Simplify
[tex]4\frac{\sqrt{6}}{3}cis(\frac{11pi}{12})[/tex]Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
Answers
1.The value of the expression after simplify will be,
''negative 43 over 24 times j plus negative 1 over 12.''
Option D is true.
2. The equivalent expression will be;
⇒ - 19.5b - 6.9
What is mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is;
''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''
Now, We can write the expression in mathematical form as;
⇒ (- 1/8 j + 2/3) - (5/3 j + 9/12)
Solve the expression as;
⇒ - 1/8 j + 2/3 - 5/3 j - 9/12
⇒ - 1/8 j - 5/3 j + 2/3 - 9/12
⇒ j (-1/8 - 5/3) + 2/3 - 3/4
⇒ j (- 3 - 40)/24 + (8 - 9)/12
⇒ j (-43/24) + (- 1/12 )
This can be written as;
''negative 43 over 24 times j plus negative 1 over 12''
Therefore, The value of the expression after simplify will be,
''negative 43 over 24 times j plus negative 1 over 12.''
Option D is true.
2. The expression is given as;
3(−4.5b − 2.1) − (6b + 0.6)
Solve the expression as;
3(−4.5b − 2.1) − (6b + 0.6)
3 x -4.5b - 3 x 2.1 - 6b - 0.6
- 13.5b - 6.3 - 6b - 0.6
- 13.5b - 6b - 6.3 - 0.6
- 19.5b - 6.9
Thus, The expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) will be;
⇒ - 19.5b - 6.9
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Solve for x log 3x+4) = 2
Answers
Step 1:
Write the equation
[tex]\log ^{3x+4}_4\text{ = 2}[/tex]Step 2:
Express the equation in exponential form
[tex]\begin{gathered} \log ^{3x+\text{ 4}}_4\text{ = 2} \\ 3x+4=4^2 \\ 3x\text{ + 4 = 16} \\ 3x\text{ = 16 - 4} \\ 3x\text{ = 12} \\ x\text{ = }\frac{12}{3} \\ x\text{ = 4} \end{gathered}[/tex]Final answer
x = 4
Solve this system of equations usingthe substitution method.y = x + 9y = - 4x – 6-
Answers
Given:
Here the system of eqution is given as
[tex]\begin{gathered} y=x+9 \\ y=-4x-6 \end{gathered}[/tex]Required:
Solve using the substitution method
Explanaton:
First put
[tex]y=x+9[/tex]in
[tex]y=-4x-6[/tex]we get
[tex]x+9=-4x-6[/tex]now isolate x
[tex]\begin{gathered} x+4x=-9-6 \\ 5x=-15 \\ x=-3 \end{gathered}[/tex]now put the value of x first equation
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]Final answer:
Solution of given system of equation by using elimination is
[tex]\begin{gathered} x=-3 \\ y=6 \end{gathered}[/tex]
a skydiver jumps out of an airplane. after 0.8 seconds, she has fallen 100 feet.after 3.1 seconds,she has fallen 500 feet.Emtiaz says that the skydiver should fall about 187.5 feet in 1.5 seconds. is his answer reasonable?
Answers
Is his answer reasonable: No, Emtiaz's answer is not reasonable because he assumed that the rate of descent was proportional.
What is the average rate of change?The average rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
Next, we would determine the rate at which the skydiver falls per seconds:
Rate = time/distance
Rate = 100/0.8
Rate = 125
Also, an equation which models the height (h) of the skydiver at a 0.8 seconds is given by:
h = 125t
At 3.1 seconds, we have:
Rate = time/distance
Rate = 500/3.1
Rate = 161.3
At 1.5 seconds, we have:
Rate = time/distance
Rate = 187.5/1.5
Rate = 125
Therefore, the average rate of change at each time interval is not equal and as such Emtiaz's answer is not reasonable because the rate increases as the time increases.
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HELP ASAP WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answers
Answer:
(4,-4)
Step-by-step explanation:
(x,y)→(x+2,y−5)
A(2,1) -> (4,-4)
:]
The Beta club is selling chocolate to raise money for Beta convention. Chocolate bars sell for $1.25 each and chocolate covered almonds sell for $2.00 each. The Beta club needs to raise more than $375 for all members to attend the convention. The students can sell up to 500 bars and covered almonds altogether.
1. Write a system of inequalities that can be used to represent this situation.
2. The club sells 100 chocolate bars. What is the least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention? Justify your answer.
Answers
The system of inequalities is 1.25x + 2y >= 375 and x + y <= 500, while the smallest number of chocolate covered almonds is 400
The system of inequalitiesWe make use of the following representations:
x = chocolate bars
y = chocolate covered almond
Using the above as a guide, and the given parameters;
We have:
1.25x + 2y >= 375 -- the amount raised
x + y <= 500 --- number of bars sold
The least number of chocolate covered almonds that must be soldFrom the question, we have
x = 100
Substitute x = 100 in x + y <= 500
100 + y <= 500
Evaluate
y <= 400
So, the least amount to sell is 400
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GET MARKED BRAINLIEST IF ANSWERED RIGHT, 30PTS
Answers
The probability that the customer came for lunch and did not order dessert is 7/113
The probability that the customer came for lunch or did not order dessert is 93/113
What is probability?It is the chance of an event to occur from a number of possible outcomes.
It is given by:
Probability = Number of required events / Total number of outcomes
We have,
Total number of customers = 113
Desert Non desert
Lunch 7 1 3
Dinner 30 63
The probability that the customer came for lunch and did not order dessert:
= 7 / 113
The probability that the customer came for lunch or did not order dessert:
= (7+13)/113 + (13 + 63)/113
= 20/113 + 73/113
= 93/113
Thus,
The probability that the customer came for lunch and did not order dessert is 7/113
The probability that the customer came for lunch or did not order dessert is 93/113
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Verify the identity:
cos(x)+sin(x)/ sin(x) =1+cot(x)
Answers
From cosecant identity the expression cos(x)+sin(x)/ sin(x) =1+cot(x) was verified.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) , where:
sin (x) = [tex]\frac{opposite\ leg}{hypotenuse}[/tex]
cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]
tan (x) = [tex]\frac{\frac{opposite\ leg}{hypotenuse} }{\frac{adjacent\ leg}{hypotenuse} } = \frac{opposite\ leg}{adjacent\ leg}[/tex]
The question gives the following identity: [tex]\frac{cos (x)+sin(x)}{sin(x)}[/tex]
First, you should rewrite the identity using the cosecant identity - csc(x)= 1/sin(x) . Then,
(cos(x)+sin(x)) * csc(x)
After that, you should expand the previous expression.
cos(x)*csc(x) + sin(x) * csc(x)
cos(x)*1/sin(x) + sin(x) * 1/sin(x)
cos(x)/sin(x) + sin(x)/sin(x)
cot(x) + 1
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Please help me with this question ASAP! I will mark as brainliest please ASAP
Answers
x³ is N²/15. The index form of a number is that digit written as an exponential expression or an unmarried number presented to another number.
What is meant by index form?A number's index form is that number written as an exponential expression or as a single number raised to another number. The exponent, or index, of an exponential expression indicates how many times the base must be multiplied by itself to evaluate the expression.
This fact can be used to write a number in index form. An index number is a number that has been multiplied by a power. The power, also known as the index, indicates how many times the number must be multiplied by itself. For example, 25 means multiplying 2 by itself five times
= 222222 = 32. There are several important index number rules:
ya × yb = y.
Therefore,
[tex]$x^3=\frac{N^2}{15}[/tex]
For [tex]$x^3=f(a)$[/tex] the solutions are
[tex]$x=\sqrt[3]{f(a)}, \sqrt[3]{f(a)} \frac{-1-\sqrt{3} i}{2}, \sqrt[3]{f(a)} \frac{-1+\sqrt{3} i}{2}$$$[/tex]
[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2},[/tex][tex]$x=\sqrt[3]{\frac{N^2}{15}} \frac{-1-\sqrt{3} i}{2}$$[/tex]
Simplify
[tex]$\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2}: \quad-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]
[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}-\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]
[tex]$x^3=\frac{N^2}{15}[/tex]
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Kaori is taking a free-throw.
H(d)H(d)H, left parenthesis, d, right parenthesis models the basketball's height (in meters) at a horizontal distance of ddd meters from Kaori.
What does the statement H(R)=4H(R)=4H, left parenthesis, R, right parenthesis, equals, 4 mean?
Answers
The height of the ball at a horizontal distance of R meters from Kaori is H(R)=4H.
Kaori taking a free throw is a guarantee. H(d) simulates the basketball's height (in meters) at d meters of horizontal separation from Kaori.
It is said that H(R) = 4H.
In this case, H(R) displays the height of a basketball instead of H(d). Therefore, it is evident that a basketball's height is 4H since H(R)=4H at d = R.
The horizontal distance from Kaori is R because d is the horizontal distance from Kaori.
Thus the height of the ball is 4H meters at a horizontal distance of R meters from Kaori, according to the expression H(R)=4H.
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solve this polynomial using factor by grouping x³+2x²+4x+8=0 show work
Answers
x³+2x²+4x+8=0
Rearrange
x³ + 4x + 2x²+ 8 = 0
x ( x² + 4 ) + 2( x² + 4) = 0
(x + 2) ( x² + 4) = 0
The factors are;
(x + 2) (x² + 4)
(x²+ 4) can further be simplified to give (x- 2i) (x + 2i)
i need help with this pls
Answers
The contrapositive of the statement is:
Jose isn't going for a bike ride if and only if he doesn't woke up early.
What is contrapositive?
A conditional statement's hypothesis and conclusion are switched, and both are then rejected, in a contrapositive. For instance, "if not B then not A" is the opposite of "if A then B." A conditional statement's contrapositive combines the inverse and converse.
The given statement is,
Jose wakes up early if and only if he is going for a bike ride.
We divide the statement into two parts.
1. Jose wakes up early.
2. He is going for a bike ride.
The negative of the statements are,
Jose doesn't wakes up early and he isn't going for a bike ride.
Therefore, the contrapositive of the statement is,
Jose isn't going for a bike ride if and only if he doesn't woke up early.
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2 Kenedi has a piece of ribbon that measures24 inches long. She cuts the ribbon into15 equal pieces to attach to her dancecostume. Kenedi uses the expression shown tocalculate the length of each piece of ribbon sheuses on her costume.241 - 15Which of the following expressions CANNOT beused to determine the length of each piece ofribbon?15F99=G (242) (15)H7+15J 241-15
Answers
Notice that the option F cannot be used to determine the lengths of each piece of ribbon because:
[tex]\frac{(\frac{97}{4})}{\frac{1}{15}}=15\cdot\frac{97}{4}\ne\frac{24\text{ 1/4}}{15}[/tex]