For a 75% success percentage, she needs to hit 23 of her final 30 throws.
The rational function for a player's free throw percentage will be:
y = (21/30) * 100
How is rational function made?A function that is the sum of polynomials is referred to as rational. If a function of one variable, x, can be written as :
[tex]f(x) = p(x)/q(x),[/tex]
where p(x) and q(x) are polynomials with q(x) = 0,
then the function is said to be rational. The phrase f(x) = (x2 + x - 2) / (2x2 - 2x - 3) denotes a rational function; in this case, 2x2 - 2x - 3 = 0.
Every constant is a polynomial, thus we know that the numerators of rational functions may also be constants. A rational function would be f(x) = 1/(3x+1), for instance.
CALCULATIONIf the basketball player is making 70% successful throw rate by making 21 of last 30 free throws
so, for raising her throw rate to 75% she should throw:
x/30 * 100 = 75%
x = 75 * 3 / 10
x = 15 * 3 /2
x = 22.5 ≈ 23
therefore , she should make 23 of her last 30 free throws to raise her success rate to 75%
For this case what you should do is write the following function:
y = (a / b) * 100
Where,
A: amount of successful free throws
B: total amount of free throws
Substituting values we have:
y = (21/30) * 100
The result is:
Y = 70% (as we expected)
a rational function that can model the player's free throw percentage is:
y = (21/30) * 100
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Use f(x) = |x| , f(x)is shifted left 5 and shifted up 2 to create g(x). Write the equation g(x).
Answer:f
(
x
+
2
)
=
3
x
+
2
Step-by-step explanation:
Interpret, in a written description, what the graph is saying about the relationship between the variables. A graph has time (hours) on the x-axis, and distance (miles) on the y-axis. A line increases to 2 hours, is constant through 3 hours, and then increases through 6 hours. a. You leave home and drive for 6 hours with no stops. b. You leave home, drive for 1 hours at a constant speed, stop for 30 minutes, continue at the same speed, stop for 1 hour and then continue at the same speed as before. c. You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before. d. You leave home, drive for 3 hours at a constant speed, and then stop for 2 hours. Finally you continue at the same speed as before.
The written description of the relationship between the variables as discussed in the task content is; Choice C; You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before.
Which answer choice is the best interpretation of what the graph is saying about the relationship between the variables?According to the task content, the time (hours) is plotted on the x-axis while the distance (miles) is plotted on the y-axis.
Since the graph is described by a line, it follows that it's slope is constant and consequently, its distance covered increases to 2 hours. This signifies driving.
Also, since the distance covered is constant through 3 hours, it follows that no distance is covered in that time and hence, speed is zero which signifies a stop.
Ultimately, when the distance increases through 6 hours, it follows that although the speed is constant, it is slower than the first 2 hour distance.
Therefore, Choice C correctly represents the interpretation of the relationship between the variables.
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a) The quadratic x^2-4-21 can be written in the form (x+a)^2+b find the values of a and b
b) Hence, or otherwise, solve the equation x^2-4x-21=0
According to the solving the value of a and b of the X² - 4X - 21 equation are:
a = -2
b= -25
What does quadratic signify in mathematics?A quadratic problem is a sort of problem in mathematics that deals with either a variable multiplied by itself – a process known as squares. The area of a square is defined as its side length multiplied by double itself in this language.
What is the purpose of quadratic?In everyday life, we employ quadratic formulas to calculate areas, determine the profit of a product, or calculate the velocity of an object. Furthermore, quadratic equations are defined as equations with at least one squared variable.
According to the given data:X² - 4X - 21
Expand to check:
For a.
(X - 2)² - 4 - 21 = (X - 2)² - 25
= X² - 4X + 4 - 25
= X² - 4x -21
= (X - 2)² - 25
a = -2 , b = -25
For b.
X² - 4X - 21 = (X - 2)² - 25 due to part a we can say that:
(X - 2)² - 25 = 0
X - 2 = ± 25
x = 7 , X = -3
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Which expression is equivalent to one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x? negative two fifteenths times x minus two two fifteenths times x minus two negative two over fifteen times x plus two one and one third times x plus two
The expression that is equivalent to the given expression is -2x/15 + 2. The correct option is the third option- negative two over fifteen times x plus two
Evaluating an ExpressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
1/5(3x +10) - (11/15)x
Clear the parentheses by applying the distributive property
1/5(3x) + 1/5(10) - (11/15)x
3x/5 + 2 - 11x/15
Collect like terms
3x/5 - 11x/15 + 2
(9x - 11x)/15 + 2
-2x/15 + 2
Hence, the expression that is equivalent to the given expression is -2x/15 + 2. The correct option is the third option- negative two over fifteen times x plus two
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the verified answer is wrong.
PLS HELP QUICKLY
Point F is between points T and K.
The points are collinear.
Answer:
the answer issssssssssssss
first blank is - 12
2nd blank is -3
17+4h+2=1−5h solve for h
Answer:
h=-2
Step-by-step explanation:
17+4h+2=1−5h
19+4h=1-5h
4h=-18-5h
9h=-18
h=-2
9 to the power of -3 as a fraction
Answer:
137174211/100000000000
Step by Step Explanation:
First, find the answer of 9^(-3), which would be 0.00137174211. Then, convert that into fraction form. Which would be 137174211/100000000000. Then simplify, which in order to simplify a fraction, there must be: 1. A number that will divide evenly into both the numerator and denominatior so it can be reduced. No such number exists for 137174211 and 100000000000. or 2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. 137174211 is not greater than 100000000000, also meaning, this fraction is in it's simplest form.
⚡️PLEASE HELP-URGENT⚡️
I only need help with 34.. but I. So confused and I need to go to bed
The error in solving for the equation in the question was that m was not appropriately converted from a negative number.
What error was made?The equation is:
-m/3 = -4
Solving gives:
3 x (-m/3) = 3 x -4
m is a negative and should remain so. The next step is:
-m = -12
m = -12 / -1
m = 12
m is therefore 12 and not -12.
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Jonathon collected 4 1/2 kg of seashells. If he gives 2 3/4 kg of seashells to his friend, what is the weight of the
remaining seashells that Jonathon has?
The remaining weight seashells that Jonathon has is 7/4 kg or [tex]1\frac{3}{4}[/tex] kg.
Define fractions.A fraction is a percentage of a whole. This entire sentence could be referring to a single location or a collection of locations. The English word "fraction" derives from the Latin word "fractio," which means "to break." As the first civilization to comprehend fractions, the Egyptians used fractions to solve a number of mathematical problems, including the distribution of food and resources and the absence of a metal currency.
Weight of the remaining sea shells = [tex]4\frac{1}{2}[/tex] - [tex]2\frac{3}{4}[/tex]
Weight of the remaining sea shells = 9/2 - 11/4
Weight of the remaining sea shells = 18-11/4
Weight of the remaining sea shells = 7/4 kg
Weight of the remaining sea shells = [tex]1\frac{3}{4}[/tex] kg
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The weight of the remaining sea shells Jonathan has is 1¾ kg.
What exactly are fractions?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. There are three major types of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator.So, the weight of the remaining sea shells: 4½ - 2¾
Now, solve the above fraction operation for the weight of remaining sea shells.
= 4½ - 2¾= 9/2 - 11/4= 18-11/4= 7/4kg= 1¾ kgTherefore, the weight of the remaining sea shells is 1¾ kg.
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Wite an equation perpendicular to y=-2x-7 that passes through the point (4,3)
Answer:
y = 1/2 x + 1.
Step-by-step explanation:
A line perpendicular to a line with slope m will have a slope of -1/m.
The line y = -2x - 7 will have a slope of -1/ -2 = 1/2.
Using the point-slope form of a straight line
y - y1 = m(x - x1)
Here m = 1/2 and (x1, y1) = (4, 3).
So, y - 3 = 1/2(x - 4)
y = 1/2x - 2 + 3
y = 1/2 x + 1.
eighteen thousand four humdred divided by nine
Answer: 2044.444444444 repeating
Step-by-step explanation:
divide 18400/9 and that's what you get in long division
Simplify the expression 7‐²(-3)²
Answer:
The answer to that question is 58
Which set of points does not represent a one-to-one function?
{(9,5), (4,9), (1,7), (8,8), (1,4)}
{(5,9), (8,3), (0, 0), (1,5), (6, 2)}
{(7,4), (1,7), (4,0), (9,5), (3, 3)}
{(9,7), (2,8), (3, 3), (8, 1), (5, 6)}
Answer:
firstg one
Step-by-step explanation:
two x's
Which expression is equivalent to (5x^−5 y^3)^−2??
thanksss
Answer: I think its 1/5x^10y^-6
Step-by-step explanation:
please let me know if I'm wrong
If you triple me and then subtract 12 the result is -87. What number am I?
Answer:
-25
Step-by-step explanation:
First, write an equation to represent the situation. To get -87, a number (lets say x) is first tripled, and then 12 is subtracted from the result.
So: -87 = 3x - 12
Then, solve for x by first adding 12 to both sides:
-87 = 3x - 12 ----> -75 = 3x
Finally, divide both sides by 3 to get x by itself:
-75 = 3x ----> -25 = x
One year, Kim pays 9260 income tax work out how much she earned that year
Answer: Kim made roughly 46,300 that year.
Step-by-step explanation:
We know that income tax = 9260
Step 1 is to find out which tax bracket Kim comes under.
The min. tax for those in the 20% bracket is 7,500. (20% * 37,500)
The min. salary for those in the 40% bracket is 45,000. (40% * 112,500)
As Kim pays 9260 in tax, we know that she falls under the 20% bracket. As such, we can conclude that :
20% * (Kim's Salary) = 9260
Kim's Salary = 9260/20%(or 0.2)
Kim's salary = 46,300
Answer: About $55,000k
Step-by-step explanation:
Find the value of cos W rounded to the nearest hundredth, if necessary.
U
24
7
W
Answer:
CosW =0.28
explaination:
first find value of the Hypotenuse side,
then find value of Cos W as recalled from
Cos W =Adjacent side/Hypotenus side
(-4,6) and (4,6) slope-intercept
The equation of the line in slope-intercept form is: y = 6.
How to Write the Equation of the Line in Slope-intercept Form?Given that the points, (-4,6) and (4,6) lie on a line, the steps below shows how to write the equation of the line in slope-intercept form.
Step 1: Find the slope of the line:
Slope (m) = change in y / change in x = (6 - 6)/(-4 - 4)
Slope (m) = 0/-8
Slope (m) = 0
Step 2: Substitute m = 0 and (x, y) = (4, 6) into y = mx + b to find the value of b
6 = 0(4) + b
6 = 0 + b
6 = b
b = 6
Step 3: Substitute m = 0 and b = 6 into y = mx + b
y = 0(x) + 6
y = 0 + 6
y = 6
In conclusion, the equation of the line in slope-intercept form is: y = 6.
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a(cosb+cosc-1)+b(cosa+cosc-1)+c(cosa+cosb-1)=0
Answer:
Proved!
Step-by-step explanation:
Given Problem:
a(cosB+cosC-1)+b(cosC+cosA-1)+c(cosA+cosB-1) = 0
Solution:
Let ABC be any triangle.
1) Consider the L.H.S (left hand side) of the given equation:
LHS =
We know that,
Projection formula:
= 0 =RHS
(2) Consider the LHS of the given equation:
Hence Proved!!
Help now...you have into 9/27/22 9:10
20 points BONUS IF YOU ANSWER QUICK!
Which phrase tells a major function of the endomembrane system?
producing and storing energy
directing the cell’s activities
manufacturing proteins
transporting substances in a cell
Answer: Transporting substances in a cell.
Step-by-step explanation: Transporting substances in a cell producing and storing energy.
Archaeologists use carbon-14, which has a half-life of 5730 years, to determine the age of artifacts in carbon dating. Write the exponentlal decay function for a 24 -mg sample. How much carbon- 14 remains after 30 millennia? (Hint: 1 millennium =1000 years)
The exponential decay function for 24 mg sample is given as
[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex]) and 0.64mg carbon - 14 will remain after 30 millennia.
Exponential function that represent the decay is given as :
[tex]F(t) = a (0.5)^{\frac{t}{h} }[/tex] (1)
where, F(t) = amount remaining after time t
a = amount of sample is decayed
t = time in years
h = half life years
The values that we have been given are :
a = 24 mg sample
h = 5730 years
Putting the required values in equation (1) we get
[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex] (2)
Now we need to find how much carbon-14 remains after 30 millennia.
That is we have to find F(t) for t = 30 millennia = 30000 years
[As 1 millennium = 1000 years]
Putting the required values in equation (2) we get
[tex]F(t) = 24 (0.5)^{\frac{30000}{5730} }[/tex]
[tex]F(t) = 24 (0.5)^{5.236}[/tex]
F(t) = 24*0.027
F(t) = 0.64 mg
Thus 0.64mg carbon - 14 will remain after 30 millennia.
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Use the distributive property
to remove the parentheses
(-3+3v+2v)(-9)
f(x)=x
3
−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x
Over which interval does fff have a positive average rate of change?
The interval in which the function has positive average rate of change is x > √3
How to determine the interval which the function has positive average rate of change?The function is given as
f(x) = x^3 - 9x
Differentiate the above function to determine the average rate of change
So, we have
f'(x) = 3x^2 - 9
Set the function to greater than 0
So, we have
3x^2 - 9 > 0
Add 9 to both sides
3x^2 > 9
Divide by 3
x^2 > 3
Take the square root of both sides
x > √3
Hence, the interval in which the function has positive average rate of change is x > √3
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Simplify each number. 64³.⁵
The result of simplifying the number 64³.⁵ using the exponent rules is
1.24x10^27
To solve this exercise we have to resolve algebraic operations following the exponent rules.
Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(64³)⁵
64 ⁽³*⁵⁾ =
64¹⁵ =
1.24x10^27
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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5. The picture below shows the amount of money in 3 banks. $5.20 $4.64 $2.16 Mrs. Doe emptied all three banks and put the money into two equal groups. How much was in each group?
Answer:
$6 in each group
Step-by-step explanation:
$5.20+$4.64+$2.16=12
12/2=6
Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total of $1215 . $445 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?
Answer: 11 hours :)
Step-by-step explanation: 1215-445=770, 770 divided by 70=11 so 11 days
Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x)-g(x)+10
The domain value for f(x)-g(x)+10 = - x²- x + 17
What are the domain of the function f(x)-g(x)+10 ?Given : f(x)=2 x+5
g(x)=x²-3 x+2
Solution:
f(x) - g(x) + 10 = 2 x+5 - x²-3 x+2 +10
f(x) - g(x) + 10 = 2 x+5 - x²-3 x+12
f(x) - g(x) + 10 = - x²- x + 17
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For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=4-2 √x
If the function f(x) = 4 - 2√x then the inverse function be [tex]x^{2}[/tex] −8x+18 = f(x)
What is meant by inverse function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.
Assume that the function is [tex]f(x) = 4 + \sqrt{x-2}[/tex] and f(x) = 4+x−2
where the x − 2 is under the radical sign.
The first step is to swap the f(x) and x.
The new function would be
[tex]$x = 4 + \sqrt{f(x) -2}x=4+ f(x)-2[/tex]
To solve the value of f(x) in the new function
x = 4 + [tex]\sqrt[2]{f(x)-2}[/tex]
x - 4 = [tex]\sqrt{f(x)-2}[/tex]
simplifying the above equation, we get
[tex](x -4^{} )^{2}[/tex] = f(x) − 2
[tex]x^{2}[/tex] − 8x +16 = f(x) − 2
[tex]x^{2}[/tex] − 8x + 18 = f(x)
The inverse of the function f(x) = 4 - 2√x is [tex]x^{2}[/tex] −8x+18 = f(x)
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find side x, giving your anwser to 1 decimal place
Answer: 10.8 cm
Following are the calculation to find the x:
Given:
Assuming the triangle is ABC:
then
∠A = 81∘
∠B = 40∘
A = 7cm
To find:
x=?
Solution:
To find the x value we use the Law of sine:
Putting the given value:
A function consists of the pairs (2,3),(x,4) , and (5,6). What values, if any, may x not assume?
A relation between a collection of inputs and outputs is known as a function.
The order pairs can't be a function also,
f(x) = -√x → D: x ≥ 0
→ R: y ≤ 0
Which of the ordered pair sets defines a function?A relation is simply a collection of ordered pairs (x, y). In formal mathematics, a function is a relation in which x1= x2 if (x1,y) and (x2, y) are both in the relation. This simply states that two ordered pairs with the same x -value but different y -values cannot exist in a function.A function's range is the set of all its outputs. Example: Consider the function f: A B, where f(x) = 2x and A and B are both sets of natural numbers. In this case, A is the domain and B is the co-domain. The range is then the result of this function.If an x value has more than one y-value associated with it, as in the relation (4, 1), (4, 2), the x-value of 4 has y-values of 1 and 2, indicating that this set of ordered pairs is not a function. If each x-value has only one y-value, the relationship is a function.The order pairs can't be a function also,
f(x) = -√x → D: x ≥ 0
→ R: y ≤ 0
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