Answer:
f(x) = -4
Step-by-step explanation:
Given function: f(x) = 4 + 4x - 4x²
Here, we are being asked to find the value of the function when x is equal to 2.
Substitute 2 as the value of x in the function and simplify:
⇒ f(x) = 4 + 4x - 4x²
⇒ f(2) = 4 + 4(2) - 4(2)²
⇒ f(2) = 4 + 8 - 4(4)
⇒ f(2) = 4 + 8 - 16
⇒ f(2) = 12 - 16
⇒ f(2) = -4
This means that when the value of x is 2, the value of the function is -4.
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Answer: [tex]\textsf{f(2) = -4}[/tex]
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Given: [tex]\textsf{f(x) = 4 + 4x - 4}x^2[/tex]
Find: [tex]\textsf{f(2)}[/tex]
Solution: We need to plug in the value of 2 into all of the x's that are present in the expression and then we just simplify the expression.
Plug in the values
[tex]\textsf{f(x) = 4 + 4x - 4}x^2[/tex][tex]\textsf{f(2) = 4 + 4(2) - 4}(2)^2[/tex]Simplify the expression
[tex]\textsf{f(2) = 4 + 8 - 4}(4)[/tex][tex]\textsf{f(2) = 12 - 16}[/tex][tex]\textsf{f(2) = -4}[/tex]After completing the steps, we were able to determine that the answer to the question would be that f(2) is equal to -4.
When evaluating StartFraction (6.28 times 10 Superscript 12 Baseline) Over (3.14 times 10 Superscript 4 Baseline) EndFraction, what will be the exponent of 10 in the quotient?
3
4
8
16
This shows that the exponent of 10 in the quotient is 8
Evaluating exponential functionGiven the exponential function below expressed as:
[tex]n=\frac{6.28\times 10^{12}}{3.14\times 10^4}[/tex]
Separate
[tex]n=\frac{6.28}{3.14}\times \frac{10^{12}}{10^4}[/tex]
According to the quotient law;
[tex]n=2\times 10^{12-4}\\n=2\times10^8[/tex]
This shows that the exponent of 10 in the quotient is 8
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Answer:3+3
Step-by-step explanation:
tbh
Help!!
Part 1: 4^3 * 4^12
Part 2: 2^2 * 2^22
This is due today and help is appreciated!
Answer:
https://www.cuemath.com/algebra/adding-exponents/
Step-by-step explanation:
https://www.cuemath.com/algebra/adding-exponents/
This should help.
A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day.
To the nearest whole percent, what is the probability that a senior takes the bus to school every day, given that he or she has a driver’s license?
17%
19%
36%
70%
The probability that a senior takes the bus to school every day, given that he or she has a driver’s license is 17%.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As per the rule of conditional probability, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license can be written as,
P(Have License | Takes school bus)
= (Probability the seniors have driver’s licenses and take the bus to school every day) / (Probability of Having a licenses)
= 0.14 / 0.84
= 0.16667 ≈ 17%
Hence, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license is 17%.
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Answer: A 17%
Step-by-step explanation:
EDGE (GOT IT RIGHT ON TEST)
PLEASE HELP ME ANSWER THIS QUESTION ASAP (it's a matrices question)
Answer:
7
Step-by-step explanation:
In a_32, the first number, the 3, refers to the row, so it's the third row.
The 2 is the column, so it's the 2nd column.
The number in the 2nd column of the 3rd row is 7
Answer: 7
which of the following rational functions is graphed below A.f(x)=1/x-4 B. F(x)=1/4x
Considering it's vertical asymptote, the rational function graphed below is given by:
A. [tex]F(x) = \frac{1}{x - 4}[/tex].
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this graph, there is a vertical asymptote at x = 4, that is, x - 4 is a term of the denominator, hence the function is given by:
A. [tex]F(x) = \frac{1}{x - 4}[/tex].
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In a class of 35 students, 5 are freshmen, 8 are sophomores, 9 are juniors and 13 are seniors. If 1 student is randomly selected, what is the probability the student is a junior
[tex]\displaystyle\frac{9}{35}[/tex] or 25.71%.
Probability is the likelihood of an event occurring. The desired outcomes are known as successful outcomes. In this scenario, the successful outcomes are when a junior is selected. The sample size is the total number of students.
Probability as a FractionSimple probability (the probability of 1 event) can easily be found as a fraction. For the fraction, the number of successful outcomes should be the numerator and the sample size is the denominator.
This means that the probability of selecting a junior is [tex]\displaystyle\frac{9}{35}[/tex].
Probability as a PercentageIn this case, it is easiest to first find the probability as a fraction, but we can then convert it to a percentage if desired.
To convert to the fraction divide the numerator and denominator (I'm rounding to 4 decimal places).
9/35 = 0.2571Then, multiply this decimal by 100, which is the equivalent of moving the decimal point 2 digits to the left.
0.2571 * 100 = 25.71%A soccer ball is kicked upward from a hill and then falls to the ground. the height, in feet, of the ball after t sec is modeled by the function h(t) = –16t2 26t 12. what is the initial height of the ball?
Answer:
12 feet
Step-by-step explanation:
-16t^2+ 26t + 12 = h(t) when t = 0 (put in '0' for 't')
12 feet = h
A map uses the scale of 3/4 an inch to represent 3 miles. If the actual distance between two cities is
25 miles, then what is the length on the map?
Answer:
6 1/ 4 inches
Step-by-step explanation:
3/4 inch / 3 miles * 25 miles = 6 1/4 inches
Siobhan deposits $1200 into a savings account that pays 5.2% annual interest compounded monthly. What will be the balance after 4 years? Round to the nearest cent.
Answer:
Siobhan deposits $1200 into a savings account that pays 5.2% annual interest compounded monthly. The amount will be $269.75.How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:The final amount becomes:A = P(1 + r/n)nt for compound interestA = final amountp = principal investedr = interest rate as a decimalt = # years investedIn this case A = 1200 ( 1.22)A = 1469.75The total was interest you must subtract out the principal amount invested.I = 1469.75 - 1200 I = $269.75
Step-by-step explanation:
Asif, Sean, Bill, Francis, and Andrew are running against each other in a 100 m race. They all have an equal chance of winning.
Show the possible orders for the first three runners crossing the finish line.
What is the probability of Andrew being one of the first three runners to cross the finish line? Assume that there will not be a tie.
Answer:
a) see below for a listing of possible orders
b) 0.6
Step-by-step explanation:
You are asked to list the possible permutations of 5 runners, taken 3 at a time. Then, you are asked for the fraction of those that have Andrew among them.
PermutationsThe formula for the number of permutations of n objects taken k at a time is ...
P(n, k) = n!/(n -k)!
Then the number of ways three can place from five contestants is ...
P(5, 3) = 5!/(5 -3)! = 5·4·3 = 60
ListingFor listing purposes, we can represent the runners with the letters ...
A: AndrewB: BillC: FrancisD: AsifE: SeanThe order we choose for listing the permutations is to list a combination of three finishers, followed by the other 5 orders in which they can finish. In order of first, second, third, we can have ...
ABC ACB BAC BCA CAB CBA ABD ADB BAD BDA DAB DBA
ABE AEB BAE BEA EAB EBA ACD ADC CAD CDA DAC DCA
ACE AEC CAE CEA EAC ECA ADE AED DAE DEA EAD EDA
BCD BDC CBD CDB DBC DCB BCE BEC CBE CEB EBC ECB
BDE BED DBE DEB EBD EDB CDE CED DCE DEC ECD EDC
P(Andrew shows)In the above list, the first three of the five lines all have Andrew as one of those who "show" in the race.
P(Andrew shows) = 3/5 = 0.6
az+17=−4z−b solve for z
An expression is defined as a set of numbers, variables, and mathematical operations. The expression az+17=-4z-b when solved for z will be z=-(b+17)/(a+4).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression az+17=-4z-b can be solved as shown below,
az + 17 = -4z - b
az + 4z = -b -17
z(a+4) = -(b+17)
z = -(b+17)/(a+4)
Thus, the expression az+17=-4z-b when solved for z will be z=-(b+17)/(a+4).
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Find the exact solution of the equation. 7^x = 8
A. x = In7 / In8
B. x = 7 / 8
C. x = In(8 / 7)
D. x = (In8 / In7)
Answer:
[tex]x = \frac{(ln8)}{(ln7)} [/tex]
Step-by-step explanation:
Solve for x
Take the logarithm of both sides of the equation to remove the variable from the exponent. We have:
[tex]ln(7x) = ln(8)[/tex]
Expand
[tex]ln(7)[/tex]
by moving x outside the logarithm. It becomes:
[tex]x \: ln(7) = ln(8)[/tex]
Divide each term in
[tex]x \: ln(7) = ln(8) \: by \: ln(7)[/tex]We have:
[tex] \frac{x \: ln(7)}{ln(7)} = \frac{ln(8)}{ln(7)} [/tex]
:. Exact form:
[tex] \frac{ln(8)}{ln(7)} [/tex]
1) Sally spent half of her allowance going to the movies. She washed the family
car and earned eight dollars. What is her weekly allowance if she ended with
twelve dollars ?
Thinking it has to be at least a multi-step equation and possibly show steps
Answer:
$4
Step-by-step explanation:
If she had earned $8 washing a car and had at the end $12 you would calculate:
12-8=4
how do you know that an equation is a hyperbola?
An equation is a hyperbola when the locus of a point whose difference in the distances from two fixed points has a constant value.
What is hyperbola?A hyperbola is a type of smooth curve lying in a plane that is depicted by the geometric properties or by equations for which it is the solution set.
In this case, an equation is a hyperbola when the locus of a point whose difference in the distances between two fixed points has a constant value.
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In the diagram below o is circumscribed about quadrilateral WXYZ what is the value of a?
A)75
B)95
C)105
or
D)125
The value of a from the given figure is 105 degrees
Circle theoremFrom the given theorem, the quadrilateral is inscribed in a circle. For the quadrilateral, the sum of the opposite angle is supplementary. Hence;
a + 75 = 180 (supplementary)
Subtract 75 from both sides
a + 75 - 75= 180 - 75
a = 180 - 75
a = 105 degrees
Hence the value of a from the given figure is 105 degrees
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Buying a $36,000 new hybrid SUV with $3000 paid up front and the rest borrowed at 4.2%
annual interest compounded weekly (52 weeks per year) over 5 years.
From the calculations, the total amount paid for the SUV is $43,708.
What is compound interest?The term compound interest has to do with an interest that is charged in both the principal and the interest.
In this case, the amount that was borrowed is $36,000 - $3000 = $33,000. Using the formula;
A = P(1 + r/n)^nt
P = $33,000
r = 4.2%
n = 52
t = 5 years
A = 33,000(1 + 0.042/52)^(52 * 5)
A = $40,708
Total amount paid = $40,708 + $3000 = $43,708
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There is a bag filled with 5 blue, 6 red and 2 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 green?
The probability of getting exactly 1 green will be 1/13.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
Given data;
No of blue marbles= 5,
No of red marbles=6
No of green marbles=2
Total no of ball = 5+6+2
Total no of ball = 13
The probability of getting one green marble is;
P(G)=1/13
Hence, the probability of getting exactly 1 green will be 1/13.
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Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
Answer:
angle of depression ≈ 53.8°
Step-by-step explanation:
the angle of depression is the measure of the angle from the horizontal downwards from the top of the flag pole.
this angle is alternate to ∠ A and is congruent to ∠ A
using the sine ratio in the right triangle
sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{25}{31}[/tex] , then
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{25}{31}[/tex] ) ≈ 53.8° ( to 1 d.p )
Angle of depression ≈ 53.8°
Can anyone help me please
Step-by-step explanation:
as the formula says for the acid of symmetry :
x = -b/2a
in the function m(x) = 2x² + 8x +3
we have
a = 2
b = 8
c = 3
the axis of symmetry is
x = -8/(2×2) = -8/4 = -2
the vertex is (h, k) out of the form
m(x) = a(x - h)² + k
we know already, a = 2
for the rest we do all the multiplications and then we compare it with the original function :
m(x) = a(x² - 2hx + h²) + k = ax² - 2ahx + ah² + k
a = 2
-2ah = 8
-2×2×h = 8
-4h = 8
h = -2
ah² + k = 3
2×(-2)² + k = 3
8 + k = 3
k = -5
so, the vertex is (-2, -5)
pls help asap!! i’ve been trying to solve this for a bit and i’m really confused
Answer:
C. b = 0 and b = 4
Trust me, I know its right :)
Answer:
b = 0,4
Step-by-step explanation:
_______________________________________________
(5)/(3b^(3)-2b^(2)-5)=(2)/(b^(3)-2)
you can solve by cross multiplying
5(b^3-2)=2(3b^3-2b^2-5)
use distributive property which you get 5b^3-10=6b^3-4b^2-10
and you can solve it from that point.
________________________________________________
Nora drives 100 miles in 2 hours. what is her rate per hour?
What is the slope of a line perpendicular to the line whose equation is
2x+2y = 24. Fully simplify your answer.
Find a data set on the internet. some suggested search terms: free data sets, medical data sets, education data sets.
introduce your data set and cite the source.
what trends do you notice in your data set?
based on the trends and the history of your data set, make a claim. what kind of test (left, right, two tailed) would you have to complete?
explain the steps needed to complete the hypothesis test. what is needed?
The data used consists Standing/Walking time (minutes per day) spent by two types of people (Lean and Obese).
How to illustrate the data?The claim is that lean people spend more time walking and standing than obese people. We will be using right-tailed test.
The steps include:
Collect a sample of both groupsCalculate the mean and standard deviation of the two groupsState the null and alternate hypothesis and alpha.Calculate Test StatisticMake a conclusion based on our test.Learn more about data on:
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Vicky is solving an equation where both sides are linear expressions. She sets each linear expression equal to y and graphs the resulting system. If the y-intercepts of the graphs are the same but the slopes are different, what is the greatest possible number of intersections for these graphs?
Answer:
it is b :) on edge
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
took the test
Can someone please help me i cant understand it?
A system of equations contains at least two equations and can have zero, one, multiple or infinite many solutions.
How to determine the solution to system of equations?From the activity review, we have the following breakdown:
Create a system of equationSolve the system by graph and by tableAssume the system of equations are:
f(x) = 2x + 4
g(x) = x² - 4
Solving by table
Start by creating a table of values for the above equations
x -3 -2 -1 0 1 2 3 4
f(x) -2 0 2 4 6 8 10 12
g(x) 5 0 -3 -4 -3 0 5 12
From the above table of values, we have:
f(x) = g(x) when x = -2 and when x = 4
Hence, the solutions to the system of equations are (-2,0) and (4,12)
Solving by graph
Start by creating a graph of the equations using a graphing tool.
From the attached graph, we have the point of intersection to be
(-2,0) and (4,12)
Hence, the solutions to the system of equations are (-2,0) and (4,12)
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A circle is centered at the point (-7,-1) and passes through the point (8,7)
The equation of a circle centered at the point (-7,-1) and passes through the point (8,7) is (x+7)² +(y+1)² = 289
Equation of a circleThe standard equation of a circle is expressed as shown
(x-a)^2 + (y-b)^2 = r^2
where:
(a, b) is the centre
r is the radius
Given the following
Centre = (-7, -1)
Determine the radius
r = √(8+7)² +(7+1)²
r² = 15² + 8²
r² = 225 + 64
r² = 289
Substitute the centre and radius
(x-(-7))^2 + (y-(-1))^2 = 289
(x+7)² +(y+1)² = 289
Hence the equation of a circle centered at the point (-7,-1) and passes through the point (8,7) is (x+7)² +(y+1)² = 289
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Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is y= 3x - 1. Which could be the other equation? y=3x+2
03x-y=2
03x-y-1 0
3x+y=1
Answer:
x+y=1 hope it's help in you
B is the midpoint of ac. ab equals 4x-1 and bc equals 5x-5. what is the length of bc?
Answer:
BC= 15
if I am right please mark it as brianliest
Help please and thank you!
Answer:
Option A
Explanation:
[tex]\rightarrow \sf sin\left(\dfrac{7\pi }{6}\right)[/tex]
[tex]\rightarrow \sf \sin \left(\pi +\dfrac{\pi }{6}\right)[/tex]
[tex]\rightarrow \sin \left(\pi \right)\cos \left(\dfrac{\pi }{6}\right)+\cos \left(\pi \right)\sin \left(\dfrac{\pi }{6}\right)[/tex]
[tex]\rightarrow \sf 0 * \dfrac{\sqrt{3}}{2}+\left(-1\right) * \dfrac{1}{2}[/tex]
[tex]\rightarrow \sf -\dfrac{1}{2}[/tex]
I need this problem solved
Answer:
x = 70
Step-by-step explanation:
