Use
f(x) = 2x − 3
and
g(x) = 4 − x2
to evaluate the expression.
Answers
The equation based on the information given will be x⁴ + 8x² - 12.
How to compute the value?It should be noted that from the information given, the expression to compute will be:
= g - g(x)²
This will be:
= 4 - (4 - x²)²
= 4 - (4 - x)(4 - x)
= 4 - (15 - 8x² + x⁴)
= x⁴ + 8x² - 12
The complete question is:
Use f(x) = 2x − 3 and g(x) = 4 − x² to evaluate the expression g - g(x)².
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Related Questions
subtract these numbers using the expanded format 74-34
Answers
Answer:
40
Step-by-step explanation: just subtract
A triangle has vertices of (0,2), (3,0), (0, -3). If it is dilated with center at the origin, and a scale factor of 2, what will be the coordinates of the image?
(0,4), (6,0), (0, -6).
(0,4), (6,0), (0, -3)
(0,7), (6,3), (0, -3)
(0,1), (3/2,0), (0, -3/2)
Answers
Answer: (0,4), (6,0), (0, -6)
Step-by-step explanation:
Dilating at the origin means we can multiply each of the coordinates by the scale factor. In this case, this means we multiply each of the coordinates by 2.
Tina is saving to buy a notebook computer. She has two options. The first option is to put $300 away
initially and save $10 every month. The second option is to put $100 away initially and save $30 every
month. After how many months would Tina save the same amount using either option? How much
would she save with either option?
After
months, Tina will save $
with either option.
Answers
Answer:
Step-by-step explanation:
The number of months is our unknown, which we will call x. y is the amount she saves. Representing the fact that she puts $10 away per month is 10x. If she puts $300 down initially and then adds 10 per month to that, the first equation is
y = 10x + 300
The same goes for the second option. Putting $30 away every month is represented as 30x, and if she is starting with 100 and adding 30 a month to it, the second equation is
y = 30x + 100
We are being asked to find the number of months where the amount Tina saves is equal. Since y is the amount Tina has saved and we want to know when these amounts are equal, we will set the equations equal to each other and solve for x, the number of months.
10x + 300 = 30x + 100 and
200 = 20x so
x = 10. After 10 months, Tina will have saved the same amount of money regardless of which option she has chosen. This is only true for 10 months though. After that, one will show more of a savings than the other.
Drag and drop the relationships below to classify them as being a function or not a function?
Answers
A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.
Determine the domain of a piece wise function?Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.
Determine the range of a piece wise function?Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.
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LMNP is a rectangle. Find the value of x and the length of each diagonal. LN=x and MP=4x-6
Answers
Answer: x = 2.
LN = MP = 2.
Solution in the photo, below.
About 21 out of 25 Texans live in An urban area
Answers
Answer:
I'm confused. Is there more to the question?
What is the surface area, measured in square centimeters, of the shapebelow? Do not include units in your answer.
Answers
SOLUTION
The figure in the question is a cuboid with
length = 7 cm, width = 3cm and height = 4cm
Surface area of a cuboid is given as
\(\begin{gathered} S=2(lw+lh+wh) \\ S=2((7\times3)+(7\times4)+(3\times4))_ \\ S=2(21+28+12) \\ S=2(61) \\ S=2\times61 \\ S=122cm^2 \end{gathered}\)Hence the answer is 122 square-centimeters
5. A group of hikers descended 1,200 feet from a
mountain in 3 hours. What was the change in elevation
per hour? Write your answer as an integer.
Answers
Answer:
300 feet an hour
Step-by-step explanation:
in three hours they went down 1200 feet so that means in 1 hour they will go down 300 feet if they take no break
7k - 3k + 11, can somebody please help me out?
Answers
Answer:
4k+11=4011
Step-by-step explanation:
7k - 3k=4k
4k+11=4011
The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish from each of the 53 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount?
Required:
State the random variable, population parameter, and hypotheses.
Answers
Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
\(H_0: \mu=1\\\\H_a:\mu\neq 1\)
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
\(H_0: \mu=1\\\\H_a:\mu\neq 1\)
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206\)
Then, we can calculate the t-statistic as:
\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427\)
The degrees of freedom for this sample size are:
\(df=n-1=53-1=52\)
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
\(\text{P-value}=2\cdot P(t<-2.427)=0.019\)
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
At the beginning of a study of individuals, 10% were classified as heavy smokers, 20% were classified as light smokers, and 70% were classified as nonsmokers. In the five-year study, it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively. A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.
Answers
Answer: 0.39
Step-by-step explanation:
Given the following classification :
Heavy smokers (H) = 10%
Light smokers (L) = 20%
Non smokers (N) = 70%
Given that :
The death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively
Let probability of death = D
P(D | N) = d
P(D | H) = 5d
P(D | L) = 3d
Hence,
P(D) = [P(H) * P(D | H) + P(L) * P(D | L) + P(N) * P(D | N)]
P(D) = [0.1 * 5d + 0.2 * 3d + 0.7 * d]
P(D) = [0.5d + 0.6d + 0.7d]
P(D) = 1.8d
A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.
P(N | D) = [P(N) * P(D | N)] / P(D)
P(N | D) = 0.7d / 1.8d
P(N | D) = 0.3888
= 0.39
The numbers on a football field indicate 10 yard increments. You walk around the perimeter of a football field between the pylons. You walk a distance of 306 2/3 yards. The playing field not including end zones perimeter and area?
Answers
Answer:
It is D.
Step-by-step explanation:
proof I just took it
You have a jar containing 55 coins, consisting entirely of nickels and quarters, worth a
total of $7.15. How many quarters are in the jar?
Answers
Answer: 22 quarters
Step-by-step explanation:
Let N be the number of nickels.
Then the number of quarters is (55-N)
The nickels contribute 5N cents to the total.
The quarters contribute 25*(55-N) cents to the total.
5N + 25*(55-N) = 715
5N + 1375 - 25N = 715
-20N = 715 - 1375 = -660
\(N=\frac{-660}{-20}\)
\(=33\)
\(55-33=22\)
So there is 22 quarters inside the jar.
Check to see if my answer is correct-
33*5 + 22*25 = 715 cents
A solid figure is composed of a cube and a right triangular
prism. The figure and some of its dimensions are shown in
this diagram.
- 8 cm
What is the volume of the figure?
A
6 cm
B
560 cubic centimeters
704 cubic centimeters
C 728 cubic centimeters
Answers
Answer:
Option B
Step-by-step explanation:
704 cubic centimeters
You can use a calculator if you want :)
Answers
Answer:
A. -0.02
Step-by-step explanation:
-\(\frac{5}{25}\)=-\(\frac{1}{5}\)
1/5 is 20%
-1/5 is -20%
-.02% is greater because it's closer to zero
A package is weighed at 4 kg to the nearest kg.
Find the largest possible weight for the package.
ANSWER ASAP PLEASE
Answers
Answer:
3.99kg
Step-by-step explanation:
you can find it by 4kg minus 1 g that stills counts as rounding
a triangle has one side length of 9cm and another side of .12cm what are 3 possible answers for the third side
Answers
If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side are: 17, 20, and 21.
What are the possible lengths for the third side?To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:
9 + 12 > x
9 + x > 12
12 + x > 9
Simplifying these inequalities, we get:
x > -3 (always true)
x > -9 (always true)
x > -3 (always true)
Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).
The possible lengths for the third side are:
9 + 12 > x, so x < 21
9 + x > 12, so x > -3
12 + x > 9, so x > -3
Therefore, the possible lengths for the third side of the triangle are:
17 (9 + 12 = 21, which is greater than 17)
20 (9 + 12 = 21, which is greater than 20)
21 (9 + 12 = 21, which is equal to 21)
So, the three possible lengths for the third side of the triangle are 17, 20, and 21.
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The complete question is:
A triangle has one side length of 9
centimeters (cm) and another side length of 12
cm.
Which answers are possible lengths for the third side?
Select three that apply
17
22
9
21
20
3
eg jammu jdndhdbshsbsbs
Answers
Answer:
A: \(3\frac{1}{3}\)
B: \(3\frac{2}{3}\)
I hope this helps!
pls ❤ and mark brainliest pls!
What is the measure of the angle formed by the minute hand and hour
hand of a clock in each case?
at 6 o'clock
at 4 o'clock
at 3 o'clock
PLEASE HELP ASAP PLEASE
Answers
Answer:
180 degrees, 120 degrees, 90 degrees
Step-by-step explanation:
each hour is 30 degrees.
at 6 o'clock the hands are straight, at 4 o'clock they make a 120 degree angle, and at 3 o'clock they make a right angle
Enter and equation relating the variables in the table. Express any value(s) in your answer as simplified fractions, if necessary.
Time (x) - 18, 45, 72, 81
Distance (y) - 8, 20, 32, 36
The equation is y =
Answers
Answer:
\(y=\dfrac49x\)
Step-by-step explanation:
Let \((x_1,y_1)\) = (45, 20)
Let \((x_2,y_2)\) = (72, 32)
using slope formula to find slope \(m\):
\(m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{32-20}{72-45}=\dfrac49\)
using point-slope formula:
\(y-y_1=m(x-x_1)\)
\(\implies y-20=\dfrac49(x-45)\)
\(\implies y-20=\dfrac49x-20\)
\(\implies y=\dfrac49x\)
. Max needs 104 cups of flour to make a batch
of pizza dough for the pizzeria. He only has
4 cups of flour. How much more flour does
he need to make the dough? (STEP BY STEP. FOR THE LAST TIME.)
Answers
To make the dough, he'll need 5 3/4 cups of floor.
What is fraction?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. In mathematics, a fraction is used to represent a portion or part of a whole. It symbolizes the equal parts of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, and the bottom number is known as the denominator.
Here,
10 1/4 cups of flour needed to make a batch=41/4 cups
4 1/2 cups of floor is there=9/2 cups
flour does he need to make the dough,
=41/4-9/2
=(41-18)/4
=23/4
=5 3/4 cups
He needs 5 3/4 cups of floor to make the dough.
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helpppppppppppppppppppp...................................
Answers
Answer: Its quadrant 3
Step-by-step explanation:
Hope this helps!
Answer:
Quadrant 3
Step-by-step explanation:
Lets have an example
Lets say we are plotting the point (-4,-4)
so, we would go left on the x-axis, to -4. So we will be in either Quadrant 2 or Quadrant 3
Now we go down 4, so we end up in Quadrant 3
Hence, The answer is Quadrant 3
Hope this helps!^^
This line plot shows how many miles Monique rode her bike this week.
Answers
Answer:
151
Step-by-step explanation:
Answer:
152 miles
Step-by-step explanation:
There are 2 Xs above 20 1/2, so she rode that distance twice. There are 3 Xs above 22 1/2, so she rode that distance three times. The other distances with Xs she only did once. We add up the distances for each X to get the total:
20.5 + 20.5 + 21.5 + 22 + 22.5 + 22.5 + 22.5 = 152 miles
32 to the power of negative 4 fifths
Answers
Answer:
0.0625
Step-by-step explanation:
hope this helps :)
Determine whether each expression is equivalent to
2x + 4y – 5 + 3x + 8 – 4y.
Check the box for Yes and leave blank for No.
x + x + y + y + y + y - 5 + x + x + x + 8 - 4y
6xy + 3 - 4y
-8y + 5x - 3
5x + 3
Answers
The algebraic expressions, \(x + x + y + y + y + y - 5 + x + x + x + 8 - 4y\) and \(5x + 3\) are equivalent to \(2x + 4y - 5 + 3x + 8 - 4y\)
To determine whether each expression is equivalent to \(2x + 4y - 5 + 3x + 8 - 4y\), apply the knowledge of algebra to solve each of the following in it's simplest form.
First, simplify \(2x + 4y - 5 + 3x + 8 - 4y\) as follows:
Add like terms
\(2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y - 5 + 8\\5x + 3\)
Next, compare or simplify where necessary each of the given algebraic expressions with \(5x + 3\)
First Option
\(x + x + y + y + y + y - 5 + x + x + x + 8 - 4y\)
Add like terms together
\(2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y -5+8\\5x + 3\)
Therefore, \(x + x + y + y + y + y - 5 + x + x + x + 8 - 4y\) is equivalent to \(2x + 4y - 5 + 3x + 8 - 4y\)
Check the box for YES.Second Option:
\(6xy + 3 - 4y\) (cannot be simplified further)
\(6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y\)
Therefore:
Leave the box BLANK for NO.Third Option:
\(-8y + 5x - 3\) (cannot be simplified further)
\(-8y + 5x - 3 \neq 2x + 4y -5 + 3x + 8 - 4y\)
Therefore:
Leave the box BLANK for NO.Fourth Option:
\(5x + 3\)
\(5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y\)
Therefore:
Check the box for YES.Thus, the algebraic expressions that are equivalent to \(2x + 4y - 5 + 3x + 8 - 4y\) are:
\(x + x + y + y + y + y - 5 + x + x + x + 8 - 4y\)\(5x + 3\)Learn more about algebraic expressions here:
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Find the measurement of angle A.
Answers
Answer:
4) a=35°
Step-by-step explanation:
I can't explain its too complicated
4 to the 5th power times 4 to the -7th power divided by 4 to the -2nd power
Answers
Answer:
1
Step-by-step explanation:
4^(5)×4^(−7)÷4^(−2)
=4^(5+(-7)-(-2))
=4^(5-7+2)
=4^(0)
=1
Hey!
Your answer is 1.Heres how i got the answer
4^(5)×4^(−7)÷4^(−2)
=4^(5+(-7)-(-2))
=4^(5-7+2)
=4^(0)
Hope this helps!
Simon bought bags of potting soil to plant flowers on his patio. A large bag contains of soil, a medium bag contains of soil, and a small bag contains of soil. If he buys one large bag, one medium bag, and two small bags of soil, how many pots can Simon fill?
Answers
Answer:
12
Step-by-step explanation:
0 is an angle in a right-angled triangle. tan 0 = 23/52 What is the value of 0? Give your answer in degrees to 1 d.p.
Answers
The value of the angle θ is approximately 24.2 degrees to 1 decimal place.
In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.
To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:
θ = arctan(23/52)
Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.
Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.
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Can x-2 be simplified more? Why?
Answers
Answer:
No:
Step-by-step explanation:
No, there is no way to further simplify this equation, unless there is a value for x.
Answer:
No. x-2 can't.
Step-by-step explanation:
Its the same reason why you can't simplify 1+1. You could add them together, but in a case like this, where one number is unknown you can't. The number is already to its simplifiest form.