Answers
Answer:
-1/2 is correct
Step-by-step explanation:
Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]. To evaluate the expression (g - f)(2), you need to first find the values of g(2) and f(2), and then subtract f(2) from g(2).
Given:
[tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \) \\ \( g(x) = \log_4(x) \)[/tex]
Let's start by calculating the values of f(2) and g(2): 1. [tex]\( f(x) = \frac{x + 3}{x^2 + 2x - 3} \)[/tex]
Substitute (x = 2): [tex]\( f(2) = \frac{2 + 3}{2^2 + 2 \cdot 2 - 3} = \frac{5}{7} \)[/tex]
2. [tex]\( g(x) = \log_4(x) \)[/tex] Substitute ( x = 2): [tex]\( g(2) = \log_4(2) \)[/tex]
Now, evaluate the expression [tex]\( (g - f)(2) \):[/tex]
[tex]\( (g - f)(2) = g(2) - f(2) = \log_4(2) - \frac{5}{7} \)[/tex]
To determine which option matches this value, calculate [tex]\( \log_4(2)[/tex]) and subtract [tex]\( \frac{5}{7} \)[/tex] from it.
Approximately,[tex]\( \log_4(2) \)[/tex] is around 0.5.
So, [tex]\( (g - f)(2) \approx 0.5 - \frac{5}{7} \)[/tex]. To compare this result with the options provided, convert the fractions to a common denominator:
[tex]\( \frac{5}{7} = \frac{35}{49} \)[/tex]. So, [tex]\( (g - f)(2) \approx 0.5 - \frac{35}{49} \)[/tex].
Now, simplify the subtraction: [tex]\( 0.5 - \frac{35}{49} = \frac{24}{49} \)[/tex]
Among the given options, option C [tex](\( \frac{1}{2} \))[/tex] is the closest to [tex]\( \frac{24}{49} \)[/tex]. Therefore, the answer is: C. [tex]\( \frac{1}{2} \)[/tex]
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Related Questions
i will give brainliest
PLEASE HELP!
Answers
Answer:
3/4
Step-by-step explanation:
It says Event Q is more likelier to occur than Event T⇒ P(T) = 1/2
⇒ P(Q) > P(T)
⇒ P(Q) > 2
A possible probability is :
P(Q) = 3/4cercaughters A mother says to her 5 years ago I 5 times as old as you were but 10 years Hence shall be only twice as old as you will find the posent age of mother T and daughter
Answers
Answer:
Daughter is now 10 The mother is 30
Step-by-step explanation:d
d=daugter
5d=mother
5d = 2d +5 +10
3d =15
d=5
5 years ago d=5 m=25
now d=10 m=30
in10 years d=20 m=40
n △IJK, m∠J=34°, m∠I=72°, and i=206. Identify j rounded to the nearest tenth.
Answers
Answer:
121.1
Step-by-step explanation:
The measurement j will be 121.1
What is law of sine?Law of sine says that ratio of sine of an angle and its opposite side is always same for every 3 angles of the triangle and their opposite sides.
In ΔABC,
sinA/a = sinB/b = sinC/c
in the given triangle ΔIJK
∠J=34°
∠I=72°
i=206
So, using law of sine,
sinI/i = sinJ/j
⇒sin72°/206=sin34°/j
⇒j=(sin34°/sin72°)*206
⇒j=121.1
Therefore, the value of j will be 121.1
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how do I convert 216 in percentage
Answers
Answer: 21600
216 as a percentage of certain number x can be calculated by dividing 216 by x, and multiplying the result by 100. For example, 216 as a percentage of 10 = (216 / 10) x 100% = 2160%.
Step-by-step explanation:
probably extremely easy but would like a little explanation on doing this when it comes to this specific subject
Answers
Answer:
look at each pair. examine each notice exponents so you find the hidden gcf
Step-by-step explanation:
Find the surface area of the prism.
Answers
Answer:
158 in²
Step-by-step explanation:
Surface area of a rectangular prism:
2(lw + lh + wh), where w is the width, l is the length and h is the height.
= 2((8 x 5) + (8 x 3) + (5 x 3))
= 2(40 + 24 + 15)
= 2(79)
= 158 in²
integrate the following by parts |xcos x dx
Answers
[tex]\displaystyle \int x \cos x ~dx\\\\=x\displaystyle \int \cos x ~dx- \displaystyle \int \left(\dfrac{d}{dx} x \displaystyle \int \cos x ~dx \right) dx\\\\=x\sin x - \displaystyle \int\left( \sin x \right) dx\\ \\=x \sin x - (-\cos x) +C\\\\=x \sin x + \cos x +C[/tex]
What is the equation of the line that passes through the point (3, 5) and has a slope
of -1/3
Answers
Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m = slopeb = y-intercept (the value of y when the line crosses the y-axis)To determine the equation of a line:
Find the slopePlug the slope into y=mx+bPlug in a point that falls on the line as (x,y)Solve for bSolving the Question
We're given:
[tex]m=-\dfrac{1}{3}[/tex]The lines passes through the point (3,5)[tex]y=mx+b[/tex]
⇒ Plug the slope into the equation:
[tex]y=-\dfrac{1}{3}x+b[/tex]
⇒ Plug in the given point (3,5) and determine the y-intercept:
[tex]5=-\dfrac{1}{3}(3)+b\\\\5=-1+b\\\\b=6[/tex]
⇒ Plug this back into the equation along with the slope:
[tex]y=-\dfrac{1}{3}x+6[/tex]
Answer[tex]y=-\dfrac{1}{3}x+6[/tex]
Please at least just look to see if its
easy for you
Answers
Answer:
4/10
2/5
6/15
Step-by-step explanation:
We can change all fraction to decimal :
2/10 = 0.2
1/10 = 0.1
4/10 = 0.4
2/5 = 0.4
4/5 = 0.8
6/15 = 0.4
Base on that we can see that 4/10, 2/5, and 6/15 are equal
~lenvy~
What is the equation of the trend line in the scatter plot?
Answers
Answer:
y=(x-1)
Step-by-step explanation:
Which lines are the directrices of the ellipse?
x = −4.25 and x = 8.25
x = −3.25 and x = 9.25
y = −4.25 and y = 8.25
y = −3.25 and y = 9.25
Answers
The lines that are the directrices of the ellipse is B. x = −3.25 and x = 9.25.
How to calculate the ellipse?From the information given, the equation of parabola will be:
= (x - 3)²/5² + (y - 2)²/3² = 1
Hence, h = 3, k = 2, a = 5, b = 3
e = ✓1 - ✓3²/5²
E = 4/5 = 0.8
The directix will be:
x = 3 + 5/0.8
x = 9.25
x = 3 - 5/0.8
x = -3.25
Therefore, lines that are the directrices of the ellipse is x = −3.25 and x = 9.25.
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Select True or False for each statement.
Statement True False
In the ordered pair (3, 5), the number 5 is the y-coordinate.
True – In the ordered pair ( 3, 5 ) , the number 5 is the y-coordinate.
False – In the ordered pair ( 3, 5 ) , the number 5 is the y-coordinate.
The origin has coordinates (0, 0).
True – The origin has coordinates ( 0, 0 ) .
False – The origin has coordinates ( 0, 0 ) .
The horizontal axis in a coordinate plane is the y-axis.
Answers
The number 5 in the ordered pair (3, 5) is the y-coordinate (TRUE)
(0, 0) is the origin on a coordinate plane (TRUE)
y-axis is the horizontal axis on a coordinate plane (FALSE).
What is an Ordered Pair?An ordered pair is a set of numbers that represents the location of a point on a coordinate plane that has an x-axis (horizontal axis) and y-axis (vertical axis).
An ordered pair is given as (x, y). Therefore, the following statements given are matched as shown below:
The number 5 in the ordered pair (3, 5) is the y-coordinate (TRUE)(0, 0) is the origin on a coordinate plane (TRUE)y-axis is the horizontal axis on a coordinate plane (FALSE).Learn more about ordered pair on:
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What is the surface area of each solid pyramid? Round answers to the nearest square unit.
Please explain how to solve the problem, not just the answer.
Answers
Answer:
The total surface area is
57ft^2.
Using the chart, determine which college is the LEAST expensive.
Answers
Answer:
college c
Step-by-step explanation:
bc its the least amount of money and has the second highest loan default
On the basis of her newly developed technique, a student believes she can reduce the amount of time schizophrenics spend in an institution. As director of training at a nearby institution, you agree to let her try her method on 20 schizophrenics, randomly sampled from your institution. The mean duration that schizophrenics stay at your institution is 90 weeks, with a standard deviation of 10 weeks. The scores are normally distributed. The results of the experiment show that patients treated by the student stay at the institution a mean duration of 84 weeks. What do you conclude about the student’s technique? Use α = .05. What are the 7 steps?
Answers
The exercise above is referred to as Hypothesis Testing which is also called Significance Testing.
What is Significance Testing?
Significance testing is a method that is used to evaluate a research question. This is important because, after you have set a research question or hypothesis, the next step is to check whether it is Null or not.
What are the seven steps involved in the above exercise are:
Two-Tailed (non-directional test)Alpha (α) = 0.05μ = 90σ = 10N = 20X = 84s = 10
Using ∝ = 0.05₂ tail, the conclusion is given as follows:
Z[tex]_{obt}[/tex] = (84-90)/10/[tex]\sqrt{10}[/tex]
= - 6/10/3.1622777
= -6/3.1622777
= -1.8973666
Z[tex]_{crit}[/tex] = for a two-tailed test with ∝ = 0.05 = = ± 1.960
Because we are looking at the left (negative, fewer) tail, Z[tex]_{crit}[/tex] = -1.960
Since | Z[tex]_{obt}[/tex] = -1.897 | [tex]\geq[/tex] | Z[tex]_{crit}[/tex] = -1.960 |
It does fall within the critical region for rejection (left tail), therefore we reject the null hypothesis (H₀) and conclude that the average time spent in the institution for the sample of patients is significantly lower than the institution's average stay.
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The length of the term is one year. Calculate the principal if the maturity value is $4,500 and the simple interest is $350.
Answers
Answer:
Easy! The answer is $4,150
Step-by-step explanation:
The $350 is interest so we will take that away from the maturity value to get 4,150!
mark BRAINLIEST IF YOU THINK I HELPED
This below in pic is the question i need reason for my answer pls help
Answers
Answer:
The triangle is equilateral, therefore each angle must be 60.
Step-by-step explanation:
100%
Đ
X
A doctor treated 24, 27, 31, 19, 26, 15, and 19 patients during the past 7 days.
Which is the median number of
patients treated by the doctor?
A 15
B. 19
C. 23
D. 24
E. 31
Answers
Answer:
C. 23
Step-by-step explanation:
Add then divide by 7
CO
8
6
4
N
Which function is graphed?
46
8
N
-8 -6 -4 -20
-2
-4
-6
-8
O A. y- *#4x23
[+ ,
1-x+4,52
Answers
calculate the social security and Medicare deductions for the following employee (assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare)
cumulative earnings before this pay period: $409,100
pay amount this period: $8,800
Answers
Answer:
Several interpretations:
1. If you're simply looking for the math involved in the employee's portion of the $8,800: 6.2% +1.45% = 7.65%. So 7.65% of $8,800 = $673.20.
2. If you are trying to calculate total FICA for this pay period, it would be 12.4% + 2.9% since these amounts are split between the employer and employee (15.3% = $1,346.40).
3. If you are trying to calculate the total for this pay period given that their YTD earnings are $417,900 (lucky employee!), they do not owe anything (see explanation below).
Step-by-step explanation:
The OASDI program limits the amount of earnings that are subject to taxation in a given year. For 2022, the contribution and benefit base, otherwise known as the taxable maximum, is $147,000. The taxable max for 2018 was $128,400).
Assuming this employee has exceeded that amount as their current YTD income is $417,900 (409,100 + 8,800), they don't owe anything.
Quick Edit:
My apologies! An additional 0.9% Medicare tax is added for taxable income exceeding $200,000 depending on their filing status. Table is available at https://fitsmallbusiness.com/
Write an equation in slope-intercept form of the line that passes through ( 7,2 ) ( 2,12 )
Answers
Answer:
y = -2x + 16
hope this helped :)
In simplest form 1 3/10 x 18=
Answers
207/5 is the simplest form of [tex]1\frac{3}{10}[/tex] ×18
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the simplest form of [tex]1\frac{3}{10}[/tex] ×18
Convert the mixed fraction to improper fraction and simplify.
[tex]1\frac{3}{10}[/tex]=23/10
Now multiply Twenty three divided by ten with eighteen.
23/10×18
Multiply 23 and 18
23×18=414
Now divide 414 by 10
414/10
Both numerator and denominator can be divided by 2 so
207/5
Hence 207/5 is the simplest form of [tex]1\frac{3}{10}[/tex] ×18
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Find the measure of the reflex angle, B.
A
75%
B
B = [?]°
Enter
Answer
Answers
Answer:
285
Step-by-step explanation:
I could be wrong but if i remember you subtract 75 from 360 which would be 285
PLEASE HELP PLEASE PLEASE HELP
Answers
Answer:
[tex]\frac{1}{4}*\frac{25}{25} = 25/100[/tex]=25%
Step-by-step explanation:
Which of the following values in the set below will make the equation 4x + 2 = 18 true?
{0, 1, 2, 3,4}
^^ those are the input numbers
Answers
Answer:
4
Step-by-step explanation:
subtract 2 on both sides you will get 4x=16 because 18-2=16 then divide both sides by 4 to get ×=4
4x+2=18
-2. -2
4×=16
4. 4
x=4
Why can't the square root cancel out the exponents in the distance formula?
Answers
Let's say instead of x2-x1, we say, "The difference between x2 and x1", let's call this value A. We'll do the same for the y variables and call that difference B, for simplicity.
For (2,3) and (4,9), we're really dealing with those differences, so A should equal 2, and B should equal 6. So far so good. But this is pretty much the "rise and run" of a triangle. 2 to the right, then 6 up. But if you walk 2 miles east, then 6 north, while you, personally, have travelled 8 miles, the distance between your starting point and where you are is NOT the way you walked.
So in the case of the triangle, using 2 as the run and 6 as the rise, to get the straight line between the starting point and the ending point, we have to do Pythagorean's Theorem, or A2 + B2 = C2 to get that last direct line between the two points. Cancelling the root and exponents removes the process to get that exact distance squared. We then take the square root of that to get the exact distance.
Sarah's family has a circular swimming pool The circumference of the pool is 25.12 m. What is its area
Answers
Answer:
4889.26m²
Step-by-step explanation:
[tex]Solution,\\\\Here,\\\\Circumference(C)=25.12 m\\\\Radius(r)=?\\\\As,\\\\\hookrightarrow Circumference=2\pi r\\\\\hookrightarrow 25.12m/2\pi =r\\\\\hookrightarrow r=39.45m\\\\Now,\\\\Area=\pi r^{2} \\\\Area=\pi \times(39.45m)^{2} \\\\Area=4889.26m^{2}[/tex]
Find teh value of teh coefficient a in the equation ax +2y =8 if a solution to the equation is the pair x=2 and y= 1
Answers
Answer:
a(2)+2(1)=8
2a+2=8
2a=8-2
2a=6
a=3
2a + 2 = 8
2a = 8-2
2a = 6
a = 6/2
a = 3
100 points! asap! Which graph best represents the solution to the system of equations shown below?
y = -2x + 14
y = 2x + 2
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 8, 3.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 8, negative 3.
A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, 8.
Answers
Answer:
A) A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair (3, 8)
Step-by-step explanation:
Given equations:
[tex]\textsf{Equation 1}: \quad y=-2x+14[/tex]
[tex]\textsf{Equation 2}: \quad y=2x+2[/tex]
Substitute Equation 2 into Equation 1 and solve for [tex]x[/tex]:
[tex]\implies 2x+2=-2x+14[/tex]
[tex]\implies 4x=12[/tex]
[tex]\implies x=3[/tex]
Substitute found value of [tex]x[/tex] into Equation 2 and solve for [tex]y[/tex]:
[tex]\implies y=2(3)+2=8[/tex]
Therefore, the solution to the system is (3, 8).
This is the point of intersection of the two lines.
The following points (-4, 3), (-2, -1), (3, 1) are vertices of a parallelogram, find the coordinates of the THREE POSSIBLE LOCATIONS, of the fourth vertex
Answers
Answer:
A’(5 , -3)
B’(1 , 5)
C’(-9 , 1)
Step-by-step explanation:
Let A be the point of coordinates (-4, 3)
Let B be the point of coordinates (-2, -1)
Let C be the point of coordinates (3, 1)
____
In this case we can form three parallelograms ABA’C, BAB’C , CAC’B
How to find the coordinates of the fourth point A’ of the parallelogram ABA’C
Since we know that the diagonals AA’ and BC of the parallelogram ABA’C intersect in their midpoint then we need to solve these two equations in order to get the coordinates of the point A’ :
[tex]\begin{aligned}\left\{\begin{array}{l}\frac{x_{A}+x_{A^{\prime}}}{2}=\frac{x_{B}+x_{C}}{2} \\\frac{y_{A}+y_{A^{\prime}}}{2}=\frac{y_{B}+y_{C}}{2}\end{array}\right.& \Leftrightarrow\left\{\begin{array}{l}-4+x_{A^{\prime}}=-2+3 \\3+y_{A^{\prime}}=-1+1\end{array}\right.\\\\& \Leftrightarrow\left\{\begin{array}{l}x_{A^{\prime}}=1+4=5 \\y_{A^{\prime}}=0-3=-3\end{array}\right.\\\\& \Leftrightarrow A^{\prime}(5,-3)\end{aligned}[/tex]
________________________
We can follow the same method for the other two parallelograms In order to get the coordinates of the points B’ and C’.
B’(1 , 5)
C’(-9 , 1)