Answers
We will have the following:
1)
[tex]g(x)-f(x)=5^x-12-3x[/tex]2)
[tex]\begin{gathered} f(x)-g(x)=log_3(5x-5)-log_3(x-1) \\ \\ \Rightarrow f(x)-g(x)=log_3(\frac{5x-5}{x-1}) \\ \\ \Rightarrow f(x)-g(x)=log_3(5) \end{gathered}[/tex]Related Questions
Frank has a circular Garden the area of the garden is 100 ft Square what is the approximate distance from the edge of Frank's garden to the center of the garden (A= 3.14r ² )
Answers
ANSWER
[tex]5.64ft[/tex]EXPLANATION
The approximate distance from the edge of the garden to the center is the radius of the garden.
The area of a circle is given as:
[tex]A=\pi\cdot r^2[/tex]We can find the radius by making r the subject of the formula:
[tex]\begin{gathered} \frac{A}{\pi}=\frac{\pi\cdot r^2}{\pi} \\ r^2=\frac{A}{\pi} \\ r=\sqrt[]{\frac{A}{\pi}} \end{gathered}[/tex]Therefore, the approximate distance from the edge of the garden to the center (radius) is:
[tex]\begin{gathered} r=\sqrt[]{\frac{100}{3.14}} \\ r=\sqrt[]{31.85} \\ r\approx5.64ft \end{gathered}[/tex]That is the answer.
what is the density of the oak board? show your work.
Answers
I think this is a physics problem.
I'll read it
a) A rectangular prism and a cylinder
b) Volume of the log = pi*r^2 x h
Volume of the log = 3.14*5^2* 30
Volume of the log = 2355 in^3
density = weight / volume
density = 4263 / 2355
density = 1.81 lb/in^3 This is the result
what is the common difference in the sequence 25,20,15,10...?
Answers
We have a arithmetic sequence: 25, 20, 15, 10...
Tipically, arithmetic sequences can be written in recursive form as:
[tex]a_n=a_{n-1}+d[/tex]where a(n) and a(n-1) are consecutive terms and d is the common difference.
In this case, we can see that each term decreases by 5 units.
Then, we can describe this sequence as:
[tex]a_n=a_{n-1}-5[/tex]which means that d = -5.
Answer: the common difference is d = -5.
The graphs of y = f(x) and y = g(x) are shown on the coordinate plane below.y = g(x) 10y = f(x)210-10-9-8-7 -6 -5 -4 -3 -2 -1 0- 1-26789 10-6-107If g(x) = k·f(x), what is the value of k?
Answers
Answer:
Explanation:
The first step is to find the equation of both lines. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m is the slope
c is the y intercept. It is the value of y at the point where the line cuts the vertical axis.
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of selected initial and final points on the line.
x1 and x2 are the x coordinates of the selected initial and final points on the line.
Considering labelled points on y = f(x),
when x1 = 0. y1 = - 3
when x2 = 2, y2 = 1
m = (1 - - 3)/(2 - 0) = 4/2 = 2
y intercept, c = - 3
The equation would be
y = f(x) = 2x - 3
Considering labelled points on y = g(x),
when x1 = 0. y1 = 6
when x2 = 2, y2 = - 2
m = (- 2 - 6)/(2 - 0) = - 8/2 = - 4
y intercept, c = 6
The equation would be
y = g(x) = - 4x + 6
The solution of both equations is the coordinate of the point of intersection. Thus,
Solution = (1.5, 0)
Given that
g(x) = kf(x), it means that
- 4x + 6 = k(2x - 3)
Substituting x = 1.5 into the equation, we have
- 4(1.5) + 6 = k(2 * 1.5) - 3
- 6 + 6 = 3k - 3
0 = 3k - 3
3k = 3
k = 3/3
k = 1
I need help with this assignment!! I already did A and B! I need help with the rest.
Answers
Given:
The roller-coster is moving in the trajectory of this curve
[tex]f(x)=3x^4-18x^3-21x^2+144x-108[/tex]Step by step solution:
To solve this complete problem we need to draw the estimated graph of this function, so that we can answer this question easily.
First of all, we need to find the roots of the given equation,to plot the curve:
let us put the random numbers that may satisfy the equation:
Let us put x = 1:
[tex]\begin{gathered} f(x)=3x^4-18x^3-21x^2+144x-108 \\ \\ f(1)=3-18-21+144-108 \\ \\ f(1)=\text{ 0} \end{gathered}[/tex]From here we can say that 1 is the root of the equation.
We will now divide this function from (x-1), so that we can get the cubic equation:
We will use long division method for division, the result we get after the division is:
[tex]f(x)=(x-1)(3x^3-15x^2-36x+108)[/tex]We will now try to factorize the cubic equations, by putting the random numbers that may satisfy the equation:
let us put x = 2:
[tex]\begin{gathered} f(x)=(x-1)(3x^3-15x^2-36x+108) \\ \\ f(2)=(2-1)(3(2)^3-15(2)^2-36(2)+108) \\ \\ f(2)=(1)(24\text{ }-\text{ 60 - 72 +108}) \\ \\ f(2)=0 \end{gathered}[/tex]From here we can say that f(2) is also the root of this cubic
We will now divide the cubic equation with (x-2), so we can break the cubic into quadratic:
Upon division the cubic equation break into following factors:
[tex]\begin{gathered} =(x-2)(3x^2-9x-54) \\ \\ which\text{ further simplified into:} \\ \\ =(x-2)(x-6)(x+3) \end{gathered}[/tex]From here we have found out four roots of the initial function that are:
x = 1,2,6,-3
Now we can easily plot the curve:
This is estimated curve, there are no sharp edges.
On the basis of this curve, we can easily answer all the questions related to this curve.
Express the ratio in simplest form:1.25naira ratio 5naira
Answers
Answer:
1:4
Explanation:
Given the ratio:
[tex]1.25\colon5[/tex]Written in fraction form, we have:
[tex]\frac{1.25}{5}=\frac{1.25}{1.25\times4}=\frac{1}{4}=1\colon4[/tex]The ratio in simplest form is 1:4.
Question 2 of 5
√16 =
Ο Α. 6
OB. 4
C. 8
OD. 3
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Answer:
Uhm if this is the square root of 16 it's B.) 4
hello) i need some help with b) include an explanation if not a problem, thanks in advance)
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What would happen if X doesn't lie on OM? If it is true that X lies on OM, if we suppose the opposite then we should have a contradiction, so the only way the contradiction doesn't happen is that it is true
Statements1. We know that BX:XA = 1:2
2. We know that M is the middle point between B and P
We need to prove that X lies on OM
Let's suppose X doesn't lie on OM
By 2, we know that 2BM = BP
If X doesn't lie on OM then the intersection between OM and BA is not X
Let's say the line that goes from O to the line BP and intersects BA on X is OX', where X'≠M
y varies directly as x. y =84 when x=6. Find y when x=12y= ?
Answers
If y varies directly as x, we have that
[tex]y\propto x[/tex]Then
[tex]y=kx(where\text{ k is a constant\rparen}[/tex][tex]\begin{gathered} When\text{ y=84 , x= 6} \\ y=kx \\ 84=6k \\ k=\frac{84}{6}=14 \end{gathered}[/tex]The relationship between x and y is given as
[tex]\begin{gathered} y=kx \\ y=14x \end{gathered}[/tex]Therefore when x= 12, y=?
[tex]\begin{gathered} y=14x \\ y=14\times12=168 \end{gathered}[/tex]Hence, the value of y when x = 12 is 168
Final answer: y = 168
1/2 + 1/5 = * Your answer
Answers
We applied the rules for adding fractions with different denominators. This is a way to achieve this. Graphically, we do the operations in this way:
Answer:
7/10
Step-by-step explanation:
1/2 + 1/5
We need to get a common denominator
1/2 * 5/5 = 5/10
1/5 * 2/2 = 2/10
We can add these together
5/10 + 2/10 = 7/10
234Weight (pounds)OA. The weight of the package is a function of the number ofpackages.B. The shipping cost is a function of the number of packages.C. The shipping cost is a function of the weight of the package.OD. The weight of the package is a function of the shipping cost.SUBMIT
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The graph representing the relation between the shipping cost and the weight of packages is shown.
It is required to choose which function is true about the functional relationship.
Since the shipping cost is at the vertical axis and the weight of packages is at the horizontal axis, it follows that the shipping cost is a function of the weight of the package.
The answer is C.
Solve for n: 400(1.16)^n=35,120
Answers
The given equation is:
[tex]400\left(1.16\right)^n=35120[/tex]It is required to solve the equation for the value of n.
Divide both sides of the equation by 400:
[tex]\begin{gathered} \frac{400\left(1.16\right)^n}{400}=\frac{35120}{400} \\ \\ \Rightarrow\left(1.16\right)^n=\frac{439}{5} \end{gathered}[/tex]Take the logarithm of both sides of the equation:
[tex]\begin{gathered} \log(1.16)^n=\log\left(\frac{439}{5}\right) \\ \text{ Apply the power property of logarithms:} \\ \Rightarrow n\log(1.16)=\log\left(\frac{439}{5}\right) \end{gathered}[/tex]Divide both sides by log (1.16):
[tex]\begin{gathered} \frac{n\log(1.16)}{\log(1.16)}=\frac{\log\left(\frac{439}{5}\right)}{\log(1.16)} \\ \Rightarrow n=\frac{\operatorname{\log}(\frac{439}{5})}{\operatorname{\log}(1.16)}\approx30.151 \end{gathered}[/tex]The value of n is about 30.151.
To solve for x, you divide each side by what number?(4.5)x = 264.5456
Answers
Answer
4.5
Step-by-step explanation
Given the equation:
[tex]4.5x=26[/tex]Dividing at both sides by 4.5, we get:
[tex]\begin{gathered} \frac{4.5x}{4.5}=\frac{26}{4.5} \\ x=\frac{52}{9} \end{gathered}[/tex]Answer:
Divide each side by 4.5
Step-by-step explanation:
(4.5)x = 264.5456
We want to isolate x
Divide each side by 4.5
(4.5)x / 4.5 = 264.5456/ 4.5
x =58.78791
The length of a rectangle is 5 inches more than the width. The perimeter is 42 inches. Find the length and the width of the rectangle.The width of the rectangle is ___ cubit inches, square inches or inches ? and the length of the rectangle is ____ cubit inches, square inches or inches?
Answers
Given
perimeter = 42 inches
length of a rectangle is 5 inches more than the width.
Find
width, length
Explanation
Let width of rectangle = x inches
length = 5 + x
Perimeter of rectangle = 2 (l + b) = 2(5+x+x) = 42
[tex]\begin{gathered} 2\times(5+x+x)=42 \\ 5+2x=21 \\ 2x=16 \\ x=8 \end{gathered}[/tex]width = 8 inches
Length = 5 + 8 = 13 inches
Final Answer
The width of the rectangle is 8 inches.
The length of the rectangle is 13 inches.
Pls help now You play a game that requires rolling a 6 sided die then randomly choosing a colored card from a deck containing 5 red cards,4blue cards, and 8 yellow cards find the probability that you will roll 3 on the die and choose a yellow card
Answers
Find the probability that you will get a 3 on a roll of a die. Since there is only one 3 in a die and there are 6 sides in a die, divide 1 by 6.
[tex]P(3)=\frac{1}{3}[/tex]Find the probability that you will get a yellow card. Divide the number of yellow cards by the total number of cards.
[tex]\begin{gathered} P(y)=\frac{8}{5+4+8} \\ =\frac{8}{17} \end{gathered}[/tex]Since the two events are independent, multiply the obtained probabilities.
[tex]undefined[/tex]Divide 30.4cm into 8 equal parts.
Find the length of each part.
Answers
Answer:
304/10÷8/1
304/10×1/8
38/10
3.8
or
304÷8
=38
The function in the form f(x)=2/5x-5 is graphed below. What is the value of x when f(x)=-9?
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−5x+8?I need the Answer please!!
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We have the next expression
[tex]-5x+8[/tex]And we must solve it for x
[tex]undefined[/tex]Marco and Jazmin each bought trees to plant from Lowe’s. Marco spent $188 on 7 lemon trees and 9 orange trees. Jazmin spent $236 on 13 lemon trees and 9 orange trees. How much did lemon trees cost? How much did orange trees cost?
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Let x be the cost of each Lemon tree and y the cost of eache orange tree. So we get that
[tex]\begin{cases}7x+9y=188 \\ 13x+9y=236\end{cases}\rightarrow6x=48\rightarrow x=\frac{48}{6}=8[/tex]having that the lemon tree cost $8 we get that
[tex]56+9y=188\rightarrow9y=188-56=132\rightarrow y=\frac{132}{9}=\frac{44}{3}[/tex]so each orange tree cost $44/3
Given the figure below, find the values of x and z. (9x + 70). (6x + 80).
Answers
( 9x+70)+(9x+70) + (6x + 80) + (6x+ 80 ) = 360
If you solve the equation you get that
x = --44/5
Now, since
z = ( 6x +80 ) = ( 6*(-44/5) + 80 ) = 136 / 5
So, there you have, x,z
you are in a hot air balloon that is 600 feet above the ground. if the angle from your line of sight to your friend is 20°, how far is he from the point on the ground.
Answers
Answer
x = 164.9 ft
Explanation:
Given the following figures
To find the distance from the point on the ground, we need to apply the SOH CAH TOA
[tex]\begin{gathered} \text{Height = 600 ft} \\ \text{Horizontal distance x} \\ \theta\text{ = 20} \\ \text{ }\tan \theta\text{ =}\frac{opposite}{\text{adjacent}} \\ \text{opposite = 600 ft} \\ \text{adjacent = x ft} \\ \tan \text{ 20 = }\frac{600}{x} \\ \text{Cross multiply} \\ x\cdot\text{ tan 20 = 600} \\ \text{x = }\frac{600}{\tan \text{ 20}} \\ \tan \text{ 20 = }0.3639 \\ \text{x = }\frac{60}{0.3639} \\ \text{x = }164\text{ .9 ft} \end{gathered}[/tex]Therefore, the distance is 164.9 ft
Two boats leave the same marina. One heads north, and the other heads
east. After some time, the northbound boat has traveled 39 kilometers, and
the eastbound boat has traveled 52 kilometers. How far apart are the two
boats
Answers
The distance travelled by the two boats forms a right triangle. Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.
It is given to us that -
There are two boats
One boat heads north while the other heads east
The boat travelling north has traveled 39 kilometers
The boat travelling south has traveled 52 kilometers
We have to find out the distance between the two boats after they have travelled the respective distances.
It is known to us that one boat heads north while the other heads east. We can see that the trajectory formed between the two boats resembles a right triangle as they start from the same point.
One leg of the right triangle formed equals to the distance travelled by the boat travelling north.
Let us say the distance travelled by the boat travelling north be "a".
=> a = 39 kilometers ----- (1)
Other leg of the right triangle formed equals to the distance travelled by the boat travelling east.
Let us say the distance travelled by the boat travelling east be "b".
=> b = 52 kilometers ------ (2)
Now, the distance between the two boats after they have travelled the respective distances is equal to the value of the hypotenuse of the right triangle formed.
Let us say the hypotenuse of the right triangle formed be "h".
According to the Pythagorean Theorem for a right triangle,
[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (3)
where, a, b = legs of the right triangle
and, h = hypotenuse of the right triangle
Substituting the values of a and b from equations (1) and (2) respectively in equation (3), we have
[tex]a^{2} +b^{2} =h^{2}\\= > 39^{2} +52^{2} =h^{2}\\= > h^{2}=1521+2704\\= > h^{2}=4225\\= > h=65[/tex]
So, the value of the hypotenuse of the right triangle formed is 65 kilometers.
Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.
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2. Calculate the gross pay for each of the following positions for a 30-hour work week: $8.50/hr $9.20/hr Locker room attendant Bus server Pantry help Waiter/Waitress $9.45/hr $7.00/hr a) Pantry help c) Waiter/Waitress b) Locker room attendant d) Bus server
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We know that this position is paid with a ratio of $8.50 per hour. So, let's multiply to find the earnings for 30 hours.
[tex]8.50\cdot30=255[/tex]So, the earnings for this position is $255.
Bus server.This position is paid 9.20 per hour. So, 30 hours earnings would be
[tex]9.20\cdot30=276[/tex]Pantry help.The earnings for this position would be
[tex]9.45\cdot30=283.50[/tex]$283.50 for 30 hours.
Waiter/Waitress.The earnings for this position are
[tex]7\cdot30=210[/tex]$210 for 30 hours.
help me; its all explained in the picture thank you
Answers
The mean, mode, and mid-range of the given numbers are 13,13,16 respectively.
What are the mean, mode, and range?The total of all the numbers is represented by the mean. The median is the number in the center of an ordered list. The most frequent number is the mode. The highest number less the smallest number is the range.
Mean = sum of the number/ total no. of observations
Mean = 117/ 9
Mean = 13
Mode: The unique number that repeatedly comes
Given,
9, 9, 10, 11, 13, 13, 13, 14, 25
Mode = 13
Range: Deduct the smaller number from the greater one.
Range = 25-9
Range = 16
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to qualify for a police academy, candidates must score in the top 21% on a general abilities test. assume the test scores are normally distributed and the test has a mean of 200 and a standard deviation of 20. find the lowest possible score to qualify
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The lowest value that is needed in order to qualify is given as 216.128
What is z score?The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from:
z = (raw score - mean) / standard deviation
Given; mean of 200 and a standard deviation of 20
P(z > c) = 21% = 0.21
1 - P(z < c) = 0.21
P(z < c) = 0.79
we are to find the critical value of z using excel function
=NORM.S.INV(1-0.21)
= 0.806421247
To get the lowest value we would have to put the values in the formula
0.8064 = (x - 200)/20
0.8064 * 20 = (x - 200)
16.128 = (x - 200
take like terms
x = 200 + 16.128
x = 216.128
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200×200 dividend by 20
Answers
We need to find the value of 200×200 dividend by 20
So,
[tex]\frac{200\cdot200}{20}=\frac{40000}{20}=2000[/tex]The weight (W kg) of a decaying radio active substance after n years is given by W= Wo(1/2)^n/100, where Wo kg is the initial weight of the substance. 1. Atleast how many years will it take for the radioactive substance to lose to 10% of its initial weight?
Answers
Answer:
332.19 years
Explanation:
The weight, W of the substance after n years is given by:
[tex]W=W_o\mleft(\frac{1}{2}\mright)^{\frac{n}{100}}[/tex]Let the initial weight = 100%
If the substance loses to 10% of its initial weight, then:
• Wo = 100%
,• W= 10%
Substitute these into the formula:
[tex]\begin{gathered} \frac{10}{100}=\frac{100}{100}\mleft(\frac{1}{2}\mright)^{\frac{n}{100}} \\ \implies0.1=\mleft(\frac{1}{2}\mright)^{\frac{n}{100}} \end{gathered}[/tex]We then solve the equation for the value of n.
Take the logarithm of both sides.
[tex]\begin{gathered} \log (0.1)=\log \mleft(\frac{1}{2}\mright)^{\frac{n}{100}} \\ \implies\log (0.1)=\frac{n}{100}\log (\frac{1}{2})^{} \end{gathered}[/tex]Then divide both sides by log(1/2):
[tex]\begin{gathered} \frac{\log (0.1)}{\log (\frac{1}{2})}=\frac{\frac{n}{100}\log(\frac{1}{2})^{}}{\log(\frac{1}{2})} \\ \implies\frac{n}{100}=\frac{\log (0.1)}{\log (\frac{1}{2})} \end{gathered}[/tex]Finally, multiply both sides by 100:
[tex]\begin{gathered} 100\times\frac{n}{100}=100\times\frac{\log (0.1)}{\log (\frac{1}{2})} \\ n=332.19\text{ years} \end{gathered}[/tex]It will take at least 332.19 years for the radioactive substance to lose to 10% of its initial weight.
Please help me this question I couldn’t understand it please.
Answers
Given:
Length of a rectangle is a+1
width of a rectangle is a
[tex]\begin{gathered} \text{Perimeter}=2(a+1+a) \\ =2(2a+1) \\ =4a+2 \end{gathered}[/tex]find the probability for each situation. question 1. A number cube is a spun two times. find the probability that it will land on a event number both times.
Answers
In a number cube, the sample space is {1,2,3,4,5,6}.
The even numbers are {2,4,6}.
Determine the probability for cube landing with even number first times.
[tex]\begin{gathered} P(A)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Determine the probability for cube landing with even number in second time.
[tex]\begin{gathered} P(B)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Since both rolling of dices are independent to each other. So probability for getting even number on both time is,
[tex]\begin{gathered} P(AandB)=P(A)\cdot P(B) \\ =\frac{1}{2}\cdot\frac{1}{2} \\ =\frac{1}{4} \end{gathered}[/tex]Answer: 1/4
A biologist measured the length and mass of 20 reptiles. The equation y = 0.3x - 2 is the line of best fit for the data, where x is the length, incentimeters, and y is the mass, in grams.Based on the equation, what is the approximate length of a reptile that has a mass of 20.5 grams?
Answers
If the mass is 20.5 grams, then you have to replace y = 20.5 in the equation.
20.5 = 0.3x - 2
and solve for x, as follows:
20.5 + 2 = 0.3x
22.5 = 0.3x
22.5/0.3 = x
75 = x
The approximate length is 75 cm