Answer:
[tex]g^{-1}[/tex](x) = [tex]\frac{5x+45}{3}[/tex]
Step-by-step explanation:
let y = g(x) and rearrange making x the subject
y = [tex]\frac{3}{5}[/tex] x - 9 ( add 9 to both sides )
y + 9 = [tex]\frac{3}{5}[/tex] x
Multiply both sides by 5 to clear the fraction
5y + 45 = 3x ( divide both sides by 3 )
[tex]\frac{5y+45}{3}[/tex] = x
Change y back into terms of x, thus
[tex]g^{-1}[/tex](x) = [tex]\frac{5x+45}{3}[/tex]
The inverse is g⁻¹(x) = (5/3)*(x + 9)
How to find the inverse?
for a function f(x), the inverse f⁻¹(x) is defined as:
if f(x) = y
f⁻¹(y) = x
For this case, we can write:
g(g⁻¹(x)) = x
(3/5)*g⁻¹(x) - 9 = x
(3/5)*g⁻¹(x) = x + 9
g⁻¹(x) = (5/3)*(x + 9)
What is the equivalent fraction of 8/12
Answer:
There are many fractions that are equivalent to 8/12. But if you are looking for the most simplified fraction, then the answer would be 2/3. Because you divide 8 and 12 both by 2. 8 divided by 2 equals 4, and 12 divided by 2 equals 6. Then you would do it again, since both can be divided by 2 again. 4 divided by 2 equals 2, and 6 divided by 2 equals 3. You cannot divide 3 by 2, so your answer would be 2/3.
PLEASE HELP ME OUT AND ILL GIVE 5 STARS ASP!!
The value of 2^3 + 4^2=
Answer: 24
Step-by-step explanation:
2^3 + 4^2
(2×2×2) + (4×4)
8+16 = 24
The measure (in inches) of the sides
)) Rachel is using ribbon to create girls' hair barrettes. For a craft fair in Springfield, she
made 12 small barrettes and 12 large barrettes, using a total of 156 yards of ribbon. Then,
for another craft fair in Norwood, she made 10 small barrettes and 11 large barrettes, which
used a total of 138 yards. How many yards of ribbon does Rachel use for each?
Answer:
small: 5 yardslarge: 8 yardsStep-by-step explanation:
Using s and L to represent the amount of ribbon used for small barrettes and large barrettes, respectively, we have ...
12s +12L = 156
10s +11L = 138
Dividing the first equation by 12 gives ...
s +L = 13
Substituting s = 13-L into the second equation gives ...
10(13 -L) +11L = 138
130 +L = 138 . . . . . . . simplify
L = 8 . . . . . . . . . . subtract 130
s = 13 -8 = 5 . . . . find s
Rachel uses 5 yards for a small barrette, and 8 yards for a large barrette.
2. which quadrant is 7pi/4 radians in?
a. quadrant I
b. quadrant II
c. quadrant III
d. quadrant IV
Step-by-step explanation:
[tex] \frac{7\pi}{4} = 2\pi - \frac{\pi}{4} [/tex]
Therefore, Quadrant IV
option D
Use a power of ten to estimate the product.
52.6 × 9
450
526
540
500
Answer:
A
Step-by-step explanation:
3y+6-y Please help! I'm awful at math
Step-by-step explanation:
So what are you looking for with that equation?
4. A video rental store rents movies at $3.95 for the first night, plus $1.25 for each additional night. When you return your movie, you pay $7.70. How many extra nights did you keep the movie?
Answer:
3 nights
Step-by-step explanation:
Set up an equation that represents the problem:
y = 1.25x + 3.95
Where y is the total cost and x is the number of additional nights you rent the movie
Substitute:
7.70 = 1.25x + 3.95
Subtract 3.95 on both sides:
7.70 = 1.25x + 3.95
-3.95 -3.95
3.75 = 1.25x
Divide by 1.25 on both sides:
3.75 = 1.25x
/1.25 /1.25
3 = x
Therefore, you kept the movie for 3 additional nights.
Answer:
3
Step-by-step explanation:
Hey can someone check this thanks ( will mark as brainliest however is first!!)
d ≤ 6
The solution set is {6, 5, 4, 3, 2, 1, 0, –1, –2, ....}
Solution:
Given expression is the inequality.
The inequality is [tex]\frac{d}{3}\leq 2[/tex].
To solve this inequality:
[tex]$\frac{d}{3}\leq 2[/tex]
Multiply by 3 on both sides of the inequality, we get
[tex]$\frac{d}{3}\times 3\leq 2 \times 3[/tex]
[tex]$d\leq 6[/tex]
That is the value of d is 6, 5, 4, 3, 2, 1, 0, –1, –2, ....
The solution set is {6, 5, 4, 3, 2, 1, 0, –1, –2, ....}
Hence d ≤ 6.
Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school. Shaquille walks to Reyna's house every morning and then they walk to school together. What is the shortest distance Shaquille could walk on his way to school when he walks with Reyna?
Answer:
The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is = 25 blocks.
Step-by-step explanation:
Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school.
So, Reyna's house, the school, and the Shaquille's house form a right triangle and the shortest distance from Shaquille's house to Reyna's house is the hypotenuse of the right triangle.
So, the shortest distance that Shaquille could walk on his way to school when he walks with Reyna is = [tex]\sqrt{12^{2} + 5^{2}} + 12 = 13 + 12 = 25[/tex] blocks. (Answer)
The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is 25 blocks.
Calculation of the shortest distance:Since Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school.
So, here the shortest distance is
[tex]= \sqrt{(12)^2 + (5)^2}+ 12\\\\[/tex]
= 13 + 12
= 25
Hence, The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is 25 blocks.
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If 5 bags weigh the same as 3 blocks, how many blocks will 9 bags weigh?
The weight of 9 bags is 5.4 blocks
Solution:
Given that,
5 bags weigh the same as 3 blocks
We have to find how many blocks will 9 bags weigh
Let "x" be the weight of 9 bags
Then,
5 bags weigh the same as 3 blocks
9 bags weight the same as "x" blocks
From proportion we can say,
5 : 3 : : 9 : x
Therefore,
[tex]\frac{5}{3} = \frac{9}{x}\\\\5x = 27\\\\x = 5.4[/tex]
Thus the weight of 9 bags is 5.4 blocks
9 bags will be equal to 5.4 blocks
Step-by-step explanation:
Step 1 :
Given,
Weight of 5 bags = weight of 3 blocks
We need to find the weight of 9 bags
Step 2 :
From step 1 , we get
Weight of 1 bag = weight of 3 blocks ÷ 5
The weight of bags is in direct proportion to the weight of the blocks.
Hence
Weight of 9 bags = 3 blocks × 9 ÷ 5
= [tex]\frac{27}{5}[/tex] blocks = 5.4 blocks
Step 3 :
Answer :
9 bags will be equal to 5.4 blocks
Someone please help! I gave this extra points because the question has a picture. I will give thanks and 5 star for any answer.
Answer:
53°
Step-by-step explanation:
x + (2x + 21) = 180
(Corresponding angles &
Supplementary angles)
3x + 21 = 180
3x = 159
x = 53°
Question 23 (4 points)
Lenny worked 7 hours on Wednesday, 6 hours on Thursday, and 9 hours on Friday.
His gross pay for all three days was $196.90.
What was his hourly rate?
$8.20
$8.95
$28.13
$65.63
Lenny's hourly rate is calculated by dividing his gross pay of $196.90 by the total number of hours worked, which is 22 hours. The calculation gives an hourly rate of $8.95.
Explanation:The question is asking to calculate Lenny's hourly rate based on his gross pay for work done over three days. To find this rate, we will add the total number of hours worked and divide the total gross pay by this number.
Calculate the total number of hours Lenny worked: 7 hours on Wednesday, 6 hours on Thursday, and 9 hours on Friday. This totals 22 hours.Divide the gross pay of $196.90 by the total number of hours (22) to find the hourly rate: $196.90 / 22 hours = $8.95 per hour.Therefore, Lenny's hourly rate is $8.95.
What is the relationship between 4, 16, and squares?
Answer:
A square has 4 sides. 4 squares have 16 sides.
Step-by-step explanation:
The degree measure of the sum of the interior angles of a convex polygon with n sides is 1800. What is the degree measure of the sum of the interior angles of a convex polygon with n + 2 sides?
A convex polygon with n + 2 sides has the sum of its interior angles equal to 2160 degrees, which is 360 degrees more than a polygon with n sides that has 1800 degrees.
The degree measure of the sum of the interior angles of a convex polygon with n sides, given as 1800 degrees, follows the formula (n - 2) times 180 degrees. For a convex polygon with n + 2 sides, we can apply the same formula: ((n + 2) - 2) times 180 = (n times 180) + (2 times 180).
Therefore, the degree measure of the sum of the interior angles of a convex polygon with n + 2 sides is 1800 degrees plus 360 degrees, giving us a total of 2160 degrees.
Write 90.04 in word form
Answer:
Ninety and four one hundredths
Step-by-step explanation:
The word form of the number is Ninety and four hundredths.
We have,
To write 90.04 in word form, you can express it as "ninety and four hundredths."
Here's an explanation:
The whole number part, 90, is read as "ninety."
The decimal part, 0.04, is read as "four hundredths."
Combining these two parts, we say "ninety and four hundredths" to represent the decimal number 90.04 in word form.
Thus,
The word form of the number is Ninety and four hundredths.
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Dean selects Teakwood stones
and Buckskin stones to pave a path in front
of his house. How many meters long will
each set of one Teakwood stone and one
Buckskin stone be?
Answer:
You didnt give us data to use
for example TEAKWOOD IS 3 METER LONG AND PATH 10 HOW LONG IS BUCKSKIN
Step-by-step explanation:
TWIJCICUL NUV.1.1)
George began making paper flowers for
the tables at the school awards banquet.
He can make 3 flowers per minute. Sue
joined him 5 minutes after he started. She
can make 4 flowers per minute. George
continued to make 3 flowers per minute.
Together, they made 190 flowers.
Which statements about the number of
flowers made are true?
A. George made 115 flowers.
B. George made 90 flowers.
C. George made 30 flowers.
D. Sue made 25 flowers.
E. Sue made 100 flowers.
F. Sue made 160 flowers.
Answer: B and E
Step-by-step explanation: B and E arecorrect because 4 x 25 is 100 and 3 x 30 equals 90 so there you have it
Answer:
B and E
Step-by-step explanation:
which of the following rectangles is similar to a rectangle that measures 12 units by 16 units? A) 18x24 B) 9x14 C) 6x10 D) 16x20
Answer:
A) 18x24
Step-by-step explanation:
The ratio of the dimensions will be the same for a similar rectangle.
12/16 = 3/4 . . . given rectangle
__
18/24 = 3/4 . . . choice A is similar
9/14 ≠ 3/4 . . . . choice B is not similar
6/10 = 3/5 . . . . choice C is not similar
16/20 = 4/5 . . . . choice D is not similar
Let f left-parenthesis x right-parenthesis equals 2 x squared plus x minus 3 and g left-parenthesis x right-parenthesis equals x minus 1. Perform the indicated operation, then find the domain. left-parenthesis f minus g right-parenthesis left-parenthesis x right-parenthesis A. x squared minus 4; domain: positive real numbers B. 2 x squared minus 4; domain: all real numbers C. x squared minus 4; domain: all real numbers D. 2 x squared minus 2; domain: all real numbers
Answer:
The option D) is correct "2 x squared minus 2; domain: all real numbers "That is [tex](f-g)(x)=2x^2-2[/tex] and domain is all real numbersStep-by-step explanation:
Given that the functions f and g are defined by
[tex]f(x)=2x^2+x-3[/tex] and [tex]g(x)=x-1[/tex]
To perform the indicated operation (f-g)(x) and then find the domain :To find (f-g)(x)
(f-g)(x)=f(x)-g(x)Substitute the values of the functions we get
[tex](f-g)(x)=f(x)-g(x)=2x^2+x-3-(x-1)[/tex]
[tex]=2x^2+x-3-1(x)-1(-1)[/tex]
[tex]=2x^2+x-3-x+1[/tex]
[tex]=2x^2-2[/tex] ( by adding the like terms )
Therefore [tex](f-g)(x)=2x^2-2[/tex] and domain is all real numbersThe option D) is correct "2 x squared minus 2; domain: all real numbers "The value of (f-g)(x) is [tex]2x^2-2[/tex]. Thus, the correct option is (D)
Two different functions are given that are as follow:
[tex]f(x)=2x^2+x-3[/tex]
[tex]g(x)=x-1[/tex]
We need to determine the value of the composite function that is (f-g)(x).
Now, by using the property of the composite function (f-g)(x) can also be written as:
[tex](f-g)(x)=f(x)-g(x)[/tex]
Substitute the values of both the functions and solve it further for (f-g)(x).
[tex]\begin{aligned}(f-g)(x)&=(2x^2+x-3)-(x-1)\\&=2x^2+x-3-x+1\\&=2x^2-2\\&=2(x^2-1)\end{aligned}[/tex]
Thus, the value of (f-g)(x) is [tex]2x^2-2[/tex]. Thus, the correct option is (D)
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Click on pictures help please
Miss C weight before she started her diet is 80 kg.
Solution:
Weight before diet = x
Weight loss percent = 8%
Present weight of Miss C = 73.6 kg
[tex]$ x-x\times \ 8 \% =73.6[/tex]
[tex]$ x-x\times \frac{8}{100} =73.6[/tex]
The denominators must be same to add/subtract the fractions.
LCM of 1 and 100 = 100
Multiply first term by [tex]\frac{100}{100}[/tex] and 73.6 by [tex]\frac{100}{100}[/tex] to make the denominator same.
[tex]$ \frac{100x}{100} - \frac{8x}{100} =\frac{7360}{100}[/tex]
[tex]$ \frac{100x-8x}{100} =\frac{7360}{100}[/tex]
Multiply by 100 on both sides, we get
100x - 8x = 7360
92x = 7360
Divide by 92 on both sides, we get
x = 80
Miss C weight before she started her diet is 80 kg.
What is X+x+x+2 equivalent to?
Answer:
3X+2
Step-by-step explanation:
X+X+X+2=3X+2
Solve the system of equations.
y=x+57
y=8x+15
Answer:
x=6, y= 63
Step-by-step explanation:
Please see attached picture for full solution.
At the beginning of a board game, players take turns
drawing 7 lettered tiles. Are drawing A's on the first two tiles dependent or
independent events? Explain.
The second pick is dependent on the first one.
Let [tex]a[/tex] be the number of tiles with the letter A, and [tex]n[/tex] be the total number of tiles.
With the first pick, you have probability [tex]\frac{a}{n}[/tex] to pick an A, because you have [tex]a[/tex] "good" cases out of [tex]n[/tex] possible cases.
The second pick depends on the first one:
If you pick an A tile on the first pick, the probability of picking another A is now [tex]\frac{a-1}{n-1}[/tex]If you didn't pick an A tile on the first pick, the probability of picking another A is now [tex]\frac{a}{n-1}[/tex]A sandwich shop sells sandwiches with several different types of meat, several types of bread, and several different types of cheese. How many different combinations can be ordered at this shop?
A. 18
B. 27
C. 36
D. 48
Answer:A. 18
Step-by-step explanation:
Answer: C. 36
Step-by-step explanation:
3x3x4=36
HELOOOOOOOOOOO ANYBODY THERE
Answer:
yes where is the question
Write and solve an equation to answer the question.
9 is what percent of 20?
=p⋅
9 is
% of 20.
To find what percent 9 is of 20, you divide 9 by 20 and multiply the result by 100. The answer is 45%.
Explanation:To determine what percent 9 is of 20, you'd set up an equation based on the mathematical definition of percentage:
p = (part/whole) * 100%
Here, our part is 9 and our whole is 20. So you arrange the numbers in the given formula:
p = (9/20) * 100%
Solving the equation gives us 45%
Therefore, 9 is 45% of 20.
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To find out what percent 9 is of 20, we can use the formula part/whole = percent/100. Using this equation, we can solve for p and find that 9 is 45% of 20.
Explanation:To find out what percent 9 is of 20, we can set up an equation using the formula:
part/whole = percent/100
In this case, the part is 9, the whole is 20, and we want to find the percent. So the equation becomes:
9/20 = p/100
To solve for p, we can cross multiply:
9 * 100 = 20 * p
Dividing both sides of the equation by 20 gives us:
900 = 20p
Finally, dividing both sides by 20 gives us the value of p:
p = 900/20 = 45
Therefore, 9 is 45% of 20.
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Chai started to run on a treadmill after setting its timer for 62 minutes. The display says that he has finished 53% of his run. How many minutes have gone by? Round your answer to the nearest tenth.
About 32.9 minutes have gone by.
To find this answer you take your percent and make it a decimal by dividing it by 100. In doing so, you'll get 0.53. Then multiply 0.53 by 62 to get 32.86. Since you have to round to the nearest tenth, you look at the hundredths place to see whether you round up (5-9) or round down (1-4). In this case, you round up making your answer 32.9 minutes.
I hope this helps!
Answer/Step-by-step explanation:
About 32.9 minutes have gone by.
To find this answer you take your percent and make it a decimal by dividing it by 100. In doing so, you'll get 0.53. Then multiply 0.53 by 62 to get 32.86. Since you have to round to the nearest tenth, you look at the hundredths place to see whether you round up (5-9) or round down (1-4). In this case, you round up making your answer 32.9 minutes.
I hope this helps!
Evaluate the expression {10 x 7} + (10 – 6).
Answer:the answer is 74
Step-by-step explanation:
What is the length of side TS?
2 StartRoot 6 EndRoot units
6 StartRoot 6 EndRoot units
24 units
8 units
Answer:
its B- 6 startroot 6 endroot units
Step-by-step explanation:
Answer:
B. 6√6
Step-by-step explanation:
EDGE2021