Answer:You will need to buy 1/2 a pound of cashews and 1/2 a pound of peanuts
Sofia used these steps to find the inverse of function f
She made a mistake in step__(2,6,4,3,5)?
She should have_____
.dived each side by 8 instead of multiplying
.replaced x with f(x)
.divided each side by 3 instead of multiplying
.added 4 to each side instead of subtract
.restricted the domain to x>0
Answer:
Step-by-step explanation:
Step 1 f(x) = [tex]\frac{3x+4}{8}[/tex] Given
Step 2 y = [tex]\frac{3x+4}{8}[/tex] Change f(x) to y
Step 3 x = [tex]\frac{3y+4}{8}[/tex] Switch x and y
Step 4 8x = 3y + 4 multiply each side by 8
Step 5 8x - 4 = 3y Subtract 4 from each side
Step 6 [tex]\frac{8x-4}{3}=y[/tex] Divide by 3 on each side
Step 7 [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex] Replace y by [tex]f^{-1}(x)[/tex]
Therefore, inverse of the function will be,
[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]
Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.
Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.
The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].
It is required to calculate the inverse of the function.
So, the steps involved in finding the inverse of the function will be,
Step 1:
Write the given function as,
[tex]f(x)=\dfrac{3x+4}{8}[/tex]
Step 2:
Change the function f(x) to y as,
[tex]y=\dfrac{3x+4}{8}[/tex]
Step 3:
Switch x and y as,
[tex]x=\dfrac{3y+4}{8}[/tex]
Step 4:
Multiply each side of the equation by 8 as,
[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]
Step 5:
Now, subtract 4 from each side of the equation as,
[tex]8x-4=3y+4-4\\8x-4=3y[/tex]
Step 6:
Now, it is required to divide each side by 3.
[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]
Step 7:
Now, replace y with [tex]f^{-1}(x)[/tex] as,
[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]
So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].
Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.
For more details, refer to the link:
https://brainly.com/question/19606498
what number is represented by this number discs
Answer:
15
Step-by-step explanation:
Triangle ABC is transformed to triangle A′B′C′, as shown below:
Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point)
a
The measure of angle ABC = The measure of angle A prime B prime C prime
b
The measure of angle ABC = The measure of angle B prime C prime A
c
The measure of angle BCA = The measure of angle A prime B prime C prime
d
The measure of angle BCA = The measure of angle C prime A prime B prime
Answer:
d one i think
hope it helps
the sum of triangle is 180 degree
Please answer the question in the picture
help me please in this problem
Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page
Answer:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
Answer:
26
Step-by-step explanation:
13 in 1/2 hour
13:1/2
26:1
The two triangles are similar, What is the length of DE?
Answer:
If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.
I hope this might help you
Mark it as brainliest answer and follow me
Is that a perfect square
Answer:
im gonna go with yes
Step-by-step explanation:
Answer:
is what a perfect square?
Step-by-step explanation:
there is no pic attached
What did philosophical pig say?
(Geometry Version)
Answer:
A: m<BOD = 95°
O: m<AOC = 75°
R: m<AOD = 113°
T: m<GUH = 61°
M: m<GUI = 92°
E: m<EUF = 37°
F: m<EUI = 160°
K: m<MAN = 30°
I: m<LAM = 40°
S: m<KAM = 80°
H: m<JAN = 140°
N: m<KAN = 110°
✅I STINK THEREFORE I HAM
Step-by-step explanation:
A: m<BOD = 57° + 38° = 95°
O: m<AOC = 18° + 57° = 75°
R: m<AOD = 18° + 57° + 38° = 113°
T: m<FUG = 31°, since, FUG ≅ HUI, therefore, m<HUI = 31°
m<FUI = 123°
m<GUH = m<FUI - (m<FUG + m<HUI)
m<GUH = 123° - (31° + 31°)
m<GUH = 61°
M: m<GUI = m<GUH + HUI
m<GUI = 61° + 31°
m<GUI = 92°
E: m<EUH = 129° (given)
m<EUF = m<EUH - (m<FUG + m<GUH)
m<EUF = 129° - (31° + 61°)
m<EUF = 37°
F: m<EUI = m<EUF + m<FUG + m<GUH + m<HUI
m<EUI = 37° + 31° + 61° + 31°
m<EUI = 160°
K: since <JAK ≅ <MAN, and m<JAK is given as 30°, therefore,
m<MAN = 30°
I: m<JAM = 110° (given), m<JAK = 30° (given)
Since <KAL ≅ <LAM, therefore,
m<LAM = ½(m<JAM - m<JAK)
m<LAM = ½(110° - 30°)
m<LAM = 40°
S: m<KAM = m<KAL + m<LAM
Since <KAL ≅ <LAM, therefore,
m<KAM = 40° + 40°
m<KAM = 80°
H: m<JAN = m<JAK + m<KAL + m<LAM + m<MAN
m<JAN = 30° + 40° + 40° + 30°
m<JAN = 140°
N: m<KAN = m<KAL + m<LAM + m<MAN
m<KAN = 40° + 40° + 30
m<KAN = 110°
Place the letters on the appropriate lines given to match the angle measure we've cakcukated, to figure out the joke.
✅We would have:
I STINK THEREFORE I HAM
Completing the Square
Solve each equation by completing the square.
1) 7x2 + 14x - 65--9
Answer:
2(30-7x)
Step-by-step explanation:
=14+14x-65-9
=14+14x-79
=60+14x
=2(30-7x)
Triangle ABC is a scaled copy of triangle DEF. Side AB measures 12 cm and is the longest side of ABC. Side DE measures 8 cm and is the longest side of DEF.
a)Triangle ABC is a scaled copy of triangle DEF with what scale factor?
b)Triangle DEF is a scaled copy of triangle ABC with what scale factor?
Answer:
a) 3/2 or 1.5
b) 2/3 or ≈.66
Step-by-step explanation:
AB corresponds to DE because they are both the longest sides of their respective triangles.
a) The scale factor would be what you would multiply 8 by to get 12. 12/8 is 3/2 or 1.5
b) The scale factor would be what you multiply 12 by to get 8. 8/12 is 2/3 or ≈.66
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 90 yd, find its length and width.
Answer:
Length of rectangle = 36 yd and width of rectangle = 9 yd
Step-by-step explanation:
Let width of rectangle = w
Length of rectangle = 4w (four times the width)
Perimeter of rectangle = 90 yd
We need to find length and width of rectangle.
The formula used will be: [tex]Perimeter \ of \ rectangle=2(l+w)[/tex]
Where l is length and w is width
Putting values and finding length and width of rectangle
[tex]Perimeter \ of \ rectangle=2(l+w)\\90=2(4w+w)\\90=2(5w)\\90=10w\\w=\frac{90}{10}\\w=9[/tex]
So,width (w) of rectangle is w= 9 yd
Finding length of rectangle = 4w = 4*9 = 36 yd
So, length of rectangle = 36 yd and width of rectangle = 9 yd
A rectangle is 2 meters long and 50 centimeters wide. What is its perimeter, in centimeters?
Answer:
250 centimeters
Step-by-step explanation:
2 meters into centimeters is 200 so 200+50=250
Answer:
100cm
Step-by-step explanation:
The fourth term of a geometric progression is 4 and the seventh term is 32/125. Find the first term, the common ratio and the sum of the first nth terms. Hence, deduce the sum to infinity.
Answer:
common ratio is 2/5
First term is 125/2
The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]
Step-by-step explanation:
The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:
[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]
Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:
[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]
So, the common ratio is 2/5
we can now determine the first term:
[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]
The sum of the first n terms is given by the formula:
[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]
and therefore, the infinite sum is:
[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]
What is the graph of the function rule?
1. y= 3x - 2 (1 point)
Algebra 1
This should be what you're looking for.
Please who ever gets right gets brainliest to
Answer:
The Trench or The Mariana Trench is the deepest part of the ocean.
Answer:
B) trench
Step-by-step explanation:
The deepest part of the ocean is called the Challenger Deep and is located beneath the western Pacific Ocean in the southern end of the Mariana Trench
I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)
Graph the function rule
Y= -3/4 x-1
1. Determine whether line KM and line ST are Parallel, Pers
Line KM has a slope of 5/8
Line ST has a slope of -8/5
Answer:
Since the slope of KM and ST are different, they are not parallel
Step-by-step explanation:
Slope of line KM = [tex]\frac{5}{8}[/tex]
Slope of ST = [tex]-\frac{8}{5}[/tex]
Determine whether the lines are perpendicular;
Solution:
We can use the slope of a line to determine whether they are perpendicular or parallel to one another.
Parallel lines do not meet one another
Perpendicular lines cross one another at an angle of 90°
Two lines are parallel if their slopes are the same;
Since the slope of KM and ST are different, they are not parallel
Simplify the expression using the properties of operations.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is
Answer:
Step-by-step explanation:
5.23x+3.76-3.67x+6.39
x(5.23-3.67) +(3.76+6.39)
1.56x + 10.15
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
Can 14,18 and 19 form a triangle?
Answer:
Yes
Step-by-step explanation:
Using the triangle formula: a+b>c , b+c>a , and c+a>b, we can conclude that these values can form a triangle because 14+18>19 , 14+19>18 , and 18+19>14.
Answer:
To confirm if this can form it, we take the lower of the two numbers , square them, and equal it to the biggest number squared. (AKA The Pythagorean Theorem).
Step-by-step explanation:
[tex]14^{2} +18^{2} = 19^{2}[/tex]
Now solve to see if it equates to be true.
196 + 324 = 361
520 [tex]\neq[/tex] 361
That means 14, 18, and 19 can't form a triangle.
Determine if the following argument always applies, sometimes applies, or never applies. Provide at least 2 examples in your explanation.
"The sum of a number and its opposite is always 1."
Answer:
Never applies
Step-by-step explanation:
Given
Argument: The sum of a number and its opposite is always 1
Assume a positive number x
The opposite of the number is negative x (i.e. -x)
The sum of both numbers is:
[tex]Sum = x + (-x)[/tex]
Open Bracket
[tex]Sum = x -x[/tex]
[tex]Sum = 0[/tex]
Now, take for instance.
[tex]Number = 5[/tex]
Opposite would be
[tex]Opposite = -5[/tex]
Their sum is:
[tex]Sum = 5 + (-5)[/tex]
[tex]Sum = 5 -5[/tex]
[tex]Sum = 0[/tex]
Another instance is:
[tex]Number = -8[/tex]
Opposite would be
[tex]Opposite = 8[/tex]
Their sum is;
[tex]Sum = -8 + 8[/tex]
[tex]Sum = -0[/tex]
Hence, the argument never applies because the sum is never 1
Understand the question explain and u will be brainiest
Simplify (6x ^ 2 + 11x - 3) + (2x ^ 2 - 17x - 4) . (1 point)
1 ) 8x ^ 2 + 6x - 1
2) 8x ^ 2 - 6x - 7
3 ) 8x ^ 2 + 6x + 1
4 ) 8x ^ 2 - 6x + 7
Answer:
2) 8x^2 -6x-7 hope this helps
Can someone help me with this.. It is timed I WILL MARK YOU AS BRAINLIEST
Answer:
1) dividend
2) divisor
3) quotient
Simplify the following expression (3x-5)(4-9x)+(2x+1)(6x^2+5)
The Miller's are comparing babysitting services for their two children.
The Babysitter's Block charges a rate of $15 an hour per child plus an initial fee of $25 per household.
Super Sitters charges a flat rate of $20 an hour per child.
For ________hours of service, both babysitting services would cost the same.
Answer:
After 5 hours of service, both babysitting services would cost the same.
Step-by-step explanation:
Babysitter's Block: y = 15x + 25
Super Sitters: y = 20x
15x + 25 = 20x
Subtract 15x from both sides;
25 = 5x
Divide both sides by 5;
x = 5
For 5 hours of service, both babysitting services would cost the same.
box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the amount of material used. sides of base
Answer:
Hence the width, length is 20 cm and height is 10 cm
Step-by-step explanation:
Since the box has a square base, let length = width = x. Also, let the height = y, therefore:
The volume of box = width * length * height
4000 = x * x * y
4000 = x²y
y=4000/x²
The surface area (SA) = area of the base + sum of the area of each side
SA = x² + xy + xy + xy + xy
SA = x² + 4xy
substitute y = 4000/x²
SA = x² + 4x(4000/x²)
SA = x² + 16000/x
Taking the derivative:
SA' = 2x - 16000/x²
making SA' = 0:
0 = 2x - 16000/x²
2x = 16000/x²
2x³ = 16000
x³ = 8000
x = 20 cm
y = 4000 / x² = 4000 / 20² = 10 cm
Hence the width, length is 20 cm and height is 10 cm
How many times does 35 go into 100 please give correct answer max points.
Answer:
100/35 = 2
35 goes into 100 2 times
Step-by-step explanation:
Bob has a coin collection made up of pennies and nickels. If he has three times as many pennies as nickels and the total face value of the coins is $416, how many coins of each kind are in the collection?
Answer:
I think its 15600..
Step-by-step explanation:
Which scenario describes this picture?
Answer:
It"s the second answer, "An 8-foot ramp leans....".
Step-by-step explanation:
Answer:
Step-by-step explanation:
⊕ An 8-foot ramp leans against a building 5 feet away.
cos x = [tex]\frac{5}{8}[/tex] ⇒ x ≈ 51.3178°