Answer:
f^-1(x) = x/2 -1Step-by-step explanation:
[tex]f(x) = 2x + 2\\\\f^-^1 (x) = ?[/tex]
Let y equal to the given equation ;
[tex]y = 2x+2\\[/tex]
Solve for x ;
[tex]y-2 = 2x\\Divide \:both\:sides\:of\:the\:equation\:by \:2\\\\\frac{y}{2} - \frac{2}{2} = \frac{2x}{2} \\\\\frac{y}{2} -1 =x\\\\x = \frac{y}{2} -1[/tex]
Change the y back to x
[tex]x = \frac{x}{2} -1 \\\\f^-^1(x) = \frac{x}{2} -1[/tex]
Identify the correct representation of the expression 3(x + 2)
A (x+ 2) + (x+2) + (x + 2)
B (x + 2) ( x +2) (x + 2)
C 3x + 32
D XXX + 333
Answer:
3x + 6
Step-by-step explanation:
It's A because x + x + x = 3x and 2+2+2 = 6
F is the mid point of EG . If EF = 5x and EG = 7x + 5, what is EG?
Evaluate
l5 - 15l
Is this right?
Answer:
10
Step-by-step explanation:
The absolute value always returns a positive value, thus
| a | = | - a | = a
Given
| 5 - 15 | = | - 10 | = 10
Chucky grabbed 12 items in the grocery store that each had a different price and had a mean cost of about $7.41. One of the items was an entire wheel of cheese that cost $39.99. Chucky then decided to put the wheel of cheese back and only buy the other 11 items. How will removing the wheel of cheese affect the mean and median?
A. Both the mean and median will decrease, but the median will decrease by more than the mean.
B. Both the mean and median will decrease, but the mean will decrease by more than the median.
C. Both the mean and median will increase, but the median will increase by more than the mean.
D. Both the mean and median will increase, but the mean will increase by more than the median.
Answer:
The mean will be (significantly) less.
Depending on the other items, the median is either affected only slightly or not at all.
Of all the answer choices, B is the correct one.
Step-by-step explanation:
So, we know that initially, Chucky had a total of 12 items. Each of the items has a different price, but the average cost of them is $7.41.
One item of the twelve was a wheel of cheese that costs $39.99.
And we want to know how the average cost and median cost will be affected if we remove this wheel of cheese.
The important thing to note here is that the average cost is $7.41. The wheel of cheese, however, costs $39.99. Thus, it is an outlier. It is significantly more expensive than the other items.
Initially, to find the mean, we had to add the 12 items together and then divide by 12. However, now that we removed the expensive outlier, the average cost will now be less.
Algebraically, we can see this. Let t be the total cost of the items excluding the cheese. Thus, the mean initially is:
[tex]7.41=\frac{t+39.99}{12}[/tex]
Find t. Multiply both sides by 12:
[tex]88.92=t+39.99\\t=48.93[/tex]
Therefore, all the other items excluding the cheese totals $48.93.
If we remove the cheese, the total is now $48.93 and with only 11 items. Thus, the mean is now:
[tex]48.93/11\approx\$4.45[/tex]
This is almost $3 less than the original mean. Thus, the mean has decreased significantly.
For the median, we really don't know. Recall that the median is simply the "middle" quantity. Assuming all the other products are similarly priced, the median may only change slightly or it may not at all. However, we can only guess for the median as it will depend on the prices of the other products. Nevertheless, it mostly likely decrease.
Edit: Added Letter Answer
Answer:
B
Step-by-step explanation:
Create a function to help determine his total cost.
12 x $7.41 = $88.92
After putting the cheese back he has 11 items and his total cost went down.
$88.92-$39.99 = $48.93
To find the average cost per item divide by 11.
$48.93/11 = $4.45 per item
The mean (average) has gone down.
The median would be the middle number, so you would need to line the cost of the items up from least to greatest. If you have an even number of items, you take the mean of the middle 2 numbers. The block of cheese would have have given Chucky 12 items so the 2 middle numbers would have been averaged.
A hypothetical 12 and 11 items:
$1 $2 $2 $3 $4 $4 $5 $6 $7 $7 $8 $39.99
Mean $7.42 Median $4.5
$1 $2 $2 $3 $4 $4 $5 $6 $7 $7 $8
Mean $4.45 Median $4
Taking the cheese away would move the middle down 1 number so it would also go down, but not as much as the mean of cost per item.
B. Both the mean and median will decrease, but the mean will decrease by more than the median.
Can someone help me with number 7. Please.
Answer:
exponent: 3; base: 4
Step-by-step explanation:
An exponent is used to signify repeated multiplication. In a typeset expression is has a superscript format. The base is the value being repeatedly multiplied.
[tex]4^3=4\cdot4\cdot4[/tex]
The exponent is 3.
The base is 4.
_____
In plain text, an exponent is preceded by a caret (^). If the exponent consists of more than a single constant or variable, it must be enclosed in parentheses. The above expression would be written as 4^3.
please solve.thank you.
Answer:
Step-by-step explanation:
let x=0.4666...
10x=4.666...
100x=46.6666...
100x-10x=46.6666... - 4.6666...
90x= 42
x=42/90
So 0.4666... is equal to 42/90
PLEASE HELP!!!!!!!!!!!!
Answers:
a = 3
x intercept = -2
===========================================================
Explanation:
f(x) is the original function given. Let g(x) be the inverse of f(x).
To find the inverse, we first replace f(x) with y to get
y = (1/3)x-2
Afterward, we swap x and y to get
x = (1/3)y-2
From here, we must isolate or solve for y. To do so, add 2 to both sides and then multiply both sides by 3
x = (1/3)y-2
x+2 = (1/3)y
3(x+2) = y
y = 3(x+2)
g(x) = 3(x+2)
This explains where the x+2 comes from in the a(x+2) expression
The value of 'a' is therefore a = 3
------------
To find the x intercept of the inverse, we replace g(x) with 0 and solve for x
g(x) = 3(x+2)
0 = 3(x+2)
0/3 = x+2
0 = x+2
x+2 = 0
x = 0-2
x = -2
The x intercept is x = -2. Plugging this x value into g(x) leads to g(x) = 0.
The g(x) graph crosses the x axis at x = -2.
The quantities xxx and yyy are proportional.
xxx yyy
111111 1\dfrac{2}{9}1
9
2
1, start fraction, 2, divided by, 9, end fraction
212121 2\dfrac{1}{3}2
3
1
2, start fraction, 1, divided by, 3, end fraction
454545 555
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
r =r=r, equals
Answer: r = 1 10/11
Step-by-step explanation: The quantities x and y are proportional.
The direct variation between {x] and {y} is discussed below.
What is direct variation?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor.
Given is that the quantities {x} and {y} are proportional.
The general equation of a straight line is -
y = mx + c
{m} - slope
{c} - intercept along the y - axis
The straight line graph also represents a direct variation between {x} and {y}. We can write -
m = (y - c)/x
Here the ratio of (y - c)/x is always constant.
So, we can write -
(y₁ - c)/x₁ = (y₂ - c)/x₂ = m = k
for c = 0, we can write -
y₁/x₁ = y₂/x₂ = m = k {constant}
Therefore, the direct variation between {x] and {y} is discussed above.
To solve more questions on direct variation, visit the link below -
brainly.com/question/14254277
#SPJ3
a right triangle has side lengths 8 15 and 17 as shown below use these lengths to find tan B sin B and cosine B
Answer:
sin(B) = [tex]\frac{15}{17}[/tex]
cos(B) = [tex]\frac{8}{17}[/tex]
tan(B) = [tex]\frac{15}{8}[/tex]
Step-by-step explanation:
I always find it easiest to model out the triangle: Angle B will be at the converging point of a and c.
Using SOH CAH TOA, we know that the Sin of an angle will be its opposite over hypotenuse. The opposite is 15, and the hypotenuse is 17.
So [tex]\frac{15}{17}[/tex] is the sin of B.
We also know that the cosine of B will be it's adjacent over hypotenuse. The adjacent is 8 and the hypotenuse is 17, so
[tex]\frac{8}{17}[/tex]
Lastly, we know the tangent of B will be it's opposite over adjacent. The opposite of B is 15, and it's adjacent is 8, so
[tex]\frac{15}{8}[/tex] is the tangent of B.
Hope this helped!
5. It is known that the product of 4.5 and y is not less than 9.
(a) Formulate an inequality to represent the above relation.
(b) Write down three integers that satisfy the inequality in (a).
Solution
Answer:
(a)
[tex]4.5y \geqslant 9[/tex]
(b) 3, 4, 5
Step-by-step explanation:
(a) 4.5 × y = 9 and above
[tex]4.5y \geqslant 9[/tex]
(b)
[tex]4.5y \geqslant 9 \\ y \geqslant \frac{9}{4.5} \\ y \geqslant 2[/tex]
Possible y values = 2 and over
eg. 3, 4, 5
hope this helps :))
The picza has an area of 785 in. What is the minimum with of a placemat that can be placed underneath it so that the pizza does not touch the table Use 3.14 forpi
10 inches
Sinches
25 inches
D.3.14 inches
Urarred 25
Type here to search
Answer:
C is the answer!!
Step-by-step explanation:
1.What is a negative times a positive 2. A Positive times positive 3. A negative times a negative 4.What is a negative divided by a positive 5.A Positive divided by positive 6. A negative divided by a negative
Answer:
See below.
Step-by-step explanation:
In multiplication and division of two numbers:
equal signs equal positive
different signs equal negative
Now you can answer every question.
1. What is a negative times a positive different signs negative
2. A Positive times positive equal signs positive
3. A negative times a negative equal signs positive
4. What is a negative divided by a positive different signs negative
5. A Positive divided by positive equal signs positive
6. A negative divided by a negative equal signs positive
Answer:
1: - x + = -
2: + x + = +
3: - x - = +
4: - divided by a + is -
5: + divided by a + is +
6: - divided by a - is +
Select all the true statements. protractor with ray lq at 0 or 180, ray lp at 50 or 130, ray ol at 90, ray ln at 60 or 120 and ray lm at 0 or 180. Group of answer choices LaTeX: m\angle QLP\:+\:m\angle PLO=m\angle MLN+m\angle NLO m ∠ Q L P + m ∠ P L O = m ∠ M L N + m ∠ N L O m ∠ Q L P + m ∠ P L O = m ∠ M L N + m ∠ N L O m ∠ Q L P + m ∠ P L O = m ∠ M L N + m ∠ N L O LaTeX: m\angle NLO+m\angle OLP\:=\:m\angle NLP m ∠ N L O + m ∠ O L P = m ∠ N L P m ∠ N L O + m ∠ O L P = m ∠ N L P m ∠ N L O + m ∠ O L P = m ∠ N L P LaTeX: m\angle QLO-m\angle QLP\:=\:m\angle MLO-m\angle MLN m ∠ Q L O − m ∠ Q L P = m ∠ M L O − m ∠ M L N m ∠ Q L O − m ∠ Q L P = m ∠ M L O − m ∠ M L N m ∠ Q L O − m ∠ Q L P = m ∠ M L O − m ∠ M L N LaTeX: m\angle\:MLN\:=\:120 m ∠ M L N = 120 m ∠ M L N = 120 m ∠ M L N = 120 LaTeX: m\angle QLP\:=50
Answer:
m ∠ M L N = 120
m < QLP =50
Step-by-step explanation:
Ray lq at 0 or 180,
ray lp at 50 or 130,
ray ol at 90,
ray ln at 60 or 120
and ray lm at 0 or 180
Lets substitute the values of the angles to check the given options
1) ∠ Q L P + m ∠ P L O =m< MLN+m< NLO m
50 +40= 120+30
90 is not equal to 150
2) m < QLO- m < QLP =m < MLO-m< MLN m
90-50 = 90-120
40 is not equal to 30
3) m< MLN\:=\:120 From the figure based on observation this is correct.
4) m < QLP =50 From the figure based on observation this is also correct.
Answer:
Given: Angle L N O ≅ Angle L N M
Angle O L N ≅ Angle M L N
Prove: Angle L N O ≅ Angle L N M
Triangles L O N and L M N share common side L N. Angles O L N and N L M are congruent. Angles O N L and L N M are congruent.
It is given that angle LNO is congruent to angle
✔ LNM
and angle OLN is congruent to angle
✔ MLN
. We know that side LN is congruent to side LN because of the
✔ reflexive property
. Therefore, because of
✔ ASA
, we can state that triangle LNO is congruent to triangle LNM.
Step-by-step explanation:
If y = – 2x + 1, what is the value of y when x = 6?
Answer:
[tex]y=-11[/tex]
Step-by-step explanation:
So we have the equation:
[tex]y=-2x+1[/tex]
To find y when x is 6, substitute x for 6. Thus:
[tex]y=-2(6)+1[/tex]
Multiply:
[tex]y=-12+1[/tex]
Add:
[tex]y=-11[/tex]
So our answer is -11 :)
Answer:
The answer is -11 which means y = -11.
how many pieces each of length 9/4metre can be cut from a rope of length 40 metre 50 cm
Answer:
18 pieces
Step-by-step explanation:
This is a division problem.
1 m = 100 cm
To convert from cm to m we divide the length in cm by 100.
40 m + 50 cm = 40 m + 50/100 m = 40.5 m
The rope is 40.5 m long.
9/4 m = 2.25 m
Each piece is 2.25 m long.
[tex] \dfrac{40.5~m}{2.25~m} = 18 [/tex]
Answer: 18 pieces
divide the sum of 13 / 5 and -12 / 7 by the product of - 31 / 7 and 1 /-2
Answer:
13/5+(-12/7)÷ -31/7×1/-2.
13/5-12/7=31/35.
-31/7×1/-2=31/14.
31/35÷31/14=14/35.
Jack bought a car for $29,000. He sold it for $10,000 3 years later. What is the percentage loss that Jack made?
Answer:
$19,000 loss
Step-by-step explanation: Cost of the car: $29,000
Cost of the car he sold for: $10,000
Total lost occurred: $29,000 - $10,000 = $19000
Therefore, the lost occurred was $19,000
Given f(x)
=
4x + 1
3
solve for F-1(3). (5 points)
Answer:
Step-by-step explanation:
First we need to find inverse function of f(x) which is written in a form of (f(x))^(-1)
That means that we are actually looking for function f(y) and we need to solve this equation for "y"
y=(4x + 1)/3
3y = 4x + 1
4x = 3y - 1
x = (3y - 1) / 4
f(y) = (3y - 1)/4
Now we simply put the value of 3 instead of y and find the answer:
f(y=3) = (3*3-1)/4 = 2
Answer is 2
What is the distance between (8, -3) and (4, -7)?
Answer:
d=4√2
Step-by-step explanation:
distance formula = √(x2-x1)²+(y2-y1)²
d=√(4-8)²+(-7-(-3))²
d=√4²+(-4)²
d=√16+16 = √32=√2²*2²*2
d=4√2
Please answer fast
Silakan
Answer:
[tex]8\frac{37}{56}[/tex]
Step-by-step explanation:
[tex]12\frac{2}{7} + 3\frac{5}{8} = \frac{86}{7} + \frac{29}{8} = \frac{688 - 203}{56} = \frac{485}{56} = 8\frac{37}{56}[/tex]
What is the range of the function represented by the table?
Answer:
the answer is the second option
Step-by-step explanation:
Range is all the y values
Mae runs a fruit stand on Monday. She used 3/4 of a bag fruit. On Wednesday she used 1/3 as much fruit as Monday. What fraction of a bag of fruit does Mae use on Wednesday
Answer:
Mae used 1/4 of the whole bag on Wednesday.
Step-by-step explanation:
From the question, we understand that the fraction of the whole bag that Mae used on Monday is 3/4.
On Wednesday, we are then told that Mae uses 1/3 as much fruit as on Monday.
This means that Mae uses 1/3 of the fruits she used on Monday. The fruits she used on Monday was actually 3/4 of the whole.
This means that on Wednesday, Mae used 1/3 of 3/4 fruits.
In Mathematics, the word "of" there stands for multiplication. Hence, Mae used 1/3 X 3/4 = 1/4 of the whole bag
Mae used 1/4 of the whole bag
State the domain and range for the function f(x) = 2x^2 - 7
Answer:
2x^2 - 7
we can plug any values of x into this The domain is All Real x.
The graph will be a parabola opening upwards with a minimum value when x = 0 and f(x) will be = -7
so the range is f(x) <= -7 or (-∞, -7]
Express 0.7 as a fraction
Answer:
7/10
Step-by-step explanation:
In 0.7 we will change the decimal to fraction. First we will write the decimal without the decimal point as the numerator. Now in the denominator, write 1 followed by one zeros as there are 1 digit in the decimal part of the decimal number. Therefore, we observe that 0.7 (decimal) is converted to 7/10
━━━━━━━☆☆━━━━━━━
▹ Answer
7/10
▹ Step-by-Step Explanation
0.7 → The 7 is in the tenth's place, therefore this is written as 7/10.
Final answer - 7/10
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Tammy drove 715 miles in 11 hours. at the same rate, how long would it take her to drive 845 miles?
Answer:
Step-by-step explanation:
So we have direct proportions here.
So
715=11
845=x
845*11/715
x=13
To check our work.
715/11=65
65*13=845.
Basically, in this formula, you use cross multiplication. So A*B=B*A. B and B go together and A and A go together/
So we can use the formula x = b*b/a. Since A is one of the A's and the other value of A is missing, we can use this formula to find it.
Hope this helped, ask me if you have any questions.
willa can type 900 words in a quarter of an hour. how many words per minute can willa type?
Answer:
Willa can type 60 words per minute
Step-by-step explanation:
60 minutes = 1 hour
1/4 hour = 1/4 × 60 minutes
= 60/4 minutes
= 15 minutes
Quarter of an hour= 15 minutes
Willa can type 900 words in 15 minutes
how many words per minute can willa type?
Words per minute= Total words in 15 minutes / 15 minutes
= 900 / 15
= 60 words per minute
Willa can type 60 words per minute
please help. I'm kinda confused.
Answer:
the first picture would be concave and the second one would be convex
Step-by-step explanation:
Well concave means to go inwards and convex means to go outwards.
what does n equal in 2n+33
Which shows the correct solution of the equation 1/2a+2/3b=50, when b=30 ?
Answer:
Step-by-step explanation:
1/2a+20=50
1/2a=30
a=10
Answer:
a= 60
Step-by-step explanation:
1/2a+2/3b=50, when b=30
Let's first subsitute 30 into b:
1/2a+2/3(30)=50
According to the order of operations, we must multiply 2/3 and 30 first. So:
2/3 times 30 equals 20.
2/3 times 30/1. 3 goes into 30 ten times, so 2 times 10= 20.
Now we got:
1/2a+20=50
Since 20 and 50 are like terms, you want to geth those two together. So, move the positive 20 to the other side where 50 is. Since 20 got moved to the opposite side, it changes signs and becomes negative.
So:
1/2a=50-20
50-20= 30
1/2a=30
Multiply each side by 2 because 2 is the only number that'll make the variable a just 1a.
1/2a times 2= 1a
30 times 2= 60, so:
1a= 60, which is also a= 60.
So a= 60.
GK=24, HJ=10, and GH=HI=IJ find each length
Answer:
please upload the figure