Answer:
[tex]{g}^{ - 1} ( - 2) = \frac{9}{2} [/tex]Step-by-step explanation:
To find g-¹( 2) we must first find g-¹(x)
To find g-¹(x) equate g(x) to y
That's
y = g(x)
We have
y = - 2x + 7
Now interchange the terms that's x becomes y and y becomes x
We have
x = - 2y + 7
Make y the subject in order to find g-¹(x)
Move 7 to the left side of the equation
- 2y = x - 7
Multiply both sides by - 1
We have
2y = 7 - x
Divide both sides by 2 to make y stand alone
That's
[tex]y = \frac{7 - x}{2} [/tex]So we have
[tex]g ^{ - 1} (x) = \frac{7 - x}{2} [/tex]Now to find g-¹(- 2) substitute the value of x that's - 2 into the expression
We have
[tex] {g}^{ - 1} ( - 2) = \frac{7 - - 2}{2} \\ {g}^{ - 1} ( - 2) = \frac{7 + 2}{2} [/tex]We have the final answer as
[tex]{g}^{ - 1} ( - 2) = \frac{9}{2} [/tex]Hope this helps you
Answer:
-10
-12
Step-by-step explanation:
Find the product. 2√3•√15 A)5√5 B)√45 C)6√5 D)18√5
First multiply the numbers inside the radicals together.
So √3 · √15 is √45.
So we have 2√45.
Note that the 2 can't be multiplied by anything since
√15 has nothing outside of the radical.
So we have 2√45.
Now, break down your square root.
√45 breaks down as 9 · 5 and 9 breaks down as 3 · 3.
Since we have a pair of 3's, a 3 comes outside of the radical
multiplying by the 2 that was previously outside to get 6.
The 5 doesn't pair up so it stays inside.
So our final answer is 6√5.
Answer:
C) [tex]6\sqrt{5}[/tex]
Arithmetic without explanation:
[tex]2\sqrt{3}* \sqrt{15}\\ = 2\sqrt{3}* \sqrt{3*5} \\ = 2\sqrt{3^2} *\sqrt{5} \\ = 2 * 3\sqrt{5} \\= 6\sqrt{5}[/tex]
Example of radical multiplication:
Take [tex]y\sqrt{x} * a\sqrt{b}[/tex] as an example:
1. Multiple the numbers inside the roots
[tex]\sqrt{x} * \sqrt{b} = \sqrt{x*b} = \sqrt{xb}[/tex]
2. Multiple the numbers outside the roots
[tex]y*a = ya[/tex]
3. Combine them and simplify
[tex]ya\sqrt{xb}[/tex]
Step-by-step explanation:
We are given the expression [tex]2\sqrt{3}*\sqrt{15}[/tex]
1. Identify the roots and multiply them
The roots are [tex]\sqrt{3}[/tex] and [tex]\sqrt{15}[/tex]
[tex]\sqrt{3} *\sqrt{15} \\= \sqrt{45}[/tex]
2. Multiply the numbers outside the root
For [tex]2\sqrt{3}[/tex] it is [tex]2[/tex] and for [tex]\sqrt{15}[/tex] it is [tex]1[/tex]
[tex]2*1 = 2[/tex]
3. Combine and simplify
Combine:
[tex]2* \sqrt{45}\\= 2\sqrt{45}[/tex]
Simplify:
*Note: [tex]\sqrt{n^2} = n[/tex]
1. Find the Prime factorization of 45
[tex]45 = 3^2 * 5[/tex]
2. Simplify the Root
[tex]2\sqrt{45} \\ = 2\sqrt{3^2 * 5} \\= 2\sqrt{3^2} * \sqrt{5} \\= 2 * 3\sqrt{5}\\ =6\sqrt{5}[/tex]
We end up with [tex]6\sqrt{5}[/tex]
On the number line, graph the solution to the inequality -5(x+1) > 7x + 31? Can you tell me how to go about doing this problem I have tried a few methods but can't figure it out.
Answer:
x < -3
Step-by-step explanation:
First we simplify:
-5x - 5 > 7x + 31
-12x > 36
x < -3.
We reverse the sign because we divided by a negative number on both sides.
That should be easy to graph.
The function h(x)=12x^8+49 is an even function. Which transformation of h(x) would result in a function that is neither even nor odd?
A) reflection over the x-axis
B) vertical stretch by a factor of 7
C) translation 8 units to the right
D) horizontal compression
Explanation of the correct answer would be nice so that I understand it better.
Answer:
The correct option is;
C) Translation 8 units to the right
Step-by-step explanation:
The function h(x) = 12·x⁸ + 49 is an even function
However a translation 8 units to the right would yield the following function;
h(x) = 12 × (x+ 8)⁸ + 49 = 12x⁸ + 768x⁷ + 21504x⁶ + 344064x⁵ + 3440640x⁴ + 22020096x³ + 88080384x² + 201326592x + 201326641
For h(1) = 516560701
Also h(-x) = 12 × (-x+ 8)⁸ + 49 = 12x⁸ - 768x⁷ + 21504x⁶ - 344064x⁵ + 3440640x⁴ - 22020096x³ + 88080384x² - 201326592x + 201326641
For h(-1) = 69177661
Therefore h(x) ≠ h(-x) after the translation 8 units to the right and the function is neither even nor odd.
pls solve no;3a,b,c the picture will be
given thank u
use trigonometry u solve it
Answer/Step-by-step explanation:
3.a. length of AC.
Hypotenuse = AC
Opposite side to 60° = 7
Therefore, [tex] sin(60) = \frac{7}{AC} [/tex]
[tex] AC*sin(60) = \frac{7}{AC}*AC [/tex]
[tex] AC*sin(60) = 7 [/tex]
[tex] AC = \frac{7}{sin(60)} [/tex]
[tex] AC = 8.1 [/tex] (to nearest tenth)
b. Length of BC
Hypotenuse = BC
Opposite side to 50° = 7
Therefore, [tex] sin(50) = \frac{7}{BC} [/tex]
[tex] BC*sin(50) = \frac{7}{BC}*AC [/tex]
[tex] BC*sin(50) = 7 [/tex]
[tex] BC = \frac{7}{sin(50)} [/tex]
[tex] BC = 9.1 [/tex] (to nearest tenth)
c. Length of AB
Use the law of sines to find AB
[tex] \frac{BC}{sin(A)} = \frac{AB}{sin(C}} [/tex]
m<C = 180 - (60 + 50) (sum of angles in a triangle) = 70°
m<A = 60°
BC = 9.1
AB = ?
[tex] \frac{9.1}{sin(60)} = \frac{AB}{sin(70)} [/tex]
Cross multiply
[tex] 9.1*sin(70) = AB*sin(60) [/tex]
Divide both sides by sin(60)
[tex]\frac{9.1*sin(70)}{sin(60)} = \frac{AB*sin(60)}{sin(60)}[/tex]
[tex]\frac{9.1*sin(70)}{sin(60)} = AB[/tex]
[tex] 9.9 = AB [/tex] (nearest tenth)
[tex] AB = 9.9 [/tex]
What is 41 degrees below 0?
Answer: -41
Step-by-step explanation:
Answer:
41 degrees below 0 is -41
If Q is the midpoint of PR, find the coordinates of R if P(l 1, -2) and Q(4, 3).
Answer:
Step-by-step explanation:
P(1, -2) ;Q(4,3)
Let R(x1,y1)
Midpoint=[tex](\frac{x_{1}+x_{2}}{2},\frac{y_1+y_2}{2})\\[/tex] = (4,3)
[tex](\frac{1+x_1}{2},\frac{-2+y_1}{2})=(4,3)\\[/tex]
Compare x coordinates and y coordinates
[tex]\frac{1+x_1}{2}=4 ; \frac{-2+y_2}{2}=3[/tex]
1+x1 = 4*2 ; -2+y2 = 3*2
1+x1 = 8 ; -2 +y2 = 6
x1= 8-1 ; y2 = 6+2
x1 = 7 ; y2 = 8
R(7 , 8)
Sumi
Cal's go cart has a gas tank with the dimensions shown below.
He uses a gas can that holds 1 liter of gas, to fill the go cart tank.
1 liter = 1000 cm
and d
cm
and d
ems
25 cm
40 cm
How many full gas cans will it take to fill the go cart's gas tank?
Answer: 8 liters can.
Step-by-step explanation:
First we need to find the volume of the cart tank . Since it is in the shape of a rectangular prism we have to multiply the length by the width by the height to find the volume.
V= 40 * 25 * 8
V = 8000
Which means that the volume is 8000 cubic centimeters.
Now convert 8000 cubic centimeters to liter.
It gives us a hint that 1 liter is equal to 1000 cm^3
So to convert 8000 cubic centimeters to liters we will have to divide it by 1000.
8000/1000 = 8 liters.
what are two characteristics of rational numbers?
Answer:The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another. Whole numbers, integers, fractions, terminating decimals and repeating decimals are all rational numbers.
Step-by-step explanation:
How many department stores have fewer than 60 pairs of boots?
Answer:
The answer is below
Step-by-step explanation:
The question is not correct, the correct question is:
The regional manager of a chain of department stores created the following stem-and-leaf plot showing the number of pairs of boots at each of the stores:
I 0 I
I 1 I 7 8
I 2 I 0 5 8
I 3 I 4 4 7 8
I 4 I 0
I 5 I
I 6 I
How many department stores have more than 60 pairs of boots
Answer:
The stem and leaf plot is a table which is used to represent a value with the first and other digit as the stem while the last digit is the leaf.
From the table attached, the first column is the stem and the remaining column are the leafs. Therefore from the table, below are the pairs of boots in different stores:
17, 18, 20, 25, 28, 34, 34, 37, 38 and 40.
All the store have fewer than 60 boots. This means that the number of stores with more than 60 pairs of boots is 0
The arc length theta shown below is 15 feet
Answer:
Part I: 2πr*X/360
Part II: 2.5 radians
Part III: 143.24°
Step-by-step explanation:
Part II: and Part III: 2π(6)*x/360 = 15, x = 143.24°
143/360 = x/2π, x = 2.5 radians
Kelly likes to fish at the lake near her house. She caught 8 fish last week, measured them, and put them back in the lake. The
lengths of the fish, in inches, are shown.
9, 12, 10, 8, 11, 12, 13,6
Assuming this data is representative of the fish in the lake, what is the mean length of the fish in the lake?
OA. 1.875 inches
OB
10.5 inches
Ос.
3.5 inches
OD
10.125 inches
Answer:The answer is OD 10.125
Step-by-step explanation:
Add all the lengths of the fish (6+8+9+10+11+12+12+13) = 81
Divide by 8
81/8
=10.125
Solve for n
3n-2=2n
N=
Step-by-step explanation:
3n-2=2n
-2=2n-3n
-2=-n
-2=-n
divide by - to get 2
A square dullhouse has an area of 361 square inches. How long is each side of the dullhouse
Answer:
19 inches
Step-by-step explanation:
Area of a square = s^2
s^2 = 361
s = 19
preform the indicated multiplication below. reduce the terms and simplify (2+i)(3-i)(1+2i)(1-i)(3+i)
Answer:
Hey there!
Expand (2+i)(3-i). You should get 7+i
Expand (7+i)(1+2i). You should get 5+15i
Expand (5+15i)(1-i). You should get 20+10i
Expand (20+10i)(3+i). You should get 50+50i as your final answer.
Let me know if this helps :)
$150 in prize money is going to be split among 6 contestants in a competition at a charity event. The person in first place receives the most money, the person in second place receives the second most, the person in third place receives the third most, and so on. Did the person in second place receive at least $40 of the prize money? (1) The person in first place won $50 (2) No individual prize was within $10 of another prize
Answer: yes
Step-by-step explanation:
adding 50 40 30 20 10 and 0 gets you 150 so 2nd place gets 40
f(13) = -3x+ 7
What’s the answer?
Answer:
3.3
Step-by-step explanation:
7-7=0
-3+-7=-10
10 divided by 3 is 3.3
Pls answer ASAP
Use the drop-down menu to answer the question. What property is the mineral in this image demonstrating? magnetism ,fluorescence, luster, or streak
Answer: fluorescence
Step-by-step explanation:
Answer:
fluorescence
Step-by-step explanation:
1 square root x times 4 square root x
Answer:
4√x
Step-by-step explanation:
4√x
A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of NOT drawing a cherry?
Answer:
The probability is 23/30, .77, or 77 percent.
Step-by-step explanation:
Add up all the non cherry options, then put them over the total, 30. You would get 23/30, or .7666666666..., which is also known as about 77 percent. So the probability is 23/30, .77, or 77 percent.
Two lawn care companies are competing for a landscaping contract. Company A charges a $250 monthly consulting fee plus $10 per square foot, whereas Company B charges a $90 landscaping fee plus $12 per square foot. When will the two companies charge the same amount?
Let x be the no.of square feet for landscaping
Company A
Monthly consulting fee = $250
Cost of landscaping of 1 sq.feet = $10
Cost of landscaping of x sq.feet = $10x
So, Total charge by company A = 250+10x ---1
Company B
Monthly consulting fee = $90
Cost of landscaping of 1 sq.feet = $12
Cost of landscaping of x sq.feet = $12x
So, Total charge by company B = 90+12x ---2
Now we are supposed to find how many square feet of landscaping will the two companies charge the same amount
So, Equate 1 and 2
[tex]250+10x=90+12x\\160=2x\\80=x[/tex]
So, the two companies charge the same amount for 80 sq.feet
Total charge by company A for 80 sq.feet = 250+10(80)= $1050
Total charge by company B for 80 sq.feet = 90+12(90)=$1170
-4 = 2t - 2
What’s da answer
Answer: the answer is -1.
the inverse operation of subtraction is addition so you would add 2 on both sides. now you have -4 + 2= -2. now the opposite of multiplication is division. so -2 divided by 2 is -1. hope this helps. Brainliest please!
Answer:
−1=t
Step-by-step explanation:
−4=2t−2
Simplify
First, add the same terms to both of the sides of this equation.
−4=2t−2
−4 + 2 =2t - 2 + 2
Secondly, simplify.
add the numbers
−4 + 2 =2t - 2 + 2
-2 = 2t - 2 + 2
Then,
-2 = 2t - 2+2
-2 = 2t
v
It's simplified to -2 = 2t
Thirdly, Divide both sides of the equation by the same term.
−2=2t
2 over −2
=
2 over 2t
Simplify
(divide the numbers)
2 over −2
=
2 over 2t
which also equals to
(simplify fraction)
−1 = 2 over 2t
-1 = t
Therefore, the solution is −1=t
m + 5 = 5
+ 5 can you guys help
Answer:
the answer would be 0 because 0+5=5
(20 PTS) Can someone please tell me how did 1/2 became 3/6?
Write in point-slope form an equation of the line that passes through the point (8, 9) with slope 7.
Answer:
y = 7x -47Step-by-step explanation:
[tex]m = 7\\(8,9)=(x_1 , y_1)\\\\y-y_1=m(x-x_1)\\\\y - 9=7(x -8)\\y-9=7x-56\\\\Collect\:like\:terms\\\\y = 7x-56+9\\\\y = 7x-47[/tex]
Use this information for problems 1 and 2. When full, one of the pools at Sapphire Island will hold 43,000 gallons of
water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute.
Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level,
Answer:
(b)
Step-by-step explanation:
This is the answer of your questions if right give 5 star!!! and Mark as brainliesr
Refrer to the attached picture on which question is written. This question will be done according to Pathagoras theorem. This question answer is √a2-25 . I want step to step explanation.
i got something different
7 t-shirt cost $28. Calculate the cost of 1 t-shirt
Answer:
One tshirt is $4
Step-by-step explanation:
28/7= 4
Answer:
$4.
Step-by-step explanation:
If 7 shirts equals 28 in total then just do 28/7 = 4.
4x7 = 28.
The Bionic Woman gives Batman a 12 second
start in a 2 kilometre race. If the Bionic Woman
runs at 5 km/min, and Batman runs at 3 km/
min, who will win the race and by how many
seconds?
Answer:
The Bionic Woman will win the race by 4 sStep-by-step explanation:
[tex]v=\dfrac st\quad\implies\quad t=\dfrac sv[/tex]
s = 2 km
t - time of run
v - speed of running
Batman:
v = 3km/min
[tex]t = \dfrac{2\,min}{3\,\frac{km}{min}}=2\,km\cdot\dfrac{min}{3\,km}=\dfrac23\,min = \dfrac23\cdot 60\,s=40\, s[/tex]
The Bionic Woman:
v = 5 km/min
[tex]t = \dfrac{2\,min}{5\,\frac{km}{min}}=2\,km\cdot\dfrac{min}{5\,km}=\dfrac25\,min = \dfrac25\cdot 60\,s=24\, s[/tex]
time from Batman's start: 24 s + 12 s = 36 s
40 - 36 = 4
Juan owes his cousin, Benito, $10.00. Benito is tired of waiting for Juan to pay him back. To try and get Juan to pay up more quickly, Benito has decided to add $1.00 per day to the amount Juan owes him. Juan also owes his brother, Tavon, $15.00. Tavon liked Benito's idea of charging additional money, but because he is Juan's brother, decided he would only charge $.50 per day. Write and solve an equation that shows the number of days it will take for Juan to owe Benito and Tavon the same amount of money.
Answer:
wat???
Step-by-step explanation:
Answer:
Hope this will help you :)
Step-by-step explanation:
Suppose you want to buy a great pair of designer jeans that were originally priced at $95, but are now on sale for 10% off. When you buy the jeans, you need to pay sales tax of 10% on the sales price. How much will you have to pay for the jeans?
Answer:
$94.05
Step-by-step explanation:
Original price of jeans=$95
Discount=10%
New price=(100% - 10%) of $95
=90% × 95
=90/100 × 95
=0.9 × 95
=$85.5
Sales tax of 10%
10% of the new price
=10/100 × 85.5
=0.1 × 85.5
=$8.55
Sales tax =$8.55
Total amount paid for the jeans= sales tax + new tax
=$8.55 + $85.5
=$94.05