Answer:
if 1cm is for 1km there are 12km
Step-by-step explanation:
it can depend on the size of the map but if there is a scale which shows how many km per cm then multiply by 12
Consider the function g(x) shown below over a domain of [1,∞).
g(x) = 2(x – 1)2 – 3
Part A
Determine g–1(x).
Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).
Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).
The inverse of a function may or may not be a function
The function g(x) is given as:
[tex]g(x) = 2(x - 1)^2 - 3[/tex]
(a) Inverse function g^-1(x)
We have:
[tex]g(x) = 2(x - 1)^2 - 3[/tex]
Replace g(x) with y
[tex]y = 2(x - 1)^2 - 3[/tex]
Swap the positions of x and y
[tex]x = 2(y - 1)^2 - 3[/tex]
Add 3 to both sides
[tex]x + 3 = 2(y - 1)^2[/tex]
Divide both sides by 2
[tex]\frac{x + 3}2 = (y - 1)^2[/tex]
Take square roots of both sides
[tex]\sqrt{\frac{x + 3}2} = y - 1[/tex]
Add 1 to both sides
[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]
Rewrite as:
[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]
Express as inverse function of g
[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]
Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]
(b) The domain, and the range of g(x) and g^-1(x)
Function g(x)
The function g(x) is a quadratic function.
So, the domain is:
Inequality: [tex]-\infty < x < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}The range is:
Inequality: [tex]f(x) \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{y|y\ge -3\}[/tex]Function g^-1(x)
The function g^-1(x) is a square root function.
So, the domain is:
Inequality: [tex]x \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{x|x\ge -3\}[/tex]The range is:
Inequality: [tex]-\infty < y < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).
(c) The graph
See attachment for the graph
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Alberto and Kali are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Alberto sold 1 small box of tangerines and 1 large box of tangerines for a total of $25. Kali sold 3 small boxes of tangerines and 9 large boxes of tangerines for a total of $165. What is the cost each of one small box of tangerines and one large box of tangerines?
please help, will give brainliest.
Answer:
s =$10, l = 15, together they are $25
Step-by-step explanation:
Alberto: 1s + 1l = 25
Kali: 3s + 9l = 165
Multiply Alberto x 3: 3s + 3l = 75
Subtract from Kali:
3s + 9l = 165
- 3s + 3l = 75
6l = 90
l = 15, Large = $15.
Substitute into one of the equations: s + l = 25
s + 15 = 25
s = 10
Ricky spends $103. 19 in additional interest and charges on monthly payments as the result of a prior bankruptcy. If Ricky had been able to save this money for one year and then put it into a savings account earning 3. 1% simple interest, how much money could he have in savings after two more years? a. $1,238. 28 b. $1,276. 67 c. $1,315. 06 d. $2,476. 56.
The amount of money he could have in savings after two more years is:c. $1,315. 06.
First step is to calculate the 12 month saving
Saving= 12 month × $103.19
Saving = $1238.28
Second step is to calculate the interest earned
Interest = Prt
Interest= $1238.28×·0.031×1
Interest= $38.39
Third step is to calculate the balance after 2 years
Saving= $1238.28 +(2 years × $38.39)
Saving= $1238.28 +$76.78
Saving= $1315.06
Inconclusion the amount of money he could have in savings after two more years is:c. $1,315. 06.
Learn more about interest here:
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Arrange in descending order: 101.121, 111.101, 101.112, 110.111
Answer:
111.101, 110.111, 101.121, 101.112
Step-by-step explanation:
Descending order means values starting with big ones and ending with the small ones.
So, in this case,
111.101, 110.111, 101.121, 101.112Hope it helps :)
help ASAP please again and again
Answer:
14
Step-by-step explanation:
I need help with this math problem. .
Answer:the answer is a
Step-by-step explanation:
If x is directly propotional to y
Given that x=8 and y=2
find x=4.
Answer:
1
Step-by-step explanation:
Using similarity
8/4 = 2/y
2 = 2/y
2y = 2
y = 2/2
y = 1
X = 8 find the slope
Answer:
the slope is 8
Step-by-step explanation:
since , x = 8 is a vertical line ,so the slope is undefined
Which condition in the figure below will prove l || m?
Answer:
m<2 + m<3 = 180°
Step-by-step explanation:
Lines intersected by a transversal are parallel if same-side interior angles are supplementary.
Answer: m<2 + m<3 = 180°
Given pr // st. pr = 7 cm. ts = 3cm tq = 5cm what the length of pt
The question is an illustration of parallel lines, and equivalent ratios
The length of pt is 11.7 cm
Given that:
[tex]pr = 7cm[/tex]
[tex]ts =3cm[/tex]
[tex]tq = 5cm[/tex]
This means that:
[tex]pr : ts = pt : tq[/tex]
Substitute values for pr, ts and tq
[tex]7cm : 3cm =pt : 5cm[/tex]
Express the ratios as fractions
[tex]\frac{7cm }{ 3cm }= \frac{pt}{5cm }[/tex]
Cancel out the common units
[tex]\frac{7}{ 3}= \frac{pt}{5cm }[/tex]
Cross multiply
[tex]3pt = 35cm[/tex]
Divide both sides by 3
[tex]pt = 11.7cm[/tex]
Hence, the length of pt is 11.7 cm
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Kate and Elena were playing a card game. The stack of cards in the middle had 25 cards in it to begin with. Kate added 5 cards to the stack. Elena then took 8 cards from the stack. Finally, Kate took 7 cards from the stack. How many cards were left in the stack?
Answer:
15
Step-by-step explanation:
step 1: 25+5=30
step 2: 30-8=22
step 3:22-7=15
PLEASE HELP ME NOWWWWWWWWWW
Answer:
36 And 59
Step-by-step explanation:
henley needs to calculate the base of a trapezoid, b, given the area, a, in inches. She need to rearrange the formula a=16(b+4). Solve the formula for b in terms of a
Answer:
b = (a/16) - 4
Step-by-step explanation:
a = 16(b + 4)
a = 16b + 64
16b + 64 = a
16b = a - 64
16b/16 = (a/16) - 64/16
b = (a/16) - 4
Answer:
b = a/16 - 4.
Step-by-step explanation:
a=16(b+4)
b+4 = a/16
b = a/16 - 4.
Please answer ASAP. Will give brainliest.
Graph the following.
[tex] \:1)3x + 6 \leqslant 0 \\ 2)2x - y < 1 \\ \: \: \: \: \: \: \: \: 3)x + 2y + 2 \geqslant 0 \\ 4)x - 2y > 3[/tex]
1. x≤-2
2. I am not able to upload the graph
3. y≥0.5 x-1
4. y<0.5 x-3/2
I need help i don't understand/
Answer:
1. A
2. C
Step-by-step explanation:
If they are corresponding, so their angle measures are the same. Hope this helps. :)
Answer:
1) 1 and 6
2) 110. these are corresponding angles so they are congruent
Step-by-step explanation:
What two numbers multiplied together equal 8 but when added together equal -6
Answer:
i believe its -4 and -2
Step-by-step explanation:
hope tha work
a store is handing out scratch-off cards to its customers .for each card a customer wins either a coupon or a free t-shirt .the ratio of coupon cards to t-shrits is 9:2 .the total of 8,250 cards how many of the cards are t-shirts cards
Step-by-step explanation:
Ratio 9:2, therefore total number of shares is 11.
because 9+2 = 11
total cards = 8,250
8,250/11 = 750
This is the value for one of the shares.
As the ratio is 9:2 we can find:
9 X 750 : 2 X 750
To see what everyone has won.
T-shirts : 2 X 750 = 1,500.
Hope you understand how it's done, if not leave a comment and I'll try to be more thorough
to convert 25 hours to minutes would you use the ratio 1/60
Answer:
Yes
Step-by-step explanation:
1 hour = 60 min
25 hours = 60 x 25 min
Select the correct answer from each drop-down menu.
Consider triangles PQR, MNO, and STU, which have resulted from rotating, reflecting, and translating triangle XYZ.
Answer:
Not Similar because they don't have equivalent angles.
Step-by-step explanation:
First one is D
Second one is A
The Triangle XYZ is Congruent to PQR by ASA congruence, the Triangle XYZ is Congruent to MNO by SSS congruence, the Triangle XYZ is Congruent to STU by SAS congruence
What is a Triangle?A triangle is a polygon with three sides, they are classified as acute angle triangle, right angle triangle, obtuse angle triangle on the basis of angles subtended by the vertices.
The triangles PQR, MNO, XYZ, STU can be seen in the figure
Triangles PQR, MNO, and STU, which have resulted from rotating, reflecting, and translating triangle XYZ.
The Triangle XYZ is Congruent to PQR by ASA congruence
From the image
XY = PQ
∠YXZ= ∠QPR
∠YZX = ∠PQR
The Triangle XYZ is Congruent to MNO by SSS congruence
From the image
XY= MN
YZ=ON
ZX=OM
The Triangle XYZ is Congruent to STU by SAS congruence
XY = ST
∠YXZ=∠TSU
XZ= SU
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So im stuck again can anyone help with #4,6,7 TwT srry 2 ask again
- #4 -
y = 12
[] First we will solve for x. Our angles with x are vertical angles, so they can be set equal to each other
8x - 61 = 6x - 13
8x - 48 = 6x
-48 = -2x
24 = x
[] Then, we will plug it into one of the angles (with x) and solve:
8x - 61
8(24) - 61
192 - 61 = 131
[] Last, these are supplementary angles so we can add them together and set it equal to 180:
131 + 3y + 1 = 180
132 + 2y = 180
2y = 48
y = 12
- #6 -
y = 22
[] First we will solve for x. These angles are vertial angles, so we can do the following:
9x + 42 = 15x
42 = 6x
7 = x -> x = 7
[] Then, we will plug it into one of the angles (with x) and solve:
15x = 15(7) = 105
[] Last, we will solve for y. These are supplementary angles so we can add them together and set it equal to 180:
4y - 13 + 105 = 180
4y + 92 = 180
4y = 88
y = 22
- #7 -
y = 9
[] First we will solve for x. They are supplementary angles so we can add them together and set it equal to 180:
x + 21 + 3x + 11 = 180
4x + 32 = 180
4x = 148
x = 37
[] Then, we will plug it into one of the angles (with x) and solve:
3x + 11 = 3(37) + 11 = 111 + 11 = 122
[] Last, we will solve for y. These are vertical angles, so they can be set equal to solve:
122 = 14y - 4
126 = 14y
9 = y
- See attached for where I pulled numbers from -
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
What property does this question use 3(x+6)-2=28
Answer: Properties of Multiplication. You can use the properties of multiplication to evaluate expressions. Commutative Property. Changing the order of factors does not change their product. Example: a x b = b x a. 4 x 20 = 20 x 4. Associative Property. Changing the grouping of factors does not change their product.
if a= { } b= {1,2} then n(a×b) is
Answer:
A={a,b,c}
B={1,2}
A×B={(a,1),(a,2),(b,1),(b,2),(c,1),(c,2)
Find the slope of the line that passes through the pair of points (-17, – 8) and (0, – 5)
Answer:
-13/-17
Step-by-step explanation:
y1-y2/x1-x2=-13/-17
4. What is 20% of 25?
Answer:
5 because 20 percent in a fraction is 1/5 so you would just divide 25 by 5. Or you could do 25 times .2 and your answer is still 5.
Step-by-step explanation:
20% of 25 is 5
25 Percentages
1% = 0.25
5% = 1.25
10% = 2.5
15% = 3.75
20% = 5
at what rate of simple interest will ₹4400 amount to ₹5610 in 5 years 6 months
Answer:
0.05 or 5%
Step-by-step explanation:
The formula for simple interest is as follows:
A = P(1+rt), with A representing the final amount, P representing the initial amount, r being the rate, and t being time. Plugging our values in, we have
5610 = 4400(1+5.5r). We know that 5 years and 6 months is 5.5 because 6 months = 0.5 years
5610 = 4400(1+5.5r)
expand
5610 = 4400 + 24200r
subtract 4400 from both sides to isolate the variable and its coefficient
1210 = 24200r
divide both sides by 24200 to isolate the variable
r = 0.05 or 5% as 0.05 * 100 = 5
what is the slope of the line?
Answer:
-8/3
Step-by-step explanation:
rise/run
rise: -8
run: 3
-8/3
someone please help me
Answer:
m = 5
Step-by-step explanation:
Since the triangles are similar in the way shown, then
6/10 = 3/m
6m = 10 × 3
m = 5
A car travels 470.7 kilometers on 52.3 liters of gas. How much gas will it need to go 345.6 kilometers?
Answer:
38.4[litres].
Step-by-step explanation:
[tex]1. \ the \ rule \ \frac{470.7[km]}{52.3[l]} =\frac{345.6[km]}{x};[/tex]
[tex]2. \ x=\frac{345.6*52.3}{470.7}=38.4[l].[/tex]
help please I'm stuck on this question
Answer:
120 yd²
Step-by-step explanation:
The floor consists of a square and a triangle
area of square = 10² = 100 yd²
area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 4 and h = 10 , then
area = [tex]\frac{1}{2}[/tex] × 4 × 10 = 2 × 10 = 20 yd²
company needs 100 + 20 = 120 yd²
In a solid cube made up of smaller black and white cubes. The black and white cubes are at alternate places of the larger cube. How many black cubes are there in the above arrangement?
There are 168 black cubes in the arranagement.
A cube has 6 faces. Each face of the cube consists of 25 white cubes and 24 black cubes.
To get the number of black cubes in the arrangement, we will use the equation below;
Number of black cubes = Total number of black cubes on a face * number of small cubes along the edgeNumber of black cubes = 24 * 7Number of black cubes = 168Hence there are 168 black cubes in the arrangement.
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