f(x)=2^x. What is g(x)?
The function g(x) is g(x)= (3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 3 to form g(x).
This means that:
g(x) = f(3x)
So, we have:
g(x)= (3x)^2
Hence, the function g(x) is g(x)= (3x)^2
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What is the slope of the line containing (-2, 5) and (4,-4)?
A. 2
OB.
mle
O C. - /3/20
D. -2
Answer:
-1.5
Step-by-step explanation:
To work out the gradient of the line, we use this equation:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Substituting in, we get:
[tex] \frac{5 - ( - 4)}{ - 2 - 4} [/tex]
Which simplifies to:
[tex] \frac{9}{ - 6} = \frac{3}{ - 2} = - \frac{3}{2} = - 1.5[/tex]
please help!!!!!!nnnn
Similar: yes
Similarity statement: [tex]ADCB \sim SVUT[/tex]
Scale factor: 1/3
What is the midpoint of the line segment graphed below?
Answer:
(4, 7/2)
Step-by-step explanation:
midpoint = x values/2, y values/2
(2x + 1) (x - 1) solve for X
Put brackets equal 0
(2x + 1) (x - 1) = 0
(2x + 1) = 0
-1, then ÷2
x = - 1/2 or - 0.5
(x - 1) = 0
+1
x = 1
So, x = - 0.5 & x = 1
Hope this helps!
Answer:
x = -0.5
x = 1
Step-by-step explanation:
Hello!
We can set each factor to 0 and solve for x in both.
(2x + 1) = 0There are 2 solutions for x, -0.5 and 1.
Please tell me fast I am on a time crunch
3 5/6 + 2 4/9 in its simplest form
Answer:
>> [tex]6\frac{5}{18}[/tex]
Step-by-step explanation:
1) Add the whole numbers first.
[tex]5+\frac{5}{6} +\frac{4}{9}[/tex]
2) Find the Least Common Denominator (LCD) of [tex]\frac{5}{6} ,\frac{4}{9}[/tex] . In other words, find the Least Common Multiple (LCM) of [tex]6,9[/tex].
Method 1: By Listing Multiples
1. List the multiples of each number.
Multiples of 6 : 6, 12, 18, ...
Multiples of 9 : 9, 18, ...
2. Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 18
3. Make the denominators the same as the LCD.
[tex]5+\frac{5\times 3}{6\times 3}+\frac{4\times 2}{9\times 2}[/tex]
4. Simplify. Denominators are now the same.
[tex]5+\frac{15}{18}+\frac{8}{18}[/tex]
5. Join the denominators.
[tex]5+\frac{15+8}{18}[/tex]
6. Simplify.
[tex]5+\frac{23}{18}[/tex]
7. Convert [tex]\frac{23}{18}[/tex] to mixed fraction.
[tex]5+1\frac{5}{18}[/tex]
8. Simplify.
[tex]6\frac{5}{18}[/tex]
Decimal Form: 6.277778
Cheers.
The addition of 3 5/6 + 2 4/9 is 113/18
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
3 5/6 + 2 4/9
Now, writing it into normal fraction
3 5/6 + 2 4/9
= 23/ 6 + 22/9
= 23/6 x 3/3 + 22/9 x 2/2
= 69/ 18 + 44/18
= 113/18
Hence, the addition is 113/18
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as part of a competition, diego must spin around in a circle 6 times and then run to a tree. the time he spends on each spin is represented by S AND THE TIME HE SPEND RUNNING is R. He gets to the tree 21 seconds after he starts spinning. If it takes diego 1.2 seconds to spin around each time, how many seconds did he spend running
The time he spent running is 13.80 seconds.
How much time did he spend running?
The equation that can be used to represent the time he gets to the tree is:
Time he gets to the tree = (time of each spin x total spins) + time he spent running
21 = (6 x 1.2) + r
21 = 7.20 + r
r = 21 - 7.20
r = 13.80 seconds
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x is directly proportional to y. When x = 4, y = 7. Work out the value
of y when x = 12
Answer:
y = 21
Step-by-step explanation:
When x is directly proportional to y:
When x increases, y also increases.
In this case, it is so you write,
1. Write down the formula: y=kx
k being the constant.
Let's use "When x = 4, y = 7" to work out the constant.
2. Substitute the 'when' values: 7=k×4
3. Rearrange to find the constant: 7÷4=k
4. Find k: k=1.75
Now let's see the new problem, 'what is y when x = 12'.
5. Substitute the values now but keep the constant: y = 1.75 × 12
6. Rearrange if needed.
7. Find the missing value: y = 21
Hope this helped and if you require further assistance from me please comment below! :)
Ps: If it was inversely proportional then the formula would be y = k / x
with k still being the constant.
Suppose that the breaking strength of a rope (in pounds) is normally distributed, with a mean of 100 pounds and a standard deviation of 16. What is the probability that a certain rope will break before being subjected to 120 pounds? (You may need to use the standard normal distribution table. Round your answer to four decimal places.)
The probability that a certain rope will break before being subjected to 120 pounds is 89.4%.
What is the probability that a certain rope will break before being subjected to 120 pounds?The probability is calculated as follows:
Mean = 100
Standard deviation = 16
The probability is obtained from the z-score.
x = mean + z-score * standard deviation
120 = 100 + z-score * 16
z-score = 20/16
z-score = 1.25
From normal distribution table, the probability with a z-score of 1.25 is 89.4%
In conclusion, the probability is obtained from the z-score.
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Find the constant of variation when t varies directly as the square of s, and t = 64 when S = 4.
Answer:
The constant of variation is 4
Step-by-step explanation:
We are looking for the constant of variation when t varies directly as the square of s
t = k s^2 where k is the constant of variation
t = 64 and s = 4
64 = k 4^2
64 = k * 16
Divide each side by 16
64/16 = k * 16/16
4 = k
The constant of variation is 4
Determine an approximate value for y if the coordinate (-0.5387 ,y) is on the unit circle
Answer:
y = 0.8425 or y = -0.8425
Step-by-step explanation:
All points in the Cartesian coordinate system have an x and y coordinate, defined by two perpendicular measurements.
If the point is on the unit circle, then the radius of the circle is defined to be 1 unit, and the corresponding right triangle follows the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
For a unit circle:
[tex]x^2+y^2=1^2[/tex]
Substituting the known value for x, and simplifying...
[tex](-0.5387)^2+y^2=(1)^2[/tex]
[tex]0.29019769+y^2=1[/tex]
Subtracting 0.29019769 from both sides to begin to isolate "y"...
[tex]y^2=1-0.29019769[/tex]
[tex]y^2=0.70980231[/tex]
Applying the square root property...
[tex]\sqrt{y^2}=\pm \sqrt{0.70980231}[/tex]
[tex]y=\pm 0.8424976171...[/tex]
So, (to 4 decimal places), the y coordinate could be either 0.8425 or -0.8425.
With only the given information, either result is a valid answer.
the domain a function g(x) is x > 3, and the range is y> 1. What are the The domain of
domain and range of its
inverse function, g
(x)?
The domain of a function is the range of its inverse, and vice versa.
So, the domain is [tex]x > 1[/tex] and the range is [tex]y > 3[/tex].
Suppose that the functions p and q are defined as follows. p(x)=x+1
q(x)=2x^2-2
The value of (p*q)(5) and (q*p)(5) is 288
How to determine the composite functions?The functions are given as:
p(x)=x+1
q(x)=2x^2-2
Calculate p(5) and q(5)
p(5)=5+1 = 6
q(5)=2(5)^2-2 = 48
The functions are then calculated as:
(p*q)(5) = p(5) * q(5)
(p*q)(5) = 6 * 48
(p*q)(5) = 288
Also, we have:
(q*p)(5) = (p*q)(5)
(q*p)(5) = 288
Hence, the value of (p*q)(5) and (q*p)(5) is 288
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Complete question
Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)
A party platter contains 38 cupcakes: 13 chocolate, 11 yellow, and 14 lemon. You randomly select one cupcake, eat it, then randomly select another cupcake. Find the probability of selecting from the platter a chocolate cupcake and then a yellow cupcake.
The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is 0.10.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)
(13 / 38) x (11 / 37) = 0.10
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1
10 ft
Cone 1
2.5 ft
8 ftl
2 ft
Cone 2
could anyone help me with this?
Answer:
Step-by-step explanation:
A=6x²
[tex]\frac{dA}{dt} =6\times 2x \times \frac{dx}{dt} \\\frac{dA}{dt}=12x \frac{dx}{dt}[/tex]
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
The graph that includes the possible values for the number of people who still need to sign up for the team is:
Number line with closed circle on 5 and shading to the right.
What is the situation and which inequality models it?Researching this problem on the internet, a team currently has 4 players, and needs at least 9.
When x players are signed, the number of players will be of 4 + x. Since the team needs at least 9 players, the inequality is:
[tex]4 + x \geq 9[/tex]
The solution is:
[tex]x \geq 9 - 4[/tex]
[tex]x \geq 5[/tex]
Which is represented as follows:
Number line with closed circle on 5 and shading to the right.
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A candy shop sells a box of chocolates for $30. It has $29 worth of chocolates plus $1 for the box. The box includes two kinds of candy: caramels and truffles. Lita knows how much the different types of candies cost per pound and how many pounds are in a box. She said,
If x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box, then I can write the following equations based on what I know about one of these boxes:
x + y = 3
8x + 12y + 1 = 30
Assuming Lita used the information given and her other knowledge of the candies, use her equations to answer the following:
How many pounds of candy are in the box?
What is the price per pound of the caramels
What does the term 12y in the second equation represent?
What does 8x + 12y + 1 in the second equation represent?
Answer:
There are 3 lbs of candy in the box.
The caramels are $8 per pound.
12y represents the total cost of truffles in the box.
8x + 12y + 1 represents the cost of caramels in the box + the cost of truffles in the box + the cost of the box.
Step-by-step explanation:
x = the number of pounds of caramels
y = the number of pounds of truffles
x + y = total lbs. and we know x + y = 3
We know x is the number of pounds of caramels.
8x = (cost per pound of caramels) × (number of pounds of caramels)
So 8 = cost of caramels
We know y = number of pounds of truffles. So 12 is the cost of truffles by pound, and 12y is the total cost of truffles in the box.
Based on all the above,
The cost of caramels in the box + the cost of truffles in the box + the cost of the box is = total cost of the box. 8x + 12y + 1 = 30
Help me please!!!!!!!!
Answer:
The ratios are not equal, so this is not a dilation.
Step-by-step explanation:
4/3 is the first ratio
3/4 is the second ratio
Since these ratios are not equal there is not a dilation.
What can you say about the y-values of the two functions f(x) = 3x² -3 and
g(x) = 2* - 3?
A. g(x) has the smallest possible y-value.
B. The minimum y-value of g(x) approaches -3.
C. f(x) and g(x) have equivalent minimum y-values.
D. f(x) has the smallest possible y-value.
The y-values of the two functions f(x) = 3x² -3 and g(x) = 2* - 3 has the minimum y-value of g(x) approaches -3 and f(x) contains the smallest possible y-value.
What is a function?It exists described as a special kind of relationship and they contain a predefined domain and range according to the function every value in the domain exists connected to just one value in the range.
Given: f(x) = 3x² -3
As we can see in the graph the first term exists 3x² and exists still positive for all x.
The range for f(x) ∈ [-3, ∞)
When x = 0 then f(x) = -3
The above value exists as the smallest possible value on the y-axis.
Given: [tex]g(x) = 2^x - 3[/tex]
[tex]2^x[/tex] exists also a positive quantity and it exists as an exponential function.
The range for the g(x) ∈ (-3, ∞)
It signifies that g(x) never touches the y-axis at -3.
We can express the minimum value of g(x) approaches -3.
Therefore, the correct answer is option B. The minimum y-value of g(x) approaches -3 and option D. f(x) has the smallest possible y-value.
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Simplify the following
Answer is 6
Firstly changing mixed fraction.
[tex] \frac{3}{2} - \frac{5}{4} + \frac{23}{4} [/tex]
By taking the LCM
[tex] \frac{6 - 5 + 23}{4} [/tex]
-5 + 23 (-) (+) = (-)
[tex] \frac{6 + 18}{4} [/tex]
[tex] \frac{24}{4} [/tex]
[tex]6[/tex]
Hope it helps you, any confusions you may ask!
Answer:
6 (work below)
Step-by-step explanation:
1 1/2 = 3/2
1 1/4 = 5/4
5 3/4 = 23/4
The least common multiple of the denominators is 4, so 3/2 will become 6/4.
6/4 - 5/4 = 1/4 + 23/4 = 24/4 = 6
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A particle travels so that its distance D (in metres) from its origin O is modelled by the equation D = 24 + 15t - [tex]\frac{t^{2} }{2}[/tex], where t is the time in minutes after the particle has started to move.
a. calculate the particle's distance from O when it first started to move.
b. determine the time when the particle first reaches O. Give your answer to 2 decimal places.
c. determine the particle's speed when it has been moving for 3 minutes. Give your answer in m [tex]S^{-1}[/tex]
(a) The particle's distance from O when it first started to move is 24 m.
(b) The time when the particle first reaches O is 15 mins.
(c) The particle's speed when it has been moving for 3 minutes is 0.2 m/s.
Particle's distance from O when it first started to move
D = 24 + 15 - t²/2
when the time, t = 0
D = 24 m
When the object first reaches OWhen the object reaches O, its final velocity, v = 0
v = dD/dt
v = 15 - t
0 = 15 - t
t = 15 mins
Speed of the particle after 3 minutesv = 15 - t
v = 15 - 3
v = 12 m/min
v = 12 m/min x 1min/60s = 0.2 m/s
Thus, the particle's distance from O when it first started to move is 24 m.
The time when the particle first reaches O is 15 mins.
The particle's speed when it has been moving for 3 minutes is 0.2 m/s.
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Which function below has the following domain and range?
Domain: {-9, - 5, 2, 6, 10}
Range: { -2, 0, 8}
O {(-9, 10), (-2,8)}
O ((-9, -2), ( – 5, 0), (2, 8), (6, 5), (10, 9))}
O ((-2,-5), (8, 10), (0, 6), (-2, -9), (0, 2)}
O {(2,0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
{(2,0),(-5,-2),(10,8),(6,0),(-9,-2)} is the correct answer (D)
Answer:
(d) {(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
Step-by-step explanation:
The domain is the list of x-values. The range is the list of y-values. You are looking for the set that matches the given lists.
ChoicesA.The list of x-values is {-9, -2}. The list is too short.
B.The list of x-values is {-9, -5, 2, 6, 10}. This matches the required domain.
The list of y-values is {-2, 0, 8, 5, 9}. The list is too long.
C.The list of x-values is {-2, 8, 0, -2, 0}. The list does not match the given domain list.
D.The list of x-values is {2, -5, 10, 6, -9}. This matches the given domain.
The list of y-values is {0, -2, 8, 0, -2}. This matches the given range.
The function of interest is ...
{(2, 0), (-5, -2), (10, 8), (6, 0), (-9, -2)}
A tower is composed of a prism with a square base and a pyramid. The base length is 20 meters, and the height of the prism is 40 meters, while the slant height of the pyramid is 10√2 meters. What is the total surface area, including the bottom base? 400√2 + 3,600 m2 200√2 + 3,600 m2 400√2 + 400 m2 4000√2 m2
The total surface area of the tower composed of a prism with a square base and a pyramid is 3600 + 400√2 m²
How to find the surface are of a composite figure?Total surface area of the tower = area of the base + 4(area of the rectangular surface) + 4(area of the triangular surface)
Therefore,
area of the base = 20² = 400 m²
4(area of the rectangular surface) = 4(40 × 20) = 3200 m²
4(area of the triangular surface) = 4(1 / 2 × 10√2 × 20) = 4(100√2) = 400√2 m²
Therefore,
total surface area = 400 + 3200 + 400√2
total surface area = 3600 + 400√2 m²
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Answer:
a)400V2 plus 3,600 m2
Step-by-step explanation:
what is the sum of .74+.19+3.09+1.98=
Answer:
6
Step-by-step explanation:
no calculator at hand ?
really ? you are using us a simple calculator ?
Answer:
6
Step-by-step explanation:
what is the sum of .74+.19+3.09+1.98=
0.74+
0.19+
3.09+
1.98=
-----------------
6
5. a. The area of an isosceles triangle is 60cm² and its base is 10cm. Find the length of its equal side.
Answer:
H = 12cm
b
I hope I was able to help
Evaluate the sum (for math nerds)
[tex]i {}^{0!} + i {}^{1!} + i {}^{2!} + i {}^{3!} + ... + i {}^{100!} [/tex]
Note that :
[tex]i = \sqrt[]{ - 1} [/tex]
Answer: i+96
Step-by-step explanation:
Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.
This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]
So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]
[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,
[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]
[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]
etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].
Meanwhile,
[tex]i^{0!} = i^1 = i[/tex]
[tex]i^{1!} = i^1 = i[/tex]
[tex]i^{2!} = i^2 = -1[/tex]
[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]
Then the sum we want is
[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]
find the product xy if
2^(x)+3^(y)=5,
2^(x+2)+3^(y+1)=18
The solution to the system of equation is (0, 1)
System of equationsGiven the following system of equation as shown below
2^(x)+3^(y)=5,
2^(x+2)+3^(y+1)=18
Rewrite
2^(x)+3^(y)=5,
2^x*2^2 + 3^y*3^1 = 18
___________
2^(x)+3^(y)=5,
4(2^x) + + 3(3^y) = 18
Let a = 2^x and b = 3^y
Substitute
a + b = 5
4a + 3b = 18
a = 5 - b
Substitute
4(5-b) + 3b = 18
20 - 4b + 3b = 18
-b = -2
b = 2
since a = 5 - b
a = 5 - 2
a = 3
Recall that a = 2^x and b = 3^y
2^x = 2
x = 0
Similarly
3^y = 3
y =1
Hence the solution to the system of equation is (0, 1)
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A closed box has a square base with side length ll feet and height hh feet. Given that the volume of the box is 29 cubic feet, express the surface area of the box in terms of ll only.
The surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
How to determine the surface areaThe volume of cuboid or box can be given as,
Volume = l × b × h
Here, (l) is the length, (b) is the width of the box and (h) is the height of the box.
A closed box has a square base with side length l feet and height h feet. Therefore, the length and width will be the same.
Then the volume of the box is 29 cubic feet. Thus,
29 = l × l × h
29 = [tex]l^2 h[/tex]
[tex]h = \frac{l^2}{29}[/tex]
The surface area of the square base box is,
Area = [tex]2l^2 + 4lh[/tex]
Substitute the value of h
Area = [tex]2l^2 + 4l\frac{29}{l^2}[/tex]
Area = ,[tex]2l^2 + \frac{116}{l}[/tex]
Therefore, the surface area of the closed box in terms of l only, which has the square base is,[tex]2l^2 + \frac{116}{l}[/tex]
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