15 Points!
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
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Related Questions
plz help me!!!!!!!
Instructions: Select the correct answer from each drop-down menu. When p2 – 4p is subtracted from p2 + p – 6, the result is . To get p – 9, subtract from this result.
-3p-6. 4p+3
5p-6 4p-15
4p+6. 4p+12
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p2+p-6-(p2-4p)=p2+p-6-p2+4p=5p-6
To get p – 9, subtract from this result x:
5p-6-x=p-9
Solving for x:
5p-6-x+x-p+9=p-9+x-p+9
4p+3=x
x=4p+3
Answer:
1) When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6
2) To get p – 9, subtract from this result 4p+3
For the triangle above, find sin A. a. 36° c. 0.9323 b. 50° d. 0.385
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we know that
in the right triangle ABC
sin A=opposite side angle A/hypotenuse
in this problem
opposite side angle A=BC-----> 10
hypotenuse=AB-----> 26
so
sin A=10/36------> sin A=0.3846------> sin A=0.385
the answer is
the option d. 0.385
Jane is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
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Simplify i^41. (2 points) i −1 −i 1
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Answer:
[tex]\large\boxed{i^{41}=i}[/tex]
Step-by-step explanation:
[tex]i=\sqrt{-1}\\\\i^2=-1\\\\(-1)^2=1\\\\\text{Use}\ a^n\cdot a^m=a^{n+m}\ \text{and}\ (a^n)^m=a^{nm}:\\\\i^{41}=i^{40+1}=i^{40}\cdot i=i^{2\cdot20}\cdot i=(i^2)^{20}\cdot i=(-1)^{20}\cdot i=1\cdot i=i[/tex]
Answer:
i
I got this right on the test!!
PLEASE HELP!!!Which pair of angles are corresponding? Two horizontal lines cut by a diagonal transversal. Angles 1, 3, 5, and 7 are located on the left-hand side of the transversal starting from the top. Angles 2, 4, 6 and 8 are located on the right-hand side of the transversal starting at the top. Question 2 options: 1 and 3 1 and 4 4 and 8 1 and 8
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______________________________________________________
Answer:
According to the description of the case, the angles should be named after this picture.
The congruents angles among each other are:
Blue: 1,4,5,8
Purple: 2,3,6,7
Therefore the three possibilities are:
a. 1 and 4
b. 4 and 8
c. 1 and 8
Step-by-step explanation:
the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of the line after dilation
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1. You have the the line y=2x-4 is dilated by a scale factor of 3/2 and centered at the origin.
2. The form of the a line is y=mx+b, where m is the slope and b is the y-intercept. As dilation conserves the parallelism, the dilated linw will have the same slolpe: 2
m=2
3. By using the y-intercept, you have:
(0,-4)
0x3/2=0
-4(3/2)=-6
(0,-6)
4. Therefore, the equation that represent that image of the line after dilation is:
m=2
b=-6
y=2x-6
The equation that represent that image of the line after dilation is
[tex]y = 2x-6[/tex]
Given :
The line [tex]y=2x-4[/tex] is dilated by a scale factor of [tex]3\div2[/tex] and centered at the origin.
Solution :
The given line has slope 2 and y intercept -4.
As dilation conserves the parallelism, the dilated line will have the same slope = 2 and the y intercept of the dilated line is
[tex]= -4\times \dfrac{3}{2}=-6[/tex]
Therefore the equation that represent that image of the line after dilation is
[tex]y = 2x-6[/tex]
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The length of a rectangle is 10 feet longer than it is wide. if each side is increased 10 feet, then the area is multiplied by 4. what was the size of the original rectangle?
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width=x ft
length=(x+10) ft
Area:
x(x+10) ft²
Given that the sides are increased by 10, then the new dimensions will be:
width=(x+10) ft
length=(x+20) ft
thus the area will be:
(x+10)(x+20)=4×(x^2+10x)
solving for x we get:
x=-10 or x=20/3
thus the original width=20/3 and length=(10+20/3)=50/3 ft
Final answer:
The original rectangle had a width of 20 feet and a length of 30 feet (20 feet + 10 feet). After solving a quadratic equation, we determined the original dimensions by setting up an equation that represented the area before and after the increase.
Explanation:
The original rectangle has a length that is 10 feet longer than its width. Let the width be represented by w feet. Therefore, the length would be w + 10 feet. After increasing each side by 10 feet, the new width is w + 10 and the new length is w + 20. The area of the new rectangle is 4 times larger than the original rectangle's area.
The area of the original rectangle is given by w(w + 10). The area of the larger rectangle is given by (w + 10)(w + 20). By multiplying the larger area, we get 4 times the original area, so (w + 10)(w + 20) = 4w(w + 10). We can simplify this equation to solve for w.
Step-by-step solution:
Set up the equation: (w + 10)(w + 20) = 4w(w + 10).Expand and simplify to: w² + 30w + 200 = 4w² + 40w.Rearrange to: 3w² + 10w - 200 = 0.Factor the quadratic equation: (3w - 20)(w + 10) = 0.Solve for w: w = 20 or w = -10 (we discard the negative solution).Thus, the original width is 20 feet and the original length is 30 feet (20 + 10).
please help compare these integers by typing the symbol that would make the statement true
12 ________ - 18
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Positive integers are always greater.
There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 3?
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Answer:
1/15
Step-by-step explanation:
The probability of spinning a number on a spinner with 15 equal areas that is a multiple of 5 or a multiple of 3 is 7/15, as there are 7 favorable outcomes (3, 5, 6, 9, 10, 12, 15) out of 15 possible results.
Explanation:The question asks for the probability of spinning a number that is either a multiple of 5 or a multiple of 3 on a spinner with 15 equal areas numbered 1 through 15. To solve this, we need to identify the multiples of each within the range of numbers on the spinner and then use the principles of probability to find the chances of landing on one of those multiples when the spinner is spun once.
The multiples of 5 between 1 and 15 are 5, 10, and 15. The multiples of 3 are 3, 6, 9, 12, and 15. Note that 15 is a multiple of both 5 and 3, so it should only be counted once. To avoid overcounting, we will list each multiple only once, which gives us the numbers 3, 5, 6, 9, 10, 12, and 15. The probability of landing on any specific number on the spinner is 1 out of 15 because there are 15 equally likely outcomes.
Since we have 7 such favorable outcomes, the probability is calculated as the number of favorable outcomes over the total number of possible outcomes, which is 7/15. So, the probability of spinning a number that is a multiple of 5 or a multiple of 3 on one spin is 7/15.
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What is the standard deviation of the data set? 29, 36, 41, 53, 45, 30, 60
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mean=( 29 + 36 + 41 + 53 + 45 + 30 + 60)/5=294/7=42
next:
sum of (x-mean)^2=[(29-42)^2+(36-42)^2+(41-42)^2+(53-42)^2+(45-42)^2+(30-42)^2+(60-42)^2]
=804
thus the variance will be:
var=(804)/(7-1)=134
thus the standard deviation will be:
σ=√134=11.576
one serving of crackers is 3/10 of the whole box of crackers. bella ate 3 servings last week. what fractonof the box did she eat?
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can someone please explain how to do this.
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x^2 - 4x+4 = 2x-4
solve for X
subtract 2x from each side:
x^2 -6x + 4 = -4
subtract 4 from each side:
x^2 -6x = -8
add 8 to both sides:
x^2 -6x +8 = 0
factor the polynomial:
x = 4 and x = 2
using the line equation replace x with 2 and 4 and solve for y
y = 2(2) - 4 = 0
y = 2(4)-4 = 4
so the 2 points the line crosses the curve is (2,0) and (4,4)
using those 2 points you can calculate the length:
distance = sqrt((x2-x1)^2 +(y2-y1)^2
distance = sqrt( (4-2)^2 + (4-0)^2)
distance = sqrt (2^2 + 4^2)
distance = sqrt (4+16)
= sqrt 20
= 2 sqrt(5) EXACT LENGTH
An average infant is 20 inches long and weighs 7.6 pounds. if the child grows to 80 inches and keeps the same proportions,how much will the child weigh
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The density of water is 1000 kilograms per cubic meter and the density of ice is about 916 kilograms per cubic meter of 700 kilograms of water and 450 kilograms of ice is combined in a container what is the volume of the water
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The volume of water can be calculated by dividing the mass of water by the density of water.
Explanation:The question asks for the volume of water when 700 kilograms of water and 450 kilograms of ice are combined in a container. To find the volume of water, we need to subtract the volume of ice from the total volume. The density of water is 1000 kg/m³, so the volume of water can be calculated by dividing the mass of water (700 kg) by the density of water (1000 kg/m³).
Volume of water = Mass of water / Density of water
Volume of water = 700 kg / 1000 kg/m³
Volume of water = 0.7 m³
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The volume of a solid gold statue can be approximated as 1000 cm3. If the density of gold is about 20/cm3, what is the mass of the statue?
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Rewrite for mass
M=d x v
M= 1000 x 20
Mass is 20,000 grams
statement must be true??
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Given that AB is the bisector of DC. The third options of all the options are True.
B is the midpoint of DC.
In geometry, to bisect an entity means to disassociate it into two equal parts. A bisector is a line, ray, or segment that divides an entity into two equal parts. For illustration, a line that bisects an angle divides the angle into two angles with equal measures. A segment that bisects a line segment divides the line segment into two segments with equal lengths. A ray that bisects an angle extends from the vertex of the angle and divides the angle into two angles with equal measures.
As it is given that AB is the bisector of DC,
therefore, B, being the foot of AB on CD is the midpoint of DC.
Since DC is bisected by AB,
therefore, [tex]\angle[/tex] ABD = [tex]\angle[/tex] ABC.
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A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?
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red 2 x
white 7 = 16 fl oz
16 x 2 = 7x
32 = 7x
7 7
x = 4 4/7 (approximately 4.6 fl oz)
You will need approximately 4.6 fl oz (or exactly 4 4/7 fl oz) of red paint.
Answer:
4.6
Step-by-step explanation:
99 POINTS
suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2176 pounds. when carrying 46 gallons of fuel, it weighs 2399 pounds. how much does the airplane weigh if it is carrying 54 gallons of fuel?
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46 - 12 = 34 gallons
2399 - 2176 = 223 pounds
so 34 gallons of gas weighs 223 pounds
find weight per pound: 223 pounds / 34 gallons = 6.5588 pounds per gallon
round to 6.6 pounds per gallon
54 gallons - 46 gallons = 8 gallons
8 gallons x 6.6 pounds per gallon = 52.8 pounds, round to 53 pounds
2399 + 53 = 2452 weight of plane with 54 gallons
The area of a sector of a circle is given by the formula below. What is the solution for S?
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where
[tex]A[/tex] is the area of the sector
[tex]s[/tex] is the central angle
To solve for [tex]s[/tex], we are going to divide both sides of the equation by [tex] \pi r^2[/tex], and then we are going to multiply both sides of the equation by 360°:
[tex]A= \pi r^2( \frac{s}{360} )[/tex]
[tex] \frac{A}{\pi r^2} = \frac{ \pi r^2( \frac{s}{360} )}{\pi r^2} [/tex]
[tex] \frac{s}{360}= \frac{A}{\pi r^2} [/tex]
[tex]\frac{s}{360}(360)= \frac{A}{\pi r^2} (360)[/tex]
[tex]s= \frac{360A}{\pi r^2} [/tex]
We can conclude that the solution for s is: [tex]s= \frac{360A}{\pi r^2} [/tex]
At the start of the year northern lights had $8000 worth of merchandise. What do we know about northern lights?
A. The company ended with a net income last year
B. It’s a retail business
C. The company ended with a net loss last year
D. It’s a service business
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Answer:
B. It's a retail Business
Step-by-step explanation:
Just by knowing that they have money worth in merchandise, you can say that they sell as a retail business, the first option A. is not posible because they dont have an income they just have inventory worth money. the C. is not possible because having $ 8000 positive value does not constitute loss and D. it's a service business, could be but the merchandise does not suffice all information.
A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability of a lock without all even digits? There to get a lock code with all even digits. There are 3,024 different 4-digit lock codes. There are to get a lock code without all even digits. The probability of a 4-digit lock code without all even digits is
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Answer:
it's 24, 3000, and 3000/3024
Step-by-step explanation:
The probability for a 4-digit lock code using numbers 1-9 with no repeats and not all even is 2,904/3,024.
Explanation:To solve this, we need to find the total number of possible 4-digit lock codes using digits 1-9 with no repeats and not all even, then divide it by the total number of 4-digit lock codes using digits 1-9 with no repeats. Specifically, the lock code includes 5 different even numbers (2,4,6,8), and 4 different odd numbers (1,3,5,7,9). If the lock code is all even, we will have 5*4*3*2 = 120 possibilities. However, the total possibilities for 4-digit lock codes are 9*8*7*6 = 3,024. Thus the number of codes that are not all even digits is 3,024 - 120 = 2,904. Therefore, the probability for a 4-digit lock code not having all even digits is 2,904/3,024.
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An ice chest contains 88 cans of apple juice, 44 cans of grape juice, 55 cans of orange juice, and 66 cans of mango juice. suppose that you reach into the container and randomly select three cans in succession. find the probability of selecting three cans of appleapple juice.
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A woman can bicycle 27 miles in the same time it takes her to walk 9 miles. she can ride 10 mph faster than she can walk. how fast can she walk
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Recall that distance = (rate)(time)
Walking speed = s
driving speed = s + 10 (mph)
27 mi 9 mi
Then t = ----------------- = ------------
(s+10) mph s mp
This equation has only one variable, s. We can solve it for s as follows:
( 27 mi) * (s ) = (9 mi)(s)+ 90 (mi)(mph)
27s = 9s + 90, or 18 s = 90, or s = 90/18 = 10/2 = 5. Her walking speed is 5 mph. Her riding speed is 5+10 mph, or 15 mph.
Both 5 mph and 15 mph sound reasonable, don't they? 5 mph on foot and 15 on the bike.
Zack borrowed $1,087 for 12 months at 11 percent interest. If he must pay 11.00 per $100, what is zacks monthly payment
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[tex] \frac{1087}{100} =10.87[/tex]
Know we know that Zack will have to pay 11.00 dollars 10.87 times each month, so we just need to multiply both quantities to find his monthly payment:
[tex]11.00*10.87=119.57[/tex] dollars
We can conclude that Zack's monthly payment will be $119.57
Would someone Please answer this question please will be thanked and also will pick brainly!! (please be honest)
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I think the Area is 465.52 because the area of a rectangle is A = WL
Describe the locus that the figure represents.
Question 13 options:
all points equidistant from line l
all points equidistant from point A and point B
none of these
all points 1 cm from line l
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Explanation:
If you draw lines from Point A to the line and and from Point B to the line (perpendicular to the line), you would see that the distances from both these points to the line would be the same. Likewise if apply the symmetry argument on both of the points, you would find out that all points on the line would be equidistant from point A and point B. Hence Option (B) is correct.
What is the value of x?
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The angle adjacent to the 100 degree outside the triangle is 80 degrees. We know this because it is a supplementary angle, or an angle that, when added along with another angle’s measurement, makes 180 degrees. The line is straight, so the other angle must be 80 degrees to add up with the 100 to make 180 degrees.
Now that we know the other unknown angle, we can use the fact that the sum of angles within a triangle make 180 degrees. The two angles inside the triangle that we know make 150 degrees (80 plus 50), so the final angle ‘x’ must be 30 degrees (180-150=30).
A town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number?
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The population of a town with an intial population of 5000, that grows at 2% every year would be 5520 after 5 years
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the population of the town after x years.
The population of 5000 grows at 2% every year. Hence:
100%+2% = 1.02, this gives:
y = 5000(1.02)ˣ
After 5 years:
y = 5000(1.02)⁵ = 5520
The population of a town with an intial population of 5000, that grows at 2% every year would be 5520 after 5 years
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Which of the following shows the true solution to the logarithmic equation 3log2(2x)=3
A.x=-1
B.x=1
C. x=-1 and x=1
D. x0 x=-1 and x=1
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Answer:
Option B is correct.
Step-by-step explanation:
Given logarithmic equation,
[tex]3log_2(2x)=3[/tex]
[tex]log_2(2x)=\frac{3}{3}[/tex]
[tex]log_2(2x)=1[/tex]
since base of the log function is 2.
we take power of 2 on both sides.
[tex]2^{log_2(2x)}=2^1[/tex]
2x = 2
x = 1
Therefore, Option B is correct.
The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.
Answers
Let one digit be x
Let the other digit = y
x + y = 16
Let the original number = 10x + y
Let the reverse number = 10y + x
10x + y - 18 = 10y + x
Comment
Bring the letters to the left and the number 18 to the right.
10x - x + y - 10y = 18 Combine like terms.
9x - 9y = 18 Divide both sides by 9
x - y = 2
Set up a set of equations and add.
x + y = 16
x - y = 2 Now add
2x = 18 Divide by 2
x = 18/2
x = 9
x + y = 16
9 + y = 16 Subtract 9 from both sides.
y = 16 - 9
y = 7
Check
Original number = 97
Reversed number 79
Difference 18 and it checks.