Answer:
g(x) = x² - 7x + 16Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
f(x) = x² - 4x + 4 shifted 3 units to the right. Therefore g(x) = f(x - 3):
g(x) = (x - 3)² - (x - 3) + 4 use (a - b)² = a² - 2ab + b²
g(x) = x² - 2(x)(3) + 3² - x - (-3) + 4
g(x) = x² - 6x + 9 - x + 3 + 4 combine like terms
g(x) = x² + (-6x - x) + (9 + 3 + 4)
g(x) = x² - 7x + 16
A park began with a population of 8 rabbits. Every year, the rabbit population triples. How long will it take for the population to reach 1,944 rabbits?
Answer:
It will take 5 years for the population to reach 1,944. Option D is correct.
Step-by-step explanation:
Initial population = I = 8
Final population = F = 1944
number of years = x
As given, the population is tripled every year that can be calculated using:
F = I*3^x
By putting values in this equation, we get
1944 = 8*3^x
1944/8 = 3^x
243 = 3^x
3^x = 243
3^x = 3^5
x = 5 bases are same so powers can be simplified.
Therefore, it will take 5 years for the population to reach 1,944. Option D is correct.
Answer:
8 • 3^y = R
Step-by-step explanation:
...................
A group of neighbors is holding an end of summer block party. They buy p packs of hot dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party. Write an equation to describe this situation
Answer:
56 divided by 8 would equal p.
Step-by-step explanation:
If you want to find how many packs there are, it would be 56 divided by 8 would equal p.
Brainiest Please :D
Answer:
The equation is [tex]p*8=56[/tex]
Step-by-step explanation:
The neighbors buy a number of packs (p) of hot dogs and each one has 8 hot dogs. To calculate the number of hot dogs resulting we have to multiply the packs (p) by the number of hot dogs in each pack (8), this is:
[tex]p*8=56[/tex]
Then to calculate p we have to clear it:
[tex]p=\frac{56}{8} =7[/tex]
The number of packs bought were 7.
The fishbowl has a diameter of 16 inches which measurement is closest to the volume of water in the fishbowl in cubic inches
Answer:
Volume of sphere = 4/3×22/7×radius×radius
4/3×22/7×8×8=268.19
Therefore the answer is approximately 268 cubic inches.
Hope this answer helps you.
3 out of five picks are orange . If 12 picks are orange , how many picks are there in all?
20 picks in total .
Which pair of terms can also be used to describe the shape of the sanbox, a square
where are the options??
Six students are working on math 2/3 of them are working on fractions. How many students are working on fractions
Answer:
4 students are working on fractions
Step-by-step explanation:
f your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus2.00, minus1.00, 0, 1.00, 2.00? Why? A. The z score of minus2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores. B. The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score. C. The z score of minus1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score. D. The z score of 0 is most preferable because it corresponds to a test score equal to the mean. E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
Answer:
E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
Step-by-step explanation:
A z score tells us how many standard deviations away from the mean a given value is.
The higher the z-score, the farther above the mean the value is. Since we are referring to the score on a test, we want the value to be as far above the mean as possible; this means that our best choice out of those given is 2.00, since it is 2 standard deviations above the mean.
Please Help!! A septic tank has the shape shown in the figure. How many gallons does it hold? (1 cu ft = 7.48 gallons.) (Round to the nearest gallon)
The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).
Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3
Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3
Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3
The tank holds 641 gallons since the volume of the tank is 85.66 cubic feet. The tank has a cylindrical part and two hemispheres.
What is the volume of the cylinder?The volume of the cylinder is V=Bh or V=2πrh.
Where B is the base area, h is the height of the cylinder and r is the radius.
What is the volume of the hemisphere?The formula for the volume of a hemisphere: V = (2/3)πr³
Where r is the radius of the hemisphere.
Calculating the Volume of the septic tank:The tank has a cylindrical part and two hemispheres.
So, the volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)
Finding the volume of the cylinder:
The height of the cylinder is h=5'9'' and the diameter is 3'6''.
(1 feet = 12 inches)
So, the diameter = 3 feet 6 inches = 3+(6/12) feet = 3.5 feet
Then, the radius r = 3.5/2 = 1.75 feet and
The height h=5 feet 9 inches = 5 + (9/12) feet = 5.75 feet
The volume of the cylinder = 2πrh
= 2π×1.75×5.75
= 63.22 cubic feet
Finding the volume of the hemisphere:
The diameter of the sphere is 3'6'' i.e., 3.5 feet
So, radius r = 1.75 feet
Then the volume of a hemisphere:
V = (2/3)πr³
= (2/3)π×(1.75)³
= 11.22 cubic feet
So,
The volume of the tank = (volume of the cylinder) +2 (volume of the hemisphere)
⇒ Volume of the tank = 63.22 + 2×11.22 =85.66 cubic feet.
Since it is given that for 1 cubic ft it holds 7.48 gallons then for 85.66 cubic ft it holds 85.66 × 7.48 = 640.73 gallons
Rounding to the nearest gallon. So, it holds 641 gallons.
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I need 7714 solar panels to power my new workshop . If each box contains 24 panels ,about how many boxes should I purchase.
Answer: 321.4167 or about 322 boxes
Step-by-step explanation:
Your basketball team scored 4 fewer than twice as many points, x, as the other team. a. Write an expression for the number of points your team scored. expression: b. The other team scored 24 points. How many points did your team score? Your team scored points.
Answer:
A) p = 2x - 4 for the expression. B) Your team scored 44 points.
Step-by-step explanation:
Let P represent the points your team made.
Since the question says "Your basketball team scored 4 fewer than twice as many points as the other team." this is how I came up with the expression.
p = 2x - 4 ( our points = 2 times more then the other teams points minus 4.
Using this expression and the given information that the other team made 24 points, I solved B.
44 = 2(24) - 4.
The expression for given statement can be found by system equation. We can create the system equation as per the statement.
(a) The expression for the number points your team scored is [tex]P=2x-4[/tex].
(b) Your team score 44 points.
Given:
Other team score [tex]x[/tex].
Let the [tex]P[/tex] is points scored by your team.
As per the statement, your basketball team scored 4 fewer than twice as many points, [tex]x[/tex] as the other team.
Convert the above statement in form of expression.
[tex]P=2x-4[/tex]
Thus, the expression for the number points your team scored is [tex]P=2x-4[/tex].
Substitute 24 for [tex]x[/tex] in above expression.
[tex]P=2\times 24-4\\P=44[/tex]
Thus, your team score 44 points.
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coefficient: A number that multiplies a variable.
Find a coefficient of x in –7x, and a coefficient of y in 9/4 y.
A stack of 9 different cards are shuffled and spread out face down. If 4 cards are tired face up, how many different 4-card combinations are possible?
Answer:
126.
Step-by-step explanation:
This is the number of combinations of 4 cards from 9 cards:
= 9C4
= 9! / 4! 5!.
A quick way of calculating this is
9*8*7*6
----------- = 9*2*7 = 126 combinations.
4*3*2*1
There are 126 different 4-card combinations possible when selecting 4 cards from a shuffled stack of 9 different cards.
To find out how many different 4-card combinations are possible from a stack of 9 different cards when 4 cards are turned face up, we need to use combinatorial mathematics. The formula needed here is the combination formula, which for selecting r items from a set of n items is given by C(n, r) = n! / (r!(n-r)!), where '!' denotes factorial.
Substituting the given values, we get C(9, 4) = 9! / (4!(9-4)!) = 9! / (4!5!) = (9×8×7×6) / (4×3×2×1) = 3024 / 24 = 126. So, there are 126 different combinations of 4 cards that can be turned face up from a shuffled stack of 9 different cards.
Evaluate the log without a calculator ( Show your work )
[tex]log_{81} 27[/tex]
Answer:
[tex]\log_{81}(27)=\frac{3}{4}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]\log_{81}(27)[/tex]
Let us change to base 3.
[tex]\log_{81}(27)=\frac{\log_3(27)}{\log_3(81)}[/tex]
[tex]\log_{81}(27)=\frac{\log_3(3^3)}{\log_3(3^4)}[/tex]
[tex]\log_{81}(27)=\frac{3\log_3(3)}{4\log_3(3)}[/tex]
[tex]\log_{81}(27)=\frac{3(1)}{4(1)}[/tex]
[tex]\log_{81}(27)=\frac{3}{4}[/tex]
Answer:
3/4 ( or 0.75).
Step-by-step explanation:
let y = log81 27, then:
27 = 81^y ( by the definition of a logarithm).
27 = 3^3 and 81 = 3^4
So 27 = 81 ^3/4
so y = log81 27 = = 3/4.
What is the distance between the points (3, 7) and (15, 16) on a coordinate plane?
The answer is 15 units
- Ap3x
I need help! C is highlighted but I don’t know if it’s correct. I give out brainliest
Answer:
Congrats! you are correct, the answer is C.) This is because if you look at the line, it intercects with the points you recieved.
C is correct because the y intercept is 1 and the slope is going down 4 for every next x value
A lion can run 50 miles per hour. This is 20 miles per hour faster than a house cat. Find the speed of the hous cat
The lion runs 50 miles per hour which is 20 more than a house cat. 20 mph + house cat mph = 50 → house cat mph = 30mph
You just have to calculate the difference.
50-20=c
c=30
PLEASE HELP! Points A and B split the circle into two arcs. Measure of minor arc is 150°. Point M splits major arc with the ratio 2:5 (point M is closer to point B). Find m∠BAM.
Answer:
30 degrees
Step-by-step explanation:
Answer: Measure of ∠BAM is 30°.
Step-by-step explanation:
As given in the question, points A and B split the circle with center O into two arcs in the attached figure below. Major of the minor arc is 150°. And, the point M splits the major arc in the ratio 2 : 5.
We are to find the measure of ∠BAM.
Since the measure of minor arc AB is 150°, so the measure of major arc AB will be
360° - 150° = 210°.
Also, point M divides the major arc AB in the ratio 2 : 5, so we have
[tex]arc~BM:arc~MA=2:5.[/tex]
Therefore, the measure of ∠BOM is given by
[tex]m\angle BOM=\dfrac{2}{2+5}\times210^\circ=\dfrac{2}{7}\times 210^\circ=60^\circ.[/tex]
We know that
the measure of the angle subtended at the center by an arc is equal to twice the measure of the angle subtended at the circumference by the same arc.
That is, on arc BC, we get
[tex]m\angle BOM=2\times m\angleBAM\\\\\Rightarrow m\angle BAM=\dfrac{m\angle BOM}{2}\\\\\\\Rightarrow m\angle BAM=\dfrac{60^\circ}{2}\\\\\Rightarrow m\angle BAM=30^\circ.[/tex]
Thus, the measure of ∠BAM is 30°.
Fred went to catch a minimun of 2 pounds of fish.He caught 5/16 pounds.He caught another fish that was 7/8 pounds.How many pounds of fish did he catch so far? What shoud be the minimun weight of the third fish so that he can catch at least 2 pounds of fish in total?
Answer:
1 3/16
Step-by-step explanation:
5/16 + (7/8= 14/16)
14/16 + 5/16= 19/16
16/16 = 1
3 LEFT OVER
1 3/16
Answer:
He caught 1 3/16 pounds of fish.
Minimum weight = 13/16 pounds.
Step-by-step explanation:
So far he caught 5/16 + 7/8
= 5/16 + 14/16 = 19/16
= 1 3/16 pounds.
Minimum wight of the third fish = 2 - 1 3/16
= 32/16 - 19/16
= 13/16 pounds.
Mr.Martin drove away from his house without his wallet.He did a 180.Where is he heading now?
Hey there!
He turned 180° degrees so he is going back to his house (to probably get his wallet)
Hope this helps you!
God bless ❤️
xXxGolferGirlxXx
FIND X. ASSUME SG IS TANGENT TO CIRCLE O AT POINT S.
We have a right triangle 9,12,15 which is 3,4,5 scaled.
So OG=15 and OH=9 (the radius) so x = 15-9 = 6
Answer: 6
There are 100 books in the library. There are non-fiction and fiction books.Write the fraction of the books that are fiction
is there anything else that you didn't include in this problem?
What is the distance between -1 and 7 on the number line? A) -8 B) -6 C) 6 D) 8
Answer:
D
Step-by-step explanation:
-1 0 1 2 3 4 5 6 7
9 units. distance is always positive.
ans. D
Which of the following represents (Picture provided)
Answer:
B.
Step-by-step explanation:
You are given the double inequality
[tex]1<x\le 6.[/tex]
This means that x is greater than 1 and less than or equal to 6.
Thus, point 1 must be excluded (with bracket "(") and 6 must be included (with bracket "]").
Hence, the correct answer is [tex](1,6].[/tex]
Answer:
b. [tex](1,6][/tex]
Step-by-step explanation:
The given inequality is [tex]1\:<\:x\le6[/tex].
We use the parenthesis [tex]()[/tex] to represent an open interval < or >.
We use the square brackets [tex][][/tex] to represent a closed interval [tex]\le[/tex] or [tex]\ge[/tex].
[tex]1\:<\:x\le6[/tex] represents [tex](1,6][/tex].
The correct choice is B.
Prove that any minimum spanning tree t of g is also a bottleneck spanning tree of g.
Answer:
Step-by-step explanation:
can you explain a little bit more ?
(Please help i only have 20 min left, Thank you!!)
Write this polynomial in descending order: –4x5 + 4x3 + x7 – 10 + 2x4.
Answer:
[tex]{x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]
Step-by-step explanation:
To write a polynomial in descending order means writing the polynomial in decreasing powers of x.
The given polynomial expresion is
[tex] - 4 {x}^{5} + 4 {x}^{3} + {x}^{7} - 10 + 2 {x}^{4} [/tex]
We start from the term with the highest degree and end with term with the least degree.
[tex] {x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]
Therefore the given polynomial written in descending order is
[tex]{x}^{7} - 4 {x}^{5} + 2 {x}^{4} + 4 {x}^{3} - 10[/tex]
Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -3 x intercepts at x = -4 and x = 4 y intercept at 6
Answer:
[ -9(x^2 - 16)] / [4(x^2 + 5x + 6)] = 0
Step-by-step explanation:
Ok this will be a rational function with denominator (x + 2)(x + 3) - to give the vertical asymptotes.
The numerator will be a(x + 4)(x - 4) to give the x-intercepts . The a is some constant.
As the y intercept is (0,6) we have:
6 = a(0-4)(0+4) / (0+2)(0+3)
6 = -16a / 6
-16a = 36
a = - 36/16 = -9/4.
So our equation is -9(x^2 - 16)/ 4(x^2 + 5x + 6) = 0.
Which is the distance between parallel lines with the equations 3x-5y=1 and 3x-5y=-3
The distance between the parallel lines 3x - 5y = 1 and 3x - 5y = -3 is 4/√34 units.
Explanation:To find the distance between two parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3, we need to use the formula for distance between two parallel lines in a coordinate plane. This formula is:
Distance = |C2 - C1| / sqrt(A^2 + B^2)
In this case, your A coefficient is 3, the B coefficient is -5, and the constants (C1 and C2) are -1 and 3 respectively (from the given equations). Substituting these values into the formula gives:
Distance = |3 - (-1)| / sqrt(3^2 + (-5)^2)
Distance = 4 / sqrt(9 + 25)
Distance = 4 / sqrt(34)
So, the distance between parallel lines with equations 3x - 5y = 1 and 3x - 5y = -3 is 4/sqrt(34) units.
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Final answer:
The distance between the parallel lines described by the equations 3x-5y=1 and 3x-5y=-3 is calculated using a standard formula for the distance between parallel lines, resulting in a distance of 4 / √34.
Explanation:
The distance between two parallel lines can be calculated using a formula once the equations of the lines are in standard form. The equations 3x-5y=1 and 3x-5y=-3 are indeed in standard form and clearly show that the lines are parallel because they have the same coefficients for x and y. To find the distance between these parallel lines, one can use the formula involving the absolute difference of the constants in the equations and the square root of the sum of squares of the coefficients of x and y.
The formula for the distance d between two parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is given by:
d = |C2 - C1| / √(A² + B²)
Applying this to our equations, we have:
A = 3, B = -5, C1 = 1, and C2 = -3.
Thus,
d = |-3 - 1| / √(3² + (-5)²) = 4 / √(9 + 25) = 4 / √34
Distance between parallel lines, standard form, and formula are essential in solving this problem.
A set of cards includes 24 yellow cards,18 green cards,and 18 blue cards. What is the probability that a card chooses at random is not green?.
➷ Find the total number of cards:
24 + 18 + 18 = 60
Find the total number of cards that aren't green:
24 + 18 = 42
The probability would be 42/60
This could be simplified to 7/10
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
710
Step-by-step explanation:
7/10
Your friend's swimming pool is in the shape of a rectangular prism, with a length of 25 feet, a width of 8 feet, and a height of 5 feet. a. What is the volume of your friend's swimming pool? b. Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool? Round your answer to the nearest whole number. c. While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool? ( ) 3 1 ft 7.5 gal ? Round your answer to the nearest whole number.
Answer:
Part a) [tex]V=1,000\ ft^{3}[/tex]
Part b) [tex]h=5\ ft[/tex]
Part c) [tex]=718\ gal[/tex]
Step-by-step explanation:
Part a) What is the volume of your friend's swimming pool?
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(25)(8)(5)=1,000\ ft^{3}[/tex]
Part b) Your swimming pool is in the shape of a cylinder with a diameter of 16 feet and has the same volume as your friend's pool. What is the height of your pool?
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1,000\ ft^{3}[/tex]
[tex]r=16/2=8\ ft[/tex] ----> the radius is half the diameter
substitute and solve for h
[tex]1,000=\pi (8)^{2} h[/tex]
[tex]h=1,000/(64 \pi)[/tex]
[tex]h=1,000/(64*3.14)=5\ ft[/tex]
Part c) While you were on vacation, 6 inches of water evaporated from your pool. About how many gallons of water evaporated from your pool?
remember that
[tex]1\ ft=12\ in[/tex]
so
[tex]6\ in=6/12=0.5\ ft[/tex]
Find the volume of water for [tex]h=5-0.5=4.5\ ft[/tex]
[tex]V=(3.14)(8)^{2}(4.5)=904.32\ ft^{3}[/tex]
so
the volume of water evaporated is equal to
[tex]1,000\ ft^{3}-904.32\ ft^{3}=95.68\ ft^{3}[/tex]
convert to gallons
remember that
[tex]1\ ft^{3}=7.5\ gal[/tex]
so
[tex]95.68\ ft^{3}=95.68*7.5=718\ gal[/tex]
a. The volume of the rectangular prism is 1000 cubic feet. b. The height of the cylindrical pool is 4 feet. c. About 750 gallons of water evaporated from the pool.
Explanation:a. The volume of the rectangular prism can be found by multiplying the length, width, and height. So, the volume is 25 * 8 * 5 = 1000 cubic feet.
b. Since the two pools have the same volume, we can use the formula for the volume of a cylinder (V = πr²h) to find the height of the cylinder. We know the diameter is 16 feet, so the radius is half of that, which is 8 feet. Plugging it into the formula, 1000 = 3.142 * 8² * h. Solving for h, we find h = 4 feet.
c. To find the gallons of water evaporated, we need to convert the units. 6 inches is 0.5 feet. The volume evaporated is 25 * 8 * 0.5 = 100 cubic feet. Since 1 cubic foot is equal to 7.5 gallons, the amount evaporated is 100 * 7.5 = 750 gallons.
Determine all numbers at which the function is continuous
Answer
Please see attached image for full understanding of the solution
If we plot the function we can see that it has a discontinuity at x = 1.
Also,
If we evaluate at x = -9, we see that the values of the piecewise function in both cases are completely different.
Therefore, x = -9 is also a discontinuity.
The right answer is option a
(discontinuity at x = 1 and x = -9)
Answer:
C
Step-by-step explanation: EDGE 2020