Answer:
x² - 6x + 4
Step-by-step explanation:
Hello!
Factor each term completely:
3x³ = (3)(x)(x)(x)-18x² = (-1)(2)(3)(3)(x)(x)12x = (2)(2)(3)(x)Common factors that are shown in all 3 terms are x and 3.
Divide each term by 3x:
(3)(x)(x)(x) ÷ 3x = (x)(x) = x²(-1)(2)(3)(3)(x)(x) ÷ 3x = (-1)(2)(3)(x) = -6x(2)(2)(3)(x) ÷ 3x = (2)(2) = 4Combine the terms: x² - 6x + 4
Given the geometric series 6+3+3/2….Find
(i) the sum of n terms.
(ii) S infinity. Hence, determine smallest value of n such that S infinity - Sn < 0.001.
12-12[1-(1)]<0.001
The least value is 11.
[tex]$$\begin{aligned}&\mathrm{S}=\frac{1}{1-(1 / 2)}=2 \\&\mathrm{~S}_{\mathrm{n}}=\frac{1-(1 / 2)^{\mathrm{n}}}{1-(1 / 2)}=2-\frac{1}{2^{\mathrm{n}-1}}\end{aligned}$$[/tex]
[tex]$$\mathrm{S}-\mathrm{S}_{\mathrm{n}}=\frac{1}{2^{\mathrm{n}-1}} < \frac{1}{1000} \text { or } 2^{\mathrm{n}-1} \geq 1000$$[/tex]
Now [tex]$2^{10}=32 \times 32=1024$[/tex]
[tex]$$\therefore n-1 \geq 10 \text { or } n \geq 11$$[/tex]
Hence the least value is 11.
If you have a positive term in your quadratic equation, it will also have a minimum value. This minimum value can be found by graphing the function or solving one of the two equations. If you have the equation y = a[tex]x^2[/tex] + bx + c, you may use the equation min = c - [tex]b^2[/tex]/4a to determine the minimum value.
A quadratic equation is a second-order polynomial equation in a single variable x a[tex]x^2[/tex]+bx+c=0. with a ≠ 0 . The fundamental theorem of algebra assures that it has at least one solution because it is a second-order polynomial equation.
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A salesperson's weekly paycheck is 25% more than a second salesperson's paycheck. The two paychecks total $1075. Find the amount of each paycheck. (Round your answers to the nearest cent.)
Evaluate.
Remember Order of Operations!
(PEMDAS)
(-7+3²) × 8
Answer:
16
Step-by-step explanation:
[tex]-7+3^2\\3^2\\=9\\=-7+9\\=-7+9 = 2\\=2\times \:8\\2\times \:8=16\\\boxed{16}[/tex]
Find all possible values for A, B, and C
AB + AB + AB + AB=CA
AAnswer:
Las Letras A B C , en matematicas el valor puede variar ; ya que ya depende del valor que se le otorge o ya si es una operacion , pues el valor que se obtiene , es decir las letras en matematicas no tiene o poseen un valor fijo
Step-by-step explanation:
Josue is the youngest of three siblings whose ages are consecutive even integers. If
the sum of their ages is 78, find Josue's age.
Answer:
39 is the sum of their ages
Step-by-step explanation:
Hope this helps :)
4 D
A bear can run 400 feet in 8 seconds.
A horse can run 290 feet in 5 seconds?
Which animal runs at the faster rate?
Horse runs at the faster rate i.e. at the rate of 58 feet per seconds.
According to the given question.
A bear can run 400 feet in 8 seconds.
A horse can run 290 feet in 5 seconds.
As we know that, the measurement of the speed at which something happens is called rate.
Therefore, form distance rate formula (rate = distance/time)
The rate of the bear = 400/8 = 50 feet/sec
And the rate of the horse = 290/5 = 58 feet/sec
Therefore, horse can run faster than bear.
Hence, horse runs at the faster rate i.e. at the rate of 58 feet per seconds.
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How did the new deal hope to stimulate industrial recovery
What is the factored form of 82+12?
O 442+80)
O4(2x+3)
O ax(x+4)
O 8x(+4)
Answer:
Option 2
Step-by-step explanation:
The sum of an integer and 7 times the next consecutive odd integer is 6. Find the value of the greater integer.
The value of the integer number is -1
How to find the value of the greater integer?The statement is given as:
The sum of an integer and 7 times the next consecutive odd integer is 6
Let the integer value be x
So, the next consecutive odd integer is x + 2
When represented as an equation, we have
x + 7(x + 2) = 6
Open the bracket
x + 7x + 14 = 6
Evaluate the like terms
8x = -8
Divide both sides by 8
x = -1
Hence, the value of the integer number is -1
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Rory has 6 pounds of ground beef to make meatballs. He uses 5/8 pound per meatball to make 9 meatballs. How many 1/8 pound meatballs can Rory make with the remaining beef?
Rory can make 43 metaballs from the remaining beef.
What are maths operations?An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations. A zero-arity operation, also known as a nullary operation, is a constant. The mixed product is an example of an arity 3 operation, also known as a ternary operation.Rory has 6 pounds of ground beef on hand for making meatballs.
He makes 9 meatballs with 5/8 pounds of meat per meatball.
We must subtract 5/8 from 6.
6 - 5/848-5/843/8There are 43/8 pounds of ground beef remaining.
As a result, the number of 1/8 pound meatballs produced from 21/8 pound ground beef can be calculated as follows:
43/8 ÷ 1/843/8 × 8/1= 43Therefore, Rory can make 43 metaballs from the remaining beef.
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What is the approximate length of the diameter, d?
7in
14in
22in
44in
Answer:
14 in
Step-by-step explanation:
the formula for the circumference of a circle is
2×pi×r
or (because the diameter is 2×r)
pi×d
with r being the radius and d being the diameter.
44 = pi×d
d = 44/pi = 14.00563499... in ≈ 14 in
what set M is the set of months hauling 31 days?
The set of months having 31 days will be S = { January, March, May, July, August, October, December }.
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
We know that there are 12 months in a year.
From these months, we get that the months that have 31 days are:
January
March
May
July
August
October
December
The set of months having 31 days will be:
S = { January, March, May, July, August, October, December }
Therefore, we get that, the set of months having 31 days will be S = { January, March, May, July, August, October, December }.
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If you pick a number between one and three and the computer picks a number between one and four, how many different outcomes are
possible if the two numbers are added together? (Hint: You may find it useful to complete a table for this problem)
2
4
7
6
None of these
The possible outcomes for the sum are the numbers in the set:
{2, 3, 4, 5, 6, 7}
So there are 6 possible outcomes.
How many outcomes are possible?
You can select a number between 1 and 3, so the options are {1, 2, 3}
The computer selects a number between 1 and 4, so the options are {1, 2, 3, 4}
The possible aditions, in the form of "your number + computer number" are:
1 + 1 = 2
2 + 1 = 3
3 + 1 = 4
1 + 2 = 3
2 + 2 = 4
3 + 2 = 5
1 + 3 = 4
2 + 3 = 5
3 + 3 = 6
1 + 4 = 5
2 + 4 = 6
3 + 4 = 7
So the possible outcomes for the sum are the numbers in the set:
{2, 3, 4, 5, 6, 7}
So there are 6 possible outcomes.
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please help! ill give branliest
Answer: That is a cold front
Step-by-step explanation:
It is a cold front because the warm air is rising because it is less dense than the cold air which is why the cold air isn’t rising because the cold air is denser than that of the warm air so it just continues moving forward
Solve this question please for me
f (x) - 2/3x - 7 find the inverse
Electricity rates. The table to the right shows the electricity
rates charged by Better Than Lightning Utilities in the winter
months.
a. Write a piecewise definition of the monthly charge W(x) for a
customer who uses x kWh in a winter month.
b. Determine the graph of W(x)
Winter (November-June)
Base charge, $8.50
First 300 kWh or less at 0.0650/kWh
Over 300 kWh at 0.0850/kWh
The piecewise function for the monthly charge W(x) for a customer who uses x hours of electricity is given by:
W(x) = 50 + 0.0650x, 0 ≤ x ≤ 300.W(x) = 69.5 + 0.0850x, x > 300.The graph of the function is given at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, we have that:
The input is the number of kWh electricity used.The output is the monthly charge.The monthly charge is calculated differently according to the number of kWh of electricity used, divided into two cases as follows:
First 300 kWh : 0 ≤ x ≤ 300.More than 300 kWH: x > 300.For up to 300 hours, the base charge of $50 plus the hourly fee of $0.0650 is charged, hence:
W(x) = 50 + 0.0650x, 0 ≤ x ≤ 300.
For more than 300 hours, the customer is charge 50 + 300 x 0.0650 = $69.5, plus the hourly fee of $0.0850, hence:
W(x) = 69.5 + 0.0850x, x > 300.
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Giselle paid an accountant 25$ per hour to do her taxes plus a 100$ one-time fee. Her total bill was $250. How many hours did the accountant work?
geometry someone help
Answer:
D. F
Step-by-step explanation:
Both F and G are not on plane P
The temperatures at sunrise and sunset are shown in the table. What was the temperature change on each day? On which day did the temperature change the most?
The temperature changes for each day are 32.12 °C (Day 1) and 33.02 °C (Day 2), respectively. The day 2 registered the highest temperature change.
How to analyze and interpret temperature changes
Herein we find a table with the temperatures at sunrise and sunset in two days and we need to determine the temperature change for each period and conclude in what day the change was the highest. The temperature change can be found by using the following formula:
ΔT = T' - T
Where:
T - Temperature at sunrise, in degrees Celsius.T' - Temperature at sunset, in degrees Celsius.The temperature changes for each day are 32.12 °C (Day 1) and 33.02 °C (Day 2), respectively. The day 2 registered the highest temperature change.
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4. What is the probability of pulling either a fork or a spoon out of the bag?
We the Probability of pulling either fork or spoon as 1.
We are given that:
We have a fork and a spoon in a bag.
Total number of items in a bag = 1 + 1 = 2
Now, we need to tell the probability of either pulling a fork or a spoon.
Now,
Probability of pulling a fork = 1 / 2 = 0.5
Probability of pulling a spoon = 1 / 2 = 0.5
So, the Probability of pulling either of them will be = 1 / 2 + 1 / 2 = 1
Therefore, we the Probability of pulling either fork or spoon as 1.
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What is the domain of g
Answer:
A
Step-by-step explanation:
The domain of g(x) is the set of all real numbers. Meaning that all the numbers between the min and max of g would be -7 ≤ x ≤ 7.
Denise is going on vacation and taking her dog Pickles along. Pickles eats 4 cups of Hungry Hound dog food each day. Denise wants to know how many days she can feed Pickles from a 24-cup bag of Hungry Hound.
Which equation can Denise use to find the number of days d she can feed Pickles from the bag.
Answer:
D
Step-by-step explanation:
Se can feed pickle freom the bag
AAAAAAAAAAnswer: 24/4 = 6
TRAIN STATIONS A train travels a straight route from Rolesville to Townsend. The railway would like to build a station along the route so that the ratio of the distance from Rolesville to the station and the distance from the station to Townsend is 3:4 . If the coordinates of Rolesville and Townsend on the map are R(1, 2) and T(8, 23) , respectively, what should be the coordinates of the new station?
coordinates of the new station= (5,98/4)
When two lines intersect at a point then the angle between them can be expressed in terms of their slopes and is given by the following formula:
tan θ = |
|where
are the slopes of the line AB and CD respectively.
If
is positive then the angle between the lines is acute. If
is negative then the angle between the lines is obtuse.
Slope of Vertical Lines
Vertical lines have no slope, as they do not have any steepness. Or it can be said, we cannot define the steepness of vertical lines.
A vertical line will have no values for x-coordinates. So, as per the formula of slope of the line,
Slope, m = (y2 – y1)/(x2 – x1)
But for vertical lines, x2 = x1 = 0
Therefore,
m = (y2 – y1)/0 = undefined
In the same way, the slope of horizontal line is equal to 0, since the y-coordinates are zero.
m = 0/(x2 – x1) = 0 [for horizontal line]
Positive and Negative Slope
If the value of slope of a line is positive, it shows that line goes up as we move along or the rise over run is positive.
If the value of slope is negative, then the line goes done in the graph as we move along the x-axis.
Let R,Q,T be the points that divide the line into 3:4 equal parts
Let the Q = (x,y)
R(1, 2) and T(8, 23) ,
x = m1x1+m2x2/m1+m2
y = m1y1+m2y2/m1+m2
X= 3.1+4.8/7
x= 3+32/7
x=35/7
x=5
y=2.3+23.4/3+4
y= 6+92/4
y=98/4
y= 24.5
(x,y) = (5,98/4)
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(100 POINTS ASAP)
Triangle EFG is shown in the graph.
The triangle will be reflected across the x-axis and then dilated by a scale factor of 2 with respect to the origin, resulting in triangle E'F'G'.
What will be the coordinates of G'?
Answer:
The coordinates of G' will be (8, 4)Step-by-step explanation:
Point G has coordinates (4, -2).
After reflection across the x-axis it s coordinates will change as per rule:
(x, y) → (x, - y)Applied to point G:
(4, - 2) → (4, 2)After dilation by a scale factor of 2 the coordinates will change as per rule:
(x, y) → (2x, 2y)Applied to point G:
(4, 2) → (2*4 = 8, 2*2 = 4)G' = (8, 4)Find the domain and range of the function F(t) = sec(3.14t/4)
The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
The Domain of a function f(x) is the set of all values for which the function is defined.
The Range of a function is the set of all values that f takes.
As, [tex]sec x=\frac{1}{cos x}[/tex] , so sec x is defined where [tex]cos x \neq 0[/tex].
It implies, sec(3.14t/4) is defined where [tex]cos(3.14t/4)\neq 0[/tex].
The cosine is 0 at [tex](2n+1)\frac{\pi }{2}[/tex] , where n is any integer.
Now, [tex]\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}[/tex]
[tex]t=2(2n+1)\\t=2+4n[/tex]
Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.
Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].
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Help asap but only if you are sure!
Answer:
D.
Step-by-step explanation:
[tex]17\% = 0.17\\0.25 = 0.25\\2/9 = 0.22\\\\0.17 \rightarrow 0.22 \rightarrow 0.25[/tex]
Answer:
D
Step-by-step explanation:
17%, 2/9= 22%, 0.25= 25%
Let f(x) = -3x+5 and g(x)=x²-2. Find the difference (g - f)(x).
(g-f)(x) =
Answer: f(x^2) = x^2 - 5
can anyone help me with this I am stuck
Using integrals, the desired probabilities and measures are given as follows:
a) P(X < 6) = 0.84375 = 84.375%.
b) P(X < 13) = 1 = 100%.
c) P(6 < X < 8) = 0.15625 = 15.625%.
d) P(X > 5) = 0.31641 = 31.641%.
e) x = 6.434.
What is the probability distribution?The distribution is given as follows, simplifying the operations:
f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.
Hence the density function is:
[tex]\int_{a}^{b} f(x) dx[/tex]
[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]
[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]
Applying the Fundamental Theorem of Calculus:
P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³
Hence, for item a:
P(X < 6) = 0.046875(6)² - 0.00390625(6)³.
P(X < 6) = 0.84375 = 84.375%.
For item b, the entire distribution is below 13, hence:
P(X < 13) = 1 = 100%.
For item c:
P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.
P(6 < X < 8) = 0.15625 = 15.625%.
For item d:
P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.
P(X > 5) = 0.31641 = 31.641%.
For item e:
We have to find b when a = 0 and P(X < b) = 0.9, hence:
0.046875b² - 0.00390625b³ = 0.9.
Using a calculator, the solution in the range of the distribution is given by:
b = x = 6.434.
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Shawn reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages?
Answer:
44
Step-by-step explanation:
20 ÷ 5 = 4 minutes per page
4 x 11 pages = 44
help me with this Select all the expressions that are equivalent to 78 • 7.
73 • 73
71879
(73)3
74 + 75
74 • 75
The expressions that are equal to 7⁸ x 7 are:
B. For (7¹⁸)/7⁹
C. For (7³)³
E. For 7⁴ x 7⁵
What are the fundamentals of exponential functions?Exponential functions now have formula f(x) = bx, where b > 0 and b 1. As in any exponential expression, b serves termed the base and x is called its exponent. The proliferation of bacteria is an example of such an exponential function.
According to the given data:A. For 7³ x 7³
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7³ ⁺ ³
Calculate the sum or difference: 7⁶
Calculate power : 117649
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: False
Solution: False
B. For (7¹⁸)/7⁹
Reduce the fraction: 7⁹
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
C. For (7³)³
simplify using exponent power rule : 7⁹
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
D. For 7⁴ + 7⁵:
Calculate the power: 2401 + 16807
Calculate the sum or difference: 19208
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: False
Solution: False
E. For 7⁴ x 7⁵:
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁴ ⁺ ⁵
Calculate the sum or difference: 7⁶
Calculate power : 40353607
simplify using exponent rule with the same base: aⁿ x aˣ
= aⁿ ⁺ ˣ
= 7⁸ ⁺ ¹
Calculate the sum or difference: 7⁹
Calculate power : 40353607
Check equivalency: True
Solution: True
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I understand that the question you are looking for is:
Select all the expressions that are equivalent to 7⁸ x 7.
A. For 7³ x 7³
B. For (7¹⁸)/7⁹
C. For (7³)³
D. For 7⁴ + 7⁵:
E. For 7⁴ x 7⁵
Answer:
none
Step-by-step explanation:
point steeler