The simplest form of the expression 2x(x − 6) − 7x2 − (13x − 3) obtained after applying the operations of mathematics is -5x²-25x-3.
What is the simplified form of an expression?The simplified form of an expression is the simplest way of expressing it, which is obtained by applying the required operations of mathematics.
The expression given as,
[tex]2x(x - 6) - 7x^2 - (13x - 3)[/tex]
Open the brackets to solve it further,
[tex]2x(x - 6) - 7x^2 - (13x - 3)\\2x^2-12x-7x^2-13x-3\\2x^2-7x^2-12x-13x-3\\-5x^2-25x-3[/tex]
The simplest form of the expression 2x(x − 6) − 7x2 − (13x − 3) obtained after applying the operations of mathematics is -5x²-25x-3.
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Ethan donated $15.00 of the $50.00 he received as a gift.
Which decimal represents the fraction of $50.00 Ethan
donated?
A. 0.15
B. 0.3
C. 0.35
D. 0.5
(WILL MARK BRAINLIEST*
Answer:
0.3
Step-by-step explanation:
15/50=0.3
OR
(15*2)/(50*2)
30/100=0.3
When placed near each other, blocks of metal A and B are magnetically attracted to each other, while blocks B and Care repelled by
each other.
Therefore, blocks A and C will be
A)
repelled by each other.
B)
attracted to each other.
C)
unaffected by each other.
D)
Not enough information given
Answer:
A) repelled by each other, I did this on usa testprep
Step-by-step explanation:
Answer:
b atracted to each other
Step-by-step explanation:
got it right on usatestprep
WILL GIVE BRAINIEST
in this equation 3x=n, John claims that for any value for x, the value of n will always be greater than or equal to the base of 3
A.2
3^2 = 9
(any number greater than one because 3^1 = 3, this is not greater than 3)
B. 0
3^0 = 1
(any number less than 1, so it can't be one, but can be a negative number or zero - any number to the power of zero is one)
Hope this helps!
Find the volume will give brainliest to whoever answers correctly
Answer:
Vol = 252 cubic ft
Step-by-step explanation:
Consider the bottom and top of the shape separately. Calculate the volumes and add them together.
Bottom of the shape is a prism. Volume of a prism:
V =
Base Area•Height
The base is a triangle. Use Area of a triangle formula:
A = 1/2b•h
A = 1/2(7)(6)
A = 21
Use 21 for Base Area for both parts of the volume calculation.
Vol of prism, continued:
V = 21•9
V = 189
Volume of a pyramid (top)
V = 1/3•BaseArea•Ht
=1/3(21)(9)
=63
Total Volume=
189 + 63
= 252 cubic ft
The price of a game console that regularly sells for $800 is reduced to $616. By what percentage is the price reduced?
Answer:23%
Step-by-step explanation: 800-616= 184
Discount is 184
percentage is 184/800 ×100/1 =23%
Emily and Jennifer are playing a game with dice. Each one has a die. If each one rolls one and the sum of the numbers are 7 or 11 they win. If the sum is 2, 3 or 12 they lose. If it is any other number there is no winner or loser.
Find the sample space by either creating a tree or a chart/table. (remember, each die has the numbers 1-6 on it).
Then find:
P (they win - if the sum is 7 or 11)
P (they lose - if the sum is 2, 3 or 12)
The total sample space. HINT: How many total possible combinations?
This experiment has 36 possible combinations, and we will see that:
P(they win) = 0.22P(they loose) = 0.11How to get the probabilities?
First, we need to find the total number of outcomes.
We have two dice with 6 outcomes each, so the total number of outcomes of the experiment of tossing the two dice is:
C = 6*6 = 36
Such that the sample space is all the numbers between 2 and 12 (because our variable is the sum of the two values).
Now, to get the probability of winning we need to count the number of outcomes that add to 7 or 11, these are:
(Add to 7)
dice 1 dice 2
1 6
2 5
6 1
5 2
4 3
3 4
(Add to 11)
dice 1 dice 2
5 6
6 5
So there are 8 outcomes, then the probability of winning is:
P = 8/36 =0.22
The probability of losing is when the sum adds to 2, 3, or 12.
The outcomes that add to that:
(Add to 2)
dice 1 dice 2
1 1
(Add to 3)
dice 1 dice 2
1 2
2 1
(Add to 12)
dice 1 dice 2
6 6
There are 4 outcomes that add to these values, so the probability of losing is:
P = 4/36 = 0.11
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Of the 4 people attending a lecture, 2 have hazel eyes.
What is the probability that a randomly selected person will have hazel eyes?
Write your answer as a fraction or whole number.
Answer: 50%
Step-by-step explanation:
Because 2 of four is half, that that the probability is a 50% chance.
Answer:
1/2
Step-by-step explanation:
Think of this like a pizza or pie:
If there are four slices and two represent hazel eyes, how many slices are "hazel eyes?" It would be 2 of 4, or 2/4.
Because this is a fraction and it can be simplified, it would be 1/2.
So there is a 50% chance that the randomly selected person of the four people will have hazel eyes.
Help!! Khan academy geomtry practice
Answer:
33.51 units³
Step-by-step explanation:
Volume of a sphere is given by the formula :
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
Because we have the radius we can plug it into the equation to give us :
V = (4/3)×π×(2)³
V = 4/3×8π
V ≈ 33.51
Units will be units³ since no measurement is given but it to the power of 3 since it is volume.
Consider the equation 4 plus v equals 8 minus startfraction 5 over 3 endfraction v.v 4 startfraction 5 over 3 endfraction v plus 4 equals 8 minus startfraction 1 over 3 endfraction v. v = 8. what is the resulting equation after the first step in the solution? v 4 = 8 – v startfraction 4 over 3 endfraction v plus 4 equals 8.v 4 = 8 4 v = 8 – 4 plus v equals 8 minus startfraction 5 over 3 endfraction v.v 2v 4 = 8
The resulting equation which is obtained after the first step in the solution of the provided equation is 2v +4=8.
What is an algebraic expression?Algebraic expression are the expression which consist the variables, coefficients of variables and constants. The algebraic expression is used to represent the general problem in the mathematical way to solve them.
Consider the following equation,
[tex]\dfrac{5}{3}v +4+\dfrac{1}{3}v=8[/tex]
To solve this equation, first we have to arrange the similar terms one side of the equation as,
[tex]\dfrac{5}{3}v+\dfrac{1}{3}v +4=8[/tex]
Solve it further by taking LCM,
[tex]\dfrac{5+1}{3}v +4=8\\\dfrac{6}{3}v+4=8\\2v +4=8\\[/tex]
Hence, the resulting equation which is obtained after the first step in the solution of the provided equation is 2v +4=8.
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Answer:
c on edge
Step-by-step explanation:
Factor each polynomial. 20 points
5a^2b^2 + 10ab +25a
8m^2n^2 - 24mn^3 +16mn
9xz^3 + 18yz^2 + 24z^2
16x^6y + 16x^2y^4 + 32x^3y^2
So, here we are to factor the polynomials :
[tex]\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\[/tex]
[tex] \longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\[/tex]
[tex]\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\[/tex]
[tex] \longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\[/tex]
[tex]\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\[/tex]
[tex]\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\[/tex]
[tex]\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\[/tex]
[tex] \longrightarrow \sf \qquad 16 {x}^{2} y(x^4 + y^3 + 2xy)\\ \\[/tex]
Some points to know :
Factorisation is the reverse process of multiplucation.The Factorisation is the process of finding two or more expressions such that their product is the given expression.Sue says the expressions for 4y and y⁴ are Equivalent when y = 5. Is She Correct? Please Justify Your Answer.
Answer:
Sue is incorrect
Step-by-step explanation:
Just substitute in the values[tex]4\times 5=20\\5^{4}=625[/tex]Since 20 does NOT equal 625, Sue is incorrectWrite each expression using exponents:
4*4*4*4*4
Answer:4^6
Step-by-step explanation:
The number of times a term is multiplied is the exponent you use.
In this problem
4 is multiplied 6 times.
Therefore: 4*4*4*4*4*4=4^6
This sphere has a radius of 9 m. What is the surface area of the sphere? Enter your answer, in exact form, in the box
[tex]\textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies SA=4\pi (9)^2\implies SA=324\pi[/tex]
There are 100 students in a band. Forty percent are 12 years old, 1/2 are 13 years old, and the rest are 14 years old. Write the portion of the band for each age
Answer:
40x 12 year olds
50x 13 year olds
10x 14 year olds
Step-by-step explanation:
40% of 100 is 40
50% of 100 is 50
100%-90%=10%, 10% of 100 = 10
Students of 12 years are 40%, students of 13 years are 50% and students of 14 years are 10%.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given, total students in band = 100
40% are of 12 years
40% of 100 = 0.4 x 100 = 40
12 years student = 40 = 40%
1/2 of 13 years
1/2 of 100 = 1/2 x 100 = 50 =50%
13 years of student = 50
and rest are 14 years
100 - 50 - 40 = 10
14 years student = 10 = 10%
Hence 40% students are 12 years, 50% are of 13 years and 10% of students are of 14 years.
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[tex]3^x - ^2 = 3^7[/tex](05.01 MC) Solve 3x − 2 = 37.
Answer:
x=㏒3(2189)
Step-by-step explanation:
What key features do the functions f(x) = 12x and g of x equals the square root of x minus 12 end root have in common?
1-Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions have an x-intercept in common.
2- Both f(x) and g(x) include domain values of [12, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
3-Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions increase over the interval (-6, 0).
4-Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
Using the domain and the range of the function, it is found that the correct option is given by:
4- Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.Function f(x) is defined by: f(x) = 12x.
Line with positive slope, hence it is increasing all over it's domain.Range is all real values.No restriction, hence the domain is also all real values.Function g(x) is defined by: [tex]g(x) = \sqrt{x - 12}[/tex]
The square root function increases over all it's domain.The range is [tex](0, \infty)[/tex].The term inside the root cannot be negative, hence the domain is [12, ∞), which is contained into the domain of f(x).This means that option 4 is correct.
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Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008
Answer:c
Step-by-step explanation:
PLS HELP MEEE I REALLY NEED HELP
a) 24.92
b) 65.616
c) 66.43
d) 6.13
e) 25.0862
f) 4.95
Which accounting principle states that a business and its owner are to be treated as separate legal entities
the economic entity concept
Answer:
economic entity principle
Step-by-step explanation:
The strength of an electrical current x flowing through the electric circuit shown is expressed as a function of time t and satisfies the following differential equation:
[tex]\displaystyle \large{L \frac{dx}{dt} + Rx = V}[/tex]
Find the strength of the electrical current x after switch S is closed at time t = 0. Assume that L, R and V are positive constants, and also that x = 0 when t = 0. Then, find [tex]\displaystyle \large{ \lim_{t \to \infty} x}[/tex]
Topic: Application of Differential Equation Reviews
Answer:
The current of the circuit at t = 0 is equal to 0.
If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Slope Fields
Separation of VariablesIntegration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Method: U-Substitution
Electricity
Ohm's Law: V = IR
V is voltage (in Volts)I is current (in Amps)R is resistance (in Ohms)Circuits
Circuit SymbolsKirchhoff's Laws (Loop and Junction Rule)InductorsStep-by-step explanation:
*Note:
In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.
Step 1: Define
Identify given.
[tex]\displaystyle L \frac{dI}{dt} + RI = V[/tex]
[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.
Step 2: Find Current Expression Pt. 1
[Kirchhoff's Law] Rewrite expression:Step 3: Find Current Expression Pt. 2
Identify variables for u-substitution.
Set u:Step 4: Find Current Expression Pt. 3
[Kirchhoff's Law] Apply U-Substitution:Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.
[Kirchhoff's Law] Integrate both sides:Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.
Back-Substitute in u and u₀:Step 5: Solve
If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:
[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}[/tex]
If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:
[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}[/tex]
∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.
---
Topic: AP Physics C - EMAG
Unit: Induction
do you know the answer to this question 4x16+3-1
Answer:
66
Step-by-step explanation:
use
P- parenthesis
E- Exponents
M-multiplication
D-Division
A- addition
S- subtraction
NOTE THAT MULTIPLICATION IS NOT MORE IMPORTANT THAN DIVISION AND SAME GOES FOR ADDITION AND SUBTRACTION.
This means that that we do it from left yo right
4×16+3-1 --> 64+3-1 --> 67-1 = 66
a funnel is in the shape of a cone with a radius of 4 inches and a height of 10 inches.
a. find the volume of the funnel. Round your answer to the nearest 10th
b. the funnel is filled with oil. how many quarts of oil are in the funnel? (1 qt = 58in ^3.) round to the nearest tenth
Answer:
A. 167.4
B. I don't know but I hope this helps :)
Step-by-step explanation:
the formula for volume of a funnel is:
V= 1/3 pi r^2 h
if we plug in the given values we are left with:
V= 1/3 (pi) 4^2 (10)
using 3.14 for pi, we get the answer:
V= 167.4
please help me, thank you if you do
Answer:
Step-by-step explanation:
1. The sequence is not arithmetic.
2. d=-30
The ages of the people in attendance at the showing of an award-winning foreign film are shown below. a graph shows age of attendees (in years) labeled 0 to 20 thru 61 to 80 on the horizontal axis and frequency on the vertical axis. 0 to 20 years at frequency 15. 20 to 40 years at frequency 40. 41 to 60 years at frequency 40. 61 to 80 years at frequency 15. which statement must be true according to the histogram? the data is symmetrical, showing that the majority of the attendees were between the ages of 30 and 50. the data is symmetrical, showing that the majority of the attendees were between the ages of 21 and 60. the data is skewed, showing that the majority of the attendees were between the ages of 30 and 50. the data is skewed, showing that the majority of the attendees were between the ages of 21 and 60.
Answer:
B
Step-by-step explanation:
i got it right on edge
Answer:
It is B
Step-by-step explanation:
A researcher is interested in whether blind Braille readers could be taught to read faster using the same techniques as sighted readers. He has blind adults complete a reading speed test before and after a six-week speed-reading course. In the beginning of the study, a randomly selected group of 121 blind Braille readers scored an average of 261 words per minute on the reading speed test. Since the sample size is larger than 30, the researcher can assume that the sampling distribution of MD is normal. He plans to use a repeated-measures t test. The researcher identifies the null and alternative hypotheses as:
If a baseball card appreciates exponentially in value by 50% over 10 years, what is its annual appreciation (growth) rate? Please use a calculator, and answer to the nearest whole percent.
we can use hmmm any value per se for the card, hmmm say let's use $2, if the baseball card was initially 2 bucks, and after 10 years it went up in value by 50%, well 50% of 2 is 1, so the new value is 3 bucks, then
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &3\\ P=\textit{initial amount}\dotfill &2\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &10\\ \end{cases} \\\\\\ 3=2(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(\frac{100+r}{100})^{10} \\\\\\ \sqrt[10]{\cfrac{3}{2}}=\cfrac{100+r}{100}\implies 100\sqrt[10]{\cfrac{3}{2}}=100+r \\\\\\ 100\sqrt[10]{\cfrac{3}{2}}-100=r\implies 4\approx r[/tex]
If m<5=53º and m∠7=125º, find the measures of each numbered angle.
m<1=
m<2=
m<3=
m<4=
m<6=
#5 = 53° #7 = 125° #6 = 55° #2 = 72° #3 = 55° #1 = 53° #4 = 127°
triangle = 180°
alternating interior angles are the same (#6 & #3 and #5 and #1)
#3 and #7 should equal 180°
#1 and #4 should also equal 180°
#6 and #7 should equal 180°
#4 and #5 should equal 180°
In a group, more than 1/2 are boys, but they are less than 2/3 of the group. Can there be:(In each case, if your answer is “yes”, find out how many boys there were. Explore all possible cases). Could there be 5 kids
Using proportions, it is found that Yes, there could be 5 kids, with 3 boys and 2 girls.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, supposing a total of 5 kids:
More than 1/2 = 50% are boys, hence there are more than 2.5 boys, as 0.5 x 5 = 2.5.Less than 2/3 = 66.67% are boys, hence there are less than 3.33 boys, as 0.6667 x 5 = 3.33.Hence, Yes, there could be 5 kids, with 3 boys and 2 girls.
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A store is selling a green rug for $54.50 and a white rug for $31.85. the green rug is marked down by 12%, and the white rug is marked up by 16%. after the markup and markdown, which rug is more expensive, and how much more expensive is it? round all dollar values to the nearest cent. a. the white rug is $1.09 more expensive than the green rug. b. the white rug is $5.35 more expensive than the green rug. c. the green rug is $1.44 more expensive than the white rug. d. the green rug is $11.01 more expensive than the white rug.
The a seer to the more expensive rug is; D: the green rug is $11.01 more expensive than the white rug.
How to calculate mark up and mark down?We are told that;
Current cost of Green rug = $54.50
Current cost of White rug = $31.85
Now the store wants to mark down the green rug by 12%. Thus;
New price of green rug = (100% - 12%) × 54.5
New price of green rug = $47.96
Now the store wants to mark up the white rug by 16%. Thus;
New price of white rug = (100% + 16%) × 31.85
New price of green rug = $36.95
Difference in New prices = $47.96 - $36.95
Difference in New prices = $11.01
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