Answer:
12750 is the answer... god bless
i dont rlly understand this if someone wants to help
The value of one square in each sample is:
(a) 2
(b) 6
(c) 3
(d) 5
How to determine the value of one square in each sample?
Let x represent the value one square. Thus, the value of one square in each sample can be determined as follow.
(a) 2x + 1 = 5 (Left side is equal to right side)
2x = 5 - 1
2x = 4
x = 4/2
x = 2
(b) 10 = x + 2 + 2
10 = x + 4
x = 10 - 4
x = 6
(c) 5 + 1 + x = 9
6 + x = 9
x = 9 - 6
x = 3
(d) 25 = 5x
x = 25/5
x = 5
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ly| ≤3
Are the lines on graph at 3 and -3 also part of the answer?
Answer:
Yes, the lines on the graph at 3 and -3 a part of the solution,
Step-by-step explanation:
The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.
Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.
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Penelope has $1,459.75 in her bank account. To pay her bills, she writes 4 checks in the amounts of $200.25, $359.45, $125, and $299.35. Then she deposits $375 into her account. Penelope’s account balance after she pays her bills and makes the deposit is $ .
Answer:
$850.70
Step-by-step explanation:
Subtract all her check amounts and add the deposit. You come up with $850.70
find dx/dy.
can you help me in this pleasee.......
Differentiate both sides of
\(y = \dfrac{x\sqrt{a^2-x^2}}2 + \dfrac{a^2}2\sin^{-1}\left(\dfrac xa\right)\)
with respect to y ; by the product rule,
\(1 = \dfrac12\sqrt{a^2-x^2}\dfrac{\mathrm dx}{\mathrm dy} + \dfrac x2 \dfrac{\mathrm d}{\mathrm dy}\left[\sqrt{a^2-x^2}\right] + \dfrac{a^2}2\dfrac{\mathrm d}{\mathrm dy}\left[\sin^{-1}\left(\dfrac xa\right)\right]\)
Use the chain rule for the remaining derivatives.
\(\dfrac{\mathrm d}{\mathrm dy}\left[\sqrt{a^2-x^2}\right] = \dfrac1{2\sqrt{a^2-x^2}}\dfrac{\mathrm d}{\mathrm dy}\left[a^2-x^2\right] \\\\ = \dfrac{-2x}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy} \\\\ = -\dfrac x{\sqrt{a^2-x^2}} \dfrac{\mathrm dx}{\mathrm dy}\)
Recall that
\(\dfrac{\mathrm d}{\mathrm dx}\left[\sin^{-1}(x)\right] = \dfrac1{\sqrt{1-x^2}}\)
Then
\(\dfrac{\mathrm d}{\mathrm dy}\left[\sin^{-1}\left(\dfrac xa\right)\right] = \dfrac1{\sqrt{1-\left(\frac xa\right)^2}}\dfrac{\mathrm d}{\mathrm dy}\left[\dfrac xa\right] \\\\ = \dfrac1{a\sqrt{1-\left(\frac xa\right)^2}}\dfrac{\mathrm dx}{\mathrm dy} \\\\ = \dfrac1{\sqrt{a^2}\sqrt{1-\left(\frac xa\right)^2}}\dfrac{\mathrm dx}{\mathrm dy} \\\\ = \dfrac1{\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy}\)
Putting everything together, we have
\(1 = \dfrac{\sqrt{a^2-x^2}}2\dfrac{\mathrm dx}{\mathrm dy} - \dfrac{x^2}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy} + \dfrac{a^2}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy}\)
\(1 = \left(\dfrac{\sqrt{a^2-x^2}}2+\dfrac{a^2-x^2}{2\sqrt{a^2-x^2}}\right)\dfrac{\mathrm dx}{\mathrm dy}\)
\(1 = \dfrac1{2\sqrt{a^2-x^2}}\bigg((a^2-x^2) + (a^2-x^2)\bigg)\dfrac{\mathrm dx}{\mathrm dy}\)
\(1 = \dfrac{2a^2-2x^2}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy}\)
\(1 = \sqrt{a^2-x^2}\dfrac{\mathrm dx}{\mathrm dy}\)
\(\boxed{\dfrac{\mathrm dx}{\mathrm dy} = \dfrac1{\sqrt{a^2-x^2}}}\)
help please! ill mark brainliest if correct
Answer:
thrid one
Step-by-step explanation:
Answer:
If im correct
EG and FH
4x10^8 has how many times more than 5 x 10^7
Answer:
8 times larger
Step-by-step explanation:
4 × \(10^{8}\) = 4 × 100000000
400000000
5 × \(10^{7}\) = 5 × 10000000
50000000
400000000 ÷ 50000000
8
HELP ME PLEASE!!! WORTH 10 POINTS!!
drag and drop each expression to correctly classify it as having a positive or negative product ( just put the ones in a positive group in that group and sam for the other one)
(5/6)(5/6) (-5/6)(5/6)
(5/6)(-5/6) (-5/6)(-5/6)
Answer:
Step-by-step explanation:
(5/6)(5/6) (-5/6)(5/6)
(5/6)(-5/6) (-5/6)(-5/6) they are they same but you can also change them and they will still be the same just backwords
Hope that helps
Hi, i know how to solve this question, but i was wondering if it was possible to solve #1 using the effective yearly rate. IE. (1+r/n)^n
Mike just bought a house for $1.3m. He paid $300k as a down-payment and the rest of the cost has been obtained from a mortgage. The mortgage has a nominal interest rate of 1.8% compounded monthly with a 30-year amortization period. The term (maturity) of the mortgage is 5 years.
1) What are Mike's monthly payments?
2) What does Mike owe at the end of the 5-year term (what is the balance at time 60, B60)?
Mike's monthly payments are approximately $19,407.43. At the end of the 5-year term (time 60), Mike owes approximately $1,048,446.96.
To solve the given problem, we can use the formula for calculating the monthly mortgage payments:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
r = Monthly interest rate
A = Loan amount
n = Total number of payments
First, let's calculate the monthly interest rate. The nominal interest rate is given as 1.8%, which means the monthly interest rate is 1.8% divided by 12 (number of months in a year):
r = 1.8% / 12 = 0.015
Next, let's calculate the total number of payments. The mortgage has a 30-year amortization period, which means there will be 30 years * 12 months = 360 monthly payments.
n = 360
Now, let's calculate Mike's monthly payments using the formula:
P = (0.015 * (1.3m - 300k)) / (1 - (1 + 0.015)^(-360))
Substituting the values:
P = (0.015 * (1,300,000 - 300,000)) / (1 - (1 + 0.015)^(-360))
Simplifying the expression:
P = (0.015 * 1,000,000) / (1 - (1 + 0.015)^(-360))
P = 15,000 / (1 - (1 + 0.015)^(-360))
Calculating further:
P = 15,000 / (1 - (1.015)^(-360))
P ≈ 15,000 / (1 - 0.22744)
P ≈ 15,000 / 0.77256
P ≈ 19,407.43
Therefore, Mike's monthly payments are approximately $19,407.43.
To calculate the balance at time 60, we can use the formula for calculating the remaining loan balance after t payments:
Bt = P * ((1 - (1 + r)^(-(n-t)))) / r
Where:
Bt = Balance at time t
P = Monthly payment
r = Monthly interest rate
n = Total number of payments
t = Number of payments made
Substituting the values:
B60 = 19,407.43 * ((1 - (1 + 0.015)^(-(360-60)))) / 0.015
B60 = 19,407.43 * ((1 - (1.015)^(-300))) / 0.015
B60 ≈ 19,407.43 * ((1 - 0.19025)) / 0.015
B60 ≈ 19,407.43 * 0.80975 / 0.015
B60 ≈ 19,407.43 * 53.9833
B60 ≈ 1,048,446.96
Therefore, at the end of the 5-year term (time 60), Mike owes approximately $1,048,446.96.
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8. Tyler and Jada wish to find the value of x, the length of side BC in this triangle. Tyler decides to set up the equation tan(56)=. Jada says she prefers an equation that has x in the numerator. What is an
equation she could use instead? (Lesson 4-8)
The equatiοn she may emplοy in a linear equatiοn is 8 tan(56) = x. x has a value οf 4.89.
What dοes a linear equatiοn mean in mathematics?A linear equatiοn in algebra is οne that οnly cοntains a cοnstant and a first-οrder (linear) cοmpοnent, like y=mx+b, where m denοtes the slοpe and b the y-intercept.
Occasiοnally, the afοrementiοned is referred tο as a "linear equatiοn οf twο variables," where x and y are the variables. Linear equatiοns are referred tο as equatiοns with pοwer 1 variables. Where ax+b = 0, where a and b are real numbers and x is the variable, is οne example with οnly οne variable.
We are given that Tyler and Jada wish tο find the value οf x, B the length οf side BC in this triangle.
Tyler decides tο set up the equatiοn 8 tan(56) =x
So, 8 tan(56) =x
x = 8 (0.611)
x = 4.89
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what is the probability that you get a total of 17 given You are playing a version of the roulette game, where the pockets are from 0 to 10 and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability that you get a total of 15 given on the first spin you spin a 2
In the roulette game, the probability that you get a total of 15 given on the first spin you spin a 2 is 8.26%
To find: the probability that you get a total of 15 in three trials
Given that you spin a 2 on the first trial.
This means, the required probability is equivalent to the probability of finding a sum of 13 in the next two trials.
In each trial, there are 11 possible outcomes as the pockets numbered from 0 to 10.
so the sample space i.e., the total number of outcomes is:
S = 11^2
S = 121
And the favourable outcomes would be,
(2, 11), (3, 10), (4, 9), (5, 8), (6, 7), (7, 6), (8, 5), (9, 4), (10, 3), (11, 2)
So, the number of favourable outcomes A = 10
Using the definition of probability,
P = A/S
P = 10/121
P = 0.0826
P = 8.26%
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The complete question is:
You are playing a version of the roulette game, wherethe pockets arefrom 0 to 10 and even numbers are red and odd numbersare black (0 isgreen). You spin 3 times and add up the values yousee. What is theprobability that you get a total of 15 given on thefirst spin youspin a 2
True or False: Proportional relationships are a type of nonlinear function.
Answer:
i belive that the answer is false
if 1343243253254353462534543254324534234542345134 times 23423543254353454325234543543543254365645654654 minus 454235435435425243543=x what does x=
Answer:
3.14635164e91
Step-by-step explanation:
BEAT THE TESTI
1. Which of the following equations have the correct
solutions Select all that apply,
2x + 5 = 19; X = 7
3+x+2-x=16; x =3
x+2/5=2; x = 8
6 = 2x -8; x = 7
14 =1/3x+5; x = 18
Step-by-step explanation:
2x + 5 = 19; X = 7: Correct
2(7) + 5 = 19
14+5=19
3+x+2-x=16; x=3 : Incorrect
3+3+2-3=16
6+2-3=16
7-3=16
4=16
x+2/5=2; x = 8: incorrect
8+2/5=2
x= 8/5
6 = 2x -8; x = 7: correct
6 = 2(7) -8
6 = 14-8
14 =1/3x+5; x = 18: Incorrect
14 = 18/3+5
14 = 6+5
look at my baby i misss him so much
Answer:
aww hes so cute what is his name
¿Donde se aplica la aritmética?
Answer:
Step-by-step explanation:
.. En este sentido, el término aritmética se aplica para designar operaciones realizadas sobre entidades que no son números enteros ... Se llama potencia a una expresión de la forma a^n, donde “a” es la base y “n” es el exponente.
a sub sandwich shop offers 16 toppings to choose from. how many ways could a person choose a 3-topping sandwich?
There are 560 ways a person can choose a 3-topping sandwich from the 16 available toppings.
Combination problemTo determine the number of ways a person can choose a 3-topping sandwich from 16 available toppings, we can use the concept of combinations.
The formula for calculating combinations is:
C(n, r) = n! / (r! * (n - r)!)
where C(n, r) represents the number of ways to choose r items from a set of n items.
In this case, we want to find C(16, 3) because we want to choose 3 toppings from a set of 16 toppings.
Thus:
C(16, 3) = 16! / (3! * (16 - 3)!)
= 16! / (3! * 13!)
16! = 16 * 15 * 14 * 13!
3! = 3 * 2 * 1
C(16, 3) = (16 * 15 * 14 * 13!) / (3 * 2 * 1 * 13!)
C(16, 3) = (16 * 15 * 14) / (3 * 2 * 1)
= 3360 / 6
= 560
Therefore, there are 560 ways a person can choose a 3-topping sandwich from the 16 available toppings.
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mr. patrick teaches math to 15 students. he was grading tests and found that when he graded everyone's test except payton's, the average grade for the class was 80. after he graded payton's test, the class average became 81. what was payton's score on the test?
Mr. Patrick instructs 15 students in math. He discovered that Payton had received a 95 on the test while grading them from average.
There are 15 kids in Mr. Patrick's class. The average score on his most recent exam was 80 for 14 candidates (not including Payton).
I'm going to use x to represent the unknowable sum of the 14 test scores. Average is computed by adding all the numbers in the set (whose average you're trying to get) together, then dividing by the total number of numbers in that set.
This was the total of their scores: x=1120.
Adding Payton's score now (I'll use the letter p to stand in for her score):
1120+p /15=81→ Her test score was included in the fifteen students' average, which was 81 1120+p=1215
P=95.
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If you flip the graph of the exponential function f(x) = 2x over the x-axis, what
is the equation of the new function?
O A. g(x) = 1/2
O B. g(x) = 2x - 1
O c. g(x) = 2-X
D. g(x) = -2X
Answer:
Step-by-step explanation:
G(x)=-2x
Answer:A
Step-by-step explanation:
Can someone help me? I pick brainlest
Answer:
A=1/4 , B= 7/16 , C= 5/8 , D= 3/4 or in other words the fourth option
Step-by-step explanation:
Set all denominators to 16
3/4 = 12/16
1/4 = 4/16
7/16 = 7/16
5/8 = 10/16
4/16 , 7/16 , 10/16 , 12/ 16
1/4 , 7/16 , 5/8 , 3/4
Answer:
D
A=1/4
B=7/16
C=5/8
D=3/4
Could I please have BRAINLIEST.
what number is the opposite of 0.93?
Answer:
- 0.93
Step-by-step explanation:
0.93 has an absolute value of 0.93 and is positive, so its opposite would be negative with the same absolute value.
The opposite number of 0.93 is -0.93.
What is opposite number?The number that produces zero when added to an is known as the additive inverse of a number, or a, in mathematics. This number is also referred to as the opposite number. In another word, oppositely positioned numbers on the number line are called opposite number.
Hence, opposite number of a positive number is a negative number and opposite number of the negative number is a positive number.
For an example, the opposite number of +7 is -7 because +7 + ( -7) = 0.
The opposite number of -0.5 is 0.5 because (-0.5) +0.5 = 0.
In this question, the given number is +0.93.
Let the opposite number of +0.93 is x.
Then it can be written that:
+0.93 + x = 0
⇒ x = 0 -0.93
⇒ x = -0.93
Hence, the opposite number of 0.93 is -0.93.
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6. Find the equation of the line that is tangent to the graph of \( f(x)=3 x^{3}-x \) and perpendicular to the line \( x+3 y-6=0 \)
The equation of the line that is tangent to the graph of f(x) = 3x³ - x and perpendicular to the line x + 3y - 6 = 0 is x - 3√3y = 2 + 2√3.
The equation of the line that is tangent to the graph of f(x) = 3x³ - x and perpendicular to the line x + 3y - 6 = 0, we need to follow these steps:
Step 1: Determine the slope of the tangent line to the graph of f(x).
To find the slope of the tangent line, we need to take the derivative of the function f(x). Taking the derivative of f(x) = 3x³ - x, we get:
f'(x) = 9x² - 1
Step 2: Find the slope of the line perpendicular to x + 3y - 6 = 0.
The given line x + 3y - 6 = 0 is in the form ax + by + c = 0, where the slope of the line is -a/b. So the slope of the line perpendicular to x + 3y - 6 = 0 is 1/3.
Step 3: Use the point-slope form to write the equation of the tangent line.
The point-slope form of a line is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
Since the line we want is tangent to the graph of f(x), we can find the x-coordinate of the point of tangency by solving the equation f'(x) = 1/3. Let's solve it:
9x² - 1 = 1/3
Multiply both sides by 3 to get rid of the fraction:
27x² - 3 = 1
27x² = 4
x² = 4/27
x = ±√(4/27) = ±2/(3√3)
Now we can find the corresponding y-coordinate by substituting x into f(x):
f(x) = 3x³ - x
When x = 2/(3√3), y = 3(2/(3√3))³ - 2/(3√3) = 2√3/9 - 2/(3√3) = (2√3 - 2)/(3√3)
So the point of tangency is (2/(3√3), (2√3 - 2)/(3√3)).
Now we can write the equation of the tangent line using the point-slope form:
y - y₁ = m(x - x₁)
where m = 1/3 (slope of the line perpendicular to x + 3y - 6 = 0) and (x₁, y₁) = (2/(3√3), (2√3 - 2)/(3√3)):
y - (2√3 - 2)/(3√3) = (1/3)(x - 2/(3√3))
Simplifying, we can multiply both sides by 3√3 to get rid of the denominators:
3√3(y - (2√3 - 2)/(3√3)) = 3√3(1/3)(x - 2/(3√3))
3√3y - 2√3 + 2 = x - 2/(√3)
Rearranging the terms and simplifying, we obtain the equation of the tangent line:
x - 3√3y = 2 + 2√3
Therefore, the equation of the line that is tangent to the graph of f(x) = 3x³ - x and perpendicular to the line x + 3y - 6 = 0 is x - 3√3y = 2 + 2√3.
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A linear function models the height of a burning candle. Candle A comes out of the mold at 211 mm, and is expected to be at 187 mm after 4 hours of burning. The model for Candle B is h=260−5t, where h is the height in millimeters and t is the time in hours. What are the initial values for each candle? What do the initial values for each candle tell you?
Use pencil and paper. If the candles begin burning at the same time, can they ever be the same height? Explain.
The initial heights are:
Candle A = 211mm
Candle B = 260m
And the two candles will never have the same height.
What are the initial values for each candle?We know that candle B height is modeled by the linear equation:
h = 260 - 5t
Then its initial height (when t = 0) is:
h = 260 - 5*0 = 260
The initial height is 260mm
And for Candle A we know that it is 211mm.
Now, let's say that the equation for candle A is:
h' = 211 - a*t
We know that after 4 hours the height is 187 mm, then:
187 = 211 - a*4
187 - 211 = a*4
-24/4 = a
-6 = a
So the linear equation is:
h' = 211 - 6t
Will the candles have the same height at some point?
To see that we need to solve:
h = h'
260 - 5t = 211 - 6t
260 - 211 = -6t + 5t
49 = -t
This gives a negative time, so no, the candles will not have the same length.
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dy dx = xy 7x − y − 7 xy − 2x 8y − 16
The solution to the differential equation e^x y = 1/2 x^2 y + 7x^2/2 - 7ln|y/2 + 1| + C
The given differential equation is: dy/dx = xy + 7x - y - 7/(xy - 2x + 8y - 16)
To solve this equation by separation of variables, we need to separate the variables y and x on different sides of the equation and integrate both sides with respect to their respective variables.
First, we will move the y term to the left-hand side of the equation and factor the denominator on the right-hand side:
dy/dx + y = xy + 7x - 7/(xy - 2x + 8y - 16)
dy/dx + y = xy + 7x - 7/[(y/2 + 1)^2 - 1]
Next, we will multiply both sides of the equation by e^x to get:
e^x dy/dx + e^x y = xe^x y + 7xe^x - 7e^x/[(y/2 + 1)^2 - 1]
Now we can use the product rule for differentiation and integrate both sides with respect to x:
d/dx [e^x y] = xe^x y + 7xe^x - 7e^x/[(y/2 + 1)^2 - 1]
∫ d/dx [e^x y] dx = ∫ [xe^x y + 7xe^x - 7e^x/[(y/2 + 1)^2 - 1]] dx
e^x y = 1/2 x^2 y + 7x^2/2 - 7ln|y/2 + 1| + C
where C is the constant of integration.
Therefore, the solution to the differential equation dy/dx = xy + 7x - y - 7/(xy - 2x + 8y - 16) is:
e^x y = 1/2 x^2 y + 7x^2/2 - 7ln|y/2 + 1| + C
where C is the constant of integration.
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Your question is incomplete but probably the full question was:
Solve The Given Differential Equation By Separation Of Variables. Dy/Dx = Xy + 7x - Y - 7/Xy - 2x + 8y - 16
What is the x-value in the solution to this system of linear equations?
2x − y = 11
x + 3y = −5
−3
−1
2
4
Answer:
4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
2x - y = 11
x + 3y = -5
Step 2: Rewrite Systems
2x - y = 11
[Subtraction Property of Equality] Subtract 2x on both sides: -y = 11 - 2x[Division Property of Equality] Divide -1 on both sides: y = 2x - 11Step 3: Redefine Systems
y = 2x - 11
x + 3y = -5
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: x + 3(2x - 11) = -5[Distributive Property] Distribute 3: x + 6x - 33 = -5Combine like terms: 7x - 33 = -5[Addition Property of Equality] Add 33 on both sides: 7x = 28[Division Property of Equality] Divide 7 on both sides: x = 4Answer:
x = 4
Step-by-step explanation:
2x - y = 11
x + 3y = -5
To calculate the value of x , firstly we need to find value of y.
solve for y
2x - y = 11subtract 2x from both side
2x - 2x - y = 11 - 2x-y = 11 - 2xchange the sign of both side of equation
y = -11 + 2xrewrite
y = 2x - 11Solve for x
y = 2x - 11x + 3y = -5substitute the value of y in the equation
x + 3( 2x - 11 ) = -5distribute 3
x + 3 × 2x - 3× 11 = -5x + 6x - 33 = -5combine like terms
7x - 33 = -5Add 33 on both side
7x - 33 + 33 = -5 + 337x = 28divide both side by 7
7x / 7 = 28 / 7x = 4Carrie buys 7/8 pound of red apples and 15/16 pound of green apples. Which answer is the most accurate estimate for how many more pounds of green apples she buys than pounds of red apple?
0 Pounds
1 Pound
1/2 Pounds (10 Points)
Answer:
0 pounds
Step-by-step explanation:
To bring \(\frac{7}{8}\) to 16ths it goes to \(\frac{14}{16}\)
Consider the number lines shown below which shows jump from one number to another. There are four different arrows, starting from the number . Match the number lines given in the first column with the correct mathematical expression that results in the number on the other side of the arrow. Number line 1 Number line 2 Number line 3 Number line 4 Number line 1 Number line 2 Number line 3 Number line 4 DRAG & DROP THE ANSWER −45−20+5-45-20+5−45−20+5 −45+10+5-45+10+5−45+10+5 −45+30−20-45+30-20−45+30−20 −45+35−15-45+35-15−45+35−15
Answer:
Step-by-step explanation:
Its number line 2.
Find the largest degree of x that can be factored out of all the terms.
a. 1
b. 2
c. 3
d. 4
The largest degree of x that can be factored out of all the terms is 1.
In this problem, we are asked to determine the largest degree of x that can be factored out of all the terms. To solve this, we need to look at the terms and identify the common factors of x. The options provided are 1, 2, 3, and 4.
If we look at the given terms, there is no variable x present in any of them. Therefore, we cannot factor out any powers of x from the terms. In other words, the degree of x in each term is 0. Hence, the largest degree of x that can be factored out of all the terms is 1, as x^1 is equivalent to x.
Factoring is a process in algebra where we break down an expression into its factors. It involves finding common factors and removing them from each term. By factoring, we can simplify expressions and solve equations more easily.
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Study the food web below and answer the following :
i. In the pyramid of numbers there is an increase in numbers towards the base. Mention a pyramid where the base will be smaller.
ii. Predict the impact of removing snakes from this food web
Answer:
predict the impact of removing snakes from this food web
line mn passes through points m(4, 3) and n(7, 12). if the equation of the line is written in slope-intercept form, y
The equation of a line in slope-intercept form is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.The equation of the line passing through points M(4, 3) and N(7, 12) in slope-intercept form is y = 3x - 9.
1. Calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates of the points M(4, 3) and N(7, 12) into the formula:
m = (12 - 3) / (7 - 4)
m = 9 / 3
m = 3
2. Now that we have the slope (m), we can use one of the points, let's say M(4, 3), and substitute its coordinates along with the slope into the slope-intercept form (y = mx + b) to find the y-intercept (b).
Let's use the coordinates (4, 3) and the slope (m = 3):
3 = 3(4) + b
3 = 12 + b
b = 3 - 12
b = -9
3. Finally, we can write the equation of the line in slope-intercept form, substituting the values of m and b that we found:
y = 3x - 9
Therefore, the equation of the line passing through points M(4, 3) and N(7, 12) in slope-intercept form is y = 3x - 9.
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A child lifts a box up from the floor. The child then carries the box with a constant speed to the other side of the room and puts the box down. How much work does he do on the box while walking across the floor at constant speed? Your answer: 0 J More than 0 J More information is needed to determine the answer.
The work done by the child on the box is also zero, regardless of the distance traveled.
How we calculate work?The child does zero work on the box because work is defined as the product of force and displacement, and in this case, there is no net force acting on the box in the horizontal direction.
Since the box is moving at a constant speed, there is no acceleration, and therefore no net force is required to keep it moving.
Without a net force, there is no force being applied over a displacement, resulting in zero work.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
Since the box's speed remains constant, there is no change in its kinetic energy.
The child's effort in lifting the box from the floor requires work, as gravity opposes the motion, but this work is not relevant to the question at hand, which specifically asks about the work done while walking across the floor.
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