Answer:
3·ln(x) -ln(1+x)
Step-by-step explanation:
You want to "solve" the expression ln(x³/(1+x)).
Rules of logarithmsThe relevant rules of logarithms are ...
ln(a^b) = b·ln(a)
ln(a/b) = ln(a) -ln(b)
ApplicationThe given log expression can be expanded as ...
[tex]\ln{\left(\dfrac{x^3}{1+x}\right)}=\ln(x^3)-\ln(1+x)=\boxed{3\ln(x)-\ln(1+x)}[/tex]
A new computer graphics company employs 10 programmers. The company decides to expand into digital animation and needs to transfer 3 of the programmers into the new department. How many different combinations of 3 programmers can be chosen to transfer to the new department?
A. 3
B. 30
C. 120
D. 840
There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department
How to determine the ways of selection?From the question, we have
Total number of programmers, n = 10
Numbers to programmers to select, r = 3
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 10 and r = 3
Substitute the known values in the above equation
Total = ¹⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 10!/(7! * 3!)
Evaluate
Total = 120
Hence, the number of ways is 120
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The Grand Teton, a mountain on the Idaho/Wyoming border, is 13,776 feet above sea level. Convert the Grand Teton's elevation into miles. (Hint: 1 mile = 5280 feet).
(Round your answer to 2 decimal places)
Answer:
2.61 miles
Step-by-step explanation:
What are units?A unit can be used for measurement and is commonly found in mathematics to describe length, size, etc.
If we know that 1 mile = 5280 feet, then we can divide the elevation in feet by the number of feet per mile.
The elevation of the Grand Teton in miles would be:
13,776 feet ÷ 5280 feet/mile ≈ 2.61 milesTherefore, the elevation of the Grand Teton is approximately 2.61 miles above sea level when rounded to two decimal places.
Answer:
2.61
Step-by-step explanation:
there are 2.54 centimeters in 1 inch how many centimeters are there in 1 foot?
Answer:
30.48cm
Step-by-step explanation:
The best way to perform conversion is by the multiplication of fractions to keep track of units. You'll see in the equation below that inches cancels out. Leaving you with cm in 1 ft.
[tex]\frac{2.54 cm}{1in}* \frac{12 in}{1ft} = \frac{30.48cm}{1ft}[/tex]
Answer:
30.48 centimeters
Step-by-step explanation:
To answer this question, keep in mind 1 foot = 12 inches. If 2.54 cm = 1 in., and you are trying to find how many centimeters there are in 12 inches (1 ft), you need to multiply (2.54)(12)=30.48
Chess is one of the oldest and most popular board games. It is played by two opponents on a checkered board with specially designed pieces of contrasting colors, commonly white and black. White moves first, after which the players alternate turns in accordance with fixed rules, each player attempting to force the opponent’s principal piece, the King, into checkmate—a position where it is unable to avoid capture. In most chess tournaments held since the middle of the 19th century, there has been a very simple scoring system used. Players who scored a win in a game were awarded a point, while those scoring draws were given a half-point. Losing a game, as you might expect, was worth zero points. Five students from AMG chess club participated in a tournament.
a)3 times Mahdi’s score is one and a half. Write an equation that represents the situation, then find Mahdi’s score. Show your work.
Mahdi's score is,
⇒ 0.5
We have to given that;
3 times Mahdi’s score is one and a half.
Now, Let Mahdi's score = x
Hence, We can formulate;
⇒ 3x = 1 1/2
⇒ 3x = 3/2
⇒ x = 1/2
⇒ x = 0.5
Thus, Mahdi's score is,
⇒ 0.5
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Question 3 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 9 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 15 feet. What is the length of the other
diagonal?
A. 12 feet
B. 9 feet
C. 15 feet
D. 21 feet
Answer:
The diagonals of a rectangle are congruent, so the other diagonal is also 15 feet.
Step-by-step explanation:
Let c represent the cost of a cookie. If I have to pay sales tax of 5.5%, write two expressions to represent the total amount I will have to pay.
These two expressions can be used to represent the total amount you will have to pay, taking into account the cost of a cookie and the sales tax of 5.5%.
To calculate the total amount you will have to pay, considering the cost of a cookie (represented by "c") and the sales tax of 5.5%, you can use the following expressions:
Expression for the sales tax amount:
The sales tax amount can be calculated by multiplying the cost of the cookie (c) by the sales tax rate of 5.5% (or 0.055). The expression would be:
Sales Tax = c × 0.055
Expression for the total amount to be paid:
To calculate the total amount you will have to pay, including the cost of the cookie and the sales tax, you need to add the cost of the cookie to the sales tax amount. The expression would be:
Total Amount = c + (c × 0.055)
Therefore, these two expressions can be used to represent the total amount you will have to pay, taking into account the cost of a cookie and the sales tax of 5.5%.
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The two expressions representing the total amount to pay after sales tax of [tex]5.5\%[/tex]:
[tex]\[ \text{Sales tax amount} = 0.055c \][/tex]
[tex]\[ \text{Total amount with tax} = 1.055c \][/tex]
To represent the total amount you will have to pay when buying a cookie, including the sales tax of [tex]5.5\%[/tex], we can start with the cost of the cookie, represented by the variable [tex]\(c\)[/tex]. The two expressions required are as follows:
1. Expression for the total amount with tax added:
The first expression represents the total amount you need to pay, which includes the cost of the cookie plus the sales tax. The sales tax of [tex]5.5\%[/tex] can be calculated by multiplying the cost of the cookie [tex](\(c\))[/tex] by [tex]0.055[/tex] (since [tex]5.5\%[/tex] is equivalent to [tex]0.055[/tex] as a decimal). Therefore, the expression becomes:
[tex]\[ \text{Total amount with tax} = c + 0.055c \][/tex]
Simplifying this expression, we can combine the two terms involving [tex]\(c\)[/tex]:
[tex]\[ \text{Total amount with tax} = 1.055c \][/tex]
2. Expression for the sales tax amount:
The second expression represents only the sales tax amount that needs to be added to the cost of the cookie. It can be calculated by multiplying the cost of the cookie [tex](\(c\))[/tex] by [tex]0.055[/tex]. Thus, the expression is:
[tex]\[ \text{Sales tax amount} = 0.055c \][/tex]
These two expressions represent the total amount you will have to pay when purchasing a cookie, accounting for the [tex]5.5\%[/tex] sales tax.
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A test to determine whether a certain antibody is present is 99.3% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.3% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.007 . Suppose the test is given to six randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all six people?
(b) What is the probability that the test comes back positive for at least one of the six people?
a) The probability that the test comes back negative for all six people is 95.8%,
b) The probability that the test comes back positive for at least one of the six people is 4.2%.
(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.
Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:
P(negative for all 6) = (0.993)^6 ≈ 0.958
Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.
(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.
The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.
The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:
P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042
Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.
In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.
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Kevin has money in two savings accounts. One rate is 11% and the other is 14%. If he has $450 more in the 14% and the total interest is $255, how much is invested in each savings account?
Kevin has $768 invested in the 11% account and $1218 invested in the 14% account.
What is the amount invested in each interest rate?Let x be the amount invested in the 11% account
y be the amount invested in the 14% account.
The equation for the two different interest rate is determined as;
y = x + $450
0.11x + 0.14y = $255
Solve the two equation simultaneously;
0.11x + 0.14(x + $450) = $255
0.11x + 0.14x + $63 = $255
0.25x = $192
x = $768
Then we can use the first equation to find y;
y = x + $450
y = $768 + $450
y = $1218
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Write a polynomial function that describes the curve below. Write the equation in factored form.
Answer:
f(x)=(x+3)(x+2)(x-3)(x-4)
Step-by-step explanation:
Answer: f(x)=(x+3)(x+2)(x-3)(x-4)
Step-by-step explanation:
Find the real zeros of the polynomial function
f
(
x
)
=
(
x
+
7
)
(
9
x^2
+
5
x
+
4
)
.
Answer:
x = -7
Step-by-step explanation:
Since f(x) = [tex](x+7)(9x^2+5x+4)[/tex], we can set both equal to 0.
x + 7 = 0 will give us x = -7.
Now, in the second equation, we will plug into the quadratic formula, when we do that, the number inside the discriminator (which is the square root) is -119. A square root of a negative number is imaginary and not real.
Therefore, the only real zero of the polynomial is -7
The jogging track is 5/9 of a mile long. If ashley jogged around it 4 times, how far did she run?
Hello!
5/9 x 4
= 4x5/9
= 20/9
= 2,2222miles
Answer the following.
CAFES LX-MEN, WIE SEEM TO
NL1.10-Practice Skis Question 10:16549
What is the value of the underlined digit in these numbers?
34.98
67.04
5.614
400.563
0.782
NOFE
The values of the underlined digits in the given numbers are as follows:
1. 8 , 2. 0 , 3. 1 , 4. 3 , 5. 8
To determine the value of the underlined digit in each of the given numbers, let's examine each number separately:
1. 34.98:
The underlined digit is the 8 in the tenths place. It represents 8/10 or 0.8.
2. 67.04:
The underlined digit is the 0 in the hundredths place. It represents 0/100 or 0.
3. 5.614:
The underlined digit is the 1 in the thousandths place. It represents 1/1000 or 0.001.
4. 400.563:
The underlined digit is the 3 in the tenths place. It represents 3/10 or 0.3.
5. 0.782:
The underlined digit is the 8 in the hundredths place. It represents 8/100 or 0.08.
Therefore, the values of the underlined digits in the given numbers are as follows:
1. 8
2. 0
3. 1
4. 3
5. 8
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find the solution set: 3²⁽ˣ⁺¹⁾-8.3ˣ⁺¹=9
Step-by-step explanation:
Not yet sure how to do this other than graphically....
.88893 ~ = x
Find the surface area of a square pyramid with side length 2 cm and slant height 5 cm.
Answer:
24 cm²
Step-by-step explanation:
area of square base = 2 X 2 = 4cm²
area of a triangle = 0.5 X width X vertical height
area of one slanted side = 0.5 X 2 X 5 = 5
there are 4 sides to square pyramid. so area of 4 slanted sides = 4 (5)
= 20cm²
total surface area = 4 slanted sides + base
= (20 + 4)cm²
= 24cm²
a cylinder has a radius of 6cm and is 14cm high calculate its surface area
Answer:
754 cm²
Step-by-step explanation:
The total surface area of a cylinder
= Lateral Surface Area + Top surface area + Bottom Surface Area
Top and Bottom surfaces are both circles
Given radius r and height h
Lateral surface area = 2πrh
Top surface area = Bottom surface area = πr²
Top + Bottom surface area = πr² + πr² = 2πr²
With r = 6 and h = 14 cm
Total surface area
= 2πrh + 2πr²
= 2πr(h + r)
= 2π · 6(14 + 6)
= 12π (20)
= 240 π
≈ 754 cm²
Let's say that you get a $600 tax refund, and you wisely decide to put it into a long-term investment that pays 5% in simple interest each year. How much money would that add up to in your banking account each year? (type your answer as two decimals and its dollar $ units)
Each year, your bank account would accumulate $30 in interest.
A bank account is a financial account provided by a bank or financial institution that allows individuals or businesses to deposit money, make withdrawals, and perform various financial transactions. Bank accounts offer a secure and convenient way to manage and store your money.
To calculate the amount of money that would accumulate in your bank account each year from a $600 tax refund invested at 5% simple interest, we can use the formula:
Interest = Principal * Rate
where:
Principal = $600 (initial investment)
Rate = 5% (0.05 in decimal form)
Interest = $600 * 0.05
Interest = $30
Therefore, each year, your bank account would accumulate $30 in interest.
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Randy divides (2xª − 3x³ − 3x² + 7x − 3) by (x² − 2x + 1) as shown below. What error does Randy make?
2x²+x+3
²-2x+1) 2x²-3x³-3x² +7x-3
2x4-4x3+2x²
x3-5x²+7x
x3-2x²+x
-3x²+6x-3
-3x²+6x-3
O
Randy's error is in the first step of the division, where he subtracts 4x² instead of adding it. The correct subtraction should be: x³ + 2x² + 5x - 3
Randy made an error in the step where he subtracted (2x² - 2x + 1) from (2x² - 3x³ - 3x² + 7x - 3).
Instead of getting -x³ + 4x² + 6x - 4 as the result, he got 2x⁴ - 4x³ + 2x². This error occurred because he forgot to change the sign of all the terms in (x² - 2x + 1) when subtracting it from the polynomial.
It should be (3x³ - 2x² + 7x - 3) divided by (x² - 2x + 1).
Let me proceed with this corrected version of the question.
Randy divides (3x³ - 2x² + 7x - 3) by (x² - 2x + 1) as,
2x² + x + 3
____________
x² - 2x + 1) 3x³ - 2x² + 7x - 3
2x³ - 4x² + 2x
_____________
x³ - 2x² + 5x
x³ - 2x² + x
____________
-3x² + 4x - 3
-3x² + 6x - 3
___________
[tex]-2x^2[/tex] + x - 3
3x³ - 2x² + 7x - 3
-(2x³ - 4x² + 2x)
______________
x³ + 2x² + 5x - 3
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Randy made an error while dividing (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). He mistakenly subtracted intermediate results from zero instead of the original polynomial, leading to an incorrect division.
Randy made an error in his division of the polynomial (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). Let's go through the division process step by step to identify the mistake:
Randy correctly started by dividing 2x⁴ by x², which gives him 2x² as the first term of the quotient.
He then multiplied (x² - 2x + 1) by 2x², which resulted in 2x⁴ - 4x³ + 2x². So far, so good.
Randy should have subtracted this result from the original polynomial (2x⁴ - 3x³ - 3x² + 7x - 3), but he mistakenly subtracted it from 0. The correct step should have been to subtract 2x⁴ - 4x³ + 2x² from (2x⁴ - 3x³ - 3x² + 7x - 3).
Here's the corrected division:
(2x⁴ - 3x³ - 3x² + 7x - 3) - (2x⁴ - 4x³ + 2x²) = -3x³ - 5x² + 7x - 3
Now, Randy should have continued the division by bringing down the next term, which is -3x², and repeated the process. However, he incorrectly moved to the next step without subtracting -3x³ - 5x² + 7x - 3 from (x² - 2x + 1).
So, Randy's error is that he failed to properly subtract the intermediate result from the original polynomial, causing the division process to go awry.
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Determine if each table shown below represents a function or not.
Answer: No
Step-by-step explanation:
The definition of a function includes that each input must have one and only one output
The first graph has the input 5 giving two different outputs so it is not a function
The second graph has the input 7 giving two different outputs so it is not a function
what is the f(x) of y=9x^6+x^4-2x^2-5
Answer:
f(x) is 579.
Step-by-step explanation:
The equation y=9x^6+x^4-2x^2-5 represents a function where y depends on the value of x. To find the f(x) of this function, we simply replace y with f(x), which gives us:
f(x) = 9x^6 + x^4 - 2x^2 - 5
This means that if you plug in a specific value of x, the function will output a corresponding value of f(x). For example, if you plug in x=2, you would get:
f(2) = 9(2)^6 + (2)^4 - 2(2)^2 - 5
f(2) = 9(64) + 16 - 8 - 5
f(2) = 576 + 3
f(2) = 579
So when x is 2, f(x) is 579.
What is the distance of (2,7) and (-5,5
Answer:
7.28 units
Step-by-step explanation:
To find the distance between two points, we use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates given, we can plug in the values:
d = √((-5 - 2)^2 + (5 - 7)^2)
d = √((-7)^2 + (-2)^2)
d = √(49 + 4)
d = √53
Therefore, the distance between (2,7) and (-5,5) is approximately 7.28 units (rounded to two decimal places).
On a piano, the formula to determine the frequency, f. Which of the following is equivalent to f?
The frequency, f, on a piano is equivalent to the pitch or tone of a specific note produced by a vibrating string or air column.
On a piano, the frequency of a particular note can be determined using the formula:
[tex]f = 2^{(n/12) }\times f0[/tex]
In this formula, f represents the frequency of the note, n is the number of half-steps from a reference note, and f0 is the frequency of the reference note.
To understand the equivalences to f, let's break down the formula components:
[tex]2^{(n/12)[/tex]: This part of the formula calculates the factor by which the frequency of the note changes based on the number of half-steps away from the reference note. It uses the exponential function with a base of 2 and raises it to the power of n/12. This term accounts for the logarithmic nature of musical pitch and determines the frequency ratio between two adjacent notes on a piano.
f0: This term represents the frequency of the reference note, which serves as a starting point for the calculation. The reference note is typically A4 (the A above middle C) and has a standard frequency of 440 Hz. However, different tuning systems or historical contexts may use alternative reference frequencies.
Combining these elements, the formula calculates the frequency of a note based on its position relative to the reference note, taking into account the logarithmic nature of musical pitch.
Therefore, "f" in the given formula is equivalent to the frequency of the note being considered on the piano. By plugging in the appropriate values for "n" (the number of half-steps from the reference note) and "f0" (the frequency of the reference note), we can determine the specific frequency of any note on the piano.
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5l, 15l, 30l, 25l,40l find the average
[tex]\underline{ \textbf{Hello !}}[/tex]
[tex]\sf{average = \frac{5+15+30+25+40}{5} =\frac{115}{5} = 23}\\\\{\boxed{\textbf{The~ average~ is~equal~to~23}}[/tex]
Which ordered pair solves this linear system?
Y= -x
Y= 2x
The ordered pair that solves the system of equation is (0, 0).
To solve this system, we can substitute the first equation into the second equation to eliminate y:
x = 2x
Solving for x, we get x = 0.
Substituting x = 0 into the first equation, we get y = 0.
Therefore, the ordered pair that solves the system is (0, 0).
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Please help me with these couple question, I will mark you as brainiest!!!
The value of the functions, f(x) at the specified x-values are;
26. A. -1
27. C. 8
28. B. 1/2
29. A. -176
What is a function?A function is a rule or definition that maps the elements of a set of input variables unto a set of output variables, such that each input maps to exactly one of the elements in the set of the output variables.
26. The function is; f(x) = 3·x² + 2·x - 1
Therefore; f(0) = 3 × 0² + 2 × 0 - 1 = -1
The correct option is therefore;
A. -1
27. The function is; g(x) = (1/2)·x³ + 2·x
Therefore; g(2) = (1/2) × 2³ + 2 × 2 = 8
The correct option is therefore;
C. 8
28. The function is; f(x) = (√(9 - x))/4
Therefore; f(5) = (√(9 - 5))/4 = 1/2
f(5) = 1/2
The correct option is therefore;
B. 1/2
29. The function is; f(x) = (11·(x - 24))/2
Therefore; f(-8) = (11 × ((-8) - 24))/2 = -176
The correct option is therefore;
A. -176
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the blank please
The solution x = 3 and y = 9 means that the point of intersection of the two lines
Other solutions are italicized below
Explaining the solution to the system of equationsThe statement in the question is given as
Solution to a system of linear equation is x = 3 and y = 9
The intersection of the points can be described as
From the origin, move 3 units right and 9 units up
The meaning of the solution is that
The point of intersection of the two lines
Can you have more than one solution to a system of linear equations?
The answer to this is No.
This is because, the lines are straights and they can only intersect once or none at all
Can you have exactyly one solution to a system of linear equations?
The answer to this is also No.
This is because, the lines are straights and they can only intersect once or none at all
Can you have no solution to a system of linear equations?
The answer to this is Yes.
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Welp this question is eating my brain
Hello!
--------------------------------------------------------------------------------------------------------
(a) y = 36° and x = 36°
DAB = 90°
so y = 90° - 54° = 36°
---------------------------------
AB // DC
so x and y are alternate-internal
so x = y = 36°
--------------------------------------------------------------------------------------------------------
(b) y = 73° and x = 68°
SPQ = 90°
so yPQ = 90° - 51° = 39°
the sum of the angles of the triangle PQR = 180°
so y = 180° - (39° + 68°) = 73°
---------------------------------
PSy = 90°
the sum of the angles of the triangle PSy = 180°
so PyS = 180° - (51° + 90°) = 39°
SyxR is a flat angle = 180°
so x = 180° - (39° + 73°) = 68°
--------------------------------------------------------------------------------------------------------
(c) y = 36° and x = 54°
The center of the triangle is K.
So the triangles NKO, MKP, MNK, POK are isosceles
NKO = MKP and MNK = POK
MKP and NKO are opposed
so MKP = NKO = 72°
K is a full angle = 360°
so MKN and PKO = 360° - (72° + 72°) = 216°
so MKN = PKO = 216°/2 = 108°
PMN = y so because MKN is isoscel.
so we know x + y = 90° because PMN = 90°
and so we know PON = OPM = y
and so we know KNO = KON = x
the sum of the angles of the triangle KNO = 180°
so KNO and KON = 180° - 72° = 108°
so x = 108°/2 = 54°
---------------------------------
the sum of the angles of the triangle MKN = 180°
so KMN and KNM = 180° - 108° = 72°
so y = 72°/2 = 36°
--------------------------------------------------------------------------------------------------------
Another question. Please help.
Answer:
[tex]y = - \frac{8}{5}x + 8[/tex]
Answer:
y = - [tex]\frac{5}{3}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 3) and (x₂, y₂ ) = (6, - 2) ← 2 points on the line
m = [tex]\frac{-2-3}{6-3}[/tex] = [tex]\frac{-5}{3}[/tex] = - [tex]\frac{5}{3}[/tex]
the line crosses the y- axis at (0, 8 ) ⇒ c = 8
y = - [tex]\frac{5}{3}[/tex] x + 8 ← equation of line
Which of these is a measure of volume?
1-the amount of foil I need to line my crock pot
2-the amount of soup that I can make in my crockpot
3-the size of the tablecloth I need to cover the dining table
4-the number of slices I can cut from a loaf of bread
Answer:
number 1 : the amount of foil i need to line my crock pot
3. Which sentence is written active voice-not passive voice?
The cheeseburgers were purchased by Micky.
Pizza was suggested instead of cheeseburgers.
O Mickey ate a cheeseburger at lunch instead of pizza.
At lunch, the cheeseburger was eaten by Micky.
Answer:
the cheeseburgers were purchased by micky
Equation
a. ŷ=3x-2
Slope
