The mathematical reasoning for Step 3 is a distributive property.
What is distributive property?It should be noted that the distributive property is the multiplication of the sum of two to more addends by a number that will give same result.
In this case, the mathematical reasoning for Step 3 is a distributive property.
Therefore, the correct option is C.
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Answer: C. Distributive Property
What is the simplified form of the quantity of x plus 6, all over the quantity of x plus 4 + the quantity of x minus 3, all over 3 ? (2 points) the quantity of x squared plus 3x minus 18, all over 3 times the quantity of x plus 4 the quantity of x squared plus 4x plus 6, all over the quantity of x plus 7 the quantity of x squared plus 3x minus 18, all over the quantity x plus 7 the quantity of x squared plus 4x plus 6, all over 3 times the quantity of x plus 4
The simplified expression of the given equation is [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]
There are three basic steps for addition or subtraction of two fractions
Step 1: Make sure the bottom numbers (the denominators) are the sameStep 2: Add the top numbers (the numerators), put that answer over the denominatorStep 3: Simplify the fraction (if possible)The given expression :- [tex]\frac{x+6}{x+4} +\frac{x-3}{3}[/tex]
Taking LCM or making the denominators same we get,
= {3(x+6) + (x-3)(x+4)}/3(x+4)
= {3x + 18 + x² +x -12}/3(x+4)
={x² + 4x + 6}/3x + 12
= [tex]\frac{x^{2} + 4x + 6}{3x + 12}[/tex]
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Answer:
i believe its B
Step-by-step explanation:
Find the z a/2 critical value needed to construct a confidence interval with level .The critical value for the confidence level 90% is.......
( round to two decimal places )
Using the z-distribution, the critical value for a confidence level of 90% is of Z = 1.65.
What is the critical value for a 90% confidence interval using the z-distribution?In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.65.
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3 to 2 if there are 120 children who like pizza, how many total
Answer:
320
Step-by-step explanation:
Is the 3 to 2 part to part? Out of every 5 people, 3 prefer pizza and 2 do not. We can us this to set up a proportion.
3/5 = 120/x The 3 represent the part that like pizza over the whole of 5. The second ratio is showing the actual number of people that liked pizza over the total number of people.
What would be multiply 3 by to get 120? 40. So, we will multiply 5 times 40 to get the total number of people. 5 x 40 = 200
Miguelle is deciding which type of heating system to put in his house. An oil system costs $2700 to install and
$900 per year to operate. A solar system costs $9000 to install and $200 per year to operate.
Determine your variables
Let=
Let=
2. Create your equations and number them.
3.Solve the linear system using ELIMINATION OR SUBSTITUTION.
Answer: (9, 10800)
Step-by-step explanation:
We will first let x be the number of years and y be the total cost.
In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.
The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.
With that in mind, let's create both of our equations:
y = 900x + 2700 (Oil system)y = 200x + 9000 (Solar system)Since y is solved for in the first equation, we can substitute it into the second equation:
[tex]900x + 2700 = 200x + 9000[/tex]
[tex]700x + 2700 = 9000[/tex] [Subtracting 200x from both sides]
[tex]700x = 6300[/tex] [Subtracting 2700 from both sides]
[tex]x = 9[/tex] [Dividing both sides by 700]
We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:
[tex]y = 900(9) + 2700[/tex]
[tex]y = 8100 + 2700[/tex] [Multiplying]
[tex]y = 10800[/tex] [Adding]
Hence, the solution to this linear system is (9, 10800).
The variable y varies directly as x. When x = 20, y = 12. What is the value of ywhen x = 15?
The value of y at x =15 is 9.
What is Direct Variation?Two variables are said to be in Direct Variation when increasing one variable the other also increases.
The direct variation is represented by
y ∝ x
y = kx
where k is the proportionality constant
the value of y =12 , x = 20
12 = k * 20
12/20 = k
k = 0.6
The equation becomes
y = 0.6 x
The value of y at x = 15 is
y = 0.6 * 15
y =9
Therefore, the value of y at x =15 is 9.
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write equation that has base of 3 stretched vertically by factor of 2/3 reflected in y axis, asymptote of y=2 and passes through point (0,3,5)
The exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]
How to determine the equation?An exponential function is represented as:
[tex]y = b^x[/tex]
The base is 3.
So, we have:
[tex]y = 3^x[/tex]
It is stretched vertically by 2/3.
So, we have:
[tex]y = \frac23(3)^x[/tex]
When reflected over the y-axis, we have:
[tex]y = \frac23(3)^{-x}[/tex]
An asymptote of y = 2, makes the function becomes
[tex]y = \frac23(3)^{-x} + 2[/tex]
Lastly, it passes through the point (0, 3.5).
So, we have:
[tex]y = \frac23(3)^{-x+h} + 2[/tex]
This gives
[tex]3.5 = \frac23(3)^{-0+h} + 2[/tex]
[tex]3.5 = \frac23(3)^{h} + 2[/tex]
Subtract 2 from both sides
[tex]1.5 = \frac23(3)^{h}[/tex]
Multiply by 3/2
[tex]2.25 = (3)^{h}[/tex]
Take the logarithm of both sides
log(2.25) = h * log(3)
Solve for h
h = 0.74
Substitute h = 0.74 in [tex]y = \frac23(3)^{-x+h} + 2[/tex]
[tex]y = \frac23(3)^{-x+0.74} + 2[/tex]
Hence, the exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]
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True or false? The graph represents a function.
5
O A. True
O B. False
Select the correct answer from each drop-down menu.
What structural element of the paragraph is the underlined sentence, and how does it connect ideas in the text?
The underlined sentence
1.the thesis statement for the text
2.the conclusion of the text
3.a piece of evidence for the texts argument
4.a piece of reasoning in the text
It connects ideas in the text by
1.making the main claim of the text
describing why the information provided matters to readers
3. relating a fact or story that demonstrates the texts argument
4. suggesting how a specific example relates to the broader argument
The underlined sentence in the text simply functions as; the conclusion of the text and connects ideas in the text, by making the main claim of the text describing why the information provided matters to readers.
What is the function of the underlined text in the passage?The underlined text in the passage functions as the conclusion to the passage in which case, the information intended to be conveyed is that on the occasion that, regular feeding, good housing, occasional gentle corrections and kindness are in place, there'd be no need for such a cat to steal.
Therefore, the structural element of the paragraph in the underlined sentence, and how it connect ideas in the text is; by making the main claim of the text
describing why the information provided matters to readers.
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select the correct answer which graph is defined by f(x)= |x^2 -x-2|
The graph of the absolute value function can be seen below.
How to get the graph of f(x)?Here we have the absolute value function:
[tex]f(x) = |x^2 - x -2|[/tex]
Notice that the argument of the absolute value function is a quadratic equation, then the graph of the function f(x) will be the graph of the quadratic equation, but such that the part below the horizontal axis is reflected.
Then the graph of the function is the one you can see below:
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How many triangles are created in the following situation:
m/A=35°, a = 12,b=16
1 triangle
2 triangles
3 triangles
no triangle
Answer:
Step-by-step explanation:
3 things of triangle are given.
2 sides + 1 angle
so, possible triangles = 1 ans
NO LINKS!! Please help me with this problem.
What is the standard form of the equation of the ellipse?
Answer:
[tex]\dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]
Step-by-step explanation:
From inspection of the given graph, we can see that the center of the ellipse is the origin (0, 0) and the longest diameter of the ellipse is across the x-axis.
Therefore, we can use the general equation of a horizontal ellipse with its center at (0, 0):
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where:
center = (0, 0)Vertices = (±a, 0)Co-vertices = (0, ±b)Foci = (±c, 0) where c²=a²−b²Major Axis: longest diameter (2a)Minor Axis: shortest diameter (2b)Major radius: one half of the major axis (a)Minor radius: one half of the minor axis (b)From inspection of the ellipse:
Vertices = (-7, 0) and (7, 0)Co-vertices = (0, 6) and (0, -6)Therefore, a = 7 and b = 6
Substitute the found values of a and b into the formula:
[tex]\implies \dfrac{x^2}{7^2}+\dfrac{y^2}{6^2}=1[/tex]
[tex]\implies \dfrac{x^2}{49}+\dfrac{y^2}{36}=1[/tex]
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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The given figure shows a Horizontal Ellipse with its centre at origin, and as we observe the figure, we can conclude that :
Length of major axis is :
[tex]\qquad \sf \dashrightarrow \: 2a = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 7[/tex]
and that of minor axis :
[tex]\qquad \sf \dashrightarrow \: 2b = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: b = 6[/tex]
Equation of Ellipse will be ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {a}^{2} } + \dfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
[ plug in the values ]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {7}^{2} } + \dfrac{ {y}^{2} }{ {6}^{2} } = 1[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{2} }{ {49}^{} } + \dfrac{ {y}^{2} }{ {36}^{} } = 1[/tex]
Find the length of a segment in the coordinate plane with endpoints (-4,-5) and (8, 1).
Answer:
Step-by-step explanation:
d = 13.416408
For:
(X1, Y1) = (-4, -5)
(X2, Y2) = (8, 1)
Answer:
L = 9.49 units
Step-by-step explanation:
From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6. These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:
12^2 = 144 and 6^2 = 36.
Combining these results in the length of the diagonal:
L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem
Rounding off, we get L = 9.49 units
which of the following statements is true about the solution of the system? 2x-y=8 and y=2x-3
Answer:
no roots.
Step-by-step explanation:
[tex]\left \{ {{2x-y=8} \atop {y=2x-3}} \right. \ = > \ \left \{ {{2x-y=8} \atop {2x-y=3}} \right. \ = > \ no \ solution.[/tex]
Your local pizza store sells medium pizzas for $6.79 each, and breadsticks for $2.49 per order.
For a party, you decide to order 4 pizzas and 2 orders of breadsticks. There is a $3 delivery fee, and a 9.4% sales tax will be added to the total. What will be the total bill after tax?
The total bill after tax is $38.44.
What is the total bill?The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14
Now, determine the total cost after delivery fee has been added : $3 + $32.14 = $35.14
Now determine the total cost after tax : (1.094) x $35.14 = $38.44
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The total bill after tax of 9.4% is $38.44.
It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price
total cost of 4 pizzas= $6.79 *4
total cost of 4 pizzas=$27.16
total cost of 2 orders of breadsticks=$2.49*2
total cost of 2 orders of breadsticks=$4.98
total cost of purchase prior to adding delivery cost=$27.16+$4.98
total cost of purchase prior to adding delivery cost=$32.14
total cost of purchase after delivery cost=$32.14+$3
total cost of purchase after delivery cost=$35.14
total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)
total cost inclusive of 9.4% sales tax=$35.14*1.094
total cost inclusive of 9.4% sales tax=$38.44
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Suppose that X-N (2,6) is a normal distribution with mean 2 and standard deviation 6. What value of x has a z-score of three?
The value of x has a z-score of three is 20
How to determine the value of x?The given parameters are:
Mean = 2
Standard deviation = 6
z = 3
The z-score is calculated as:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]3 = \frac{x -2}{6}[/tex]
Multiply through by 6
18 = x - 2
Add 2 to both sides
x = 20
Hence, the value of x has a z-score of three is 20
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35 Please help with this question.
The critical values are 0.622, 0.707, 0.789 and 0.834
How to determine the critical values?The sample size is given as:
n = 8
Calculate the degrees of freedom using
df = n - 2
So, we have:
df = 8 - 2
df = 6
Using the table of values of critical values, we have:
Critical values = 0.622, 0.707, 0.789 and 0.834
By comparing the critical values and the linear correlation coefficient, we can conclude that there is no significant linear correlation.
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The pH of a fruit juice is 5.6. Find the hydronium ion concentration, [H3O+], of the juice. Use the formula pH=-log[H3O+].
The hydronium ion concentrate H 30 plus as approximately? moles per liter
The hydroxonium ion concentration of the fruit juice whose pH as given in the task content is; 5.6 can be evaluated as; [H3O+] = 2.51 × 10^-6.
What is the hydroxonium ion concentration of the fruit juice whose pH is 5.6?Since the given pH of the fruit juice is 5.6, the hydroxonium ion concentration of the fruit juice can be evaluated by means of the formula as follows;
pH=-log[H3O+].
5.6 = -log[H3O+].
-5.6 = log[H3O+].
[H3O+] = antilogarithm (-5.6)
[H3O+] = 2.51 × 10^-6.
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Graph the line Y=2/5X+5
After defeating the fire breathing dragon, the knight decides
to celebrate his victory with a celebratory goblet made out of Dragon Alloy #17, which is 36% gold, 9% silver, and 55% magic steel. The dwarves have Dragon Alloy #11, which is 36% gold, 28% magic steel, and the rest silver. They also have Dragon Alloy #15, which is 36% gold and 64% magic steel. How many grams of each
alloy should the dwarves combine to get 1 kg of Dragon Alloy #17?
250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:
(0.36x) + (y * 0.36) = 1(0.36) (1)
Also:
0.28x + 0.64y = 1(0.55) (2)
From both equations:
x = 0.25, y = 0.75
250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.
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You have a $10,000, you must choose between Gamble A and Gamble B. Gamble A will cost $5,000. If you win, you will get $15,000, but if you lose, you will get nothing. On the other hand, Gamble B will cost $10,000 that will give $30,000 if you win, otherwise get nothing if lost. You are risk averse, and your preference for wealth (W) is specified by the relationship U(W)= √W. Probability of wining is 0.4 and losing is 0.7. Which gamble will you choose and why?
A pie with a temperature of 140∘F is taken out of the oven and placed on a windowsill to cool. Its temperature as a function of t minutes is given by
T(t)=68e−0.0174t+72
How long, to the closest minute, will it take for the pie to cool to 80∘F?
The time taken to the closest minutes for the pie to cool to 80∘F is 123 minutes
TemperatureT(t) = 68e^−0.0174t + 72
80 = 68e^−0.0174t + 72
80 - 72 = 68e^−0.0174t
8 = 68e^−0.0174t
e^−0.0174t = 8/68
e^−0.0174t = 0.11764705882352
take natural log of both sidesln e (−0.0174t) = ln (0.11764705882352)
1 × −0.0174t = -2.1400661634962708
-0.0174t = -2.1400661634962708
divide both sides by -0.0174t = -2.1400661634962708 / -0.0174
t = 122.9923
Approximately,
t = 123 minutes
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correct the error 4⁴- 4³=4¹
The error is that
[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]
Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.
Given that L1 || L2, find the measures of angles a and b when 0 = 43°
Answer:
a = 43 degrees
b = 137 degrees
Step-by-step explanation:
according to the alternate interior angle theorem, angle a equals angle theta, so angle a = 43 degrees
angle b is the supplement of angle a, so angle b = 180-angle a, or 137
If someone could help me with this problem
The equation of the given Absolute Value Function is; y = |-2x + 4|
How to interpret Linear Graphs?We can see that the given graph is a Linear graph but since it is V-shaped, we can say that it is a graph of an absolute value function.
Now, from the graph we see that;
At x = 0, y = 4
At x = 1, y = 2
At x = 2, y = 0
At x = 3, y = -2
At x = 4, y = 0
At x = 5, y = 2
We can see that the y-intercept is at y = 4.
Slope between two consecutive points is;
(2 - 4)/(1 - 0) = -2
Equation is; y = -2x + 4
Now, this is an absolute value function and as such we will write it as;
y = |-2x + 4|
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Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
√29x6
Name? [? ]
Degree? [
I need help with the slope
Answer:
1/5 :D
Step-by-step explanation:
Lets pick 2 point on the graph :)
We need this to find the slope!
Lets use (-5,1) and (0,2) :)
First we subtract the y coordinates! :)
2 - 1 = 1
Then we subtract the x coordinates!
0 - (-5) = 5
Now we divide!
1/5
Our answer is 1/5!
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
first choice : 1/5
Step-by-step explanation:
need 2 points
one point is (0,2)
another is (5,3)
slope formula is
y2 - y1 / x2 - x1
3 - 2 / 5 - 0
1/5
The equation y=123.1(1.065)* models the number of college students (in thousands) who studied abroad each year from 1998 through 2013. In this equation, y is the
number of students from a certain country studying abroad (in thousands) and x represents the number of years after 1998.
a. Estimate the number of students studying abroad in 2003.
b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.
The estimate of the number of students studying abroad in 2003 is 169 and the estimate of the number of students studying abroad in 2018 is 433
a. Estimate the number of students studying abroad in 2003.The function is given as:
y = 123(1.065)^x
Where x represents years from 1998 to 2013
2003 is 5 years from 1998.
This means that
x = 5
Substitute the known values in the above equation
y = 123(1.065)^5
Evaluate the exponent
y = 123 * 1.37008666342
Evaluate the product
y = 168.520659601
Approximate
y = 169
Hence, the estimate of the number of students studying abroad in 2003 is 169
b. Assuming this equation continues to be valid in the future, use this equation to predict the number of students studying abroad in 2018.2018 is 20 years from 1998.
This means that
x = 20
Substitute the known values in the above equation
y = 123(1.065)^20
Evaluate the exponent
y = 123 * 3.52364506352
Evaluate the product
y = 433.408342813
Approximate
y = 433
Hence, the estimate of the number of students studying abroad in 2018 is 433
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In math class, James, Hadley, and Gwen were challenged to go stand on the field in a random location and find the distance between themselves using only one length. They were also each given a protractor to find the angle between each other. Using this diagram, solve for the missing side lengths of the triangle. Round to the nearest hundredth. A triangle where James, Hadley, and Gwen are labelled on the vertices. The angle of James is 61 degrees, Hadley is 73 degrees, and Gwen is 46 degrees. The one length that is labelled is between James and Hadley and measures at 15 meters. Gwen to Hadley is what? Gwen to James is what?
The interior angles of the triangle of 61°, 73°, and 46°, and the distance from James to Hadley of 15 meters gives;
Gwen to Hadley ≈ 18.24 metersGwen to James ≈ 19.94 metersHow can the distances between the students be found?The given angles are;
At James's location; 61°
At Hadley's location; 73°
At Gwen's location; 46°
The distance between James and Hadley = 15 meters
The angle facing the distance between James and Hadley is the angle at Gwen, 46°
The angle facing the distance between Gwen and James is the angle at Hadley, 73°
The angle facing the distance between Gwen and Hadley is the angle at James, 61°
The angle that faces the 15 meter length is the angle at Gwen, which is 46°
By the rule of sines, the distance from Gwen to Hadley is therefore;
[tex] \frac{15}{sin( 46 ^ \circ)} = \frac{Gwen \: to \: Hadley}{sin( 61 ^ \circ)} [/tex]
Which gives;
[tex] Gwen \: to \: Hadley= \frac{15 \times sin( 61 ^ \circ) }{sin( 46 ^ \circ)} \approx 18.24[/tex]
Gwen to Hadley ≈ 18.24 metersSimilarly, we have;
[tex] \frac{15}{sin( 46 ^ \circ} = \frac{Gwen \: to \: James}{sin( 73 ^ \circ)} [/tex]
Therefore;
[tex] Gwen \: to \: James = \frac{15 \times sin( 73 ^ \circ) }{sin(46 ^ \circ)} \approx 19.94 [/tex]
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Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Answer:
14 days
Step-by-step explanation:
let assume they both work on Monday (today)
devin works every 7 days,that is devin works every Monday.
jamie has to work for 14 days inorder to work with devin again
90. Find 33.3% of 81.