Answer:
m=[tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The slope is found with the equation m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]:
[tex](x_1,y_1)=(3,1)\\(x_2,y_2)=(1,4)\\m=\frac{(4)-(1)}{(1)-(3)}\\m=\frac{3}{-2}[/tex]
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
272 bison
Step-by-step explanation:
y(5)=240[tex](1+0.025)^{5}[/tex]
y(5) = 271. 5 bison ≈272 bison
Givenf(x)=4x^2 - 1, and g(x) = 2x - 1, find g(f(2)).
Given f(x) = x^2 and g(x)=x - 1, write each composite function.State the domain of each:2.f(g(x)) 3.g(f(x))
The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(x) = 4x² - 1. and g(x) = 2x - 1.
Now, g(f(2)) is the output of f(2) is the input of g(x).
∴ f(2) = 4(2)² - 1.
f(2) = 15.
Now, g(f(2)) = 2(15) - 1.
g(f(2)) = 29.
Also given,
f(x) = x² and g(x) = x - 1.
Now, 2.f(g(x)).
2.f(g(x)) = 2.f(x- 1).
2.f(g(x)) = 2(x - 1)².
2.f(g(x)) = 2(x² - 2x + 1).
2.f(g(x)) = 2x² - 4x + 2.
2.f(g(x)) = 2x² - 2x - 2x + 2.
2.f(g(x)) = 2x(x - 1) - 2(x - 1).
2.f(g(x)) = (x - 1)(2x - 2).
There is no restriction to the domain of this quadratic function.
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A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is
Select one:
a. S = {$0, $1, $2, $3}
b. S = {$0, $3, $6, $9}
c. S = {-$2, $1, $4, $7}
The sample space S for the net amount you win (after deducting the cost of pay) is S = {-$2, $1, $4, $7}.
What is cost?
A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to obtain it.
Let, a game consists of drawing three cards at random from a deck of playing cards.
You win $3 for each red card that is drawn.
It costs $2 to play.
After deducting the cost of pay the amount will start from -$2.
For first red card drawn you win $3.
So, the amount becomes, -$2 + $3 = $1.
For second red card drawn you again win $3.
So, the next amount becomes $1 + $3 = $4.
For third red card drawn the amount becomes,
$4 + $3 = $7.
Hence, the sample space S for the net amount you win is
S = {-$2, $1, $4, $7}.
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Find the perimeter of a quadrilateral with the following vertices.
(−6, −2), (0, −10), (5, 2), (−1, 10)
a.40
b.52
c.23
d.46
The perimeter of the quadrilateral is 46 units, so the correct option is d.
How to find the perimeter of the quadrilateral?The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.
Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:
L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
The length between the first two vertices: (−6, −2), (0, −10)
L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10
The length between the second two vertices: (0, −10), (5, 2)
L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13
The length between the third two vertices: (5, 2), (−1, 10)
L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10
The length between the fourth two vertices: (−1, 10), (−6, −2)
L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13
Then the perimeter is:
P = 10 + 13 + 10 + 13 = 46
The correct option is D.
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Simplify. Rewrite the expression in the form y^n. y^5/y^3=
Answer:
y^2
Step-by-step explanation:
a^m/a^n = a^(m - n)
y^5/y^3 = y^2
The minimum monthly payment for Brian's credit card is 3.5% of his balance or $25, whichever is higher. If Brian's balance at the end of his last billing cycle was $722, what is his minimum monthly payment?
The minimum monthly payment for Brian is $25.
How to find the minimum payment?The minimum payment is the smallest amount of money you must pay each month to maintain the status of your account. The statement balance is your total account balance for that billing cycle. The current balance is the sum of your most recent bill plus any charges.
From the information, the minimum monthly payment for Brian's credit card is 3.5% of his balance or $25
Since the balance was $722, the amount will be:
= 3.5% × $722
= 0.035 × $722
= $25.27
Since $25.27 is more than $25, the minimum monthly payment is $25.
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observations 1 2 3 4 5 6 num. of defects 10 18 13 15 9 12the number of runs up and down for the preceding data is:
The number of runs up and runs down for the preceding data is 5.
What is runs up ?Runs up refers to the number of observations that are higher than the number of observations before them.
What is runs down ?Runs down refers to the number of observations that are lower than the number of observations before them.
As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.
Therefore,
Runs up = 2nd + 4th + 6th observations
= 3
As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down
Therefore,
Runs down= 3rd +5th observations
=2
Therefore,
Runs up + Runs down =3+2
=5
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Choose the equation for the line in slope-intercept form. A graph of a diagonal line on a coordinate plane going up and to the right. The line passes through the points zero comma negative 3 and 2 comma negative 2. y=2x+3 y=12x+3 y=12x−3 y=−12x−3
The soccer field is 105 meters long. The football field is 120 yards long. Which is longer?
The football field is longer than soccer field.
What is a expression? What is a mathematical equation? What is unit conversion?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
We have a soccer field that is 105 meters long and a football field is 120 yards long.
In one yard, we have -
1 yard = 0.9144 meters
Then, in 120 yards, we will have -
120 x 0.9144 = 109.728 meters
Now, 109.728 meters > 105 meters.
Therefore, the football field is longer than soccer field.
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the sum of two number 12 when three times the first number is added to 5 times the second number the results is 44
Answer:
one number is 8 and other is 4
Step-by-step explanation:
So we can say x+y=12.
And 3x+5y=44
For x+y=12, we can subtract x to get: y=12-x
Plug that in to get 3x+5(12-x)=44
3x+60-5x=44
Subtract 44: -2x+16=0
2x=16
x=8
12-8=4.
Answer to this question
In the picture
[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]
PLEASE HELP 50 POINTS
The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)
How to find an expression equivalent to another trigonometric expressionIn this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:
cos 3x / (sin x · cos x)
Second, use trigonometric formulas:
cos (x + 2x) / (sin x · cos x)
(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)
cos 2x / sin x - sin 2x / cos x
csc x · cos 2x - sec x · sin 2x
The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.
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Find the equation of a line that passes through the points (1,2) and (5,6). Leave your answer in the form y = m x + c.
The formula for the line passing through the intersection of (3, 2) and A B (5 , 6) equals y = 2x - 4
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.
We will comprehend the slope-finding method and its applications in this article
According to our question-
Let A be the initial point ( 3 , 2 )
Let B be the second point ( 5 , 6 )
A ( x₁ , y₁ ) = A ( 3 , 2 ) ( 3 , 2 )
B ( x₂ , y₂ ) = B ( 5 , 6 ) ( 5 , 6 )
The slope of the line is now determined by,
Slope m is equal to (y2 - y1) / (x2 - x1)
By changing the values, we obtain
Slope m is equal to (6 - 2)/(5 - 3)
= 4 / 2
= 2
Slope of the line therefore equals 2.
The equation for the line is now y - y1 = m (x - x1).
By changing the values, we obtain
y - 2 = 2 ( x - 3 ) ( x - 3 )
y - 2 = 2x - 6
2 is added to both sides of the equation to get
y = 2x - 4
HENCE, The formula for the line passing through the intersection of (3, 2) and A B (5 , 6) equals y = 2x - 4.
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HELP LIKE ASAP
WXY is the image of RST after a translation 3 units up. Select all of the statements that are always true.
options:
_ The length of side TR equals the length of side WX
_ The length of side RS equals the length of side WX
_ The measure of angle R equals the measure of angle W
_ The measure of angle R equals the measure of angle X.
The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.
What is translation transformation?A geometry translation is an isometric transformation, meaning that the original figure and the image are congruent.
Given that, WXY is the image of RST after a translation 3 units up.
As we know in translation, both figures are congruent so, we have,
WX = RS
XY = ST
WY = RT
And
∠ R = ∠ W
∠ S = ∠ X
∠ T = ∠ Y
Hence, The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.
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will the line y=4x+1 pass through the point (2,9)?
Answer: Yes
Step-by-step explanation:
y=4x+1
(2,9) 2 is x, 9 is y
9=4(2)+1
9=8+1
9=9
If X is the midpoint of TV, TV bisects RS, and TR is parallel to VS, state five pairs of objects (segments or angles) that must be congruent and give a reason why for each pair.
According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Alternate Interior Angle Theorem?According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.Is it true or false that different interior angles are always congruent? Although untrue, this assertion is a typical misunderstanding. Keep in mind that when the lines are parallel, alternate inner angles are congruent.Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposing sides of the transversal when two lines are crossed by another line (referred to as the Transversal). These two pairs of alternate interior angles in this illustration are c and f.To learn more about Congruent refer to:
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5. What is the value of 6(x-2)(x-3) + 4(x-2)(x - 5) when x = -3?
Answer:
340Step-by-step explanation:
[tex]\tt 6(x-2)(x-3) + 4(x-2)(x - 5)[/tex]
When, x = -3
----------------------------------------------
To find the value of 6(x-2)(x-3) + 4(x-2)(x - 5), we need to substitute x with -3.
[tex]\tt 6\left(-3-2\right)\left(-3-3\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]
[tex]\tt (6)(-5)(-3-3)+4(-3-2)(-3-5)[/tex]
[tex]\tt -30\left(-6\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]
[tex]\tt -30\left(-6\right)+4\left(-5\right)\left(-3-5\right)[/tex]
[tex]\sf -30\left(-6\right)+4\left(-5\right)\left(-8\right)[/tex]
[tex]\tt 180+4\left(-5\right)\left(-8\right)[/tex]
[tex]\tt 180-\left(-160\right)[/tex]
[tex]\tt 180-\left(-160\right)[/tex]
[tex]\tt =340[/tex]
Therefore, the value of 6(x-2)(x-3) + 4(x-2)(x - 5) is 340!
____________________
Hope this helps!
Have a great day!
Question
Solve for p.
2(p+1)=18
Responses
p = 8
p, = 8
p = 8.5
p, = 8.5
p = 9.5
p, = 9.5
p = 10
Answer:
p=8
Step-by-step explanation:
[tex]2(p+1)=18\\\frac{2(p+1)}{2}=\frac{18}{2}\\p+1=9\\p+1-1=9-1\\p=8[/tex]
Answer:P=8
Step-by-step explanation:
I TOOK THE TEST
I need help im a little confused
Answer:
p=45-2.5f
Step-by-step explanation:
5f+2p=90
We have to isolate p in one side
5f+2p=90
-5f. -5f
2p=90-5f
/2. /2. /2
p=45-2.5f
Hopes this helps please mark brainliest
use strong induction to show that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20
MAIN ANSWER: using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴
supporting answer The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the
2²=4
2⁴=16
4+16=20
final answer is 20=2²+2⁴
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Using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴
What is positive integer?
Natural numbers are those in mathematics that are utilised for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering.
The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the
2²=4
2⁴=16
4+16=20
Final answer is 20=2²+2⁴
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Brody loves to read, and he counts the number of books he reads each year. This year, he used a graph to keep track of the books he read. By his birthday, he read 15 books. The following graph shows how many books he read for the months following his birthday.
How many books does Brody read each month?
Brody reads 8 books each month.
What is the slope of a line?The slope of a line indicates the direction and the steepness of the line. The formula for the slope of a line passing through the points (x₁,y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁).
Give the graph of the line.
The graph of the line passes through points (0,15) and (5,55)
To find the number of books Brody read each month, find the slope of the line.
The slope of the line is:
m = (55 - 15)/ (5 - 0)
m = 8
Hence, Brody reads 8 books each month.
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18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product? Circle the letter of the correct answer.
The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)
Writing an expression using the Greatest common factor and distributive propertyFrom the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.
The given expression is
18 + 24
First, we will determine the greatest common factor of 18 and 24
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Thus,
The greatest common factor is 2 × 3 = 6
Now, we will write the expression using the greatest common factor and the distributive property
18 + 24
6(3 + 4)
Hence, the expression is 6(3 + 4)
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Graph the solution to the inequality on the number line.
Solution to the inequality on the number line is y < 4 and y > −4.
What is inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
When resolving an inequality, you can do one of the following:
• Add the same amount to each side;
• Subtract the same amount from each side;
• Multiply or divide each side by the same positive amount.
You must flip the inequality symbol if you multiply or divide each side by a negative number.
Let's solve your inequality step-by-step.
|y| < 4
Solve Absolute Value.
|y| < 4
We know y < 4 and y > −4
y < 4 (Condition 1)
y > −4 (Condition 2)
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An airline estimates that the probability that a random call to their reservation phone line result in a reservation being made is 0.31. You want to estimate the probability that exactly one of the next four calls result in a reservation being made. Describe the design of a simulation to estimate this probability. Explain clearly how you will use the partial table of random digits below to carry out your simulation.
The probability that exactly one of the next four calls results in a reservation being made is 40.75%
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
A random call to their reservation phone line results in a reservation being made is 0.31
Now, we find
Exactly one call gets resevervation = 4 * (1-0.31)3(0.31)
= 0.4075 = 40.75%
Now we can simulate an experiment by using random numbers from 0 to 100,000 as probability values between 0 and 31,000 are p to reservation otherwise they don't.
Hence, the probability that exactly one of the next four calls results in a reservation being made is 40.75%
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The points A, B, and C, shown on the number line, have weights 1, 1,
and 3 respectively.
A=2 B=4 C=7
What is the weighted average of points A, B, and C?
O 1.33
O 4.33
O 5.4
O 9.0
Answer:
4.33
Step-by-step explanation:
See picture attachment.
The weighted average of points is M = 5.4
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the weighted average be represented as M
Now , the value of M is
The points A, B, and C, shown on the number line, have weights 1, 1,
and 3 respectively.
A = 2 , B = 4 and C = 7
To find the weighted average of points A, B, and C with the given weights, we need to use the formula:
The weighted average M = (weight of A * value of A + weight of B * value of B + weight of C * value of C) / (total weight)
Plugging in the given values, we get:
The weighted average M = (1 * 2 + 1 * 4 + 3 * 7) / (1 + 1 + 3)
The weighted average M = (2 + 4 + 21) / 5
The weighted average M = 27 / 5
The weighted average M = 5.4 (rounded to one decimal place)
Hence , the weighted average of points A, B, and C with the given weights is 5.4
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After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t) = 1. 35te−2. 802t † models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink). A. What is the maximum average BAC during the first 3 hours? (Round your answer to three decimal places. ) mg/mL b. When does it occur? (Round your answer to two decimal places. ) h
The maximum average BAC during the first 6 hours is about 0.177 mg/ml.
What is average ?
The middle number in a group of numbers is the average value, which is determined by dividing the sum of all the values by the variety of values.
When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
The maximum is found where the derivative of C(t) is zero.
dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0
Solving for t gives ...
t = 1/2.802
So, the maximum C(t) is ...
C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL
The maximum average BAC during the first 6 hours is about 0.177 mg/mL.
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Bob bad $50. he spent $28.67 for a new backpack. How much money does he have left?
Answer: $21.33
Step-by-step explanation: 50 - 28.67 = 21.33
1. Write two equivalent expressions to represent the area of this rectangle.
2. Write two equivalent expressions to represent the perimeter of this rectangle.
(pls add an explanation)
The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Here, perimeter =2(x-2+5)
= 2(x+3)
= 2x+6 units
Area of a rectangle =length × width
= (x-2) × 5
= 5x-10 square units
Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.
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Vivi needs to solve the system of equations below using elimination.
4× + 6y =-14
-× +3y=-10
Which correctly describes a possible first step Vivi could take?
D. Multiply each term in the 2nd equation by 2.
b. Multiply each term in the 2nd equation by -4.
C. Multiply each term in the 2nd equation by 4.
d. Both a and c could work.
A possible first step Vivi could take is multiply each term in the second equation by 2 and she can also multiply each term in the second equation by 4. The correct option is d. Both a and c could work.
Elimination method: Determining a possible first stepFrom the question, we are to determine the statement that correctly describes a possible first step Vivi could take
From the given information,
The given system of equations is
4x + 6y = -14
-x + 3y = -10
To eliminate y, we can multiply each term in the second equation by 2 and then subtract
2 × [-x + 3y = -10
-2x + 6y = -20
Then, subtract
4x + 6y = -14
-{ -2x + 6y = -20
------------------------
6x = 6
To eliminate x, we can multiply each term in the second equation by 4 and add the equations,
4 × [-x + 3y = -10
-4x + 12y = -40
Then, add
4x + 6y = -14
+{ -4x + 12y = -40
--------------------
18y = -54
Hence, we can multiply each term in the second equation by 2 and we can also multiply each term in the second equation by 4.
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A boat travels about 6 kilometers per hour in still water. If the boat is on a river that flows at a constant speed of
kilometers per hour, it can travel at a speed of (6+r) kilometers per hour downstream. On one particular river, a
boat travels 12 kilometers down stream. The amount of time it takes the boat travel depends on the speed of river
and is expressed by the equation t(r) =
12
(6+r)
The graph is shown below.
What does t(3) mean in this situation?
At what value of r does the graph have a vertical asymptote? Explain
how you know and what this asymptote means in this situation.
The function in the context of this problem is modeled as follows:
t(r) = 12/(6 + r)
In which the input and output of the function are given, respectively, by:
r is the velocity of the river.t(r) is the time it takes to cross the river considering the given velocity.Then the numeric value at t = 3 represents the time in hours it takes for the boat to cross the river when the velocity of the river is of 3 kilometers per hour.
What is the vertical asymptote of the function?The vertical asymptote of a function are the values of the input for which the function is not defined.
A fraction is not defined at the zeros of the denominator, hence:
t + 6 = 0
t = -6 is the vertical asymptote of the function.
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