24. OPEN-ENDED Complete the table so that when t is the
independent variable, the relation is a function, and when
t is the dependent variable, the relation is not a function.
Answers
The following table shows how the relation is a function when t is the independent variable and not a function when t is the dependent variable:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
A vertical line drawn from the independent variable axis (x-axis) meets the function graph only once because a function is a relationship between an input and an output in which each input has just one output.
The independent variable is the input, while the dependent variable is the output.
Filling out the table in such a way that when t is the independent variable, the relationship is a function, and when t is the dependent variable, the relation is not a function, results in the following table:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
Given that each value of the independent variable t has a corresponding value of the velocity v, the aforementioned is a function.
However, when t is the dependent variable, the independent variable value of 1 produces two outputs of 1 and 5, which results in the following table:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
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Related Questions
5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts
are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three
complete sentences, explain how the graphs of the functions for the two months are similar
and how they are different.
Answers
The function exists
Last month: 2x + 3y = 1,470
Next month: 2x + 3y = 1,593
What is meant by functions?An expression, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable)
Given: Profit of every sandwich = $2
Profit of every wrap = $3
Let x be the number of sandwich and
y be the number of wrap
Last month: 2x + 3y = 1,470
Next month: 2x + 3y = 1,593
Both still have the same profit. $2 for sandwiches and $3 for wraps.
The only reason why there exists a difference in the total amount exists the change in the number of sandwich or wrap sold in a given month.
Therefore, the next month's total sale exists higher than last month's total sale, it exists safe to assume that the sale of sandwich or wrap exists higher than last month's sale.
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Determine if the equation is linear. If so graph the function (x+y=1)
Answers
Answer:
The equation is linear
Step-by-step explanation:
Make the equation in y=mx+b form
which is y=-x+1 and because the x is not the first power it must be linear
Graph:
PLEASE HELP URGENT HELP PLEASE!!!!!!!!!!!!!!!!
Answers
Answer:
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
Step-by-step explanation:
separate y from everything
[tex]w = y(h - 5c^{3})[/tex]
now divide everything by the thing in the parenthesis
[tex]\frac{w}{h - 5c^{3}} = y[/tex]
now flip it
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
that is your answer
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Answers
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]4x^2+10x-4 divided by 2x-1
Answers
The division of 4 · x² + 10 · x - 4 by 2 · x - 1 is equal to (2 · x + 6) + 2 / (2 · x - 1).
How to divide a polynomial by algebra properties
In this problem we find a second grade polynomial, also known as quadratic function, being divided by a first grade polynomial, also known as linear function. The complete procedure is shown below:
4 · x² + 10 · x - 4 Given4 · x² - 2 · x + 12 · x - 4 Definition of subtraction / Distributive property(4 · x² - 2 · x) + (12 · x - 6) + 2 Existence of additive inverse / Modulative, commutative and associative property2 · x · (2 · x - 1) + 6 · (2 · x - 1) + 2 Definition of power / Definition of multiplication / Distributive property(2 · x + 6) · (2 · x - 1) + 2 Distributive and commutative properties(2 · x + 6) + 2 / (2 · x - 1) Dividing (5) by (2 · x - 1) / ResultThe resulting polynomial is (2 · x + 6) + 2 / (2 · x - 1).
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Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their respective distances traveled after x hours is represented in the table and graph below.
Answers
Solution
- In order to find which of the trains is moving faster, we should calculate the average speeds of both trains and compare them.
- The y-values of both trains are the Distance in Miles and the x-axis is the time in hours.
- Thus, the best way to calculate their average speeds is to find the slope of both datasets.
- The formula for calculating the slope is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ (x_1,y_1)\text{ and (}x_2,y_2)\text{ are coordinates chosen} \end{gathered}[/tex]- Thus, with the above information, we can proceed to solve the question
Speed of Coal Freight Train:
[tex]\begin{gathered} \text{ Choosing } \\ (x_1,y_1)=(1,49) \\ (x_2,y_2)=(2,98) \\ \\ m_C=\frac{y_2-y_1}{x_2-x_1}=\frac{98-49}{2-1} \\ \\ \therefore m_C=49\text{miles per hour} \end{gathered}[/tex]Speed of Grain Freight Train:
[tex]\begin{gathered} \text{Reading off the graph that passes through the origin, we choose:} \\ (0,0)\text{ and }(1,45) \\ \\ \therefore m_G=\frac{45-0}{1-0}=45 \\ \\ m_G=45\text{miles per hour} \end{gathered}[/tex]- From the above calculations, we can easily observe that the Speed of the Coal Freight Train is greater than the speed of the Grain Freight Train
Final Answer
"The Coal Freight Train is traveling at a faster speed" (OPTION 2)
15. Name the indicated parts of this diagram.AC __________________AE __________________DE __________________AB __________________ADE __________________________ACE = _______°CAB = _______°
Answers
SOLUTION:
We want to name the indicated parts on the diagram, their names are;
For the angles, we have;
[tex]\begin{gathered} \measuredangle ADE=22^o\text{ }(Inscribed\text{ }Angle) \\ \measuredangle ACE=44^o\text{ }(Central\text{ }Angle) \\ \measuredangle CAB=90^o\text{ }(Angle\text{ }between\text{ }radius\text{ }and\text{ }tangent) \end{gathered}[/tex]A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
If a bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. The height of the 7th bounce of the ball is 0.7.
Determining the height of the ballGiven data:
First bounce = 3.75 feet
Successive bounce = 79% or 0.79%
Bounce = 7
Now let determine the height of thee 7th bounce of the ball using this formula
Height = First bounce × (Successive bounce) ^ Number of bounce
Let plug in the formula
Height = 3.75 × (0.79 ) ^7
Height = 0.7
Therefore the height is 0.7.
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v - 4 > 22 solve the inequality of v and simplify your answer as much as possible. plsssss do this!!!
Answers
Answer:
v > 26
Step-by-step explanation:
v > 22 + 4
v > 26
there is no qouificient ( I don't know how to spell that) of v so that's your answer
What are the vertex and range of y = |x 2| − 3? (−2, −3); −[infinity] < y < [infinity] (−2, −3); −3 ≤ y < [infinity] (0, −1); −[infinity] < y < [infinity] (0, −1); −3 ≤ y < [infinity]
Answers
(x,y) = (1,14).
A parabola's vertex is the location where its symmetry line and parabola intersect. The range of values that we are permitted to enter into our function is known as the domain of a function.
What is the definition of vertex form?A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, which, when graphed, results in a parabola.Locate a parabola's vertex,Finding a parabola's vertex Standard FormComparing the parabola's equation to the formula y = ax2 + bx + c in standard form is the first step.Step 2: Apply the formula h = -b/2a to find the vertex's x-coordinate.Step 3: Substitute x = h in the calculation ax2+ bx + c to obtain the vertex's y-coordinate (k). The range of values that we are permitted to enter into our function is known as the domain of a function.To learn more about Parabola Vertex refer to:
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Given the circle below, find the value of x.251L (9x+26)*
Answers
Given the following:
Then:
[tex]a=\frac{b-c}{2}[/tex]In this case, we are given:
a = (9x + 26)
b = 251
To find c, we rest a whole circle (360) and rest angle b:
[tex]c=360-251=109[/tex]And now, we use the formula from above:
[tex]9x+26=\frac{251-109}{2}[/tex]And solve for x:
[tex]\begin{gathered} 9x+26=\frac{142}{2} \\ . \\ 9x=71-26 \\ . \\ x=\frac{45}{9} \\ . \\ x=5 \end{gathered}[/tex]The answer is the last option, x = 5
Water flows through a pipe at a rate of 7 liters every 9.5 hours. Express this rate of
flow in pints per week. Round your answer to the nearest whole number.
Answers
The rate of water flow per week is 124 liters.
What is the of water flow?
Running water naturally travels along the slope in a direction determined by gravity. This is referred to as a water flow.
Given is, the water flows through a pipe at a rate of 7 liters every 9.5 hours.
So,
water flows per hour = [tex]\frac{7}{9.5}[/tex]
Hours in a week = 7 x 24 = 168 hours
Water flow per week = hours in a week x water flow per hour.
[tex]= 168 x \frac{7}{9.5} \\= 123.7894[/tex]
Water flow per week = 124 liters.
Therefore, the water flow per week is 124 liters.
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assume that movement of a molecule is limited. it can move to the opposite side of the container or stay where it is. if the movement is random, what is the probability (0-100%) that the molecule will move to the opposite side?
Answers
The Probability that that the molecule will move to the opposite side is 50% .
In the question ,
it is given that
there a molecule is free to move to the opposite side of the container , or stay where where it is ,
As per the given information
the molecule can move to opposite side or stay where it is ,
and the movement of the molecule is random
as the container had two sides ( shown in figure given below )
the probability that the molecule moves to the opposite side is 1/2 ,
in percent it can be written as 50% .
the correct option is (c) .
Therefore , The Probability that that the molecule will move to the opposite side is 50% .
The given question is incomplete , the complete question is
Assume that movement of a molecule is limited. it can move to the opposite side of the container or stay where it is. if the movement is random, what is the probability (0-100%) that the molecule will move to the opposite side?
(a) 0%
(b) 25%
(c) 50%
(d) 100%
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6. a) The mass of eight apples is 1 200 g. What is the average mass of one apple in kilograms? b) A5 kg bag of apples costs R65. What is the cost of 500 grams of apples? Approximately how many apples will have a mass of 1 kilogram?
Answers
a. The average mass of one apple in kilograms is 150g.
b. The cost of 500 grams of apples is R6.5
How to calculate the values?A. When the mass of eight apples is 1 200g, the average mass of one apple in kilograms will be:
= Total mass / Number of Apple
= 1200g / 8
= 150g
B. A 5 kg bag of apples costs R65. The cost per kg will be:
= Amount / Number of g
= R65 / 5000
= R0.013
The cost for 500 grams will be:
= 500 × R0.013
= R6.50
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(7, 8) and (-1, 0)find the distance between the two points?
Answers
The distance (d) between two points is computed as follows:
[tex]d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:
[tex]d\text{ = }\sqrt{(-1-7)^2+(0-8)^2\text{ }}[/tex][tex]d\text{ = }\sqrt{(-8)^2+(-8)^2}=\sqrt{128}[/tex]Can you help me with my math problem. im not sure where i got it wrong
Answers
Answer:
The value of k is;
[tex]k=-7.1842[/tex]Explanation:
Given the equation:
[tex]-3\cdot16^{-k-7}+8=3[/tex]To solve, let us subtract 8 from both sides;
[tex]\begin{gathered} -3\cdot16^{-k-7}+8-8=3-8 \\ -3\cdot16^{-k-7}=-5 \end{gathered}[/tex]then, we can then divide both sides by -3;
[tex]\begin{gathered} \frac{-3\cdot16^{-k-7}}{-3}=\frac{-5}{-3} \\ 16^{-k-7}=\frac{5}{3} \end{gathered}[/tex]To solve further we need to take the logarithm of both sides;
[tex]\begin{gathered} 16^{-k-7}=\frac{5}{3} \\ \log 16^{-k-7}=\log \frac{5}{3} \\ (-k-7)\log 16=\log \frac{5}{3} \\ \text{dividing both sides by log 16, we have;} \\ \frac{(-k-7)\log 16}{\log 16}=\frac{\log\frac{5}{3}}{\log16} \\ -k-7=\frac{\log\frac{5}{3}}{\log16} \end{gathered}[/tex]finding the value of the log;
[tex]-k-7=0.1842\text{ (to 4 decimal place)}[/tex]solving for k;
[tex]\begin{gathered} -k-7=0.1842 \\ -k=0.1842+7 \\ -k=7.1842 \\ k=-7.1842 \end{gathered}[/tex]Therefore, the value of k is;
[tex]k=-7.1842[/tex]Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
Answers
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Given,
Select all the unique triangles that can be drawn to only have angle measures 40° and 100° and side length 3.
What are unique triangles?
Unique triangles are triangles that are different based on their configuration, which derives from the positioning of the given parameters to correspond with different congruency requirement.
The conditions for the congruency of two triangles are;
SSS: The Side-Side-Side rule; two triangles are congruent if all three sides of one triangle are congruent to the three sides of the other triangle
SAS: The Side-Angle-Side rule; two triangles are congruent if two sides and the included angle of one are congruent to two sides and an included angle in the other triangle
ASA: The Angle-Side-Angle rule; two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and an included side of the other triangle
SAA: The Side-Angle-Angle rule; Two triangles are congruent if two angles and an a non included side of one triangle are congruent to two angles and the non included side of the other triangle.
The configuration of the unique triangles can therefore, be ASA and SAA, which gives the triangles;
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°
ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°
Please see attached drawings of the two unique triangles
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Given the figure below, determine the angle that is an alternate interior angle with respect to. 1. To answer this question, click on the appropriate angle.
Answers
In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).
m∠6 = m∠3
or
m∠4 = m∠5
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A (4, 5), B (12,9); 3 to 1 The coordinates of P are:
Answers
By applying line ratio, the coordinates of P are: [10, 8].
How to determine the coordinates of P?Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point A (4, 5)Point B (12, 9)m:n = 3:1Substituting the given parameters into the formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(3(12) + 1(4))/(3 + 1)], [(3(9) + 1(5))/(3 + 1)]
P(x, y) = [(36 + 4)/4], [(27 + 5)/4]
P(x, y) = [40/4, 32/4]
P(x, y) = [10, 8].
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Remington purchased a new cell phone for $350 and added an annual warranty plan that cost him $35 per year. In what year will Remington's average annual cost of owning the phone be $122.50? Type your answer....
Answers
Answer:
3 years and 6 months
Step-by-step explanation:
35 × 3= 105 + 17 = 122
2.916 a month × 6 = 17. 496. And round to the nears while number = 17.50 = 105 + 17.50 = 122.5 or 122.50 zero fir place holder.
Use the equation one sixth plus s equals 21 over 30 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
(Its due in 45 minutes so help answer it plsss)
Answers
s is 4/15 of the equation one sixth plus s equals 21 over 30.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
one sixth plus s equals 21 over 30
This can be written as
one sixth can be written as 1/6.
21 over 30 can be written as 21/30.
so the equation is 1/6+s=21/30.
Let us separate the variable s to find the value of s.
s=21/30-1/6
The LCM of 30 and 6 is 30
s=21-5/30
s=16/30=4/15
Hence s is 4/15 of the equation one sixth plus s equals 21 over 30.
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Write the equation in standard form for the hyperbola with vertices (-2,0) and (2,0) and a conjugate axis of length 14
Answers
Solution
- The equation of a hyperbola is given s:
[tex]\begin{gathered} \frac{(x-h)^2}{a}-\frac{(y-k)^2}{b}=1 \\ \\ where, \\ coordinates\text{ of the vertices}=(h\pm a,k) \\ Length\text{ of conjugate axis}=2b \end{gathered}[/tex]- Thus, we can find that:
[tex]\begin{gathered} (\pm2,0)=(h\pm a,k) \\ \\ k=0 \\ \therefore h+a=2 \\ h-a=-2 \\ \text{ Subtract both equations, we have:} \\ 2a=4 \\ a=\frac{4}{2}=2 \\ \\ h+a=2 \\ h+2=2 \\ h=2-2=0 \\ \\ \text{ Thus, we have that the center of the hyperbola is: }(h,k)=(0,0) \\ \\ 2b=14 \\ \text{ Divide both sides by 2} \\ b=\frac{14}{2}=7 \end{gathered}[/tex]Final Answer
The equation of the parabola is:
[tex]\frac{x^2}{2^2}-\frac{y^2}{7^2}=1[/tex]How can I complete the square of this equation Y=2x(x+5)
Answers
Answer: [tex]y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}[/tex]
Step-by-step explanation:
[tex]y=2x^2 +10x\\\\y=2(x^2 + 5x)\\\\y=2 \left(x^2 +5x +\frac{25}{4} \right)-\frac{25}{2}\\\\y=2 \left(x+\frac{5}{2} \right)^2 -\frac{25}{2}[/tex]
Sophie can type 129 words in 3 minutes. How many minutes will it take her to type 559 words?
Answers
EXPLANATION:
To solve the exercise we must make a rule of three.
The exercise is as follows:
[tex]\begin{gathered} 129\text{ }words\text{ }\rightarrow3\text{ minutes} \\ 559\text{ words}\rightarrow x \\ \frac{559\times3}{129}=13\text{ minutes} \\ \text{the answer is 13minutes} \end{gathered}[/tex]5-52: the first card selected from a standard 52-card deck is a king. a. if it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. if the king is not replaced, what is the probability that a king will be drawn on the second selection? c. in part (b), are we assuming the card selections are independent? justify your answer.
Answers
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability.
The probability of getting a king card is 1/13 or 0.077.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Total number of probability - 52
Now, the first selected card is king and it is returned to the deck.
So it contains no effect on the second selection card.
Then, we have to estimate probability to obtain a king
probability = favourable outcomes for a king / total possible outcomess
= 4 king cards / 52 cards in total
= 4 / 52 = 1 / 13
The probability of getting a king card is 1 / 13 or 0.077
Therefore, the correct answer is option B. 1/13, or 0.077.
The complete question is:
The first card selected from a standard 52-card deck was a king. It isreturned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/4 or 0.25
B. 1/13, or 0.077
C. 12/13, or 0.923
D. 1/3 or 0.33
E. None of the above
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POSSIBLE POINTS
Write and solve the given inequality: twice the difference of three times a number and five is at most the sum of four times a number and six.
O [8,00)
O (8,00)
O(-0,8)
O(-0,8]
Answers
The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
Let the number be x,
Twice the difference of three times a number and five = 2(3x - 5)
The sum of four times a number and six is (4x + 6)
2(3x - 5) ≤ (4x + 6)
6x - 10 ≤ 4x + 6
6x - 4x ≤ 6 + 10
2x ≤ 16
x ≤ 8
x can be any positive number less than or equal to 8.
Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
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Solve the following equation for y, simplifying all fractions: 6x + 10y = - 80 a) y = 3 X - 8 5 3 X 8 b) y alw c) y -x + 8 w л | о л | d) y = x – 8
Answers
Solving a linear equation with 2 variables
First isolate y term
10 y = -6x - 80
Now divide by 10
y = (-6/10)x -(80/10)
y = (-3/5)x - 8
Jodi bough a new car with 14 gallon gas tank. Around the town she is able to drive 336 miles on one tank of gas. on her first trip traveling on highways, she drives 448 on one tank of gas.A: Write a compound inequality in compact from the represents how many miles Jodi can drive on a tank of gas. Let m represent the number of miles per gallon.B: Rewrite the compound inequality as two simply inequalities separate by either and or, or.C: Solve each simple inequality. Then write the solution in compact form.
Answers
We have the following:
A.
Let m represent the number of miles per gallon, the inequality would be as follows
[tex]\frac{336}{14}\leq m\leq\frac{448}{12}[/tex]B. In two simple inequalities we have this
[tex]m\ge\frac{336}{14}\text{ or }m\leq\frac{448}{14}[/tex]C.
[tex]\begin{gathered} m\ge24\text{ or }m\leq32 \\ 24\leq m\leq32 \end{gathered}[/tex]Is the image an example of an angle?
B
65°
A
C
O No; AB and BC intersect in more than one point.
O Yes; AB and BC do not form a line and share an endpoint.
O No; AB and BC form a line.
O Yes; AB and BC are perpendicular to each other.
Answers
Yes, the image an example of an angle AB and BC do not form a line and share an endpoint.
What is an angle ?An angle is formed when two lines are extending from a point .
Using this Knowledge it can be deduced from the figure that line BA and BC are extending from point B. Hence forming an angle of 65 degrees
Analyzing the options
option A is wrong as line AB and BC intersected only on one point. formation of a line do not typically say if an angle is formed or not hence making option c incorrect. There is no perpendicular line formed in th figure .
This leaves option B as the correct option
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Jennifer is thinking about getting an MBA. She will give up making $27,500 a year for the two years it takes to complete the MBA. She will also pay $45,000 in total costs to get the degree. Assume she will make $67,500 a year after she gets her MBA. How long will it take for Jennifer to recover her investment?
Answers
Answer:
un year
Step-by-step explanation: