Answer:
See below
Step-by-step explanation:
A function is continuous within an interval if its first derivative exists
[tex]\text{The first derivative of }\dfrac{2x+3}{x\:-\:2} = \dfrac{d}{dx}\left(\dfrac{2x+3}{x\:-\:2}\right) = -\dfrac{7}{\left(x-2\right)^2}[/tex]
Let's call this first derivative g(x)
g(x) is defined at all values of x except at x=2 since at this value the denominator becomes 0 and g(x) is not defined.
So the function has a discontinuity at x = 2
But in the interval (2, ∞ ) the function g(x) always has a real value so f(x) is continuous in that interval
Determine whether the system is consistent. x1 x2 x3 = 7 x1 - x2 2x3 = 7 2x1 3x3 = 15
The given system is not consistent.
Given system of equations are:
[tex]x_1+x_2+x_3=7\\x_1-x_2+2x_3=7\\2x_1+3x_3=15[/tex]
Here the indeterminants are [tex]x_1,x_2,x_3[/tex]. A system of equations is consistent if it has at least one set of solution values for the indeterminants.
So we try to solve the above system of equations.
Subtracting the first two solutions, we get,
[tex](x_1+x_2+x_3)-(x_1-x_2+2x_3)= 0[/tex]
⇒ [tex]2x_2-x_3=0[/tex]
⇒ [tex]x_3=2x_2[/tex]
Rewriting all the three equations using this substitution,
[tex]x_1+x_2+2x_2=7\\x_1-x_2+4x_2=7\\2x_1+6x_2=15[/tex]
This implies,
[tex]x_1+3x_2=7\\x_1+3x_2=7\\2x_1+6x_2=15[/tex]
Since the first two equations are same, we need to solve the equations,
[tex]x_1+3x_2=7\\2x_1+6x_2=15[/tex]
Multiplying the first equation by 2 and then subtracting, we get,
0 = -1, which is impossible.
So the system has no solutions.
Hence the system is inconsistent.
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1. In a study of how college education costs have changed since 1980,
each year's average cost of tuition is expressed as a percentage of the
1980 cost. Which term refers to the 1980 cost?
(a) Reference value
(c) Rate of inflation
(b) Index number
(d) Price index
1. Which of the following expressions are equivalent? Select all that apply. Use mathematics to show why they are equivalent.
A. 2 (x+4)
B. 8+2x
C. 2x+4
D. 3 (x+4)-(4+2)
E. x +4
A rental car company charges $22.50 per day to rent a car and $0.10 for every mile driven. salma wants to rent a car, knowing that: she plans to drive 275 miles. she has at most $140 to spend
Salma can rent the car for at most 5 days while driving 275 miles
Although part of your question is missing, you might be referring to this full question: A rental car company charges $22.50 per day to rent a car and $0.10 for every mile driven. Salma wants to rent a car, knowing that: she plans to drive 275 miles. She has at most $140 to spend. Write and solve an inequality which can be used to determine, the number of days Salma can afford to rent the car while staying within her budget
The equation which addresses this problem is:
22.5x + 0.10(275) <=140
Let x be the number of days Salma can afford to rent the car
Per day rent of the car = $22.5
Cost per mile = $0.10
Plan to drive = 275 miles
Budget with Salma = $140
Equation:
22.5x + 0.10(275) <= 140
Solving the equation we get x <= 5
So, Salma can rent the car for at most 5 days while driving 275 miles
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The picnic shelter must be at least overline 10 feet from any edge of the park. On graph paper with the distance between grid lines representing 10 feet, a city engineer makes a scale drawing of the park, as shown below. The region where the picnic shelter CANNOT be built is shown shaded. The corners of both the park and the region where the picnic shelter may be built are at the intersections of grid lines. The corners of the picnic shelter must also be at the intersections of grid lines. How many different locations in the park are possible for the placement of the picnic shelter?
Answer:
52
Step-by-step explanation:
since the shaded region is an exclusive counting the grid between 13*4 gives 52
We can see here that the number of locations in the park that are possible for the placement of the picnic shelter is C. 52
What is graph paper?Graph paper, also known as grid paper or coordinate paper, is a type of paper that has a grid of equally spaced horizontal and vertical lines drawn on it. The lines form a pattern of squares or rectangles, which facilitates drawing graphs, charts, diagrams, and geometric shapes with precision.
We can see here that multiplying the length and breadth of the picnic shelter using the unshaded boxes, we have:
13 × 4 = 52
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characteristics of a number may be positive negative or always zero
Answer:
There is nothing positive or negative about zero. Zero is just zero. It is NEITHER positive NOR negative. To the right of zero on number line are positive numbers and on the left of zero, lie the negative numbers on the number line.
Answer:
Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative.
A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____ sampling.
A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.
What is systematic sampling?Systematic sampling is a statistical method used in survey methodology that involves selecting elements from an ordered sampling frame. An equiprobability method is the most common type of systematic sampling. The list is traversed in a circular fashion in this approach, with a return to the top once the end of the list is reached. Systematic sampling is a probability sampling method in which we randomly select one of the first k elements and then select every kth element after that. Using this method, each element in the population has a known and equal chance of being selected (also known as Epsem). As a result, systematic sampling is functionally equivalent to simple random sampling (SRS).Therefore, a probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is systematic sampling.
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What is the classification for this polynomial?
-4a³b5 + 3a²
A. monomial
B. binomial
C. trinomial
It's been a while but I think binomial. There are two nonzero terms, -4a3b5, and 3a2, making it a binomial.
|−9| − |−5| i hate next gen but help pls
Answer:
4
Step-by-step explanation:
[tex]\mathrm{-9 = 9, -5 = 5,\:because\:they\:are\:in\:absolute\:value}\\9 - 5 = 4[/tex]
Answer:
-4
Step-by-step explanation:
−9 − (−5)
Multiply
−1 by −5.
−9 + 5
Add
−9 and 5.
you get...
−4
HELP PLEASE ILL GIVE U 100 POINTS PLS HELP AND THE LAST ONE IS 20
Answer:
20
Step-by-step explanation:
Match the mathematical expression with its translation.
1 .
x divided by y
6 x = y
2 .
the product of two numbers
x + y = 6
3 .
x subtracted from y
4 .
the sum of two numbers is six
x + y
5 .
the product of two numbers is six
x - y
6 .
x minus y
y = x - 6
7 .
the sum of x and y
xy
8 .
six times a number equals y
y ÷ x
9 .
y divided by x
y - x
10 .
six less than a number is y
xy = 6 HELP...
Answer:
x divided by y - x/y
the product of two numbers - xy
x subtracted from y - y-x
the sum of two numbers is six - x+y=6
the product of two numbers is six - xy=6
x minus y - x-y
the sum of x and y - x+y
six times a number equals y - 6x=y
y divided by x - y divided by x
six less than a number is y - y=x-6
Step-by-step explanation:
1+2+3+4+...+4567+4568+4569=? ill mark brainliest
Answer: 10440165 ==> sum of sequence
Step-by-step explanation:
4569+1=4570
4570/2=2285==> Average number in the sequence
4569-1+1=4569 numbers in the sequence. I find the number of numbers in the sequence by subtracting the last number in the sequence by the first number in the sequence (4569-1) and adding 1 to the difference.
2285*4569=10440165 ==> sum of sequence
ƒ(x) = −4x² + 10x + 13
Find f(7)
Answer:
-113
Step-by-step explanation:
Plug in 7 for x and you get -4(7)² + 10(7) + 13
7² = 49 so -4(49) = -196
10(7) = 70
Add them all up and you get -113 (-196 + 70 + 13 = -113)
Cherries cost £3.50 per 1000 g.
Calculate the cost of 420g of cherries.
The cost of 420 grams of cherries is £1.47.
How to find the cost of cherries?Cherries cost £3.50 per 1000 grams.
Therefore, the cost of 420 grams of cherries can be calculated as follows:
1000 grams of cherries = £3.50
420 grams of cherries = ?
cross multiply
cost of 420 grams of cherries = 3.50 × 420 / 1000
cost of 420 grams of cherries = 1470 / 1000
cost of 420 grams of cherries = 147 / 100
cost of 420 grams of cherries = £1.47
Therefore, the cost of 420 grams of cherries is £1.47.
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Answer:
Step-by-step explanation:
Cost of 420g cherries
147 ÷ 100
=1.47
therefore the cost of 420 of cherries
= £1.4
The parent graph for a linear function and an absolute value function are shown below. Compare and contrast the two functions. Please include information about the characteristics of each graph, including, but not limited to domain/range, shape of the graph, etc.
From the left, the first graph's characteristics is as follows
v shaped representing two straight line graphIt has two slopes, one is negative the other is positive slopeThe intercept is 0The domain is - 10 to 10The range is - 10 to 10The graph passed through the originThe second graph characteristics is as follows
The shape represents a single straight line graphThe graph has one positive slopeThe intercept is zeroThe domain is - 10 to 10The range is - 10 to 10This graph passed through the originWhat is a graph?A graph is a pictorial representation of values used in data presentation. A graph is very useful in research as the values can help show the relationship between the data obtained. Graphs can also be used to predict events and can have multiple other uses depending on the type of graph and the nature of data plotted.
A graph has so many features that varies by the type of graph and the information it is representing. The graph treated here is a straight line graph and the equation is: y = mx + c
where m is the slope , and c is the intercept
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7. Charlotte needs to order thread to sew buttons onto marching band uniforms.
A 400-yard spool of thread is sold for $5.
• Each uniform needs 50 buttons.
There are 100 uniforms that need buttons.
• Each button requires of a yard of thread.
How much money should Charlotte ask for in the budget to spend on thread?
Using proportions, it is found that Charlotte should ask for $62.5 in the budget to spend on thread.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Each uniform needs 50 buttons, and there are 100 uniforms, hence the number of buttons needed is:
50 x 100 = 5000.
Each button requires of a yard of thread, hence the number of yards needed is:
5000 x 1 = 5000 yards.
A 400-yard spool of thread is sold for $5, hence the budget needed is:
(5000/400) x 5 = $62.5.
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A man is walking away from a lamppost with a light source h = 4 m above the ground. The man is m = 2 m tall. How long is the man's shadow when he is d = 15 m from the lamppost? [Hint: Use similar triangles.]
-2/-5+4/3 .,,,,,,,, nr
P
Answer:
1.73 repeated
Step-by-step explanation:
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5 STAR RATING
Answer:
12/15
Step-by-step explanation:
Simplify (9-2a)-(4+3a)
Answer:
subtract the numbers[tex]9 - 4 =5 = -5a + 5[/tex]
Step-by-step explanation:
( a ) = a
( 9 - 2a ) = 9 - 2a
= 9 - 2a - 4 -3a
- (a + b ) = -a -b
-( 4 + 3a ) = -4 - 3a
= - 2a - 3a + 9 - 4
- 2a - 3a = - 5a = -5a + 9 - 4
give me a thanks
Find the volume of the solid.
Answer:
15.75
Step-by-step explanation:
1/2 * b*h*l
1/2 * 4.5 * 3.5 * 2
Answer:
10.5
Step-by-step explanation:
Firstly, you must multiply the length and width of the rectangular base to get its area.
Then, you certainly must multiply the base area with the height of the pyramid.
Last but not least, divide the result from step 2 by three, and you will get the volume of a rectangular pyramid.
Rita and Tina each make $11 an hour working as cashiers at a supermarket. Last week, Rita worked r hours while Tina worked t hours. Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage. Which expressions represent the total weekly wages of both Rita and Tina?
Rita and Tina's total weekly wages can be represented as
,
, or
.
Reset Next
Answer: it is .
Step-by-step explanation:
Rita and Tina each make $11 an hour -> 11r for Rita and 11t for Tina in the week
Rita also worked overtime hours and got paid an extra $32 -> Rita and Tina's total weekly wages can be represented as 11r + 11t + $32 (or 11(r+t) + 32)
five more than the product of two and a number,
decreased by seven;
evaluate when a = 8
Key Words
five
more than
product
two
a number
decreased by
seven
Replace With
5
+
x
2
a
7
Write and evaluate the expression. Then, complete the
statements.
First, write the expression
Second,
Third,
The answer is
8 in for the variable, a.
by using
PLS PLS PLS PLS PLS PLS
Answer:
D. (-2, -8)
Step-by-step explanation:
y = 3x - 2
y = 5x + 2
The solution to these system of equations is the point where the lines intersect.
These lines intersect at (-2, -8)
The following values represent the amount of money (in dollars) 10 people have in their wallets: 10, 12, 19, 5, 6, 8, 1, 13, 4, 7 what is the median?
The median of all these numbers in dollars is 7.5.
How to obtain median when no. of given data are odd ?When the no. of given data are odd we arrange those nos. in an order increasing or decreasing order and the middle no. is the median of the given odd numbers.
According to the given question the following values represent the amount of money (in dollars) 10 people have in their wallets: 10, 12, 19, 5, 6, 8, 1, 13, 4, 7 and we have to find the median.
First we observe that no. of people is even so there will be two middle nos.
Now lets arrange these nos. in an order from least to greatest which is
1, 4, 5, 6, 7, 8, 10, 12, 13, 19 in this 7 and 8 are middle numbers.
So, to find the median of all these nos. we will divide these two middle nos. by 2.
∴ ( 7 + 8 )/2
= 15/2
= 7.5.
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Koran makes these claims. For each claim, decide whether you agree or disagree. Explain your reasoning using at least one of the data displays.
Considering the box plot and the histogram, we have that the conclusions are as follows:
b. Disagree, as the histogram shows the interval of the lowest value and the highest value needed to to find the range of the data-set, but not these values explicitly like the box plot. Thus, the range would also be given in an interval and not an exact value.
c. Disagree, as the box plot gives only the five number summary, not the measures between them, hence, the total number can only be found using the histogram.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
What does a box-and-whisker plot shows?A box and whisker plot shows five things:
The minimum value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum value.What is the range of a data-set?The range of a data-set is given by the difference between the largest value in the data-set and the smallest.
The box plot gives these values explicitly, while the histogram show the number of times each range appears, hence, in statement b:
Disagree, as the histogram shows the interval of the lowest value and the highest value needed to to find the range of the data-set, but not these values explicitly like the box plot. Thus, the range would also be given in an interval and not an exact value.
Statement cDisagree, as the box plot gives only the five number summary, not the measures between them, hence, the total number can only be found using the histogram.
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. Which graph has f(x) = 1xI as its parent function?
Answer: Im not sure
Step-by-step explanation:
you didnt list/provide the graphs for me to answer. :I
Janice has some beads that she can divide equally among herself and four friends with no beads left over. Which could be the number of beads Janice has?
A 576
B 384
C 480
D 240
Answer:
Can be C or D
Step-by-step explanation:
Janice and her 4 friends means there are 5 people in total.
She will divide them and so beads will be left which means no remainder.
so we have to look for a number divisible by 5
480 and 240 both are divisible by 5
Write an equation representing the fact that the product of two consecutive odd integers is 255. use x to represent the smaller integer.
The first odd number = 15
The second is then = 17
The Consecutive numbers are:Consecutive numbers are those that appear consecutively after one another in the range of smallest to largest. An illustration would be the sequence of numbers 1, 2, 3, 4, 5, and so on.
Where can I find consecutive numbers?Let x be the first of the following numbers to represent it algebraically. Following that, the numbers x + 1, x + 2, and x + 3 would be arranged in order. You must make sure that your first selection is an even number if the question requires consecutive even numbers.
According to the given information:We can employ the expression "2n," where n is any integer, to ensure that the result is even. By using the expression "2n + 1," we can ensure an odd number.
"2n + 3" will be the following odd number:
(2n + 1)(2n + 3) is the component of the odd integers, and it equals 255:
(2n + 1)(2n + 3) = 255
4n2 + 8n + 3 = 255
4n2 + 8n - 252 = 0
n2 + 2n - 63 = 0
(n + 9)(n -7) = 0
n = -9 and n = 7
We can disregard n = -9 because we are informed that the figures must be positive.
If n = 7,
The first odd number = 2(7) + 1 = 15
The second is then 17
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I understand that the question you are looking for is:
The product of 2 positive, consecutive odd numbers is 255 .
Part A: Write a quadratic equation in standard form to represent this problem
Part B: What are the 2 numbers?
Part C: Show your work for Part B.
OURSE
4. Which statement is false? (1 point)
Every integer is a real number.
Every real number is a rational number.
Every positive rational number has a square root.
Every integer is a rational number.
Answer:
Every positive rational number has a square root.
Step-by-step explanation:
this is not true because there are prime numbers
