The quadratic equation is of the form y = ax² + bx + c
In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree just 2, or simply known as a quadratic.
x is the only variable. A parabola with its axis of symmetry parallel to the y-axis represents the graph of a univariate quadratic function, as seen to the right.A quadratic equation is produced if the quadratic function is set to zero. The roots of an univariate function are the solutions to the univariate equation.When authors speak to a quadratic polynomial, they may mean "having degree exactly 2" or "having degree at most 2". If the degree is less than 2, this scenario may be referred to as a "degenerate case." Which of the two is intended will typically depend on the context.In some circumstances, like in the instance of a second-order polynomial, the word "order" is used to denote "degree." The word "degree of a polynomial" refers to the highest degree of a non-zero term in a polynomial, whereas the term "order" typically refers to the lowest degree of a non-zero term in a power series.Complete question: The table represents a quadratic function. Write an equation of the function in standard form.
[tex]$$\begin{array}{lllll}x & -9 & -7 & -5 & -3\end{array}$$$\begin{array}{lllll}y & 0 & 8 & 8 & 0\end{array}$[/tex]
y=
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Find the inequality that creates the following graph
Answer:
|2x - 3| ≥ 1
Step-by-step explanation:
Since the absolute value function is always ≥ 0 we can conclude that
|2x - 3| ≥ 0 so we can eliminate choices 2 and 4
That leaves two possibilities:
|2x - 3| ≥ 1 and |2x - 3| ≤ 1
There are two ways to go about solving this
Pick a point in the given graph on each side of the segment marked in red and see which of the two inequalities both points satisfy
Two points which are on both segments are x = 0 and x = 1
Plug x = 0 into |2x - 3|
|2x - 3| at x = 0
=> | 2 ·0 - 3|
=> |0 - 3|
=> |-3|
= 3
Since 3 ≥ 1, point x = 0 satisfies |2x - 3| ≥ 1
But it does not satisfies |2x - 3| ≤ 1 since 3 is not less than or equal to 1
So the correct inequality is |2x - 3| ≥ 1
Can you please help me with this
Let's classify the angles.
3.The angles are alternate interior angles.
4.The
7+4(1-8p)
I’m confused is it -32p+11 or 11-32p
Answer:
Either. They are both correct
Step-by-step explanation:
So 7+4(1-8p): 7+4-32p => 11-32p => -32p+11.
Answer:
11-32p
Step-by-step explanation:
The answer is 11-32p because your only distributing the 4 to the 1 and 8p.
David requires at least $250 to hold his birthday party. If David can save $43 a month, how many months will he need to save to be able to afford his birthday party?
a. Write an inequality that describes this situation.
b. Solve the inequality. Show all your work.
c. Write your answer in a complete sentence.
Answer:
Step-by-step explanation:
Let David will need m months to save to able to afford his birthday party.
Then 43m>=250 that is m>=5.814 .
But since months are whole numbers
So We take m>=6.
He will need at least 6 months to save to able to afford his birthday party.
The answer is 6 months .
In anatomy, a student learned that the average resting heart rate is between 60 and 100 beats per minute. The student decided to record the heart rate of people over five minutes while waiting in line at the pharmacy. The dot plot shows the results.
Dot plot with 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
Which statement below best describes the shape of the distribution?
The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed left, with fewer values on the left end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The shape of the distribution for the given dot plot is as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
What does a dot plot show?A dot plot shows the number of times that each measure appears in the data-set.
In the context of this problem, we have that from the given dot plot, the measures are as follows:
62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.
The mean is the sum of all observations divided by the number of observations, hence, applying it's formula, it is given by:
74.55.
The median is the middle value of the data-set, the value of which 50% of the measures are greater and 50% are less. The data-set in this problem has 20 elements, hence the median is the mean of the 10th and the 11th elements, which are 72 and 75, respectively, hence:
Median = (72 + 75)/2 = 73.5.
The median is less than the median, hence the distribution is skewed to the right, which means that the third option is correct.
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Answer:
The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
Step-by-step explanation:
its not skewed right and this is the next one that makes sense
Harry works at Memorial Mall on the weekends. Last Saturday he worked 6 1/2 hours and on
Sunday he worked 7 3/4 hours. He earns $9.50 per hour. How much did he earn last
weekend?
Trent decided bicycle to Austin and back. Hisaverage speed to Austin was 45 km/h. The averagespeed on his return trip was 30 km/h. The trip toAustin was 1 hour less than his time bicycling on hisreturn trip. How many hours did the trip to Austinlake?
Consider the relation,
[tex]\text{Time}=\frac{\text{ Distance}}{\text{ Speed}}[/tex]Let the distance between Trent and Austin is 'd' kilometers.
Then the time taken by Trent to reach Austin is given by,
[tex]T_1=\frac{d}{45}[/tex]Similarly, the time taken by Trent on his return trip is given by,
[tex]T_2=\frac{d}{30}[/tex]Given that the trip to Austin was 1 hour less than the return trip,
[tex]\begin{gathered} T_2-T_1=1 \\ \frac{d}{30}-\frac{d}{45}=1 \\ d(\frac{1}{30}-\frac{1}{45})=1 \\ d(\frac{45-30}{30\times45})=1 \\ d=\frac{30\times45}{15} \\ d=2\times45 \\ d=90 \end{gathered}[/tex]Solve for the total time of the trip as,
[tex]\begin{gathered} T=T_1+T_2 \\ T=\frac{90}{45}+\frac{90}{30} \\ T=2+3 \\ T=5 \end{gathered}[/tex]Thus, the total time required for complete trip is 5 hours.
2 + 31 x 1/10 + 4 x 1/1000 is greater than, less than, or equal to 2.324?
Answer:
greater
Step-by-step explanation:
if it wasn't bidmas then the product would be 5.104 which is greater than 2.324
The graph of a function f(x) shown in orange is moved two units to the left to obtain the function in blue. Which of the following represents the blue graph
The equation of the blue line is y = 2(2 - x).
Equation of A(1,0) and B(0, -2)
Use y = mx + c,
m = change of x axis ÷ change of y axis
The difference in x-coordinates equals the difference in y-coordinates, and the difference in y-coordinates equals the difference in y-coordinates.
m = (y2 - y1) ÷ (x2 - x1)
To get the slope, plug in the parameters of both x and y into to the equation.
m = (2 - 0) ÷ (0 - 1)
m = -2
The value of b calculated using the expression of a line formula.
b = 2
Now that you have the measurements of m (slope) and b (y-intercept), plug them into y = m x + b to determine the equation of the line.
y = −2x+2
Because the line is two primary components to the left, the parallel line's equation is,
y = -2x + 2 + 2
y = -2x + 4
y = 2(2 - x)
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The prices of the 19 top-rated all-season fires for a specific tire size, are as follows. Answer parts (a)-(0)$87 $116 $98 579 582 592 594 589 594 $81$107 $112 5103 596 586 $92 $75 $99 $90a) Determine Q2b) Determine Q1c) Determine Q3
Simone, these are the steps to calculate Q1, Q2, and Q3.
Step 1: You need to put all the values in order from the lowest to the greatest.
Step 2: The tenth value from left to right is the median or Q2.
Step 3: The
write and solve the inequality that represents -1/3 is > than or = to the product of -4/5 and a number
Answer:
[tex] - \frac{1}{3} \geqslant - \frac{4}{5} x[/tex]
[tex] \frac{1}{3} \leqslant \frac{4}{5} x[/tex]
[tex]5 \leqslant 12x[/tex]
[tex]12x \geqslant 5[/tex]
[tex]x \geqslant \frac{5}{12} [/tex]
The leadership class plans to sell t-shirts for a fundraiser, but they need to decide which company to use.
Custom Ink charges $6.50 for each t-shirt. Tees-4-U charges a flat fee of $250 plus $5.50 for each t-shirt.
A. How many shirts would have to be ordered to for the two companies to charge the same amount?
B. If they plan to order 600 t-shirts, which company would charge them less?
C. How much are they saving by going with the more economical company?
Using linear functions, it is found that:
A. The costs will be the same when 250 shirts are bought.
B. The Tees-4-U Company would charge them less.
C. They are saving $350 by going with the more economical company.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the cost functions in the context of this problem, we have that:
The slope represents the cost per shirt.The intercept represents the flat fee.Hence the functions for the cost of buying x shirts are given as follows:
Custom Ink: C(x) = 6.5x.Tees-4-U: T(x) = 250 + 5.5x.The costs will be the same when:
C(x) = T(x)
Hence:
6.5x = 250 + 5.5x
x = 250
For item b, the costs are given as follows:
C(250) = 6.5(600) = 3900.T(250) = 5.5(600) + 250 = 3550.The amount saved in item c is:
3900 - 3550 = 350.
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11. Does the table show a proportional relationship?
If so, what is the value of y when x is 10?
X 5 6 7 8
Y 1 2/3 2 2 1/3 2 2/3
The value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].
What is proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
Given Data
X 5 6 7 8
Y 1 2/3 2 2 1/3 2 2/3
Yes, the table shows proportional relationship.
Value of Y when X will be 10 is
x = 10
= 3[tex]\frac{1}{3}[/tex]
the value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].
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Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
By using division, when the restaurant needs at least 736 knives and there are currently 155 knives, if each set on sale contains 12 knives then he minimum number of sets of knives Kaj should buy is 49 sets
The total number of knife that restaurant needs = 736 knives
Number of knives that restaurant has = 155 knives
The number of knife that he want to buy = 736-155
= 581
Number of knives on one set = 12
To find the number of set he wants to buy, we have to use division
Number of sets he wants to buy = 581/12
= 48.41
≈49 sets
Hence, by using division, when the restaurant needs at least 736 knives and there are currently 155 knives, if each set on sale contains 12 knives then he minimum number of sets of knives Kaj should buy is 49 sets
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Find the value of 2y-9 given that -3y-2=4.
Simplify your answer as much as possible.
2y - 9 =
In linear equation, 4 is the Simplify your answer .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.2y-9 ............1
-3y-2=4 .............2
From equation (2)
- 3y = 4 + 2
- 3y = 6
y = 6/-3 ⇒ -2
value of y put in equation 2
-3y-2=4
- 3 * -2 - 2 = 4 ⇒ 6 - 2 ⇒ 4
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If you answer these questions correctly you are really smart. What is 2+2*2, what is 3+3*3, what is 6+6*6.
The value of the numbers that are given will be:
1. 6
2. 12
3. 42
How to calculate the value?It should be noted that based on the information given, PEDMAS is important. This implies that multiplication will come first before addition. This will be illustrated thus:
1. 2 + 2 × 2
= 2 + 4
= 6.
2. 3 + 3 × 3
= 3 + 9
= 12
3. 6 + 6 × 6
= 6 + 36
= 42..
Therefore, it should be noted that we multiplied first before adding.
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I need help I don’t know how to do this
if f(x) = 5x-7, then what is the solution to f(x) =4
The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.
What is the value of x when the output value f(x) = 4?A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.
Given the data in the question;
f( x ) = 5x - 7f(x) = 4x = ?To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.
f( x ) = 5x - 7
4 = 5x - 7
Collect like terms
4 + 7 = 5x
5x = 11
Divide both sides by 5
5x/5 = 11/5
x = 11/5
Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).
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Write the following sentence in algebraic language:Number k is 4/5 of the number t.
To write the sentence:
Number k is 4/5 of the number t in algebraic language, we can proceed as follows:
[tex]k=\frac{4}{5}t[/tex]We need to express that k is equal to the four-fifths of t.
Then, the answer is k = (4/5)*t.
Does anybody know how to answer this to?
The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk if the total distance is 32 miles? How many miles will they run?
They will walk 7 laps and run 17 laps for a total of 32 miles.
They will walk 12 laps and run 20 laps for a total of 32 miles.
They will walk 14 laps and run 18 laps for a total of 32 miles.
They will walk 10 laps and run 22 laps for a total of 32 miles.
Question 3(Multiple Choice Worth 2 points)
(Three-Column Tables LC)
PART 2
The data below shows the ratio of brown to green crayons in four kindergarten classrooms.
12 to 20
10 to 25
14 to 35
30 to 75
Which table below correctly shows these ratios in a three-column table?
Brown 20 25 35 75
Green 12 10 14 30
Total 32 35 49 105
Brown 12 10 14 75
Green 20 25 35 30
Total 30 35 44 105
Brown 12 10 14 30
Green 20 25 35 75
Total 32 35 49 105
Brown 12 25 14 30
Green 20 10 35 75
Total 42 35 49 100
Using proportional relationships, it is found that:
They will walk 12 laps and run 20 laps for a total of 32 miles.The correct option for the second problem is:Brown 12 10 14 30
Green 20 25 35 75
Total 32 35 49 105
What is a direct proportional relationship?In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:
y = kx.
For the first question, we have that out of a total distance of 8 miles, they:
Walk 3/8 of the distance.Run 5/8 of the distance.Hence the proportional relationships for the distances are given as follows:
Walked = 3/8 x Total Distance.Ran = 5/8 x Total Distance.For a total distance of 32 miles, the distances walked and ran are given as follows:
Walked: 3/8 x 32 = 3 x 4 = 12 miles = 12 laps.Ran: 5/8 x 32 = 5 x 4 = 20 miles = 20 laps.For the second question, we have that the table has to following the given ratios of the first row to the second row, with the third row being the sum of the first two rows, hence the third table is correct.
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A motorboat travels 282 kilometers in 6 hours going upstream. It travels 402 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Let,
B = the speed of the boat in still water
S = the speed of the stream
Use the equation for distance.
Rate * Time = Distance
Upstream:
(B-S)6 = 282
Downstream:
(B+S)6 = 402
Simply first:
(B-S)6 = 282
(B-S) = 282/6
B-S=47
(B+S)6 = 402
(B+S) = 402/6
B+S=67
Solve by elimination. Add the two equations.
B-S=47
+ B+S=67
2B = 114
B = 114/2
B = 57 km/hr (the speed of the boat in still water)
Substitute this into either equation and solve for S.
B+S=67
57 + S = 67
S = 67 - 57
S = 10 km/hr (the speed of the stream)
At your child's birth, you begin contributing monthly to a college fund. The fund pays an APR of 4.1% compounded monthly. You figure your child will need $30,000 at age 18 to begin college. What monthly deposit is required?
the monthly deposit that will be required will be equal to $ 1214 by compound interest.
We are given the information that:
Amount (A) = $ 30,000
Time = 18 years
Compound interest rate = 4.1 %
Now, let the principal amount be x.
So, by using the formula for compound interest, we get that:
30,000 = x ( 1+ 0.041)¹⁸
30,000 = x (1.041)¹⁸
30,000 = x × 2.06
x = 30,000 / 2.06
x = 14563 ( approx.)
Monthly deposit = 14563 / 12 = 1214 (approx.)
Therefore, the monthly deposit that will be required will be equal to $ 1214 by compound interest.
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Indicate whether the following statement is
TRUE or FALSE. −17 is an integer
Answer:
TRUE
Step-by-step explanation:
an integer is a whole number from the set of negative, non-negative, positive and 0 numbers.
ex : -1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5
-17 is a negative whole number
so yes, -17 is an integer
1) Find the measures of the following angles: a) 2x+250 3x-450 t b) e, I l l 12y by-30° g
a) the two angles are supplementary, then:
(3x - 45) + (2x + 25) = 180
(3x + 2x) + (-45 + 25) = 180
5x - 20 = 180
5x = 180 + 20
5x = 200
x = 200/5
x = 40
Then, the measure of the angles are:
3x - 45 = 3*40 - 45 = 75°
2x + 25 = 2*40 + 25 = 105°
b) the two angles are complementary, then:
(2y) + (6y - 30) = 90
(2y + 6y) - 30 = 90
8y = 90 + 30
8y = 120
y = 120/8
y = 15
Then, the measure of the angles are:
2y = 2*15 = 30°
6y - 30 = 6*15 - 30 = 60°
c) the two angles are vertical angles, then they are congruent, that is,
2z + 7 = 5z - 23
7 + 23 = 5z - 2z
30 = 3z
30/3 = z
10 = z
Then, the measure of the angles are:
2z + 7 = 2*10 + 7 = 27°
5z - 23 = 5*10 - 23 = 27°
d) the two angles are alternative exterior angles, then they are congruent, that is,
4x - 5 = 3x + 15
4x - 3x = 15 + 5
x = 20
Then, the measure of the angles are:
4x - 5 = 4*20 - 5 = 75°
3x + 15 = 3*20 + 15 = 75°
20 points!!! pls hurry!!! I need the CORRECT answer in three hours or less!!! What is the slope of this line? A. -1/3 B. -2/3 C. 1/3 D.2/3
Answer:
D
Step-by-step explanation:
RISE/RUN = slope
This slope will be POSITIVE because it rises in quadrant 1.
Rise=2, run=3
Slope= 2/3
Hope that helps
I need the area of the irregular shape
The area of the irregular shape is found as 50 sq. cm.
What is defined as the area?The total space occupied by a flat (2-D) ground or the shape of an object is defined as its area. Sketch a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of many smaller unit squares.For the given question;
The irregular shape is composed of two rectangles.
The formula for finding the area is;
Area = length x breadth
The area of the top rectangle is;
Top area = 4 x (3 + 5 + 2)
Top area = 4 x 10
Top area = 40 sq. cm.
The area of the bottom rectangle is;
Bottom area = 5 x 2
Bottom area = 10 sq. cm.
Total area = Top area + Bottom area
Total area = 40 + 10
Total area = 50 sq. cm.
Thus, the area of the irregular shape is found as 50 sq. cm.
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Connor edits 34
pages in 8 hours. Complete the table using equivalent ratios
If Connor edits 34 pages in 8 hours. Using the equivalent ratios, the table has been completed.
The equivalent ratios are the ratios that has same value when we compare them. We can check two or more ratios and check whether they are equivalent or not.
Connor edits 34 pages in 8 hours
Number of pages he edits in 8 hours = 34 pages
Number of pages he edits in 1 hour = 34/8 = 17/4 pages
Number of pages he edits in 12 hours = (17/4)×12
= 51 pages
Complete the table
Hence, if Connor edits 34 pages in 8 hours, using the equivalent ratios, the table has been completed
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slope -3 passes through (4,-1) solve and write in slope intercept form
Answer:
y = -3x + 11
Step-by-step explanation:
(4, -1) m = -3
y = -3x + b
y + 1 = -3(x-4)
-3(x-4) = -3x + 12 - 1
y = -3x + 11
3 times the sum of a number and 5
SHOW WORK
Answer:
3(n +5)
Step-by-step explanation:
You want the math expression that means "three times the sum of a number and five."
SumA sum is represented using a plus sign. "A number" is represented using a variable. "x" is a variable commonly used for an unknown value. "n" can also be used to represent "a number."
The sum of a number and 5 will be ...
n + 5
TimesWe want an expression that is 3 times that sum, so we multiply it by 3:
3(n +5) . . . . . . 3 times the sum of a number and 5
__
Additional comment
Note that the expression above is not the same as 3n+5, which would represent "the sum of 3 times a number and 5".
6 is 15% of what number
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
6 ===> 15%
Step 02:
Percentage:
percentage = part / whole * 100
percentage = 15
part = 6
whole = number = x
[tex]\begin{gathered} 15\text{ = }\frac{6}{x}\cdot100 \\ x\cdot15\text{ = }6\cdot100 \\ x\text{ = }\frac{6\cdot100}{15}=40 \end{gathered}[/tex]The answer is:
The number is 40