Answer: 2x + 8
Step-by-step explanation:
( 6x + 2 ) - ( 4x - 6 ) =
6x - 4x = 2x
2 - -6 = 8
Your local library holds a penny drive in which people in the community are asked to donate their spare pennies to the library. When you stop by to donate some pennies, you hear someone announce that she plans to donate pennies for one month in the following manner: she will donate 1 penny today, 2 pennies tomorrow, 4 pennies the next day, and will continue to double the number of pennies that she donates each day thereafter.
The amount donated by the person follows a geometric progression, which is given by an exponential function.
First part:
The relationship between the amount donated and the day of the month is not a constant rate relationshipSecond part;
Please find attached the graph of the Amount Donated to the Days which is shaped as the graph of an exponential equationWhat is an exponential function?An exponential function is one in which the input variable is an index of a constant
A constant rate relationship is one in which at all points of the function, the ratio of the output to input stays the same or is a constant.
The given parameters are;
The Pennies a person plans to donate to the library on each day of the month, is given by the following table;
Day. Amount Donated
1. 1
2 2
3 4
4 8
First part
Required;
If the relationship between the day and the amount donated is a constant rate relationship
Solution;
Given that we have;
1/1 = 2/2 ≠ 4/3 ≠ 8/4, the relationship between the day of the month and the amount donated is not a constant rate relationship
Second part;
The shape of the graph of Day to the Amount Donated
Solution;
The sequence of the day has a constant difference of one day, which is given by the equation;
U = 1 × n
Where;
U = The day of the month
n = The number of days
The sequence for the amount donated is given by the exponential function;
S = a•r^n
Where;
a = The first term = 1
r = The common ratio = 2
U = The number of days
The graph of Amount Donated to the Days is therefore the graph of an exponential function, please see the attached graph of Amount Donated to the Day of the month
The possible questions obtained from a similar question are;
First part; If the amount donated and the days have a constant rate relationship
Second part; The shape of the graph of the Amount Donated to the Day of the month
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fcbdxfhbdxfnxfgmndfgxhbnxf
ANSWER:
A. The midline of the function is y = 2
STEP-BY-STEP EXPLANATION:
we can determine the answer from the graph, just like this:
Therefore, the only correct option is A. The midline of the function is y = 2
a high school has 1446 students enrolled. a middle school 1/6 as many enrolled as the high school. how many ( m) are enrolled in the middle school? is this a adidtive or multiplicative question?
High school = 1446 students
Middle school = 1/6 as many as Highschool
Multiply 1/6 by the number of students enrolled at the high school.
m = 1/6 (1446) = 241
It is a multiplicative question
In his music class, Mr. Thompson played short samples of 80 classical pieces of music. The students were able to identify 16 of the pieces.
What percent of the classical pieces did the students identify?
The students were able to identify 16 of the pieces out of 80 which is 20 % in the percentage form.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.
The students were able to identify 16 of the pieces out of 80.
We have to determine the percentage of the classical pieces the students identify.
As per the given information, the required solution would be as:
⇒ (16/80) × 100
⇒ (0.20) × 100
⇒ 20 %
Therefore, the percentage of the classical pieces the students identify would be 20 %.
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2. Based on the diagram, what property can we use to prove ABCD is aparallelogram?
there are 4 properties we can use to prove if it is a parallelogram, in which 3 of them involve seeing if the sides are parallel or congruent, however for those we must know the value for the angles or sides, the other property is to prove that the diagonals bisect each other.
To prove the diagonals bisect each other is to see if the point of crossing divides into equal parts.
in this case since the division of the points gives the same values for both diagonals we can say that ABCD because the diagonals bisect each other.
Addison has x pennies and y nickels. She has a minimum of 16 coins worth no more
than $0.40 combined. Solve this system of inequalities graphically and determine
one possible solution.
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go?
The probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go is 0.3240
Probability:
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes.
Given,
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go.
Here we need to find the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go.
Let us consider this as,
Binomial Problem with
n = 5 and
By converting the percentage into decimal value,
=> 48/100 = 0.48
p(to go) = 0.48
Then the value is,
P(x=3) = 5C3(0.52)^3*(0.48)2
P(x=3) = 0.3240
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Solve for x and simplify the answer
2x^2+2x=-3
Please help I’ll mark you as brainliest if correct!!
Answer:
x (y + 1)
Step-by-step explanation:
Simplify the following:
x y + x
Factor x out of x y + x:
Answer: x (y + 1)
Which function is shown in the graph? A. f(x) = x2 – 3x – 10 B. f(x) = x2 + 3x – 10 C. f(x) = x2 + x - 12 D. f(x) = x2 – 5x – 8
The graph shown have roots of x = -2 and x = 5
We could solve for x in each of the quadratic equations or we could plot the graphs of each of the quadratic equation.Then we pick the one with the roots of -2 and 5.
Plotting the graphs:
The roots of quadratic functionis the value of x when y is equal to zero.
From the graph attached above, f(x) = x² + 3x – 10 representing the blue parabola has roots of (-5, 0) and (2, 0).
This means the roots are -5 and 2.
Hence, the function in the graph is f(x) = x² + 3x – 10
There are 4 triangles and 2 circles. What is the simplest ratio of circles to total shapes?
Answer:
1:3
Step-by-step explanation:
circles:total
2:4+2
=2:6
=1:3
Reason
There are 2 circles and 4+2 = 6 shapes total.
The ratio of circles to total shapes is 2:6 which reduces to 1:3
The order is important since 3:1 is different from 1:3.
Write an equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex.
An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.
What is the vertex form of the parabola?The standard vertex form of the parabola is given by,y = a(x - h)² + k where (h, k) is the vertex.
Real numbers, a, h, and k are included here, where a ≠ 0. A point on the parabola is represented by the variables x and y, respectively.Given:
f(x) = 4x²
Vertex = (10,4)
a = 4
The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.
The equation can be written as,
y = a(x - h)² + k where (h, k) is the vertex.
Replacing the value of the vertex, we get
y = 4(x - 10)² + 4
y = 4(x² - 20x + 100) + 4
y = 4x² - 80x + 400 + 4
y = 4x² - 80x + 404
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9. Please help. Thank you
By definition, a one-to-one function is a function that maps distinct elements of its domain to distinct elements of its codomain.
Graph 1
From this graph, we see that for distinct elements of x, we have the same value of y. For example:So this function is NO a one-to-one function.
• f(2) = f(-2) = 4.
T
Graph 2
From this graph, we see that for distinct elements of x, we have the same value of y. For example:is function is NO a one-to-one function
• f(2) = f(4) = 4.
Th.
Graph 3
From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.
Graph 4
From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.
Graph 5
From this graph, we see that for distinct elements of x, we have different values of y.This function is a one-to-one function.
Graph 6
From this graph, we see that for distinct elements of x, we have the same value of y.This function is NO a one-to-one function.
Answer• Graph 1: No
,• Graph 2: No
,• Graph 3: Yes
,• Graph 4: Yes
,• Graph 5: Yes
,• Graph 6: No
A basketball team played six games. In those games, the team won by 8 points, lost by 6, won by 9, won by 10, lost by 4, and won by 7. What was the mean difference in game scores over the six games?
The mean difference in game scores over the six games is 4.
What is mean?The ratio of the overall sum of data to the total number of data sets is known as the mean. Mean is often computed by adding up all the data and dividing it by the total number of data.
Given that a basketball team played six games. In those games, the team won by 8 points, lost by 6, won by 9, won by 10, lost by 4, and won by 7.
The data's mean difference will be determined as follows:
Mean = ( 8 - 6 + 9 + 10 - 4 + 7 ) / 6
Mean = 4
Therefore, the mean difference in game scores over the six games is 4.
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will post a full pictures it did not fit
They will be parallel because the same transformations have been applied to it
What is the slope of the line that passes through the points (9,1) and (10,−1)? Write your answer in simplest form.
The slope of the linear equation that passes through the points (9,1) and (10,−1) is -2.
How to get the slope of the line?For a linear equation that goes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that our line goes through the points (9,1) and (10, −1), so we can use these two values in the equation for the line, we will get:
slope = (-1 - 1)/(10 - 9) = -2/1 = -2
So the slope of the linear equation is -2.
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What is the equation of the parabola with focus at (1, 1) and directrix y = -1?
The equation of the parabola having focus (1,1) and directix y = -1 is
y = x²/4 - x/2 + 1/4
The focus of the parabola (h , k + p) = (1,1)
The directrix of the parabola is y = -1
From, the focus
k + p = 1
k = 1 - p
The formula of directrix is
y = k - p (1)
Substituting the value of directrix and k
-1 = 1 -p -p
-1-1 = -2p
-2 = -2p
p = 1
Substituting the value p in equation (1)
k = 0
Now, we have got the vertex of the parabola (h ,k) is (1,0)
The equation of the parabola is
(x-h)² = 4p (y - k)
(x - 1)² = 4 (1) (y - 0)
( x -1 )² = 4(y )
x² - 2x + 1 = 4y
x²/4 - 2x/4 + 1/4 = y
y = x²/4 - x/2 + 1/4
which is the equation of the parabola.
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You are multiplying as many 5s and 2s as you want but you must have at least one of each. What could the last digit of the product be?
The last digits of multiplying 5s and 2s with at least one of each will be zero (0)
Multiplication of numbersFrom the question, we are to determine what the last digit of the product could be
From the given information,
We are multiplying as many 5s and 2s as we want but we must have at least one of each
Since we must have at least one of each of 5 and 2, we will always have a 5 × 2
But, 5 × 2 = 10
NOTE: 10 multiplied by any number will always result in a number with a last digit of zero (0)
Example
2 × 5 × 2 × 2 × 2 × 2 = 160
5 × 2 × 5 × 5 × 5 × 5 = 6250
Thus, the last the digit of the product will be 0
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number 7 please help mequestions: find the sum of each infinite geometric serie
The sum to infnity of the series is;
[tex]S\infty\text{ = 1,066}\frac{2}{3}[/tex]Here, we want to find the sum to infinity of the given geometric series
We have this as follows;
[tex]S_{\infty}\text{ =}\frac{a}{1-r}[/tex]a is the first term which is 800
The common ratio is r and it is the second term divided over the first or the third over the second
We have this as;
[tex]\frac{200}{800}\text{ = }\frac{50}{200}\text{ = }\frac{1}{4}\text{ =0.25}[/tex]Substituting these values, we have it that;
[tex]S_{\infty}\text{ = }\frac{800}{1-0.25}\text{ = }\frac{800}{0.75}\text{ = 1,066 }\frac{2}{3}[/tex]ZA and ZB are supplementary angles. If m/A= (7x - 20)° and
m/B = (2x - 7)°, then find the measure of ZB.
Answer:
Measure of angle B = 39
Step-by-step explanation:
(7x-20) + (2x-7) = 180 (combime like terms)
9x - 27 = 180 (move 27 to the other side)
9x = 207 (divide both sides by 9)
x = 23
2x - 7 (subsititute x with 23)
2 (23) - 7
46 - 7
39
measure of angle b = 39
The following sequence is a geometric sequence
17
,
51
,
153
,
459
,
1377
,
...
Find the sum of the first 13 terms of this sequence.
What is the common ratio for this sequence?
r
=
What is the index of the final term of this sum?
last index =
What is the sum?
Sum =
Answer:
13,551,737
Step-by-step explanation:
You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....
Common ratioThe common ratio is found by dividing a sequence term by the one before it:
r = 51/17 = 3
The common ratio is 3.
IndexThe index of the 13th term of the sequence is n = 13.
SumThe sum of n terms of a geometric sequence with first term a1 and common ratio r is ...
Sn = a1·(r^n -1)/(r -1)
For a1 = 17, r = 3, and n = 13, the sum is ...
[tex]S_{13}=17\cdot\dfrac{3^{13}-1}{3-1}=17\cdot\dfrac{1594322}{2}=\boxed{13,\!551,\!737}[/tex]
Valentina knits 16 centimeter of scarf each night.How manynightswillValentinahavetospendknittinginordertoknitatotalof48centimetersofscarf?
You have the following information:
- Valentina knits 16 cm of scarf each night.
To determine how many night does Valentina need to knit 48 cm of scarf, you simply calculate the quotient between 48 cm and 16 cm, just as follow:
48/16 = 3
Hence, Valentina needs 3 days to knit 48 cm of scarf
make f the subject when d= 2(1-f) / f-4
[tex]d(f-4)=2(1-f)\\\\frac{d(f-4)}{d} =\frac{2(1-f)}{d} \\f-4=\frac{2(1-f)}{d} \\f=\frac{2(1-f)}{d} +4[/tex]
Attached is the solution
Answer:
Step-by-step explanation:
d= 2(1-f) / f-4
d = 2 - 2f / f-4
d = 1/2 - 2f - f
d = 1/2 - f
0=1/2-f-d
f = 1/2 - d
Rectangle ABCD is congruent to rectangle EFGH. If side EF is 8 feet and side BC is 9 feet, what is area of rectangle EFGH?
Answer:
64 is the area!
- love bri <3
Please help me find the horizontal asymptote.
Answer:
[tex]y=3/2[/tex]
Step-by-step explanation:
[tex]f(t)=\frac{3t^{1/3}}{(64t^2 +4)^{1/6}} \\ \\ =\frac{3}{(64+4t^{-2})^{1/6}} \\ \\ \\ \lim_{t \to \infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \\ \lim_{t \to -\infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \therefore y=3/2[/tex]
What is the missing angle
Answer:
45 degrees
Step-by-step explanation:
The triangle is a 45, 45, 90 meaning that both angles other than the 90 are the same.
Another way to solve is you know that a triangle's angles = 180
Take the 180 and subtract 90 for the right angle
and then subtract 45 for the labeled angle and your answer is 45
Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years)
consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the
2016 Gallup poll of 1,754 Millenials, 55% had a favorable opinion of Sanders than Hillary Clinton
(38%). Calculate the 90% confidence interval for for Hillary Clinton.
*round to two decimals
The 90% confidence interval for Hillary Clinton is
to
Answer:
favorable opinion of Sanders than Hillary Clinton
(38%). Calculate the 90% confidence interval for for Hillary
4m
In a class of 50 students, on average, 10 will be left-handed. If a class includes 25 "lefties", estimate how many students are in the class.
The total number of lefties present in the class are 125.
What is meant by the term percentage?Percentage is an assessment of a portion in relation to a whole, frequently expressed as how many of some there are per 100.A group with half girls as well as half boys is an instance of a situation in which the percentage of boys with in group is equal to 50%.For the given question;
The total students in the class are 50.
There are 10 out of 50 on an average students be left-handed.
Let the percentage of left handed be 'x'.
Then, x% of 50 = 10
x = 10×100 / 50
x = 20%.
Now the average number of left-handed students are 25.
The total students will be.
Let 'y' be the total number of students.
Then, 25 is the 20% of y.
20% of y = 25.
y = 25 ×100 / 20
y = 125
Thus, the total number of lefties present in the class are 125.
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Dina goes to a carnival. Some rides at the carnival have a height requirement, but others do not. Dina is tall enough to go on all rides.
What is a mathematical question you can ask about this situation? What information would you need to know to answer your question?
The mathematical question that can be asked in a situation when Dina goes to a carnival and some rides have a height requirement is how many extra centimeters of height Diana has? The information required to solve this question is the required height for the ride and the height of Diana.
According to the question,
We need to ask a mathematical question. Let's solve a mathematical question in the given situation by taking one example.
If the required height to ride is 150 cm and the height of Diana is 165 cm, how many extra centimeters of height Diana has than the required height?
Solution:
Required height = 150 cm
Dian's height = 165 cm
Extra height = Diana's height - required height of the ride
Extra height = 165 cm - 150 cm
Extra height = 15 cm
Hence, in this supposed situation, Diana's height is 15 cm extra than the required height of the ride.
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Combine the like terms in this expression: -x3 + 2xy + 4y - xy + 2x - 11y
A. -7xy
B. 2xy + 15
C. 23X + y
D. - X + XY -7y
Answer:
[tex]{ \rm{ {x}^{3} + 2xy + 4y - xy + 2x - 11y}} \\ \\ = { \rm{ {x}^{3} + (2xy - xy) + 2x + (4y - 11y)}} \\ \\ = { \rm{ {x}^{3} + 2x + xy - 7y}}[/tex]