Answer:
The next term in the sequence is 5/2 or 2.5.
========================
Given series:
-20, 10, - 5, ...We notice that this is a geometric progression.
The common ratio is:
r = -5/10 = 10/ -20 r = - 1/2To find the next term multiply the last term by the common ratio:
[tex]t_n=rt_{n-1}[/tex]The 4th term is:
[tex]t_4=(-1/2)*(-5)=5/2=2.5[/tex]The graph shows a system of inequalities.
Graph of two inequalities. One is a dashed line increasing from left to right passing through negative 5 comma 0 and 0 comma 5, and it has shading above the line. The second is a dashed upward opening parabola with a vertex at negative 2 comma negative 9 and x-intercepts at negative 5 comma 0 and 1 comma 0. This parabola is shaded on the inside.
Which system is represented in the graph?
y > x2 + 4x – 5
y > x + 5
y < x2 + 4x – 5
y < x + 5
y ≥ x2 + 4x – 5
y ≤ x + 5
y > x2 + 4x – 5
y < x + 5
The system of inequalities having the given feasible regions and points at (-5, 0), and (0, 5), and (-2, -9), (-5, 0), and (1, 0) is the option;
y > x² + 4•x - 5
y > x + 5
How can the required system of inequalities be found?The coordinates of the given points on the linear inequality are;
(-5, 0), and (0, 5)
Slope, m, of the linear inequality is therefore;
m = (5 - 0)/(0 - (-5)) = 1
The equation of the inequality is therefore;
y - 0 > 1•(x - (-5)) = x + 5
Which gives;
y > x + 5Quadratic Inequality;
The coordinates of the points on the quadratic inequality are;
Vertex point = (-2, -9)
x-intercept = (-5, 0), and (1, 0)
Therefore, we have;
y > (x + 5)•(x - 1) = x² + 4•x - 5
y > x² + 4•x - 5The correct option is therefore;
y > x² + 4•x - 5
y > x + 5
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Answer:
y > x2 + 4x – 5
y > x + 5
Step-by-step explanation:
If you put this system into desmos you will see that it matches the photo shown in the question, and it would need to be both greater than symbols because the dotted lines indicate that it is not included in the solution.
What's the forecasted capital expenditure based on the information below? • Net PP&E beginning of period: 15,000 • Net PP&E end of period: 17,500 Depreciation expenses: 2,400
The forecasted capital expenditure related to the information below exists at 4,900.
Therefore, the correct answer is option b) 4,900.
What is Capital?Capital exists directed as the lifeblood of any business. It exists the group of assets of the business that contains their financial value to create the production of goods and services.
For calculating the forecasted capital-
Net PP&E beginning of period = 15,000
Net PP&E end of period = 17,500
Depreciation expenses = 2,400
Forecasted capital expenditure = Net PP&E end of period + Depreciation expenses - Net PP&E beginning of the period
= 17500 + 2400 - 15,000
Forecasted capital expenditure = 4,900
Therefore, the correct answer is option b) 4,900.
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The complete question is:
What’s the forecasted capital expenditure based on the information below?
Net PP&E beginning of period: 15,000
Net PP&E end of period: 17,500
Depreciation expenses: 2,400
Review Later
a) 2,500
b) 4,900
c) 100
d) -100
11
A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively. Which sentence about the points is true?
OA
A, B, C, and D lle on the same line.
OB.
AB and CD are perpendicular lines.
OC. AB and CD are parallel lines.
OD. AB and CD are intersecting lines but are not perpendicular.
OE. AC and BD are parallel lines.
For the given coordinates of A, B, C, and D as (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively, OD, AB and CD are intersecting lines but are not perpendicular (third option) is the correct assertion.
Reasons for the Choice
Because parallel lines never intersect, the fact that lines AB and CD come to a point proves that they are not parallel. It indicates that they are intersecting lines. (Refer to the attached figure)The location where lines AB and CD intersect is not at a straight angle. As a result, lines AB and CD are not parallel.Because the distances separating the two lines differ, AC and BD are not parallel. As a result, lines AB and CD do indeed intersect, but not at a straight angle. Consequently, despite not being perpendicular, both lines intersect.Therefore, the lines OD, AB, and CD are intersecting lines but are not perpendicular.
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Which figure does NOT belong?
Answer:
C (third figure from left)
Step-by-step explanation:
The spirals in the first, second, and fourth figures are all clockwise from the outer end, i.e., if you trace these three spirals with your finger from the outside to the inside, your finger will move clockwise.
However, if you did the same with the third figure, you would see that the spiral is anti-clockwise from the outside moving in.
Therefore, the third figure doesn't belong.
PLEASE HELP
Determine which quadratic equation reveals its maximum or minimum value without changing the form of the equation.
y=x² + 4x-3
y = -3(x+4)² + 1
y=(x-9)(x + 7)
y=2x²-5x+4-10
y=x²+(3+1)x-3
y=x²+3x+1x-3
y=x(x+3)-1(x+3)
y=(x-1)(x+3)
Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
Set A: 1 2 3 23 24 25
Set B: 9 10 11 14 16 18
If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.
Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.
Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
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The Black Pearl is following a course that is represented by the equation. + ? = 14. . The interception course of the Flying Dutchman is represented by the equation
Use the graphing method to determine the coordinate point where the two ships’ paths meet.
According to the graph, the ships’ paths do not meet at any point.
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the point where the two ships' path meet?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x = 5y - 40
-4x + 10y = 20
Make y the subject in the second equation, by adding 4x to both sides of the equation
4x -4x + 10y = 20 + 4x
This gives
10y = 20 + 4x
Divide both sides by 10
y = 2 + 0.4x
Substitute y = 2 + 0.4x in 2x = 5y - 40
2x = 5(2 + 0.4x) - 40
Expand
2x = 10 + 2x - 40
Subtract 2x from both sides of the equation.
2x - 2x = 10 + 2x - 2x - 40
Evaluate the like terms
0 = 10 - 40
Evaluate the like terms
0 = -30
The above equation is not true.
This means that the ships’ paths do not meet at any point.
This can be confirmed using the attached graph.
From the graph, we can see that the lines of 2x = 5y - 40 and -4x + 10y = 20 do not intersect
Hence, we can conclude that the ships’ paths do not meet at any point.
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Decimals from greatest to least
.750
.475
-0.123
.675
.253
Answer:
0.75, 0.675, 0.475, 0.253, -0.123
Step-by-step explanation:
Positive Numbers will always be greater than negative numbers, so you know -0.123 comes at the end.
Example
0.ABC
The tenth's place (A in the number above) holds the most weight. 0The hundreth's place (B in the number above) holds the second most weight. The thousandth's place (C in the number above) holds the third most weight.
Comparing 0.75 and 0.675 is the same as comparing 75 and 67.5. When in doubt, you can multiply the decimals by 100 to determine their order of value.
120 high school seniors were asked,
"Are you going to the graduation
party?" Of those 120 students, 75 said yes. Estimate the population mean
that a senior will say they are going to the graduation party.
Using proportions, the estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.
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 or inverse proportional, can be built to find the desired measures in the problem.
The estimate of a population proportion is the sample proportion. In this problem, the sample proportion is of 75 out of 120 students, hence:
p = 75/120 = 0.625 = 62.5%.
The estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.
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I need help asap. everythings in the image
The function in terms of the time (t) is t=d/r and the value of the time (t) for the given values is 5.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
For the given example: a=2 and b=7.
In the exercise is asked the equation for the time (t) in the function of the distance (d) and the rate (r).
Thus, if d=rt, we will have t= d/r
Replacing the variables for the given values for finding t. The question gives:
distance (d) =40
rate (r) = 8
Thus, you will have t= 40/8. Then, t=5
Therefore, the answer is the fourth option.
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Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
The factored form of the given quadratic expressions are
1. (x -1)(x +7)
2. (x -2)(x -3)
3. (x +1)(x -7)
4. (x -1)(x +6)
5. (x -3)(x +4)
6. (x +2)(x -4)
7. (x +1)(x -5)
8. (x -1)(x +3)
9. (x +4)(x -4)
10. (x +3)(x -4)
11. (x -3)(x -6)
12. (x +2)(x -7)
13. (x -2)(x -5)
14. (x -3)(x -8)
15. (x +5)(x -6)
Factoring quadratic expressionsFrom the question we are to factor the given quadratic expressions
1. x² + 6x - 7
x² +7x -x - 7
x(x +7) -1(x +7)
(x -1)(x +7)
2. x² -5x +6
x² -3x -2x +6
x(x -3) -2(x -3)
(x -2)(x -3)
3. x² -6x -7
x² -7x +x -7
x(x -7) +1(x -7)
(x +1)(x -7)
4. x² +5x -6
x² -x +6x -6
x(x -1) +6(x -1)
(x -1)(x +6)
5. x² + x - 12
x² +4x -3x -12
x(x +4) -3(x +4)
(x -3)(x +4)
6. x² -2x -8
x² -4x +2x -8
x(x -4) +2(x -4)
(x +2)(x -4)
7. x² -4x -5
x² -5x +x -5
x(x -5) +1(x -5)
(x +1)(x -5)
8. x² + 2x - 3
x² +3x -x -3
x(x +3) -1(x +3)
(x -1)(x +3)
9. x² - 16
(x +4)(x -4)
10. x² -x -12
x² -4x +3x -12
x(x -4) +3(x -4)
(x +3)(x -4)
11. x² -9x +18
x² -6x -3x +18
x(x -6) -3(x -6)
(x -3)(x -6)
12. x² -5x -14
x² -7x +2x -14
x(x -7) +2(x -7)
(x +2)(x -7)
13. x² -7x +10
x² -5x -2x +18
x(x -5) -2(x -9)
(x -2)(x -5)
14. x² -11x +24
x² -8x -3x +24
x(x -8) -3(x -8)
(x -3)(x -8)
12. x² -x -30
x² -6x +5x -30
x(x -6) +5(x -6)
(x +5)(x -6)
Hence, the factored form of the given quadratic expressions are
(x -1)(x +7)
(x -2)(x -3)
(x +1)(x -7)
(x -1)(x +6)
(x -3)(x +4)
(x +2)(x -4)
(x +1)(x -5)
(x -1)(x +3)
(x +4)(x -4)
(x +3)(x -4)
(x -3)(x -6)
(x +2)(x -7)
(x -2)(x -5)
(x -3)(x -8)
(x +5)(x -6)
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1) The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to determine whether there is a correlation between percentage of vote and income
level at the 0.01 significance level with a null hypothesis of ρs = 0.
A) The test statistic is between the critical values, so we fail to reject the null hypothesis. There is no
evidence to support a claim of correlation between percentage of vote and income level.
B) The test statistic is not between the critical values, so we fail to reject the null hypothesis. There is no
evidence to support a claim of correlation between percentage of vote and income level.
C) The test statistic is between the critical values, so we reject the null hypothesis. There is sufficient
evidence to support a claim of correlation between percentage of vote and income level.
D) The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient
evidence to support a claim of correlation between percentage of vote and income level
Option C is correct. The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.
How to find the correlationThe scatter plot is the plot that is used to show the correlation that is known to exist between the given data sets that is of interests. It helps by showing the existing relationship between the x values and the y values in the question.
When we look at the graph properly, if we are to rule a line we would find out that most of the data points in the equation fall under the line in the data set. This shows that there is high correlation between these two variables.
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You need a 75 % alcohol solution. On hand, you have a 260 mL of a 30% alcohol mixture. You also have 95 % alcohol mixture . How much of the 95% mixture will you need to add to obtain the desired solution? You will need mL of the 95% solution
[tex]30 \: percent \: alcohol \: in \: 260 \: ml \\ alcohol = 0.3 \times 26 0= 78 \: ml[/tex]
[tex]c( \gamma ) = \frac{78 + 0.95\gamma }{260 + \gamma } \times 100[/tex]
[tex]c( \gamma ) = 75[/tex]
[tex] \frac{78 + 0.95\gamma }{260 + \gamma } = 0.75[/tex]
[tex]78 + 0.95\gamma = 0.75 \gamma + 195 \\ 0.2 \gamma = 117 \\ \gamma = 585[/tex]
[tex]we \: need \: 585 \: ml \: of \: 95% \: alcohol[/tex]
Answer:
You will need 585 mL of the 95% solution.
Step-by-step explanation:
How to make 3 dimensional object become 4 dimensional object
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.What is a 4 dimensional shape?A four-dimensional shape (4D) is a mathematical extension of a three-dimensional or 3D space.
Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects.
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.Learn more about dimensional shapes here:
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Craig has a watch that is losing time. For every minute that passes, his watch loses 10 seconds. If Craig set his watch correctly at 9am, what time whould it show when it is 10am on the house clock?
Answer:
9:50 am
Step-by-step explanation:
because 10 x 60 is equal to 1 hour, so you get 600 seconds subtracted from 10am. 600 seconds is equal to 10 minutes. so 10 am - 10 minutes = 9:50am
5=logb(32) what does b equal
Answer: 2
Step-by-step explanation:
When a^b = c, loga(c) = b
So b^5 = 32 and b is 2
In 5-card poker, find the probability of being dealt the following hand. Refer to the table. Note that
a standard deck of playing cards has 52 cards-4 suits (clubs, diamonds, hearts, spades), where
each suit has 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King).
no pair
The probability of being dealt no pair is
(Type an integer or decimal rounded to eight decimal places as needed.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
Number of
Outcomes
Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
The probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favourable outcomes = 1302540
The probability of being dealt no pair:
P(no pair) = 1302540/2598960
P(no pair) = 0.5011
In percentage:
P(no pair) = 50.11%
Thus, the probability of being dealt no pair is 0.5011 or 50.11% if the tandard deck of playing cards has 52 cards-4 suits.
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1. If A = {a, b, c, d}, B={c, d, e, f}, C={x, y, z} find (A-B)
Answer
here
A={a,b,c,d}
B={c,d,e,f}
C={x,y,z}
A-B={e,f}
The function y = x2 + 3 is a transformation of the function y = x2. How is the y-intercept of the function affected by the transformation?
The y-intercept of the graph of y = x2 is shifted down 3 units.
The y-intercept of the graph of y = x2 is shifted to the left 3 units.
The y-intercept of the graph of y = x2 is shifted to the right 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
-----------------------------------------------------------------------------------------------
Answer on Edmentum is:
The y-intercept of the graph of y = x2 is shifted up 3 units.
Explanation:
The graph of a function in the form y = f(x) + k is the graph of f shifted up k units. The graph of y = x2 + 3 is the graph of y = x2 shifted 3 units up, so the y-intercept of the graph of y = x2 is shifted up 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the parent function f(x) = x^2
If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;
g(x) = f(x) + 3
g(x) = x^2 + 3
Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3
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A metallurgist has one alloy containing 26% copper and another containing 69% copper. How many pounds of each alloy must he use to make 53 pounds of a third alloy containing 50% copper?
The pounds of alloy that contains 26% copper that would be used is 23.42 pounds.
The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.
What are the linear equations that represent the question0.26a + 0.69b = (53 x 0.5)
0.26a + 0.69b = 26.50 equation 1
a + b = 53 equation 2
Where:
a =pounds of alloy that contains 26% copperb = pounds of alloy that contains 69% copperHow many pounds of each alloy should be in the third alloy?Multiply equation 2 by 0.26
0.26a + 0.26b = 13.78 equation 3
Subtract equation 3 from equation 2
12.72 = 0.43b
b = 12.72 / 0.43
b = 29.58 pounds
a = 53 - 29.58 = 23.42 pounds
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I, so confused please help me asap!
Quadrilaterals are plane shapes that are bounded by four straight sides. Thus, the required answers to the questions are:
46. True. Other examples include kites, rhombus, etc.
47. False.
46. When a plane shape is bounded by four straight sides of equal or different lengths, it is called a quadrilateral. Examples include trapezium, kite, rhombus, rectangle, square, etc. Each of these examples has individual properties.
Thus the required answer to question 46 is; True. It can be observed that with respect to their individual properties, other quadrilaterals which have a pair of opposite angles to be equal include: kite, rectangle, rhombus, etc.
47. A ray segment is a given line that points or heads in a specific direction. So that the direction in which the ray moves is very important.
Thus in the given question, the required answer is; False. This is because the two given rays are moving in opposite directions. Though the two rays may have the same length of the segment.
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If Lonnie has 40 plants and half of his plants die...how many plants does that
equal?
A 20
B 15
C 25
Answer:
20
Step-by-step explanation:
We know that she initially had 40 plants. The half of 40 is 20. That is also the number of plants that died.
Answer: A. 20
Step-by-step explanation:
Given Information:
Original = 40 Plants
New = Half Died
Find the number of plants that died:
40 × (1 / 2) = 40 / 2 = 20 Plants
or
40 ÷ 2 = 20 Plants
Therefore, it equals to [tex]\boxed{20 \:Plants}[/tex]
Hope this help!! :)
Please let me know if you have any questions
How to Convert 11010112 to base 10?
Answer:
So this is all you need to do!
Hope it helped you:)
The population of a rabbit colony triples every 3 days. The population starts at 10 rabbits. Write an exponential function that will model the population of the colony after, t, days have passed.
Answer:
DO not working in you
Step-by-step explanation:
PLEASE help me in answering
Answer:
Step-by-step explanation:
The population at various days is as follows since population triples every 3 days
Day Population
0 10
3 30
6 90
9 270
.... ......
This can be modeled by the general equation
[tex]n_{t} = n_{0}(r)^{t/k}[/tex]
where
[tex]n_{t}[/tex] is the population after t days
[tex]n_{0}[/tex] is the population at start (10)
[tex]r[/tex] is the rate at which population changes ie 3
[tex]t[/tex] is the number days from start
[tex]k[/tex] is the number of days at which the population triples(here k =3 days)
We can check this by plugging in values for each of the variables
At day 0, population = 10(3)⁰ = 10. 1 = 10
Similarly populations for days 3, 6, 9 are:
[tex]\\\\10.3^{3/3} = 10. 3^1 = 10.3 = 30\\10.3^{6/3} = 10. 3^2 = 10.9 = 90\\\\10.3^{9/3} = 10. 3^3 = 10.27 = 270[/tex]
There are 3
denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills. There are half as many
$10-bills as $5-bills. If there is $115 altogether, find the number of
each type of bill in the wallet.
The number of $1, $5 and $10 are 49, 44 and 22 respectively.
How to use equation to find the number of bills?There are 3 denominations of bills in a wallet: $1, $5, and $10.
There are 5 fewer $5-bills than $1-bills.
let
x = number of $1 bills
Hence,
number of $5 bills = x - 5
There are half as many $10-bills as $5-bills.
number of $10 bills = 1 / 2 (x - 5)
Therefore,
x + x - 5 + 1 / 2 (x - 5) = 115
2x - 5 + 1 / 2 x - 5 / 2 = 115
2x + 1 / 2 x - 5 - 5 / 2 = 115
5 / 2 x - 7.5 = 115
2.5x = 115 + 7.5
x = 122.5 / 2.5
x = 49
Number of $1 bills = 49
Number of $5 bills = 49 - 5 = 44
Number of $10 bills = 1 / 2 (49 - 5) = 22
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Graph the line y+3x=-3
Answer: y = -3x-3 (Choose values for x)
Step-by-step explanation:
1st change the equation to y = mx+b form
In order to change the equation to y = mx+b form subtract the 3x to both sides.
The equation now becomes y = -3x-3
2nd we can either choose values for x such has (-2,-1,0,1,2) and plug in those values into our equation y = -3x-3
For example, if we plug in x= -2 we get y= -3(-2)-3 which becomes y =3. We then plot the point (-2,3) because -2 is our x coordinate and 3 is our y coordinate.
Or we can plug the equation into a calculator that will graph the equation for you.
5. If 15 men can finish a work in 16 days in how many days will 8 men can finish the same work? a. 15 b. 20 c. 30 d. 42
Answer:
C. 30
Step-by-step explanation:
15 men do work in 16 days
This means that 7.5 men (15/2) would do that same work in 32 days (16x2).
If the number of men increase, the amount of days decrease.
8 men would do that work in 30 days
8 men > 7.5 men
30 days < 32 days
Answer:
Option c.
Step-by-step explanation:
It is an inverse proportion, fewer workers more days to finish the job.
15 -----16
8 ----- x
x = (16)(15)/8 = 240/8 = 30 days
Hope this helps
Find a formula for the nth term in this
arithmetic sequence:
a₁ = 7, a2 = 4, a3 = 1, a4 = -2, ...
an
=
[?]n +
Answer:
[tex]a_{n} = -3n + 10[/tex]
Step-by-step explanation:
The arithmentic function formula is:
[tex]a_{n} = a_{1} + d(n-1)[/tex]
Let's plug in what we know. [tex]a_{1}[/tex] (the first term in our sequence) is 7. d (the common difference) is -3. This means we are subtracting 3 every time.
Plugging that in to the formula, we get
[tex]a_{n} = 7 -3(n-1)[/tex]
Now we distribute and combine like terms.
[tex]a_{n} = 7 - 3n +3[/tex]
[tex]a_{n} = 10 - 3n[/tex]
Change the order to fit the format and you get
[tex]a_{n} = -3n + 10[/tex]
find the x-intercept of the graph of the equation y=(x+2)(x-1)
Answer:-2,0 & 1,0
Step-by-step explanation:
Substitute them in with zero product property
If f(x) = -1x + 1and g(x) = x4, what is (f º g)(x)?
Answer:
(f º g) = [tex]-x^4+1[/tex]
Step-by-step explanation:
So it's important to note that the notation: "(f º g)" isn't f(x) * g(x), it's a composite function, where you essentially have two functions, with one of the functions being the argument of one of the functions.
This means we can plug in the function g(x) as x into the function f. So let's do that
Original Function:
f(x) = -1x + 1
Plug in x^4 (this is the value of g(x)) as x into the function
f(g(x)) = [tex]-(x^4)+1[/tex]
Distribute the negative sign
f(g(x)) = [tex]-x^4+1[/tex]