How many solutions exist for |1/2x + 1| = 5?
Answers
There are two solutions for the equation |1/2x + 1| = 5: x = 8 and x = -12.
To determine the number of solutions for the equation |1/2x + 1| = 5, we need to consider the possible cases based on the absolute value expression.
Case 1: 1/2x + 1 = 5
In this case, we isolate the absolute value expression by subtracting 1 from both sides:
1/2x = 4
To solve for x, we multiply both sides by 2:
x = 8
This is one solution.
Case 2: 1/2x + 1 = -5
In this case, we isolate the absolute value expression by subtracting 1 from both sides:
1/2x = -6
To solve for x, we multiply both sides by 2:
x = -12
This is another solution.
Therefore, we have found two solutions for the equation |1/2x + 1| = 5: x = 8 and x = -12.
It's important to note that the absolute value function |1/2x + 1| can be equal to 5 for both positive and negative values of x, resulting in two solutions.
The absolute value function yields the positive magnitude of the expression inside the absolute value bars, so we consider both positive and negative solutions.
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Related Questions
(-1/3x+9.5)+ x(3/4+2.5)
Answers
Answer:
35/12 x + 19/2
Step-by-step explanation:
Answer: =35/12x+9.5
Step-by-step explanation: look at the picture it have the explain
use a number line to solve the sum
2+5
Answers
Answer:
"7" Would be your answer.
Step-by-step explanation:
Explain the difference between using area and volume with 2-D and 3-D figures.Each answer must be explained in detail using the correct vocabulary to receive full credit.
Answers
The area is defined as the region covered by two-dimensional shapes. The area of different shapes depends on their dimensions. The 2d shapes include circle, triangle, square, rectangle, parallelogram, pentagon, hexagon, etc. Hence, all these shapes have different areas. It is measured in square units.
Volume is a parameter that is defined only for three-dimensional objects. For each three-dimensional shape, such as sphere, cube, cuboid, cylinder, cone, etc., the volume is different. It is measured in cubic units.
The key difference between area and volume is: the area is the region covered by a 2d-shape whereas volume is the space occupied by a 3d shape.
Steve and Michelle Neely are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted $2000 for their reception. If the reception hall charges a $60 cleanup fee plus $30 per person, find the greater number of people that they may invite and still stay within their budget. ( round down to the nearest whole person )
Answers
We have a budget of $2000. This is the maximum cost of the reception.
The cost has a fixed part, that is $60, and a varaible part, which is $30 per person.
Then, if n is the number of people invited, then the cost can be expressed as:
\(C(n)=60+30\cdot n\)We know that this cost has to be $2000 at most, so we can find n as:
\(\begin{gathered} C(n)=60+30n\le2000 \\ 60+30n\le2000 \\ 30n\le2000-60 \\ 30n\le1940 \\ n\le\frac{1940}{30} \\ n\le64.67 \end{gathered}\)Then, as n ≤ 64.67, the maximum number of people they can invite with this budget is 64 people.
Answer: 64 people.
What steps should be taken to calculate the volume of the prism? Select three options. A rectangular prism with a length of 9 and one-half feet, width of 24 feet, and height of 6 feet. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. Use the formula V = B h to find the volume of the prism. The volume of the prism, V is (114) (6) = 684 feet cubed. The volume of the prism, V is (228) (6) = 1,368 feet cubed.
Answers
The volume of the rectangular prism will be 1368 cubic feet. Then the correct formula is C.
What is the volume of the rectangular prism?
Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
V = B x H
Where B is the base area of the prism. Then we have
A rectangular prism with a length of 9 and one-half feet, a width of 24 feet, and a height of 6 feet.
Then the volume of the prism will be
V = 9.5 x 24 x 6
V = 1368 cubic feet
Then the correct formula is C.
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The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p).^1(a) What is the meaning of the derivative f^1(8)? What are its units?
The derivative f'(8) gives the rate of change of the quantity (in pounds) of coffee sold as we increase the price (in dollars).
The units of the derivative are always output units from original function input units from original function . For the original function, the output is pounds of coffee sold, and the input is the price in dollars per pound.
Thus the units for f′(8) are pounds dollars/pound.(b) Is f′(8) positive or negative? Explain. We interpret the rate given by the derivative as the input increases, so the price per pound is increasing. From the law of supply and demand, as the price increases, the quantity sold decreases. Thus we expect
f′(8) to be negative.
Answers
The answers to both subparts are shown:
(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.
(B) The unit of f'(5) is pounds/dollar.
What is derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument.
Calculus's core tool is the derivative.
We may find the slope of a function at any point by using its derivative. We can find numerous derivatives by adhering to certain rules.
For instance: A constant value, such as 3, always has a slope of 0.
(A) Meaning of derivative of: f'(5)
We have: Q = f(p) ...(1)
Differentiating Q in relation to p results in:
qQ/dp = f'(p) ...(2)
The rate of change of the price per pound in relation to the volume of coffee sold is implied by equation (2).
If p = 5, we get:
qQ/dp = f'(5) ...(3)
The rate at which the price per pound changes in relation to the amount of coffee sold at $5 per pound is implied by equation (3).
(B) Unit of f'(5):
Equation (3)'s result that qQ/dp = f'(5) suggests that f'(5) units are pounds/dollar.
Therefore, the answers to both subparts are shown:
(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.
(B) The unit of f'(5) is pounds/dollar.
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Correct question:
The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p). (a) What is the meaning of the derivative f '(5)? The rate of change of the price per pound with respect to the quantity of coffee sold. The supply of coffee needed to be sold to charge $5 per pound. The rate of change of the quantity of coffee sold with respect to the price per pound when the price is $5 per pound. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound. The price of the coffee as a function of the supply. What are the units of f '(5)? dollars dollars/pound pounds/(dollars/pound) pounds dollars/(pound/pound) pounds/dollar
Arrange the integers 1,4,8,12,17,32 so that all consecutive integers add to a perfect square. Enter your answer with numbers separated by commas.
Answers
One possible answer is: 1, 8, 17, 32, 4, 12
I don't know if there's a methodical way to get this answer. I used trial and error. I started with 1 and looked through the list to see what adds to 1 to get a perfect square. That would be 8 since 1+8 = 9 = 3^2
The process is repeated but this time for 8. After a bit of guess and checking, we see that 8+17 = 25 = 5^2.
Then after 17 is 32 because 17+32 = 49 = 7^2.
Keep doing this until all of the values are used up. If you get stuck, then try backtracking to a previous branch/path where everything worked and try another fork in the road. If that doesn't work, then try starting the sequence with a completely different value (instead of 1).
Other answers may be possible. I haven't checked all possible permutations.
Help no links Pleaseeeeeee
Answers
Answer:
\(\huge\boxed{z=6;\ x=12.5}\)
Step-by-step explanation:
If two figures are similar, then corresponding sides are in proportion.
Therefore:
\(\dfrac{z}{15}=\dfrac{4}{10}\qquad|\text{cross multiply}\\\\10z=(15)(4)\\\\10z=60\qquad|\text{divide both sides by 10}\\\\\boxed{z=6}\)
\(\dfrac{x}{5}=\dfrac{10}{4}\qquad|\text{cross multiply}\\\\4x=(5)(10)\\\\4x=50\qquad|\text{divide both sides by 4}\\\\x=\dfrac{50}{4}\\\\\boxed{x=12.5}\)
100 POINTS PLEASE HELP FAST
Select the correct answer.
The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time?
Answers
The top left graph represents the weight of the radioactive isotope over time.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
\(y = ab^x\)
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for the function in this problem are given as follows:
a = 96, b = 0.5.
Hence the function is given as follows:
\(y = 96(0.5)^x\)
Two points on the graph of the function are given as follows:
(1,48) and (2, 24).
Hence the top left graph represents the weight of the radioactive isotope over time.
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Answer:
Graph W
Step-by-step explanation:
The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.
Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).
The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.
Initial weight: 96 grams
After 1 hour: 96 / 2 = 48 grams
After 2 hours: 48 / 2 = 24 grams
After 3 hours: 24 / 2 = 12 grams
After 4 hours: 12 / 2 = 6 grams
After 5 hours: 6 / 2 = 3 grams
So, the points on the graph would be:
(0, 96), (1, 48), (2, 24), (3, 12), (4, 6), (5, 3)Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.
If the median is 3.5, we can assume the mean is ____________than 3.5
Answers
We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
What is mean?The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.
According to question:We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.
For example, consider the following two data sets:
Set 1 data: 1, 2, 3, 4, and 5.
The median is 3.
The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.
Data set 2: 1, 2, 3, 4, 10
The median is 3.
The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.
In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.
Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
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You deposit $300 in an account that earns simple interest at an annual rate of 6.5%.
If no other deposits or withdrawals were made, what is the total amount of money in the account at the end of 8 years?
Answers
Total amount of money in the account will be $456.
How much money will be in the account after 8 years?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.
The formula for simple interest is: Simple Interest = Principal × Rate × Time
Principal (P) is $300
Rate (R) is 6.5%
Time (T) is 8 years.
Simple Interest = $300 × 0.065 × 8
Simple Interest = $156
Total Amount = Principal + Simple Interest
Total Amount = $300 + $156
Total Amount = $456.
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Determine the endpoints of the midsegment connecting side YX and side YZ. Question options: A) (4, 3) and (8, 0) B) (9, –4) and (7, 4) C) (4, 3) and (5, –1) D) (1, 2) and (7, 4)
Answers
Answer:c) (4,3) and (5.-1)
Step-by-step explanation:
The endpoints of the midsegment connecting side YX and side YZ
(4, 3) and (-3/2, 11/2).
What is a midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
X = (7, 4)
Y = (1, 2)
Z = (-4, 9)
The midpoint of YX is (4, 3).
i.e
x = (1 + 7)/2 = 4 and y = (2 + 4)/2 = 3
The midpoint of YZ is (-3/2, 11/2).
i.e
x = (-4 + 1)/2 = -3/2 and y = (9 + 2)/2 = 11/2
Thus,
The endpoints of the midsegments are
(4, 3) and (-3/2, 11/2).
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y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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Can you guys tell me this is very important
Answers
Answer:
2 weeks
Step-by-step explanation:
Write an equation that represents each side of the figure. Write your equations in slope-intercept form.
Answers
Answer:
Top: y=3
Top right: y=-3/2x+6
Bottom right: y=3/2x-6
Bottom: y=-3x
Bottom left: y=-3/2x-6
Top left: y=3/2x+6
Step-by-step explanation:
Top: y=3
Top right: y=-3/2x+6
Bottom right: y=3/2x-6
Bottom: y=-3x
Bottom left: y=-3/2x-6
Top left: y=3/2x+6
Find the length of side X in simple radical form with a rational denominator
Answers
The length of side X in simple radical form with a rational denominator is 10/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 2 × 5/√3
Hypotenuse, x = 10/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The ratio of top dogs to fat cats was 24 to 19. if they were 152 fat cats, how many top dogs were there?
Answers
The ratio shows how many times one value is contained in another value.
The number of top dogs is 192.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of top dogs to fat cats was 24 to 19.
if they were 152 fat cats.
This means,
Number of top dogs = 24x
Number of fat cats = 19x
Now,
Number of fat cats = 152
This means,
152 = 19x
x = 8
Now,
Number of top dogs = 24x
= 24x
= 24 x 8
= 192
Thus,
The number of top dogs is 192.
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100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answers
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
what is 3 +(-4) on a number line
Answers
need help with this with a summary and all work shown to help me understand better
Answers
Given:
\(a=49\text{ and b=7.}\)a varies directly b.
Required:
We need to find the equation that relates a and b.
Explanation:
Given that a varies directly as b. It can be written as follows.
\(a=\beta b\)\(Substitute\text{ a =49 and b =7 in the equation to find the value of }\beta.\)\(49=\beta(7)\)Divide both sides by 7.
\(\frac{49}{7}=\beta\frac{7}{7}\)\(\beta=7\)\(Substitute\text{ }\beta=7\text{ in the equation.}\)\(a=7b\)Final answer:
The equation that relates a and b.
\(a=7b\)I NEED HELP
Check all the equations.
8 = j – 4
the quotient of a number and two
k + 46
Twelve is the sum of a number and six.
30y
5x = 45
Answers
Answer:
8=j-4 the quotient of a number and two=n/2
12=j
Step-by-step explanation:
Twelve is the sum of a number and six.=n+6=12, n=6
k plus forty six (k+46)
y multiplied by 30 (30y)
5x=45=
x=9
sorry the answers are mixed up
Answer: ADF
Step-by-step explanation: have a great day and good luck!!! <3
Can I get help with this, I’m so confused
Answers
The linear and exponential equations for the amount of money in the banks indicates;
TCF Bank Equation
y = 100·x + 1000
Well Fargo Bank Equation
y = (1.06)ˣ
The number of years it will take for both accounts to have the same amount of money is about 17 years
What is an exponential equation?An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.
The equation for calculating the amount in each bank, based on the details are;
TCF Bank;
Amount invested = $1,000
Amount added each year = 100·x
The TCF Bank Equation is; y = 100·x + 1000Well Fargo Bank Equation
The percentage of the amount earned as interest each year = 6% = 0.06
The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ
Therefore; y = 1000·(1.06)ˣ
The Well Fargo Bank Equation is; y = 1000·(1.06)ˣWhen the amount in the two accounts have the same amount of money, we get;
1000·(1.06)ˣ = 100·x + 1000
Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1
(1.06)ˣ = 0.1·x + 1
Solving the above equation using the substitution method and graphing indicates that we get;
x = 0, and x ≈ 17.125732
Therefore, it takes about 17 years for the two accounts to have the same amount of money
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Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is qual to the number of gift bags. Raoul needs to make. Then find how many wristbands and how many movie passes raoul can put in each gift bag if he evenly distributes the items.
Please help I am stuck I am doing work nonstop on all weekends if I don’t get this right and done please help and will give brainlesst for the correct answer
Answers
Answer:
Step-by-step explanation:
I do know give me brainliest first
Answer:
24 gift bags
Step-by-step explanation:
Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!
May I have heart, 5 star, and brainliest please?
Graciela begins the month with $300 and is spending $20 per
week. Her brother Sergio begins the month with $150 and is saving $10 per week. Sergio wants to know when they will have the same amount of money.
W
Let represent the number of weeks since the beginning of the
month. Which equation represents this situation?
Answers
Answer:
300-20w=?
150+10w=?
Step-by-step explanation:
Answer:
Step-by-step explanation:
320
(24x3 − 14x2 + 20x + 6) ÷ (4x2 − 3x + 5) = Q +
R
4x2 − 3x + 5
Answers
Answer:
Q= 6x+1
R= -7x+1
Step-by-step explanation:
Answer:
Q= 6x+1 R=-7x+1
Step-by-step explanation:
edge
(+3
+(+2)
help me with directed numbers pls
Answers
Answer:
5
Step-by-step explanation:
(+3 + (+2))
Remove the brackets.
3 + (+2)
3 + 2
Add the numbers.
= 5
Answer:
+5 or 5
Step-by-step explanation:
(+3)+(+2)
=> According to the rule, ( + )( + ) = ( + )
So,
=> +3+2
=> +5
A local business had various advertising campaigns. It had television ads numbered 1,2,3,4,5,6, newspaper and magazine ads numbered 1,2,3,4,5, and social media ads labeled 1,2. If a single advertisement campaign is picked at random, what is the probability that the advertisement is a social media ad AND has an odd number?
Provide the final answer as a fraction.
Answers
Answer:
1/2
Step-by-step explanation:
The probability that the advertisement is a social media ad and has an odd number is 1/13.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, A local business had various advertising campaigns. It had television ads numbered 1,2,3,4,5,6, newspaper and magazine ads numbered 1,2,3,4,5, and social media ads labeled 1,2.
We need to find If a single advertisement campaign is picked at random, what is the probability that the advertisement is a social media ad AND has an odd number,
Probability = favorable outcomes / possible outcomes
Number of social media ads with an odd number = 1
Total number of ads = 13
We know that,
P(that the advertisement is a social media ad AND has an odd number)
= 1/13.
Hence, the probability that the advertisement is a social media ad and has an odd number is 1/13
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Does anyone know how to
Solve the system of equations.
−3x+y=2
7x−8y=1
Answers
add 3x to both sides, so y = 3x + 2
then add that into the other equation for y.
7x - 8(3x +2) = 1
7x- 24x - 16 = 1
-17x - 16 = 1
-17x = 17
x= -1
now that you know what x is, you can find out y with the equation we made earlier. y = 3x+2
y = 3(-1) + 2
y = -3 + 2
y = -1
Holly use 7 sheets tissue paper to make one flower. she bought a package with 500 sheets of tissue paper about how many tissue flowers will she be able to make.
Can you break it down so I can show my daughter
Answers
Answer:
70
Step-by-step explanation:
What U will first want to do is divide 500 by 7 and U will get 71.42.
Then Im guessing sense it says about it will round to about 70 Paper Flowers.
Hope This Helps!!!
70
What you will first want to do is divide 500 by 7 you will get 71.42.
rounded about 70 tissue things-
Consider the following graph of an exponential function.
Answers
Answer:
A= All are real numbers
B=y>-2
c= the graph is not increasing
d= the graph is decreasing for all real numbers of x
none for both
Step-by-step explanation:
A= All are real numbers
B=y>-2
c= the graph is not increasing
d= the graph is decreasing for all real numbers of x
none for both