Answers
The painting is a square, which means all its sides are equal.
If x is the length of one side, then, all the remaining 3 sides also have the same length: x.
The area of a square is the square if its side, then, for a square with sides x:
[tex]\text{Area}=x\cdot x=x^2[/tex]We know that the area of the painting will be 400 square inches, then:
a. The equation that can be set up to find the length of a side is:
[tex]x^2=400in^2[/tex]b. We can solve the equation by finding a number that multiplied by itself gives 400. For this case, we have two solutions. 20 and -20, since:
[tex]20^2=20\cdot20=400[/tex]And:
[tex](-20)^2=(-20)\cdot(-20)=400[/tex]-20 is also a solution because as a negative number, when multiplied by itself, gives a positive one. (A product between negative numbers gives always a positive number).
c. We have two solutions, however, only one of them makes sense: the 20. A negative length makes no sense, so we can discard the second solution (-20).
d. The length of the wood trim needed to go around the painting is then 20 inches. (we should not forget the units.)
Related Questions
You have 900 feet of fencing to enclose a rectangular plot that borders on
a river. If you do not fence the side along the river, find the length and
width of the plot that will maximize the area. What is the largest area that
can be enclosed?
The width, labeled x in the figure, is
(Type an integer or decimal.)
feet.
X
River
900-2x
x
Answers
Answer:
A = 101250 meter²
Step-by-step explanation:
Answer:
Maximum area enclosed will be 101250 meter².
Step-by-step explanation:
Let the length of the rectangular plot is x meters and the width is y meters.
900 meters is the length of the fence which represents the length of the three sides of the plot.
Therefore,
x + 2y = 900
y =  meters
Now the area of the rectangular plot will be
A = Length × Width
= (x)(y)
= 
= 450x - 
We know for the maximum area we will differentiate the area and equalize it t the zero.

= 450 - x
For the maximum area, 
Therefore, 450 - x = 0
x = 450
and y = 
y = 
y = 450 - 225
= 225 meters
Now the area enclosed A = 450 × 225
A = 101250 meter²
How do I simplify???
Answers
1. [tex]i^{23}[/tex] = - i
2. [tex]\sqrt{-128}[/tex] = 8i√2
Explanation:Steps to simplify complex numbers:
Write the division as a fraction when dividing complex numbers. Then multiply both the numerator and the denominator by the denominator's conjugate. Then, use FOIL or the Distributive Property to simplify.Understanding how complex numbers work in their various operations requires simplifying complex numbers.1. To simplify [tex]i^{23}[/tex]
We can rewrite [tex]i^{23}[/tex] as [tex](i^{4)^{5} } (i^{2} . i )[/tex]
write [tex]i^{4}[/tex] as [tex](i^{2} )^{2}[/tex]
[tex](i^{4)^{5} } (i^{2} . i )[/tex] = [tex]((i^{2} )^{2} )^{5} (i^{2} . i)[/tex]
we know [tex]i^{2}[/tex] = -1
((-1²))⁵ [tex](i^{2} .i)[/tex]
we know that -1² = 1
= 1⁵ [tex](i^{2} .i)[/tex]
= 1 [tex](i^{2} .i)[/tex]
= [tex](i^{2} .i)[/tex]
here [tex]i^{2}[/tex] =-1
-1 . [tex]i^{}[/tex]
= - i
so [tex]i^{23}[/tex] is -i
2. To simplify [tex]\sqrt{-128}[/tex]
= [tex]\sqrt{(- 1) . (128)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{128}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (64)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (8) . (8)}[/tex]
here [tex]}\sqrt{-1}[/tex] = i
substituting i we get
= i . 8 √2
= 8i√2
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Melanie invests $3,000 at 12% simple interest for 1 year. How much is in the account at the end of the 1 year period?
Answers
We have the following:
We must apply the simple interest formula which is the following:
[tex]A=P\cdot(1+rt)[/tex]Where, P is the principal 3000
r is the interest rate 0.12
t is time in years
A is the total value
replacing:
[tex]\begin{gathered} A=3000\cdot(1+0.12\cdot1) \\ A=3000\cdot1.12 \\ A=3360 \end{gathered}[/tex]The answer is $3360 at the end of the 1 year period
help asap pleaseee
What are the coordinates of the vertices of triangle A’B’C’ after a reflection across a line through point P with a y-intercept at y=-2, followed by a translation T<3,3>?
Answers
Answer:
Coordinate A would be (12,3)
Coordinate B would be (12,7)
Coordinate C would be (10,5)
Write 56% as a fraction in simplest form.
Answers
Answer:
[tex]\frac{14}{25}[/tex]
Step-by-step explanation:
per cent means 'out of 100 ' , then
56%
= [tex]\frac{56}{100}[/tex] ( divide numerator/ denominator by 4 )
= [tex]\frac{14}{25}[/tex] ← in simplest form
Can you please help with with this?
Thanks
Answers
Answer:
slope is 3
Step-by-step explanation:
8-5/-2-(-3)=3/1=3 3 is the slope
Image to problem- https://postimg.cc/G8VnJLTq
Answers
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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-9- -8x2= -209 Solve this equation by taking square roots
Answers
The value of the quadratic equation given as -9- -8x^2= -209 is 5
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to solve the quadratic equation?The quadratic equation is given as
-9- -8x^2= -209
Add 9 to all sides of the equation
So, we have
-8x^2= -200
Divide both sides of the equation by -8
x^2= 25
Take the square roots
x = 5
Hence, the solution of the equation is 5
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Lana’s Linoleum Luxuries makes rectangular kitchen tiles with an area of t square inches.
Answers
The area in square inches of the tile is 9 / 4 t .
How to find the area of a rectangle?She makes rectangular kitchen tiles with an area of t square inches.
Therefore,
area of the rectangular kitchen tiles = lw
t = lw
l = t / w
w = t / l
Therefore, the tile is 3 / 4 as long and 3 times wide as her kitchen tiles.
Hence,
area of the tile = 3 / 4 t / w × 3(t / l)
area of the tile = 9 / 4 × t² / lw
where
lw = t
Hence,
area of the tile = 9 / 4 × t² / t
area of the tile = 9 / 4 × t
Therefore,
area of the tile = 9 / 4 t
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Please do this for me .I need it as soon as possible
Note:This is grade 6 maths
Answers
Answer:
9.6 but the 6 is recurringAnswer:
9 [tex]\frac{3}{4}[/tex]
13[tex]\frac{2}{3}[/tex]
3[tex]\frac{4}{6}[/tex] or 3 [tex]\frac{2}{3}[/tex] simplified
Step-by-step explanation:
For the fraction part, could how many total spaces between the numbers then count how many spaced over to the pointer.
For #16, there are 4 spaced between 9 and 10. The pointer is pointing to 3 spaces from 9 so the fraction is 3/4.
For #18, there are 6 spaces and the pointer is at the 4th space. You can see that if you counted every 2 spaces as I unit, you would have a total of 3 spaces and the pointer is over 2 of those three spaces. That would get your simplified answer of 2/3.
Iris's checking account pays simple interest at 3% per year. She has $185 in
her account. Write a linear function to model the amount of money in her
checking account at any time t.
Answers
The linear function to model the amount of money in her checking account at any time t is 185 + 5.55t.
What is an interest?An interest simply means the extra amount that's borrowed when one borrows money or when one saves.
In this case, the checking account pays simple interest at 3% per year. She has $185 in her account.
The amount of money in the account at anytime will be:
= 185 + (PRT/100)
P = principal
R = rate
T = time
= 185 + [(185 × 3 × t)/100]
= 185 + 5.55t
The function is 185 + 5.55t.
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Grace is driving to a concert and needs to pay for parking. There is an automatic fee of $11 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $4 for every hour she had her car in the lot. How much total money would Grace have to pay for parking if she left her car in the lot for 6 hours? How much would Grace have to pay if she left her car in the lot fort hours?
Answers
For 6 hours
Grace will pay = $11 + 6 x $4
= $11 + $24
= $35
for t hours
Grace will pay = $11 + t x $4
= $11 + $4t
= $( 11 + 4t )
on a recent holiday weekend, a sample of 500 drivers was stopped by the police. 300 drivers were under 30 years of age. a total of 250 were under the influence of alcohol. of the drivers under 30 years of age, 175 were under the influence of alcohol. what is the probability that a driver selected at random from the sample of 500 is under 30 and not under the influence of alcohol?
Answers
P(A). P(Y)= 0.5*0.6=0.3
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. The probability of an event is a number between 0 and 1.
Number of cases of A, N(A)= 250,
So,
P(A)=250/500 =0.5
and
N(Y)= 300, so P(Y)=300/500 =0.6
N(A and Y)= 175 so P(A and Y)= 175/500=0.35
A and Y are mutually exclusive implies A and Y donot have any elements in common, but here there are 175 people who are below 30 years and under the influence of alcohol, So they are not mutually exclusive!!
For A and Y to be independent, the Probability of A intersection Y should be equal to the product of their respective probabilities,
in this case P(A). P(Y)= 0.5*0.6=0.3 which is not equal to P( A intersection Y) (0.35)
So, A and Y are not mutually Independent also.
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For what values of b is the difference between the fractions [tex]\frac{2b-1}{2}[/tex] and [tex]\frac{1+5b}{4}[/tex] negative? (for 25 points) i will give you brainlyiest or smthing if u give answer
Answers
The value of b for which the difference between the fractions
(2b - 1) / 2 and (1 + 5b) / 4 negative will be;
⇒ b < -3
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
Two fractions are,
⇒ (2b - 1) / 2 and (1 + 5b) / 4
Since, The difference between the fractions (2b - 1) / 2 and (1 + 5b) / 4 negative.
So, we can formulate;
⇒ (1 + 5b) / 4 - (2b - 1) / 2 < 0
Solve for b, as;
⇒ 1 + 5b - 2 (2b - 1) < 0 x 4
⇒ 1 + 5b - 4b + 2 < 0
⇒ b + 3 < 0
Subtract 3 both side;
⇒ b + 3 - 3 < 0 - 3
⇒ b < -3
Therefore, The value of b for which the difference between the fractions (2b - 1) / 2 and (1 + 5b) / 4 negative will be;
⇒ b < -3
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-12/7 = 6w solve for w and simplify your answer as much as possible
Answers
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Use the constraints of the real-world situation to predict the height of the water balloon at 15 seconds. Use complete sentences to support your answer.
Answers
From the linear model we can see that the height of the balloon after 15 seconds is 0 feet.
Depending on the context, the phrase "linear model" is used differently in statistics.
The word is frequently used interchangeably with a linear regression model since it occurs most frequently in relation to regression models. The phrase has a different connotation when employed in time series analysis, though. The term "linear" is used in each instance to denote a subclass of models for which a significant decrease in the complexity of the underlying statistical theory is feasible.From the linear model we can see that the water balloon is thrown from a height of 40 feet upwards.
Now the balloon reaches a height of 70 feet and then falls back down on earth due to gravity.
At about 10 seconds the balloon falls on the ground and splashes.
Hence for further time the balloon is always at the ground.
Therefore at time of 15 seconds the height of the balloon is always 0 feet as represented in the linear model.
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A normally distributed data set of 600 values has a mean of18.5 and a standard deviation of 3.25.What is the approximate number of values in the dataset expected to be 22 or greater?
Answers
Note the in such type of questions the term 'probability' and 'proportion' can be used in place of each other. It is because the probability gives the proportion of favorable outcomes to the total outcomes.
Let X be the random variable representing the number of data points greater than or equal to 22.
Given that the mean and standard deviation is 18.5 and 3.25, respectively.
Consider the formula for z-score as,
[tex]z=\frac{x-\mu}{\sigma}[/tex]So the probability is calculated as,
[tex]\begin{gathered} P(X\ge22)=P(z\ge\frac{22-18.5}{3.25}) \\ P(X\ge22)=P(z\ge1.08) \\ P(X\ge22)=P(z\ge0)-P(0\leq z\leq1.08) \\ P(X\ge22)=0.5-\emptyset(1.08) \end{gathered}[/tex]From the Standard Normal Distribution Table,
[tex]\emptyset(1.08)=0.3599[/tex]Substitute this value,
[tex]\begin{gathered} P(X\ge22)=0.5-0.3599 \\ P(X\ge22)=0.1401 \end{gathered}[/tex]Thus, there is 0.1401 or 14.01% probability that a data will be greater than or equal to 22.
So, the 14.01% of the data is expected to be 22 or greater.
Filling and Emptying Tanks
1) Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters
per minute. How many liters of water remain in the tank after the following amounts of
time?
a) 30 seconds
c) t minutes
b) 7 minutes
c) 18 liters
2) For how many minutes, t, has the water been draining when Tank B contains the
following amounts of water?
a) 75 liters
Period: 6
b) 32.5 liters
d) v liters
Answers
Answer:
a) 78.75
b) 62.5
a) 2 minutes
b) 19 minutes
c) 24 minutes and 48 seconds
This question is worth 2 extra credit points. You do not have to complete it if you do notwant to.EXm4 ---> possible beginning ---->2or ------>ma . m2 or ----->(m2)Give a possible beginning to the following expression. (see example above)moHTML EditoreВ
Answers
How is it 840g plsss help!
Answers
Step-by-step explanation:
Let's say first piece is x. First and third ratio is 1:4 so it would be
4x - x = 360
3x = 360
x = 120 Third piece is 120g. Now we just multiply the rest.
2 × 120 = 240g
4 × 120 = 480g, total 840g
Answer:
840 g
Step-by-step explanation:
Ratio:Ratio of weight of 3 pieces = 1 : 2 : 4
Weight of 3 pieces = x , 2x , 4x
Weight of third piece - weight of first piece = 360 g
4x - x = 360
3x = 360
Divide both sides by 3,
x = 360÷ 3
x = 120 g
Weight of first piece = x = 120 g
Weight of second piece = 2x = 2*120 = 240g
Weight of third piece = 4x = 4 *120 = 480 g
Weight of the whole cake = 120 + 240 + 480
= 840 g
HELP ME PLEASE!!!!! will give brainlist
Answers
Answer:
y=3x+3
Step-by-step explanation:
i use point (-1,0) and (0,3) then 3-0/0-(-1)=3/1=3 so (0,3) 3 is the y intercept plug in so y=3x+3is the equation
Answer:
See below
Step-by-step explanation:
Find two convenient points to calculate the slope:
0,3 and -1,0 slope = m = (3-0) / ( 0 - -1) = 3
and the y axis intercept = 3 (from looking at graph)
line equation is y = mx + b ( where b is the y-axis intercept)
y = 3x + 3
(-8) • 2/3 = I dont know and yea I'm confused lol
Answers
Simplify 3(8a – 4b + 5)
Group of answer choices
24a – 4b + 5
11a – 4b + 5
11a – 7b + 8
24a – 12b + 15
Answers
Answer:
24a -12b + 15
Step-by-step explanation:
Answer:
=24a - 12b + 15
Step-by-step explanation:
3(8a-4b+5)
Apply the distributive law: m(a+b+c) = ma + mb + mc
3 (8a - 4b + 5 ) = 3 · 8a + 3( -4b)+ 3 · 5
= 3 · 8a + 3( - 4b) + 3 · 5
Simplify 3 · 8a + 3( -4b) + 3 · 5 : 24a - 12b + 15
= 24a - 12b + 15
Mr. Jonas took out a loan of $12,400. The interest rate is 3% per year, and the interest is not compounded. How much amount will Mr. Jonas have to repay after 4 years?
Answers
Jonas have to repay $13888 after 4 years.
Given
Principle amount of loan (P) = $12,400
Rate of interest (R) = 3%
Time period (T) = 4 years
Also the interest is not compounded, hence it is simple interest.
The formula for simple interest is (PTR)/100
Where,
P = Principle amount
T = time period
R = rate of interest
By substituting the values in the formula we get,
Simple interest = (12400 x 4 x 3) / 100
Simple interest = 1488
Hence adding this interest to Principle sum we get
12400 + 1488 = 13888
Jonas has to repay $13888 after 4 years.
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about 5% of americans have blue eyes. suppose 3 people are selected at random from the us population. what is the probability that all 3 have blue eyes?
Answers
If about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.
About 5% of americans have blue eyes
The probability of a person having blue eyes = 5% = 5/100
Eyes colour of a person is an indepedent event, which means the eye colour of one individual is independent of the other. The probability of one individual having blue eyes or not is independent of another person.
In case of independent event the probability of A intersection B = probability of A multiplied with probability of B
P(A∩B) = P(A) x P(B)
P(A∩B∩C) = P(A) x P(B) x P(C)
The probability that all 3 have blue eyes = 5/100 x 5/100 x 5/100
= 125/1000000
= 1/8000
Therefore, if about 5% of americans have blue eyes, the probability of 3 people selected at random having blue eyes is 1/8000.
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at eaton centre, let us imagine that $60 was spent on four shirts. how could we determine the average cost of each shirt?
Answers
Answer: 60 divided by 4
Step-by-step explanation:
Answer:
The average would be $15 for each shirt.
Step-by-step explanation:
divide the amount of money by the amount of shirts.
just need 8 thanks..
Answers
Answer:
8a)
D: [tex]1\leq x\leq 3[/tex].
R: [tex]0\leq y\leq 4[/tex]
8b)
D: [tex]x\geq 0[/tex]
R: [tex]y\geq 1[/tex]
Step-by-step explanation:
8a) The domain is the set of all possible numbers the x values could be. If there is no corresponding y value for an x value, that x value would not be considered part of the domain.
In the question, the function starts at x = 1 and continues until 3. The ends of the function are closed, so it is inclusive. This can be written as [tex]1\leq x\leq 3[/tex].
The range is all the possible y values. The function does not go below y = 0 and has a maximum of 4. The ends of the function are closed, so it is inclusive. This can be written as [tex]0\leq y\leq 4[/tex]
8b) We can do the same for this problem. The x has a minimum at 0 and continues to go on without an upper bound(as indicated by the arrow), is also includes the point where x=0. Therefore, the domain can be written as [tex]x\geq 0[/tex].
As for the range, the y minimum is 1 and the function continues to increase as shown by the upwards slope and arrow. The function also includes the point where y=1, so it can written as [tex]y\geq 1[/tex]
a salesperson has found that the probability of a sale on a single contact is approximately .03. if the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale?
Answers
The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.
If the probability of making a sale is 0.03 then the probability of not making a sale must be 1-0.03 which is 0.97.
So looking at contacting 100 prospects, you could say there are two general outcomes. Either the salesman makes no sales at all, or he makes at least one sale. There are no other possible outcomes, so the probability of those two outcomes must add up to 1.
So the probability of making of at least one sale is 1 minus the probability of making no sales.
The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.
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Find an equation in the form y=mx + b
Answers
Answer:
A) [tex]y = \frac{1}{10}x + 28[/tex]
B) $116.5
Step-by-step explanation:
The data we are given is:
• for 440 minutes of usage, the total cost is $72
• for 940 minutes of usage, the total cost is $122
A)
In order to find an equation in the form [tex]y = mx + b[/tex], we must first express the given data as coordinates in the form [tex](x, y)[/tex].
We are told that [tex]x[/tex] is the number of monthly minutes, and [tex]y[/tex] is the total monthly fee. Therefore the first piece of data expressed as coordinates is (440, 72), and for the second piece of data, it is (940, 122).
Now that we have the coordinates, we can make an equation using the formula:
[tex]\boxed{\frac{y - y_1}{y_2 - y_1}= \frac{x - x_1}{x_2 - x_1}}[/tex],
where [tex](x_1, y_1)[/tex] is (440, 72) and [tex](x_2, y_2)[/tex] is (940, 122).
Substituting the values into the formula, we get:
[tex]\frac{y - 72}{122 - 72}= \frac{x - 440}{940 - 440}[/tex]
⇒ [tex]\frac{y - 72}{50} = \frac{x - 440}{500}[/tex]
⇒ [tex]50 \times \frac{y - 72}{50} =50 \times \frac{x - 440}{500}[/tex] [Multiplying both sides of the equation by 50]
⇒ [tex]y - 72 = \frac{x - 440}{10}[/tex]
⇒ [tex]10y - 720 = x - 440[/tex] [Multiplying both sides by 10]
⇒ [tex]10y = x +280[/tex] [Adding 720 to both sides]
⇒ [tex]y = \frac{1}{10}x + 28[/tex] (Answer)
B)
To find the total cost if 885 minutes are used, we have to replace [tex]x[/tex] in the above equation with 885:
[tex]y = \frac{1}{10}(885) + 28[/tex]
⇒ [tex]y = 88.5 + 28[/tex]
⇒ [tex]y = 116.5[/tex]
Therefore, the total cost will be $116.5. (Answer)
Or Lillian bought cupcakes for her sister's birthday party. 12 out of the 40 cupcakes had sprinkles on top. What percentage of the cupcakes had sprinkles?\
Answers
Percentage of the cupcakes that had sprinkles = 30 %
Percentage
Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.
Proportion
The proportion formula is used to depict if two ratios or fractions are equal. We can find the missing value by dividing the given values. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The first step is to divide 12 by 40 to get the answer in decimal form:
12 / 40 = 0.3000
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.3000 * 100 = 30.00%
Percentage of the cupcakes that had sprinkles = 30 %
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