[tex]a = l \times w \\ a = (10y + 4w)(10y - 4w) \\ a = 10y(10y - 4w) + 4w(10y - 4w) \\ a = 100 {y}^{2} - 40wy + 40wy - 16 {w}^{2} \\ a = 100 {y}^{2} - 16 {w}^{2} [/tex]
ATTACHED IS THE SOLUTION
20) Flud LM if Pelut M is between Points L and N.
LM = 12x - 8, MN = 14, aud LU = 6x + 30
The value of the distance LM in which M is the midpoint between L and N is 64 units.
What is midpoint?
In mathematics. the term midpoint states the middle line of the line segment joining the two sides of the triangle make the third side parallel to the line segment and it also bisect the third side.
According to the question, the point M is the midpoint between L and N. The given parameters are: LM = 12x-8; MN = 14; and LN = 6x + 30
Using standard midpoint property, the distance LN can be written as:
LN = LM + MN ⇒ 6x + 30 = 12x-8 + 14
Taking variables terms one side, we get
6x = 36 ⇒ x = 6
Therefore,
LM = 12x-8 ⇒ 12(6) - 8 = 72 - 8 = 64
Hence, the value of the distance LM in which M is the midpoint between L and N is 64 units.
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = - [tex]\frac{1}{5}[/tex] x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (50, - 10) ← 2 points on the line
m = [tex]\frac{-10-0}{50-0}[/tex] = [tex]\frac{-10}{50}[/tex] = - [tex]\frac{1}{5}[/tex]
the line crosses the y- axis at (0, 0 ) ⇒ c = 0
y = - [tex]\frac{1}{5}[/tex] x + 0 , that is
y = - [tex]\frac{1}{5}[/tex] x ← equation of line
When should you cross multiply with fractions
Answer:
fractions are cross multiplied in two situations:
division:
for e.g what is [tex]\frac{3}{2}[/tex]÷[tex]\frac{7}{5}[/tex]
to solve this expression we cross-multiply fractions:
=15/14
In equation:
for eg [tex]\frac{8x}{7}[/tex] = [tex]\frac{2}{9}[/tex]
to solve this we cross multiply:
8x(9)=2(7)
72x=14
x=14/72
In equation cross multiplication can only be carried out if denominator is same for e.g [tex]\frac{2}{1}[/tex]+ [tex]\frac{8x}{7}[/tex] = [tex]\frac{4}{7}[/tex] cannot be cross multiplied until denominator of 8x and 2 is same
Plss mark as brainliest
By cross multiplying, you can simplify the equation and solve for the unknown variable.
Cross multiplication is a technique used when solving equations involving fractions. It is typically used when you have a proportion or an equation with fractions, and you want to eliminate the denominators and solve for the unknown variable.
Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. This technique is useful for simplifying equations and solving for the unknown variable.
You should cross multiply with fractions when you have an equation in the form:
a/b = c/d
To cross multiply, you would multiply ad (product of the numerators) and bc (product of the denominators) and set them equal:
ad = bc
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Lily is behind on her homework. The ritualistic teacher assigned exactly 5 homework assignments every day for the past 9 learning days. Here is the amount of homework assignments Lily has been able to get done each night (if she didn’t finish some of the 5 assignments from the night before, she would start work on them the next day): 3, 6, 2, 4, 3, 7, 1, 3, 2. If Lily doesn’t finish all her assignments, she won’t be able to go on a fun field trip next month. Lily can’t do more than 10 assignments in one night. There is one more homework night, with 5 more assignments. Can Lily still make it to the field trip?
Answer:
she cannot go on the field trip.
Step-by-step explanation:
Day 1 = 5, done = 3, remaining = 2.
Day 2 = 2 + 5, done = 6, remaining = 1
Day 3 = 1 + 5, done = 2, remaining = 4
Day 4 = 4 + 5, done = 4, remaining = 5
Day 5 = 5 + 5, done = 3, remaining = 2 + 5
Day 6 = 2 + 5 + 5, done = 7, remaining = 5
Day 7 = 5 + 5, done = 1, remaining = 4 + 5
Day 8 = 4 + 5 + 5, done = 3, remaining = 1 + 5 + 5
Day 9 = 1+ 5+ 5+ 5, done = 2, remaining = 4+5+5
Day 10 = 4+5+5+5, done = 10(maximum assignment done assumed), remaining = 4 + 5
At the end of day 10, she had 9 remaining assignments, so she cannot go on the field trip.
8. In the Aribic system , the value of a digit is based on what?
Answer
In the Arabic system, the value of a digit is based on the position of the specific digit.
What is the value of the Arabic numbers?The ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 serve as the basic building blocks for the decimal, or base ten, a place-value number system that makes up Hindu-Arabic numerals. According to its position, every digit in a number has a place value. The figure zero is theirs. Arabic uses a base-ten system, where each number must be placed in a specified order to represent a particular value. Egyptian, Indian, and Arab contributions were used to construct the Arabic numeral system over millennia.To learn more about Arabic system visit:
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3 In an election, a good candidate may lose because 40% of voters do not cast their votes due
to various reasons. Form an equation and draw the graph with data. From the graph, find:
(i) The total number of voters, if 720 voters cast their votes.
The total number of voters is 1200, and out of that 720 voters cast their votes.
Let's take total voters = V
The percentage of voters do not cast their votes due to various reasons is 40%.
Therefore, Voters did not cast their votes = (40÷100)V = 0.4V
As 0.4V voters did not cast their votes. To calculate the total number of voters who cast votes, divide (total) by (non-casted-voters):
Voters casted their votes = V - 0.4V = 0.6V
0.6V = 720
=> V = 1200
The total number of voters is 1200 if 720 voters cast their votes.
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What is the distance between (8,-3) and (4, -7)?
Choose 1 answer:
6
9
√32
√42
Answer:
C. 32Step-by-step explanation:
Use the distance formula.
Distance:
[tex]\Rightarrow \sf{\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}}[/tex]
y₂=(-7)
y₁=(-3)
x₂=4
x₁=8
[tex]\sf{\sqrt{\left(4-8\right)^2+\left(-7-\left(-3\right)\right)^2}}[/tex]
Solve.
Use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtractDo parentheses first.
(4-8)=-4
[tex]\sf{\left(-4\right)^2+\left(-7-\left(-3\right)\right)^2}[/tex]
-7-(-3)=-7+3
-7+3=-4
[tex]\sf{\left(-4\right)^2+\left(-4\right)^2}[/tex]
Do exponents.
[tex]\sf{(-4)^2=4^2=4*4=16}[/tex]
Then, you add.
16+16
[tex]\Rightarrow \boxed{\sf{32}}[/tex]
Therefore, the correct answer is C. 32.
The base of a 15-foot ladder is 3 feet from a building. If the ladder reaches the flat roof, how tall is the building?
I need serious help with this one.
Whoever helps me thank you god bless
Answer:
Try 20.
Step-by-step explanation:
To round 19.5 to the nearest whole number consider the tenths’ value of 19.5, which is 5 and equal or more than 5. Therefore, we have to round up: the whole number part of 19.5, 19, increases by 1 to 20, and the decimal point and all digits (.5) are removed.
19.5 rounded to the nearest whole number = 20
Write the numbers below (expressed in expanded form) in standard form.
500,000 +90,000+ 6000+600 + 80 + 1
900,000+ 50,000+6000+800+ 10 +6
90,000+ 6,000+0+0+1
60,000,000+ 9.000,000+ 500,000+ 90,000+ 6.000 + 100+60 + 8
1,000+ 900+50 +8
90 000,000+ 5.000.000 + 500,000+ 90,000+ 6.000+600 + 10 + 8
Answer:
1. 596,681
2. 956,816
3. 96,001
4. 69,596,168
5. 1958
6. 95,596,618
Step-by-step explanation:
1. 500,000 + 90,000 + 6000 + 600 + 80 + 1 = 596,681
2. 900,000 + 50,000 + 6000 + 800 + 10 + 6 = 956,816
3. 90,000 + 6,000 + 0 + 0 + 1 = 96,001
4. 60,000,000 + 9,000,000 + 500,000 + 90,000 + 6.000 + 100 + 60 + 8 = 69,596,168
5. 1,000 + 900 + 50 + 8 = 1958
6. 90,000,000 + 5,000,000 + 500,000 + 90,000 + 6,000 + 600 + 10 + 8 = 95,596,618
I hope this helps!
Please help, random thing that was assigned
Answer:
I think options BCDE. There is an angle presented in the picture. There are parallel lines. Also skew lines and line segments.
Step-by-step explanation:
Hope it helps! =D
Given the area of a square window is 36 ft2, what is the measure of one side? Show your work.
Answer:
The length is 6 ft
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
36 = s^2
Take the square root of each side
sqrt(36) = sqrt(s^2)
6 =s
The length is 6 ft
Answer:
6 ft
Step-by-step explanation:
We know that the formula to find the area of a square is :
Area = a² ( length × width)
According to the question they've already given the area of the square as 36ft².
So, to find the the measure of a one side, let the in unknown measure of a side be a.
Remember that, all the sides of a square are equal to each other.And now, using the formula let us find the value of a ( length of a one side).
[tex] \sf \: Area = a² \\ \sf 36 = a² \\ \sf \: \sqrt{36} = a \\ \sf6ft = a[/tex]
Here is the histogram of a data distribution.
Which best describes the shape of this distribution?
A. Bimodal skewed
B. Bimodal symmetric
C. Unimodal symmetric
D. Unimodal skewed
E. Uniform
The given distribution is (A) Bimodal skewed as the distribution has 2 humps.
What is Bimodal skewed?If a histogram has one hump, it is unimodal; if it has two humps, it is bimodal; and if it has many humps, it is multimodal. If a histogram is not symmetric, it is referred to as skewed. It is positively skewed if the upper tail is longer than the lower tail. They can have multiple peaks or be bimodal (two peaks) (or many peaks). But a single distribution with two peaks characterizes a bimodal distribution. Typically, it appears as two separate bell curve shapes contained within two normal distributions on a graph that is displayed side by side.As the given graph has 2 humps, we can conclude that the given distribution is an (A) Bimodal skewed.
Therefore, the given distribution is (A) Bimodal skewed as the distribution has 2 humps.
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Suppose 91% of students chose to study French their sophomore year, and that meant that there were 819 such students. How many students chose not to take French their sophomore year?
Using percentage we can calculate that 81 students did not take French.
In mathematics, a number or ratio that is expressed as a fraction of 100 is referred to as a percentage. Although the abbreviations "pct" and "pc" are also often used, the percent symbol "%" is the one that is most frequently used. A % is a number that has neither established units of measurement nor dimensions.
The percentage can be calculated by taking the value and dividing it by the total value, then multiplying the result by 100. using the formula (Value/Total Value) × 100% to calculate percentages.
Let the total number of students be x.
Now 91% of this students is equal to 819.
Now using the properties of percentages we can write:
91% of x = 819
or, x = 900
Number of students who did not take French = 900 - 819 = 81
Hence using percentages we can say that 9% or 81 students did not take French.
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the switchboard in a minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on mondays. experience shows that the existing staff can handle up to six calls in an hour. let x
On Mondays at noon, the switchboard in a Minneapolis legal firm receives an average of 5.5 incoming calls. Consequently, X's standard deviation is 2.35 calls.
The current personnel can handle up to six calls in an hour, according to experience.
A Poisson distribution with an average number of calls of 5.5 on Mondays around lunchtime can be used to model the scenario that is being given.
Thus, the following equation represents the standard deviation for the number of calls received, X:
2.35 calls make up the standard deviation of X.
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HELP i forgot how to do probability omg
The tree diagram of the outcomes and the number of possibilities is added as an attachment
How to make the tree diagram for the probability?The given parameters are:
Red balls = 6
Blue balls = 4
This means that the total number of balls is
Total number of balls = Red balls + Blue balls
Substitute the known values in the above equation
So, we have the following equation
Total number of balls = 6 + 4
Evaluate the sum in the above equation
So, we have the following equation
Total number of balls = 10
From the question, we understand that the selection is without replacement, and the number of selections is 2
This means that the sample space in total selections is
{RR, RB, BR, BB}
Where
B represents blue and R represents red
Next, we use the sample space {RR, RB, BR, BB} to make the required tree diagram
See attachment for the tree diagram
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which small digit represent M so that the number 2m234 and is divisible by 3
Answer:
m = 1
Step-by-step explanation:
A number is divisible by 3 if the sum of the digits is a multiple of 3
the given number is 2m234 and we are asked to find the smallest m
Adding up known digits gives 2 + 2 + 3 + 4 = 11
The next multiple of 3 is 12
So 11 + m = 12
m = 1
The other possibilities are
m = 4, m = 7
Does the function f of x equals 3 times the quantity 1 over 2 end quantity to the x power represent growth or decay? what is the y-intercept of f(x)? growth; 0 comma one-half growth; (0, 3) decay; 0 comma one-half decay; (0, 3)
For the exponential function f(x) = 3(0.5)^x, we have that:
The function represents exponential decay.The y-intercept of the function is given by point (0,3).What is an exponential function?An exponential function is modeled according to the rule given below:
[tex]y = ab^x[/tex]
In which the parameters are described as follows:
a is the initial value of the function, hence the y-intercept is of (0,3).b is the rate of change of the function, determining if it represents exponential growth (|r| > 1) or exponential decay (|r| < 1).For this problem, the rule of the exponential function is given by:
y = 3(0.5)^x.
Hence the parameters are:
a = 3, b = 0.5.
Then:
The function represents exponential decay, as |b| = 0.5 < 1.The y-intercept of the function is given by point (0,3), as the coefficient a has a value of a = 3.More can be learned about exponential functions at https://brainly.com/question/25537936
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Answer:
decay; (0,3)
Step-by-step explanation:
find the standard form of the equation of the ellipse given the following properties. foci \displaystyle \left(0,\pm3\right)(0,±3) vertices \displaystyle \left(0,\pm13\right)(0,±13).
The standard form of the given equation of the ellipse according to the given properties is [tex]b^{2}[/tex] = ± 4√2.
Here the foci are given which are ( 0,3) and to the eight (0, ±3) and the vertices are (0,13) and (0, ±1), so we have to find the standard form these values to put these values in a formula which is given below
The formula we are using in this is to form an equation :
[tex]\frac{(x-k)^{2} }{a^{2} }[/tex] + [tex]\frac{(y-k)^{2} }{b^{2} }[/tex] = 1
[tex]\frac{x^{2} }{a^{2} }[/tex] + [tex]\frac{y^{2} }{b^{2} }[/tex] = 1
[tex]\frac{x^{2} }{36}[/tex] + [tex]\frac{y^{2} }{32}[/tex] = 1
After solving the equation given above
we get [tex]b^{2}[/tex] + 4 = 36
Subtract - 4 on both sides then we get
[tex]b^{2}[/tex] + 4 - 4 = 36 - 4
[tex]b^{2}[/tex] = 32
[tex]b^{2}[/tex] = ± 4√2
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Match each relationship on the right with the correct description on the
left.
Direct
variation
Indirect
variation
Joint
variation
The amount of time it takes to
drive some place depends on
the distance.
The volume of a can depends
on its radius and on its height.
The time it takes to shingle a
roof depends on how many
workers are helping shingle the
roof.
Each relationship should be matched with the correct description as follows:
Direct variation: the amount of time it takes to drive some place depends on the distance.Joint variation: the volume of a can depends on its radius and on its height.Indirect variation: the time it takes to shingle a roof depends on how many workers are helping shingle the roof.What is direct variation?Direct variation can be defined as a type of proportional relationship in which a variable is directly proportional to another variable.
What is an indirect variation?An indirect variation can be defined as a type of proportional relationship in which a variable is inversely proportional to another variable. This ultimately implies that, an indirect variation represents two variables that are inversely proportional to each other.
In conclusion, a joint variation describes a situation in which a variable depends on two other variables which share a directly proportional relationship.
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Reuters reports that 15 percent of australians smoke. by introducing tough laws banning brand labels on cigarette packages, australia hopes to ultimately reduce the percentage of people smoking to 10%. answer the following questions based on a sample of 240 australians..
The mean of the sampling distribution of proportion is 0.15
The probability the sample proportion will be within 0.04 of the population proportion is 0.9182
The probability the sample proportion that will be within 0.02 of the population proportion is 0.6157
P(Smokers) in Australia= 15/100=0.15
Sample, n =240
Part a, The mean of the sampling distribution of proportion:
μ₂ = P(Smokers)
= 0.15
The mean of the sampling distribution of proportion is 0.15
The standard deviation of the sampling distribution of proportion is,
δ [tex]=\sqrt{p\frac{(1-p)}{n} }[/tex]
[tex]=\sqrt{0.15\frac{(1-0.15)}{240} }[/tex]
[tex]=0.0230[/tex]
The standard deviation of the sampling distribution of proportion is 0.0230
Part b, The probability the sample proportion will be within +/-0.04 of the population proportion:
To find this, we first, compute the z score then find probability based on standard normal table.
For 0.15-0.04, p=0.11 and converts to:
[tex]z=\frac{p-u_{p} }{standard deviation} \\[/tex]
[tex]=\frac{0.11-0.15}{0.0230}[/tex]
= -1.74
For 0.15+0.04, p=0.19, and converts to:
[tex]z=\frac{0.19-0.15}{0.0230}[/tex]
= 1.74
From the standard normal distribution table, the associated probability for z values and subtracts the probability is,
[tex]=p(-1.74\leq z\leq 1.74)[/tex]
[tex]=0.9591-0.0409[/tex]
[tex]=0.9182[/tex]
Hence, the probability the sample proportion will be within 0.04 of the population proportion is 0.9182
Part c, the probability the sample proportion will be within 0.02 of the population proportion:
First, compute the z score then find probability based on standard normal table.
For 0.15-0.02, p=0.13, and converts to:
[tex]=\frac{0.13-0.15}{0.0230}[/tex]
=-0.87
For 0.15+0.02, p=0.17, this converts to:
[tex]=\frac{0.17-0.15}{0.0230}[/tex]
=0.87
From the standard normal distribution table, the associated probability for z values and subtracts the probability is,
[tex]=p(-0.87\leq z\leq 0.87)[/tex]
[tex]=0.8079-0.1922[/tex]
[tex]=0.6187[/tex]
Hence, the probability the sample proportion will be within 0.02 of the population proportion is 0.6157
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Find an estimate for the mean time. Please fast !!
Mean time = 142 minutes
What is the mean of data?One of the the most common expression for the mean of a statistical distribution with random variables is the average of all the terms. The mean of any given data can be found out by adding all numbers in the data set and then dividing that by the number of values.
First calculate the mid point of the time interval :
(15+17)/2=16
(17+19)/2 = 18
(19+21)/2= 20
(21+23)/2= 22
Multiply each time mid point with respective frequency :
16*5=80
18*12= 216
20*7= 140
22*6= 132
Adding this and dividing by the total number of times that is 4:
= (80+216+140+132)/4
= 568/4
Mean time =142 minutes
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the population standard deviation for the height of college hockey players is 3.2 inches. if we want to estimate 95% confidence interval for the population mean height of these players with a 0.55 margin of error, how many randomly selected players must be surveyed?
Given,
Population Standard deviation = 3.2 inches
Required confidence interval (C) = 95%
Margin of error = 0.55
Let h be the number of randomly selected players surveyed.
∝ = 1 - C = 1 - 0.95 = 0.05
∝/2 = 1 - C / 2 = 0.05/2 = 0.025
Score of ∝/2 = 2.5 - 0.025 = 2.475
We know,
Margin of error = 0.55
Standard deviation = 3.2
∵ 0.55 = 2.475 x 3.2/ √h
√h = √0.144/1000
∴ h = 12
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Point G is on line segment FH. Given G H= 8, F H= 3x +3, and FG=2x, determine the numerical length of FG.
The length of line segment FG is 10 units.
What is a line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies within those endpoints. The Euclidean distance between two endpoints of a line segment determines its length. In real life, a line segment might be a stick, a pencil, or a ruler. The sun's rays are an illustration of a ray. The sun is where the sun's rays begin, but there is no end to them.So, the length of FG:
FG + GH + FH2x + 8 = 3x + 33x - 2x = 8 - 3x = 5So, insert x = 5 in 2x:
FG = 2xFG = 2(5)FG = 10Therefore, the length of line segment FG is 10 units.
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Write the quadratic equation that has roots [tex]\frac{(-1-\sqrt{2})}{3}[/tex] and [tex]\frac{(-1+\sqrt{2})}{3}[/tex] if its coefficient with [tex]x^{2}[/tex] is equal to -3/5.
The quadratic equation is [tex]-3/5x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]
Quadratic Equation:
A quadratic function is a function of degree two.
The general form of the quadratic equation is
x² + (sum of roots)x + Product of roots.
Given,
Here we have the roots,
[tex]\frac{-1-\sqrt{2} }{3} ,\frac{-1+\sqrt{2} }{3}[/tex]
And the coefficient with x² is equal to -3/5.
Through the given details we have to find the quadratic equation.
To find the equation we have to identify the sum of roots and the product of roots.
So, the sum of roots is,
[tex]= > \frac{-1-\sqrt{2} }{3} +\frac{-1+\sqrt{2} }{3}[/tex]
[tex]= > \frac{-1 }{3} +\frac{-1 }{3}\\= > \frac{-2}{3}[/tex]
Now the product of roots is,
[tex]= > \frac{-1-\sqrt{2} }{3} \times\frac{-1+\sqrt{2} }{3}[/tex]
[tex]= > \frac{1-\sqrt{2}-\sqrt{2}-2 }{3}=\frac{-1-2\sqrt{2} }{3}[/tex]
So, the quadratic equation is,
[tex]= > -3/5x^2-2/3x-\frac{1+2\sqrt{2}}{3}[/tex]
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If you wanted to know which number, when raised to the exponent 3, results in 1,331, which action should you perform?
Find the cube of 1,331.
Find the square root of 1,331.
Find the cube root of 1,331.
Find the square of 1,331.
====================================================
Reason:
The cube root undoes the cubing operation.
It's similar to how the square root undoes squaring.
Your calculator should have a cube root button, or an nth root button. If not, then you can type in 1331^(1/3)
The exponent of 1/3 is the same as a cube root.
The result of 1331^(1/3) is 11
11^3 = 11*11*11 = 1331
Interpretation: You have a box that is 11 cm by 11 cm by 11 cm. The volume is 11^3 = 1331 cubic cm.
As you can see, the cube root is useful if you know the volume and want to work backwards to determine the side length of the cube.
the cube root of 1331 = ∛(11 × 11 × 11) = 11.
The square root of 1331 is 36.48287.
Solve the system of equations by substitutión.
y =-4x+5
y = 3x - 16
Answer:
y = - 4x + 5 ---1
y = 3x - 16 ---2
Substitute 1 into 2:
- 4x + 5 = 3x - 16
7x = 21
x = 3
Substitute x into 1:
y = - 4(3) + 5
= - 7
The height of a ball in feet can be found by the function h(t)=-16t^2+80t+5 where t is the elapsed time in seconds. Find the time or times that the ball is 34 feet high to the nearest tenth of a second
The times that the ball is 34 feet high to the nearest tenth of a second is equal to 4.61 and 0.39 seconds.
How to calculate the times?In order to determine the time or times for this ball at a height of 34 feet, we would simply substitute the value of the height into the function h(t) as follows;
h(t) = -16t² + 80t + 5
34 = -16t² + 80t + 5
Re-arranging the equation, we have:
16t² - 80t + 34 - 5 = 0
16t² - 80t + 29 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-80)\; \pm \;\sqrt{-80^2 - 4(16)(29)}}{2(16)}\\\\x = \frac{80\; \pm \;\sqrt{6400 - 1856}}{32}\\\\x = \frac{80\; \pm \;\sqrt{4544}}{32}[/tex]
x = (80 ± 8√71)/32
x = (80 + 8√71)/32 and x = (80 - 8√71)/32
x = 4.61 and 0.39 seconds.
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Write the ratio 60: 145 in the form 1: n, where n is a fraction in its simplest form.
Answer:
n = 29/12 is the simplest form
Step-by-step explanation:
145 ÷ 60 = 29/12
What is the contrapositive of the following statement?
"If it does not have four legs, then it is a fish."
If it is a fish, then it does not have four legs.
If it has four legs, then it is not a fish.
If it is not a fish, then it has four legs.
If it does not have four legs, then it is not a fish.
The contrapositive statement of "If it does not have four legs, then it is a fish." is "If it is not a fish, then it has four legs" .Option C
What is a contrapositive statement?A contrapositive statement is simply defined as a law or rule obtained by contradicting the conclusion and hypothesis of a statement.
It includes the exchange of both the hypothesis and conclusion of a particular conditional statement before negating both the hypothesis and conclusion.
It is also known for the combination of a converse and an inverse statement.
The hypothesis and conclusion are switched or interchanged
A contrapositive statement is represented as;
x y is equivalent to y ~x
Given the statement:
"If it does not have four legs, then it is a fish."
The contrapositive statement would be;
If it is not a fish, then it has four legs.
We can see that the hypothesis and conclusion were interchanged accordingly.
Hence, the statement is "If it is not a fish, then it has four legs"
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Answer: C: If it is not a fish, then it has four legs.
Step-by-step explanation: Hope that helped!