The equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].
What is perpendicular lines?
When two geometric objects intersect at a right angle, they are considered to be perpendicular in elementary geometry. By using the perpendicular symbol,, the condition of perpendicularity can be graphically represented. Between two lines, a line and a plane, or between two planes can be used to define it.
Consider the given equation of line
5x + 4y = 10
Convert it into the form y = mx + c
⇒ 4y = -5x + 10
y = -5/4x + 10/4
y = -5/4x + 5/2
Here the slope of line is, -5/4.
The slope of perpendicular line is negative reciprocal of the slope of given line.
So, the slope of perpendicular line is,
[tex]-\frac{1}{(-5/4)} = \frac{4}{5}[/tex]
Also the line passes through the point (5, -4).
By using the point slope form to find the equation of line
[tex]y-y_1 = m(x-x_1)\\y-(-4) = \frac{4}{5}(x-5)\\ y+4=\frac{4}{5}x - 4\\ y = \frac{4}{5}x - 4 - 4\\ y = \frac{4}{5}x - 8[/tex]
Hence, the equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].
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5) Consider the equation : y=7x+8
and the linear function represented by the table of values below. Select all of the statements that are correct.
The correct students about the function are;
B: The function represented by the table has a greater rate of change.
C: The function y = 7x + 8 has the greatest y-intercept.
How to Interpret the Function Table?We are looking at the equation;
y = 7x + 8
The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, the slope of the given equation is 7 while the y-intercept is 8.
From the table, the rate of change which is also is simply the slope from the formula;
m = (y₂ - y₁)/(x₂ - x₁)
m = (32 - 16)/(4 - 2)
m = 8
Looking at the given options, only options that are correct are Options B and C.
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PLEASE I REALLY NEED HELP, MY MATH CLASS IS DUE TOMORROW!!!!! ASAP!!!!!!
Answer:
13.3 ft
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
The surface area of a square-based pyramid is made up of:
1 square (the base)4 congruent triangles (the sides)Given:
Total SA = 158 feet²s = 5 feeth = l feetFind the area of the square base and the area of one of the triangles by substituting the given values into the formulas:
[tex]\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2[/tex]
[tex]\textsf{Area of one of the side triangles} = \dfrac{1}{2} \cdot 5 \cdot l= 2.5l \; \sf ft^2[/tex]
Substitute these values along with the given total surface area into the formula and solve for l:
[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=\dfrac{133}{10}\\l&=13.3\; \sf ft\end{aligned}[/tex]
Therefore, the missing length is 13.3 feet.
according to census data, in 1950 the population of the u.s. amounted to 151.3 million persons, and 13.4% of them were living in the west. in 2000, the population was 281.4 million, and 22.5% of them were living in the west. is the difference in percentages practically significant? statistically significant? or do these questions makes sense? explain briefly.
The difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.
Here, we are given that 13.4% of the population in the US lived in the West in 1950 and 22.5% in 2000.
Thus, the difference in percentage = 22.5 - 13.4 = 9.1%
We observe that the difference is large, this means that the difference in percentages is practically significant.
Now, to determine whether the difference is statistically significant it is appropriate to conduct a two-sample z-test and it is only appropriate to conduct the test of significance when the samples are simple random samples.
In this case, the samples are not simple random samples, because the data given contains information on all individuals in the population. Moreover, it is not appropriate to determine whether the difference in percentages is statistically significant as the samples are not probability samples.
Thus, the difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.
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Can someone explain how to simplify radicals, cube roots, and rational radicals? Also how do I simplify a radical that has exponents?
An expression with a square root is referred to as a radical expression.
How to simplify radicals, cube roots, and rational radicals?Radical simplification:
Find the biggest square factor of the radicand while simplifying a radical.When a radical's radicand doesn't have a square number factor, it is said to be in its simplest form.Eg : [tex]\frac{x^{\sqrt{9} } }{x^{\sqrt{4} } } =x^{3-2} = x^{1} = x[/tex]Cube root simplification:
The process here is the polar opposite of cubing a phrase. When calculating a term's cube root, we look for the word that, when multiplied by itself three times, yields the term we are calculating the cube root of.Eg : [tex]\sqrt[3]{27} =\sqrt[3]{3^{3} } = [3^{3}]^{\frac{1}{3}} = 3[/tex]Rational radical simplification :
Find the greatest radicand factor that is a perfect power of the index. Utilizing that factor, rewrite the radicand as the product of two factors.Use the product rule to rewrite the radical as the union of two radicals.Reduce the perfect power to its simplest form. Eg :[tex]\frac{2}{\sqrt{5} -1} \\\\=\frac{2}{\sqrt{5} -1} *\frac{\sqrt{5}+1}{\sqrt{5}+1} \\\\=\frac{2(\sqrt{5} +1) }{4} \\\\=\frac{\sqrt{5} +1 }{2}[/tex]
Exponential radical simplification :
Exponents should be multiplied together when you're simplifying exponential expressions that have been increased to another exponent. Working out each exponent the difficult way will demonstrate that this is true for both positive and negative exponents.Eg :[tex](5^{2} )^{3} \\=(5^{2} ) (5^{2} )(5^{2} )\\=25 *25*25\\=15625[/tex]
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a pair of 6-sided dice is thrown. someone tells you that both the dice are showing an even number. with this information, what is the probability of the total (when you sum up the dice) being equal to 8?
As per the given dice, the probability of the total being equal to 8 is 1/9 or 11.11%.
Probability:
In statistics, probability refers the possibility of the particular event.
Given,
Here we need to find the probability of the total (when you sum up the dice) being equal to 8.
In order to calculate this probability, we must first calculate all the possible combinations of two six-sided dice that add up to 8.
Hence both the dice are showing an even number, the possible combinations are (2, 6), (4, 4), and (6, 2). the total number of possible combinations for two six-sided dice is 36 (6 x 6).
So, the probability of the total being equal to 8 is 3/36 or 1/9 or 11.11%.
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Mawsynram, a village in India, is the wettest place on earth. It gets about 11,850 millimeters of rain per year.
About how many centimeters of rain fall in the village?
About how many inches if rain fall in the village?
Answer: 467 inches and 1185 centimeters
Step-by-step explanation:
1. Divide by 10 to find centimeters
2. Divide by 25.4 and round to find inches
What is the solution?
Answer:
336.
Step-by-step explanation:
8P3 = 8! / (8 - 3)!
= 8*7*6*5*4*3*2*1 / 5*4*3*2*1
= 8*7*6
= 336
How do you integrate 1/ln(x)?
The integration of 1/ln(x) is not possible as We permit y = lnx, we then recognize that x = ey.
By differentiating each aspects of this equation with admire to y we get:dx/dy = ey, because the exponential characteristic differentiates to itself whilst differentiated with admire to its power.
In mathematics, the logarithmic quintessential characteristic or quintessential logarithm li(x) is a unique characteristic. It is applicable in issues of physics and has variety theoretic significance. In particular, in keeping with the high variety theorem, it's far a excellent approximation to the high-counting characteristic, that is described because the variety of high numbers much less than or same to a given value x.
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Max is already 224 miles into his road trip. if he is averaging 52 miles per hour and the trip is 640 miles total, how many more hours does he have left to drive.
you toss a pair of six-sided dice. (a) determine the number of possible pairs of outcomes. (recall that there are six possible outcomes for each die.)
36 is the number of possible pairs of outcomes by probability.
What is a probability answer?
Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.
The probability value is given as a number between 0 and 1. Probabilities are always between 0 and 1. The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes.
We have two dice in this question. A die is known to be make up of 6 faces.
Therefore the number of faces for two dice = 6*6 = 36
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Which of the following is quadratic equation whose quadratic roots are 2 and 3?
The required quadratic equation which has the roots -2, and -3 is (C) x²+5x+6=0.
What is a quadratic equation?Any equation in algebra that can be written in the standard form where x stands for an unspecified amount, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
Factoring, using square roots, completing the square, and the quadratic formula is the four ways to solve a quadratic problem.
So, the product of a quadratic equation's elements can be used to represent any quadratic equation.
The necessary equation is created as follows:
(x - (-2))(x - (-3)) = 0
(x + 2)(x + 3) = 0
x² + 5x + 6 = 0
Therefore, the required quadratic equation which has the roots -2, and -3 is (C) x² + 5x + 6 = 0.
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Correct question:
Form a quadratic equation whose roots are -2,-3.
(A) x² - 6x + 5 = 0
(B) x² - 5x - 6 = 0
(C) x² + 5x + 6 = 0
(D) x² - 5x + 6 = 0
How do you divide 56.87 by 14 with explanation?
In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
26 points are scored in the fifth game.
What is Average?The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
First four games, a netball team scores an average of 31 points per game.
x/4=31
Let x represents four games
x=124
After the fifth game, the average for the first five games is 30
y/5=30
Let y represents five games
y=150
We need to find the number of points scored in fifth game.
x-y
124-150
26
Hence, 26 points are scored in the fifth game.
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What is 15 cm/year converted to inches per month? Round to the nearest hundreth.
The required conversion of the 15 cm/year is given as 0.5 inches per month.
Given that,
15 cm/year converted to inches per month is to be determind.
Conversion of the units is defined as the multiplying the original value with the unit factor.
Here,
1 cm = 0.4 inch
1 year = 12 month,
Substitute these values in the expression = 15 cm / year
= 15 × 0.4 / 12
= 0.5 inches per month.
Thus, the required conversion of the 15 cm/year is given as 0.5 inches per month.
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A veterinarian surveys households in her area to find out how many pets they own. She estimates that households have 1.8 pets on average, with a margin of error of ±0.4 pets. There are 1,200 households in her area.
1. The minimum number (Lower Limit) of pets one can find in the area is 1,680 pets, given the margin of error.
2. The maximum number (Upper Limit) of pets in the area will be 2,640 pets, given the margin of error.
What is the margin of error?The margin of error shows the statistical difference between actual and projected results in a random survey sample.
In other words, the margin of error reveals the level of unpredictability in research outcomes.
The statistical difference can be explained with an upper limit (maximum) and lower limit (minimum) between which the statistical value lies, thereby offering some level of confidence.
Average (mean) number of pets in each household = 1.8 pets
The margin of error = ±0.4 pets
The total number of households in the area = 1,200
Upper limit (maximum) of pets in the area = 2,640 pets (1,200 x 1.8 +0.4)
Lower limit (minimum) of pets in the area = 1,680 pets (1,200 x 1.8 - 0.4)
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Question Completion:What are the minimum and maximum numbers of pets you expect to find in her area?
Help me on this problem!
Answer:
B. Since [tex]\triangle ABC \cong \triangle DEF[/tex] by SSS and [tex]\triangle DEF \cong \triangle GHJ[/tex] by SAS, [tex]\triangle ABC \cong \triangle GHJ[/tex] by the Transitive Property of Congruence.
The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS
How to determine the congruent statement and the reason?From the question, we have the following parameters that can be used in our computation:
Triangles = ABC, DEF and GHJ
There are several theorems that make any two triangles to be congruent
One of these theorems is the SSS congruent theorem
The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent
From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark
AC and GJ
CB and JH
This implies that these sides are congruent sides
For the triangle to be congruent by SSS, the following angles must also be congruent
AB must be congruent to GH
Hence, the congruent statement on the congruency of the triangles is (d)
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Find the value of x in the triangle shown below: 2.5 6.5 Choose 1 answer: I =6 3 = V48.5 x = 9 x = V9
Answer:
x = 6 units
Step-by-step explanation:
We know that, By pythagoras theorem,
Hypotenuse2 = base2 + perpendicular2
Given, Hypotenuse = 6.5
perpendicular = 2.5
base = x
So, by putting the values,
6.52 = 2.52 + x2
42.25 = 6.25 + x2
36 = x2
Hence, x = 6 units
Solvex² - 5x 24 = 0 by factoring.
The solutions are x =
and x =
x = 8 , -3 are the factor of x .
What is factor ?
The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.
Factors are the figures that can divide an amount precisely. There is therefore no residual after division.
x² - 5x - 24 = 0
x² - ( 8 - 3 )x - 24 = 0
x² - 8x + 3x - 24 = 0
x(x - 8 ) + 3 ( x - 8) = 0
( x + 3 ) ( x - 8 ) = 0
x = 8 , -3
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The complete question is -
x² - 5x - 24 = 0 by factoring.
The solutions are x =
-(4x+20) < −7(x + 15/7)
Answer: x < 5/3
Step-by-step explanation:
-(4x + 20) < −7(x + 15/7) ............................ Question
-4x - 20 < -7(x + 15/7) ................................ Distribute
-4x - 20 < -7x - 15 ...................................... Distribute
-4x - 20 + 20 < -7x - 15 + 20 ................... Add 20 to both sides
-4x < -7x + 5 ............................................... Simplify
-4x + 7x < -7x + 5 + 7x ............................. Add 7x to both sides
3x < 5 .......................................................... Simplify
3x / 3 < 5 / 3 .............................................. Divide both sides by the same factor
x < 5/3 ......................................................... Simplify
What is the square root of "0.9"?
The value of [tex]\sqrt{0.9}[/tex] is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.
The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.
The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.
Since, 3*3*0.1
= 9*0.1
= 0.9
[tex]\sqrt{3*3*0.1} \\[/tex]
= 3([tex]\sqrt{0.1}[/tex])
[tex]\sqrt{0.9}[/tex] ≈ 0.94868329805
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Correct Question:
What is the value of [tex]\sqrt{0.9}[/tex]
if you have 10 apples and eat 7 halves how much apple do u have left?
You will have 3 1/2 left of apples
Answer:6.5 apples
Step-by-step explanation:
7 *.5=3.5 whole apples
10 apples- 3.5 apples=6.5 apples
Linear equation: -1
2
(6x + 10) = 13
Step 1: –3x – 5 = 13
Step 2: –3x = 18
Step 3: x = –6 Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
The answer of the provided question is the addition property of equality and then the division property of equality
What is addition property?Regardless of the sequence in which the numbers are added, the total of any two or more numbers is always the same. This characteristic may be expressed in the formula A + B = B + A. For instance, 2 + 4 Equals 4 + 2 = 6. As a result, both sets add up to 6, therefore 2 + 4 = 4 + 2.
We have multiplied both sides of the equation by 5 to move from Step 1 to Step 2:
[tex]-3x -5 +5 = 13 +5\\ -3x = 18[/tex]
We have divided both sides of the equation by -3 to go from Step 2 to Step 3:
[tex]-3x/-3 = 18/-3\\ x = -6[/tex]
These procedures can be categorized as...
first the equality's addition property, then its division property
However, since multiplication and division are the same thing, but with reciprocal numbers, and since addition and subtraction are the same thing, but with opposite numbers, any of the above answers may theoretically be right.
(adjust 5, divide by -3) = (adjust 5, multiply by -1/3)
(subtract 5 and divide by 3) equals (subtract 5 and multiply by 1/3).
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Find the derivative for y=eu(x); u(x) is a function in terms of x.
The derivative for y=eu(x); u(x) is a function in terms of x is dy/dx = eu'(x) + u(x)e .
A derivative is the rate of change of a function with respect to a certain variable . There are certain rules of differentiation which help us to evaluate the derivatives of some particular functions. :
Power Rule.Sum and Difference Rule.Product Rule.Quotient Rule.Chain Rule.This equation can be solved using the product rule of derivatives :
According to the product rule derivative of uv will be taken as -
u(v)' + v(u)'
where (') represents derivative of the variable.
Therefore accordingly -
y = eu(x)
differentiating with respect to x
dy/dx = e(u(x))' + u(x)(e)'
dy/dx = eu'(x) + u(x)e ( derivative of e=e)
Therefore the derivative in terms of x is dy/dx = eu'(x) + u(x)e .
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Sara calculated the product 33 × 34 × 35 × 36 × 37 × 38 and got a number. Which of these digits will be in the ONES place of the number?
Answer:
It's the digit 3.
Step-by-step explanation:
Since all digits from 33 to 38 are digits not less than 3, it follows that in the result there will be at least one digit bigger than 3. Since 33 to 38 represent a set with six numbers, we can conclude that the product of those numbers must have at least six digits to the left of the decimal, which is the ones place. Therefore, the digital 3 gets into the ones place.
Question 9 An S corporation is generally set up to: implement an expansion strategy attract capital reduce tax burdens easy entry into an industry take advantage of limited liability
Generally speaking, a S corporation is put up to reduce the tax obligations. It is Option (3).
A business form known as a S corporation is one that is allowed by the tax code to distribute its taxable income, credits, deductions, and losses to its shareholders directly. This provides it certain advantages over the more popular C corp. The S corp, an alternative to the limited liability company, is only available to small firms with 100 or fewer stockholders (LLC). S corporations and LLCs are both referred to as "pass-through entities" since they don't pay corporate taxes, instead, they pay their owners, who are then in charge of paying the necessary taxes.
One sort of legal corporate structure that is popular among small businesses is the S corporation, commonly referred to as a S corp or S corp or S subchapter. Another is a limited liability company (LLC). A corporation with 100 shareholders or fewer can profit from incorporation while still being taxed as a partnership thanks to the requirements of a S corp. S corporations and LLCs are both pass-through companies, which means they don't pay corporate taxes and provide their owners and principals with limited liability protection. LLCs, however, offer more flexibility.
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Correct Question:
An S corporation is generally set up to:
1. implement an expansion strategy
2. attract capital
3. reduce tax burdens
4. easy entry into an industry
5. take advantage of limited liability
Write a triangle congruence statement
please help me do this I've been stuck for over an hour
Find the missing length indicated. Leave your answer in simplest radical form.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
so the longest leg of the larger triangle will be "z" and the shorter leg of it will be "y", so let's find those fellows using proportions
[tex]\cfrac{x}{16}=\cfrac{9}{x}\implies x^2=144\implies x=\sqrt{144}\implies \boxed{x=12} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{x}=\cfrac{25}{16}\implies \cfrac{y}{12}=\cfrac{25}{16}\implies y=\cfrac{(12)(25)}{16}\implies \boxed{y=\cfrac{75}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{z}=\cfrac{9}{x}\implies \cfrac{~~ \frac{75 }{4 } ~~}{z}=\cfrac{9}{12}\implies \cfrac{75}{4z}=\cfrac{3}{4}\implies 300=12z \\\\\\ \cfrac{300}{12}=z\implies \boxed{25=z}[/tex]
this data is normally distributed. what percent of the data is in the shaded region 68% 50% 95% 99.7%
As per the empirical rule, the percent of data in the shaded region is 68%.
In statistics, the empirical rule states that When you use a standard normal distribution also known as Gaussian Distribution we have to consider the following
=> Around 68% of values fall within one standard deviation of the mean.
=> Around 95% of the values fall within two standard deviations from the mean.
=> Other all of the values are about 99.7% that fall within three standard deviations from the mean.
Therefore, this facts are the 68 95 99.7 rule. And it is also called the Empirical Rule because the rule originally came from observations.
Here we have given the the data is normally distributed. And we need to find the percent of data is in the shaded region.
While we looking into the following diagram and according to empirical rule,68% of the data falls within one standard deviation of the mean.
Because, the center part is the shaded region,
So, it can be calculated as,
=> 34 + 34 = 68%
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If 2|8 –2x| = 20, x could equal which of the following?
Answer: x can equal 9 or -1
Step-by-step explanation:
A report card shows that a student earns 21 21 points on a test with a total of 25 25 points. What percentage of the total points has the student earned on the test?.
When a report card shows that a student has earned 21 points on a test with a total of 25 points, it can be concluded to state that the student has secured 84 percentage of the total points of the test.
The computation of the percentage of points secured by the student out of the total available points in a test can be done using the generalized formula and the use of provided information into the same as below,
Percentage = Scored Secured / Total Points x 100
Percentage = 21 / 25 × 100
Percentage = 0.84 × 100
Percentage = 84 percentage.
Therefore, the student has earned 84 percentage of total points on a test.
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