Answer:
The answer is
[tex]y = \frac{4}{3} x + 3[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
y = 4/3x - 5
Comparing with the general equation above
Slope/ m = 4/3
Since the lines are parallel their slope are also the same
So we have
Slope of parallel line = 4/3
Equation of the line using point (−6,−5) and slope 4/3 is
[tex]y + 5 = \frac{4}{3} (x + 6) \\ y + 5 = \frac{4}{3} x + 8 \\ y = \frac{4}{3} x + 8 - 5[/tex]We have the final answer as
[tex]y = \frac{4}{3} x + 3[/tex]Hope this helps you.
Least to greatest
3/4 5/8 2/3 4/7 2/5
Answer:
Step-by-step explanation:
Least to greatest:
2/5, 4/7, 5/8, 2/3, 3/4
Find the equation of a line containing the point (8.3) and has a slope of 5. Write
the equation in slope-intercept form
Answer:
[tex]y=5x-37[/tex]
Step-by-step explanation:
So we want to find the equation of a line with a slope of 5 and passes through (8,3).
To do so, we can use the point-slope form. This point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Let's let (8,3) be x₁ and y₁ and let's let m equal 5. Therefore:
[tex]y-3=5(x-8)[/tex]
Distribute the right:
[tex]y-3=5x-40[/tex]
Add 3 to both sides:
[tex]y=5x-37[/tex]
That would be our equation in slope-intercept form.
And we're done!
Consider the statement,
Irrational numbers are closed under subtraction
Is the statement true or false? If false, justify with a counterexample
false; The numbers 2 and 7 are irrational, but V2 - cannot be simplified to an irrational number.
true
false; The number 2 is irrational, but 2 - 2 = 0 and is not irrational
false; The numbers 10 and 6 are irrational, but
/10
V6 14 2 and 2 is not irrational
How do I Simplify i^54
Answer:
[tex]i^{54}=-1[/tex]
Step-by-step explanation:
First, recall the 4 basic imaginary exponents:
[tex]i^1=i \text{, }i^2=-1\text{, }i^3=-1\text{ and } i^4=1[/tex]
So, we want to find:
[tex]i^{54}[/tex]
This is the same as:
[tex]=i^{52}\cdot i^2[/tex]
52 is 4 times 13. Thus:
[tex]=(i^4)^{13}\cdot i^2[/tex]
Since we know that i to the fourth is 1:
[tex]=(1)^{13}\cdot i^2[/tex]
Simplify:
[tex]=i^2[/tex]
And this equals:
[tex]=-1[/tex]
So:
[tex]i^{54}=-1[/tex]
what is K+(-5/3)=-44/3
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf k = - 13}}}}[/tex]
Step-by-step explanation:
[tex] \sf{k + ( - \frac{5}{3} ) = - \frac{44}{3} }[/tex]
When there is a ( + ) in front of an expression in Parentheses, there is no need to change the sign.
That means the expression remains the same.
⇒[tex] \sf{k - \frac{5}{3} = - \frac{44}{3} }[/tex]
Move 5/3 to right hand side and change it's sign
⇒[tex] \sf{k = - \frac{44}{3} + \frac{5}{3} }[/tex]
While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same.
⇒[tex] \sf{k = \frac{ - 44 + 5}{3} }[/tex]
Calculate
⇒[tex] \sf{k = \frac{ - 39}{3} }[/tex]
Divide -39 by 3
⇒[tex] \sf{k = - 13}[/tex]
Hope I helped!
Best regards!!
Robert has available 400 yards of fencing and wishes to enclose a rectangular area. Express the areaAof the rectangle as a function of the widthwof the rectangle. For what value ofwis the arealargest? What is the maximum area?
Answer:
The answer is below
Step-by-step explanation:
a)Given that the length of fencing available is 400 yards. This means that the perimeter of the rectangle is 400 yards.
the perimeter of a rectangle is given as:
Perimeter = 2(length + width) = 2(l + w)
Hence;
400 = 2(l + w)
200 = l + w
l = 200 - w
The area of a rectangle is given as:
Area = length × width
Area = (200 - w) × w
Area = 200w - w²
b) For a quadratic equation y = ax² + bx + c. it has a maximum at x = -b/2a
Hence, for the area = 200w - w² a=-1, b = 200, the maximum width is at:
w = -b/2a = -200/2(-1) = -200/-2 = 100
A width of 100 yard has the largest area
c) l = 200 - w = 200 - 100 = 100 yards
Area = l × w = 100 × 100 = 10000 yd²
The maximum area is 10000 yd²
Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find
Complete question is;
Multiple-choice questions each have 5 possible answers, one of which is correct. Assume that you guess the answers to 5 such questions.
Use the multiplication rule to find the probability that the first four guesses are wrong and the fifth is correct. That is, find P(WWWWC), where C denotes a correct answer and W denotes a wrong answer.
P(WWWWC) =
Answer:
P(WWWWC) = 0.0819
Step-by-step explanation:
We are told that each question has 5 possible answers and only 1 is correct. Thus, the probability of getting the right answer in any question is =
(number of correct choices)/(total number of choices) = 1/5
Meanwhile,since only 1 of the possible answers is correct, then there will be 4 incorrect answers. Thus, the probability of choosing the wrong answer would be;
(number of incorrect choices)/(total number of choices) = 4/5
Now, we want to find the probability of getting the 1st 4 guesses wrong and the 5th one correct. To do this we will simply multiply the probabilities of each individual event by each other.
Thus;
P(WWWWC) = (4/5) × (4/5) × (4/5) × (4/5) × (1/5) = 256/3125 ≈ 0.0819
P(WWWWC) = 0.0819
One angle of a right triangle measures 36.5 degrees. What is the measure of the other small angle?
Answer:
53.5 DEGREES
Step-by-step explanation:
90 + 36.5 = 125.6
180 - 126.5 = 53.5 degrees
The measure of the other small angle will be 53.5 degree.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In a right triangle, One angle measures 36.5 degrees.
Now,
Since, The triangle is a right triangle.
So, One of the angle = 90 degree
And, One angle measures 36.5 degrees.
Let the measure of the other small angle = x degree
Since, The sum of all the interior angles in a triangle = 180 degree
So, We can formulate;
⇒ x + 90 + 36.5 = 180
⇒ x + 126.5 = 180
⇒ x = 180 - 126.5
⇒ x = 53.5 degree.
Thus, The measure of the other small angle will be 53.5 degree.
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A team of 17 softball players need to choose three players to refill the water cooler. How many different ways are there to select 3 players?
=======================================================
Explanation:
If order mattered, then we'd have 17*16*15 = 4080 different permutations. Notice how I started with 17 and counted down 1 at a a time until I had 3 slots to fill. We count down by 1 because each time we pick someone, we can't pick them again.
So we have 4080 different ways to pick 3 people if order mattered. But again order doesn't matter. All that counts is the group itself rather than the individual or how they rank. There are 3*2*1 = 6 ways to order any group of three people, which means there are 4080/6 = 680 different combinations possible.
An alternative is to use the nCr formula with n = 17 and r = 3. That formula is
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
where the exclamation marks indicate factorials
The number of different ways that are there to select 3 players is 680.
Calculation of the number of different ways:
Since there is A team of 17 softball players need to choose three players to refill the water cooler.
So here we can say there are [tex]17\times 16\times 15 = 4080[/tex]
And, since we have to select 3 people so the no of ways should be [tex]3\times 2\times 1 = 6\ ways[/tex]
So, here the number of different ways should be
[tex]= 4080\div 6[/tex]
= 680
Therefore, The number of different ways that are there to select 3 players is 680.
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Janae has 280 dimes in her piggy bank she has 10 times as many pennies how many pennies does Janae have
Answer:
She has 28 pennies
Step-by-step explanation:
Janae has 280 dimes in her piggy bank she has 10 times as many pennies .
If she has 280 dimes in piggy bank
And has 10 times as many pennies
Let dimes= x
Let pennies= y
X= 10y
But x= 280
280= 10y
280/10 = y
28 = y
She has 28 pennies
Estimate then find the quotient 2,800÷25
Answer:
112
Step-by-step explanation:
Insert <, >, or = in the appropriate space to make a true statement.
1-3 _-4
1-311
-4
Answer:
>
Step-by-step explanation:
1 - 3 ?? -4
-2 ?? -4
The appropriate symbol for this ?? relation is >.
1 -3 > -4
Which statements are true based on the diagram
Answer:
Can you show the diagram please?
A car was purchased new in 2019 for $32,650. In 2020 the car is $23,834.50. Find the rate of depreciation for that one year?
Answer:
Rate of depreciation = 27%
Step-by-step explanation:
Given:
Purchase price = $32,650
Rate in 2020 = $23,834.50
Find:
Rate of depreciation
Computation:
Depreciation = Purchase price - Rate in 2020
Depreciation = $32,650 - 23,834.50
Depreciation = $8,815.5
Rate of depreciation = [8,815.5 / 32650] 100
Rate of depreciation = 27%
What does it mean to multiply a number by -1?
Answer:
Multiplying a number by -1 means the sign on the number is made opposite. If the number was positive, it becomes negative. If the number was negative, it becomes positive.
edmentum answer!!
To which subset of the real number system does the number LaTeX: 1.\overline{5}1. 5 ¯ belong? Group of answer choices irrational numbers whole numbers natural numbers rational numbers
Answer:
rational numbers
Step-by-step explanation:
In a group of 58 learners at Nakambuda C.S, 34 learners have chosen the field of Agriculture. What fraction of learners will be doing Agriculture?
learners of Agriculture: 34/58
semplify it
divide by 2
34 > 17
58 > 29
they are prime numbers, so can't be semplify anymore
17/29 will do Agriculture
in percentage we have a proportion:
17 : 29 = x : 100
x = (17 * 100) / 29 = 1700 / 29 ≅ 48,62
8x-3+19 What number does x stand for in this problem?? PLEASE ANSWER I WILL GIVE 50 POINTS!!!
Answer: x=4
Step-by-step explanation:
8x-13=19
first, add 13 to both sides.
8x= 32
then, divide both sides by 8 to isolate x.
x= 32/8
x=4
3 points] Write the equation of the line passing through (-1, 4) and (2,-2) in lope – intercept form.
Answer:
y = - 2x + 2
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 ) = (- 1, 4) and (x₂, y₂ ) = (2, - 2)
m = [tex]\frac{-2-4}{2+1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2 , thus
y = - 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, - 2 ), then
- 2 = - 4 + c ⇒ c = - 2 + 4 = 2
y = - 2x + 2 ← equation of line
Sue deposited $1,500 into two different accounts.
- She deposited $600 into an account that pays 7.5% simple interest.
- She deposited $900 into an account that pays 6% compounded annually.
If Sue does not deposit additional money into the accounts and she doesn't withdraw any money from the accounts, which is closest to the total balance she will have in the two accounts at the end of 5 years
$915 I’m pretty sure
Four big water bottles can hold 8 gallons of water. How much water can ten big water bottles hold.
Step-by-step explanation:
Part 1
To find out the amount of water ten big water bottles can hold, we have to find out how much water is in each water bottle. To do this, we divide the amount we are looking for by the number of items.
8 ÷ 4 = 2
Part 1 answer: Each water bottle can hold 2 gallons of water.
Part 2
Now that we know the amount of water in each water bottle, we can find out how much water 10 water bottles can hold. To do so, we multiply our previous answer, 2, by the number of items (10).
2 • 10 = 20
Part 2 answer: 10 water bottles can hold 20 gallons of water.
Our final answer: 20 gallons
I hope this helps you!
a bee has mass of 0.02 kg
Your question is not complete
What are the roots of the equation? 0=x4−x3+4x2−6x−12 Select all correct answers. −6 −2 −1 1 2 6 i√6 −i√6 √6 −√6
Answer:
3rd Option: -1
5th Option: 2
7th Option: i√6
8th Option: -i√6
Step-by-step explanation:
Graph the function first to find our real root factors.
When you find your real root factors, factor the equation down with x + 1 and x - 2 and then use Quadratic Formula to find complex roots.
Answer:
-2, 1. i[tex]\sqrt{6}[/tex], and -i[tex]\sqrt{6}[/tex]
Step-by-step explanation:
just took the test
Which property would be used first to make the following problem easier to work? 2/3 x (3/2 x 5) associative property of multiplication multiplicative property o commutative property of multiplication distributive property
Answer:
5
can be done by multiplication multiplicative property
Step-by-step explanation:
2/3 * (3/2 * 5)
1st = 2/3 * 3/2 * 5
2nd = 2 * 3 * 5
3 * 2
3rd = 3 * 5
3
therefore
the answer = 5
Answer:
[tex]\Large \boxed{\mathrm{associative \ property \ of \ multiplication}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
The associative property of multiplication can be use to make the problem easier to solve.
In associative property of multiplication, when we multiply a bunch of numbers, we can group the numbers in any combination.
[tex]a \times (b \times c) = (a \times b) \times c[/tex]
[tex]\rule[225]{225}{2}[/tex]
Our hearts beat approximately 70 times per minute. Express in scientific notation how many times the heart beats over a lifetime of 73 years (ignore leap years). Round the decimal factor in your scientific notation answer to two decimal places.
Answer:
2.69 x [tex]10^{9}[/tex]
Step-by-step explanation:
We are given the heart's speed - 70 bpm
We count the number of minutes in 73 years :
1 year = 365 days1 day = 24 hours1 hour = 60 minutes73 x 365 x 24 x 60 = 38,368,800 minutesWe multiply the heart's bpm with 73 years worth of minutes
38,368,800 x 70 = 2,685,816,000
Write the number in scientific notation = 2.68581 x [tex]10^{9}[/tex] ≈ 2.69 x [tex]10^{9}[/tex]
The number of times a heart will beat in 73 years is required.
The heart will beat [tex]1.6\times 10^{11}\ \text{times}[/tex] in a lifetime.
AlgebraThe number of times heart beats per minute is 70.
Number of years in a lifetime is 73 years
Ignoring leap year a year has 365 days.
So minutes in a leap year is
[tex]365\times 24\times 60\times 60[/tex]
Minutes in a lifetime of 73 years
[tex]73\times 365\times 24\times 60\times 60[/tex]
The product of beats per minute and the minutes in a lifetime will given the required heart beats
[tex]70\times 73\times 365\times 24\times 60\times 60=1.6\times 10^{11}\ \text{beats}[/tex]
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If FH = 9x + 15 and GH = 5x + 4,
then FG = ?
Answer:
FG = 39
Step-by-step explanation:
From the question given:
FH = 9x + 15
GH = 5x + 4
FG = ?
From the question given above, we can say that G is the midpoint of FH. This implies that:
FH = FG + GH
With the above idea in mind, we can obtain FG as follow:
FH = 9x + 15
GH = 5x + 4
FG = ?
FH = FG + GH
9x + 15 = FG + 5x + 4
Rearrange
FG = 9x + 15 - 5x - 4
FG = 9x - 5x + 15 - 4
FG = 4x + 11
Next, we shall determine the value of x. This can be obtained as follow:
Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e
FG = GH
With the above idea in mind, we can obtain the value of x as follow:
FG = 4x + 11
GH = 5x + 4
FG = GH
4x + 11 = 5x + 4
Collect like terms
11 - 4 = 5x - 4
7 = x
x = 7
Thus, we can obtain the value of FG as follow:
FG = 4x + 11
x = 7
FG = 4x + 11
FG = 4(7) + 11
FG = 28 + 11
FG = 39
***Check ***
FH = 9x + 15
x = 7
FH = 9(7) + 15 = 63 + 15 = 78
GH = 5x + 4
x = 7
GH = 5(7) + 4 = 35 + 4 = 39
FG = 4x + 11
x = 7
FG = 4(7) + 11 = 28 + 11 = 39
FH = FG + GH
FH = 78
FG = 39
GH = 39
FH = FG + GH
78 = 39 + 39
78 = 78
Which of the following must describe a irrational number? A. a number with a repeating or terminating decimal expansion B. a number with a nonterminating decimal expansion C. a decimal with a nonrepeating decimal expansion D. a number with a nonrepeating and nonterminating decimal expansion
Answer:
D.
Step-by-step explanation:
A irrational number can be defined as those numbers which are real but can NOT be expressed in simple fractions. The term 'irrational' means 'a number which can not be expressed in ratio of two integers', 'no ratio.'
When a irrational number is expressed in decimal, the numbers keep on expanding without repeating andd without terminating, which means it keeps on expanding infinitely.
For example, π (pi) is an irrational number. When it is expressed in decimals it keeps on expanding non-repeatedly and unendingly.
Another example of an irrational number is √2.
Thus the correct statement that defines irrational number is option D.
Answer:
D. a number with a nonrepeating and nonterminating decimal expansion
Step-by-step explanation:
Prove the following using a proof by contradiction:The average of four real numbers is greater than or equal to at least one of the numbers.
The average of four real numbers is greater than or equal to at least one of the numbers.
Answer:
By contradiction it can be proved that:
Average of four real numbers will be greater than or equal to at least one of the four real numbers.
Step-by-step explanation:
Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.
As a result, we prove the fact.
Here, let the four number be:
[tex]p, q, r, s[/tex]
The average will be Sum of all numbers divided by count of numbers.
[tex]\dfrac{p+ q+ r+ s}4[/tex]
Now, let us assume the opposite that the average is less than all the numbers.
i.e.
[tex]\dfrac{p+ q+ r+ s}4 <p[/tex]
[tex]\dfrac{p+ q+ r+ s}4 <q\\\dfrac{p+ q+ r+ s}4 <r\\\dfrac{p+ q+ r+ s}4 <s[/tex]
Now, let us add all of them:
[tex]\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4<p+q+r+s\\\Rightarrow p+q+r+s<p+q+r+s[/tex]
Which can never be possible hence, our assumption is contradicted.
our assumption is wrong.
Therefore, by contradiction it is proved that:
Average of four real numbers will be greater than or equal to at least one of the four real numbers.
An average of four real numbers will be greater than or equal to at least one of the four real numbers.
What is average?
An average is simply defined as the mean of the given set of numbers. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.
Prove the following using proof by contradiction.
The average of four real numbers is greater than or equal to at least one of the numbers.
Method of a contradiction means we assume opposite to the fact to be proved and then we contradict our assumption.
Let the four numbers be a, b, c, and d.
The average will be
[tex]\rm \dfrac{a+b+c+d}{4}[/tex]
Now let us assume the opposite that the average is less than all the numbers.
[tex]\rm \dfrac{a+b+c+d}{4} < a\\\\\rm \dfrac{a+b+c+d}{4} < b\\\\\rm \dfrac{a+b+c+d}{4} < c\\\\\rm \dfrac{a+b+c+d}{4} < d[/tex]
Let us add all of them.
[tex]\rm \rightarrow \dfrac{a+b+c+d}{4} +\dfrac{a+b+c+d}{4} +\dfrac{a+b+c+d}{4}+\dfrac{a+b+c+d}{4} < a+b+c+d\\\\\rightarrow \dfrac{4(a+b+c+d)}{4} < a+b+c+d\\\\\rightarrow a+b+c+d < a+b+c+d[/tex]
That can never be possible hence, our assumption is contradicted.
Our assumption is wrong.
Therefore, by contradiction, it is proved that;
An average of four real numbers will be greater than or equal to at least one of the four real numbers.
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A survey was conducted at Giant Supermarket where 50 students were randomly chosen and asked
whether they liked apples or bananas. Of the 50,36 students said they like apples, 30 students like
bananas and 5 students do not like either apples or bananas. How many students like both apples
and bananas? How many students like only apples or only bananas?
Answer:
The answer for both apples and bananas is 21
The answer for only apples or only bananas is 45
Step-by-step explanation:
36 plus 30 minus 45
50-5 is 45
only apples or bananas is 15 + 9
Paul has $40,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $40,000?
Answer:
.18n+2400-.06n=6000
.12n=3600
n=3600/.12=$30000 at 18%, $10000 at 6%
Step-by-step explanation: