For n = 4, all of the given expressions are equivalent except 16 and
(n - 2).
What is Substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
The expressions are;
1. 16
2. n - 2
3. 1/16
4. 1/n²
Now, Put n = 4 in all given expression we get;
The first expression is,
16
The second expression is,
n - 2
= 4 - 2
= 2
The third expression is,
1/16
The fourth expression is,
1/n²
= 1/4²
= 1/16
Hence, Third and fourth expression are same.
So, For n = 4, all of the given expressions are equivalent except 16 and
(n - 2).
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The complete question is this.
If n = 4, all of the following expressions are equivalent except _____.
16
n -2
1/16
1/n ^ 2
The formula A = 1/2 S^2 expresses the area of an isosceles right
triangle in terms of the length, s, of a leg of the triangle.
Which equation expresses the length of a leg of an isosceles right
triangle in terms of the area?
Answer:
[tex]s = \sqrt{2a} [/tex]
Step-by-step explanation:
A = 0.5S^2
2A = S^2
Therefore,
[tex]s = \sqrt{2a} [/tex]
To express the length in terms of the area, is an illustration of change of subject of formula.
The equation that express S in terms of the area is: [tex]S =\sqrt{2A}[/tex]
Given that:
[tex]A = \frac 12S^2[/tex]
First, multiply both sides by 2
[tex]2 \times A = \frac 12S^2 \times 2[/tex]
[tex]2 \times A = S^2[/tex]
[tex]2A = S^2[/tex]
Take positive square roots of both sides
[tex]\sqrt{2A} = \sqrt{S^2[/tex]
[tex]\sqrt{2A} = S[/tex]
Rewrite the equation as:
[tex]S =\sqrt{2A}[/tex]
Hence, the equation that express S in terms of the area is: [tex]S =\sqrt{2A}[/tex]
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A triangle has side lengths of (5.3p+ 7.6) centimeters, (3.8p – 4.3) centimeters,
and (2.4q - 7.4) centimeters. Which expression represents the perimeter, in
centimeters, of the triangle?
Answer:
The perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres
Step-by-step explanation:
Let a, b and c be the sides off a triangle. Its perimeter P = a + b + c.
Now, the triangle has side lengths (5.3p+ 7.6) centimetres, (3.8p – 4.3) centimetres, and (2.4q - 7.4) centimetres.
Let a = (5.3p+ 7.6) cm , b = (3.8p – 4.3) cm and c = (2.4q - 7.4) cm
So the perimeter of the triangle is P = a + b + c
substituting the values of a, b and c, we have
P = (5.3p + 7.6) cm + (3.8p – 4.3) cm + (2.4q - 7.4) cm
opening the brackets and collecting like terms, we have
P = (5.3p + 3.8p + 2.4q + 7.6 - 4.3 - 7.4) cm
P = (9.1p + 2.4q - 4.1) centimetres
So the perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres
PLZ HELP 235 people are at RSM summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp?
Answer:
number of girls = 90
Number of boys = 125
Number of adults = 20
Step-by-step explanation:
Total people at the summer camp= 235
Let
number of girls=x
Number of boys = x + 35
Number of adults = x - 70
Total people at the summer camp= number of girls + Number of boys + Number of adults
235 = x + (x+35) + (x - 70)
235 = x + x + 35 + x - 70
235 = 3x - 35
Add 35 to both sides
235 + 35 = 3x
270 = 3x
Divide both sides by 3
x= 270/3
= 90
x = 90
number of girls= x = 90
Number of boys = x + 35
= 90 + 35
= 125
Number of adults = x - 70
= 90 - 70
= 20
Total = 90 + 125 + 20
= 235
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20
In a bakery that sells cookies there are 4 oatmeal cookies for every 11 chocolate cookies.If there are 285 cookies altogether how many oatmeal cookies are there?
Answer:
There are 76 oatmeal raisen cookies altogether.
Step-by-step explanation:
4 + 11 = 15
285/15 = 19
19 * 4 = 76
you deposit $3000 into an account that pays 8% compounded quarterly. how much will you have in 10 years?
Answer:
$5400 USD
Step-by-step explanation:
Investment=3,000
Interest=8% = .08
Time=10 years
([3000 x .08 x 10] + 3,000
[240 x 10] + 3,000
2,400 + 3,000= 5,400
Which of the following measures of central tendency are resistant to outliers? (May be more than one correct answer) Group of answer choices Median Mode Mean Range Inter-quartile Range (IQR) Standard Deviation
Answer
Median
Step-by-step explanation:
It should be noted that medians are resistant to outliers.
Outliers simply means the data records which are different from every other record. It escapes normality. The outlier affects mean, inter-quartile range, mode and the range.
It should be noted that the median isn't affected by outliers. The reason for this is that the median depends on the arrangement and the order of the data. For example, when one changes the lowest score in a given set of numbers, the order won't be affected.
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Manny is participating in a Bike-a-thon and travels at a constant rate of 6 miles in 20 minutes.
Manny rode his bike for 3 hours. How far did he travel?
Manny rode his bike for 1.5 hours. How far did he travel?
I will give 20 extra points for you <3
Answer:
1. 54
2.?
Step-by-step explanation:
:) Have a nice day
I need help asap please! <3
7/5 + 2/3 - 1 = ayuda porfa
Answer:
[tex]1\frac{1}{15}[/tex]
Step-by-step explanation:
[tex]\frac{7}{5}+\frac{2}{3}-1\\[/tex]
Convertir elemento a fracción: 1 = 1/1
[tex]=-\frac{1}{1}+\frac{7}{5}+\frac{2}{3}[/tex]
Mínimo común múltiplo de 1,5,3 = 15
Ajustar fracciones según el mcm
[tex]=-\frac{15}{15}+\frac{21}{15}+\frac{10}{15}[/tex]
Dado que los denominadores son iguales, combine las fracciones:
[tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\= \frac{-15+21+10}{15}\\\\[/tex]
Sumar Restar los números: -15 + 21 + 10 = 16
[tex]=\frac{16}{15}\\\\16\div 15 = 1 \: remainder 1\\\\=1\frac{1}{15}[/tex]
If you add two negative integers, what will the sign on the sum be? Explain.
Answer:
Negative
Step-by-step explanation:
If both are negative, they can't grow when you add them. If I owe someone 3 dollars, then I owe them 3 more, I don't owe them 0, I owe them 6. The equation would be My amount of money-3-3
What is the relationship between the 8’s in 8,809
Answer:
Their place values
Step-by-step explanation:
On eight is in thousands while the other is in hundreds
Answer:
"8" on the left is ten times the value of the "8" on the right
Step-by-step explanation:
I am going to assume that the comma " , " denotes divisions of "thousands" and not the European system where the comma represents a decimal point.
(refer to attached for definitions of place values)
we can see that for the number 8,809 :
1) the 8 on the left is in the thousands place and hence represents 8000.
2) the 8 on the right is in the hundreds place and hence represents 800.
in order to find the relative order of difference between the two digits, we simply we divide the value of the two digits:
8000 ÷ 800 = 10
Hence the "8" on the left is ten times the value of the "8" on the right
Name one pair of rays that are not opposite rays.
Answer:
ED and EC
Step-by-step explanation:
If the two rays which extend in the opposite direction having same endpoint is said to be opposite rays.
From the picture attached,
Rays having same endpoint E but not in the opposite directions are ED and EC.
This pair of rays meet at point E having different directions.
Similarly EA and EB is the other pair of rays having same end point (at E) but not in opposite directions.
find the arrival time if the plane took off at 8:35am and flew for 2 hr. 55 min. include am or pm in your answer
Please Help Brainliest to whoever can give a clear explanation for this problem!
In triangle ABC, [tex] \angle A = 90 [/tex], AC = 1, and AB = 5. Point D lies on ray AC such that [tex]\angle DBC = 2\angle CBA[/tex]. Compute AD.
See the attached sketch. Let [tex]\beta[/tex] denote angle ABC and [tex]\beta'[/tex] denote angle CBD. Then [tex]\beta'=2\beta[/tex].
From the sketch, we see that
[tex]\tan\beta=\dfrac15[/tex]
[tex]\tan(\beta+\beta')=\tan(3\beta)=\dfrac{AD}5[/tex]
Write [tex]\tan(3\beta)[/tex] in terms of [tex]\tan\beta[/tex]. Recall the angle sum identity for tangent:
[tex]\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}[/tex]
This gives us
[tex]\tan(3\beta)=\dfrac{\tan\beta+\frac{2\tan\beta}{1-\tan^2\beta}}{1-\tan\beta\cdot\frac{2\tan\beta}{1-\tan^2\beta}}=\dfrac{\tan\beta(\tan^2\beta-3)}{3\tan^2\beta-1}[/tex]
and plugging in [tex]\tan\beta=\frac15[/tex] leaves us with
[tex]\tan(3\beta)=\dfrac{37}{55}[/tex]
and so AD = 5 * 37/55 = 37/11.
what is the decimal that is greater than 3/10 and less than 2/5
Answer:
0.31 - 0.39
Step-by-step explanation:
3/10 = 0.3
2/5 = 0.4
All the values between 0.3 and 0.4 excluding 0.3 and 0.4 (can't be 0.3 or 0.4)
The decimal number that is greater than 3/10 and less than 2/5 will be;
⇒ 0.35
What is Decimal number?A decimal number is a number that consists of a whole and a fractional part.
Given that;
A decimal number is greater than 3/10 and less than 2/5.
Now,
Let a decimal number = x
So, We get;
⇒ 3/10 < x < 2/5
Since, We have;
⇒ 3/10 = 0.3
⇒ 2/5 = 0.4
Thus, The decimal number that is greater than 3/10 and less than 2/5 is 0.35.
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write a polynomial of least degree with roots 6 and. -8
Answer:
y = x² + 2x - 48
Step-by-step explanation:
Given the roots of the polynomial are x = 6 and x = - 8 , then the corresponding factors are
(x - 6) and (x + 8) and the polynomial is the product of the factors, that is
y = (x - 6)(x + 8) ← expand using FOIL
y = x² + 2x - 48
20=v−7 what does v equal?
Answer:
27
Step-by-step explanation:
20=v-7
v=20+7
v=27
Hence, v equals to 27
[tex]\huge\mathbb\purple{EXPLAIN}[/tex]
[tex]20 = v - 7[/tex]
[tex]v = 20 + 7 = 27[/tex]
what is the solution to the inequality 3/2m -4 > 4/5 + 7/10m
Answer:
m > 6
Step-by-step explanation:
[tex]3/2m -4 > 4/5 + 7/10m\\\\\frac{3}{2}m-4>\frac{4}{5}+\frac{7}{10}m\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\\frac{3}{2}m-4+4>\frac{4}{5}+\frac{7}{10}m+4\\\\Simplify\\\\\frac{3}{2}m>\frac{24}{5}+\frac{7}{10}m\\\\\mathrm{Subtract\:}\frac{7}{10}m\mathrm{\:from\:both\:sides}\\\\\frac{3}{2}m-\frac{7}{10}m>\frac{24}{5}+\frac{7}{10}m-\frac{7}{10}m\\\\Simplify\\\\\frac{4}{5}m>\frac{24}{5}\\\\\mathrm{Multiply\:both\:sides\:by\:}5\\\\5\times\frac{4}{5}m>\frac{24\times\:5}{5}\\\\Simplify\\\\4m>24[/tex]
[tex]4m>24\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4m}{4}>\frac{24}{4}\\\\Simplify\\\\m> 6[/tex]
Please help it’s due in 19 min
Answer:
yellow
Step-by-step explanation:
ITS YELLOW IM GOOD AT THIS TRUST ITS YELLOW
Triangle ABC has vertices A(4,8) B(-3,2) and C(-1,6). Triangle ABC is dilated so that the new vertices are A'(12,24) B'(-9,6) and C'(-3,18). What is the scale factor?
Find the domain and range of each relation (use interval notation). Then determine if each relation is one-to-one.
Express 0.1 as a fraction.
Step-by-step explanation:
Write 0.1 as
0.1
1
Multiply both numerator and denominator by 10 for every number after the decimal point
0.1 × 10
1 × 10
=
1
10
Reducing the fraction gives
1
10
In fraction form the number 0.1 can be written as 1/10.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p/q.
The given number is: 0.1
Since the given number is a decimal number,
And it has only in digit after decimal.
Therefore,
Divide and multiply by 10 with this number,
[tex]0.1 \times \dfrac{10}{10} = \dfrac{1}{10}[/tex]
Hence,
The fraction from of the number 0.1 is 1/10
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whats the answer 5(x-y+2)
whats the answer 5(x-y+2)
Answer :
5x - 5y + 10
Step-by-step explanation:
5(x - y + 2)
5(x) + 5( - y) + 5(2)
5x - 5y + 10
[tex]\boxed{\boxed{\bold{THANKS}}} [/tex]
suppose the equation for line A is given by 2x-5y=15, if line A and B are parallel and the point (-10,3) lies on line B, then write the equation in slope intercept for line b.
Answer:
y=2/5x + 7
Step-by-step explanation:
First, you have to rewrite 2x-5y=15 to slop intercept form.
To do that you have to first subtract 2x from both side to cancel it out.
2x- 2x-5y= 15 -2x.
-5y= -2x+15
Next, you divide 5 on both side to leave the y by itself.
y= -2x/-5 + 15/-5
Simplify
y= 2/5x + (-3) 2/5 is our slope
Now that we found the slope, we need to the y-intercept of line b
y=2/5x + b
To find the y-intercept, we substitue x and y with the coordinates (-10,3)
3= 2/5(-10) +b
Now we just solve for b
3= -4 +b
3-(-4) = b
7=b
Now we have identified that 7 is the y intercept
The full equation is y= 2/5x +7
I hope this helped :)
Use the segment to complete the statements the value of x is
Answer:
Step-by-step explanation:
A number decreased by twelve is twice the opposite of ten. Find the number.
Answer:
-8
Step-by-step explanation:
Let n = the number.
A number decreased by twelve is twice the opposite of ten.
n - 12 = 2 * (-10)
n - 12 = -20
n = -8
find the roots of the quadratic equation using factoring. 6m^2 - 23M + 10 = 0
m₁ = 10/3
m₂ = 1/2
Step-by-step explanation:6m² - 23m + 10 = 0
6m² - 2m - 20m + 10 = 0
3m(2m - 1) - 10(2m - 1) = 0
(3m - 10)(2m - 1) = 0
3m - 10 = 0 =>3m = 10 => m₁ = 10/3
2m - 1 = 0 => 2m = 1 => m₂ = 1/2
(-2, 8) (9, 10) (1,7) (3, 9) (10, 12)
Function
Not a Function
Answer: function
Step-by-step explanation: To determine whether the relation shown here
is a function, remember that a relation is a function if each x term
corresponds to exactly one y term.
In the data set show, each x term, -2, 9, 1, 3, and 10 appears only once.
This means that each x term corresponds to exactly one y term.
So yes, the relation is a function.
please help ill give 10 points and a brainly to who ever who can answer this. thanks!!!
Answer:
Step-by-step explanation:
Which of these is a simplified form of the equation 9y + 6 = 9 + 2y + 2y?
Answer:
y=3/5
Step-by-step explanation:
9y+6=9+2y+2y
9y+6=9+4y
9y-4y=9-6
5y=3y=3/5