Lucy paid $120 for an item at the store that was 20 percent off the original price. what was the original price?

Answer:

A

Step-by-step explanation:

1 Factor out the common term ss.

\frac{s(25{s}^{2}+12)}{5s}

5s

s(25s

2

+12)

​

2 Cancel s.

\frac{25{s}^{2}+12}{5}

5

25s

2

+12

​

Answer:

[tex]\textsf{Increasing function}: \quad \left[0, \dfrac{1}{16}\right)[/tex]

[tex]\textsf{Decreasing function}: \quad \left(\dfrac{1}{16}, \infty\right)[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\sqrt{x}-2x[/tex]

As a negative number cannot be square rooted, the domain of the function is restricted to [0, ∞).

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]

Differentiating produces an algebraic expression for the gradient as a function of x.  Therefore, differentiate the given function:

[tex]\begin{aligned}f(x) & = \sqrt{x}-2x\\& = x^{\frac{1}{2}}-2x\\\implies f'(x) & = \dfrac{1}{2}x^{\left(\frac{1}{2}-1\right)}-2x^{(1-1)}\\ & = \dfrac{1}{2}x^{-\frac{1}{2}}-2x^0\\ & = \dfrac{1}{2\sqrt{x}}-2\end{aligned}[/tex]

Increasing function

To find the interval where f(x) is increasing, set the differentiated function to more than zero and solve for x:

[tex]\begin{aligned}f'(x) & > 0\\\implies \dfrac{1}{2\sqrt{x}}-2 & > 0\\\dfrac{1}{2\sqrt{x}} & > 2\\\ \dfrac{1}{2} & > 2\sqrt{x}\\\dfrac{1}{2 \cdot 2} & > \sqrt{x}\\ \dfrac{1}{4} & > \sqrt{x}\\ \sqrt{x} & < \dfrac{1}{4}\\\left(\sqrt{x}\right)^2 & < \left(\dfrac{1}{4}\right)^2\\ x & < \dfrac{1}{16}\end{aligned}[/tex]

As the domain is restricted, the function is increasing when:

[tex]\textsf{Solution}: \quad 0 \leq x < \dfrac{1}{16}[/tex]

[tex]\textsf{Interval notation}: \quad \left[0, \dfrac{1}{16}\right)[/tex]

Decreasing function

To find the interval where f(x) is decreasing, set the differentiated function to less than zero and solve for x:

[tex]\begin{aligned}f'(x) & < 0\\\implies \dfrac{1}{2\sqrt{x}}-2 & < 0\\\dfrac{1}{2\sqrt{x}} & < 2\\\ \dfrac{1}{2} & < 2\sqrt{x}\\\dfrac{1}{2 \cdot 2} & < \sqrt{x}\\ \dfrac{1}{4} & < \sqrt{x}\\ \sqrt{x} & > \dfrac{1}{4}\\\left(\sqrt{x}\right)^2 & > \left(\dfrac{1}{4}\right)^2\\ x & > \dfrac{1}{16}\end{aligned}[/tex]

Therefore, the function is decreasing when:

[tex]\textsf{Solution}: \quad x > \dfrac{1}{16}[/tex]

[tex]\textsf{Interval notation}: \quad \left(\dfrac{1}{16}, \infty\right)[/tex]

Note: The answer quoted in the original question is incorrect for the quoted function (please refer to the attached graph for proof).

Differentiation Rules

[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]

LCM can help us to compare the two of the given fractions. The correct option is A, -(3/4) < -(5/16).

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

Bring both the terms to the same denominator for easy comparison. Now, since the LCM of 4 and 16 is 16. Therefore, we can write the two of the fractions as,

-(3/4) = -(3×4)/(4×4) = -12/16

-(5/16) = -5/16

Further, we can write the comparison of the two fractions as,

-12/16 < -5/16

-(3/4) < -(5/16)

Hence, the correct option is A, -(3/4) < -(5/16).

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The slope of the line AC is equal to the slope of the line CE.

We have the points:

A = ( - 3 , 6 )

C = ( - 1 , 3 )

Slope of AC will be:

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope of AC = m₁ = ( 3 - 6 ) / ( - 1 + 3 )

m₁ = - 3 / 2

m₁ = - 1.5

Now,

C = ( - 1 , 3 )

E = (3 , - 3)

Slope of AC = m₂ = ( - 3 - 3 ) / ( 3 + 1 )

m₂ = - 6 / 4

m₂ = - 3 / 2

m₂ = - 1.5

So, we get that:

m₁ = m₂  

Therefore, we get that, the slope of the line AC is equal to the slope of the line CE.

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An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. a) R=R is a reflexive property.

b) 5-P  Substitution Property, c) If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b is a substitution property, d) a=4 Then it can be said that a = b e)DEIR then DF = LR Segment Addition Postulate

f)VW - WY - VT is a Transitive Property

What is Expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

We have match the given expression with an appropriate property.

a) R=R is a reflexive property.

b) 5-P  Substitution Property

c) If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b is a substitution property

d) a=4 Then it can be said that a = b  

e)DEIR then DF = LR Segment Addition Postulate

f)VW - WY - VT is a Transitive Property

Therefore .a) R=R is a reflexive property. b) 5-P  Substitution Property, c) If 3 = x and y = -2 Then the expression y = x + b can be written as -2 = 3 + b is a substitution property, d) a=4 Then it can be said that a = b e)DEIR then DF = LR Segment Addition Postulate f)VW - WY - VT is a Transitive Property.

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The plane where the point is located and which has a fixed z coordinate (1,2,3) is y=2x.

Given that,

The plane where the point is located and which has a fixed z- coordinate (1,2,3).

The plane has the point (1, 2, 3) and the z-axis.

Any plane that has the z-axis is of the type that (0,0,1)

Therefore, By cross product of the two points we can find the equation.

Let take a matrix with x,y and z

We can se in the picture there is a matrix.

We now find the determination of that matrix .

determination means the scalar value calculated for a given square matrix is the determinant of a matrix. The determinant is a concept in linear algebra, and its components are square matrixes. It can be viewed as the matrix transformation's scaling factor. useful for performing calculus operations, computing the inverse of a matrix, and solving systems of linear equations.

-2x+y=0

y=2x

Therefore, The plane where the point is located and which has a fixed z coordinate (1,2,3) is y=2x.

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Answer:

X= 2/3

Step-by-step explanation:

-2(x+1/3)+9x=4

Distribute: -2x-2/3+9x=4

Combine: 7x=14/3 ----- 4/1+2/3=12/3+2/3=14/3

Clear the fraction: 21x=14 ------- 7·3x=14/3·3/1

Divide: X=2/3 ------ 14/21÷ 7/7=2/3

X=2/3           Hope This Helps :)

Answer:

[tex] \sf \large \: x = \frac{2}{3} [/tex]

Step-by-step explanation:

−2(x+1/3)+9x=4

Step 1: Simplify both sides of the equation.

−2(x+1/3)+9x=4

(−2)(x)+(−2)(1/3)+9x=4(Distribute)

−2x+−2/3+9x=4

(−2x+9x)+(−2/3)=4(Combine Like Terms)

7x+−2/3=4

7x+−2/3=4

Step 2: Add 2/3 to both sides.

7x+−2/3+2/3=4+2/3

7x=14/3

Step 3: Divide both sides by 7.

7x/7 = 14/3/7

x=2/3

Answer: 14/24 or 7/12

Step-by-step explanation: keep on dividing 2 or just divide by 4

Answer:

length = 99 yards

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2(l + w) ← l is the length and w the width

given  P = 356 and w = 79 , then

356 = 2(l + 79) ← divide both sides by 2

178 = l + 79 ( subtract 79 from both sides )

99 = l

the length of the field is 99 yards

$829.08

Step-by-step explanation:

43,112 ÷ 52 = 829.08

Answer:

odd

Step-by-step explanation:

the answer is odd, my dead grandma just finished this question since she failed 7th grade.

Answer: 4289

Step-by-step explanation:

Total = 2400+(2400-511) = 4289

Answer:2

Step-by-step explanation: x+1+2x=3x+1        3x+1=7        3x=7-1       x=6/3   x=2

hope it helps

Answer:

3

Step-by-step explanation:

x+1+2x=7

variables should be on the left and the whole number on the right.

something like this: x+2x=7-1

simplify the equation: 3x=6

find x: x= 6/3=2

so u know x is 2

then substitute the 2 into x. so 2+1 =3#

Your answer is three.

Answer:

The answer is D

Answer:

1/2

Step-by-step explanation: because it is shaded or not

The inequality for 2/3 I 4v + 6 I - 2 ≤ 10 is -6≤v≤3.

Given the inequality is 2/3 I 4v + 6 I - 2 ≤ 10

Isolate the variable by dividing each side by factors that don't contain the variable.

2/3 I 4v + 6 I  ≤ 10 +2

arrange the constants on the right side.

2/3 I4v + 6I ≤ 12

multiply the terms.

8v + 12/3 ≤ 12    or -8v - 12/3 ≤ 12

8v + 12 ≤ 36       or  -8v -12 ≤ 36

8v ≤ 36 -12         or  -8v ≤ 36 + 12

8v ≤ 24               or   -8v ≤ 48

v ≤ 24/8              or    v ≤ 48/8

v ≤ 3                   or    v≥-6

therefore, -6 ≤ v ≤ 3.

Hence the inequality is -6 ≤ v ≤ 3.

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Answer:

f(4)=9

Step-by-step explanation:

The given function is

F(x)=3x-3

so,

f(4)=3*4-3

f(4)=12-3

f(4)=9

putting 4 in place of x we get answer of the question.

Answer:

3:2

Step-by-step explanation:

Divide 15 and 10 by 5.

Answer:

help this yuo what is yuor problem

Answer:

∠C = 180 - 3α

Step-by-step explanation:

The interior angles of a triangle always add up to 180°

So A + B + C = 180

C = 180 - (A + B)

= 180 - (α + 2α)

= 180 - 3α

Answer:

25 spells

Step-by-step explanation:

each colored box is 5 spells so count by five to see how many spells Ginny casts

The number of spells is 25, that the spells Ginny casts.

Here, we have,

from the given information we get,

we have to find that number spells that the spells Ginny casts.

we have,

the tape diagram gives that,

the ratio of luna and ginny is:=>  4 : 5

so, let , Ginny casts = 5x spells

luna casts = 4x spells

now, we have,

ATQ, 4x+5x = 45

=> 9x= 45

=> x = 45/9

=> x = 5

so, we get,

Ginny casts = 5*5 spells

                    = 25 spells

Hence, The number of spells is 25, that the spells Ginny casts.

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Answer: no she dosen't

Step-by-step explanation:

If you were to add up all three numbers

49.95+19.95+21.95=91.85

Which means she is $1.85 short to buy all of the items

Answer:

[tex]10^{-4}[/tex]

Step-by-step explanation:

0.0001

1/10,000

1/[tex]10^{4}[/tex]

[tex]10^{-4}[/tex]

The number of cashews in the can are 52.

Here, we are given that the ratio of walnuts to peanuts in a can of mixed nuts is 3 to 5.

⇒ walnuts : peanuts = 3 : 5

The number of walnuts in the packet are = 18

⇒ 18 : peanuts = 3 : 5

18/ peanuts = 3/5

peanuts = (5/3) × 18

peanuts = 30

Now, we know that the total number of nuts = 100

⇒ cashews + walnuts + peanuts = 100

cashews + 18 + 30 = 100

cashews + 48 = 100

cashews = 100 - 48

cashews = 52

Thus, the number of cashews in the can are 52.

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The value of P'(t) will be , P'(t) = -10t + 75 and value of P'(7) will be equal to 5 and rate of change of price will be $5 thousands per year in dollars.

It is given that median home price is represented by P(t) = -5t² + 75t - 30.

We have to find out the values of P'(t) and P'(7).

What is differentiation ?

Differentiation is a method in which the function's rate of change compared to the rate of change of the independent variable is calculated.

As per the question ;

The equation given is ;

P(t) = -5t² + 75t - 30

So ;

Differentiating the above equation with respect to t , we get ;

[tex]\frac{d}{dt}[/tex] (P(t)) = [tex]\frac{d}{dt}[/tex] ( -5t² + 75t - 30 )

[tex]\frac{d}{dt}[/tex] (P(t)) = P'(t) = -5 × 2 × t + 75

⇒ P'(t) = -10t + 75

And

The value of P'(7) will be ;

P'( t = 7) = -10 × 7 + 75

P'(7) = - 70 + 75

P'(7) = 5

Also ;

P(11) = 190

P(3) = 150

And

The rate of change of price will be ;

[tex]\frac{P(11) - P(3)}{11 - 3}[/tex]

= 190 - 150 / 8

= 40 / 8

= 5

Thus , the value of P'(t) will be , P'(t) = -10t + 75 and value of P'(7) will be equal to 5 and rate of change of price will be $5 thousands per year in dollars.

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Answer:

x=is the number searched

we have to solve this equation:

(2/5)x=14

x=14*5/2=35

35

Step-by-step explanation: