Which equation is the inverse of y = 100-x²?

Oy=± √100-x

O y=10± √√x

Oy=100+√x

Oy=+√x-100

Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives

The perimeter of a rectangle, P is given by the formula

P = 2(L + W) ≤ 57 units of wire

width, W = 2 units

length, L = 1 + W

= 1 + 2

= 3

The perimeter of the rectangle is given by

P = 2(L + W)

plugging the values of L and W

P = 2 (3 + 1)

P = 2 (4 )

P = 8 units

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Means if a number is bigger than other number.

The sum of the fraction 74/10 + 42/5 is 15 4/5.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the fraction will be illustrated as:

= 74/10 + 42/5

Change to mixed numbers

= 7 4/10 + 8 2/5

= 7 4/10 + 8 4/10

= 15 8/10

= 15 4/5

The value is 15 4/5.

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When we differentiate the given function with respect to x we get

(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²

what is Differentiation?

Differentiate is used for calculating rates of change.

How to Differentiate function?

Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.

Here, we have

y = 2x⁵ + 2x⁴ / 5x² -3

when we differentiate a given function with respect to x, we get

dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²

dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²

Hence, after differentiating the given function with respect to x, we get

(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²

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Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.

She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.

The amount she will earn in her hourly wages and commission is as follows:

amount earn in commission = 15% of 2046

amount earn in commission = 15 / 100 × 2046

amount earn in commission = 30690 / 100

amount earn in commission = 306.9 dollars

Therefore,

amount earn in hourly wages = 2046 - 306.9

amount earn in hourly wages = 1739.1 dollars.

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Answer:

13

Step-by-step explanation:

56/7 = 8

13 - 5 = 8

15/7 = 13 - 5

The missing number in the expression is 13.

We have,

To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.

Unknown value = x

Starting with the equation 56 / 7 = x - 5, simplify the left side:

56 / 7 = x - 5

8 = x - 5

x = 8 + 5

x = 13

Thus,

The missing number in the expression is 13.

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Answer:

Step-by-step explanation:

A=60

B=75

C=45

D=60

E=75

F=45

G=90

The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given that the graph of the function has increased and decreasing orders on the coordinate plane.

The interval in which the given graph of the function is increasing is,

(-∞,-6)

(-4,-1)

(3,6)

(8,∞)

Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

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The amount in the account is $3499. 2

The formula for determining compound interest is given as;

A = P ( 1 + r/ n) ^nt

Given that;

Substitute the values into the formula, we have;

A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)

Find the exponential value

A = $3000 ( 1 + 0. 04 / 0. 5) ^2

A =  $3000( 1+ 0. 08)^2

Expand the bracket, we get;

A = $3000 (1. 08)^2

A = $3000(1. 17)

multiply through

A = $3499. 2

Hence, the value is $3499. 2

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The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.

What is a Percentage Increase?

The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.

Steps to Calculate Percentage Increase?

Here, in the question, it is given that,

The original amount (X) or the fuel bill in 2021 is £76.

The new amount (Y) or the fuel bill in 2022 is £89.

So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,

[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]

Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,

[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]

Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.

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The number of square cm of cheese layers that Anna needs to put on the pizza is  30.25π square cm.

What is the area of a circle?

In geometry, the area of a circle is the space occupied by the circle.

To find the area of a circle having radius "r", we can use the formula.

               Area of a circle = π×r².

In the given question, the diameter of the pizza is 11 cm.

so the radius will be = 11/2 = 5.5 cm.

                Area of the pizza = π×r²

                                              = π×(5.5)²

                                              = 30.25π square cm.

Hence, the number of square cm of cheese layers that need to be put on the pizza is  30.25π square cm.

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Using the points (5, 1273) and (10, 2546), equation for the line is 5y =  1273x.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Given,

Coordinates (5, 1273) and (10,2546)

For slope, m

m = y₂ - y₁/ x₂ - x₁

m = 2546 - 1273/10 -5

m = 1273/5

Equation in y = mx form,

y = 1273/5 x

Cross multiplying,

5y =  1273x

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The transformations of g(x) that would result in odd functions are (a)-g(x)   , (b)g(2x)  and (d)g(–x) ,

In the question ,

it is given that,

the function is g(x) = 3x³ + x

We know that the function f(x) is called an odd function if f(-x) = -f(x) .

Option(a)

the transformation is given as -g(x)

-g(x)  = -(3x³ + x) = -3x³ - x

g(-x) = 3(-x)³ + (-x) = -3x³ - x

so , this is odd function .

Option (b)

the transformation is given as g(2x)

g(-2x) = 3(-2x)³ + (-2x) = -24x³ - 2x

-g(2x) = -{3(2x)³ + (2x)} = -( 24x³ + 2x ) = -24x³ - 2x

so , this is  odd function .

Option (c)

the transformation is given as g(x)-3

(g(-x) - 3) =  3(-x)³ + (-x) - 3 = -3x³-x-3

-(g(x) - 3) = -{(3x³ + x) -3} = -3x³ - x +3

So, so , this is not an odd function

Option (d)

the transformation is given as g(-x)

g(-(-x)) = g(x) = 3x³+x

-g(-x) = -(3(-x)³ + (-x)) = -(-3x³ - x) = 3x³+x

so , this is odd function .

Therefore, the odd transformations are -g(x)   , g(2x)  and g(–x) ,

The given question is incomplete , the complete question is

The function g(x)=3x³+x is an odd function. Which transformation of g(x) would result in odd functions? Check all that apply

(a) -g(x)

(b) g(2x)

(c) g(x) − 3

(d) g(–x)

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The linear equation in the slope-intercept is:

y = (-1/5)*x  - 26/5

And it can be written as:

y = (-1/5)*(x + 1) - 5

We can write the equation for line L as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if we want our line to be perpendicular to y= 5x, then we must have:

a*5 = -1

a = -1/5

So our line is something like:

y = (-1/5)*x + b

And the line passes through (-1, -5), replacing these values:

-5 = (-1/5)*-1 + b

-5 = 1/5 + b

-5 - 1/5 = b

-26/5 = b

The linear equation is:

y = (-1/5)*x  - 26/5

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Answer:156

Step-by-step explanation:

The mean is 38.5. It tell us that the average distance a heavy ball was thrown is 38.5 feet.

A stem-and-leaf plot is table that displays a data set in ascending order.  used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. In this stem-and-leaf plot, the stem is the tens digit and the leaf is the units digit. For example, in the number 32, 3 is the stem 2 is the leaf.

The mean is a measure of the center of a dataset that is used to determine the average of a set of numbers

Mean = sum of numbers / total numbers in the data set

(20 + 21 + 24 + 31 + 32 + 36 + 41 + 43 + 47 + 51 + 51 + 65) / 12

462 / 12 = 38.5

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Answer:

9/7 or 1.285714

Step-by-step explanation:

Answer:9/7

Step-by-step explanation:

Variation refers to differences in characteristics between individuals of the same species or between different genera or species. The formula is y = 0.25x.

Therefore,

y=0.25 x

the initial statement is y ∝ x

to convert to an equation multiply by k  the constant of

⇒ y=k x

to find k use the given condition

y=0.5 when x=2

[tex]$y=k x \Rightarrow k=\frac{y}{x}=\frac{0.5}{2}=0.25$$[/tex]

the equation is y = 0.25x

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The variation equation  is [tex]y=\frac{1}{5} x[/tex]

Calculation

Given, y =2 and x=10

we know the direct relation in y∝ x

so, y = kx, where k is the proportionality constant

2= k*10

k = [tex]\frac{2}{10} =\frac{1}{5}[/tex]

Therefore, the direct variation equation for this situation is [tex]y=\frac{1}{5} x[/tex]

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If a standardized exam's scores are normally distributed. The z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.

mu = population mean = 1487

sigma = population standard deviation = 314

x =1870

z = (x - mu)/σ

z = (1870-1487)/314

z = 1.22 (approximately)

x =1250

z = (x - mu)/σ

z = (1250-1487)/314

z = -0.75

x =2170

z = (x - mu)/σ

z = (2170-1487)/314

z = 2.18 (approximately)

x =1390

z = (x - mu)/σ

z = (1390-1487)/314

z = -0.31 (approximately)

Therefore the z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.

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Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.

The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).

Given,

Factor sipping distributive property,

For the numbers 28 and 49

GCF:

28 + 49

7(4) + 7(7)

7(4+7)

7(11)

77

Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.

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The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x

The definitions of the functions are given as

f(x) = √4x and g(x) = √16x

Evaluate the square roots in the above equations

This gives

f(x) = 2√x and g(x) = 4√x

To find the composition (f - g)(x), we make use of

(f - g)(x) = f(x) - g(x)

Substitute the known values in the above equation So, we have the following equation

(f - g)(x) = 2√x - 4√x

Evaluate the like terms

This gives

(f - g)(x) = -2√x

Hence, the value of the composition is (c) (f - g)(x) = -2√x

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Answer:

B (x = 3 + √5)

Explanation:

x² + 9 = 5

Take square root of both sides

x + 3 = ± √5

Add 3 to both sides

x = 3 + √5 or x = 3 - √5

Answer:

Step-by-step explanation:

$2.40             12.45 mi
___        *        ___          =   ?  ;
1  mi.               1              

The units of miles— "mi" —cancel out to "1" ;

   since:  " mi/ mi = 1 "

  and we have:
    $2.40  * 12.45  =  ?  ;

                             =  $29. 88 ; {using a calculator};

       ⇒ which corresponds to:  Answer choice:  [D]:  $29.88 .
_____
Hope this is helpful!

  Best wishes!
_____

Answer:

0=0

Step-by-step explanation:

Answer: Infinite Solutions

Step-by-step explanation:

Hello! Let's solve this equation.

[tex]\sf{6x-5=6x-5}[/tex]

↓

[tex]\sf{6x=6x-5+5}[/tex]

↓

[tex]\sf{6x=6x}[/tex]

[tex]\sf{6x-6x}[/tex]

↓

[tex]\sf{0}[/tex]

[tex]\textbf{So as you see, all the terms \textit{cancel out.}}\\\textbf{The \textsf{given equation} has \textit{\underline{infinite solutions.}}}\\\textbf{The equation is true for any x-value.}[/tex]

[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]

Answer:

(−∞,1/3)∪(1/3,∞),{yly≠1/3}

Step-by-step explanation:

Step-by-step explanation:

"down by one" means that the y values (the function result values) are all decreased by 1.

so, k = -1

The product doubles when one of the factors in a multiplication problem is doubled

A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.

In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.

For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:

= 4 × 3 = 12

Therefore, the product doubles too.

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The missing terms in the two column proof are;

Reason 1; Perpendicular bisector

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Reason 4; Reflexive Property of Congruence

Reason 5; Definition of Isosceles Triangle

Reason 6; AAS Congruency Postulate

From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC

Now, we have the two column proof as follows;

Statement 1; AO ⊥ BC

Reason 1; Perpendicular bisector

Statement 2; ∠AOB and ∠AOC are right angles

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Statement 4; AO ≅ AO

Reason 4; Reflexive Property of Congruence

Statement 5; AB ≅ AC

Reason 5; Definition of Isosceles Triangle

Statement 6; ΔAOB ≅ ΔAOC

Reason 6; AAS Congruency Postulate

The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.

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