Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total of
$
1215
.
$
445
was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?

After expanding logarithm equation is : [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_{10} m^3}{n^4 \\ p^-2} \\[/tex]

apply formula log a^x = x log a

[tex]= > \frac{3 log_{10} (m)}{\frac{n^4}{p^2} }\\ \\= > \frac{3 log_{10} (m) p^2}{{n^4} }[/tex]

Thus, after expanding the logarithm equation is :  [tex]\frac{3log_{10}(m)p^2}{n^4}[/tex]

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The angle made by the vector is [tex]\theta[/tex] such that

[tex]\tan(\theta) = \dfrac{18.4\,\rm m}{-28.7\,\rm m} \approx -0.6411[/tex]

Before taking the inverse tangent of both sides, recall that [tex]\arctan[/tex] returns a number between -π/2 and π/2 radians, or -90° and +90°. The vector in the diagram clearly makes an angle between 90° and 180°, however, so we use the fact that tangent has a period of π rad / 180° to write

[tex]\theta \approx \arctan(-0.6411) + 180^\circ n[/tex]

where [tex]n\in\Bbb Z[/tex].

Now,

[tex]\arctan(-0.6411) \approx -0.5701 \,\mathrm{rad} \approx -32.6639^\circ[/tex]

Add 180° to this to recover the correct angle.

[tex]\theta = \arctan(-0.6411) + 180^\circ \approx \boxed{147.34^\circ}[/tex]

Answer:

i guess X=5 because 3+5=8?

Step-by-step explanation:

After dividing the paint in each container there are 3.65 liters of paint in each container.

what is division?

in the process of dividing a number up into equals parts and getting how many same numbers can be made. this process opposite of multiplication.

Quantity of red paint = 6.54 liters

Quantity of blue paint = 6.09 liters

by addition, quantity of purple paint = 12.63 liters

According to the question 1.68 liters paint left over then remaining paint by Subtraction = 10.95 liters 10.95 liters paints divided into 3 containers then the paint in each container is 3.65 liters.

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Answer: -4

Step-by-step explanation:

5 - (x - 2)²=

5 - (-1 - 2)²=

5 - (-3)²=

5 - (3)²=

5-9=-4

Answer:45

Step-by-step explanation:

Answer:

15.5

Step-by-step explanation:

We are trying to find out:

38.7% of what number is 6?

38.7% as a decimal is .387

.387x = 6  Divide both sides by .387

x = 15.503875969

Round 15.5

Answer: 202 ounces

Step-by-step explanation:

Because all you had to do is add all the ounces to get the amount he drank between 9 am and 2 pm!

Answer:

(6*2)+(10*1)+(2*3)+(1*8)

Step-by-step explanation:

6 notebooks for 2 dollars each: 6*2 dollars spent

10 folders for 1 dollar each: 10*1 dollars spent

2 packs of pencils for 3 dollars each: 2*3 dollars spent

1 lunch box for 8 dollars each: 1*8 dollars spent

Add all the dollars spent per item type for total dollars spent

An expression does not have an equal sign

Based on the sample space, the probability of P(32) is 1/90

The probability of an event is the chance or the likelihood that the event would occur.

Note that the chance or the likelihood is represented as a numerical value

The sample space is given as

Space = two-digit numbers

There are 90 two-digit numbers

So, the sample size is

Size = 90

There is only one two-digit number with the value 32

So, we have

n(32) = 1

The probability of selecting 32 is

P(32) = n(32)/Size

So, we have

P(32) = 1/90

Hence, the probability of P(32) is 1/90

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The correct interpretation for the given expression is the sum of x and y raised to the power of half n

The expression is given as

(x + y)^n/2

To interpret the expression, we start by evaluating the expression in the bracket and the exponent

So, we have

Hence, the correct interpretation for the given expression is the sum of x and y raised to the power of half n

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Answer:

Graph in the image above

Step-by-step explanation:

The annual academic scholarship amount is $15000.

This problem can be solved by unitary method and also by addition and subtraction.

Total annual tuition fee of Marshal is $20000.

His annual earning through the scholarship is $11000.

He also took an loan of about $20000 from student loan.

Total fee for the four years Bachelor's degree in Physics is = $20000×4

                                                                                                   = $80000

He cleared $20000 by student loan then remaining amount

 =(80000-200000)

 = $60000

Then the amount he earned through the scholarship program in total to clear the dues = $60000

Annual amount of scholarship is =$15000

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The correct answer is 2x - y +7 =0.

Various equations like equation of slope, y-intercept, slope- intercept must be known.

We have a line equation in the provided problem, and we must determine the slope and intercepts in order to create the graph. Assuming that m is the slope and c is the y-intercept, the slope intercept form is known as y=mx+c. We may determine the slope by utilizing the slope intercept formula.

The equation for the line in the problem can be written using the point-slope formula. The linear equation's point-slope form is: (y-y1) = m(x-x1)

( y - (3))=-2(x-2)

y - 3 = 2x + 4

2x - y +7 =0

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Answer:

x = -6.36

Step-by-step explanation:

(18 + x) × 28 = 326

Divide both sides by 28

18 + x = 11.64

Subtract 18 from both sides

x = -6.36

The pair of numbers that have the greatest common factor of 3 will be:

18 and 15

6 and 9

3 and 9

It should be noted that the factor of a number can be multiplied with another number that get the original number.

Therefore, the of pair of numbers that have the greatest common factor of 3 will be:

18 and 15

6 and 9

3 and 9

It should be noted that they have 3 as a common factor.

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Answer:

66

Step-by-step explanation:

63% of 109 is 68.67 the closest answer is 66

The equation that is equivalent to the slope formula is y₂ = m(x₂ - x₁) + y₁

An equation is an expression that shows the relationship between two or more numbers and variables.

The slope between two points A(x₁, y₁) and B(x₂, y₂) is:

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

m = (y₂ - y₁) / (x₂ - x₁)

m(x₂ - x₁) = y₂ - y₁

y₂ = m(x₂ - x₁) + y₁

The equation that is equivalent to the slope formula is y₂ = m(x₂ - x₁) + y₁

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If the inverse of f exists, it is represented by f⁻¹ and exists only if f is a bijective function.

If x = -3 then (f ⁰ g⁻¹)(x) is 23.

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.

An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.

Let the two functions be f(x) = 3x² - 4 and g(x) = x - 2

(g⁻¹)(x) = 1 - 2

(g⁻¹)(x) = -1

substitute (g⁻¹)(x) value in (f ⁰ g⁻¹)(x)

(f ⁰ g⁻¹)(x) = (f ⁰ ) (-1)

then f(x) equation is 3 x² - 4 substitute -1 in x

f(-1) = 3(-1)² - 4

f(-1) = -1

Now when x = -3 the (f ⁰ g⁻¹)(x) value is

f(-3) = 3(-3)² - 4

f(-3) = 23

Therefore, the value of (f ⁰ g⁻¹)(x) for x = -3 is 23.

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The direct variation equation can be used to find other combinations of x and y is y² = 4x³/27

Direct variation is variation in which one quantity increases as another quantity increases or decreases as anothe rquantity decreases.

Since we have that the square of y varies directly as the cube of x.

Writing this as a direct variation mathematically, we have

y² ∝ x³

So, the direct variation equation is

⇒ y² = kx³ where k = constant of proportionality

Now, given that when x = 4, y = 2.

Substituting the values of x and y into the equation, we have

y² = kx³

2² = k(3)³

4 = k(27)

k = 4/27

Substituting the value of k into the expression, we have

y² = kx³

y² = 4x³/27

So, the direct variation equation can be used to find other combinations of x and y is y² = 4x³/27

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Answer: d3 = - 17/2

correction:  This is an explicit formula

All we have to do is plug n = 3 in the formula to find the 3rd term.

2. d(3)=-5(1/2)3-1

= -5/4

Step-by-step explanation:

Answer:

base of 3 --> 3^4 (three to the fourth); base of 9 --> 9^2 (nine squared)

Step-by-step explanation:

3 x 3 = 9 x 3 = 27 x 3 = 81 = 3^4

You multiply 3 by itself 4 times.

9 x 9 = 81 = 9^2

You multiply 9 by itself 2 times.

The missing angles of the Triangle are; ∠1 = 62°; ∠2 = 45° and ∠3 = 22°.

We know that the sum of angles on a straight line is 180 degrees. Thus, we can say that;

∠1 + 118° = 180°

∠1  = 180 - 118

∠1 = 62°

We also know that sum of angles in a triangle is equal to 180°. Thus;

∠1 + ∠2  + 73 = 180

Plugging in the relevant value gives;

62 + ∠2  + 73 = 180

∠2 = 180 - 135

∠2 = 45°

∠2 + ∠3 = 180 - (∠1 + 49)

∠2 + ∠3 = 180 - (62 + 49)

45° + ∠3 = 69

∠3 = 22°

Thus, we conclude that the missing angles of the Triangle are; ∠1 = 62°; ∠2 = 45° and ∠3 = 22°.

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Answer:

7/12

Step-by-step explanation:

i used lowest common denomator

Answer:

answer is 7/12

Step-by-step explanation:

hope this helps

The amount of markup on a single rose is $2.96

Profit = Selling Price – Cost Price.

We have,

We can consider the cost price as:

Bought amount = $12.96

We can consider the selling price as:

Selling amount = $48.48

Now,

Markup price can be considered as the profit:

Profit = Sellin price - Cost price

Profit = $48.48 - $12.96

Profit = $35.52

Since in a dozen we have 12 roses the markup price for each rose is:

= $35.52 / 12

= $2.96

Thus the amount of markup on a single rose is $2.96

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Answer:

x = 30 + 5y / 2

Step-by-step explanation:

The slope of the line parallel to the given line is 2/5.

Slope of a line is the measure of the steepness and the direction of the line.

Given that, an equation of a line, 2x−5y = 30

Converting the equation in slope intercept form,

2x−5y = 30

5y = 2x - 30

y = 2/5x - 30

We know that the slope of two parallel lines are equal.

Hence, The slope of the line parallel to the given line is 2/5.

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[tex]y =\begin{cases}x + 1 \: \: \: \: \: \: \: \: x >2\\x + 2 \: \: \: \: \: \: \: \: x \leqslant 2\end{cases}[/tex]

According to the graph,

Let y = [tex]{m_1}[/tex]x + [tex]b_1[/tex] [[tex]b_1[/tex] = 2]

when x = -2 , y = 0

-2[tex]m_1[/tex] + 2 = 0 [[tex]{m_1}[/tex] = 1]

→ So when x ≤ 2 , y = x + 2

Let y = [tex]m_2[/tex]x + [tex]b_2[/tex]

[tex]m_2 = \frac{4 - 3}{3 - 2} = 1 \: \: \: \: \: \: \: \: \: \: [m = \frac{y_2 - y_1}{x_2 - x_1} ][/tex]

when x = 2 , y = 3

3 = 2 × 1 + [tex]b_2[/tex] , [tex]b_2[/tex] = 1

→ So when x > 2 , y = x + 1

[tex]y =\begin{cases}x + 1 \: \: \: \: \: \: \: \: x >2\\x + 2 \: \: \: \: \: \: \: \: x \leqslant 2\end{cases}[/tex]

Answer:1/8a^9b^12

or in other words, D. Last one

Step-by-step explanation:

The required length of a rectangle in simplest form is (a + 10) / 3(a + 8).

What is a rectangle?

A rectangle is a geometrically closed figure with four sides in which the opposite pair of sides are equal to each other. The angle at all the vertices of the rectangle is 90 degrees.

The calculation for the length of a rectangle in simplest form.

Given the value of the width of a rectangle = (a + 10) / 3 a + 24

The length of a rectangle in the simplest form is given by: (a + 10) / 3(a + 8)

Hence, the required length of a rectangle is (a + 10) / 3(a + 8).

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Step-by-step explanation:

what did your teacher do in class ? nothing ?

it is really not that complicated :

the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

it tells us how many units y changes when x changes by a certain number of units.

e.g. a slope of 2 = 2/1 means that when we increase x by 1, y increases by 2.

a positive slope means that the line goes up (seen while going from left to right).

a negative slope means that the line goes down.

therefore, a slope of 0 means a flat, horizontal line.

while for a vertical line the slope is the result of a division by 0 and is therefore undefined (some like to symbolize this by infinity).

parallel simply means to have the same slope. parallel lines imitate each other's behavior and attributes perfectly except for the absolute physical location.

perpendicular (at a 90° angle) slopes now simply turn x and y in the ratio upside-down and flip the overall sign of the slope.

e.g. the perpendicular slope of 2 = 2/1 is -1/2.

oh, and the slope of a function or curve that is not a line ?

then we go point by point, as the function does not have one slope for everything. and the slope of the function at a particular point is the slope of the tangent line at that point.

all clear now ?

After expanding logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]log_3[xy^\frac{1}{3} + z^2]^3[/tex]

apply formulas log a^x = x log a

=> [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]

Thus, after expanding the logarithm equation is : [tex]3.log_3(xy^\frac{1}{3} + z^2)[/tex]

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