A rectangle has a length this is three times its width. If the area of the rectangle is 27 square feet, what are the dimensions of the rectangle

ANSWER

1.

[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]

2.

[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]

3.

[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) [/tex]

EXPLANATION

1. The given logarithmic expression is

[tex] log_{4}(3x) [/tex]

Use the product rule:

[tex] log_{a}(mn) = log_{a}(m) + log_{a}(n) [/tex]

We apply this rule to obtain:

[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]

2. The given logarithmic expression is

[tex] log_{3}( \frac{27}{x} ) [/tex]

We apply the quotient rule:

[tex]log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n) [/tex]

This implies that;

[tex]log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x) [/tex]

We simplify to get;

[tex]log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x) [/tex]

Apply the power rule:

[tex] log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]

[tex]log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x) [/tex]

simplify;

[tex]log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x) [/tex]

[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]

3. The given logarithmic expression is;

[tex] log_{4}( {x}^{5} ) [/tex]

Apply the power rule of logarithms.

[tex]log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]

This implies that,

[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) .[/tex]

probably the formula is 4×(x-1.6)

Answer:

4) 4(x−32)

Step-by-step explanation:

Answer:

[tex]C(h)=\$30+xh[/tex]

Step-by-step explanation:

Let

C-----> the cost of having a plumber spend h hours at your house

h----> the number of hours

x----> the cost per hour of labor

we know that

The linear equation that represent the cost C is equal to

[tex]C(h)=\$30+xh[/tex]

In this linear equation in the slope-intercept form (y=mx+b)

the slope is equal to [tex]m=x\frac{\$}{hour}[/tex]

the y-intercept b is equal to [tex]b=\$30[/tex] ---> charge for coming to the house

Answer:

C = 30 + x * h

Step-by-step explanation:

The total cost for the plumber is his initial fee plus the number of hours times the cost per hour

C = 30 + x * h

Answer:

The height of the second box is [tex]6\ in[/tex]

Step-by-step explanation:

we know that

If the two boxes are congruent

then

The volume of the first box is equal to the volume of the second box

The length of the first box is equal to the length of the second box

The width of the first box is equal to the width of the second box

The height of the first box is equal to the height of the second box

so

Find the height of the first box

Remember that

The volume of the box is equal to

[tex]V=LWH[/tex]

substitute the values and solve for H

[tex]72=(3)(4)H[/tex]

[tex]H=72/(12)=6\ in[/tex]

Answer:

865.08

Step-by-step explanation:

✯Hello✯

↪  The answer is 865.08

↪  Times both of them by 10 so they are whole numbers

↪  Then it will be 534 x 162 = 86508

↪  Then divide by 100

❤Gianna❤

To multiply 53.4 and 16.2, calculate 534 * 162, then adjust the result by placing the decimal point two places from the right to get 865.08. This gives the final product of 865.08.

To find the product of 53.4 and 16.2, follow these steps:

        Here, 53.4 has one decimal place and 16.2 also has one decimal place, making a total of two decimal places.

Therefore, 53.4 * 16.2 equals 865.08.

Answer:

2/4

Step-by-step explanation:

1/4 = 0.25

3/4 = 0.75

0.75 - 25 = 0.50

0.50 is your answer

Answer:

5/7

Step-by-step explanation:Let

x------->the probability of its complement

we know that

The Complement Rule states that the sum of the probabilities of an event and its complement must equal

so

in this problem

2/7 + x = 1

solve for x

Adds 1- 2/7  both sides

x= 1 - 2/7

x= 5/7

Answer:

5/7

Step-by-step explanation:

Answer:

9 servings of meat.

Step-by-step explanation:

The first ratio you are given is 8:36. You are trying to figure out what 2:__ is.

8/36 x  2/X

Multiply 2 x 36 and get 72. Now divide 72 by 8 to get 9.

Answer:

The answer really is 9 servings of meat.

Step-by-step explanation:

I had the same question and I got it right...but mine said: Write a proportion that could be used to solve this problem. Do not solve it.

Answer:

  C)  (x - 4)

Step-by-step explanation:

A root makes a factor be zero. The root of 4 will make the factor x-4 be equal to zero.

Answer:

(x-4)

Step-by-step explanation:

the roots of a polynomial are −3, 4, 5, and −7.

When 'a' is a root of the polynomial then (x-a) is a factor

Lets write the factors for all the root given

[tex](x-(-3))(x-4)(x-5)(x-7)[/tex]

[tex](x+3)(x-4)(x-5)(x-7)[/tex]

Check with the options, which factor is in our polynomial

(x-4) is one of the factor

Answer:

x=3

Step-by-step explanation:

[tex]GT=\frac{HF.TS}{SF}=\frac{4.8\times 21}{12}=8.4 [/tex]

Answer:

105

Step-by-step explanation:

to get this you must first divide 17.5 by 2.5 to see how many times to multiply 15 by 2.5

sorry if it does not make scence

Answer: 2.94 ft²

Step-by-step explanation:

Observe the figure attached:

The line LM divide the triangle into two right triangles.

Find the heigh "h" as following:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(40\°)=\frac{h}{2.7}\\\\h=(2.7)(sin(40\°))\\h=1.73ft[/tex]

Apply the formula for calculte the area of a triangle:

[tex]A=\frac{Bh}{2}[/tex]

Where B (B=3.4 ft) is the base and h is the height (h=1.73ft)

Then:

[tex]A=\frac{(3.4ft)(1.73ft)}{2}=2.94ft^2[/tex]

Answer:

120 feet

Step-by-step explanation:

1. find the length of the pool (2*20 = 40 feet)

2. add the sides 2L + 2W

    2L = 2*40 = 80

    2W = 2*20 = 40

    80+40=120

Answer:

[tex]\large\boxed{\tan x(\cot x-\cos x)=1-\sin x}[/tex]

Step-by-step explanation:

[tex]Use\\\\(\tan x)(\cot x)=1\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\text{distributive property:}\ a(b-c)=ab-ac\\======================\\\\\tan x(\cot x-\cos x)=(\tan x)(\cot x)-(\tan x)(\cos x)\\\\=1-\left(\dfrac{\sin x}{\cos x}\right)(\cos x)=1-\sin x[/tex]

Answer:

[tex]4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )[/tex]

Step-by-step explanation:

Let's start by breaking down each of the radicals:

[tex]\sqrt[3]{16x^3y}[/tex]

Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of [tex]x^3[/tex], and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:

[tex]\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}[/tex]

We can apply this same technique of "extracting cubes" to the second term:

[tex]\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}[/tex]

Replacing those two expressions in the parentheses leaves us with this monster:

[tex]2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})[/tex]

What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:

[tex]4, \sqrt[3]{2} , x[/tex]

We can factor those out to give us a final, simplified expression:

[tex]4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )[/tex]

Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.

Answer:

$77,380

Step-by-step explanation:

If she gets a 6% raise next year she will make 106% of what she makes this year.  

106% is 1.06 as a decimal.  Multiply her salary by 1.06 to find out how much she will make next year...

$73,000(1.06) = $77,380

Answer:

77,380

Step-by-step explanation:

divide 73000 by 100% and you get 730, then you multiply it by 6 since you need a 6% raise. once you get this value, you simply add it to the 73000 and you get the answer

I think you're answer is five hundred seventy six

Answer:

1/4.

Step-by-step explanation:

I am assuming that there are 3 even and 3 odd tiles in each bag.

Probability( drawing an even tile form one bag) = 3/6 = 1/2.

The probability  of drawing  an even from the first and an even from the second = 1/2 * 1/2 = 1/4 (answer).

The individual probabilities  are multiplied because the 2 events are independent.

Answer:

9/36

Step-by-step explanation:

domain and range are both infinite

Answer:

[tex]6k[/tex]

Step-by-step explanation:

Let

k-----> the variable

we know that

The phrase " The product of a number and six" is equal to multiply the variable k ( the number) by 6

so

[tex]6k[/tex]

Answer:

The measure of the angle A is [tex]53.13\°[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC

The tangent of angle A is equal to the opposite side to the angle A divided by the adjacent side to angle A

so

[tex]tan(A)=\frac{BC}{AB}[/tex]

substitute

[tex]tan(A)=\frac{4}{3}[/tex]

[tex]<A=arctan(\frac{4}{3})=53.13\°[/tex]

Answer:

dx/dy =  (x^4 -  2x^5y -  6xy^2) /  (5x^4y^2 - 4x^3y +  2y^3).

Step-by-step explanation:

x^5y^2 − x^4y + 2xy^3 = 0

Applying the Product and Chain Rules:

y^2*5x^4*dx/dy + 2y*x^5 - (y*4x^3*dx/dy + x^4) + (y^3* 2*dx/dy + 3y^2*2x) =0

Separating the terms with derivatives:

y^2*5x^4*dx/dy - y*4x^3*dx/dy + y^3* 2*dx/dy =  x^4 -  2y*x^5 -  3y^2*2x

dx/dy =  (x^4 -  2x^5y -  6xy^2) /  (5x^4y^2 - 4x^3y +  2y^3)

Answer:

[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]

Step-by-step explanation:

The given equation is

[tex]x^5y^2-x^4y+2xy^3=0[/tex]

Differentiate with respect to y.

[tex]\frac{d}{dy}(x^5y^2)-\frac{d}{dy}(x^4y)+\frac{d}{dy}(2xy^3)=0[/tex]

Using product rule we get

[tex]x^5\frac{d}{dy}(y^2)+y^2\frac{d}{dy}(x^5)-x^4\frac{d}{dy}(y)-y\frac{d}{dy}(x^4)+2x\frac{d}{dy}(y^3)+2y^3\frac{d}{dy}(x)=0[/tex]           [tex](fg)'=fg'+gf'[/tex]

[tex]x^5(2y)+y^2(5x^4\frac{dx}{dy})-x^4(1)-y(4x^3\frac{dx}{dy})+2x(3y^2)+2y^3\frac{dx}{dy}=0[/tex]

[tex]2x^5y+5x^4y^2\frac{dx}{dy}-x^4-4x^3y\frac{dx}{dy}+6xy^2+2y^3\frac{dx}{dy}=0[/tex]

Isolate [tex]\frac{dx}{dy}[/tex] terms on left side.

[tex]5x^4y^2\frac{dx}{dy}-4x^3y\frac{dx}{dy}+2y^3\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]

[tex](5x^4y^2-4x^3y+2y^3)\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]

Isolate [tex]\frac{dx}{dy}[/tex] term.

[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]

Therefore the value of [tex]\frac{dx}{dy}[/tex] is [tex]\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex].

Answer:

b.  secx

Step-by-step explanation:

We have given a trigonometric expression.

csc(x)/cot(x)

We have to simplify it.

Since we know that

csc(x) is reciprocal to sin(x).

cscx = 1/sinx

cot(x) is ratio of cos(x) and sin(x).

cotx = cosx/sinx

Then, given expression becomes,

[tex]\frac{1/sinx}{cosx/sinx}[/tex]

[tex]\frac{1}{sinx}[/tex] × [tex]\frac{sinx}{cosx}[/tex]

[tex]\frac{1}{cosx}[/tex]

csc(x)/cot(x)   = secx

Answer:

See attached picture.

Step-by-step explanation:

Graph the function as (x,y) points.

(-3,5)

(4,6)

(6,-9)

(9,-10)

These are graphed in black on the picture.

To graph the inverse, switch the points from (x,y) to (y,x).

(5,-3)

(6,4)

(-9,6)

(-10,9)

These are graphed in red on the picture.

Answer:

The ratio of their surface areas is [tex]\frac{4}{49}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem the scale factor is equal to the ratio [tex]\frac{2}{7}[/tex]

and

Remember that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore

In this problem the ratio of their surface areas is [tex](\frac{2}{7})^{2}=\frac{4}{49}[/tex]

Final answer:

The ratio of the surface areas of two similar solids with a linear dimension ratio of 2:7 is 4:49.

Explanation:

The question deals with the concept of geometric similarity and the ratio of surface areas for similar solids. When two solids are similar, the ratio of their surface areas is the square of the ratio of their corresponding linear dimensions. Therefore, if the ratio between the lengths of their edges is 2:7, then the ratio of their surface areas would be the square of this ratio, which is (22):(72) or 4:49.

Answer:

-7

Step-by-step explanation:

7 and -7 squared both equal 49

Answer:

I'm pretty sure it'd be set {3,6}

Answer:

A

Step-by-step explanation:

The equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a polygon ABCDE is reflected to produce polygon A'B'C'D'E' in the picture.

As we know, the reflection is the geometric transformation which create a mirror image of the object, but size or shape does not change.

The y-axis is the axis of reflection in this case.

The equation for the y-axis is x = 0

Thus, the equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ2

Answer: 9 feet.

Step-by-step explanation: The formula to convert inches to feet is to divide the amount in inches by 12. 108/12 = 9.