Which of these expressions is equivalent to log (20/3)

Answer:

[tex]\large\boxed{Q1.\ A=\dfrac{5}{6}x^2}\\\boxed{Q2.\ 250m^{12}n^{-3}=\dfrac{250m^{12}}{n^3}}\\\boxed{Q3.\ \dfrac{81x^{16}y^{36}}{16z^{28}}}\\\boxed{Q5.\ y^\frac{1}{2}=\sqrt{y}}[/tex]

Step-by-step explanation:

[tex]Q1.\\\\\text{The formula of an area of a triangle:}\\\\A_\triangle=\dfrac{bh}{2}\\\\b-\ \text{base}\\h-\text{height}\\\\\text{We have}\ b=\dfrac{5}{3}x,\ h=x.\ \text{Substitute:}\\\\A_\triangle=\dfrac{\left(\frac{5}{3}x\right)(x)}{2}=\dfrac{5x^2}{(3)(2)}=\dfrac{5}{6}x^2[/tex]

[tex]Q2.\\\\2(5m^4n^{-1})^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=2(5^3)(m^4)^3(n^{-1})^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(2)(125)(m^{4\cdot3})(n^{-1\cdot3})\\\\=250m^{12}n^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{250m^{12}}{n^3}[/tex]

[tex]Q3.\\\\\left(-\dfrac{3x^4y^9}{2z^7}\right)^4\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{3^4(x^4)^4(y^9)^4}{2^4(z^7)^4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{81x^{4\cdot4}y^{9\cdot4}}{16z^{7\cdot4}}=\dfrac{81x^{16}y^{36}}{16z^{28}}[/tex]

[tex]Q4.\\\\\left(x^0y^{\frac{1}{3}\right)^\frac{3}{2}\cdot x^0\qquad\text{use}\ a^0=1\ \text{for any value of}\ a\ \text{except}\ 0\\\\=\left(1\cdot y^\frac{1}{3}\right)^\frac{3}{2}\cdot1\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=y^{\left(\frac{1}{3}\right)\left(\frac{3}{2}\right)}\qquad\text{cancel 3}\\\\=y^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\=\sqrt{y}[/tex]

Answer:

It is 6x9

Step-by-step explanation:

Simple match 9x6 54 and 7x2 14 well I would rather have 54 units of cake that 14 Lol

Answer:

The rectangular cake pan has greater volume compared to the round cake pan.

Explanation:

If baking this cake, I would use a rectangular cake pan because it's volume is a total of 108 square inches. The round cake pan, on the other hand, has the total volume of 76.97 square inches. In conclusion, the rectangular cake pan has greater volume compared to the round cake pan.

Note:

Hope this helps! Have a wonderful rest of your day!

-kiniwih426

50% because half of 40 is 20

40-20 = 20. 20 divided by 40 = 0.5. Therefore, it was a 50% decrease

[tex]\( 44 - 11 \)[/tex] factors to [tex]\( 33 \)[/tex] when using the greatest common factor method.

To factor the expression [tex]\( 44 - 11 \)[/tex] using the greatest common factor (GCF), we first need to find the GCF of the two numbers.

The numbers 44 and 11 have a common factor of 11.

Now, we can factor out 11 from both terms:

[tex]\( 44 - 11 = 11 \times (4 - 1) \)[/tex]

This simplifies to:

[tex]\( 44 - 11 = 11 \times 3 \)[/tex]

Finally, we calculate the product: [tex]\( 11 \times 3 = 33 \)[/tex]

So, the factored expression for [tex]\( 44 - 11 \)[/tex] using the GCF is [tex]\( 33 \)[/tex].

To summarize:

[tex]\( 44 - 11 = 11 \times (4 - 1) \)[/tex]

[tex]\( 44 - 11 = 11 \times 3 \)[/tex]

[tex]\( 44 - 11 = 33 \)[/tex]

Therefore, [tex]\( 44 - 11 \)[/tex] factors to [tex]\( 33 \)[/tex] when using the greatest common factor method.

Complete Question:

Factor the expression using the GCF. 44 - 11 = _____

Answer:

[tex]V_{box}=3u^{3}[/tex]

Step-by-step explanation:

The complete question is

If the box holds 24 of these sugar cubes what is the total volume of the box.

The sugar cubes are 1/2 x 1/2 x 1/2

The total volume of the box would be the volume of each sugar cube multiplied by 24, because the box is formed by those 24 sugar cube.

The volume of one sugar cube

[tex]V_{cube}=\frac{1}{2}\times \frac{1}{2} \times \frac{1}{2}=\frac{1}{8} u^{3}[/tex]

We have 24 of them, so the volume of the whole box is

[tex]V_{box}=24\frac{1}{8}u^{3}\\ V_{box}=3u^{3}[/tex]

Therefore, the volume of the box is

[tex]V_{box}=3u^{3}[/tex]

To find the total volume of the box holding 24 sugar cubes, calculate the volume of a single sugar cube and multiply by 24.

The total volume of the box can be determined by finding the volume of a single sugar cube and multiplying it by the number of cubes in the box. Since the question does not provide specific dimensions of the sugar cube, let's assume the cube has sides of 1 cm. The volume of a cube is found by cubing the length of a side. So, the volume of a single sugar cube is 1 cm x 1 cm x 1 cm = 1 cubic cm. Since the box holds 24 sugar cubes, the total volume of the box is 24 cubic cm.

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Answer:

i think A or B but im not sure

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

-2 and -3 are connected

While positive 2 and -3 are also connected

So youre looking for which two x's share a y

Perimeter = 24m

Cost of half metre(1/2m) = €1.20

Cost of one metre = €2.40

Cost of fencing = 24 × 2.40 = €57.60

HOPE THIS WILL HELP YOU

Answer:

£57.6

Step-by-step explanation:

Given :The pen must have a perimeter of 24 m

Every half meter of fencing costs him £1.20

To Find : Work out the cost of the fence used to make the sheep pen.

Solution :

Cost of fencing 0.5 m = £1.20

Cost of fencing 1 m = [tex]\frac{1.20}{0.5}=2.4[/tex]

The pen must have a perimeter of 24 m

So, cost of fencing 24 m = [tex]2.4 \times 24 = 57.6[/tex]

Hence the cost of the fence used to make the sheep pen is £57.6

0.53 is 69.96 divided by132

Answer:

The answer is 0.53

Answer: $32.45

Step-by-step explanation:

Because....

55%  × 59 = $32.45

You could also write 55% as 0.55.

So it will look like this :

0.55 × 59 = 32.45.

It will still give you the same answer :)

* Hopefully tis helps:) Mark me the brainliest:)!!

Answer:

Expression for Base Area is 16y²  and height of the prism is y² + y + 3.

Step-by-step explanation:

Given: Expression for volume of a prism = [tex]16y^4+16y^3+48y^2\:cubic\:units[/tex]

To find: Expression for the Base area and Height of the Prism.

We know that

Volume of a prism = Base Area × height

So we need to factorize given expression of volume into two factors in which 1st is for Base area and 2nd is for Height of the prism.

[tex]Volume=16y^4+16y^3+48y^2[/tex]

Take 16y² common from each terms, we get

[tex]Volume=16y^2(y^2+y+3)[/tex]

It is factorized in two factors,

So,

Base Area = 16y²

Height = y² + y + 3

Therefore, Expression for Base Area is 16y²  and height of the prism is y² + y + 3.

Answer:

d is the answr

Step-by-step explanation:

hence x is1

hope it helps you!!!!!!

Answer:

x = 3

Step-by-step explanation:

Combine the 3 fractions on the left side.

[ note x ≠ - 1, 0, + 1 as this would make the fractions undefined ]

Multiply the numerators/ denominators by the lowest common multiple of

x - 1, x + 1, x , that is x(x - 1)(x + 1), that is

[tex]\frac{x(x+1)}{x(x-1)(x+1)}[/tex] + [tex]\frac{2x(x-1)}{x(x-1)(x+1)}[/tex] - [tex]\frac{3(x-1)(x+1)}{x(x-1)(x+1)}[/tex] = 0

distribute and simplify the numerators

[tex]\frac{x^2+x+2x^2-2x-3(x^2-1)}{x(x-1)(x+1)}[/tex] = 0

[tex]\frac{x^2+x+2x^2-2x-3x^2+3}{x(x-1)(x+1)}[/tex] = 0

[tex]\frac{3-x}{x(x-1)(x+1)}[/tex] = 0

The denominator cannot equal zero only the numerator, hence

3 - x = 0 ⇒ x = 3

Answer:

Length=8     Width=4

Step-by-step explanation:

Step 1- make an equation. The equation for perimeter is usually 2l+2w=P, but since the length is twice as long, we'll 2l x 2 =4l. So our equation is

4l + 2w = 24. note that 8+16 = 24

Step 2- Since 16 is 8 x 2, we know that the length is 16 and width is 8. We divide both those numbers because there is 2 lengths and 2 widths.

Answer:

5

Step-by-step explanation:

Answer:

The correct answer option is -7.

Step-by-step explanation:

We are asked to determine the minimum value of y on the graph of [tex]y = sin x - 6 [/tex].

[tex]y' = cos(x) = 0[/tex]

[tex]x = arccos(0) = \pm\frac{\pi }{2} +2k\pi[/tex] where 'k' is any integer.

So, [tex] y = sin ( \frac { \pi} { 2 } ) - 6 = 1 - 6 = -5 [/tex] (it is the absolute minimum value)

and [tex]y=sin(\frac{-\pi}{2}+2\pi )-6 = sin(\frac{3\pi}{2})-6 [/tex] = -7 (absolute minimum y value)

Answer:

The correct answer option is -7.

We are asked to determine the minimum value of y on the graph of . where 'k' is any integer.

So,  (it is the absolute minimum value)and  = -7 (absolute minimum y value)

Answer:

1/2

Step-by-step explanation:

You can add fractions which have the same denominator. 3 and 6 share multiples and so can form a common denominator. 3 can become 6 by multiplying by 2. Multiply both numerator and denominator of 5/3 by 2. It becomes 10/6 +-7/6 =3/6=1/2

Answer:

120 square centimeters

Step-by-step explanation:

The question says the formula already.

Area = bh

b = base length   b = 10

h = height length   h = 12

Area = 10 · 12

Area = 120 square centimeters

Answer: B. 120 square centimeters

Step-by-step explanation:

Given : The area of a parallelogram is found using the formula [tex]bh[/tex], where b represents the length of the base and h represents the length of the height.

Then , the area of a parallelogram that has a base of 10 centimeters and a height of 12 centimeters will be:-

[tex]\text{Area}=10\times12\\\\\Rightarrow\text{Area}=120\text{ square centimeters}[/tex]

Therefore , the area of the parallelogram = 120 square centimeters

Answer:

The value of x is [tex]4\ cm[/tex]

Step-by-step explanation:

step 1

Find the radius of the sphere

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]SA=784\pi\ cm^{2}[/tex]

substitute and solve for r

[tex]784\pi=4\pi r^{2}[/tex]

Simplify

[tex]r^{2}=196[/tex]

square root both sides

[tex]r=14\ cm[/tex]

step 2

Find the diameter

Remember that

The diameter is two times the radius

so

[tex]D=2(14)=28\ cm[/tex]

step 3

Find the value of x

we have

[tex]D=28\ cm[/tex]

[tex]D=4(x+3)\ cm[/tex]

equate the equations

[tex]4(x+3)=28[/tex]

[tex](x+3)=7[/tex]

[tex]x=7-3=4\ cm[/tex]

The correct answer is D.[tex](5x^4-9x^3+7x-1)[/tex].

To simplify the given polynomial expression, one would typically look for like terms that can be combined. However, in the expression provided, there are no like terms. Each term in the expression [tex](5x^4, -9x^3, 7x, and -1)[/tex]has a different power of x or is a constant with no x term at all.

Since there are no common terms to combine, the expression is already in its simplest form. Therefore, the simplified expression remains as it was originally given:

[tex]\[ 5x^4 - 9x^3 + 7x - 1 \][/tex]

Answer:

The equation is in standard form. You will have to convert it to slope intercept form, which is -0.125x + 3.75 = y

Step-by-step explanation:

s = x and a = y, therefore 0.5x + 4y = 15

0.5x + 4y = 15

0.5x + 4y = 15  first subtract  0.5x

4y = -0.5x + 15   then divide all by 4

y = -0.125x + 3.75  slope intercept form

Answer:

D.51,00

Step-by-step explanation:

To turn percentages to decimals you divide by 100. 80/100=.8. Now multiply this by how many people attended the game. .8 x 64,000= 51,200

Answer:

(a) [tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]    circle centered on the point (0,0) and with a constant radius [tex]r = 6[/tex].

(b) [tex](x-1) ^ 2 + y ^ 2 = 1[/tex]  circle centered on the point (1, 0) and with radio [tex]r=1[/tex]

Step-by-step explanation:

Remember that to convert from polar to rectangular coordinates you must use the relationship:

[tex]x = rcos(\theta)[/tex]

[tex]y = rsin(\theta)[/tex]

[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]

In this case we have the following equations in polar coordinates.

(a) [tex]r = 6[/tex].

Note that in this equation the radius is constant, it does not  depend on [tex]\theta[/tex].

As

[tex]r ^ 2 = x ^ 2 + y ^ 2[/tex]

Then we replace the value of the radius in the equation and we have to::

[tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]

Then [tex]r = 6[/tex] in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius [tex]r = 6[/tex].

(b) [tex]r = 2cos(\theta)[/tex]

The radius is not constant, the radius depends on [tex]\theta[/tex].

To convert this equation to rectangular coordinates we write

[tex]r = 2cos(\theta)[/tex]     Multiply both sides of the equality by r.

[tex]r ^ 2 = 2 *rcos(\theta)[/tex]     remember that [tex]x = rcos(\theta)[/tex], then:

[tex]r ^ 2 = 2x[/tex]        remember that [tex]x ^ 2 + y ^ 2 = r ^ 2[/tex], then:

[tex]x ^ 2 + y ^ 2 = 2x[/tex]         Simplify the expression.

[tex]x ^ 2 -2x + y ^ 2 = 0[/tex]     Complete the square.

[tex]x ^ 2 -2x + 1 + y ^ 2 = 1[/tex]

[tex](x-1) ^ 2 + y ^ 2 = 1[/tex]  It is a circle centered on the point (1, 0) and with radio [tex]r=1[/tex]

Simplify 6x/9 to 2x/3

2x/3(x + y)

Simplify

= 2x(x + y)/3

Answer:

Step-by-step explanation:

First step: calculate the difference:

[tex]\$246.95-\$199.95=\$47.00[/tex]

Second step: calculate the ratio of the difference and the original price:

[tex]\dfrac{\$47.00}{\$246.95}\approx0.1903219[/tex]

Third step: Convert to the percent:

[tex]0.190319\cdot100\%=19.0319\%\approx19\%[/tex]

The percent of change if the original price is $246.95 and the new price is $199.95 is 19.0%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The original price is $246.95 and the new price is $199.95.

Change in price = 246.95-199.95

= $47

The percentage of each value to the overall value when there are two or more values that sum up to 100 is the actual number.

The percent of change = (Original price-New price)/Original price ×100

= 47/246.95 ×100

= 4700/246.95

= 19.03

= 19.0%

Therefore, the percent of change with the given original price and the new price is 19.0%.

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Answer:

Step-by-step explanation:

I believe it should be 252 total pretzels so since theres nine friends and each one gets 28 so 28 x 9 equals 252. Hope it helps :)

Answer:

See below.

Step-by-step explanation:

a. A person with 20-100 vision can see  from a distance of 20 feet what a person with 20-20 vision can see from 100 feet.

b. If you have 20-40 vision you can see from 20 feet what a person with 20-20 vision can see from 40 feet.

Answer:

The explanations are provided below:

Step-by-step explanation:

a.  A person with 20-100 vision can see from a distance of 20 feet what a person with 20-20 vision can see from a distance of 100 feet. This simply means that the person can see about 100 feet what a normal sighted person can.

b.  A person with 20-40 vision can see from a distance of 20 feet what a person with 20-20 vision can see from a distance of 40 feet.

This is the same as explanation (a).The person can see from a distance of 40 feet what a normal person can see.

Answer:   [tex]\bold{c)\quad \dfrac{\pi}{2}}[/tex]

Step-by-step explanation:

sin is an odd function and cos is an even function.

To convert a sin graph to a cos graph, shift the sin graph [tex]\dfrac{\pi}{2}[/tex] units to the right --> C = [tex]\dfrac{\pi}{2}[/tex]

Answer:

[tex]\large\boxed{B.\ (x,\ y)\to(x-4,\ y-2)}[/tex]

Step-by-step explanation:

[tex](-5;\ 4)\xrightarrow{(+4,-2)}(-1;\ 2)\\\\-5+4=-1\to(x+4)\\4-2=2\to(y-2)[/tex]

Answer:

8 times? I'm not sure its actually 8 times with remainder of 4

Step-by-step explanation:

8 x 7 = 56

[tex]60 \div 7 = 8.57[/tex]

What exactly does the question consist of

6(b+5) would be the factorization

The algebraic representation of the given statement is:

[tex]n^2 + (n + 1)^2 = 85[/tex]

Expanding and simplifying:

[tex]n^2 + (n^2 + 2n + 1) = 85[/tex]

[tex]2n^2 + 2n + 1 = 85[/tex]

[tex]2n^2 + 2n + 1 - 85 = 0[/tex]

[tex]2n^2 + 2n - 84 = 0[/tex]

Dividing the equation by 2 to simplify:

[tex]n^2 + n - 42 = 0[/tex]

Now, we can solve this quadratic equation using the quadratic formula:

[tex]n = [-b ± √(b^2 - 4ac)] / (2a)[/tex]

Where a = 1, b = 1, and c = -42:

n = [-(1) ± √((1)^2 - 4(1)(-42))] / (2(1))

n = [-1 ± √(1 + 168)] / 2

n = [-1 ± √169] / 2

n = [-1 ± 13] / 2

This yields two possible values for n:

n₁ = (-1 + 13) / 2 = 12 / 2 = 6

n₂ = (-1 - 13) / 2 = -14 / 2 = -7

Since n represents the smaller of the two consecutive integers, we discard the negative value.

Therefore, the smaller integer (n) is 6.

To solve this problem algebraically, we first translate the given statement into an equation. We know that the sum of the squares of two consecutive integers can be represented as[tex]n^2 + (n + 1)^2, v[/tex]where n is the smaller integer. Setting this expression equal to 85, we get the equation [tex]n^2 + (n + 1)^2 = 85.[/tex]

We then expand and simplify this equation to get a quadratic equation in standard form: [tex]2n^2 + 2n - 84 = 0.[/tex]

Next, we use the quadratic formula to solve for n, which gives us two possible values. Since we are looking for the smaller of the two consecutive integers, we discard the negative solution.

Thus, the smaller integer is n = 6.

Complete question:

The sum of the squares of two consecutive integers is 85. Using n to represent the smaller of the two consecutive integers, express this statement in algebraic form