one fifth of a number plus five times that number is equal to seven times the number less 18​

Answer:

The third term is [tex]24x^2y^2[/tex]

Step-by-step explanation:

The formula used to find the third term of the expansion (2x+y)^4 is called Binomial Theorem

The Binomial Theorem is:

[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]

In the given question x = 2x

a = y

n = 4

We have to find the third term, so value of k will be 2 as k starts from 0

Putting the values in the Binomial Theorem

[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex]

[tex]{n \choose k}==\frac{n!}{k!(n-k)!}[/tex]

Putting the values:

[tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]

So, the third term is [tex]24x^2y^2[/tex]

Answer:

Heya mate here's the answer

let the 4th angle be x

so 75°+ 75°+75° +x= 360°

=> x= 360 - 225

=> x = 135°  

therefore the 4th angle= 135°

hope this helps

Step-by-step explanation:

Answer:

The answer in the procedure

Step-by-step explanation:

Remember that

[tex]1\ cm=10\ mm[/tex]

Elevated to the cube both sides

[tex](1\ cm)^{3}=(10\ mm)^{3}[/tex]

[tex](1)^{3}\ cm^{3}=(10)^{3}\ mm^{3}[/tex]

[tex]1\ cm^{3}=1,000\ mm^{3}[/tex]

[tex]b=-1[/tex]

.............................

Answer:

X=2, X= -5/3

Step-by-step explanation:

let's solve your equation step-by-step

3x^2-x-10=0

step 1: factor left side of equation.

(3x+5)(x-2)=0

step 2: set factors equal to 0.

3x+5=0  or x-2=0

x= -5/3 or x=2

Answer:   [tex]\bold{a.\quad -\dfrac{2\sqrt{6}}{5}}[/tex]

Step-by-step explanation:

[tex]sin\theta=\dfrac{y}{h}\implies y=-1, h=5\\\\\\\text{Use Pythagorean Theorem to find x:}\\x^2 + y^2 = h^2\\x^2 + (-1)^2=5^2\\x^2+1=25\\x^2=24\\x=\sqrt{24}\\x=2\sqrt{6}[/tex]

[tex]\text{Since }\theta\text{ is between }\pi\text{ and }\dfrac{3\pi}{2} \text{ (Quadrant III)},\text{ then x and y are negative.}\\\implies x=-2\sqrt{6}\\\\\\cos\theta = \dfrac{x}{h}\quad =\boxed{-\dfrac{2\sqrt{6}}{5}}[/tex]

Answer:

D

Step-by-step explanation:

The y-intercept is the number or constant at the end of the equation.

D sets both of their y-intercepts to -6, so it's correct.

=============================================

Explanation:

Plug x = 0 into f(x)

f(x) = 4x + 1

f(0) = 4(0) + 1

f(0) = 1

The y intercept of f(x) is 1

----------

Now plug x = 0 into g(x)

g(x) = 3^x - 2

g(0) = 3^0 - 2

g(0) = -1

The y intercept of g(x) is -1

----------

Note how the y intercepts are 2 units apart.

Each of the answer choices are in the form of f(x) + M and g(x) + N. The goal is to see which M and N values will be 2 units apart. In this case, that would be choice C where M = -1 and N = 1

We see that f(x) - 1 = f(0) - 1 = 1 - 1 = 0 and g(x) + 1 = g(0) + 1 = -1 + 1 = 0

Therefore, f(x) - 1 and g(x) + 1 have the same y intercept of 0.

Answer: 34.93 units

Step-by-step explanation:

The volume of a rectangular prism can be calculated with this formula:

[tex]V=Bh[/tex]

Where "V" is the volume, "B" is the base area and "h" is the height.

Since we need to find the height, we must solve for "h":

[tex]h=\frac{V}{B}[/tex]

We know that the volume of that wooden chest (which is in the shape of a rectangular prism) is 524 cubic units and the base area is 15 square units. Then:

[tex]V=524units^3\\B=15units^2[/tex]

Subsitituting these values into [tex]h=\frac{B}{V}[/tex], we get that the height of the chest is:

 [tex]h=\frac{524units^3}{15units^2}=34.93units[/tex]

That is true for sure!!!

The statement 1/5⁻² =25 is true.

The statement 1/5⁻² = 25 is true.

To simplify the expression, we can rewrite 1/5⁻² as 5²/1. When we have a negative exponent in the denominator, it moves to the numerator and becomes positive.

Therefore, 1/5⁻² is equivalent to 5²/1.

Since 5² equals 25, we can conclude that 1/5⁻² is indeed equal to 25.

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Answer:

67

Step-by-step explanation:

you have to divide

Answer

Step-by-step explanation:$149.50 is the answer

Answer:

a

Step-by-step explanation:

The question is missing the specific equation needed to estimate average annual snowfall for Columbia, South Carolina at 34 degrees north latitude. Factors like latitude and climate patterns influence snowfall levels, and based on Columbia's location, low snowfall would be expected.

The student is asking about an equation to estimate average annual snowfall for a specific location based on its latitude, in this case, Columbia, South Carolina, which is at 34 degrees north latitude. Unfortunately, the explicit equation needed to estimate the snowfall is not provided in the question or the contextual information. Generally, to estimate snowfall or precipitation levels using latitude, additional climatic data such as elevation, proximity to oceans or large bodies of water, and prevailing wind patterns are also necessary.

However, referring to the geographical regions mentioned, it's noted that certain latitudes often correspond with specific climate patterns. The comparison with other regions suggests that areas farther away from the equator, especially those close to either the Arctic Circle or the Antarctic Circle, experience more extreme temperatures and snowfall. Given the subtropical zone where Columbia, South Carolina, is located, the expected average snowfall would likely be relatively low compared to higher latitudes.

Answer: 324π units²

Step-by-step explanation:

The formula for the surface area of a sphere is: A=4πr²

Now we just plug in 9 for r:

A = 4π(9)²

A = 4π*81

A = 324π

Answer:

1018 units^2

Step-by-step explanation:

The surface area of a sphere is given by A = 4pi(r)^2, where r is the radius.

Here, A = 4(3.14159)(9 units)^2 = 1018 units^2, to the nearest integer.

Answer : The correct answer is, [tex]29\frac{62}{7}[/tex]

Step-by-step explanation :

The given expression is:

[tex]10\frac{3}{7}+19\frac{5}{9}[/tex]

Step 1 : Convert mixed fraction into fraction.

[tex]\frac{73}{7}+\frac{176}{9}[/tex]

Step 2 : Taking L.C.M

[tex]\frac{(9\times 73)+(176\times 7)}{63}[/tex]

[tex]\frac{(657)+(1232)}{63}[/tex]

[tex]\frac{1889}{63}[/tex]

Step 3 : Convert fraction into mixed fraction.

[tex]=29\frac{62}{7}[/tex]

Thus, the correct answer is, [tex]29\frac{62}{7}[/tex]

Answer:  She has 525 costumers.

Step-by-step explanation:

We know that the costumer base is  [tex]\frac{2}{3}[/tex] residential and  [tex]\frac{1}{3}[/tex] business. This means that:

[tex]\frac{2}{3}=350[/tex] residential customers

Let be "x" the total costumers Athy has and "y" the number of business costumers.

Then "x" must be:

[tex]x=350+y[/tex]

Then, in order to find "y" , we need to multiply the number of residential costumers by  [tex]\frac{1}{3}[/tex] and divide the product by [tex]\frac{2}{3}[/tex] :

[tex]y=\frac{(350)(\frac{1}{3})}{\frac{2}{3} }\\\\y=175[/tex]

Substituting we get that "x" is:

 [tex]x=350+175=525[/tex] costumers

[tex]\bf f(x)=x-1\qquad \qquad g(x)=3\cdot f(x)\implies g(x)=\underline{3(x-1)} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} x&g(x)\\ \cline{1-2} 1&0\\2&3\\3&6 \end{array}\qquad \qquad (\stackrel{x_1}{1}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6})[/tex]

[tex]\bf slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-0}{3-1}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=3(x-1)\implies y=\underline{3(x-1)}[/tex]

The table that represents g(x) = 3⋅f(x) when f(x) = x − 1 is that of Option D;

x g(x)

1 0

2 3

3 6

f(x) = x − 1

We want to find; g(x) = 3⋅f(x)

This means that; g(x) = 3(x - 1)

Looking at the options, the input values to be used are x = 1, 2 3.

When x = 1; g(x) = 3(1 - 1 )

g(x) = 0

When x = 2; g(x) = 3(2 - 1)

g(x) = 3

When x = 3; g(x) = 3(3 - 1)

g(x) = 6

Looking at the options, only the table in option D is correct.

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Answer:

the first one

Step-by-step explanation:

the number of mistakes went from 19 the first week of class to 0 the 20th week

Jerod will need 19 pages to display all his 112 photos.

If you divide 112 by 12 you get 18.6667.

Since Jerod cannot break his paper into a half for the .6667 space, he would need to use 19 pages in total. All his 18 pages will have 6 photos each but his last 19th will have 1 photo left on it.

Hope this helps!!!

Mark as Brainliest Please!!!

[tex]\bf Py+qy=-4y+8\implies Py+qy+4y=8\implies \stackrel{\textit{common factor}}{y(P+q+4)}=8 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{8}{P+q+4}~\hfill[/tex]

Answer:

y =  8 / (P + q + 4)

Step-by-step explanation:

Group ALL y terms on the left side:  Py + qy + 4y = 8.

Factor y out of the left side:              y(P + q + 4) = 8

Divide both sides by (P + q + 4):        y =  8 / (P + q + 4)

Answer: 45.71 - 6x = y

Step-by-step explanation:

45.71 - 6x = y

x= the amount 1 pack of markers cost

y= how much money Heather has after the donation

Answer: The required expression for amount left in her bank after the donation is given by [tex]Amount\ left=45.71-6x[/tex]

Step-by-step explanation:

Since we have given that

Amount of her saving = $45.71

Number of packs of markers to donate to her school = 6

Let the cost of each pack of markers be 'x'.

So, Amount left in her bank account after the donation is given by

[tex]Amount\ left=45.71-6x[/tex]

Hence, the required expression for amount left in her bank after the donation is given by

[tex]45.71-6x[/tex]

Answer:

Before Tax: $240

After Tax: $259.20

Step-by-step explanation:

If we are trying to find the original price then here:

216/1.08 = 200

This took away the tax now we need to take away the discount:

200 x 1.2 = 240

Before Tax: $240

After Tax: $259.20

The original after tax price of the flute is $259.20.

The first step is to remove tax from the sales price.  In order to remove tax, divide the sales price by (1 + tax): $216 / 1.08 = $200

The second step is to remove the effect of discount. In order to do this multiply 200 by (1 + discount): 200 x 1.2 = $240.

The after tax original price = $240 x 1.08 = $259.20

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Answer:

8 pages/ minute

Step-by-step explanation:

To find the rate, we take the pages and divide by the minutes

368 pages / 46 minutes

8 pages/ minute

Answer:

y = 0.75x

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k substitute either of the 2 points into the equation

Using (12, 9 ), then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{9}{12}[/tex] = 0.75, so

y = 0.75x ← equation of variation

Answer:

=13.73 ft²

Step-by-step explanation:

The diameter of the largest possible circle that can be cut out of  a square is equal to the length of the side of the square.

Therefore the diameter of the circle cut from a square of side 8ft =8ft

r=4ft

Area of the remaining board= Area of square- area of circle

=side²-πr²

=8²-π×4²

=64-16π

=13.73 ft²

Answer:

48.28

Step-by-step explanation:

2800:58 = 48.28

Answer:

C

Step-by-step explanation:

recall the property [tex]a^{1/b}= \sqrt[b]{a}[/tex]

if we apply this to this case,

[tex]x^{1/4} = \sqrt[4]{x}[/tex]

- [tex]x^{1/4} = - \sqrt[4]{x}[/tex]

Answer:

x = 8

Step-by-step explanat

Answer:

6

Step-by-step explanation:

Answer:

AB = 4 cm

Step-by-step explanation:

The tangent and secant are drawn from an external point to the circle.

Then the square of the measure of the tangent is equal to the product of the external part of the secant and the entire secant.

let AB = x, then

x(x + 5) = 6²

x² + 5x = 36 ( subtract 36 from both sides )

x² + 5x - 36 = 0 ← in standard form

(x + 9)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 4 = 0 ⇒ x = 4

However x > 0 ⇒ x = 4 ⇒ b = 4 CM

Answer:

The answer is B

Step-by-step explanation:

happy cheating

Answer:

The answer is B

Step-by-step explanation:

And it's not cheating just trying to make it through high school.

Answer:

C is your answer I did this test before.

Step-by-step explanation:

good luck.

C is your answer

We have given that,

when using the rational root theorem, which of the following is a possible root of the polynomial function below

F(x)=3x^3-x^2+4x+5

The rational root theorem says, a rational zeros of a polynomial is of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

p/q=±a0/a1

from the given polynomial a1=3 and a0=5

p/q=±3/5

+3/5 is not in the option so the correct option -3/2

So the root of the given polynomial is -3/5

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