Please help me simplify this fraction. Or is it already in its simplest form?

The height of the triangle is approximately [tex]4.35\text{ mm}[/tex]

Step-by-step explanation:

The area of a triangle can be calculated by using the Heron's formula.

Heron's formula:  

Suppose a triangle has sides [tex]a'[/tex], [tex]b'[/tex] and [tex]c'[/tex], then the semi-perimeter [tex]S[/tex] of the triangle is represented by the expression,

[tex]S=\frac{a'+b'+c'}{2}[/tex]

The area [tex]A[/tex] of the traingle is formulated below.

[tex]\fbox {\begin\\A=\sqrt{s(s-a')(s-b')(s-c')}\end{minispace}}[/tex]

To calculate the area of the triangle with sides [tex]9 \text{ mm}[/tex] , [tex]6 \text{ mm}[/tex] and [tex]12 \text{ mm}[/tex], first find the semi-perimeter.

[tex]S=\frac{9+6+12}{2}\\S=\frac{27}{2}\\S=13.5 \text{ mm}[/tex]

Now, the area of the triangle is calculated below.

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}\\A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\A=\sqrt{13.5 \times 4.5 \times 7.5 \times 1.5}\\A=\sqrt{\frac{135}{10}\times\frac{45}{10}\times\frac{75}{10}\times\frac{15}{10}} \\A=\sqrt{\frac{(15\times3\times3) \times (15\times3) \times (15\times5) \times15}{100\times100}}\\A=\frac{15\times15\times3\sqrt{15 } }{100} \\A=2.25\times3\times3.87\\A=26.122[/tex]

Area A of a triangle with a altitude P and one side as base B on which the altitude P is drawn, can be calculated as,

[tex]\fbox{\begin\\A= \left[\frac{1}{2}(B)(P)\right]\\\end{minispace}}[/tex]

Now, the area of the same triangle can also be calculated as,

[tex]A=\frac{1}{2}(12)(x)\\A=6x[/tex]

In the above calculations, area of the triangle is calculated in two ways.

Therefore, both the areas can be equated to obtain the altitude [tex]x[/tex].

[tex]6x=26.122\\x=\frac{26.122}{6}\\x=4.35[/tex]

Thus, the height of the triangle is evaluated as [tex]\fbox{4.35 \text{ mm}}[/tex].

Learn more:

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2. Which undefined term is needed to define an angle? https://brainly.com/question/3717797

3. Look at the figure, which trigonometric ratio should you use to find x? https://brainly.com/question/9880052

Answer Details

Grade: Junior High School

Subject: Mathematics

Chapter: Area of triangle

Keywords: area of triangle, heron's formula, base multiplied by height, base multiplied by perpendicular, base multiplied by altitude, right triangle, altitude corresponding to base, area of right triangle

Answer:

4.3 mm

Step-by-step explanation:

I got it correct on founders edtell

Answer:

(2, 22 )

Step-by-step explanation:

Given the 2 equations

y = 7x + 8 → (1)

y = x + 20 → (2)

Substitute y = 7x + 8 into (2)

7x + 8 = x + 20 ( subtract x from both sides )

6x + 8 = 20 ( subtract 8 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2

Substitute x = 2 in (2) for corresponding value of y

y = x + 20 = 2 + 20 = 22

Solution is (2, 22 )

Answer:

(2,22)

Step-by-step explanation:

A-P-E-X :)

[tex]\frac{1}{30}[/tex]

Multiply the numerators together. [tex]-1*-1=1[/tex]

Multiply the denominators together. [tex]6*5=30[/tex]

Put the two products together in a new fraction. [tex]\frac{-1}{6}*\frac{-1}{5}=\frac{1}{30}[/tex]

Answer:

1/30

Multiply the numerators together.  

Multiply the denominators together.  

Put the two products together in a new fraction.

Step-by-step explanation:

The volume of the cube with edges of eight feet is approximately 18.96 cubic yards.

To find the volume of a cube, you need to know the length of one of its edges. In this case, the edge length is given as eight feet.

Volume of a cube = (Edge length)³

Volume = 8³ = 512 cubic feet.

Now, we need to convert cubic feet to cubic yards. Since 1 cubic yard is equal to 27 cubic feet:

Volume in cubic yards = 512 cubic feet / 27 cubic feet per cubic yard ≈ 18.96 cubic yards.

So, the volume of the cube is approximately 18.96 cubic yards.

To know more about volume:

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Answer:

[tex]\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}[/tex]

Step-by-step explanation:

[tex]\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}[/tex]

Answer: [tex]x^{16}\ y^{22}[/tex]

Step-by-step explanation:

The given expression : [tex]\dfrac{(x^6y^8)^3}{x^2y^2}[/tex]

Using identity , [tex](a^m)^n=a^{mn}[/tex] , we have

[tex]{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}[/tex]

Now, [tex]\dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}[/tex]

( its also an equivalent expression to given expression.)

Using identity , [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex] , we have

[tex]\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}[/tex]

Hence, the expression is equivalent to given expression :

[tex]x^{16}\ y^{22}[/tex]

Answer:

The polygon has 9 sides

Step-by-step explanation:

We need to equate the given expression to the given value and solve for n.

The sum of the interior angles, s, in an n-sided polygon is given by the expression:

[tex]s = 180(n - 2)[/tex]

We want to use this formula, to calculate how many sides has a polygon if the sum of the interior angles is 1,260°.

We solve the following equation for n.

[tex]180(n - 2) = 1260[/tex]

Divide through by 180 to get:

[tex] \frac{180(n - 2)}{180} = \frac{1260}{180} [/tex]

[tex]n - 2 = 7[/tex]

Add 2 to both sides to get:

[tex]n = 7 + 2[/tex]

[tex] \therefore \: n = 9[/tex]

Hence the polygon has 9 sides

Answer: d

Step-by-step explanation:

Check the picture below.

so a full circle is 360°, then if we just go 140° more, we'll be landing at 500°.

If we go from the 140° location and add say 360°, well end up 500, if we add another 360°, we'll be at 860° or the same location of 140° and 500°, and if we add again 360° we'll be landing on the same spot again and again.

(140 + 360n)°.   where "n" is an integer.

The expression that represents the measures of all angles that are co-terminal with a 500° angle is 140 + 360n

Co-terminal angles are angles in a standard position

The angle is given as:

Angle = 500

Add 0 to 500

Angle = 500 + 0

Express 0 as -360 + 360

Angle = 500 - 360 + 360

Evaluate the difference

Angle = 140 + 360

Express as a function

f(1) = 140 + 360 * 1

Substitute 1 for n

f(n) = 140 + 360 * n

This gives

f(n) = 140 + 360n

Hence, the expression that represents the measures of all angles that are co-terminal with a 500° angle is 140 + 360n

Read more about co-terminal angles at:

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Answer:

(3,4)

Step-by-step explanation:

The system of equations is:

x+6y=27

7x-3y=9.

I looked up "metodo de igualacion". It is basically American for doing substitution.

However, the only difference is you are asked to solve both equations for a variable.

The first equation looks easy to solve for x. So I'm going to solve both equations for x.

x+6y=27

Subtract 6y on both sides:

x     =-6y+27

7x-3y=9

Add 3y on both sides:

7x    =3y+9

Divide both sides by 7:

x     =3/7 y +9/7

So both equations are solved for x.  You want to find when the x's are the same because you are looking for a common amongst the lines given.

So we have

-6y+27=3/7 y  +9/7

I hate the fractions honestly so I'm going to multiply both sides by 7 so they will no longer be for now:

-42y+189=3y + 9

Now add 42y on both sides:

         189=45y+9

Subtract 9 on both sides:

        180=45y

Divide both sides by 45:

            4=y

If 4=y, then y=4.

So now once we have obtain 4 for y, we will use one of the equations given along with it to find x. Just choose one. Choose the easier looking one to you.

I like the x=-6y+27 with y=4.

So replace y with giving you:

x=-6(4)+27

x=-24+27

x=3

So the solution is (x,y)=(3,4).

x=3 and y=4.

By using the method of substitution, we isolate one variable, substitute it in the other equation, and solve for the remaining variable. Applying these steps to the provided system of equations gives us the solution x=3, y=4.

The provided system of equations can be solved using the method of substitution. For this method, we first need to isolate one variable in one of the two equations. In this case, let's isolate 'x' from the first equation, which gives us:
x = 27 - 6y.
Now, we substitute this 'x' value into the second equation to get:
7(27 - 6y) - 3y = 9.
This simplifies to:
189 - 42y - 3y = 9
Combining like terms gives us:
-45y = -180
We can solve for 'y' by dividing each side by -45:
y = 4.
Substituting this value of 'y' back into the first equation gives us:
x = 27 - 6(4) = 3.
Therefore, the solutions for the system are x=3 and y=4.

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Answer:

D. More Than 1 Solution

Step-by-step explanation:

Let the system of equations be:

[tex]a_1x+b_1y=c_1...(1)[/tex]

[tex]a_2x+b_2y=c_2...(2)[/tex]

If the graph of equation (1) and (2) are the same, then the two graphs coincide with each other.

What that means is that; the two graphs intersects at infinitely many points.

Therefore the system must have infinitely many solutions.

In other words the system has more than one solution.

NB: At least one solution means exactly one solution and/or more than one solution. But lines that coincide cannot have exactly one solution.

Answer:

B.the set of all first elements of the function

Step-by-step explanation:

the domain is all the x variables in a function

Answer:

B. The set of all first elements of the function.

Step-by-step explanation:

We have been given a incomplete sentence. We are asked to complete our given sentence.

We know that the domain of a function is all real values of independent variable for which a function is defined and gives exactly one output.

We know that independent variable is x, which is first element of a point, therefore, the domain of a function is the set of all first elements of the function.

Answer:

21.26 inches to the nearest hundredth.

Step-by-step explanation:

By the Pythagoras theorem

d^2 = 14^2 + 16^2   (where d = the length of the diagonal).

d^2 = 452

d = 21.26 inches.

Answer:

21.26 inches.

Step-by-step explanation:

It can be inferred that the shape of the monitor is a rectangle, in which the length of the monitor is 16 inches and the height of the monitor is 14 inches. The diagonals of the rectangle cut it into two congruent right-angled triangles. Therefore, to find the length of the diagonal of the monitor, use the Pythagoras Theorem. Since the base (b) is 16 inches and the perpendicular (p) is 14 inches, the distance of the hypotenuse (i.e. the diagonal, denoted by h) can be found by the following formula:

[tex]h^2 = b^2 + p^2 [/tex]

Plugging in the values:

[tex]h^2 = 16^2 + 14^2[/tex]

Simplifying gives:

[tex]h^2 = 452[/tex]

Taking square root on both sides gives:

h = 21.26 inches (to the nearest 2 decimal places)

Therefore, the measure of the diagonal is 21.26 inches!!!

Answer:

[tex]\^v=-\frac{3}{5}i+\frac{4}{5}j[/tex]

Step-by-step explanation:

We have the following vector

[tex]v=3\sqrt{2}i-4\sqrt{2}j[/tex]

First we calculate its magnitude

The magnitude of the vector v will be

[tex]|v|=\sqrt{(3\sqrt{2})^2 + (4\sqrt{2})^2}\\\\|v|=\sqrt{9*2+16*2}\\\\|v|=\sqrt{18+32}\\\\|v|=5\sqrt{2}[/tex]

Now to create a unitary vector in the opposite direction to v, we divide the vector v between the negative of its magnitude

we call this new vector "[tex]\^v[/tex]"

[tex]\^v=\frac{3\sqrt{2}}{-5\sqrt{2}}i-\frac{4\sqrt{2}}{-5\sqrt{2}}j[/tex]

[tex]\^v=-\frac{3}{5}i+\frac{4}{5}j[/tex]

Answer:

(gof) (1) = 0

Step-by-step explanation:

f(x) = -4x + 7

g(x) = 2x - 6

(gof) (1)

First find f(1)

f(1) = -4(1) + 7

f(1) = -4+7=3

Then put 3 in for x in g(x)

g(f(1) = 2(f(1))-6

        = 2 (3) -6

        = 6 -6

        = 0

[tex](g\circ f)(x)=2(-4x+7)-6=-8x+14-6=-8x+8\\\\(g\circ f)(1)=-8\cdot1+8=0[/tex]

Answer:

1 triangle is possible

Step-by-step explanation:

If there are two sides and a non included angle is given then there could be 0,1 or 2 triangles depend on the measure of the given angle and the lengths of the given sides.

We will discuss some conditions which will clarify that how many triangles are there in the given condition.

CASE 1: If A is obtuse and a>b then there is 1 triangle.

CASE 2: If A is obtuse and a<b then there is 0 triangle.

CASE 3:  If A is acute and a>b then there is 1 triangle.

CASE 4:  If A is acute  and h<a<b then there are 2  triangles possible.

CASE 5: If A is acute  and a=h then there is 1 right angle triangle.

CASE 6: If A is acute and a<h then there are 0 triangles possible.

Therefore according to the given condition A= 6° which is acute and a>b, So this condition matches the CASE 3:

According to this there is 1 triangle possible....

Answer:

[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]

Step-by-step explanation:

1st boat:

Parabola equation:

[tex]y=ax^2 +bx+c[/tex]

The x-coordinate of the vertex:

[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a[/tex]

Equation:

[tex]y=ax^2 -2ax+c[/tex]

The y-coordinate of the vertex:

[tex]y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10[/tex]

Parabola passes through the point (-8,1), so

[tex]1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1[/tex]

Solve:

[tex]c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}[/tex]

Parabola equation:

[tex]y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}[/tex]

2nd boat:

Parabola equation:

[tex]y=ax^2 +bx+c[/tex]

The x-coordinate of the vertex:

[tex]x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0[/tex]

Equation:

[tex]y=ax^2+c[/tex]

The y-coordinate of the vertex:

[tex]y_v=a\cdot 0^2+c\Rightarrow c=-7[/tex]

Parabola passes through the point (-8,1), so

[tex]1=a\cdot (-8)^2-7\\ \\64a-7=1[/tex]

Solve:

[tex]a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7[/tex]

Parabola equation:

[tex]y=\dfrac{1}{8}x^2 -7[/tex]

System of two equations:

[tex]\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.[/tex]

Step-by-step explanation:

200 calories come from fat, out of 5000 calories total.  We can find the percentage with a proportion:

200 / 5000 = x / 100

x = 4

4% of the total calories come from fat.

Answer:

3x+8 I think

Step-by-step explanation:

add 5, -1 and 4

Answer:

The CORRECT answer is C,  7x+4

Step-by-step explanation:

Answer:

A. Draw a line from the segment to any point on the fold line.

Step-by-step explanation:

When using the paper folding method to find the midpoint of a line segment we take the following steps:

These steps include statements B, C, and D. Drawing a line from the segment to any point on the fold line, which is statement A,  is not included in these steps because it is not needed.

Thus, choice A is not a step in using paper folding to find the midpoint of a line segment.

Answer:

The answer should be 1.4<h<1.6

Step-by-step explanation:

Multiply 7 and 8 by 0.2 to find out what 20% is. 7*0.2=1.4 and 8*0.2=1.6. So it should be at or between those two numbers making the inequality 1.4<h<1.6

When an adult sleeps between 7 to 8 hours, they spend between 1.4 and 1.6 hours in REM (Rapid Eye Movement) sleep, which is associated with dreaming.

Given that an adult sleeps 7 to 8 hours, roughly 20% of this time is spent in REM or Rapid Eye Movement sleep, typically associated with dreaming. To find out how much time is spent in REM sleep, we calculate 20% of the total sleep time. If 20% of 7 hours is 1.4 hours and 20% of 8 hours is 1.6 hours, then the correct inequality showing how much time, in hours, is spent in REM sleep is 1.4 < h < 1.6 where 'h' represents number of hours in REM sleep.

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Answer:

-3

Step-by-step explanation:

If a line is perpendicular to another the product of their slope should equal -1. The slope of the first equation is -1 and -1*1=-1 so the slope of the second equation is 1. That means that the equation looks like y=x+b. We know that when x is 4 y is 1. So plugging in those values you get 1=4+b, subtracting 4 you get -3=b. So the y-intercept is -3

Answer:

this was last last year sorry u never got an answer

Answer:

r ≤ 29, r-5

The sale price can be compared with the regular price, r-5 ≤ 24

Step-by-step explanation:

Amount to spend = $24

Regular price = r

Sale = $5

Sale Price = r-5

The regular price will be $5, at the max, more than the amount Roopesh has to spend.

The sale price will be $24 or less than that for Roopesh to afford.

Inequality for regular price:

r-5 ≤ 24

r ≤ 29

So, the product Roopesh can afford is $29 or less than that.

What is the unknown? r ≤ 29

Following expression can represent the sale price:

Sale price = r-5  

The sale price can be compared with the regular price with the following:

Inequality representing the situation: r-5 ≤ 24

Answer:

Step-by-step explanation:

What is unknown?

We are missing the regular price of an item

Which expression can represent the sale price?

$24 - x = the sales price

and the x equals the original price since we don't know the actual price.

Which comparison could  be used?

$24 spend on a birthday gift to a the shopping sale offering $5 off the regular price.

And the rest I don't know son or girl

Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]

Step-by-step explanation:

First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1)  by the denominator (which is 2) of the fraction:

[tex]\frac{1}{2}=0.5[/tex]

Now you must add 0.5 to the whole number part. Then:

[tex]1+0.5=1.5[/tex]

In order to find the ratio of cleaner to water, you must divide 1.5  cups of cleaner by 12 cups of water.

Therefore, the ratio is:

[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]

Answer:

1

Step-by-step explanation:

To solve, combine like terms.

Subtract 6x from both sides.

[tex]2=3x-1[/tex]

Add 1 to both sides.

[tex]3=3x[/tex]

Divide both sides by 3.

[tex]1=x[/tex]

Answer:

Explicit form:    [tex]a_n=8+4n[/tex]

Seventh term:  [tex]a_7=36[/tex]

You gave the recursive form:

[tex]a_n=a_{n-1}+4 \text{ with } a_1=12[/tex]

Step-by-step explanation:

You already have the recursive formula which is:

[tex]a_n=a_{n-1}+4[/tex] where [tex]a_1=12[/tex].

Maybe you looking for the explicit form and also the 7th term?

You were just looking for the 7th term.  Sometimes you can read the recursive formula pretty easily and understand the pattern that is happening.

[tex]a_{n-1}[/tex] is the term right before [tex]a(n)[/tex].  Just like [tex]a_5[/tex] would be the term right before [tex]a_6[/tex].

Anyways becak to our recursive for a sequence that was given:

[tex]a_{n}=a_{n-1}+4[/tex] says term=previous term+4.

So you adding 4 over and over to generate the terms of a sequence.  This is arithmetic sequence because it is going up by same number (or could go down by same number).  The common difference is 4.

[tex]a_1=12[/tex]

[tex]a_2=12+4=16[/tex]

[tex]a_3=16+4=20[/tex]

[tex]a_4=20+4=24[/tex]

[tex]a_5=24+4=28[/tex]

[tex]a_6=28+4=32[/tex]

[tex]a_7=32+4=36[/tex]

Now if you don't like that. You could just blindly without trying to understand the meaning of it just plug numbers in:

[tex]a_1=12[/tex]

For if we wanted to know the 2nd term; we would plug in 2 for n:

[tex]a_2=a_{2-1}+4[/tex]

[tex]a_2=a_1+4[/tex]

[tex]a_2=12+4[/tex]

[tex]a_2=16[/tex]

Plug in 3 for the 3rd term:

[tex]a_3=a_{3-1}+4[/tex]

[tex]a_3=a_2+4[/tex]

[tex]a_3=16+4[/tex]

[tex]a_3=20[/tex]

Plug in 4 for the 4th term:

[tex]a_4=a_{4-1}+4[/tex]

[tex]a_4=a_3+4[/tex]

[tex]a_4=20+4[/tex]

[tex]a_4=24[/tex]

Plug in 5 for the 5th term:

[tex]a_5=a_{5-1}+4[/tex]

[tex]a_5=a_4+4[/tex]

[tex]a_5=24+4[/tex]

[tex]a_5=28[/tex]

Plug in 6 for the 6th term:

[tex]a_6=a_{6-1}+4[/tex]

[tex]a_6=a_5+4[/tex]

[tex]a_6=28+4[/tex]

[tex]a_6=32[/tex]

Plug in 7 for the 7th term:

[tex]a_7=a_{6-1}+4[/tex]

[tex]a_7=a_5+4[/tex]

[tex]a_7=32+4[/tex]

[tex]a_7=36[/tex]

Now if you look at the points we just got (I will just go up to 4 terms):

n  (treat as x)  |  1           2                3                 4

a(n) (treat as y|  12        16               20                24

The explicit form in not in terms of other terms of the sequence.  You are looking here for an equation that relates n (x) to a(n) (y).

I'm just going to use x and y until the end where I will replace them back in terms of n and a(n).

This is a line because the's rise/run (the slope) is the same per choosing of points.

That is the following is true:

[tex]\frac{16-12}{2-1}=\frac{20-16}{3-2}=\frac{24-20}{4-3}[/tex] son on....

These all the the value 4, the same number that the arithmetic sequence is going up by.  

So in an arithmetic sequence, the common difference is the slope of the line.

I'm going to use point-slope formula which is [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

So we have m=4 and [tex](x_1,y_1)[/tex] could be any of the 7 we found, but I will choose (1,12) for it:

[tex]y-12=4(x-1)[/tex]

Add 12 on both sides:

[tex]y=12+4(x-1)[/tex]

[tex]a_n=12+4(n-1)[/tex].

This is actually in the form of most books formulas for an explicit form which is [tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term and d is the common difference.

So another way to do the problem:

You would have to know the following are equivalent:

[tex]a_n=a_{n-1}+d[/tex] with [tex]a_1 \text{ is given}[/tex]

and

[tex]a_n=a_1+d(n-1)[/tex].

If you know these are equivalent then you could compare [tex]a_n=a_{n-1}+d[/tex] to [tex]a_n=a_{n-1}+4[/tex] and determine d is 4.

You could also see that [tex]a_1[/tex] is give as 12.

Then you just plug into:

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_n=12+4(n-1)[/tex].

You could also simplify this equation just a bit.

You could distribute and then combine a pair of like terms.

Like so,

[tex]a_n=12+4(n-1)[/tex]

[tex]a_n=12+4n-4[/tex]

[tex]a_n=8+4n[/tex]

Answer:

Option C.   2508 cubic inches is the correct answer

Step-by-step explanation:

From the figure we can see that, a sink

Points to remember

Volume of hemisphere = (2/3)πr³

Where 'r' is the radius

To find the volume of large hemisphere

Here radius = 13 in

Volume V₁ =  (2/3)πr³

 = (2/3) * 3.14 * 13³

 = 4599.33 cubic inches

To find the volume of small hemisphere

Here radius = 13 - 3 = 10 in

Volume V₂ =  (2/3)πr³

 = (2/3) * 3.14 * 10³

 =2093.33 cubic inches

To find the volume of sink

Volume = V₂ - V₁

  = 4599.05 - 2093.33

 =2505.72 ≈ 2508 cubic inches

Option C.   2508 cubic inches is the correct answer

Answer:

It is D. (x + 1)^2 + (y - 3)^2 = 16.

Step-by-step explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2  where  the center is (h, k) and the radius is r.

So substituting the given values the required equation is:

(x + 1)^2 + (y - 3)^2 = 4^2.

Answer:

D. [tex](x+1)^2+(y-3)^2=16[/tex]

Step-by-step explanation:

We are asked to write equation of a circle whose center is at point [tex](-1,3)[/tex] and whose radius is 4 units.

We know that equation of a circle is standard form is in format [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the center of circle.

Upon substituting [tex]h=-1[/tex], [tex]k=3[/tex] and [tex]r=4[/tex] in the standard form of circle, we will get:

[tex](x-(-1))^2+(y-3)^2=4^2[/tex]

[tex](x+1)^2+(y-3)^2=16[/tex]

Therefore, our required equation would be [tex](x+1)^2+(y-3)^2=16[/tex] and option D is the correct choice.

Answer:

Range : {11,13,17,25}

Step-by-step explanation:

Given

f(x) = 2x+7

and

Domain = {2,3,5,9}

To find the range, the values in domain will be put in the function one by one

So,

f(2) = 2(2)+7 = 4+7 = 11

f(3) = 2(3)+7 = 6+7 = 13

f(5) = 2(5)+7 = 10+7 = 17

f(9) = 2(9)+7 = 18+7 = 25

Therefore the range is {11,13,17,25} ..