Find the rule for (3,1) (6,2) (9,3) (12,4) (15,5)
​

Find the ratio of the known sides and calculate X.

1. The smaller triangle is half the size of the lager one:

6/12 = 1/2

10/12 = 1/2

This means x is half the length of 16

x = 16/2 = 8

2.  18/30  = 3/5

     9/15 = 3/5

This means x is 3/5 of 25

x = 25 * 3/5 = 15

3. 32/24 = 1 1/3

   16 /12 = 1 1/3

X is 1 1/3 times the length of 21

x = 21 x 1 1/3

x = 28

4.  12/15 = 4/5

    20/25 = 4/5

x is 4/5 the length of 40

x = 40 * 4/5

x = 32

Answer:

3x yrs old

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

6/7 divided by 3/14​ is 4.

Find common denominators.

6/7 would be changed into 12/14.

3/14 would stay the same because its denominator is already 14.

12/3 = 4

Therefore, 6/7 divided by 3/14​ is 4.

Answer:

The answer is 4

Step number one use the butterfly method:

6 14

-- ×---- =84/21

7 3

Step 2: Divide since it's improper

84÷21=4

4 21

-- × --- =4

1 21

Answer:

9a^2 +  3ab  - 6b^2

Step-by-step explanation:

(3a-2b)(3a+3b)

First term of each grouping is 3a and 3a.

Multiply those you get 9a^2.

Outer term of each grouping is 3a and 3b.

Multiply those you get 9ab.

Inner term of each grouping is -2b and 3a.

Multiply those you get -6ab.

Last term of each grouping is -2b and 3b.

Multiply those you get -6b^2.

Add up all your products from above.

9a^2+9ab+-6ab+-6b^2

There are like terms here.  The 9ab+-6ab which is 3ab.

So you can write your expression now as:

9a^2 + 3ab  +-6b^2

9a^2 +  3ab  - 6b^2

Step-by-step explanation:

[tex]\text{Use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd:\\\\(3a-2b)(3a+3b)\\\\=(3a)(3a)+(3a)(3b)+(-2b)(3a)+(-2b)(3b)\\\\=9a^2+9ab-6ab-6b^2\qquad\text{combine like terms}\\\\=9a^2+3ab-6b^2[/tex]

The perimeter of the walls is  6 + 6 + 8 + 8 = 28 feet.

The perimeter of the window is 2 + 2 + 1.5 + 1.5 = 7 feet.

Total = 28 + 7 = 35 feet of tape.

I would say B.35 is the answer.

Answer:

[tex]\frac{1215}{32}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex], hence

[tex]a_{6}[/tex] = 5 × [tex](\frac{3}{2 )} ^{5}[/tex] = 5 × [tex]\frac{243}{32}[/tex] = [tex]\frac{1215}{32}[/tex]

The sixth term of the geometric sequence is 1215/32 given that the first term a₁=5 and common ratio r=3/2. This can be obtained by using formula for nth term of the geometric sequence.

Sequence is s collection of objects in a particular order and repetitions are allowed.

   Geometric Sequence:

a, ar, ar¹, ..., arⁿ⁻¹ is a geometric sequence, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.

From the definition, nth term of a geometric sequence is arⁿ⁻¹.

Given that, a₁=5 and r=3/2​

To find sixth term, put n=6 ⇒ arⁿ⁻¹=(5)(3/2)⁶⁻¹

                                                       =(5)(3/2)⁵

                                                       =5(3⁵/2⁵)

                                                       =5×(243/32)

                                                       =1215/32

Hence the sixth term of the geometric sequence is 1215/32 given that the first term a₁=5 and common ratio r=3/2.

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Answer:

201.143 (approx.) cm²

area of circle = (pi)x(radius)^2

= 22/7 x (8)^2

=22/7 x 64

= 1408/7

= 201.142857143

= 201.143 cm^2 (approx.)

Answer:

the approximate area of circle is 201 cm²

D is the correct option.

Step-by-step explanation:

From, the given figure, the diameter of the circle is 16 cm.

The radius is half of the diameter.

Hence, the radius of circle is 16/2 = 8 cm

The area of a circle is given by

[tex]A=\pi r^2[/tex]

Substituting the value of r and π

[tex]A=3.14(8)^2\\\\A=200.96\\\\A\approx201[/tex]

Therefore, the approximate area of circle is 201 cm²

D is the correct option.

Answer:

12

Step-by-step explanation:

[tex]\frac{Parts of Water}{Parts of Concentrate} =3[/tex]

3/1=3

9/3=3

36/12=3

Answer:

[tex]y=\frac{1}{2}x-6[/tex]

Step-by-step explanation:

The general equation of a line: [tex]y = ax+b[/tex]

In our case a is given

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

Now we plug in for a and we get:

[tex]y=\frac{1}{2}*x+b[/tex]

Now we plug in our coordinates into this equation and we solve for b

[tex]-3=\frac{1}{2}*6+b\\b = -6[/tex]

So the equation of the line is [tex]y=\frac{1}{2}x-6[/tex]

Answer:

[tex]y=\frac{1}{2}x-6[/tex]

Step-by-step explanation:

Since the Inclination of the line was already given to us. Let us use Inclination of line formula:

[tex]m=\frac{y-y_0}{x-x_0}[/tex]

Plugging it in those values then we have the equation of the line:

[tex]\frac{1}{2}=\frac{y+3}{x-6}[/tex]

Rewriting, multiplying both sides

2y+6=x-6

2y=x-12 Rearranging

[tex]y=\frac{1}{2}x-6[/tex]

Answer:

[tex]f(g(x)) =\sqrt{6x^2-1}[/tex]

Step-by-step explanation:

Given

f(x) = √2x-5

and

g(x) = 3x^2+2

We have to find the composition of both function

f(g(x)) means that we have to put function g in place of x in function f.

[tex]f(g(x))= \sqrt{2*g(x)-5}\\ =\sqrt{2(3x^2+2)-5}\\=\sqrt{6x^2+4-5}\\=\sqrt{6x^2-1}[/tex]

..

The composite function f(g(x)) is given by f(g(x)) = √(6x^2 - 1).

To find the composite function f(g(x)), you need to substitute the expression for g(x) into the function f(x). Here's how you can do it step by step:

Start with the function g(x):

g(x) = 3x^2 + 2

Now, substitute this expression into the function f(x):

f(g(x)) = √(2(3x^2 + 2) - 5)

Simplify the expression inside the square root:

f(g(x)) = √(6x^2 + 4 - 5)

Further simplify the expression inside the square root:

f(g(x)) = √(6x^2 - 1)

So, the composite function f(g(x)) is given by:

f(g(x)) = √(6x^2 - 1)

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the assumption being, that there's a 7% sales tax on any item in the store.

so if you buy the jacket, you pay 25.5 plust 7% of 25.5.

and if you buy the shoes for price say "s", then you pay "s" plus 7% of "s".

whatever those two amounts are, they must be $60, because that's all you have in your pocket anyway.

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 25.5}}{\left( \cfrac{7}{100} \right)25.5}\implies 0.07(25.5)~\hfill \stackrel{\textit{7\% of "s"}}{\left( \cfrac{7}{100} \right)s}\implies 0.07s \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{jacket}}{25.5}+\stackrel{\textit{jacket's tax}}{0.07(25.5)}+\stackrel{\textit{shoes}}{s}+\stackrel{\textit{shoe's tax}}{0.07s}~~=~~\stackrel{\textit{in your pocket}}{60} \\\\\\ 25.5+1.785+s+0.07s=60\implies 27.285+1.07s=60 \\\\\\ 1.07s=60-27.285\implies 1.07s=32.715\implies s=\cfrac{32.715}{1.07}\implies s\approx 30.57[/tex]

Answer:

309

Step-by-step explanation:

(2x-)^5

step 1

1 5 10 10 5 1

step 2

1(2x¹-3^0) 5(2x²-3^5) 10(2x³-3^4)

10(2x^4-3³) 5(2x^5-3²)

1(2x^0-3¹)

step 3

(2x) (10x²-243) (20x³-81) (20x^4-27)

(10x^5-9) (2-3)

step 4

2 -243-61-7 +1 -1=309

The coefficient of [tex]x^3[/tex] in the expansion of [tex](2x-3)^5[/tex] is 720

The correct answer is an option (E)

"It refers to a number or quantity placed with a variable."

"The alphabetic character that expresses a numerical value."

"It is a mathematical expression which consists of numbers, variables and mathematical operations."

" [tex](a-b)^3=a^3-3a^2b+3ab^2- b^3[/tex] "

" [tex](a-b)^2=a^2-2ab+b^2[/tex] "

For given question,

We have been given an expression [tex](2x-3)^5[/tex]

We need to expand given expression.

[tex](2x-3)^5\\\\= (2x-3)^3\times (2x-3)^2\\\\=[(2x)^3-3(2x)^23+3(2x)(3)^2- 3^3]\times ((2x)^2-2(2x)(3)+3^2)\\\\=[8x^3-36x^2+54x-27]\times [4x^2-12x+9]\\\\=-243+810x-1080x^2 +720x^3-240x^4+32x^5\\\\=32x^5-240x^4+720x^3-1080x^2+810x-243[/tex]

Therefore, the coefficient of [tex]x^3[/tex] in the expansion of [tex](2x-3)^5[/tex] is 720

The correct answer is an option (E)

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Answer:

128 units^3

Step-by-step explanation:

[tex]v = \frac{b \times b \times h}{3} = \\ = \frac{8 \times 8 \times 6}{3} = \\ = 128 \: {units}^{3} [/tex]

Step-by-step explanation:

base areas x height / 3

a^2 . h / 3

8^2 . 6 / 3

= 128 units^3

iyi ödevler

have a good lesson

Answer:

[tex]\large\boxed{\dfrac{(2x^3y)^3}{(4xy^2)^2(xy^3)}=\dfrac{x^6}{2y^4}}[/tex]

Step-by-step explanation:

[tex]\dfrac{(2x^3y)^3}{(4xy^2)^2(xy^3)}\qquad\text{use}\ (ab)^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{2^3(x^3)^3y^3}{4^2x^2(y^2)^2xy^3}\qquad\text{cancel}\ y^3\\\\=\dfrac{8x^{(3)(3)}y^3\!\!\!\!\!\diagup}{16x^2y^{(2)(2)}xy^3\!\!\!\!\!\diagup}\\\\=\dfrac{8\!\!\!\!\diagup^1x^9}{16\!\!\!\!\!\diagup_2x^2y^4x}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{x^9}{2x^{2+1}y^4}\\\\=\dfrac{x^9}{2x^3y^4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=\dfrac{x^{9-3}}{2y^4}\\\\=\dfrac{x^6}{2y^4}[/tex]

Answer:

the answer is D

Step-by-step explanation:

a is not it has a negative

a b is not it has an equation in it

so that leaves it to see and d c does not work

because it has to have two variables per one number

Answer:

[tex]x^{4}[/tex]

Step-by-step explanation:

[tex]\frac{x^{5}y^{2}  }{xy^{2} }[/tex]

= [tex]x^{4}[/tex]

Question 1:

For this case we have the following expression:

[tex]\frac {x ^ 5y ^ 2} {xy ^ 2}[/tex]

We eliminate similar terms in the numerator and denominator:

[tex]\frac {x ^ 5} {x}[/tex]

By definition of division of powers of the same base we have to place the same base and subtract the exponents:

[tex]\frac {x ^ 5} {x} = x ^ {5-1} = x ^ 4[/tex]

ANswer:

Option D

Question 2:

For this case we must indicate which expression is not equal to 125.

We tested option A:

[tex]5 (\frac {5 ^ 3} {\frac {2} {5}}) ^ 2 =[/tex]

Simplifying we have:

[tex]5 (\frac {5 ^ 3 * 5} {2}) ^ 2 =\\5 (\frac {5 ^ 8} {4}) =\\\frac {5 ^ 9} {4}[/tex]

The expression is not equal to 125.

Answer:

option A

Answer:

y - 15000 = 12500(x-3)

Answer:

x^4+100x^2-5x^2-500=0

x^2(x^2+100)-5(x^2+100)=0

(x^2+100)(x^2-5)=0

from first expression

x^2+100=0

x^2=-100

x= root under -100

Therefore x=-10

from next expression

x^2-5=0

x^2=5

Or x=2.23

Step-by-step explanation:

Answer:

x = ± sqrt(5)

x = ±10i

Step-by-step explanation:

x^4+ 95x^2-500=0

What two numbers multiply to -500 and add to 95

-5 * 100 = -500

-5 +100 = 95

(x^2 - 5) (x^2 + 100) = 0

Using the zero product property

x^2 -5 =0          x^2 +100 =0

x^2 -5+5 =0      x^2 +100-100 = 0-100

x^2 =5               x^2 = -100

Take the square root of each side

x = ± sqrt(5)       x = imaginary numbers

                           x = ±10i

This statement would be true: if the vertex of an angle is at the center of the circle, then it would be the central angle.

Answer:

$384.00

Step-by-step explanation:

Since $8..0 is 1 hour, just multiply 48 x 8! Hope this helps!

Answer:

320

Step-by-step explanation:

The reason that you  48* 8 is because the 48 has overtime included in it so you would only 40*8.

If pressure is constant

then PV= nRT

is equivalent to V= ( nR/P) T

V= kT ( where k is constant nR/P)

As V is directly proportional to T

So V1/T1 = V2/T2

Answer:

The correct answer

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Answer:

Amy is correct because a nonlinear association could increase along the whole data set, while being steeper in some parts than others. The scatterplot could be linear or nonlinear.

Step-by-step explanation:

Both linear and nonlinear associations could increase along the whole data set. That's why Joseph and the fourth option are incorrect.

Answer:

[tex]2\ miles[/tex]

Step-by-step explanation:

we know that

The distance around the park is equal to the perimeter of the rectangular park

The perimeter is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]L=\frac{3}{4}\ mi[/tex]

[tex]W=\frac{1}{4}\ mi[/tex]

substitute the values

[tex]P=2(\frac{3}{4}+\frac{1}{4})[/tex]

[tex]P=2(\frac{4}{4})[/tex]

[tex]P=2\ mi[/tex]

Answer:

3 219⁄1000 km. [2 mi.]

Step-by-step explanation:

P = 2l + 2w

P = 2[¾] + 2[¼]

P = 1½ + ½

P = 2

I am joyous to assist you anytime.

4x + 3y = -6

Step-by-step explanation:

Answer:

D) 1/27

Step-by-step explanation:

The question is: 3^(-3).

Note that there is a negative sign in the number at the power place. This means that you must flip the number, and in this case, put it over 1. The rest is solved as usual:

3^-3 = 1/(3^3) = 1/(3 * 3 * 3) = 1/27

1/27, or D) is your answer.

~

Step-by-step explanation and answer:

The given equations P=2T=3Q can be split up into

P=2T..................(1)

P=3Q................(2)

since they are all equal.

Rewrite the given equation

3Q + 4T = 26  .............(3)

as

3Q + 2(2T) = 26  ...........(4)

and substitute (1) and (2) into (4)

P + 2(P) = 26 .................(5)

Multiply (5) by two to get

6P = 2*26 = 52   ..............(6)

as given.

Answer:

see explanation

Step-by-step explanation:

Given P = 2T = 3Q, then

3Q + 4T = 26 can be expressed as

P + 2P = 26

3P = 26 ( multiply both sides by 2 )

6P = 52 ← as required

Answer:

x ≥ 0

Step-by-step explanation:

The domain of the function is the inputs, or in this case, the x values.

The inputs are  x greater than or equal to zero all the way to infinity.

Answer:

Step-by-step explanation:

The domain includes 0 and all real numbers greater than 0:  x ≥ 0

Answer:

43.60

Step-by-step explanation:

12.36+31.24

Answer:

X is parallel to Z

X || Z

Step-by-step explanation:

This is called the transitive property.

It says something like:

If f is related to g and g is related to h, then f is related to h.

The parallel relationship is transitive.

That is,

if X is parallel to Y and Y is parallel to Z, then X is parallel to Z.