(3a) 3 3aaa 3·3·3a 3a3a3a 3·3·3a 3

5/25 = x/20

To solve a proportion cross multiply:

(5 * 20) = (25 * x)

Simplify:

100 = 25x

Divide both sides by 25:

x = 100/25

x = 4

The answer would be A

The solution of ⁶P₂ would be,

⇒ ⁶P₂ = 30

We have to given that,

An expression to solve,

⇒ ⁶P₂

Now, By definition of permutation, we get;

⇒ ⁶P₂

⇒ 6! / (6 - 2)!

⇒ 6! / 4!

⇒ 6 × 5

⇒ 30

Therefore, The solution of ⁶P₂ would be,

⇒ ⁶P₂ = 30

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Question 1:

Substitution.

x+y=2

y=-x+2

2x+(-x+2)=4

x=2

(2)+y=2

y=0

Solution: (2,0)

There is one solution

Question 7 is too confusing, just find where the points intersect at (-5,2).

Question 9:

Elimination.

(-1)y=2x+6

y=2x+2

New: -y=-2x-6

0=-4

No Solution

Question 11:

Just look at explanations.

It's (5,17) both lines etc..

Final answer:

The set of equations for Line A and Line B has one solution. The graph correctly represents the solution (-5, 2) if the lines intersect 5 units to the left and 2 units up. Equations C and D have no solution since the lines are parallel, and the solution to Lines C and D is (5, 17), with both lines passing through this point.

Explanation:

Question 1: To determine the relationship between Line A: x + y = 2 and Line B: 2x + y = 4, we can solve for y in both equations.

For Line A, y = 2 - x.

For Line B, y = 4 - 2x.

Since the coefficients of x are different in the two equations, and the y-intercepts are also different, the lines are not parallel nor identical. Therefore, they intersect at exactly one point, which means there is one solution to the set of equations.

Question 7: The coordinates of the solution is given as (-5, 2). Among the options, the one showing the lines intersecting at the point 5 units to the left and 2 units up represents the correct set of lines, so the graph that corresponds to this description contains the solution.

Question 9: Comparing the two equations: Equation C: y = 2x + 6 and Equation D: y = 2x + 2, we see that both have the same slope but different y-intercepts. Because they have the same slope but different y-intercepts, these lines are parallel and never intersect. Hence, there is no solution to this set of equations.

Question 11: To find the intersection point, we set the equations of Line C: y = x + 12 and Line D: y = 3x + 2 equal to each other and solve for x:

x + 12 = 3x + 2

Subtract x from both sides: 12 = 2x + 2

Subtract 2 from both sides: 10 = 2x

Divide by 2: x = 5

We then substitute x = 5 into one of the equations to find y:

For Line C: y = 5 + 12 = 17.

Hence, the solution to the set of equations is (5, 17), and both lines pass through this point, which lies between the two axes, but that is irrelevant to why it is the solution.

Answer:

5

Step-by-step explanation:

Evaluate (5 x)/8 + 10 where x = -8:

(5 x)/8 + 10 = 10 - 8×5/8

5/8 (-8) = (5 (-8))/8:

(-8×5)/8 + 10

(-8)/8 = (8 (-1))/8 = -1:

5×-1 + 10

10 - 5 = 5:

Answer: 5

D.

36/16 sqrt = 6/4, since the square root applies to denominator and numerator.

A rational number is a number that can be expressed as the quotient or fraction of two integers. None of the given options are rational in the provided question.

A rational number is a number that can be expressed as the quotient or fraction of two integers. In this question, we need to determine which of the given options is rational.

To identify a rational number, we need to check if the number can be written in the form a/b, where a and b are integers. Let's analyse each option:

From the analysis, we can see that none of the given options is rational.

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The answer is:

The domain for the function is:

Domain:(-∞,-3)∪(-3,∞)

Since we are working with fractions, the only restriction that we will have for the function is when the denominator of the function tends to 0.

We are given the function:

[tex]f(x)=\frac{x^3} +27}{x+3}[/tex]

We have two expressions:

The first expression (numerator) has no restriction, however, we can find a restriction at the second expression (denominator) because when a fraction has a denominator equal to 0, the function does not exist on the real numbers.

For the denominator, we have that it tends to 0 at:

[tex]x=-3[/tex]

So, the domain for the given function will be:

Domain:(-∞,-3)∪(-3,∞)

Hence, the answer is the second option, the domain for the function is:

Domain:(-∞,-3)∪(-3,∞)

Have a nice day!

Answer:

[tex]\large\boxed{\dfrac{3s^2+19s-4}{(s-1)^2(s+5)}=\dfrac{3s^2+19s-4}{s^3+3s^2-9s+5}}[/tex]

Step-by-step explanation:

[tex]s^2-2s+1=s^2-s-s+1=s(s-1)-1(s-1)=(s-1)(s-1)=(s-1)^2\\\\s^2+4s-5=s^2+5s-s-5=s(s+5)-1(s+5)=(s+5)(s-1)\\\\\text{Therefore}\ LCD\ \text{is}\ (s-1)^2(s+5).[/tex]

[tex]\dfrac{3s}{s^2-2s+1}+\dfrac{4}{s^2+4s-5}=\dfrac{3s(s+5)}{(s-1)^2(s+5)}+\dfrac{4(s-1)}{(s-1)^2(s+5)}\\\\\text{use the distributive property}\\\\=\dfrac{(3s)(s)+(3s)(5)+(4)(s)+(4)(-1)}{(s-1)^2+(s+5)}=\dfrac{3s^2+15s+4s-4}{(s-1)^2(s+5)}\\\\=\dfrac{3s^2+19s-4}{(s-1)^2(s+5)}[/tex]

Answer:

P(x) = 2(f+g)(x)

Step-by-step explanation:

perimeter of the rectangle = 2( length + width )

Answer:

The area of triangle D'E'F' is four times the area of triangle DEF.

Answer:

A) 47

B) 65

C) 01

Step-by-step explanation:

A stem and Leaf is a unique way of representing data, in which every data value is split into a “stem” and “a leaf” . The “Stem” is the first Digit of the number and The “Leaf” is the second digit of the data value.

As we seen in the Key provided to us at the foot of the page, 6│3 represent 63,also

6│0 3 4 represents : 60,63,64

0│1 5 8 represents : 01,05,08

Using this rule we expands the data given to us and answer the questions given to us.

A) Number of people represented in data

0│1 1 2 2 3 4 4 4 4 5 8 = 01 01 02 02 03 04 04 04 04 05 08 = 11 Entries

In the same way , we count the other data and see that

Total number of data values are : 11+8+8+9+4+5+2= 47

B) The range of the Data: It the Difference of the largest Data value and the Lowest Data Value

Largest Data Value : 66

Smallest Data Value : 01

Range = 66-01 = 65

C) The mode : It the Data value which is repeated the most:

01 : 4 times

10 : 3 times

31 : 3 times

32 : 3 times

Hence the mode is 01

u can see the solution in pic

Answer:

Option D. 8

Step-by-step explanation:

we have

[tex]f(x)=\frac{x^{2}-16 }{x-4}[/tex]

Remember that

[tex]x^{2}-16 =(x+4)(x-4)[/tex]

substitute

[tex]f(x)=\frac{(x+4)(x-4)}{x-4}[/tex]

Remove the discontinuity at x=4

Simplify

[tex]f(x)=(x+4)[/tex]

so

Find the value of f(4)

For x=4

[tex]f(4)=(4+4)=8[/tex]

Answer:

8

Step-by-step explanation:

I have the plato platform

Answer:

[tex]\boxed{\text{\$2313.40}}[/tex]

Step-by-step explanation:

The tax rate is $3.78/$100 assessed

[tex]\text{Tax} = \text{\$61 200 assessed} \times \dfrac{\text{\$3.78}}{\text{\$100 assessed}}[/tex]

Cancel the $100 assessed.

612 × $3.78 = $2313.40

Angela's real estate tax will be [tex]\boxed{ \textbf{\$2313.40}}[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^{16}}{x^3}\implies \cfrac{x^{16}}{1}\cdot \cfrac{1}{x^3}\implies x^{16}\cdot x^{-3}\implies x^{16-3}\implies x^{13}[/tex]

Answer:

x^13

Step-by-step explanation:

when you divide variables with exponents you subtract them. So x^16-3 = x^13

Answer:

The answer is $9669.65 ≈ $9670.

Step-by-step explanation:

The formula to be used is :

[tex]A=P(1+r)^{nt}[/tex]

For first part :

p = 7800

r = [tex]5.2/100/12=0.00433[/tex]

t = 5

[tex]A=7800(1.00433)^{5}[/tex]

A = $7970.04

For second part:

p = 7970.04

r = [tex]33.6/100/12=0.028[/tex]

t = 7

[tex]A=7970.04(1.028)^{7}[/tex]

A = $9669.65

So, the answer is $9669.65 ≈ $9670.

ANSWER

f(x)

Domain:(-∞,∞)

Range:(-∞,∞)

[tex] {f}^{ - 1} (x)[/tex]

Domain:(-∞,∞)

Range:(-∞,∞)

The given function is

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

This is a polynomial function.

All polynomial functions are defined everywhere.

The domain is all real numbers.

Or

(-∞,∞).

The range is also all real numbers.

(-∞,∞).

The domain of the inverse function equals the range of the function.

(-∞,∞).

The range of the inverse function equals the domain of the function.

(-∞,∞).

[tex]

7x-4=5x+15 \\

2x=11

x=\boxed{\frac{11}{2}}

[/tex]

Hope this helps.

r3t40

5x^5•y^2 + 15x^2•y^3 + x^3•y^5

GCF = (x^2)(y^2)

The greatest common factor of the given polynomial is x²y².

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

The given expression is 5x⁵y²+15x²y³+x³y⁵.

In the given expression, there are three terms 5x⁵y², 15x²y³ and x³y⁵

5x⁵y²=5×x×x×x×x×x×y×y

15x²y³=3×5×x×x×y×y×y

x³y⁵ =x×x×x×y×y×y×y×y

So, the common factor = x×x×y×y

= x²y²

Therefore, the greatest common factor is x²y².

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The answer is d

[tex]x = \sqrt{{20}^{2}-{7}^{2}} [/tex]

The expression x = √(20² - 7²) can be used to determine the side length of side AC option (d) is correct.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have:

Triangle ABC is a right triangle with sides shown in the figure.

From the Pythagoras theorem:

20² = 7² + x²

x² = 20² - 7²

x = √(20² - 7²)

Thus, the expression x = √(20² - 7²) can be used to determine the side length of side AC option (d) is correct.

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Answer:

[tex]h=V/(\pi r^{2})[/tex]

Step-by-step explanation:

we know that

The formula for the volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius

h is the height of the cylinder

Solve for h

That means -----> isolate the variable h

Divide by πr² both sides

[tex]V/(\pi r^{2})=h[/tex]

Rewrite

[tex]h=V/(\pi r^{2})[/tex]

Answer:

The formula for the Volume of a cylinder [note: area of circle times height]:

     V = Πr2h

 Solve for r in terms of h

     r2 = V / (Πh)

For this cylinder, V=539.

     r2 = 539 / (Πh)

     r = √(539/(Πh))

This is also:

     r = 23.1 / √(Πh)

     r = 13.1 / √h

Answer:

i)

-2

ii)

a0 = 5.5

a1 = -44

Step-by-step explanation:

i)

Given a geometric sequence, the common ratio is the ratio between any two adjacent values. In our case we have the following geometric sequence;

a0, -11, 22, a1, 88, -176

To find the common ratio we can simply divide 22 by -11 or divide -176 by 88;

common ratio = 22/(-11) = -2

ii)

To find a0, we use the common ratio;

(-11)/a0 = -2

a0 = (-11)/(-2)

a0 = 5.5

We do the same for a1;

88/a1 = -2

a1 = 88/(-2)

a1 = -44

Answer:

True

Step-by-step explanation:

64x³ + 125

64x³ = (4x)³ ← a perfect cube

125 = 5³ ← a perfect cube

Thus 64x³ + 125 ← is a sum of cubes

It is true that the expression which is given below is a sum of cubes.

The given expression is:

                          [tex]64x^{3} +125[/tex]

As we can see that there are two terms in it:

one is [tex]64x^{3}[/tex] and the second one is [tex]125[/tex].

So, at first, we will see [tex]64x^{3}[/tex]        

[tex]64x^{3}=4^{3} *x^{3}[/tex]

from the above, we can state that [tex]64x^{3}[/tex] is a cube of [tex]4x[/tex].

Now, we will look at [tex]125[/tex].

So, [tex]125=5^{3}[/tex]

Therefore, we can also state that [tex]125[/tex] is a cube of [tex]5[/tex].

Hence, the given statement is true.

The sum of cubes (a3 + b3) formula is expressed as a3 + b3 = (a + b) (a2 - ab + b2).

Sum of cubes:The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.

The formula to find the sum of cubes of n natural numbers is S = [n2 (n + 1)2]/4, where n is the count of natural numbers that we take.

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0.95c

100% minus 5% is 95%, or 0.95. This means Sally only has to pay 0.95 times the grocery bill, or c, which represents 0.95c.

Answer:

16.3

Step-by-step explanation:

took k12 test

Answer:

16.3

x = 16.3cm

Step-by-step explanation:

I just took the test, and I got 100%!!!

Answer:

[tex]y=-\frac{1}{16}x^2[/tex]

Step-by-step explanation:

The focus of the parabola is (0,-4)

and the directrix is y=4.

The equation of this parabola is given by:

[tex]x^2=-4py[/tex]

The vertex of this parabola is at the origin.

The value of p is the distance from the vertex to the focus.

p=0--4=4

The equation of the parabola is

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

[tex]x^2=-16y[/tex]

Or

[tex]y=-\frac{1}{16}x^2[/tex]

Answer:

7. 5/6 8. 3/12

Step-by-step explanation:

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{3}{ r}\\[2em] [x-(-1)]^2+[y-1]^2=3^2\implies (x+1)^2+(y-1)^2=9[/tex]

The equation of the circle will be ( x + 1 )² + ( y - 1 )² = 9.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle can be written as,

( x - h)² + ( y - k )² = r².

Given that the circle below is centered at (-1, 1) and has a radius of 3. The equation of the circle will be written as,

( x - h)² + ( y - k )² = r².

( x + 1 )² + ( y - 1 )² = 9.

Hence, the equation can be written as ( x + 1 )² + ( y - 1 )² = 9.

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The area of the rhombus with diagonals of 8m each is 32 square meters.

The area of a rhombus can be calculated using the formula:

Area = (diagonal1  diagonal2) / 2

Given that the diagonals of the rhombus are 8m and 8m, we can plug these values into the formula:

Area = (8  8) / 2

Area = 64 / 2

Area = 32 square meters

To explain the calculation step by step:

1. Identify the diagonals: In a rhombus, the diagonals are perpendicular bisectors of each other and they bisect each other at right angles. Here, both diagonals are 8m each.

2. Plug into the formula: Substitute the lengths of the diagonals into the formula for the area of a rhombus.

3. Calculate the product: Multiply the lengths of the diagonals together.

4. Divide by 2: Since the formula for the area of a rhombus involves dividing the product of the diagonals by 2, perform this division to find the final answer.

5. Final answer: The area of the rhombus is 32 square meters.

So, the area of the rhombus with diagonals of 8m each is 32 square meters.

Complete question:

Find the area of the rhombus.

8 m

8 m

8 m

8 m

Answer:

3/7

Step-by-step explanation:

its 3/7 because there are 3 weekend days and there are 7 days in total in one week, so out of the week there is 3 weekend days.

i hope this helps :)

The probability will be "[tex]\frac{1}{7}[/tex]". A further solution is below.

According to the question,

Number of days in a week,

Number of weekend,

Now,

The probability of you picking weekend day from the days of the week will be:

= [tex]\frac{Number \ of \ weekend}{Number \ of \ days \ in \ week}[/tex]

By substituting the values, we get

= [tex]\frac{1}{7}[/tex]

Thus the response above is appropriate.

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