In a radio station contest, 20 people are eligible for a prize drawing. There will be 2
winners, and each winner gets two tickets to an upcoming concert. How many
different sets of 2 winners can be chosen?

The inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore,  the inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].

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After dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

We are given the expression

4√162 x⁴ / 4√2 y⁸

We need to divide the expression and simplify it.

First, cancelling the terms that are same in the numerator and the denominator:

√162 x⁴ / √2 y⁸

Now , using the properties of the exponents, we get that:

= √81 x² / y⁴

= 9 x ² / y⁴

Therefore, after dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

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Sides of Quadrilateral A is 6, 9, 9 and 12.

It is given that Quadrilateral B is a scaled copy of Quadrilateral A,

and have shortest side = 2

To find the length of sides of quadrilateral, first we will find the ratio of the shortest side of quadrilateral A to that of quadrilateral B as shown below :

B : A = 2 : 6 = 1 : 3

This shows that the quadrilateral B is 3 times smaller than A.

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Triangle ABC with coordinates A (2, 4),

B (3, 6), and C (5, 1) is translated

4 units horizontally is (6,4), (7,6) ,( 1,9)

A triangle is a basic polygon with three sides and three internal angles. It is one of the fundamental shapes in geometry in which the three vertices are connected together, and it is represented by the symbol. Triangles are categorized into many sorts based on their sides and angles. All geometrical shapes have unique qualities relating to sides and angles that aid in their identification. The following are some of the most important qualities of a triangle.

There are three sides, three vertices, and three internal angles in a triangle.

The angle sum property of a triangle asserts that the sum of a triangle's three internal angles is always 180°. Consider the triangle PQR shown above .

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The value of x for the equation log₈2=x is 0.333

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties. These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

Given,

log₈2=x

It can be expressed in the form -

2 = 8ˣ

2 =  2³ˣ

As base is same -

1 = 3x

x = 1/3

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The values of  f(−4), f(−2), and f(3) for given piecewise function are 0, -4, and -3.5 respectively.

What is piecewise function ?

Whenever the summation of two functions is different over different intervals, the sum is a piecewise function.

Here, the given piecewise function f(x) is :

[tex]\begin{aligned}f(x)&=\left\{\begin{matrix}\frac{-1}{2}x-2 \text{ if} \:x \neq -2&\\-4 \:\:\:\:\:\:\;\;\text{ if }x = -2\end{matrix}\right.\end{aligned}[/tex]

Now, let us find the value of f(-4) :

for x = -4 the function f(x) is (-1/2)x -2, substituting x = -4 in place x :

f(x) =  (-1/2)x - 2

f(-4) = (-1/2)*(-4) - 2  

f(-4) = 2 - 2

f(-4)  = 0

similarly, for f(-2) :

for x = -2 the function f(x) is -4 only that is :

f(-2) = -4

For, let us find the value of f(3) :

for x = 3 the function f(x) is (-1/2)x -2, substituting x = 3 in place x :

f(x) =  (-1/2)x - 2

f(3) = (-1/2)*(3) - 2  

f(3) = -3/2 - 2

f(3)  = - 3.5

Therefore, the values of  f(−4), f(−2), and f(3) are 0, -4, and -3.5 respectively.

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Answer:

x + 6 = -6

Step-by-step explanation:

Assuming x = -6

[tex]x+6=0[/tex]

Subtract 6

[tex]x+6-6=0-6[/tex]

Simplify arithmetic

[tex]x=0-6[/tex]

Simplify arithmetic(again)

[tex]x=-6[/tex]

we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.

Hope this helps, have a great day!

Answer:

a = 9

Step-by-step explanation:

Step 1: Add 3 to both sides

2a – 3 = 15

2a – 3 + 3 = 15 + 3

Step 2: Simplify

add the numbers ( 2a = 18 )

Step 3: Divide both sides by the same factor

2a = 18

2a 18

––– = –––

2 2

Step 4: Simplify

l

Cancel the terms that are in both the numerator and the denominator

l

l

Divide the numbers

l

a = 9

Answer: a = 9

Adult tickets that were sold were 210 .

Let the no. of children be x and no. of adults be y .

According to ques .

x + y = 385     - eq 1

4 x + 6 y = 1960          - eq 2

Solving linear equation in 2 variable by method of substitution ,

multiply   - eq 1 by 4 ,

4 x + 4 y = 1540     - eq 3

multiplying  - eq 3 by - 1

- 4 x - 4 y = - 1540         - eq 4

Adding  - eq 2 and   - eq 4

2 y = 420

y = 210

Hence , 210 adult tickets were sold .

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Answer:

x=3

Step-by-step explanation:

Answer:

The graph of g(x) = -|x| - 8.

Expression as a single logarithm of 5 log₇2-2 log₇y is Log (2x/3y).

Log a + Log b = Log ab

Log a - Log b = Log (a/b)

so starting with the bracket, we have;

Log 2 + Log X - Log 3y

Furthermore, we have;

Log 2x - Log 3y

Finally, we have;

Log (2x/3y)

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Here we need to evaluate some mathematic expressions in some given values, we will get:

3x-  4 is equal to 17 when x = 7.

-5x + 8 is equal to -7 when x = 3.

Here we have some expressions that we need to evaluate. Evaluating an expression means that we replace the variables (usually denoted by letters) with numerical values.

The first expression is:

3x-  4

And we we want to evaluate it in x = 7.

So just replace the x by the number 7 and then do the operations:

3*7 - 4 = 21 - 4 = 17

The expression is equal to 17 when x = 7.

Now let's do it again for second expression:

-5x + 8  with x = 3.

Replacing the variable by the number we get:

-5*3 + 8 = -15 + 8 = -7

So that is the basic procedure to evaluate mathematic expressions.

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Answer:

4

Step-by-step explanation:

because if it has two Pairs that's 2 on each side of the side of the shape

so, when you have a figure of 2 parallel sides id would be a parallelogram

Answer:

2/375

Step-by-step explanation:

We can multiply 8/15 by 1/100 to get

[tex]\frac{8}{15} *\frac{1}{100}=\frac{8}{1500}[/tex]

Now we simplify this fraction into simplest form.

2/375

The original price of a ticket is a  $56.95.

According to the statement

We have to find that the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

An amusement park offers a ticket for $12.95 off the original price p.

Then

Discounted price is that the amount of sum that extracted from the initial price when buyers receive some style of leverage from the vendor. during this case, discounted price of the ticket is $44 which was $12.95 but the initial price.

Then the first price would be:

$44 + $12.95 = $56.95

So, The original price of a ticket is a  $56.95.

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The expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power is  [tex]z^{-18}.y^{18}[/tex] .

The given expression is [tex](\frac{y^{-3}.z^5}{z^{-4.y^6}} )^{-2}[/tex]

Let us take the numerator terms to denominator.

When shifting numerator terms to denominator the sign of the power will be changed.

[tex](\frac{1}{z^{-4.y^6.y^{3}.z^{-5}}} )^{-2}[/tex]

Combine like terms in denominator:

[tex](\frac{1}{z^{-9}.y^9} )^{-2}[/tex]

[tex](z^9.y^{-9})^{-2}[/tex]

[tex]z^{-18}.y^{18}[/tex]

Hence, [tex]z^{-18}.y^{18}[/tex]  is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power.

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The solution 'x' of the expressed logarithmic expression is 17.65.

A logarithmic equation one in which the variable x contains a logarithm.

The variable in an exponential formula is signified by an exponent. To solve exponential equations, first see if both sides of the equation can be presented as powers of the same number. Because unless you can't, start taking the common logarithm of both equation sides and solve the problem using property 7.

Now, as per the stated log expression;

3 ln x + ln 5 = 7

Apply the Power Rule on the first term of the given equation;

ln x³ + ln 5 = 7

Now, by the Product Rule, we can re-write the equation in the form;

ln (x³×5) = 7

ln (5x³) = 7

Using the exponent form of the log on both side.

e∧ln (5x³)  = e⁷

As, we have the same base for the obtained expression. Use the exponent rule;

(5x³)  = e⁷

x³ = e⁷/5

Substitute the value of exponent e = 2.72

x³ = (2.72)⁷/5

x³ = 5507.5

Take cube root on both side;

x = 17.65

Thus,  solution for the value of 'x' for expressed logarithmic expression is 17.65.

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Answer:

80,000 numbers.

Step-by-step explanation:

Since the number is 6-digits and is larger than 599,999, it would be between 600,000 and 999,999.

Between those two numbers (included), there are [tex]999999 - 600000 = 399999[/tex] numbers.

In addition, we know that the number is a multiple of 5. Therefore, we should divide this number by 5 to find how many of the numbers in that group are divisible by 5.
Since it's difficult dividing 399,999 by 5, I would divide 400,000 by 5, as we must also include 600,000.

[tex]\frac{400000}5 = 80000[/tex]

Answer: 9/9^4 in Simplest form is 1 / 729

Answer:

17x and 3x

Step-by-step explanation:

like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.

Answer:-55

Step-by-step explanation:

-11 times 5= -55

Answer:

A) y =  2.91x + 64.61 with x hours after 6:00 am

B) at 2:00pm, temperature is 87.89°

Step-by-step explanation:

(>>Regression Equation y = bx + a )With b- Sum of products/Sum of Square = sq/SSx. a = My- bMx,)

set 6.00 am is an original time, when x = 0

use the unit: hour to get a new table

X time 0, 0.75, 1.5, 2.5, 3, 3.75, 4.5, 5

Y temp 65°, 67", 68° ,72° ,74", 75° ,77° ,78°

a). with temperature y and x hour after 6:00 am,

can get Sum of x = 21 Mx = 2.63

Sum of - 578 My = 72.25

SSx = Sum of (X-Mx)² = 22.25

= sum of (X-Mx)(}-My)= 64.75

So b= sq/SSx =64.75/22.25 = 2.91

a= My- bMx = 72.25 - 291 x 2.63 = 64.61

So regressing equation Y= 2.91x + 64.61

b). at 02:00 pm , means 8 hours after 6:00 am

meaning X-8, )= 2.91×8 + 64.61 = 87.8)

The required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°

Given that,
The table shows the recorded temperature on a certain day starting at 6:00 am.

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

Here,
The standard form of the regression equation,
y = bx + a,
where b = sum of product/sum of squares a = My - bMx
Since
b = 2.91 , My = 72.25, Mx = 2.63
a = 72.25 - 2.91 * 2.63
a = 64.6
The required regression equation is,
y = 2.91x + 64.6

B)
For 2.00 PM, x = 8
Now,
y = 2.91 * 8 + 64.6
y = 87.8°

Thus, the required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°

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Answer:

  0

Step-by-step explanation:

You want the sum of numerator and denominator such that their difference is 2 and the reciprocal is equal to the original fraction.

We want a fraction such that ...

  x/y = y/x

  y = x +2

Substituting for y, we have ...

  x/(x +2) = (x +2)/x

  x^2 = x^2 +4x +4 . . . . . cross multiply

  0 = 4(x +1) . . . . subtract x^2, factor

  x = -1 . . . . . . . . the value of x that satisfies the equation

Then the denominator is ...

  y = x +2 = (-1) +2 = 1

The sum is ...

  x +y = (-1) +1 = 0

The sum of numerator and denominator is zero (0).

Answer: 4

Step-by-step explanation: Divide both sides by -3 so the x is by itself. When you divide both sides by -3, you get x =4.

Answer:

4

Step-by-step explanation:

Divide -3 on both sides so that x is by itself

-3x = -12

-3      -3

-3 is cancelled out

-12 divided my -3 is 4

Since both numbers are negative it would end up positive.

If the numbers are both positive then it would be positive as well.

And if one number is positive and the other is negative then the answer would be negative.

The answer would be: 4

I hope it helps! Have a great day!

Step-by-step explanation:

-by-step explanation:

y=\frac{2}{x+1}-3y=

x+1

2

−3

asymptotes:

x+1 = 0

x = -1

y = -3

asymptotes: x = -1, y = -3

x int: (-\frac{1}{3}, 0)(−

3

1

,0)

y int: (0, -1)

D: (-infinity, -1) (-1, infinity) x cannot be -1

R: (-infinity, -3) (-3, infinity) y cannot be -3

Answer:

∠ GRS = 74°

Step-by-step explanation:

∠ GRS + ∠ QRG = ∠ QRS , that is

∠ GRS + 105° = 179° ( subtract 105° from both sides )

∠ GRS = 74°

Answer:

75°

Step-by-step explanation:

While it may appear that QRS is a straight line, it is not so since m∠QRS = 179° and if it was a straight line, it would be 180°

The figure actually represents three rays with endpoint at R

The three rays are RQ, RS and RG

Draw another ray RT with endpoint at R and opposite to ray RG. Opposite rays have angles that add up to 180°

Therefore m∠GRT = 180°

m∠SRT = m∠QRG since they are opposite angles

Since m∠QRG = 105°, therefore m∠SRT = 105°

m∠GRS + m∠SRT=180° since these angles are formed by two opposite rays

Substituting we get
m∠GRS + 105 = 180

m∠GRS = 180-105 = 75°

Answer: its C because when you put it in order you should easily find it in the question. So, 1, 2, 3, 4, 5, 6, 9, 12, 15 is the full order but C is the closest answer to the question. Hope its right!