Solve each system by substitution.
4y - 6 = 2x , y - 3x = 9

The vakues based on the function f(x) = -x² + x + 6 will be:

12

0

12

When x = -2, the value will be:

f(x) = -x² + x + 6

= -2² + 2 + 6

= 4 + 2 + 6

= 12

When x = 0

f(x) = -x² + x + 6

= 0² + 0 + 6

= 0

When x = 2

f(x) = -x² + x + 6

= 2² + 2 + 6

= 12

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Answer:

after 5 hours: 14.5 inches

after t hours: 2 + 2.5t

Step-by-step explanation:

2 + 2.5t

2 + 2.5(5) = 2 + 12.5 = 14.5

The correct option is B. 1/11.

The probability of choosing 2 white marbles is 1/11.

A combination is an arithmetical technique for determining the number of different arrangements in a set of items in which the sequence of the selection is irrelevant.

You can choose the objects in any order in combinations. Permutations and combinations are often confused.

Now, as pet the stated question.

The total number of red marble in the bag are 5.

The total number of blue marble in the bag are 2.

The total number of white marble in the bag are 4.

The total number of yellow marble in the bag are 1.

The combination for selecting the 2 white marbles out of 4 are;

⁴C₂ = 4!/(4-2)!2!

⁴C₂ = 6

Ans, the combination for selecting the 2 marbles out of total 12 are;

¹²C₂ = 12!/(12-2)!2!

¹²C₂ = 66

Thus, the combination for selecting the 2 white marbles out of total 12 is;

= ⁴C₂ / ¹²C₂

= 6/66

= 1/11

Therefore, the the probability of outcome of the 2 white marbles out of total 12 marbles is 1/11.

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Length of Side of cube - shaped storage container is 2 units .

Given : Volume of container = 8 cubic units .

To find : the length of one side of the container .

Formula for volume of cube :  Volume of cube = [tex]x^{3}[/tex] .

According to ques .

[tex]x^{3}[/tex] = 8

Solving cubic equation ,

finding cube root of 8 and hence finding value of x .

[tex]\sqrt[3]{8}[/tex] = x

x = 2  

2 * 2 * 2 = 8 .

Hence , length of each side of cube - shaped storage container = 2 units .

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To use the equality to find ratio of a:b, the ratio of a:b is 9 : 2

The ratio expression is given as

2a : 9b

In order to to use the equality to find ratio of a:b, we make use of the following representations

mx : ny => m : n = y : x

Using the above as a guide, we have

2a : 9b => a : b = 9 : 2

Rewrite as

a : b = 9 : 2

Hence, to use the equality to find ratio of a:b, the ratio of a:b is 9 : 2

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Answer:

The answer is 10n-8

Step-by-step explanation:

Hope this helps!!

Answer:

8!

Step-by-step explanation:

8!=8*7*6*5*4*3*2*1

The total number of protons and neutrons in an atom exists directed as the mass number. The atomic mass number of an atom with 10p and 10 n exists 20.

The total number of protons and neutrons in an atom's nucleus is known as the mass number. Protons plus neutrons equal mass number.

The neon atom has 10 protons and 10 neutrons with the atomic number 10. It has 10 protons and neutrons inside of its nucleus, along with ten electrons outside, due to its atomic weight of 20.179.

Ne is an inert, colorless noble gas that is also the second-lightest of the noble gases. Due to its distinctive reddish glow, it is frequently utilized in lamps and signs.

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The midpoint is at  ( -8 , 9/2 , 4)

In the given statement is

To find the midpoint of the line segment joining the pair of points

W(-12,8,10) and Z(-4,1,-2)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} , \frac{z_{1} +z_{2} }{2}[/tex] )

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points W(-12,8,10) and Z(-4,1,-2)

Solving for the midpoint , we have,

m = ([tex]\frac{-12+(-4)}{2} , \frac{8+1}{2} ,\frac{10+(-2)}{2}[/tex])

m =( [tex](\frac{-16}{2} ) ,\frac{9}{2} , \frac{8}{2}[/tex])

m = ( -8 , 9/2 , 4)

Therefore, the midpoint is at  ( -8 , 9/2 , 4)

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According to the given statement the thermal conductivity is :

0.0003(W/(m* c))

Thermal conductivity is defined as the rate at which heat is transported by conduction through a unit cross-section surface of a material that whenever a temperature gradient exists perpendicular to the area.

The material's thermal conductivity is defined as the ratio of the rate of heat flow per unit area to the negative of the temperature gradient: dQdt=KAdTdx.

0.03 watts (W) per meter (m) per degree Celsius as a result, thermal conductivity is:

= 0.03(W/(m* c))

while we want the heat conductivity of the batting in w/cm•c

The only distinction is between metre and cm.

As a result, we must convert meter's to centimeters.

we are aware

1m =100cm

As a result, thermal conductivity may be written as.

= 0.03(W/(m* c))

we can replace 1m as 100cm.

= 0.03(W/(100m* c))

No simplifying the equation we get:

=  0.0003(W/(m* c))

According to the given statement the thermal conductivity is :

0.0003(W/(m* c)).

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The simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is (b + 12)/12.

According to the given question.

We have an expression

(1/3)(b + 12) - (1/4)(b + 12)

As we know that, simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is given by

(1/3)(b + 12) - (1/4)(b + 12)

= (b + 12)[(1/3) -(1/4)]             (taking (b + 12) common from each expression)

= (b + 12)[ (4-3)/12 ]

= (b + 12)[1/12]

= (b + 12)/12

Hence,the simplification of the given expression (1/3)(b + 12) - (1/4)(b + 12)  is (b + 12)/12.

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The difference between the numbers will be:

1. -11.

2. 43

3. -/15

The difference between the numbers will be:

1. (-5) - 6

= -5 - 6

= -11

2. 35 -(-8)

= 35 + 8

= 43

3. 2/5 - 3/5.

= -1/5

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The first five terms of the sequence (geometric) are: 2, 6, 18, 54, 162.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Now, given formula: [tex]a_n=3a_{n-1}[/tex], a₁ = 2.

For n = 2, a₂ = 3 (a₁) = 3 (2) = 6

For n = 3, a₃ = 3 (a₂) = 3 (6) = 18

For n = 4, a₄ = 3 (a₃) = 3 (18) = 54

For n = 5, a₅ = 3 (a₄) = 3 (54) = 162.

Hence, The first five terms of the sequence (geometric) are: 2, 6, 18, 54, 162.

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Answer:    x>2

Step-by-step explanation:

Answer:

Step-by-step explanation:

In rational functions, the discontinuities are caused by the denominator terms. Since the denominator of a fraction is non-zero, any term that is multiplied by the denominator is also non-zero.

If x = -1 then x+1 is 0.

So, the discontinuities are shown as x = -1

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The dimension of the string is A=13'1".

The dimension of the string is A=19'5",B=1'9" and C=25'5".

1. Given that two strings

In the 1st line given 3'3",5'6",8'9" and 1'4".

In the 2nd line given A and 5'9"

Feet is nothing but there is usually a focus on measuring in feet when working with lumber, pipe, or shingles.

Feet are either denoted with the letter "ft" or an apostrophe (').

Inches are nothing but one foot is twelve inches long. The sign for feet and inches is the same.

A single apostrophe (') is used for feet. A double apostrophe (") is used for inches.

Now, We will add the 1st line given dimension.

That is 3'3"+5'6"+8'9"+1'4"=18'10".

Now the 2nd line will be

A+5'9"=18'10"

A=18'10"-5'9"

A=13'1"

Therefore, the dimension of the string is A=13'1".

2.Given that three strings

In the 1st line given 75'8".

In the 2nd line given A and 56'3".

In the 3rd line given 17'8",B,30'10" and C.

Now, We will add the 2st line given dimensions.

That is A+56'3"=75'8"

A=75'8"-56'3"

A=19'5"

Now the 3nd line will be

B+17'8"=19'5"

B=19'5"-17'8"

B=1'9"

And

30'10"+C=56'3"

C=56'3"-30'10"

C=25'5"

Therefore, the dimension of the string is A=19'5",B=1'9" and C=25'5".

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Shop A is more expensive by 1.8 % percentage .

It is given that shop A has Marked price =Rs 25,000, Discount=10%, Putting above values in equation (1) we get

          [tex]S.P=25000\times\frac{100-10}{100} \\\\S.P=25000\times\frac{90}{100} \\\\\S.P=22500[/tex]

Rate of VAT 13% is given by

                        [tex]=\frac{13}{100} \times 22500\\\\=2925[/tex]

The amount to be payed for buying mobile set is [tex]=22500+2925=25425[/tex]

It is given that shop B has Marked price =Rs 24,000, Discount=8%, Putting above values in equation (1) we get

             [tex]S.P=24000\times\frac{100-8}{100} \\\\S.P=24000 \times\frac{92}{100} \\\\S.P=22080[/tex]

Rate of VAT 13% [tex]=13\% \ 22080[/tex]

                            [tex]=\frac{13}{100} \times 22080\\\\=2870.4[/tex]

The amount to be payed for buying mobile set is[tex]=22080+2870.4=24950.4[/tex]

As the amount of shop A is more than shop B so , shop A is more expensive

Percentage [tex]= \frac{25425-24950.4}{25425}\times100[/tex]

                    [tex]= \frac{474.6}{25425}\times100\\\\=0.01866\times100\\\\=1.8\%[/tex]

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Answer:

x=82.7

Step-by-step explanation:

3x+6-6=248

3x=248

x=82.7

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: 3x + 6 - 6 = 248[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 248[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{248}{3} [/tex]

The approximate value will be :

[tex]\qquad \sf  \dashrightarrow \: x \approx82.67[/tex]

The figure have 4 pairs of parallel sides after the 90 degree rotation.

What is 90° rotation of an object ?

For every point in the plane (x, y), a 90° rotation can be described by the transformation P(x, y) → P'(-y, x). We can achieve this same transformation by performing two reflections.

It is given that figure has 4 sets parallel sides is graphed on a grid and is then rotated 90 degrees clockwise.

The figures with 4 sets parallel sides are : square, rectangle, rhombus  

Let us consider square as our figured graphed in grid :

Now, Transformation involves moving a shape from one position to another, 90 degrees clockwise transformation that carries the square onto itself that is after rotation there will be 4 pairs of parallel sides.

Therefore, the figure have 4 pairs of parallel sides after the 90 degree rotation.

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By finding the surface area of the box, we can see that the cost to cover the box is $285

We assume that we need to cover the 6 faces of the box, then we need to find the total surface area.

The surface area is given as:

S = 2( B*H + H*W + B*W)

Where:

Then the surface area is:

S = 2*(7ft*9ft + 7ft*2ft + 9ft*2ft) = 190ft^2

Now we know that the paper costs $1.50 per square foot, then the cost to cover the box is:

cost =  190*$1.50 = $285

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By combining the like terms, the simplified form of the expression -5a-4a+b is -9a+b

Given,

The algebraic expression = -5a-4a+b

Combine the like terms

-5a-4a+b=(-5-4)a+b

=-9a+b

simplified form is -9a+b

Hence, By combining the like terms, the simplified form of the expression -5a-4a+b is -9a+b

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-3 < x < 3

Isolate the variable by dividing each side by factors that don't contain the variable.

The function y= |x+1| is increasing for the domain -1 < x < ∞ and decreasing for the domain -∞ < x < -1.

As given in the question, for what domain intervals is the function y= |x+1| increasing and/or decreasing is to be determined.

Here,
Given function,
f(x) = |x + 1|
Given functions absolute function,
Whose domain is all real numbers from -∞ to ∞.
And when we plot the graph of the function, we see that its decreasing from -∞ to -1 and increases from -1 to ∞.

Thus, The function y= |x+1| is increasing for the domain -1 < x < ∞ and decreasing for the domain -∞ < x < -1.

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The expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.

Option (A) is correct.

It is required to choose the expressions.

Index laws are the rules for simplifying expressions involving powers of the same base number. Index (indices) is the exponent which is raised to a number.

Given:

It follows from the task content that the equivalent expression as in the task content can be determined by the laws of Indices.

Now, according to laws of indices;

[tex]3^{2x} =( 3^{2}) ^{x}[/tex]

Thus, we now have;

[tex]= (3^{2} )^{x} )/3^{3} \\= (9^{x} )/3^{3} \\= (9^{x} )/27[/tex]

Therefore, the expressions which is equivalent to the given expression; 3^(2x -3) is; the quantity 9 to the power of x end quantity over 27.

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Using the graph, the value of r(-2) is 8

From the question, we are to determine the value of r(-2)

The given graph is the graph of the function r(x), and we have that

y = r(x)

To determine the value of r(-2), we will trace from the point where x = -2 on the graph to the parabola (the curve of a quadratic function), and then read the corresponding value on the y-axis by tracing this point to the y-axis.

On the graph, if we trace from the point x = -2, to the curve, we will find out that the value of y is 8.

Thus,

From y = r(x), we can write that

8 = r(-2)

∴ r(-2) = 8

hence, the value of r(-2) is 8

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The conversion of decimal number directly to binary number will be faster.

The number conversion deals with the operation to change the base of the number.

Binary number - It contains only 2 numbers that are 1 and 0.

Decimal number - It contains 10 numbers that are from 0 to 9.

Hexadecimal number - It contains 16 numbers that are from 0 to F.

Convert the decimal number 431 to binary will be

431 / 2 = 215 with 1 remainder

215 / 2 = 107 with 1 remainder

107 / 2 = 53 with 1 remainder

53 / 2 = 26 with 1 remainder

26 / 2 = 13 with 0 remainder

13 / 2 = 6 with 1 remainder

6 / 2 = 3 with 0 remainder

3 / 2 = 1 with 1 remainder

1 / 2 = 0 with 1 remainder

The decimal number 431 to binary number will be 110101111.

Convert first to hexadecimal and then from hexadecimal to binary. Then we have

(431)₁₀ = (1AF)₁₆ = (110101111)₂

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Answer:

Melanie's employer must pay the agency a sum of $1,091.67

Step-by-step explanation:

job = $52,400

agency fee = 25% of 1 month's pay

52,400 / 12 = $4,366.67

.25 x $4,366.67 = $1,091.67

The expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D

Algebraic expressions are expressions that consists of terms, variables, coefficients, and constants.

They are also made up of arithmetic operations such as division, addition, multiplication, subtraction, etc

From the information given, we have that;

B is the number of blue bikes

And there are 9 red bikes

The expression for the sum of blue and red bikes is written as;

B + 9

Thus, the expression that represents the sum of the number of blue bikes and the 9 red bikes is B + 9. Option D

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Answer:

B= 67

Step-by-step explanation:

Being vertically opposite angle