7. A. Write a second equation so that the system will have no solutions. B. Write a second equation so that system
will have infinitely many solutions. 2x - 4y = 22

7x - 3 > 24 can be described as an inequality.

An algebraic expression consists of unknown variables, numbers and arithmetic operators.  It does not contain any equality or inequality symbols.

Variables are number represented with a letter in an expression. Numbers includes 1, 2, 3 etc. Basic operators are addition, subtraction, multiplication and division.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

For example x > y.

Therefore, we can denote 15x -10 as an expression and 7x - 3 > 24 is denoted as an inequality.

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The center of the circle is  (3,-3)   and the radius is 6  , the graph is drawn below .

In the question ,

the equation of the circle is given as

(x-3)²+(y+3)² = 36 ,

we know that the general equation of the circle is

(x - h)² + (y - k)² = r²

where , the center is (h,k) and the radius is r .

So , on comparing the given equation with general equation of the circle , we get

h = 3 and k = -3

and r² = 36

So, r = 6 .

the center is (h,k) = (3,-3)

and the radius is 6 .

the graph of the circle (x-3)²+(y+3)² = 36 is shown below .

Therefore , The center of the circle is  (3,-3)   and the radius is 6 .

The given question is incomplete , the complete question is

Graph the circle (x-3)²+(y+3)² = 36 and find the radius and center of the circle ?

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The percentage is the measure of the portion of a quantity present in the whole. The remaining computers are 75.

Percentage of quantity is proportional to its portion or fraction in a whole.

To convert the percentage into fraction divide the percentage value by 100.

Suppose the total number of employee's computer be x.

Then, as per the question after adding 25 more computers, the following equation can be written,

85% of x = 80% of x + 25

=> 85x/100 = 80x/100 + 25

=> 85x/100 - 80x/100 = 25

=> 5x/100 = 25

=> x = 500.

The remaining computers are  given as

15% of x = 15/100 × 500

              = 75

Hence, the number of remaining employee's computer after adding 25 more computers are 750.

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Answer:  2 abd the answer is that

Step-by-step explanation:

Answer: 40k⁶-15k⁴

Step-by-step explanation:

[tex](8k^4-3k^2)(5k^2)=\\\\8k^4(5k^2)-3k^2(5k^2)=\\\\8(5)(k^{4+2})-3(5)(k^{2+2})=\\\\40k^6-15k^4[/tex]

Result of [tex]8k^{4} -3k^{2}[/tex] multiplied by [tex]5k^{2}[/tex] is [tex]40k^{6}-15 k^{4}[/tex]

Algebra and Exponent

To answer this question you need to know about algebra and exponent rule.

[tex]8k^{4} -3k^{2}[/tex] multiplied by [tex]5k^{2}[/tex]

It means the operation will become:

[tex]5k^{2} (8k^{4} -3k^{2} )=[/tex]

The way to calculate algebraic multiplication with 2 or more variables is the way I call 'rainbow'.

[tex]5k^{2} (8k^{4} -3k^{2} )=[/tex]

[tex]5k^{2}[/tex] multiplied by [tex]8k^{4}[/tex],  [tex]5k^{2}[/tex] multiplied by [tex]-3k^{2}[/tex] first, then the two are added.

[tex](5k^{2}) (8k^{4} )=[/tex]

The way to multiply this is by: numbers multiplied by numbers and letters multiplied by letters

[tex]=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )[/tex]

Then how to multiply the letters, this uses the rule of exponents. If there are 2 same variables are multiplied, then the result is a variable with the power of the sum of the two powers.

[tex]a^{m} a^{n} =a^{m+n}[/tex]

Which means,

[tex]k^{2}k^{4} =k^{6}[/tex]

Then,

[tex]=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )\\=40k^{6}[/tex]

Also same with above,

[tex]=(5k^{2} )(-3k^{2} )\\=((5)(-3))((k^{2} )(k^{2} )\\=-15k^{4}[/tex]

[tex]=5k^{2} (8k^{4} -3k^{2} )\\=((5k^{2})(8k^{4})+((5k^{2})(-3k^{2})\\=(40k^{6})+(-15k^{4} )\\=40k^{6}-15k^{4}[/tex]

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Answer: B

Step-by-step explanation:

2.5/4.5 = x/2.25

x = 1.25 in

If the angle A and angle B are supplementary then the measure of angle A is = 93° .

In the question ,

it is given that

the two angles A and B are supplementary ,

we know that when two angles are supplementary their sum is 180° .

So , the sum of measure of angle A and angle B will be 180° ,

that is ,

given that measure of angle A = (7x - 12)°

measure of angle B = (7x - 18)°

So , according to the question ,

(7x - 12) + (7x - 18) = 180°

7x + 7x - 12 - 18 = 180

14x - 30 = 180

14x = 180 + 30

14x = 210

x = 210/14

x = 15

So , the measure of angle A = (7*15 - 12) = 105 - 12 = 93°

Therefore , If the angle A and angle B are supplementary then the measure of angle A is = 93° .

The given question is incomplete , the complete question is

Angle A and angle B are supplementary angle. If angle A = (7x - 12)° and angle B = (7x - 18)° , then find the measure of angle A ?

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The polynomial function with the lowest degree with a leading coefficient of 1 and zeros is 1, -1(multiplicity 3), and 3i is [x³+(2-3i)x²-(3+6i)x+9i].

So, the equation of the curve with a leading coefficient of 1 or the polynomial function with a leading coefficient of 1 f(x) can be expressed as (x-a)* (x-b)* if a, b, and c are the zeros of a polynomial (x-c).

Now, calculate as follows:

Therefore, the polynomial function with the lowest degree with a leading coefficient of 1 and zeros is 1, -1(multiplicity 3), and 3i is [x³+(2-3i)x²-(3+6i)x+9i].

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Answer:

-2<x<3

Step-by-step explanation:

I have attached the work required to solve this problem as well as a pretty good explanation to each step.

Answer:

the first, second and last option

Step-by-step explanation:

The amount owed by the debtor is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer:

B )  x = 2 + √2 or x = 2-√2

Step-by-step explanation:

See attachment...

Hope this helps! :)

The value of the expression given as 26 + 15 is -11.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, the value of -26 + 15 will be:

= -26 + 15

= -11

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Area of rectangle is the product of Length and Width, so by using this the length of garden will be 13 feet.

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a type of quadrilateral. As a result, it is also referred to as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

suppose x = width of rectangular garden.

length of the garden is  5 feet longer than width.

now, x+5 = Length

Area of rectangle L X B = [tex]x X(x+5)[/tex]

Garden's area is = 104 square feet

Then,

[tex]x X (x +5) = 104\\x^{2} + 5x - 104=0\\(x-8)(x+13)=0\\x=8,-13[/tex]

Now, width ==8

Therefore, Length = x+5= 13

13feet is the length of the garden.

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Answer:

( 3 , 0 )

Step-by-step explanation:

When the reflection is over the y-axis , the y-coordinate is the same

and x-coordinate changes its Sign

So for ( -3 , 0) is reflected over y-axis

Then x-coordinate = 3

Then y-coordinate =0

So the new point = ( 3 , 0 )

The machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test using the normal distribution.

What is Normal Distribution?

The Normal Distribution, often known as the Gaussian Distribution, is the most important continuous probability distribution in probability theory and statistics. It is also referred to as a bell curve on occasion. In every physical science and in economics, a huge number of random variables are either closely or precisely described by the normal distribution. Additionally, it may be used to roughly represent various probability distributions, reinforcing the notion that the term "normal" refers to the most common distribution.

Let X denotes the scores.

In the question, It is given that:

Normal distribution with p=400 and 60.

[tex]X \sim N(\mu=400, \sigma=60)\\$$$\frac{X-\mu}{\sigma}(=Z) \sim N(0,1)$\\i.e. $P(Z \leq z)=\Phi(z)$[/tex]

Let 'a' be the score to be in the top 10% of all machinists.

[tex]\begin{aligned}&P(X \leq a)=1-0.10=0.90 \\&\text { or, } P\left(\frac{X-\mu}{\sigma} \leq \frac{a-400}{60}\right)=0.90 \\&\text { or, } \Phi\left(\frac{a-400}{60}\right)=0.90=\Phi(1.282) \\&\text { or, } \frac{a-400}{60}=1.282 \\&\text { or, } \mathbf{a}=\mathbf{4 7 6 . 9 2}\end{aligned}[/tex]

So,

The score a machinist need in order to be in the top 10% is 476.92.  

Hence,

a machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test.

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Answer: [tex]\frac{8.1}{5}[/tex]

Step-by-step explanation:

First of all, I multiplied both sides by 5.

8 x 5 is 40, and 13 x 5 is 65.

This gives 65/40

Now, I divide 65 and 40 by 8.

65/8 is 8.1

and 40 divided by 8 is 5.

So the answer is 8.1/5

The linear function is 2/3 x=y-1. Therefore, option D is the correct answer.

A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.

Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.

Option A:

In the function y=3x², the highest degree is 2, so it is quadratic function.

Option B:

The function y=1/3x is not a linear function.

Option C:

In the function y=x³+5, the highest degree is 3, so it is cubic function.

Option D:

In the function 2/3 x=y-1, the highest degree is 1, so it is linear function.

The linear function is 2/3 x=y-1. Therefore, option D is the correct answer.

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The expression is an arithmetic progression and the solution is

aₙ = a + ( n - 1 ) d

where a = 1

d = -1

n = 82

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the number of terms n = 82

Let the first term of the arithmetic progression be a = 1

Now , the common difference is d = -80 - ( -79 )

                                                         = -1

So , the expression for arithmetic progression is :

aₙ = a + ( n - 1 ) d

Substituting the values , we get

a₈₂ = 1 + ( 82 - 1 ) ( -1 )

a₈₂ = 1 + ( -81 )

a₈₂ = -80

And ,

a₈₁ = 1 + ( 81 -1 ) ( -1 )

a₈₁ = 1 + ( - 80 )

a₈₁ = -79

And so on ,

so , the expression is

aₙ = a + ( n - 1 ) d

where n = 82

d = -1

And the first term is a = 1

Hence , The expression is an arithmetic progression and the solution is

aₙ = a + ( n - 1 ) d

where a = 1

d = -1

n = 82

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Here is the proof:

1. Length AB = Length DC

2. Angle BAC = Angle ACD (AB is parallel to CD, so the opposite interior angles are equal)

3. AC length = AC length (2 lines coincide)

Principle of Side - Angle - Side

then the two triangles are said to be congruent

So Length BC = Length DA

Congruence is a condition where two flat shapes have the same size and are said to be congruent.

The characteristics of two triangles that are said to be congruent are:

1. When the pairs of corresponding sides are equal in length. Usually called the side-by-side criterion.

2. Two pairs of corresponding sides are equal in length and the angles between them are equal. Commonly referred to as the side-angle-side criterion.

3. Two pairs of congruent angles and the same side lengths. Also known as angle-side-angle

After doing proportional we will get:
i) Express y in terms of x : y = kx

ii) The value of y when x = 11 is 33

iii)  the value of x when y = 12 is 4

What is proportional?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality as well as proportionality constant, then the two sequences of numbers are proportional as well as directly proportional. If corresponding elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences seem to be inversely proportional. This definition is frequently expanded to include connected variable quantities, also known as variables. Variable has a different meaning in mathematics than it does in everyday language (see variable (mathematics)); such two concepts share the same name due to a shared etymology.

i) y ∝ x

y = kx

when y = 6, x = 2

6 = 2k

k = 3

y = kx

ii) y = 3x

y = 3(11)

y = 33

iii) y = 3x

12 = 3x

x = 4

iv) For the graph:

x  0  1  2

y  0  3 6

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In the given function the rate of change is -2 and the initial value is 7. Therefore, Harry is incorrect.

The given function is y=7-2x.

The rate of change, or the slope, is calculated as Δy/Δx , or (y2−y1)/(x2−x1). The slope-intercept equation of a line is y=mx+b , where m is the slope and b is the initial value.

Given that, the rate of change is 7 and the initial value is -2.

In the given function y=7-2x

Here, slope or the rate of change is -2 and the y-intercept or initial value is 7.

In the given function the rate of change is -2 and the initial value is 7. Therefore, Harry is incorrect.

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(7x-30) is the expression which you can use that is equivalent to 5x -2(15-x).

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Given: [tex]5x-2(15-x)[/tex]

On solving the above equation we get ,

⇒ 5x - 2 (15) + 2 (x)

⇒ 5x - 30 + 2x

⇒ (5x + 2x) - 30

⇒(7x - 30)

Hence, we can say that (7x-30) is the expression which we can use and that is equivalent to 5x -2(15-x).

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Answer:

Step-by-step explanation:

a; i

b; i

Step-by-step explanation:

The unit rate per carton is 2

The 8 bushels of apples cost is $63.60 i.e, option(A.)

What do you mean by Cost ?

           Cost (c) : is the total cost of the purchase.

           Rate (r) : is the cost of each individual item.

            Number (n) : is the number of items you want to purchase.

      These are related in the following way:

      c = n * r

Given,

Bushels of apples cost = $7.95

8 bushels of apples cost will be = $7.95 * 8

                                                     = $63.6 or $63.60

Hence, the 8 bushels of apples cost is $63.60 i.e, option(A.)

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Answer:

∴ x = 10.7 (to 3sf), y = 18

Step-by-step explanation:

(3x)° + (4x-15)° = 90° (right angle given) ------ equation (1)

(3x)° + (4x-15)° + (5y)° = 180° (adjacent angles on a straight line) ------ equation (2)

From equation (1),

3x + 4x - 15 = 90

              7x = 75

             ∴ x = 10.7 (to 3sf)

Subtract equation (1) from equation (2):

(3x+4x-15+5y) - (3x+4x-15) = 180 - 90

                                      5y = 90

                                     ∴ y = 18

Shape of the distribution of the mean is appropriately normal.

The sampling distribution for a given population is the frequency distribution of the different outcomes that can occur for a population statistic.

In statistics, the population is the entire pool from which statistical samples are drawn. Population can refer to an entire group of people, things, events, visits, or measurements. Populations can therefore be described as aggregated observations from subjects grouped according to common characteristics.

From the given information

X:- impact force produced

X follows normal distribution with mean 30 and standard deviation of 3

n=3

As we know that when random sample is drawn from normal population then sample mean always follows normal distribution irrespective with sample size.

Shape of the distribution of the mean is appropriately normal.

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