3 (x - 17) < 9 (1 - 3x)

Answer:

first row is 11

2nd row is 16

3rd row is 34,41,25

Step-by-step explanation:

45-18-16=11

55-25-14=16

18+16=34

100-41-34=25

( 0, 5) , ( 1, 3) , (2, 1) are the only ordered pair of positive integer(x, y) that satisfy Linear inequality  2x+ y ≤ 5

The given linear inequality is 2x + y ≤ 5

This is a question of linear inequality

Linear inequality is solved as linear equality and than the signs are taken care of

if x= o

2(0) + y = 5

y = 5

if x= 1

2(1) +y = 5

2 + y= 5

y =3

If x= 2

2( 2) + y = 5

y=1

Hence, ( 0, 5) , ( 1, 3) , (2, 1) are the only ordered pair of positive integer(x, y) that satisfy Linear inequality 2x+ y ≤ 5

The correct question is how many ordered pairs of positive integers (x, y) is 2x + y ≤ 5?

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Answer: 8

Explanation: Based on the given conditions, formulate: 580800 ÷ 363 ÷ 200

Reduce the fraction: 8

Answer: 8

Answer:

the ans is 8.00 the first one

Step-by-step explanation:

the missing value (3,7),(8, y) is y = 21/8

Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.

Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.

Inverse variation is y = k. 1/x

given y = 7

x = 3

So, 7 = k. 1/3

So, the value of k = 21

We can conclude that the value of constant variation is 21

when x = 8, the value of y will be -

y = k.1/x

y = 21 . 1/8

y = 21/8

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you don’t have a negative side to the graph and your number is completely different

The points for the ordered pairs of the linear function has been plotted in the graph shown in the image attached below.

A linear function is a straight line graph consisting of domain elements (x-values) and their corresponding range elements (y-values).

Given the function, y = 1/2x + 1 having the following domain elements (x-values):

D: {-8, -4, 0, 2, 6}

Find the corresponding y-value to each of the x-values by substitution

When x = -8, then:

y = 1/2(-8) + 1

y = -4 + 1

y = -3

(-8, -3)

When x = -4, then:

y = 1/2(-4) + 1

y = -2 + 1

y = -1

(-4, -1)

When x = 0, then:

y = 1/2(0) + 1

y = 0 + 1

y = 1

(0, 1)

When x = 2, then:

y = 1/2(2) + 1

y = 1 + 1

y = 2

(2, 2)

When x = 6, then:

y = 1/2(6) + 1

y = 3 + 1

y = 4

(6, 4)

Thus, the points for the ordered pairs of the linear function has been plotted in the graph shown in the image attached below.

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Answer:

this cant be simplified further

Step-by-step explanation:

17 is prime

Answer:

associative property

Step-by-step explanation:

because the variables match

Answer: I think its 4/16

Step-by-step explanation:

please let me know if I'm wrong.

Question 15:

Option B is the correct answer

If the Patriots win their division, then they will go to the playoffs:

- Invalid conclusion was made.

Question 16:

Option D is the correct answer.

Conclusion: Ethan's boy scout dues are free:

- Drawn using the law of detachment.

The Law of Detachment states that we must detach ourselves from the outcome in order to allow what we desire to materialize in the physical universe.

Example:

If p equals q and p is also true. Then q is true.

We have,

- If the Patriots win their next game, then they will win their division.

- If the Patriots win their next game, then they will go to the playoffs.

Each statement's conclusion is drawn using the law of detachment.

Therefore, if the patriots win their division, then they will go to the playoffs is an invalid conclusion made.

Ethan sold $1000 worth of popcorn.

Conclusion: Ethan's boy scout dues are free.

This conclusion was drawn using the law of detachment.

Thus,

Therefore, if the patriots win their division, then they will go to the playoffs: - Invalid conclusion made.

Conclusion: Ethan's boy scout dues are free:

- Drawn using the law of detachment.

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Sure I can help!!!!

Step by step explanation: - + - = -

2/3+1/2 (LCM is 6)

=2/3 (6) + 1/2 (6)

=4 + 3

=7

I really hope this helps!!!! have a great day!!!

Answer:

12.56 km

Step-by-step explanation:

C = 2πr

= 2 x 3.14 x 2

= 12.56 km

Answer:

12.56km or 12,560m

Step-by-step explanation:

c = 2πr
c = (2)(3.14)(2)
c = (6.28)(2)
c = 12.56

The difference  [tex]f^{}[/tex] between the charge for large lawns and the charge for small lawns is given by the linear equation   [tex]f^{}[/tex]  = 5H +4.40, which is D option

For small lawns the company charge is given by the linear  equation S = 23H + 15.95.

For large lawns, the company charge is given by the linear equation L = 28H + 20.35.

  [tex]f^{}[/tex]  represent the difference between the charge for large lawns and the charge for small lawns.

So, the equation can be written as   [tex]f^{}[/tex]  = (28H + 20.35) - (23H + 15.95)

this can be simplified as
 [tex]f^{}[/tex]  = 28H + 20.35 -23H - 15.95

 [tex]f^{}[/tex] = 28H- 23H + 20.35 - 15.95

 [tex]f^{}[/tex]  = 5H + 4.40

Hence, the difference between the charge for large lawns and the charge for small lawns is given by the linear equation   [tex]f^{}[/tex]  = 5H +4.40, which is D option

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The lengths of the sides of the quadrilateral are 10, 12, 14, 16, respectively.

Quadrilaterals are figures with four sides, the statement indicates that such lengths are four consecutive even integers. Two even numbers are consecutive when their difference is equal to 2.The mathematical definition of the perimeter is shown below:

52 = x + (x + 2) + (x + 4) + (x + 6)

52 = 4 · x + 12

4 · x = 40

x = 10

Then, the lengths of the sides of the quadrilateral are 10, 12, 14, 16, respectively.

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Yo what up?, Answer:

2/3 yards.

Best Explanation Possible:

Nothing lol just do the math.

1/6 x 4 = 4/6 = 2/3 of a yard per hour

LOL have a good day hope you do good in school kiddo.

We can state that, 5 represents the output of the function at x = 2.

A function is a relation whereby each input gives only one possible output for the function.

For example, "f(x)" is the output of a typical function that is given by an input of "x".

Given the function statement, f(2) = -5, the input is x = 2, the output is -5. This means that, the function that has an input of 2, will give an output of -5.

-5, therefore, represents the output of the function when the input, x = 2, that is, f(-2) = -5.

Thus, we can state that, 5 represents the output of the function at x = 2.

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The property with each of Tyrone's steps for solving the equation is;

4x = 2 - 4(2 - 3x)

4x = 2 - 8 + 12x

4x = - 6 + 12x

4x - 12x = -6

-8x = - 6

x = -6 / - 8

x = 3/4

Therefore, the solution to Tyrone's equation for x is 3/4

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Answer:

At 10 hours both companies charge the same rate. So Company A is cheaper if the time is less than 10 hours and after 10 hours, company B is cheaper.

Step-by-step explanation:

It is given that Chloe is deciding between two landscaping companies for her place of business. Company A charges $70 per hour and a $150 equipment fee. Company B charges $55 per hour and a $300 equipment fee. Let A A represent the amount Company A would charge for t t hours of landscaping, and let B B represent the amount Company B would charge for t t hours of landscaping.

Now, we need to write an equation for each situation, in terms of t , t, and determine the number hours, t , t, that would make the cost of each company the same.

Now,

Let A(t) = 70t + 150

Let B(t) = 55t + 300

Further, on equating both the equations at same rate to determine the time t;

=> 70t + 150 = 55t + 300

=> 15t = 150

=> t = 10

Therefore, at 10 hours both companies charge the same rate. So Company A is cheaper if the time is less than 10 hours and after 10 hours, company B is cheaper.

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Answer:

FG = 51

Step-by-step explanation:

2/5 of 85 = 34

The value of EF is 34

So the value of FG would be the value of EG - EF

85 - 34 = 51

The equation that has no solution will be:

a. -2x + 4 = 2x + 4

b. 12x-2x = 10x -8

d. 3x - 12 = 3(x-4) +1

It should be noted that -2x + 4 = 2x + 4

-2x - 2x = 4 - 4

-4x = 0

It has no solution

Also, 12x-2x = 10x -8 and 3x - 12 = 3(x-4) +1has no solution.

The only equation with solution will be:

3x + 10 = 2x

3x - 2x = -10

x = -10

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Answer

I think it should be

2^3x =10         //log

log(2^3x) = log(10)

3x*log(2) = log(10)

3x = log(10) / log(2)

3x = log₂ 10

Answer: log₂ 10 = 3x

Answer:

Angle W

Step-by-step explanation:

An angle can be identified by the order of points, with the vertex in the middle (like angle WXY and angle YXW) or by the vertex (angle X).

You should be aware of the fundamental theorem of algebra (FTCoA). If a quadratic has roots at [tex]r_1[/tex] and [tex]r_2[/tex], then we can factorize it as

[tex](x - r_1) (x - r_2)[/tex]

Expanding, this is equivalent to

[tex]x^2 - (r_1 + r_2) x + r_1 r_2[/tex]

Now, if we can also write this

[tex]x^2 + bx + c[/tex]

then we must have

[tex]x^2 + bx + c = x^2 - (r_1 + r_2) x + r_1r_2 \\\\ ~~~~ \implies \begin{cases} b = -(r_1 + r_2) \\ c = r_1r_2 \end{cases}[/tex]

(By the way, these are known as Vieta's formulas.)

We're told that the quadratic,

[tex]p(x) = 3x^2 - 6x + 8,[/tex]

has roots [tex]x=\alpha[/tex] and [tex]x=\beta[/tex], so by the FTCoA, we can write

[tex]p(x) = 3 (x - \alpha) (x - \beta)[/tex]

Expanding this last form, we have the identity and exact values

[tex]3x^2 - 6x + 8 = 3 (x^2 - (\alpha + \beta) x + \alpha\beta) \\\\ ~~~~ \implies x^2 - 2x + \dfrac83 = x^2 - (\alpha + \beta) x + \alpha\beta \\\\ ~~~~ \implies \begin{cases} \boxed{\alpha + \beta = 2} \\\\ \boxed{\alpha\beta = \frac83} \end{cases}[/tex]

(i) We want to construct a new quadratic [tex]p_{\rm i}(x)[/tex] such that its roots are [tex]x=\alpha^2[/tex] and [tex]x=\beta^2[/tex]. By the FTCoA, we would have

[tex]p_{\rm i}(x) = (x - \alpha^2) (x - \beta^2)[/tex]

Expanding,

[tex]p_{\rm i}(x) = x^2 - (\alpha^2 + \beta^2) x + \alpha^2\beta^2[/tex]

Now, notice that

[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 2^2 - 2\cdot\dfrac83 = -\dfrac43[/tex]

[tex]\alpha^2\beta^2 = (\alpha\beta)^2 = \left(\dfrac83\right)^2 = \dfrac{64}9[/tex]

It follows that

[tex]p_{\rm i}(x) = x^2 + \dfrac43 x + \dfrac{64}9[/tex]

which we can rewrite with integer coefficients by scaling each term by a factor of 9 to get

[tex]p_{\rm i}(x) = \boxed{9x^2 + 12x + 64}[/tex]

(ii) Now we want a quadratic [tex]p_{\rm ii}(x)[/tex] with roots at [tex]2\alpha[/tex] and [tex]2\beta[/tex]. This means

[tex]p_{\rm ii}(x) = (x - 2\alpha) (x - 2\beta) \\\\ ~~~~~~~~ = x^2 - 2 (\alpha + \beta)x + 4\alpha\beta[/tex]

[tex]\implies p_{\rm ii}(x) = x^2 - 4x + \dfrac{32}3[/tex]

or more cleanly, scaling by 3,

[tex]p_{\rm ii}(x) = \boxed{3x^2 - 12x + 32}[/tex]

(iii) Now the roots are [tex]x=\frac\alpha2[/tex] and [tex]x=\frac\beta2[/tex], which gives

[tex]p_{\rm iii}(x) = \left(x - \dfrac\alpha2\right) \left(x - \dfrac\beta2\right) \\\\ ~~~~~~~~ = x^2 - \dfrac{\alpha + \beta}2 x + \dfrac{\alpha\beta}4[/tex]

[tex]\implies p_{\rm iii}(x) = x^2 - x + \dfrac8{12}[/tex]

[tex]\implies p_{\rm iii}(x) = \boxed{12x^2 - 12x + 8}[/tex]

(iv) If the roots are [tex]x=\frac\alpha{\alpha+1}[/tex] and [tex]x=\frac\beta{\beta+1}[/tex], we have

[tex]p_{\rm iv}(x) = \left(x - \dfrac\alpha{\alpha+1}\right) \left(x - \dfrac\beta{\beta+1}\right) \\\\ ~~~~~~~~~= x^2 - \left(\dfrac\alpha{\alpha+1} + \dfrac\beta{\beta+1}\right) x + \dfrac{\alpha\beta}{(\alpha+1)(\beta+1)}[/tex]

Note that

[tex]\dfrac\alpha{\alpha+1} + \dfrac\beta{\beta+1} = \dfrac{\alpha(\beta+1) + \beta(\alpha+1)}{(\alpha+1)(\beta+1)} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{2\alpha\beta + \alpha + \beta}{\alpha\beta + \alpha + \beta + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{\frac{16}3 + 2}{\frac83 + 2 + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{22}{17}[/tex]

[tex]\dfrac{\alpha\beta}{(\alpha+1)(\beta+1)} = \dfrac{\alpha\beta}{\alpha\beta + \alpha + \beta + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \dfrac{\frac83}{\frac83 + 2 + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \dfrac8{17}[/tex]

[tex]\implies p_{\rm iv}(x) = x^2 - \dfrac{22}{17}x + \dfrac8{17}[/tex]

[tex]\implies p_{\rm iv}(x) = \boxed{17x^2 - 22x + 8}[/tex]

482 rounded off to nearest 100 is 500 and 482 rounded off to nearest 1000 is zero.

By maintaining a number's value while moving it closer to the next number, rounding off makes the number easier to understand. It is done for entire numbers as well as decimals at different places such as hundreds, tens, and tenths. To maintain the major figures, numbers are rounded off.

At a concert there were 482 people in the audience:

(a) With a number line, 482 was rounded to the nearest hundred.

(b) Since 4 is the hundredth value of 482 and there is no previous thousand to 499. So when 499 is rounded to the nearest thousand, equals 0.

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Step-by-step explanation:

you can ask any questions for clarification

Answer: d. $264 hope this helps :)

Step-by-step explanation:12x22=264

Reyna will need 0.048 quart of orange juice.

In this question, we have been given a recipe for a punch call for 12 fluid ounces of orange juice.

Reyna needs to make 4 batches of punch for a party.

We need to find number of quarts of orange juice Reyna will need.

From given conditions, we formulate:

= 4 × 12 ÷ 1000

= 12 ÷ 250                  .................(Separate out the common factor)

= 6/125

= 0.048 quart

Therefore, Reyna will need 0.048 quart of orange juice.

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Answer: 3/4

Step-by-step explanation:

You have to find one single number that goes into both the numerator and the denominator. In this case, it was 8.

24/8 = 3

32/8 = 4

Answer:

1st one is 3/4

second one is 32

I cant really see the third one

fourth one is $1.03

Step-by-step explanation:

The answer to the formula are-

Part 1:  7√6 - 4√6

As both the digits have the same value √6. It means they can simply be added with sign to solve.

=  7√6 - 4√6

Take √6 common from both;

= √6(7 - 4)

= 3√6

Thus, the simplification of the expression is 3√6.

Part 2: -0.7√7 + 2.3√7

Here, also the common term is √7.

= √7( -0.7 + 2.3)

Simply add the number with sign.

= 1.6√7.

Thus, the simplification of the number is 1.6√7.

Part 3: √45 + √20

In thus, first write the number in its prime factors;

= √3×3×5 + √2×2×5

Take the root of 3 and 2 from the first and second digits of expression.

= 3√5 + 2√5

Now, both have the same term √5.

= √5(3 + 2)

Do the addition;

= 2√5

Thus, the simplification of given expression is 2√5.

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