Simplify each expression. 25¹/₂

( 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:

this cant be simplified further

Step-by-step explanation:

17 is prime

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: 2

Step-by-step explanation:

= Convert  1 2/3 to an improper fraction (which is 5/3)

= Convert 1 1/5 to an improper fraction (which is 6/5)

= Proceed to cancel out the common factor of 5 so your answer should start to look like this

1/3 * 6

= Now cancel the common factor which is three

Therefore your answer is 2

Hope it helps ^^

Answer:

1/2,187

1/367

3^-7

Step-by-step explanation:

I hope this helped, have an amazing day! :D

The normal price of the car on the basis that the sale price of the car was £7500 is £10,000.

The fact that the normal prices are reduced by 25% means that the actual price paid eventually is 75%, which is 100% minus discount of 25%, hence, the actual price of £7500 paid eventually represents 75% of normal price

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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

Answer: d. $264 hope this helps :)

Step-by-step explanation:12x22=264

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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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!!!

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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Answer:

[tex]Y=\frac{1}{2}x +2[/tex]

Step-by-step explanation:

When y=2,X=0

When Y =7,X=10

X coordinates come first

(0,2)(10,7)

(x1,y1)(x2,y2)

To find the slope(M)=y2 -y1/x2 -x1

M=7-2/10-0

M=5/10=1/2 (Simplest form)

The equation of a line is given by Y=Mx + C

Where c is the Y intercept which is 2

- The equation of the line = Y=[tex]\frac{1}{2} x +2[/tex]

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:

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:

Step-by-step explanation:

m= [ -3-(-3)] ÷ [-8-7} = 0

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the y-intercept.

y= mx+b

-3= (0)(7)+b

b=-3

Write the equation in slope intercept form as:

y= mx+b

y= (0)x-3

y= -3

Hence, the equation of the line is y= -3.

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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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]

The value of the given expression for x=1/1250is 3/5. The correct option is (G).

Given the expression is f(x)=[tex]3x^{\frac{1}{3}}[/tex].

The cube root of a number is the factor that we want multiply by itself three times to get that number. The symbol for the cube origin is 3  cube roots, the last cube root. Finding the cube root of any number is the opposite of cubing a number.

We will simplify the given expression by using substitution method and cube root.

Firstly, we will substitute x=1/125 in the given expression f(x)=[tex]3x^{\frac{1}{3}}[/tex], we get

f(x)=[tex]3\left(\frac{1}{125}\right)^{\frac{1}{3}}[/tex]

As we know that the cube root of √125 is 5.

Now, we want to simplify the above equation, we get

f(x)=3(1/5)

f(x)=3/5

Hence, the value of [tex]f(x)=3x^{\frac{1}{3}}[/tex] for x=1/125 is 3/5.

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Answer

I think it should be

Answer:

[tex]\boldsymbol{\boxed{f(-4) = -1}}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x) = \left \{ {{x + 3, x < -1} \atop {-4x -2,x \geq 1}} \right.[/tex]

[tex]-4 < -1 \Longrightarrow f(-4) = -4 + 3 =-1[/tex]

[tex]\boxed{f(-4) = -1}[/tex]

Answer:

The answer is C = 0.652 in standard form

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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Based on the estimated number of defective batteries and the number of batteries that were actually defective, the percent error of Jake's estimate is 20%

The percent error of a problem can be found by the formula:
= (Expected results - Actual results) / 100%

Expected results = 12 defective batteries

Actual results = 10 defective batteries

Jake's percentage error is therefore:

= (12 - 10) / 100%

= 2 / 10 x 100%

= 0.2 x 100%
= 20%

In conclusion, the percent error of Jake's estimate is 20%.

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Answer:

Step-by-step explanation:

6n - 12 = 3( 2n- 4 )

6n - 12 = 6n - 12

0 = 0

this equation is always true

By solving the percent application, the result is 45% of 120 is 54 and 81 is 75% of 108.

(A) 45% of 120

Multiply 45/100 with 120 =(45/100) x 120 = (45 x120) / 100 = 54.

(B) 81 is 75%

Formula = Number x 100/Percent

             = 81 x 100/ 75 = 108

Following shows the steps on how to derive this formula and find out 75% of what number is 81. Then take 100% of that figure. Setup the equation

81/75% = Y/100%

Solve for Y

Using cross multiplication of two fractions, we get

75Y = 81 x 100

75Y = 8100

Y = 8100

100 = 108

Hence, by solving the percent application, the result is 45% of 120 is 54 and 81 is 75% of 108.

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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).

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 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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We get that an equation to represent this relationship the relation of increase in radius with respect to time as R = r + 16 t where t is the time and r is the initial radius.

We are given that, the wave travels at a rate of 16 feet / sec when George jumps off a tire swing in the circular pond.

So, this means that the radius of the wave increases by 16 feet in every second.

Now, let the initial radius be r and the radius after t seconds be R.

So, the equation will become:

R = r + 16 t

where 16 t represents the increase in radius in t seconds.

Therefore, we get that an equation to represent this relationship the relation of increase in radius with respect to time as R = r + 16 t where t is the time and r is the initial radius.

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