put them in order from least to greatest: 2.5 6.7 6.9 7.5 1.8 1.6

The equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]

Given,

m = [tex]\frac{-3}{4}[/tex]

The point = (8,-1)

The point-slope form of the line

[tex](y-y_{1} )=m(x-x_{1})[/tex]

Substitute the values in the equation

[tex](y-(-1))=-\frac{3}{4}(x-8)\\ y+1=-\frac{3}{4}(x-8)[/tex]

Hence, the equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]

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Only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.

We have a set of mixed numbers.

We have to identify which set of mixed numbers has a difference less than 1.

A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers. Any mixed fraction can be converted into normal fraction using the formula -

[tex]X\frac{Y}{Z} =\frac{Z\times X+Y}{Z}[/tex]

According to the question -

Let us solve them one by one (for difference to be less than 1, the denominator should be less than numerator) -

Hence, only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.

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Answer:

It will take approximately 20 years for the investment to double. The amount after 10 years will be $17,033.

Step-by-step explanation:

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The wavelength of the waves on a string that is vibrating at 220 MHz is 2.20 m. These waves move at a 4840 rpm rate as they move up and down the string.

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm). According to the available data, the wavelength is more frequently expressed in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (VL), ultraviolet (UV), and gamma radiation ().

V=∧F

V=220×22

V=4840m/s

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The cost of 8 oranges is $7.52

The first step is to find the cost of one orange

6 oranges cost 5.65

1 orange= 5.64/6

= 0.94

Therefore the cost of 8 oranges can be calculated as follows

= 0.94×8

= 7.52

Hence 8 oranges cost $7.52

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The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.

The Scale Factor is employed to scale shapes in different dimensions. Geometry teaches us about numerous geometrical shapes in two and three dimensions. The scale factor is a metric considering similar figures that appear the same but have distinct scales or measures.

The basic formula for computing this same scale factor is, Scale factor = Dimension of the new shape x Dimension of the original shape If indeed the original figure is scaled up, then the formula is expressed as Scale factor = Larger figure dimensions /Smaller figure dimensions.

The size of the ant = 1/2 inch.

the model size is = 1 foot.

                             = 1 foot = 12 inch

The scale factor of the model  =  Larger figure dimensions ÷ Smaller figure dimensions.

                                                  = 12/.5

                                                  = 24 inch or 2 foot

The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.

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The y-intercept is the amount she got as gifts during her graduation.

The equation in slope intercept form is $630 + $60b

The slope intercept form is used to write equations for equations for linear equations with two variables. The graph for a  slope intercept form is a straight line.

The form for  slope intercept form is: y = mx + b

Where:

The y-intercept is the constant. It represents the point where the slope touches the y-axis.

The first step is to determine how much are earnings are and how much the gift is.

The equations that would be used to determine this are:

a +2b = 750 equation 1

a + 4b = 870 equation 2

Where:

a = gift

b = amount earned weekly while working on the golf course

Subtract equation 2 from equation 1: 2b = 120

Divide both sides of the equation by 4: b = $60

Substitute for b in equation 1

a + 2(60) = 750

a + 120 = 750

a = 750 - 120

a = 630

The y-intercept is $630.

The equation in slope intercept form is: $630 + $60w

Where w is the number of weeks that Betty works.

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Answer:

1.76.

Step-by-step explanation:

1.32 ÷ 12 = 0.11

16 x 0.11 = 1.76.

Hope this helped! ..・ヾ(。＞＜)シ xx

Answer: If you're solving for the substitution method then your answer would be (1,3)

Step-by-step explanation:

Answer:

x = -4/5

y = 9/5

Step-by-step explanation:

-3y + 2x = -7

8x - 3y = -1

make one of the equations y=....

-3y + 2x = -7

-3y = -7 - 2x

  y = (-7 - 2x)/3

now put (-7 - 2x)/3 where y is in the other equation

8x - 3y = -1

8x - 3((-7 - 2x)/3) = -1

8x - 1*(-7 - 2x) = -1

8x + 7 + 2x = -1

solve for x

8x + 7 + 2x = -1

8x+2x = -8

10x = -8

x = -8/10

x = -4/5

now put -8/10 in one of the equations to get what y is

-3y + 2x = -7

-3y + 2(-8/10) = -7

-3y - 16/10 = -7

-3y = -7 + 16/10

-3y = -70/10 + 16/10

-3y = -54/10

y = -54/10 * -1/3

y = 18/10

y = 9/5

Answer$550.32

Step-by-step explanation: 7day = $320

commission = 8% of 2879

=230.32

 total earnings = 320 + 230.32

= 550.32

Answer:

[tex]{ \tt{f•g(x) = 4(2x + 5) {}^{2} }} \\ = { \tt{4(4 {x}^{2} + 20x + 25)}} \\ = { \tt{ {8x}^{2} + 80x + 100}} \\ \\ { \tt{f•g( - 3) = 8 {( - 3)}^{2} + 80( - 3) + 100 }} \\ { \tt{f•g( - 3) = 72 - 240 + 100}} \\ { \tt{f•g( - 3) = - 68}} \\ \\ \\ { \tt{g•f(x) = 2( {4x}^{2}) + 5 }} \\ { \tt{ = {8x}^{2} + 5 }} \\ { \tt{g•f( - 3) = 8 {( - 3)}^{2} + 5}} \\ { \tt{g•f( - 3) = 77}}[/tex]

The center of the given ellipse is given as (-1, 2)

Center of the Ellipse

To find the center of the ellipse, we need to rearrange the equation into the standard equation of ellipse.

[tex]4x^2 + 9y^2 + 8x - 36y + 4 = 0\\\frac{(x+1)^2}{2} + \frac{(y-2)}{4} = 1[/tex]

The center of the ellipse is given as

[tex]center = (-1, 2)[/tex]

The foci of the ellipse  are the reference points in an ellipse and it helps to derive the equation of the ellipse. There are two foci for the ellipse i.e F1 and F2

[tex]F_1= (-1 + \sqrt{5}, 2)\\ F_2 = (-1, -\sqrt{5}, 2)[/tex]

The center of the given ellipse is (-1,2) while the foci are stated above.

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The inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is  x < 4

The given parameters are

Flat cost = $58

Rate = $3 per gigabyte

Budget = Under $70

The equation is represented as:

Total cost = Flat cost + Rate * Number of gigabyte

So, we have

y = 58 + 3x

The budget is under 70

So, we have

58 + 3x < 70

Subtract 58 from both sides

So, we have

3x < 12

Divide both sides by 3

So, we have

x < 4

Hence. the inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is  x < 4

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The positive interval is (0,2) and the negative range is calculated as (-4,0) and (2,4).

A graph is used to show the relationship between variables on a coordinate plane.

The domain of the function is [-4,4].

The zeros are: -2,0 and 2.

The positive interval is between (0,2).

The range of negative values is (-4,0) to (2,4). This is the set of x values in the graph. The graph demonstrates that the x value is between -4 and 4.

Thus, the domain is [-4,4]. The zeros of the function: Where it crosses the x- axis. The graph touches the x-axis when it is at -2,0 and 2. As a result, the function has the following zeros:-2,0 and 2.

Positive interval:

On the graph, positive values range from x = 0 to x = 2.

Consequently, the positive interval is (0,2).

Negative duration:

This is the x values when the function gives a negative result.

The graph shows negative values from x = -4 to x = 0, then from x = 2 to x = 4.

The negative range is therefore (-4,0) and (2,4).

Hence, the positive interval is (0,2) and the negative range is (-4,0) and (2,4).

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The number of apples Chee bought is 2, and the number of peaches she bought is 8

From the question, we are to determine the number of apples, x, and the number of peaches, y, that Chee bought

From the given information,

She bought $6 worth of apples and peaches

and

Each apple costs $1 and each peach costs $0.50

Then, we can write that

$1 × x + $0.50 × y = $6

x + 0.50y = 6

Also,

She bought 4 times as many peaches as apples

That is,

y = 4x

Now, we will solve the system of equations graphically

x + 0.50y = 6

y = 4x

From the graph, the solution to the system of equations is x = 2, y = 8.

Hence, the number of apples Chee bought is 2, and the number of peaches she bought is 8

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According to the question, determine whether the given sequence converges or diverges.

The given sequence is: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} }[/tex]

Taking limits tends to infinity on both sides. And dividing numerator and denominator by [tex]n^{2}[/tex]

Therefore, the final term can be re-written as: [tex]a(n) = \frac{9+3n^{2} }{n+8n^{2} } = \frac{3}{8}[/tex].

Hence, the given sequence converges and the limit is [tex]\frac{3}{8}[/tex].

What converges and diverges in limits?

When the limits of the sequence exist and have finite value that means the sequence is a convergent sequence. The calculated value is a real number. And the tem divergence means limits do not exist.

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The equation of the line in slope-intercept form with a slope of -3/8 and y-intercept of (0 , 12) is y = (-3/8)x + 12.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given that the slope of the line is -3/8 and the y-intercept is (0 , 12), write the equation of the line by simply plugging in its values.

y = mx + b

y = (-3/8)x + 12

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The given statement is not correct because anyone above 18 years can vote.

It is given that if you are over 18 years old, then you vote in all elections.

We have to determine the truth value , if you are 21 years old and do not vote.

What is the truth value ?

Truth value is the attribute which states that whether the statement is true or false.

As per the question ;

If you are over 18 years old , then you vote in all elections, and if you are 21 years old and do not vote.

The criteria to vote in the elections is to be over 18 years.

Here ;

21 years age is greater than 18 years criteria , that's why it is not possible that you can't vote if you are 21 years old.

The statement is not correct.

Thus , the given statement is not correct because anyone above 18 years can vote.

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The solution using the square root property for given complex numbers would be x = 10i where i is an imaginary number.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,

where a, and b are real numbers and i is an imaginary number.

We have been given the equation of complex numbers x² = -100

Using the square roots property to solve the above equation

⇒ x² = -100

⇒ x = √-100

⇒ x = √(-1×10×10)

∵ i² = - 1 or i = √-1

Here i is an imaginary number.

⇒ x = 10(√-1)

⇒ x = 10i

Therefore, the solution of given complex numbers would be x = 10i where i is an imaginary number.

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Using trigonometric functions, the value of 2 cos x is equals to √3.

One of the six mathematical functions used to express the side ratios of right triangles, the trigonometric function includes the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). The graphic shows these six trigonometric functions in respect to a right triangle.

Cos (π/6) = √3/2

So. f(x) = 2 cos x

⇒ f(x) = 2 cos(π/6)

⇒ f(x) = 2 × √3/2

f(x) = √3

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Answer:

1470 in³, 716 in²

Step-by-step explanation:

The figure is a cylinder, and it's volume can be found using the following formula:

Volume of cylinder

= area of circle base ×height

= πr²h

Identify the value of r and h:

From the diagram, the radius (r) is 6 in. while the height (h) is 13 in.

Using the formula,

volume of cylinder

= π(6²)(13)

= 468π

= 1470 in³ (3 s.f.)

The surface area of a cylinder is the total area of all its faces, i.e. the sum of the area of its two circular bases and its curved surface area.

Formula

Surface area of cylinder

= 2πr² +2πrh

Surface area of cylinder

= 2(π)(6²) +2(π)(6)(13)

= 72π +156π

= 228π

= 716 in² (3 s.f.)

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Answer:

m = 5d

Step-by-step explanation:

m = 5d

The lowest possible integer value of x is 3 such that (x ≥ 3).

For the given question;

The area of rectangle A is bigger than the area of rectangle B.

The sides of the rectangle A are 2x-3 and 5 cm.

Area = length×breadth

Area A = (2x - 3)(5)

Area A = 10x - 15

The sides of the rectangle B are x = 2 and 3 cm.

Area = length×breadth

Area B = (x + 2)3

Area B = 3x + 6

As area B > area B

Then,

10x - 15 ≥  3x + 6

Solving the inequality;

10x - 3x ≥ 6 + 15

7x ≥ 21

x ≥ 3

Thus, the minimum value of the x is 3 to make the area A bigger than Area B.

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Answer: 81

Step-by-step explanation: The square root and the squared function cancel each other out

The number of ways can five of the nine us supreme court justices agree is 3024 ways.

The number of ways that five of the nine us supreme court justices agree will be calculated thus:

= 9! / 5!

= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2) / (5 × 4 × 3 × 2)

= 3024

There'll be 3024 ways.

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The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.  

With an example, what is compound interest?

Principal - $400

rate of interest is compounded annually

g(x) =  400( 1.03)ˣ equation 1.

Formula used

A = P( 1 + r )ⁿ

here n = x

Solution:

Putting the value of n, and principal in the formula

A = P( 1 + r )ⁿ ................... equation 2

now comparing both equation 1 and equation 2,

400( 1.05)ˣ =  400( 1 + r )ˣ

( 1.05)ˣ = ( 1 + r  )ˣ

1.05 = 1 + r

r = 1.05 - 1

r = 0.05

r % = 0.05 × 100

r % = 5 %

thus, the constant percent rate of change =  5 %

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The given lograthimic expression  log₃ y + 4 log₃ t can be written as log₃(yt^4).

According to the given question.

We have an logarithmic expression

log₃ y + 4 log₃ t

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the product  and power rule we know that

log(mn) = logm + logn

Thereofore, the given lograthimic expression  log₃ y + 4 log₃ t can be written as

log₃ y + 4 log₃ t

= log₃ y + log₃ t ^4

= log₃(yt^4)

Hence, the given lograthimic expression  log₃ y + 4 log₃ t can be written as log₃(yt^4).

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