What are the solution(s) of 2(x+3)²/₃=8 ?

The slope can be found as the quotient or rise/run.

Rise - difference of y-coordinates of two points, run - difference of x-coordinates of same two points.

Find the slope using the first two pairs of coordinates in the table:

The y-intercept is the point of intersection of the line with the y-axis.

This point has x = 0 coordinate. On the table we can see the corresponding y- coordinate is  - 2:

The equation of the line is obtained by substituting the values of m and b into slope-intercept form:

The slope is 1/3 and the y-intercept is -2, so the equation is:

y = (1/3)*x - 2

if we use the first two pairs on the table we get:

(-3, -3) and (0, -2)

Then the slope of the linear relation will be:

a = (-2 - (-3))/(0  - (-3)) = (-2 + 3)/3 = 1/3

The slope is 1/3.

We can see that the point (0, -2) is on the table, so the y-intercept is y = -2

How to write the equation?

The linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Then we will get:

y = (1/3)*x - 2

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After rationalizing the denominator for the expression √3 x / 2y, we get that the result is [√6xy)] / 2y.

The removal of a radical or imaginary number from the denominator of an algebraic fraction is referred to as rationalization. That is, eliminate the radicals from a fraction to leave only a rational integer in the denominator.

Rationalizing the divisor suggests that you get eliminate the novel within the divisor. 

by the rules of radicals, We can rephrase this as √(5x) / √(2y)

The expression will then be multiplied by √(2y) / √(2y).  Keep in mind that this results in 1, and multiplying this by the first expression has no effect on the original issue.

On multiplying we get-

[√(3x) * √(2y)] / [√(2y) * √(2y)]

[√6xy)] / 2y 

Therefore, after rationalizing the denominator for the expression √3 x / 2y, we get that the result is [√6xy)] / 2y.

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The required simplification of rational expression is 2c + 3.

What is a rational number?

Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.

Simplifying the rational expression: 6c² + 9c / 3c

Given a rational expression,

6c² + 9c / 3c

On simplifying, we get,

For numerator, 6c² + 9c: 3c (2c + 3)

For denominator, 3c

Now, 6c² + 9c / 3c = 3c (2c + 3) / 3c

= 2c + 3

There exist no restriction to this problem.

Hence, the required simplification of rational expression is 2c + 3.

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Answer: Create a lookup from the unusable fraction format to one that you can use in excel:

First column in the lookup should be the fraction in unusable format

Second column should be the fractions in a usable format, first format the cells in second column > Format Cells menu > Number tab > Category as Fraction > Type "Up to one digit (1/4)"

Manually in the corresponding cells the equivalent values (for example, below in cell H2 write 5/8)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Firstly you should times the first decimal of the column by the number that is the numerator. So the second column the numerator is 2 so you times the first number by 2 which gives you 0.10. You do this for every column then you get you answer.

Answer:

Click on the profile and you should see next to the thank you button a add person icon.

Step-by-step explanation:

The scores from least to greatest is -8. -6, 4, 7

The absolute value of the scores from least to greatest is 4, 6, 7, 8

A negative number is a number that is less than zero. Negative numbers are denoted with a minus sign in front of the number. The further away from zero a negative number is, the smaller the number. Examples of negative numbers are -2, -9.

A positive number is a number that is greater than zero. The further away from zero a positive number is, the greater the number. Examples of negative numbers are 2, 9.

The scores from least to greatest is: -8. -6, 4, 7

The absolute value of a number is when the negative signs from the numbers are removed.

The absolute value of the scores from least to greatest is: 4, 6, 7, 8

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The product or quotient is: b. 0.91.

Quotient can be defined as what we arrived at or the answer we get  when we divide a numerator by a denominator.

Example of quotient is when we divide 10 which is a numerator by 2 which is the denominator which in turn gives us the answer 5.

Now let find or determine the quotient of 0.6734 divided by 0.74:

Hence,

Quotient=0.6734/0.74

Quotient=0.91

The correct option is B which is 0.91 because when 0.6734 is divided by 0.74 it will gives us 0.91.

Therefore the product or quotient is: b. 0.91.

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8.1

Step-by-step explanation:

according it bidmas or pemdas depending on your syllabus division comes first so 9/10 is 0.9 then doing 9 x 0.9 is 8.1

For the direct variation y = (-3/8) when x = (-2/3), the value of y is y = 1(11/16).

So,

The equation of variation is: [tex]\frac{x}{y}=\frac{16}{9} ; x=3 ; y=?[/tex]

Therefore, for the direct variation y = (-3/8) when x = (-2/3), the value of y is y = 1(11/16).

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The correct question is given below:
For the direct variation y = (-3/8) when x = (-2/3), how do you find the constant of variation and find the value of y when x = 3?

We get the composite function for the relationship between area and time as A = π (16t + r )².

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, we know that, the area of circle is given by:

A = π r²

Now, r increases by 16 feet every second.

So, the composite function will become:

A = π (16t + r )²

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

Therefore, we get the composite function for the relationship between area and time as A = π (16t + r )².

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Step-by-step explanation:

a ratio of 5:5:6 tells us first that there are 5+5+6 = 16 units in all the sides lengths of the triangle.

we don't know how large a single unit is yet, but we know, we have 16 of them.

we also know that all 3 sides together is 32 cm.

and that is another form to bring all side lengths together.

so, we know now that

32 cm = 16 ratio units.

therefore, one ratio unit is 32/16 = 2cm.

therefore, the sides are actually :

2×5 = 10 cm

2×5 = 10 cm

2×6 = 12 cm

so, we have an isoceles triangle (the 2 legs are equally long : 10 cm) with a baseline of 12 cm.

that means the height to the baseline splits the triangle in half (into 2 equal right-angled triangles).

and the height of the main triangle we get via Pythagoras from these smaller triangles :

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.

10² = (baseline/2)² + height² = 6² + height²

100 = 36 + height²

64 = height²

height = 8

the area of a triangle is

baseline × height / 2

so, in our case the area of the triangle is

12 × 8 / 2 = 12 × 4 = 48 cm²

If the observation deck is 871 feet high, the horizontal distance from the base of the skyscraper out to the ship is: 784.25 feet.

Given:

Angle of depression (∅) = 48°

Opposite side = 871 feet

Let x represent the horizontal distance

Hence,

tan 48° =871/x

x = 871/tan 48°

x= 871/ tan(0.8377)

x= 871/ 1.1106125

x =784.25 feet

Therefore If from the observation deck of a skyscraper, Ian measures a 48∘ angle of depression to a ship in the harbor below. If the observation deck is 871 feet high, the horizontal distance from the base of the skyscraper out to the ship is: 784.25 feet.

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Answer:

49.02

Step-by-step explanation:

Ok, so this is a conversion problem and it wants you to get 45 euros to whatever amount of dollars that equals. So first, you need to get the conversion rate.

1 euro/1.14 dollars

Now, plug in the 43 Euros to the front of the conversion rate

43 euros (1 euro/1.14 dollars)

You want what you start with on the bottom of the conversion factor, so switch the rate around

43 euros (1.14 dollars/1 euro)

Then, multiply what is on top, then divide by what is on the bottom.

49.02 dollars/1=49.02 dollars

The euros go away because they cancelled out.

The composition of f(x) and g(x) gives:

(f ◦ g) (x) =  x²  + 9x + 20

Here we have the two functions:

f(x) = x² + 5x +6

g(x) = x +2

And we want to find the composition:

(f ◦ g) (x)

The composition means that we need to evaluate f(x) in g(x), so we get:

(f ◦ g) (x) = f( g(x))

Then we will get:

(f ◦ g) (x) = g(x)² + 5*g(x) +6

Now, replacing g(x) we get:

(f ◦ g) (x) = (x + 2)² + 5*(x + 2) + 6

Expanding that, we get:

(x + 2)² + 5*(x + 2) + 6 = x² + 4x + 4 + 5x + 10 + 6 = x²  + 9x + 20

(f ◦ g) (x) =  x²  + 9x + 20

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√3+ √11 is greater than 5 .

We first assume that √3+ √11 is greater than 5. Then we check if our assumption is correct.

So suppose that √3+ √11 > 5

Squaring on both sides and using the identity [tex](a+b)^2=a^2+b^2+2ab[/tex],

⇒ 14 + 2√33 > 25

Subtracting 14 from both sides,

⇒ 2√33 > 11

Again squaring,

⇒ 132 > 121

This is a true statement. So our assumption that √3+ √11 is greater than 5 is right.

Therefore, √3+ √11 > 5

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The term probability refers to the chance that an event would occur or not occur. The chance that an event must occur is one  and the chance that the event would never occur is zero.

Now let us keep these ideas in our mind and answer the questions;

In the second diagram;

P(pink) = 1/3

P(blue) = 1/2

P(yellow) = 1/6

In 420 spins, the number of yellow = 1/6 * 420 = 70

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Answer: 5/3x

Step-by-step explanation:

add 5 to both sides and divide by 3

Based on the information given, Brody is older than Nathan, then;

Brody's age is 15 years.

Algebraic expressions are expressions comprising of variables, terms, factors, constants, and coefficients.

They are also made up of mathematical operations like addition, subtraction, multiplication, parenthesis, bracket, division, etc

From the information given, we have that

It is represented thus;

5x + x + 2 = 80

collect like terms

6x = 80 - 2

Subtract like terms

6x = 78

Make 'x' the subject of formula

Divide both sides by 6

x = 78/6

x = 13

But we have that;

Brody's age  = x + 2

Substitute the value of x

Brody's age = 13 + 2

Brody's age = 15 years

Thus, Brody's age is 15 years.

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The approximate area of Colorado is 105875 square miles

The area of a shape is the amount of space on the shape

The given parameters are

Shape: Rectangle

Length = 385 miles

Width = 275 miles

See attachment for the drawing of the sketch of Colorado with the labelled dimensions

The given parameters are

Shape: Rectangle

Length = 385 miles

Width = 275 miles

The area of a rectangle is

Area = Length * Width

So, we have

Area = 385 miles x 275 miles

Evaluate the product

Area = 105875 square miles

Hence. the approximate area of Colorado is 105875 square miles

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[tex]\cfrac{6}{7}\div \left(-\cfrac{11}{2} \right)\implies \cfrac{6}{7}\cdot \left(-\cfrac{2}{11} \right)\implies -\cfrac{12}{77}[/tex]

Answer:

[tex](5,\, -2)[/tex].

Step-by-step explanation:

For a line segment in a plane, the [tex]x[/tex]-coordinates of the midpoint is the average of the [tex]x\![/tex]-coordinates of the endpoints. Likewise, the [tex]y[/tex]-coordinates of the midpoint is the average of the [tex]y\![/tex] coordinates of the endpoints.

For example, the midpoint of the line segment joining [tex](x_{a},\, y_{a})[/tex] and [tex](x_{b},\, y_{b})[/tex] is:

[tex]\begin{aligned} \left(\frac{x_{a} + x_{b}}{2},\, \frac{y_{a} + y_{b}}{2}\right)\end{aligned}[/tex].

In this question, [tex]x_{a} = 8[/tex], [tex]x_{b} = 2[/tex], [tex]y_{a} = (-5)[/tex], [tex]y_{b} = 1[/tex]. Thus, the midpoint of the line segment joining the two points would be:

[tex]\begin{aligned} \left(\frac{8 + 2}{2},\, \frac{(-5) + 1}{2}\right)\end{aligned}[/tex].

Simplify to obtain:

[tex]\begin{aligned} \left(5,\, -2\right)\end{aligned}[/tex].

Hence, the midpoint of the line segment joining [tex](8,\, -5)[/tex] and [tex](2,\, 1)[/tex] would be [tex](5,\, -2)[/tex].

Answer:

1.2115/12 times

7=25.179

2.?????????

The midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

It follows from the task content that the midpoint of the line segment joining the two points (-3, 8) and (-8, 2) is to be determined.

Since the midpoint of a line is given by coordinates;

x = (x1 + x2)/2 and y = (y1 + y2)/2.

It follows that we have;

x = (-3+(-8))/2

x = -11/2

while; y = (8+2)/2

y = 10/2

y = 5.

Ultimately, the midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).

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For line segment CD, we have that:

10. The length is of 5 units.

12. The midpoint is of (0.5,0).

14. The slope is of -4/3.

The endpoints are given as follows:

c(-1,2) and d(2,-2).

The length is given by the distance between the two endpoints, hence:

[tex]CD = \sqrt{(2 - (-1))^2+(-2-2)^2}[/tex]

CD = sqrt(25) = 5.

The length is of 5 units.

The midpoint is the mean of the coordinates, hence:

The midpoint is (0.5,0).

The slope, taking two points, is given by change in y divided by change in x, hence:

m = (-2 - 2)/(2 - (-1)) = -4/3.

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The temperature when the plane reaches an altitude of 9,000 is 37.1

From the question, we are to determine what the temperature would be when the plane reaches an altitude of 9,000

From the given information,

There is a 1.3 drop in temperature for every thousand feet that an airplane climbs

and

The temperature on the ground is 48.8

Thus,

When the plane reaches an altitude of 9,000 feet, the temperature will be

48.8 - (9 × 1.3)

= 48.8 - 11.7

= 37.1

Hence, the temperature when the plane reaches an altitude of 9,000 is 37.1

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(forgive me if I may mess up, its been a while)

900+50+6+3/100

The graph of each number on a number line for 3.5 will lie exactly between 3 and 4.

In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.

Now the given number is,

3.5

Now if we take number the distance between point 3 and 4 will be 10 units.

So Distance from 3 ahead 5 units = 3.5

And distance from 4 behind 5 units = 3.5

Thus, 3.5 will lie in between 3 and 4 on the number line.

     3.0   3.1    3.2   3.3   3.4   3.5  3.6   3.7   3.8   3.9   4.0

      .         .       .       .       .         .       .       .       .        .       .          

Thus, the graph of each number on a number line for 3.5 will lie exactly between 3 and 4.

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