Find the vertex of the parabola y=2x^2+8x+7.

The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.

In order to calculate the radius of the exoplanet's orbit, we would apply  Kepler's Third Law of planetary motion.

Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:

T² = 2π√(r³/GM)

Where:

Making radius (r) the subject of formula, we have:

Radius, r = ∛(GMT²/2π)

Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².

Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds

Substituting the given parameters into the formula, we have;

Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)

Radius, r = 4.71 × 10¹¹ meters.

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Given the expression;

Step 1:

Step 2:

Step 3:

The solution is;

Answer:  600,000 + 70,000 + 5,000 + 400 + 30 + 2

Explanation:

Each digit forms a different number depending on its place value.

The 6 is in the hundred thousands place value, so the 6 in 675,432 corresponds to 600,000. Similar ideas apply for the other digits as well

The numbers that Linda should put on her number line are 5,10,15,20...1000 .

Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.

The numbers are skip counted. so each number differs from the preceding number by 5.

let us take the number counting starts from 0. so the second number will be 5+5=10

The third number 10+5 = 15 and so on and so forth.

Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.

A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.

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1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.

2. The balance in Tammy's investment account at the end of last year was $7,585.

The percentage is the proportion of a value in relation to another.

Percentages show how much a variable is contained in another.

The percentage gives the fractional value of the decrease in the investment account.

Initial investment = $8,200

Decrease in investment = 7.5%

Decrease in dollars = $615 ($8,200 x 7.5%)

Balance = $7,585 ($8,200 - $615)

Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.

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Step 1

Given;

Required; To factor it out into products of prime factors.

Step 2

A prime factor is a factor that is a prime number. In other words: any of the prime numbers that can be multiplied to give the original number is a prime factor. Examples of prime factors are; 1,2,3,5 etc. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number.

Step 3

Find the prime factor of 540

Therefore, the prime pr

16 ounces is equivalent to 453.6g when rounding to nearest tenth.

What is rounding off ?

Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.

To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here the given data is :

1 ounce = 28.35 grams

Conversion of ounce to grams :

This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.

The easiest way about this is simply multiply 16 by 28.25g

1 ounce = 28.35 grams

16 ounce = x

x = 16 x 28.25

x= 453.6 g

From the calculations above, 16 ounces is equivalent to 453.6g.

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To find the area of a circle given its radius,

The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;

The area of the circle is 200.96 inches squared

From the given figure

The 2 triangles have one equal angle of measure 88

The side of length 3 and the side of length 1 have a ratio 3: 1

The side of length 6 and the side of length 2 have a ratio 6: 2, when we divide both terms of the ratio by 1, it becomes 3: 1

That means we have one equal angle and two proportional sides

Since the angle is between the proportional sides, then

The 2 triangles are similar by the SAS postulate

Answer B

Answer:

You were right. The answer is (C)

Step-by-step explanation:

Remember, the line always goes up in the top right corner, also the first dot is 2,20, to 4,40, to 6,60, and last 8,80 which is the number of the same total amount and number of hours.

The cost of Sneakers, pair of pants, Jacket and T-shirt are $95, $50, $100 and $290 respectively.

This can be solved by forming linear equations. A linear equation is the one which can be represented in the form ax + b = 0 where a, b are coefficients and x is the independent variable. Let us assume the cost of Sneakers be 's', cost of Pants be 'p', cost of Jacket be 'j' and cost of t-shirt be 't'.

The cost of all the items is equal to $535

s + p + j + t = $535                 ......(1)

Sneakers cost $5 less than the jacket

s = j - $5                                 ......(2)

Pants cost $50 less than the jacket

p = j - $50                              ......(3)

T-shirt cost $10 less than three times the jacket

t = 3j - $10                              ......(4)

Putting the values of equation (2), (3) and (4) in equation (1)

j - $5 + j - $50 + j + 3j - $10 = $535

6j = $535 + $65

=> 6j = $600

=> j = $100 which is the cost Jacket.

Now, s = $100 - $5 = $95 which is the cost of Sneakers.

p = $100 - $50 = $50 which is the cost of pair of pants.

t = $300 - $10 = $290 which is the cost of t-shirt.

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The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:

• For the larger triangle and the triangle on the left

From this equation, we can solve for z, to get:

Then, z equals 3√5

• Similarly, with the larger triangle and the one on the right:

From this expression, we can solve for x, like this:

Then, x equals 6

• With the triangles on the right and on the left:

Solving for y, we get:

Then, y equals 2√5

The graph of the figure is attached below.

Given equation of line:-

y = (-3/2)x - 1

First we will find the x and y intercepts of the line to plot in the line.

Putting x = 0 to find the y-intercept, we get,

y = (-3/2)(0) - 1

y = -1

Hence, the coordinates of the point are (0,-1).

Putting y = 0 to find the x-intercept, we get,

0 = (-3/2)x - 1

1 = (-3/2)x

x = -2/3

Hence, the coordinates of the point are (-2/3,0).

We can find another point on the line.

Putting x = 2, we get,

y = (-3/2)(2) - 1

y = -3 - 1

y = -4

Hence, the coordinates of the point are (2,-4).

Plotting these in a graph, we can get a straight line.

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Given the two functions:

We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:

When we plug in "4", into "x", we have:

Answer:

h = 9 cm

Explanation:

The volume of the solid can be calculated as:

So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:

Then, dividing by 147 into both sides, we get:

Therefore, the height h of the solid is 9 cm.

Answer:

124

Step-by-step explanation:

Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.

[tex]31(4)=124[/tex]

1) f(x)-3

Therefore, f(x)-3=2x-4-3

2) f(x-3)

Thus, f(x-3)=2(x-3)-4

3) f(-3x)

Then, f(-3x)=2(-3x)-4

4) -3f(x)

Hence, -3f(x)=-3(2x-4)

The correct option is True, there is enough information given to say that both line are parallel.

For the given question.

The two lines are given with angles measure from 1 to 8.

Where,

As, the sum of the angles is;

∠4 + ∠3 = 91° + 89°

∠4 + ∠3  = 180° (supplementary angles)

Thus, we can say that both lines are parallel to each other.

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Answer:

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

The lengths of the major and minor axis of the ellipse, are;  4√6 and 4√3 respectively.

An ellipse describes the locus of a point on a curve, such that the sum of the distance between two focal points from the points on the curve is a constant.

The function of the ellipse can be calculated as follows;

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Where (h, k) = The coordinates of the center of the ellipse

a = The length of the semi-major axis

b = The length of the semi-minor axis

Now,

[tex]\dfrac{(x-3)^2}{12} + \dfrac{(y+ 4)^2}{24} =1[/tex]

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2√6

b = √(12) = 2√3

The length of the major axis is 2a

The length of the minor axis is 2b

The length of the major axis will be;

2a = 2 × 2√6 = 4√6

The length of the minor axis will be;

2b = 2 × 2√3 = 4√3

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The value of interior angle x for the given pentagon if found as 88 degrees.

For the given question;

The exterior angles of the pentagon are given in figure.

Find all the interior angles for given angles using linear pair as all are straight lines.

The sum of all the interior angle of pentagon is 540.

Thus,

118 + 147 + 66 + 121 + x = 540

x = 540 - 452

x = 88

Thus, the value of interior angle x for the given pentagon if found as 88 degrees.

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Let x represent the number of pounds of coffee that she bought.

From the information given,

cost per pound of coffee = $8.73

Cost of x pounds of coffee = 8.73 * x = 8.73x

Initial amount that she had = $90

After spencing $8.73x, the amount left is $63.81. This means that

90 - 8.73x = 63.81

8.73x = 90 - 63.81

8.73x = 26.19

x = 26.19/8.73

x = 3

She bought 3 pounds of coffee

Answer: 40000

+ 5000

+ 800

+ 3

Step-by-step explanation:

The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.

Answer:

Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.

From the given expression, it is found that:

a) When x = 7 and y = 11, the numeric values are given as follows:

b) They will only have the same numeric value when x = y.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.

The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.

In the context of this problem, the expressions are given as follows:

When x = 7 and y = 11, the numeric values are given as follows:

The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.

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First, lets perform each transformation and then take a look at its graph:

1.

The only etiquette that matches this plot is: Function decreases as x increases

2.

The only etiquette that matches this plot is: x-intercept at (1.5 , 0)

3.

The only etiquette that matches this plot is: Asymptote of x = 0