Factor completely 640-10x^2

Answer:

Book: Library is most similar in relation to the following word pair Water: Ocean. Both pairs are closely related and are often found together.

Answer: There is no solution for these equations.

Explanation: This equation system is not solvable. Because we cannot eliminate x or y while holding one of them in the equation.

Answer:

option A

Step-by-step explanation:

The slope intercept form of a linear equation is expressed as: [tex]y=mx+b\text{ where }m\ne0[/tex]

The slope described how the y value changes as x changes. If it's positive then that means as x increases, y increases and if it's negative then that means as x increases, y decreases.

Knowing this information, there is only one reasonable option in this case. Given the equation: [tex]y=x+6[/tex], we know that it has a slope of positive one, meaning it's increasing. Given the equation: [tex]y=-\frac{3}{4}x+4[/tex], we know that it has a slope of negative three fourths, meaning it's decreasing.

The graph shown is increasing so option A is the only reasonable option in this case.

Answer:

71

Step-by-step explanation:

the circle standard form is

(x - h)² + (y - k)² = r²

r being the radius, (h, k) being the coordinates of the center.

fully multiplied that is

x² - 2hx + h² + y² - 2ky + k² = r²

we have here

4x² + 12x + 4y² - 40y - B = 0

our first step is to bring this back to an excision in x² and y². so, we divide everything by 4.

x² + 3x + y² - 10y - B/4 = 0

by comparing this to the general equation we see

3 = -2h

h = -3/2 = -1.5

-10 = - 2k

k = 5

-B/4 = h² + k² - r² = 9/4 + 25 - (3×sqrt(5))² =

= 9/4 + 25 - 9×5 = 9/4 + 25 - 45 = 9/4 - 20

-B = 9 - 80 = -71

B = 71

The mode is the most common value in a set of data and is typically used for categorical data such as eye color.

The mean and median, on the other hand, are measures of central tendency used for numerical data.

Since eye color is a categorical variable, the mode would be the appropriate measure to use to determine the most common eye color in Andrew's survey.

It can be seen that the mean, median, and mode are the most common measures of central tendency for a set of data, and typically, you use the mode with categorical, ordinal, and discrete data and this is the appropriate data collection that Andrew should use to find the most common eye color and not mean or median.

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Answer:

m∠14 = 80°

Step-by-step explanation:

Angles m∠13 and m∠14 lies on a straight line. Angles on a straight line sums up to 180°.

Hence we can say that,

m∠13 + m∠14 = 180

100 + m∠14 = 180

m∠14 = 180 - 100

m∠14 = 80

Answer:

4 x [tex]10^{8}[/tex]

Step-by-step explanation:

Round the number to

400,000,000

4 x [tex]10^{8}[/tex]

We moved the decimal 8 places.

Answer:

4 x 10^8 (four times ten to the power of eight) is the best approximation of the number 399,867,231 written in scientific notation.

Step-by-step explanation:

The required distance c between the point of marching formation is given as C = √61.

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,

The distance formula is given as,

C = √[[x₂ - x₁]² + [y₂+ - y₁]²]

Put the given point in the above equation,
C = √[[3 + 2₁]² + [4 + 2]²]
C = √25+36
C = √61

Thus, the required distance c between the point of marching formation is given as C = √61.

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The specialty fees will of the project will be $175,000.

What is specialty fee in a project?

Specialty fee of a project is associated with the cost or money that is given for some special task for e.g. hiring a architect or other specialist.

To calculate the amount of money that will be spent on specialty fees, we need to multiply the total amount of money raised (35,000,000) by the specialty fee percentage (0.5%).

specialty fees = 35,000,000 * 0.005 = 175,000

So, $175,000 will be spent on specialty fees.

Also, To calculate the amount of money that will be spent on service commission, we need to multiply the total amount of money raised (35,000,000) by the service commission percentage (2%).

service commission = 35,000,000 * 0.02 = 700,000

So, $700,000 will be spent on service commission.

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To raise $35,000,000 for a project's financing, a corporation will issue shares and bonds. The project's specialist fees will be $175,000 in total.

The cost or amount paid for a project's specialty work, such as employing an architect or another specialist, is known as the specialty fee. We must multiply the entire cash raised ($35,000,000) by the proportion of speciality fees ($0.5%) to determine the amount that will be used for fees.

35,000,000 * 0.005 = 175,000 in specialist fees.As a result, specialist fees will cost $175,000. Additionally, we must multiply the total sum of funds raised (35,000,000) by the service commission rate (2%), in order to get the amount that will be used for service commission. service commission: 35,000,000 * 0.02 = 700,000 , The service commission will therefore receive $700,000.

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A function transformation is one that converts one function or graph into another, usually related function or graph.

Given function, f(x)

Transformed function is y = -3f(x + 2)

To find each points transformed function:

        After transformation the function becomes,

        y = -3(-4 + 2)

        y = -3 x -2

        y = 6

        Then the transformed points are (-4 , 6).

        After transformation the function becomes,

        y = -3(-2 + 2)

        y = 0

        Then the transformed points are (-2 , 0).

       After transformation the function becomes,

        y = -3(0 + 2)

        y = -3 x 2

        y = -6

        Then the transformed points are (0 , -6).

        y = -3(1 + 2)

        y = -3 x 3

        y = -9

        Then the transformed points are (1 , -9).

        y = -3(3 + 2)

        y = -3 x 5

        y = -15

        Then the transformed points are (1 , -15).

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It is possible to find out the number of people who attended the event. Hence option B is correct.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that, a total of 24 cases of forks and each case of forks contains 36 packages each containing 12 forks.

Form about information, calculate the number of forks.

A total of 24 cases of spoons and each case of spoons contains 45 packages each containing 12 spoons.

Form about information, calculate the number of spoons.

Given that at the end of the event, 12 forks and 18 spoons were not given out to guests.

Form these we can get information that how many spoon used.

Since each guest will receive 2 forks and 3 spoons at the beginning of the event.

Using this information we can get the number of people who attend the event.

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Answer:

Step-by-step explanation:

To prove that OHAP is a square, we need to show that all four sides are congruent and all four angles are right angles.

Since AOB is a right isosceles triangle, we know that angle OAB and angle OBA are both congruent to 90 degrees, which means that they are both right angles. Since [OH] is the altitude relative to [AB], it bisects angle OAB, which means that angle AOH and angle HOA are both congruent to 45 degrees. Since P is the symmetric of H with respect to OA, we know that OA is congruent to OP, and we also know that OH is congruent to OP. Therefore, all four sides of OHAP are congruent, which means that OHAP is a square.

Answer:

B will get more $

Step-by-step explanation:

3000 annual rate 6% so half a year is 3%, compounding semiannually for 6 years =  12 times

so 3000*(1+3%)^12 =4277.28

$4000 invested for four years compounded quarterly at 2.7%. so every quater is 2.7%/4 =0.675%, compounding quarterly for 4 years =  16 times

so 4000*(1+0.675%)^16=4454.57

There are 720 possible gate codes your apartment complex have.

The subject matter of the math discipline of algebra is symbols and the arithmetic operations performed on them. Variable describes these symbols because they don't have any fixed values. We frequently notice values that are in constant flux in our day-to-day problems.

To represent these shifting values, however, is always necessary. These values are frequently represented in algebra with symbols like x, y, z, p, or q; these symbols are referred to as variables.

The gate code at your apartment complex is three numerical digits followed by # sign.



There are 10 digits (0 to 9).

Compute the number of possible gate codes if each code contains non-repeating digits as follows.

The first 3 place in the code must be filled by three non-repeating digits.

So, there are 10 possibilities for the first digit, 9 possibilities for the second digit and 8 possibilities for the third digit.

Hence, the three non-repeating digits can occur in 10×9×8 ways.

The three non-repeating digits are followed by "#" sign. The sign # can occur in only one way.

Combine the above results and obtain the number of possible gate codes as,

10×9×8×1=720

Thus, there are 720 possible gate codes.

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The line running through endpoints (5.-4) and (-1,8) has an equation in slope-intercept form of y = -4x + 8

Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. Equations are mathematical statements that prove the equality of several mathematical equations and are used in algebra. In the solution 3x Plus 5 = 14, for example, the equal sign places the variables 3x Plus 5 and 14 apart. It is possible to explain the relationship between two sentences that are located on each side of a letter using a mathematical formula.

Here,

provided are points 5.–4. (-1,8)

slope is equal to m=y2-y1/x2-x1.

form of the slope intercept: y = mx + c

In order to determine the equation for the line passing between the points (5, -4), (-1, 8),

The slope and intercept are represented by the formula y = mx + c.

-4 is the slope, while 8 is the intercept.

The line's equation for going through the endpoints (5.-4) & (-1,8) is y = -4x + 8 in slope-intercept form.

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The precise middle value of a data set when it is ordered is called the median.Consequently, 7 is the needed median for the specified data set.

The precise middle value of a data set when it is ordered is called the median.Separating the lowest 50% of data from the top 50% of values is a measure of central tendency.If you have an odd or even number of data points, the processes for calculating the median will be different.

The exact middle value in an ordered data set is known as the median.It is a metric of central tendency that separates the bottom and top half of the data.

Sort the provided data set into the following order: 1, 4, 5, 7, 8, 9, 15, and 16.

Eight terms total, all even.

The data set's median is equal to the nth term, the eighth term, and the fourth term. = 7

Consequently, 7 is the needed median for the specified data set.

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Answer:

We can use the equation:

amount of a given nutrient / % of recommended daily amount = recommended daily amount

Here, we know that 69 grams of carbohydrates is 22% of the recommended daily amount, so we can plug in the given values and solve for the recommended daily amount:

69 / 0.22 = Recommended Daily Amount

Recommended Daily Amount = 69 / 0.22 = 313.64 grams (rounded to one decimal place)

So, the total recommended daily amount of carbohydrates in grams is 313.6 grams.

The triangles are similar as follows:

ABC ~ DEF

The criteria is AA(angle angle)

Similar triangles are the triangles that have corresponding sides as a ratio of each other and corresponding angles congruent to each other.

Therefore, the corresponding angles of the triangles are suppose to be congruent and the corresponding sides in proportion for it to be similar.

Hence, If two triangles have two of their angles equal, the triangles are similar by AA(angle angle).

Therefore, the triangles are similar by AA.

Triangle ABC is similar to triangle DEF.

The criteria for the similarity is AA.

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The trigonometric identities equivalent to cos(2·x)/cos(x) are;

cos(x) - (sin(x))/(tan (x))

2·cos(x) - sec(x)

Trigonometric identities are equations of trigonometric functions that are correct for the values of the input and output variables in the equations.

The trigonometric identity for cos(2·x) is specified as follows;

cos(2·x) = cos²x - sin²x

Therefore;

cos(2·x)/(cos(x)) = (cos²x - sin²x)/(cos(x))

(cos²x)/(cos(x)) = cos(x)

sin²(x)/(cos(x) = sin(x) × sin(x)/(cos(x)) = sin(x)·tan(x)

(cos²x - sin²x)/(cos(x)) = (cos²x)/(cos(x)) - sin²(x)/(cos(x)

(cos²x)/(cos(x)) - sin²(x)/(cos(x) = cos(x) - sin(x)·tan(x)

cos(2·x) = 2·cos²x - 1

Therefore; cos(2·x)/cos(x) = (2·cos²x - 1)/cos(x)

(2·cos²x - 1)/cos(x) = 2·cos(x) - 1/cos(x)

2·cos(x) - 1/cos(x) = 2·cos(x) - sec(x)

cos(2·x) = 1 - 2·sin²x

cos(2·x)/cos(x) = (1 - 2·sin²x)/cos(x)

(1 - 2·sin²x)/cos(x) = sec(x) - 2·sin(x)

The expressions equivalent to cos(2·x)/cos(x) are therefore;

cos x - (sin x)·(tan x) and 2·cos x - sec x, which are I and III

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Answer: 510$

Step-by-step explanation:

So you multiply the number of bookmarks by the amount they were sold for. So, 340 x 1.50 = 510. 510$!

Answer:

The mass number of the other isotope is 10.01613 amu.

Step-by-step explanation:

Let the percentage abundance of the first isotope be: 10B5 = 19.80%

Then, the percentage abundance of the second isotope will be xB5 = 80.20%

Mass of one isotope = 10.012938 amu

(10*19.80 + x*80.20)/100 = 10.012938 

198 + x*80.20 = 1001.2938 

x*80.20 = 1001.2938 - 198

x*80.20 = 803.2938

x = 803.2938 / 80.20

x = 10.01613

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Answer:

[tex] {h \: }^{2} + 6h + 10[/tex]

Answer:

a

Step-by-step explanation:

|x|<a means -a<x<a

or x lies between -3 and 3

The approximate area of the shaded region of the circle is 191 metres squared.

The radius of the circle below is given as 9 metres. The approximate area of the shaded region of the circle can be found as follows:

area of the shaded region = area of the circle - area of the sector uncoloured

Therefore,

area of the circle = πr²

where

Therefore,

area of the circle = π × 9²

area of the circle = 81π m²

Hence,

area of the sector uncoloured = ∅ / 360 × πr²

where

Therefore,

area of the sector uncoloured = 90 / 360 × π × 9²

area of the sector uncoloured = 1 / 4 × π × 81

area of the sector uncoloured = 81 / 4 π

Hence,

area of the shaded region = 81π  - 20.25π

area of the shaded region = 60.75π

area of the shaded region = 190.755

area of the shaded region = 191 m²

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The point that satisfies this inequalities y > -(1/3)x - 2 and y > 2x + 6 is (2, 15)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept.

Given the linear inequalities:

y > -(1/3)x - 2    (1)

y > 2x + 6       (2)

Plotting both inequalities:

The point that satisfies this graph is (2, 15)

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Answer: The appropriate dosage of medicine for a 180 Ib person is 12 ounces.

Step-by-step explanation:

From the word problem, we know that:

Since we are given w (the amount the person weighs is 180 Ib), we can plug the value into the equation to solve for t.

t= 3 + 0.05 (180)

t = 3 + 9

t = 12

So the appropriate dosage of medicine for a 180 Ib person is 12 ounces.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{4 }{ 5 }\implies \cfrac{\$ 4}{5~apples}\implies \cfrac{0.8}{1}~\cfrac{\$}{apples}~\hfill \textit{80 cents per apple}[/tex]

Answer:

  x = 0 and x = 16

Step-by-step explanation:

You want the solution to √(2x+4) -√x = 2.

We eliminate the radicals by squaring until there aren't any. After the first squaring, we have to separate the radical term from the others.

  [tex]\sqrt{2x+4}-\sqrt{x}=2\\\\(2x+4)-2\sqrt{(2x+4)(x)}+(x)=4\qquad\text{square both sides}\\\\3x=2\sqrt{x(2x+4)}\qquad\text{add $\sqrt{x(2x+4)}-4$}\\\\9x^2=4(2x^2+4x)\qquad\text{square both sides}\\\\x^2-16x=0\qquad\text{subtract the right side from both sides}\\\\x(x -16) = 0\qquad\text{factor}[/tex]

The solutions to this are the values of x that make the factors zero. Those values are x=0 and x=16. Trying these in the original equation, we have ...

  √(2·0 +4) -√0 = 2 -0 = 2 . . . . . . x=0 is a solution

  √(2·16 +4) -√16 = 6 -4 = 2 . . . . . x=16 is a solution

The two solutions to the equation are x=0 and x=16.

Answer:

2 inches

Step-by-step explanation:

The radius is simply the distance from the edge if you were at the center, which is equal to half the diameter. So given the diameter is 4 inches, we divide that by two, [tex]\frac{4\text{ inches}}{2}=2\text{ inches}[/tex] and that's our radius!

To solve for x in the equation A = 6x + 5, we can first subtract 5 from both sides, giving us A - 5 = 6x. This simplifies to A = 6x + 5. Dividing both sides by 6 gives us x = (A-5)/6.

Similarly, we can solve for x in the equation B = 4x + 45. Subtracting 45 from both sides gives us B - 45 = 4x, and dividing by 4 gives us x = (B-45)/4.

To find the measure of A, we can substitute the value of x that we found into the equation for A.

A = 6x + 5

A = (6 * (B-45)/4) + 5

A = (3/2) * B - 45/2 + 5

A = (3/2) * B + 5/2

So the measure of A is (3/2) * B + 5/2.