If the parabola of equation y=k−x2 is tangent to the line of the equation y=x then what is the value of k ?

on solving 6th term in the binomial expansion of (4x + 1)^8 in simplest form is 3584.

A binomial is an algebraic expression with two terms. For example, a + b, x - y, etc are binomials. We have a set of algebraic identities to find the expansion when a binomial is raised to exponents 2 and 3.

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

we know ,

So the 6th term in the equation

is ,8c5 -4x^8-5 = 8c34x^3 is , = 3584

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Three fundamental ideas provide the foundation for all basic geometry notions. The three are the plane, line, and point.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

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Three basic ideas form the basis of all basic geometry concepts. The three are planes, lines, and points.

Euclid, the father of geometry, was a brilliant mathematician. Learn about the history of Euclid and some of the mathematical ideas we use today, and see how important they have become. The terms ``ge'' and ``metria'', meaning ``measure,'' are of geometric origin. For over 2000 years, the Greek approach to geometry has served as the foundation of geometry.

Geometry is the study of various mathematical or actual forms, figures, and sizes. In geometry, you will discover the concepts of points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles, and area.

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Answer:

------------------------------

Solve in below steps, using log and exponent rules:

The graph of the inequality: 3x + y > 7

Can be seen in the image below.

We want to see which graph represents the inequality:

3x + y > 7

We can rewrite the inequality in slope-intercept form as:

y > -3x + 7

So we just need to graph the line:

y = -3x + 7

With a dashed line, and then shade all the region above the line.

To graph the line, you need to find two points that lie on the line.

if we evaluate the line in x = 0 we wll get:

y = -3*0 + 7

y = 7

if x = 1

y = -3*1 + 7

y = -4

Then we have the points (0, -7) and (1, -4), now we can graph these two points and connect them with a dashed line, then shade the region above.

The graph of the inequality is the one below.

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There are 0.16 gallon is used to paint each chair.

What is gallon?

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters.

as given, Four gallon of paint are used to paint 25 chair.

i.e. 4 gallon ⇒ 25 chairs

and If each chair used the same amount of paint then how many gallon are used to paint each?

i.e. how many gallons ? ⇒ 1 chair

∴ 4 gallon ⇒ 25 chairs

∴ 25 chairs ⇒ 4 gallon

∴ 1 chairs ⇒ 4 / 25 gallon

∴ 1 chairs ⇒ 0.16 gallon

Therefore, there are 0.16 gallon is used to paint each chair.

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The date Mr. Remy Osta will resume duty after his 50 days leave which lasted from February 10, 2008 is March 31, 2008

A leap year is a year which has 366 days, that is, the days in February are 29 days.

So,

From February 10, 2008

The days remaining in February is 19 more days

The days of march is 31 days

Hence,

19 days + 31 days

= 50 days

Therefore, Mr. Remy Osta will resume duty on March 31, 2008

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The measure of the interior non-adjacent angle as required in the task content is; 95°.

Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.

On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;

x + x - 32.

where, x is the measure of the interior non-adjacent angle.

Hence, x + x - 32 = 158

2x = 158 + 32

2x = 190

x = 95°.

Ultimately, the measure of the interior non-adjacent angle is; 95°.

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Answer:

Point C

Step-by-step explanation:

Lines m and t are on the same plane

We can see that they intersect at Point C

Answer:

Taylor

Step-by-step explanation:

2.5km in 17 mins time 2=5km in 34mins 3km in 20 mins times 2=6km in 40 mins

If the rate of the change in the input to the change in the output is the same for every point in the table, then the table represents a linear function.

If a table of values shows a constant rate of change, it is linear.

A non-vertical graph that is a straight line is linear. An equation that can be written in the form y=mx+b is linear. If a table of values shows a constant rate of change, it is linear.

Linear relationships can be modeled using the slope-intercept form y=mx+b, As x increases, y increases by a proportional amount.

A linear function is a linear relationship that obeys the rules of a function and has a graph that forms a straight line. Function notation is used to express a linear relationship when there are clearly defined inputs and outputs.

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Answer:

M = (36.5-8)/5

[M = 5.7 miles/day]

Step-by-step explanation:

The goal is 36.5 miles.  The remaining miles needed to achieve this goal is reduced by the miles already ridden, 8 miles.

(36.5 - 8) = 28.5 miles remaining.

We are asked to find a value for M, which is the average number of miles Ian would have to ride to reach his goal.  By average, we can assume it is the average miles/days remaining.  The days remaining are 5, so we have:

(28.5 miles remaining)/5 days = 5.7 miles/day

An equation for M using these steps would be:

M = (36.5-8)/5

Answer:

2 over 1

Step-by-step explanation:

I'm not really sure what you mean in the question but I've substituted the values in

Answer: If you're asking for the answer if 16,000 divided by 4, it would be 4000, don't know for sure if that's what you were asking for! Hope I helped!

Answer: $20.95

Due to credit rating being fair:

Secured APR = 7.00%

Loan amount = sale price + tax - down payment

New car  =  [tex]19027 + (19072 x 0.045) - 1200 = 18730.24[/tex]

Used car = [tex]15635 + (15635 x 0.045) - 1200 = 15138.575[/tex]

---------------------------------------------------------------------------

Monthly interest = loan amount [tex]x 0.07 x 1/12[/tex]

New car = [tex]18730.24 x 0.07 x 1/12 = 109.26[/tex]

Used car = [tex]15138.575 x 0.07 x 1/12 = 88.31[/tex]

Thus, the difference is [tex]109.26 - 88.31 = $20.95[/tex]

The area of the said triangle is 10 cm²

Here we have been given the right-angled triangle with base 5 cm and altitude 4 cm.

To find the area of a triangle we can either use Heron's formula or the other formula where area of a triangle = 1/2 X base X height

Since we have been given the base and the height we need to use the latter.

Hence area of the said triangle will be

1/2 X 5 X 4 cm²

= 10 cm²

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Answer:

7/10

Step-by-step explanation:

How do you add a fraction?

First you have to check if they have common denominator. If so, add the numerators and keep the denominator. If Not, you have to find common denominator before added. After that,  check if your fraction need to be simplify.

Solve:

Least common multiplier of 10 and 5 is 10

[tex]\frac{3}{10}+\frac{2}{5}[/tex]

Since [tex]\frac{3}{10}[/tex] already have a denominator of 10 we keep it.

[tex]\frac{2}{5}=[/tex] [tex]\frac{2\times2}{5\times2}[/tex] [tex]=\frac{4}{10}[/tex]

Now we have;

[tex]\frac{3}{10}+\frac{4}{10}[/tex]

Apply fraction Rule which is; [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]

[tex]=\frac{3+4}{10}[/tex]

3 + 4 = 7

[tex]=\frac{7}{10}[/tex]

Hence, [tex]\frac{3}{10}+\frac{2}{5}=\frac{7}{10}[/tex]

RevyBreeze

Answer:

24

Step-by-step explanation:

120 x 0.20 = 24

The values of x and y are -1 and 4 respectively.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given are two equations, -2x+3y=14 and x+2y=7

Solving equations by using substitution method,

-2x+3y=14..........(i)

x+2y=7

x = 7-2y.......(ii)

Using eq(ii) in eq(i)

-2(7-2y) + 3y = 14

-14+4y+3y = 14

7y = 28

y = 4

Put y = 4 in eq(ii)

x = 7-2(4)

x = -1

Hence, the values of x and y are -1 and 4 respectively.

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A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°).

Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.

A rectangle has four vertices since it has four sides, four angles, and four corners. The intersection of two sides forms the "vertices" of a polygon. They are corners, to put it another way.

Rectangles' basic characteristics include:

Four-sided shapes include rectangles.

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Answer: Yes, after 7 weeks, they will have the same amount of money

Step-by-step explanation: So let’s say Joyce will be equation 1, so it would be - T = 13 + 6x, where T represents the total money, and x represents the number of weeks. And let’s say Enrique will be equation 2, which will be - T = 80 - 5x, where once again, T represents the total money, and x represents the number of weeks.

So, let’s start going off numbers, we will start at 5 weeks, when we put that in, Joyce will have $43 and Enrique will have $65, so we know it will be more than 5 weeks, so let’s try 8 weeks, Joyce will have $61 and Enrique will have $40, so it’s below 8, so how about we try 7, at 7 weeks, Joyce will have $55, and Enrique will have $55 too. So this means, after 7 weeks, Joyce and Enrique will have the same amount of money

As per the following diagram, the angle measures of triangle EFC is 118°

The term angle in math is known as a figure which is formed by two rays or lines that shares a common endpoint.

Here we have given that an artist uses colored tape to divide sections of a mural and she needs to cut a piece of paper to cover triangle EFC while she works on other sections.

According to the diagram, here we know that the value of

=> DE = EF

And the value of

=> EB = FB

Here we know that the value of the angles,

=> ∠EDB = ∠EFB = 90°

Thus implies that the angles,

=> ∠DFB = ∠FEB = 31°

Then the value of the angle is calculated as,

=> ∠EDB =∠EFB = 90° - 31°

=> ∠EDB = ∠EFB = 59°

Then the value of the angle ABC is calculated by sum the values of the angles, then we get,

=> ∠ABC = ∠EDB + ∠EFB = 59 + 59 = 118°

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The solution is the point where the two lines intersect i.e. (-1,-7). The graph for the given system of equations is attached below wherein the blue line represents y=2x-5 and the green line represents y=-x-8.

What is system of equation?

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.

For solving the equations graphically, we need to find points for plotting

So, for y = 2x-5,

The y-intercept is -5, so we need to place a point on the graph at (0,-5).  For the another point, put x=1, we get y= -3. So we need to place another point at (1,-3).

Similarly for y = -x-8,

The y-intercept is -8, so we need to place a point on the graph at (0,-8).  For the another point, put x=1, we get y= -9. So we need to place another point at (1,-9).

The solution is the point where the two lines intersect.

When the two lines intersect,

2x-5=-x-8

3x=-3

x=-1

So, y=-7

Hence, the two lines intersect at (-1,-7).

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Answer:

Here are two data points that can be used to represent this relationship:

(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.

(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.

Step-by-step explanation:

In this situation, the independent variable is the number of hours that Susan works, and the dependent variable is the amount of money that she gets paid.

Here are two data points that can be used to represent this relationship:

(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.

(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.

We can use these two data points to represent the relationship between the number of hours that Susan works and the amount of money that she gets paid. It shows that, As her work hours increase, her pay increases as well.

Answer:

a^m + a^n = a^m+n

Step-by-step explanation:

This is true for any value of a and n except 0.

The event with the largest probability is rolling a number higher than 2, so the correct option is B.

First, the fact that a 2 was rolled before does not affect the next rolls of the dice, so that information is extra.

Now we just need to see which option has the largest probability.

A) There are only one number lower than 2, then the probability of this event is p = 1/6

B) There are 3 numbers higher than 2, then the probability is p = 3/6 = 1/2

C) The probability of get another 2 is 1/6

We can see that the event with the largest probability is B, so that one is the most likely to occur.

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In order to respond to the query ,of bar graph we must first comprehend what a compound Tim received 4 emails on Thursday and 8 SMS on Monday, making up 0.52 of all communications.

A blended bar chart is used to display the rates of two connected sets of data. In this investigation, two forms of data—emails and emails used, but they are both grouped together under the term "messages" and are shown as vertical bars in the graph.

Here,

14+16+14+15+14=73 messages in total.

A total of 38 emails were sent: 6 + 10 + 10 + 4 + 8

Email to message ratio is 38/73, or 0.52.

Emails therefore made up 0.52 of the messages.

Tim received 4 emails on Thursday, 8 texts on Monday, and 0.52 of the messages were emails, as shown by an examination of the composite bar chart that we used to come up with the answers to the three questions.

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Answer:

12

Step-by-step explanation:

Only (i), (ii), (iv) and (v) are Pythagorean triplets. A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.

Pythagoras, Gauss, Edison, Hawking. The following are the most noted discoveries of each.

Pythagoras, 500 B.C. School Of Mathematics and Pythagorean theorem.Edison, Year 1879 - Invention of incandescent light bulb.Gauss, Year 1801 - Therom of Alegbraic Solution. Stephen Hawking Year1980 - Studies in cosmology particularly contributing to the context of black holes.

you can check by taking largest side square

and adding square of rest two sides

17^2= 15^2+ 8^2

82^2= 18^2+80^2

26^2= 24^2+10^2

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