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The addition of the polynomials [tex]\rm (2x^4 +x^3-4x^2 +3)[/tex] and [tex]\rm (4x^4-2x^3-x^2 +10x +2)[/tex] is [tex]\rm 6x^4 -x^3-5x^2 +10x +5\\[/tex].

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

The polynomials are shown below.

[tex]\rm (2x^4 +x^3-4x^2 +3)\ and \ (4x^4-2x^3-x^2 +10x +2)[/tex].

We have to find the addition of the polynomials.

On adding the polynomials, we have

[tex]\rm (2x^4 +x^3-4x^2 +3) + (4x^4-2x^3-x^2 +10x +2)\\\\2x^4 +x^3-4x^2 +3 + 4x^4-2x^3-x^2 +10x +2\\\\6x^4 -x^3-5x^2 +10x +5\\[/tex]

Thus, the addition of the polynomials is [tex]\rm 6x^4 -x^3-5x^2 +10x +5\\[/tex].

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Answer:

A. Determine 1% of 56, both of them

Step-by-step explanation:

The ratio of the height of the model to the height of the actual ATT Building is 0.00814

An equation is an expression used to show the relationship between two or more variables and numbers.

12 inches = 1 ft.

Height of model = 60 inches = 60 inches * 1 ft per 12 in = 5 ft.

Height of  ATT Building = 614 ft.

Ratio of the height of the model to the height of the actual ATT Building = 5 ft / 614 ft = 0.00814

The ratio of the height of the model to the height of the actual ATT Building is 0.00814

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Money = (1/2×6×7+1/2*3.14*3.5^2)×5.60+150= $375.30

Answer:

the slope is undefined

Step-by-step explanation:

x=-2 is a horizontal line, if the line you're looking for is perpendicular to a straight line then its a vertical line, making the slope undefined

Answer:

3/20 & 15%

Percent:

0.15 move 2 right and get 15%

Fraction:

15/100 simplifies to 3/20

3/20,15%

yan po answer

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Answer:

80.78°

Step-by-step explanation:

When the 30 cm long string will be bent in the form of a sector it's two sides will be radii of the sector and lower part be the arc. Length of the arc can be found as given below.

Length of the string = 30 cm

radius of sector (r)= 8.8 cm

Length of the arc (l) = 30 - 2*8.8 = 30 - 17.6 = 12.4 cm

Let the sector makes [tex]\theta[/tex] angle at the centre of the circle.

Formula for length of arc of a sector is given as:

[tex]\huge \red{l=\frac{\theta}{360\degree}\times 2\pi r}[/tex]

Plugging the values of l and r in the above formula, we find:

[tex]12.4 = \frac{ \theta}{360 \degree} \times 2(3.14)(8.8) \\ \\\implies12.4 = \frac{ \theta}{360 \degree} \times 55.264 \\ \\ \implies \: \theta = \frac{12.4 \times 360 \degree}{55.264} \\ \\ \implies \: \theta =80.775 \degree \\ \\ \implies \: \theta \approx \: 80.78 \degree[/tex]

Graphs that represent direct variation are proportional functions

The graph represents a direct variation

From the graph, we have the following ordered pairs

(x,y) = (0,0), (2,4) and (3,9)

Rewrite as:

(x,x^2) = (0,0^2), (2,2^2) and (3,3^2)

The above means that, the equation of the graph is:

[tex]y = x^2\\[/tex]

i.e. y varies directly to the square of x

Where the proportionality constant is 1

Hence, the graph represents a direct variation

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The value of x according to the described angles is; 8

If two angles A and B are complementary, it follows that A + B = 90 and Cos A = Sin B.

From the statement above, it follows that;

Collect like terms;

Divide both sides by 3;

x = 24/3 = 8.

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Step-by-step explanation:

in ascending order;

4/15 ,1/5 ,2/3

Answer:

1/5 < 4/15 < 2/3

Step-by-step explanation:

First of all, we will take the LCM of the denominators. the LCM will be 15, so we will multiply the fraction by the number that will give 15 in the denominator

Now the numerators are different but denominators are the same.

We can easily arrange these in ascending order.

Answer:

x=64

Step-by-step explanation:

0=1/8x-8

8=1/8x

8/1/8=1/8x/1/8

x=64

Answer:

$7.20 for 12 rolls

Step-by-step explanation:

let x = the price of one roll

5x = $3

x = $3/5

12 • x = total cost

12 • $3/5 = total cost

$36/5 = total cost

$7.20 = total cost

Answer:

$100.00

Step-by-step explanation:

Compound interest is calculated by multiplying the initial loan amount, or principal, by the one plus the annual interest rate raised to the number of compound periods minus one. This will leave you with the total sum of the loan including compound interest.

The amount I have to pay back in full is approximately 100 dollars.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

The formula for compound interest compounded semi-annually is,

A = P(1 + (r/2)/100)²ⁿ. (two semi-annuals in one year)

Therefore, A = 95(1 + (5.2/2)/100)²ˣ¹.

A = 95(1 + 0.026)².

A = 95(1.026)².

A = 95×1.052676.

A = $100 approximately.

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Answer:

Option D

Step-by-step explanation:

Given the following question:
Original price = $22.99
Total price = $24.10

[tex]\frac{24.1-22.99}{22.99} \times100=24.1-22.99=1.11\div22.99=0.0482818617\times100=4.82818617[/tex]
[tex]4.82818617[/tex]
[tex]8>5[/tex]
[tex]=4.83[/tex]

The sales tax of the basketball was "4.83% or option D."

Hope this helps.

Answer:

scalene acute

Step-by-step explanation:

Since the 3 sides are unequal and the 3 interior angles are less than 90° it is scalene acute

Answer:

Scale acute

Step-by-step explanation:

Hi there!

This is a scalene triangle, meaning that none of the sides have the same length.

Because all of its interior angles are acute, meaning that they all measure less than 90 degrees, this is an acute triangle.

Therefore, this is a scalene acute triangle.

I hope this helps!

Answer:

34% or 34 out of 100

Step-by-step explanation:

Answer:

2 stars, 2 question marks, or two blank spaces

Step-by-step explanation:

your answer should be

2 and 10

Answer:

4cm

Step-by-step explanation:

height² = hypotenuse²- base ²

h²= 5²-3²

= 25-9

=16

h= √16

h=4cm

Answer:

The answer would be 342

Step-by-step explanation:

Multiply 19 by 18 and you get 342

Answer:

Square root of 37, about 6.08

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

18^2 + b^2 = 19^2

324 + b^2 = 361

b^2 = 37

b= sqrt37

b about equal to 6.08

Answer: Also can i have brainliest?

The ball will hit the ground 5 seconds after being thrown.

Step-by-step explanation:

The correct function is: h(t)= -16t^2+64t+80

You can rewrite the Quadratic function given in the exercise with making h(t)=0. Then this is:

0= -16t^2+64t+80

Now you can simplify the equation dividing both sides by -16. So you get:

0= t^2-4t-5

To find the solution of the Quadratic equation, you can factor it. In order to do this, it is necessary to find two numbers whose sum is -4 and whose product is -5. These number would be -5 and 1.

Therefore, you get this result:

0= (t-5) (t+1)

t1=5

t2=-1

Since the time cannot be negative, you can conclude that the ball will hit the ground 5 seconds after being thrown.

For the path of a ball being thrown maximum height is 144 units, time taken to reach maximum height is 2 units and time, it take to hit the ground is 5 units.

Projectile motion is the motion of the body, when it is thrown in the air taking the action of gravity on it.

The path of a ball being thrown off a building can be modeled by the equation

[tex]y= -16t^2+64t+80[/tex]

Comparing this equation, with standard form of quadratic equation, we get,  a=-16, b=64 and c=80.

Thus, the maximum height time can be given as,

[tex]t=-\dfrac{b}{2a}\\t=-\dfrac{64}{2(-16)}\\t=2\rm sec[/tex]

Thus, the time taken to reach maximum height is 2 seconds.

Again by the equation,

[tex]y= -16t^2+64t+80[/tex]
As it reaches maximum height after the 2 seconds. Therefore,

[tex]y_{max}= -16(2)^2+64(2)+80\\y_{max}= 144\rm[/tex]

This can be find out with the following formula,

[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t=\dfrac{-64\pm\sqrt{64^2-4(-16)(80)}}{2(-16)}\\t=\dfrac{-64\pm96}{-32}\\[/tex]

Taking negative sign,

[tex]t=\dfrac{-64-96}{-32}=5\\[/tex]

Taking positive sign,

[tex]t=\dfrac{-64+96}{-32}=-1\\[/tex]

Thus the time, it take to hit the ground is 5 units.

80 is the constant coefficient of the equation, which represent the height in the feet.

Hence, for the path of a ball being thrown maximum height is 144 units, time taken to reach maximum height is 2 units and time, it take to hit the ground is 5 units.

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Answer:

D- Strong Negative

Step-by-step explanation:

The points have correlation because they form a line. The slope of the line is negative, so the correlation is strong negative. The points would be all over the place if the correlation was weak.

The correlation of the given data is Strong and negative.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

Given, points in a cartesian plane Where all points are on a Straight line that indicates the correlation is strong. Since,

To evaluate the degree of relationships between data variables, correlation coefficients are utilized. The most popular gauge of the strength and direction of a linear link between two variables is known as a Pearson correlation coefficient.

And the given line is decreasing from left to right indicating the slope of the given Data is negative. Thus the correlation of the given points is negative.

Due to the fact that the points form a line, they are correlated. The correlation is strongly negative because the line's slope is negative. If the link was poor, the points would be scattered all over the place.

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Answer:

Answer is below :)

Step-by-step explanation:

Hope this helps you!

Answer:

  PS ≈ 6.08

Step-by-step explanation:

All of the side lengths are given except PS. It can be found using the Law of Cosines, twice.

The first use of the Law of Cosines will be to find the cosine of the angle at X.

  QR² = QX² +RX² -2(QX)(RX)cos(X)

  cos(X) = (QX² +RX² -QR²)/(2·QX·RX) = (8² +10² -4²)/(2·8·10) = 37/40

__

Now, the Law of Cosines can be used to find PS:

  PS² = PX² +SX² -2(PX)(SX)cos(X)

  PS² = 16² +15² -2(16)(15)(37/40) = 37

  PS = √37 ≈ 6.083

The length of PS is about 6.08 units.

_____

As the attachment shows, the problem can also be solved using a geometry app to draw the figure and make the measurement.

Percent is count of number per 100 numbers. The total amount Ms Clark pays including the tip is given by: Option B: $36.60

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

It is given that:

Total cost that Ms Clark pays = Cost of meal + tip amount

Now, tip amount is 20% of $25.50

It is calculated as:

[tex]Tip = \dfrac{25.50}{100} \times 20 = 5.1\text{\:(In dollars)}[/tex]

Thus, tip amount = $5.1

And thus, Total cost that Ms Clark pays = $25.5 + $5.1 = $30.6

Thus,

The total amount Ms Clark pays including the tip is given by: Option B: $36.60

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Answer:

y= ⅗x +1

Step-by-step explanation:

Given line: y= ⅗x +4

Gradient= ⅗

The gradient of the line can be found from the coefficient of x. This applies only when the equation is in the slope-intercept form (y= mx +c).

In the slope-intercept form, the coefficient of y is 1 and all the other terms and constant is on the right-hand side of the equation while the y term is on the left-hand side.

Parallel lines have the same gradient. Thus the line parallel to y= ⅗x +4 would have the equation of y= ⅗x +c, where c is the y-intercept.

To find the value of c, substitute a pair of coordinates into the equation.

Given that the line passes through (-5, -2), we can substitute this coordinates into y= ⅗x +c.

When x= -5, y= -2,

-2= ⅗(-5) +c

-2= -3 +c

c= -2 +3

c= 1

Thus, the equation of the line is y= ⅗x +1.

Answer:

[tex]2p(7p = 7) \\ 14 {p}^{2} = 14p \\ 14 {p}^{2} - 14p = 0[/tex]