Evaluate −6a^3+8a^2+8a+1, when a=5.

Answer:

x = 0, 6

Step-by-step explanation:

8x(x-6) = 0

x = 0, 6

We are given with an AP (Arithmetic Progression) with first term being -7, and the common difference being the difference between any succeding term from any term and the term itself, so common difference = -11 - (-7) = -11 + 7 = -4, so now before finding the sum of 21 terms, let's recall that ;

Where, d is the common difference, a is the first term, and n is the number of terms and [tex]{\bf S_n}[/tex], being the sum of n terms, so putting all the values in the formula, we will have ;

[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}\{2\times -7+(21-1)-4\}}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}(-8+20\times -4)}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-8-80)}{2}}[/tex]

[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-88)}{2}}[/tex]

[tex]{:\implies \quad \sf S_{21}=-21\times 44}[/tex]

[tex]{:\implies \quad \boxed{\bf{S_{21}=-924}}}[/tex]

Answer:

x=-2

y=-11

Step-by-step explanation:

4x-3=-x-13

5x-3=-13

5x=-10

x=-2

y=4(-2)-3

y=-11

Answer:

isosceles triangle is shown in fig

Answer:

128

6

12

48

Step-by-step explanation:

Answer:

make it clearer

Step-by-step explanation:

Answer:

Mean: 12.9

Mode: 14,15

Median: 14

Step-by-step explanation:

Step-by-step explanation:

1) if the initial figure ABCD, then the figure A'B'C'D' is reduction of the initial one.

2) the scale factor is 0.5: the ratio of all the corresponded coordinates is 2:1 [D(8;4) - D'(4;2); C(4;0)-C'(2;0); B(0;-2)-B'(0;-1) and A(-4;4)-A'(-2;2)].

Mark the quadrilaterals ABcD and A'B'C'D'

The image is reduced in size hence it's reduction

Take 2 sides two calculate scale factor

Scale factor:-

The amount invested in the account that gives a 5.25% interest is  $18400.

The amount invested in the account that gives a 3.75% interest is 27600.

0.0525a + 0.0375b = 2001 equation 1

a + b = 46000 equation 2

Where:

a = amount invested in the account that gives a 5.25% interest

b = amount invested in the account that gives a 3.75% interest

Multiply equation 2 by 0.0525

0.0525a + 0.0525b = 2415 equation 3

Subtract equation 1 from equation 3

414 = 0.015b

b = 27600

Subtract 27600 from 46000

46000  27600 = $18400

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Answer:

BC = FE

Step-by-step explanation:

given ,

BA = FD and the measure of angle ABC = the measure of angle DFE

If we have BC = FE then according to the SAS criterion the two triangles are congruent

Answer:

1 - 52= 52 33= 33 52 > 33, so -52 dollars has the greater magnitude. 1 - 141 = 14 [23] = 23 14 < 23, so 23 feet has the greater magnitude.

Step-by-step explanation:

Hope This Helps

that is the complete answer to the question

Answer: C) 1/16

Hope this helps :)

[tex]~~~~~~ \textit{Savings Earned Amount} \\\\ S=P\left(1+r\right)^{t} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$14500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years\dotfill &5 \end{cases} \\\\\\ S=14500\left(1+0.075\right)^{5}\implies S=14500(1.075)^5\implies A\approx 20816.63[/tex]

Answer:

The slope of the line is -1

Step-by-step explanation:

You need to use the slope formula

Slope Formula: y2 - y1 / x2 - x1

**The numbers represent subscripts but the subscripts aren't on computers**

Your Coordinate Points:

(7, -3) and (3, -7)

Do -7 - (-3) / 3-7

First, do -7 - (-3)

The negatives cancel to an addition problem.

-7 + 3

Now do -7 + 3. This is a subtraction problem that should be negative.

-7 + 3 = -4

Next, do 3 - 7

That should be 4

-4/4 is what we have right now.

Do -4 divided by 4 which has to contain a negative.

That is simply -1.

The slope of the line is -1

Answer: I.

Step-by-step explanation:

Capitalism is clearly not the answer. Capitalist governments such as America have their fingers into the economic trading.

Socialism and Communism sound plausible, but Communism is giving people money by their work, and Socialism is everything is owned by the public. Both still involve themselves in markets, so the answer is I

Answer:

d.

No economic system is free from government involvement.

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

A = 1/2 bh

A = 1/2 (6)(18)

A = 1/2 (108)

A = 54

Area of the Obtuse triangle whose measures are 6 and 18 is 54 square units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the area of the obtuse triangle whose base is six units and height is eighteen 18 units.

A triangle whose any one of the angles is an obtuse angle or more than 90° is called Obtuse.

The area of triangle is 1/2×Base×Height

Half base times of height

Area of triangle=1/2×6×18

=54 square units

Area is 54 square units.

Hence, Area of the Obtuse triangle whose measures are 6 and 18 is 54 square units.

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#SPJ7

Answer:

Step-by-step explanation:

Find the length of semicircle

Find the perimeter

For rectangle

Perimeter:-

For semicircle:-

Perimeter:-

Total:-

Answer:

in this problem. Not that the total number of ways of taking one or more alternative out of ...

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

Well, honestly not sure how to solve this but I'll try.

Each correct answer is giving 4 points but the probability to choose the correct one is 1/5

Each incorrect one gives -2 points and the chance to pick a wrong answer is 4/5.

Obviously, the chance to lose points is more. But is taking the risk and guessing worth it? Well, it depends on how many points the correct answer gives. If it makes up for the possible loss of points, then it is in his interest to guess, otherwise he will end up losing more than they win.

If we sum the two chances to find averagely how many points the student will get, then I guess that would be the correct answer:

4(1/5) + (-2)(4/5) = 4/5 - 8/5 = -4/5

He will get averagely -4/5 points, so I believe it isn't in his interest. It means that the points he gets don't make up for the possible loss of points if you choose answers randomly. (Wow, I'm glad teachers don't do this on tests 0_0)

This is my theory though, not sure how to go for solving this, just thinked logically. I hope this helps, but don't trust me and copy paste my answer on your test or whatever. Think if this is correct first because I'm not sure

Answer:

18 square yards

Step-by-step explanation:

because if you do 3x3 twice then add the two numbers you get you will get 18.

1) The net area between the two functions is 2.

2) The net area between the two functions is 4/3.

3) The net area between the two functions is 17/6.

4) The net area between the two functions is approximately 1.218.

5) The net area between the two functions is 1/2.

The area between the two curves is determined by definite integrals for a interval between two values of x. A general formula for the definite integral is presented below:

[tex]A = \int\limits^{b}_{a} {[f(x) - g(x)]} \, dx[/tex]   (1)

Where:

Now we proceed to solve each integral:

The lower and upper limits between the two functions are 0 and 1, respectively. The definite integral is described below:

[tex]A = \int\limits^1_0 {x^{0.5}} \, dx - \int\limits^1_0 {x^{2}} \, dx[/tex]

[tex]A = 2\cdot (1^{1.5}-0^{1.5})-\frac{1}{3}\cdot (1^{3}-0^{3})[/tex]

[tex]A = 2[/tex]

The net area between the two functions is 2. [tex]\blacksquare[/tex]

The lower and upper limits between the two functions are -3 and -1, respectively. The definite integral is described below:

[tex]A = - 4 \int\limits^{-1}_{-3} {x} \, dx - \int\limits^{-1}_{-3} {x^{2}} \, dx - 3 \int\limits^{-1}_{-3}\, dx[/tex]

[tex]A = -2\cdot [(-1)^{2}-(-3)^{2}]-\frac{1}{3}\cdot [(-1)^{3}-(-3)^{3}] -3\cdot [(-1)-(-3)][/tex]

[tex]A = \frac{4}{3}[/tex]

The net area between the two functions is 4/3. [tex]\blacksquare[/tex]

The definite integral is described below:

[tex]A = \int\limits^{1}_{0} {x^{2}} \, dx + 2\int\limits^{1}_{0}\, dx + \int\limits^{1}_{0} {x} \, dx[/tex]

[tex]A = \frac{1}{3}\cdot (1^{3}-0^{3}) + 2\cdot (1-0) +\frac{1}{2}\cdot (1^{2}-0^{2})[/tex]

[tex]A = \frac{17}{6}[/tex]

The net area between the two functions is 17/6. [tex]\blacksquare[/tex]

The definite integral is described below:

[tex]A = \int\limits^{0}_{-1} {e^{-x}} \, dx+ \int\limits^{0}_{-1} {x} \, dx[/tex]

[tex]A = -(e^{0}-e^{1}) + \frac{1}{2}\cdot [0^{2}-(-1)^{2}][/tex]

[tex]A \approx 1.218[/tex]

The net area between the two functions is approximately 1.218. [tex]\blacksquare[/tex]

This case requires a combination of definite integrals, as f(x) may be higher that g(x) in some subintervals. The combination of definite integrals is:

[tex]A = \int\limits^{\frac{\pi}{3} }_0 {\sin 2x} \, dx - \int\limits^{\frac{\pi}{3} }_{0} {\sin x} \, dx + \int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin x} \, dx -\int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin 2x} \, dx[/tex]

[tex]A = -\frac{1}{2}\cdot (\cos \frac{2\pi}{3}-\cos 0)+(\cos \frac{\pi}{3}-\cos 0 ) -(\cos \frac{\pi}{2}-\cos \frac{\pi}{3} )+\frac{1}{2}\cdot (\cos \pi-\cos \frac{2\pi}{3} )[/tex]

[tex]A = \frac{1}{2}[/tex]

The net area between the two functions is 1/2. [tex]\blacksquare[/tex]

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Answer:

A, C, D

All 3 of those simplfiy to 4√5

The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.

The center is the point that is equidistant to every point on the circumference. First, we need to determine the coefficients of the general equation of the circle, whose form is described below:

x² + y² + D · x + E · y + F = 0   (1)

We need three distinct points of the circumference to determine one solution.

If we know that (x₁, y₁) = (1, 2), (x₂, y₂) = (3, 4) and (x₃, y₃) = (3, 2), then the system of linear equations is:

D + 2 · E + F = -5   (2)

3 · D + 4 · E + F = - 25   (3)

3 · D + 2 · E + F =  - 13   (4)

The solution of the linear system is D = - 4, E = - 6 and F = 11.

Now we proceed to transform the expression into its standard form by completing the squares:

x² + y² - 4 · x - 6 · y + 11 = 0

(x² - 4 · x + 4) + (y² - 6 · y + 9) - 2 = 0

(x - 2)² + (y - 3)² = 2

The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.

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Answer:

160

Step-by-step explanation:

FEJ angle is the large angle and the number in red shows how big it is. Remember the whole thing is 180 degrees.

Answer:

It will take 16 hours to earn $144.

Step-by-step explanation:

If Adam earns $36 in 4 hours,

36 = 4k

k = 9

Therefore, expression for total earnings will be,

y = 9x

a). For y = $144,    144 = 9x      x = 16 hours

Plug in the value of p:-

16+2q=40

Subtract 16 from both sides:-

2q=40-16

2q=24

Divide both sides by 2:-

q=12 ✓

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Here we would be using distance formula to calculate the distance between those two points.

★ Points are,

★ Distance Formula :

★ We have :

x1 = 3

x2 = -2

y1 = 9

y2 = 4

★ Substituting the values :

Centroid of a triangle :-

Midpoint of two points:-

Answer:

y  = 60.3

Step-by-step explanation: