Factor the binomial expansion. 81x4 – 648x3 + 1,944x2 – 2,592x + 1,296

Answer: $183,731

Step-by-step explanation:

After 30 years, the interest is $183,731

O is parallel to q

let's take the angle opposite to angle 4 is alpha

angle 4 = angle alpha ( vertically opposite angles)

angle alpha = angle 3 ( as angle 4 = angle 3).

hence o is parallel to q as both the angles are equal

Answer: y = 4x + 5/4

Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.

Answer:

Domain: [1, infinity)

Range: All real numbers or (- infinity, + infinity)

Step-by-step explanation:

Hope this helps

Answer:

y = -t

Step-by-step explanation:

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

⇒ parametric equation of line passing through a point (a₁, b₁, c₁)

   and parallel to a vector <a, b, c> is given by :

   x =a₁ + at ,   y = b₁ + bt   ,   z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line,   x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is=  <2, -1, 3>

now using above formula,

equation of line is =   x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t    (answer)

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Answer: [tex]4.5 \text{ cm}^{2}[/tex]

Step-by-step explanation:

[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2}(3)(3)\\\\\boxed{A=4.5 \text{ cm}^{2}}[/tex]

The area of the triangle will be equal to 4.5 square centimeters.

The space occupied by any two-dimensional figure in a plane is called the area. The space covered by the triangle in the two-dimension is called an area of the triangle.

The area of the triangle ABD will be calculated as:-

Area = [tex]\dfrac{1}{2}[/tex] x Base x height

Area = [tex]\dfrac{1}{2}[/tex] x 3 x 3

Area = 4.5 cm.

Therefore the area of the triangle will be equal to 4.5 square centimeters.

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Probability helps us to know the chances of an event occurring. The probability of winning the bet is 0.125.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given the odds on a bet are 7:1, therefore, there are a total of 8 cases out of which only one case is of winning. Thus, the probability of winning the bet will be,

Probability = 1/8 = 0.125

Hence, the probability of winning the bet is 0.125.

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The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.

We have a quadrilateral shown in the picture.

The diagonal divides the quadrilateral into two triangles

The area of the quadrilateral = area of the triangle ADC + area of the

                                                   triangle ADB

= (1/2)3.42×4.39 + (1/2)5.44×3.42

= 7.5069 + 9.3024

= 16.80 square units

Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

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Answer:

[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]

so y = 3x - 3

since 3x + 6 is on the bottom,

[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]

so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)

Answer:

They are not similar because corresponding sides are not proportional.

Condition for similarity of two triangles -

The ratio of corresponding sides should be equal.

Condition for congruence of two triangle -

Any of the following -

Side side side

side angle side

angle angle

angle side angle

Answer:

1/2(6-8), 1/2(-3+7)=-1,2

Answer: C - (-1, 2)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

dvdywuwhfuwi eurue wuid

Part 1

[tex]D \cup E[/tex] denotes the union of the two sets (in other words, all the elements in both sets).

This means it is [tex](-\infty, 4) \cup [7, \infty)[/tex]

Part 2

[tex]D \cap E[/tex] denotes the elements shared between both sets.

This means the answer is [tex](4, 7][/tex]

[tex]|\Omega|=10\cdot9=90\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6.7\%[/tex]

Answer:

y = 4x - 5

Step-by-step explanation:

y = mx + b

By putting above values in equation (i)

-1 = 4 (1) + b

-1 = 4 + b

-5 = b

b = -5

y = 4x - 5

Answer:

110

Step-by-step explanation:

Suppose lines EH and BD are parallel:

Angle <GFE and angle <ABC are supplementary so their sum is equal to 180

2x + 10 + x  + 20 = 180 add like terms

3x + 30 = 180 subtract 30 from both sides

3x = 150 divide both sides by 3

x = 50

We are asked the value of <ACD

<ABD and <ACD are also supplementary so we can find the value od <ACD:

x + 20 + <ACD = 180 we know x = 50 so we can replace x with that

50 + 20 + <ACD = 180

70 + <ACD = 180 subtract 79 from both sides

<ACD = 110

Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]

[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]

8 × -3 = -24

Answer: Options 1 and 2

Step-by-step explanation:

To model exponential decay, the base of the exponential has to be less than 1.

Model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

Model exponential decay equation

Option C and D have the base value greater than 1. So it can't be model exponential decay equation.

Hence, the model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

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Answer:

x= 0, y= -1

Step-by-step explanation:

To obtain the values of x and y from a system of equations, start by labelling the given equations.

8x +5y= -5 -----(1)

7x -3y= 3 -----(2)

Let's solve by elimination.

Here, I will be working to eliminate the y term. This is done by ensuring both equations have the same numerical value in the coefficient of y.

(1) ×3:

24x +15y= -15 -----(3)

(2) ×5:

35x -15y= 15 -----(4)

Add the two equations together since the coefficient of y has opposite signs.

(3) +(4):

24x +15y +35x -15y= -15 +15

59x= 0

Divide both sides by 59:

x= 0

Now, substitute the value of x into any equations to find the value of y.

Substitute x= 0 into (1):

8(0) +5y= -5

5y= -5

Divide both sides by 5:

y= -5 ÷5

y= -1

Additional:

For similar questions on system of equations, do check out the following!

The correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have:

A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C.

As the value of MOE is 0.13 degrees

It is a serious problem because the margin of error is quite narrow in comparison to the shift from year to year.

Thus, the correct option would be The margin of error is quite small compared to the change year over year, so it is a significant issue option third is correct.

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Substituting into the formula d=m/v,

[tex]7.98=\frac{m}{60}\\\\m=\boxed{478.8 \text{ gm}}[/tex]

The area of the rectangular garden given the length and width is 16 1/2 square feet

Area of a rectangular garden = length × width

= 5 1/2 feet × 3 feet

= 11/2 × 3

= 33/2

= 16 1/2 square feet

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The function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Given that:-

The cost of the 250 minutes is $25 and if the time extends from 250 minutes then the function will be expressed in the form of.

C(x) = 25 + 0.2 (x)

Here C(x) is the total cost and the x is in minutes.

Hence the function will be given as C(x) = 25 + 0.2(x) here x is in minutes.

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Answer:

40 divided by 10

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: -15625

Step-by-step explanation:

The explicit formula for the sequence is

[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]

Answer:

the answer is -7+-25=-32