Use the rectangular prism to answer the question.
Choose all the expressions that can be used to find the volume of the rectangular prism.
A 12 +12
OD 6 + 8 + 12
B 16 +16
E 6 + 6 + 6 + 6
C. 8+8+8

9514 1404 393

Answer:

  [tex]\displaystyle S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}[/tex]

Step-by-step explanation:

The sequence terms appear to have numerators that are powers of 3, and denominators that are a linear (arithmetic) sequence with a first term of 1 and a common difference of 3.

  numerator: 3^x

  denominator: 1 +3(n -1) = 3n-2

Then the sum of n terms of the sequence can be described by ...

  [tex]\displaystyle \boxed{S_n=\sum_{k=1}^n{\frac{3^k}{3k-2}}}[/tex]

Comparing the parabola's equation to the formula [tex]y = ax^2 + bx + c[/tex] in standard form is the first step. In step 2 Apply the formula h = -b/2a to find the vertex's x-coordinate. In step 3 Substitute x = h in the expression [tex]y = ax^2 + bx + c[/tex]  to obtain the vertex's y-coordinate (k).

The equation of the parabola's axis of symmetry is the vertex's x-coordinate. The axis of symmetry for a quadratic function in standard form, [tex]y = ax^2 + bx + c[/tex] is a vertical line, [tex]x=b^2a[/tex].

The intersection of two lines or rays that create an angle is known as the vertex of the angle.

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The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Advantages include:

Disadvantages:

Additional expenses include

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Answer:

P(A) * P(B)

.25*.55

.1375

Step-by-step explanation:

P(A) * P(B)

.25*.55

Answer:

9 because the opposite of -9 is 9

hope this helped gl

Step-by-step explanation:

The coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)

An equation is an expression that shows the relationship between two or more variables and numbers.

Let (x, y) represent the coordinate of the midpoint E. Point E is the midpoint of CD, hence:

x = [(-7) + (-3)] / 2 = -5

y = [(-2) + (-5)] / 2 = -3.5

Therefore the coordinates of the midpoint of CD with endpoint at C(-7,-2) and D(-3,-5) is E(-5, -3.5)

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Answer:

B) One solution

Step-by-step explanation:

Clearly, the two linear equations graphed have one point of intersection, which means one solution.

Answer:

B

Step-by-step explanation:

the solution is the intersection of the two lines

Answer:

x = 12

Step-by-step explanation:

i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]

ii. 29 - 5 = 2x

iii. 24 = 2x

iv. x = 24/2

v. x = 12

Answer:

38.13m²

Step-by-step explanation:

We find the area of ;

Rectangule and semicircle

Area of rectangle :

Length * width

Length = 8m ; width = 3m

Area = 8 * 3 = 24m²

Area of semicircle = 1/2 πr²

Radius, r = 3m

A = 1/2 * 3.14 * 3²

A = 1/2 * 3.14 * 9

A = 14.13 m²

Area of patio :

(24 + 14.13)m²

= 38.13m²

Answer:

Step-by-step explanation:

you should give the function, if i haven't it, how can i help you.

i can give u some tips, put 1.5, 2.5, 2 in function respectively. then calculate them, u will get the answer.

Answer:

.45

Step-by-step explanation:

it wants u to divide 5.40 by 12

HOPE THIS HELPS CHU (≧w≦)

The formula for continuously compounded interest is:

A = P * e^(rt)

where:

A is the final amount

P is the initial amount (the principal)

r is the annual interest rate (in decimal form)

t is the number of years the interest is compounded

Substituting in the given values, we get:

A = $28,000 * e^(0.0525 * 4) = $28,000 * e^0.21 = $28,000 * 1.23 = $28000*1.23 = 34,540

Therefore, there will be $34,540 in the account after 4 years.

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Answer:

3(6m)+m=18m+m=19m so your answer would be A. 19m

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

You just do 6 / 1/4 = 24

As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.

The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two collinear and an equal marker in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar).  An identity holds true regardless of the value given to the variables.

given

Equation as given:

y = 6 (x - 1/2)(x+3)

To identify the equation's graph's y-intercept

Put x = 0 in place of it in the equation.

y = 6 (0 - 1/2)(0+3)

Apply the math operation, then find y.

y = -9

As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.

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Answer:

12 red marbles in the bag

Answer:

0.14

Step-by-step explanation:

The answer is: 0.14

I hope this helps!

Table (x, y) equals (0, 0), (6, 3), and (12, 6) represents a linear relationship that is also proportional.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The first option is linear but not proportional as 3 ×2 = 6 and 6×2 = 12.

By observing the given options we conclude that the third option is linear and proportional as,

6 ÷ 2 = 3 and 12 ÷ 2 = 6.

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Answer:

[tex]m = 10\sqrt 3[/tex]

[tex]n = 10[/tex]

Step-by-step explanation:

Required

Find m and n

Considering the given angle, we have:

[tex]\sin(60) = \frac{Opposite}{Hypotenuse}[/tex]

This gives:

[tex]\sin(60) = \frac{m}{20}[/tex]

Make m ths subject

[tex]m = 20 * \sin(60)[/tex]

[tex]\sin(60) =\frac{\sqrt 3}{2}[/tex]

So, we have:

[tex]m = 20 *\frac{\sqrt 3}{2}[/tex]

[tex]m = 10\sqrt 3[/tex]

Considering the given angle again, we have:

[tex]\cos(60) = \frac{Adjacent}{Hypotenuse}[/tex]

This gives:

[tex]\cos(60) = \frac{n}{20}[/tex]

Make n the subject

[tex]n = 20 * \cos(60)[/tex]

[tex]\sin(60) =\frac{1}{2}[/tex]

So, we have:

[tex]n = 20 *\frac{1}{2}[/tex]

[tex]n = 10[/tex]

Answer:

136in^2

Step-by-step explanation:

Answer:

A = 0.5 × [ sqrt(17^2 - 15^2) ] × 15 + 0.5 × [ sqrt(25^2 - 15^2) ] × 15 = 210 in^2

Answer:

20 inches

[tex]c = \sqrt{12 ^{2} + 16 ^{2} } \\ c = \sqrt{400} \\ c = 20[/tex]

On solving the provided question, we cans ay that By unitary method, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

By unitary method,

original length of pipe = 3/9 inch

shortened length of pipe = 2/9

so, the amount to be removed = original - shortened = 3/9 - 2/9 = 1/9

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Answer:

Step-by-step explanation:

(99)3 =

(99) x 3 =

(90 + 9) x 3 =

(90) x 3 + (9) x 3 =

90 x 3 + 9 x 3 =

270 + 27 =

297

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Evaluate (99)^3 using suitable identities.

(99)^3 = (100 - 1)^3

since, (a - b)^2 = a^3 - b^3 - 3ab (a-b)

Where,

Now,

(99)^3

=> (100)^3 - (1)^3 - 3(100)(1)(100 - 1)

=> 1000000 - 1 - 3(100)(100 - 1)

=> 1000000 - 1 - 300 (99)

=> 1000000 - 1 - 29700

=> 970299 Ans.

Given:

The terms of a sequence are:

[tex]-6,-\dfrac{11}{2},-5[/tex]

To find:

The number of terms whose sum is -25.

Solution:

We have, the given sequence:

[tex]-6,-\dfrac{11}{2},-5[/tex]

Here, the first term is -6.

[tex]-\dfrac{11}{2}-(-6)=-5.5+6[/tex]

[tex]-\dfrac{11}{2}-(-6)=0.5[/tex]

Similarly,

[tex]-5-(-\dfrac{11}{2})=-5+5.5[/tex]

[tex]-5-(-\dfrac{11}{2})=0.5[/tex]

The difference between consecutive terms are same. So, the given sequence is an arithmetic sequence with common difference 0.5.

The sum of n terms of an arithmetic sequence is:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Where, a is the first term, d is the common difference.

Putting [tex]S_n=-25,a=-6,d=0.5[/tex], we get

[tex]-25=\dfrac{n}{2}[2(-6)+(n-1)0.5][/tex]

[tex]-50=n[-12+0.5n-0.5][/tex]

[tex]-50=-12.5n+0.5n^2[/tex]

[tex]0=0.5n^2-12.5n+50[/tex]

Splitting the middle term, we get

[tex]0.5n^2-2.5n-10n+50=0[/tex]

[tex]0.5n(n-5)-10(n-5)=0[/tex]

[tex](0.5n-10)(n-5)=0[/tex]

Using zero product property, we get

[tex](0.5n-10)=0[/tex] and [tex](n-5)=0[/tex]

[tex]n=\dfrac{10}{0.5}[/tex] and [tex]n=5[/tex]

[tex]n=20[/tex] and [tex]n=5[/tex]

Therefore, the sum of either 5 or 20 terms is -25.

Answer:

The answer is 7/9

Step-by-step explanation:

Had this on my quiz one time

Answer:

7-9

Step-by-step explanation:

The solution to the inequality is (-∞, 4.05) .An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Both equations and inequalities are mathematical phrases created by connecting two expressions.

The equal sign (=) in an equation denotes that the two expressions are regarded as equal.

In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

Given the inequality:

-3(4 – x) 6 < 9 – 2x

Solving the inequality:

(-12 + 3x)6 < 9 - 2x

-72 + 18x < 9 - 2x

20x < 81

x < 4.05

Therefore the solution to the inequality is (-∞, 4.05)

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