9. The sum, Sn, of the first n terms of a geometric progression is given by Sn = 3" - 1.
(a) the sum of the first 8 terms. ​

I hope it helps you

An compound inequality that describes the acceptable weights for a 20 oz box is 19.25 ≤ x ≤ 20.75.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To determine the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

We are Given that, cereal manufacturer has a tolerance of 0.75 oz for a box of cereal that is supposed to weigh 20 oz.

Let the weight of cereal box be; w

Now, the inequality is

20-0.75 ≤ x ≤ 20+0.75

Add 20 on both sides of an inequality, we get

19.25 ≤ x ≤ 20.75

Here, 19.25 ≤ x ≤ 20.75

Therefore, an absolute value inequality to find the range of acceptable weights is 19.25 ≤ x ≤ 20.75.

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Answer:

[tex]y=-\frac{5}{2}x-24[/tex]

Step-by-step explanation:

[tex]2x-5y=-12\\5y=2x+12\\y=\frac{2}{5}x+\frac{12}{5}\\[/tex]

if two lines perpendicular,

[tex]m_{1} .m_{2}=-1\\ \frac{2}{5} .m_{2}=-1\\m_{2}=-\frac{5}{2}[/tex]

the line perpendicular to this line is

[tex]y=-\frac{5}{2}x+k[/tex] ; k ∈ R

the line passes through the point (10,-1)

so,

[tex]-1=-\frac{5}{2} (10)+k\\-1=-25+k\\k=-24[/tex]

∴the equation of the line perpendicular to 2x-5y=-12 that passes through the point (10,-1) is

[tex]y=-\frac{5}{2}x-24[/tex]

Answer:

m is the slope and b is the y intercept

Step-by-step explanation:

Answer:

Step-by-step explanation:

6)b) Sin A - x Cos A = 0

Sin A = x Cos A

[tex]\dfrac{Sin \ A}{Cos \ A} = x[/tex]

[tex]\dfrac{1}{x}=\dfrac{1}{\dfrac{Sin \ A }{Cos \ A}}=1*\dfrac{Cos \ A}{Sin \ A}=\dfrac{Cos \ A}{Sin \ A}[/tex]

[tex]RHS = x +\dfrac{1}{x}\\\\\\[/tex]

         [tex]= \dfrac{Sin \ A}{Cos \ A}+\dfrac{Cos \ A}{Sin \ A}\\\\\\=\dfrac{Sin \ A*Sin \ A}{Cos \ A*Sin \ A}+\dfrac{Cos \ A * Cos \ A}{Sin \ A* Cos \ A}\\\\\\= \dfrac{Sin^{2} \ A}{Cos \ A*Sin \ A}+\dfrac{Cos^{2} \ A}{Cos \ A* Sin \ A}\\\\= \dfrac{Sin^{2} \ A+Cos^{2} \ A}{Cos \ A*Sin \ A}\\\\=\dfrac{1}{Cos \A*Sin \ A}\\\\= \dfrac{1}{Cos \ A}*\dfrac{1}{Sin \ A}\\\\=Sec \ A * Cosec \ A[/tex]

          = LHS

7a) 1 - Sin A = 1/2

     [tex]1 = \dfrac{1}{2}+ Sin \ A\\\\1-\dfrac{1}{2}=Sin \ A\\\\\dfrac{1}{2}=Sin \ A\\[/tex]

⇒ A = 30°

Sec² A = Sec² 30° = [tex](\frac{2}{\sqrt{3}})^{2}=\frac{2^{2}}{(\sqrt{3)^{2}}}=\frac{4}{3}[/tex]

[tex]tan^{2} \ A = tan^{2} 30 = (\dfrac{1}{\sqrt{3}})^{2} = \dfrac{1}{3}[/tex]

LHS = 6 Sec² A + 9 tan² A

       [tex]= 6*\dfrac{4}{3}+9*\dfrac{1}{3}\\\\\\=2*4 + 3*1\\\\\\= 8 + 3\\\\= 11 = RHS[/tex]

Answer:

Step-by-step explanation:

   If the points P, Q, V and K are collinear, they will follow the segment addition postulate.

Measure of segment VP will be 214 units.

   It's given in the question,

By segment addition postulate,

            KQ + VQ + VP = KP

Substitute the values in the expression,

(11x + 5) + (17x + 6) + (14x + 4) = x + 630

(11x + 17x + 14x) + (5 + 6 + 4) = x + 630

42x + 15 = x + 630

42x - x = 630 - 15

41x = 615

x = [tex]\frac{615}{41}[/tex]

x = 15

Therefore, measure of VP = (14x + 4)

                                           = 14(15) + 4

                                          = 214 units

Measure of segment VP will be 214 units.

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Answer:

x + 2 + 3x = 30

Step-by-step explanation:

Both lengths are unknown, but Ginny's car length is described in terms of Zach's car length, so we choose a variable for Zach's car length.

Let x = Zach's car length.

Zach's car length is x.

"Ginny's car is 2 more than 3 times the length of Zach's car."

Ginny's car length is 2 + 3x.

Add the lengths:

x + 2 + 3x

"The sum of the lengths of both cars is 30 inches."

x + 2 + 3x = 30

Answer: x + 2 + 3x = 30

Answer:

3a^2+8/6a^2

Step-by-step explanation:

there ya go hope this helps

Answer:

1.6667

Step-by-step explanation:

It took awhile to get this

Answer:

a=24

b=7

now

24+(7-4)

24+3

27

so the answer is 27

Answer:

a = 9

b = 2

Step-by-step explanation:

Given : a = 9

a = b + 7

9 = b + 7

b = 9 - 7 = 2

Answer:

8x-7

Step-by-step explanation:

-11 + 8x - 2 + 6

8x-7 .........

Answer:

X=-5/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution of a linear system is the intersection of the lines.

We can see the lines A and B intersect at the point (7.5, 12) which is the solution.

See attached for better visualization.

Answer:

(7.5,12.5)

Step-by-step explanation:

Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

Step-by-step explanation:

Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero

Step-by-step explanation:

First, let's write down what we know.

AB = 3x

AC = 5x+21

Since B is the midpoint, AB is half the length of AC. The sum of AB + AB is equal to the length of AC.

AB + AB = AC

Let's plug in our values.

3x + 3x = 5x + 21

Simplify the left side.

6x = 5x + 21

Subtract 5x from both sides.

x = 21

Now, let's plug in 21 for x in AB

AB = 3x = 3(21) = 63

Step-by-step explanation:

Distance = √(x_2 - x_1)² + (y_2 - y_1)²

Distance = √[(-a) - a]² + (b - b)²

Distance = √[-2a]² + (0)²

Distance = √4a²

Distance = 2a

Answer:

64w^2

Step-by-step explanation:

Because 8w is in parentheses, you must apply the exponent to both the 8 and w.

So, it becomes (8*8)(x*x) which equals (64)(x^2).

Which then gives you your final answer, 64x^2.

Answer:

17

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]8^{2}[/tex] +[tex]15^{2}[/tex] =[tex]c^{2}[/tex]

64  + 225 = [tex]c^{2}[/tex]

289 = [tex]c^{2}[/tex]

[tex]\sqrt{289}[/tex] = [tex]\sqrt{c^{2} }[/tex]

17 = c

Answer:  1  1/2

You can write this as 1 & 1/2

The whole part is 1. The fractional part is 1/2

==========================================================

Explanation:

Let's say we had 18 cookies to hand out to 12 students.

How many cookies does each student get?

Using a calculator shows that 18/12 = 1.5 which means they get one whole cookie each

The leftovers is 18-12 = 6

Then notice how 6/12 = 1/2

So that's how the improper fraction 18/12 becomes the mixed number 1 & 1/2

So each student gets 1 full cookie, plus half a cookie.

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

Or we could do the problem like this

18/12 = (12+6)/12

18/12 = (12/12)+(6/12)

18/12 = 1 + (1/2)

18/12 = 1 & 1/2

Answer:

You cant check your answer by yourself

if your procces is Right then obviously your answer will be correct

I hope you will understand

thank you

jay Nepal

Answer:

The balance would be $160 from whatever it was before the 4 months.

Step-by-step explanation:

Since the bank balance is being added by 40 for each month for 4 months, 4 * 40 is just 4*4 with an extra zero on the end. so that would be $160.

So if the balance before was $40, then the new balance after 4 months would be $200.

If there's no money previously, then there is now $160 after 4 months.

If there's a value before the $40 for 4 months, let me know and I will explain and tell you what it is.

Answer:

x = -25

Step-by-step explanation:

[tex]3 - \frac{x}{5} = 8[/tex]

[tex]5(3 - \frac{x}{5} ) = 5 \times 8[/tex]

[tex]5 \times 3 - 5 \times \frac{x}{5} = 5 \times 8[/tex]

[tex]15 - 5 \times \frac{x}{5} = 40[/tex]

[tex]15 - x = 40[/tex]

[tex] - x = 40 - 15[/tex]

[tex] - x = 25[/tex]

[tex]x = - 25[/tex]

Answer:

x = - 25

Step-by-step explanation:

Given

3 - [tex]\frac{x}{5}[/tex] = 8 ( subtract 3 from both sides )

- [tex]\frac{x}{5}[/tex] = 5 ( multiply both sides by 5 to clear the fraction )

- x = 25 ( multiply both sides by - 1 )

x = - 25

Step-by-step explanation:

Qualitative data are discrete, for instance, "Yes/No" type questions. They are usually presented in bar charts or pie charts to show the portion of different populations with certain characteristics in a single experiement (e.g. Not allergic to ginger VS allergic to ginger).

Qualitative data are usually continuous, and can show a trend or distribution numerically. They are usually presented by, for instance, line charts (e.g. Distribution of resident age in block E)

Answer:

According to my equation it's 20°

Answer:

y = 17

Step-by-step explanation:

3x = y - 5, for x = 4

=> 3(4) = y - 5

=> 12 = y - 5

=> 12 + 5 = y

=> 17 = y

Answer:

7 quarts

Step-by-step explanation:

you subtract the amount that the first aquarium can hold from the second amount