what does it mean for statements to be logically equivalent?

Answer:

The constant factor between consecutive terms of a geometric sequence is called the common ratio.

Example:

To find the common ratio , find the ratio between a term and the term preceding it. r=42=2. 2 is the common ratio.

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Answer:

x=6

Step-by-step explanation:

Step 1:

Subtract 3x from both sides:

4x + 8 - 3x = 3x + 14 - 3x

x + 8 = 14

Step 2:

Subtract 8 from both sides:

x + 8 - 8 = 14 - 8

x = 6

Answer:

√1681=41

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

yes,

as AB = CD Which means both their values are same

CD = EF ( which also means their values are same)

as, AB have same values as CD and EF also have same values as CD so,

AB = EF.

hope this answer helps you dear take care!

[tex]\\ \sf\longmapsto m(n+r)=5p[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{5p}{(n+r)}[/tex]

we are done

Answer:

I'm not sure directly but try spliting them up first.

Step-by-step explanation:

Sorry!

Answer:

its - 1 31 over 33

Step-by-step explanation:

Answer:

Common ratio: -3

Geometric sequence: an=5(-3)^n-1

Step-by-step explanation:

Each number multiplied by -3 gets the product of the next number. (5*-3= -15)

Answer:

[tex]x = \frac{1}{2}y[/tex] or [tex]y = 2x[/tex]

Step-by-step explanation:

Basically, x is 2 times smaller than y, or

y is 2 times larger than x.

For example, when x equals 4, y is 2 times greater, so y = 4 * 2 = 8

Another example:

When y equals 12, x must be 2 times smaller than that, so x = 12 / 2 = 6

I don't know which one you're looking for, but try putting in

x = 1/2y or y = 2x

Hope this helped!

Answer:

im not quite sure but i think it's asking for the gradient so i think it's 2

Step-by-step explanation:

becasue gradient = rise/run

so 10/5

hope this helps :))

Answer:

21.413

Step-by-step explanation:

Change the divisor 0.63512 to a whole number by moving the decimal point 5 places to the right. Then move the decimal point in the dividend the same, 5 places to the right.

We then have the equations:

1360000 ÷ 63512 = 21.413

and therefore:

13.6 ÷ 0.63512 = 21.413

Both calculated to 3 decimal places.

Answer:

[tex]m=7[/tex]

Step-by-step explanation:

[tex]5\left(m-3\right)-4\left(m-2\right)=0[/tex]

[tex]5\left(m-3\right)-4\left(m-2\right)[/tex]

[tex]5m-15-4m+8[/tex]

[tex]m-7[/tex]

[tex]m-7+7=0+7[/tex]

[tex]m=7[/tex]

GOOD LUCK!! :)

Answer:

y=2x-3

Step-by-step explanation:

refer to picture plz

Answer:

the desired equation is y = 2x - 3

Step-by-step explanation:

Parallel lines have the same slope.  Thus, a new line parallel to y = 2x - 4 has the slope 2.  

Find the equation of the new line by writing out the slope-intercept form

y = mx + b.  Substitute -1 for y and 1 for x:

-1 = 2(1) + b, which yields b = -3

Then the desired equation is y = 2x - 3

Original line: y = -5/6x - 1

A line that is parallel to the original will have the same slope. To find the new y-intercept, we'll take the original line, plug in the given point, and solve for b.

y = -5/6x + b

-2 = -5/6(5) + b

-2 = -25/6 + b

b = 13/6

Parallel Line: y = -5/6x + 13/6

A line that is perpendicular to the original will have the opposite reciprocal slope. To find the new y-intercept, we'll take our perpendicular slope, plug in the given point, and solve for b.

y = 6/5x + b

-2 = 6/5(5) + b

-2 = 6 + b

b = -8

Perpendicular Line: y = 6/5x - 8

Hope this helps!! :)

Answer: - 4d

Step-by-step explanation:

In the equation, there's an invisible 1 in front of the first d, so let's add that.

1d - 2d - 3d

Since all the terms in the above equations are like terms, we would focus on only subtracting. We would first subtract 2d from 1d.

- 1d - 3d

We then subtract 3d from - 1d. This would give us our answer.

- 4d

Answer:

y = 3/4x + 2

Step-by-step explanation:

Answer:

2.13

Step-by-step explanation:

Step-by-step explanation:

[tex]| 2.35 – 4.89 | + | 8.39 – 3.72 |\\\\|-2.54|+|4.67|\\\\2.54+4.67\\\\\boxed{\underline{7.21}}[/tex]

Answer:

77 degrees and 90 degrees

The angle d is shown as 90 by the perfect right angle. The angle e has to equal 180 when added to f. So 180-103=77.

Answer:

Step-by-step explanation:

substituting in the values of s, b,t and n in the expression then,

(2.4 × -7.2 × 4.8) - (-7.2 × 4.8 × -9.6)

= - 82.944 -331.776

= -248.832

Answer:

The first one/answer.

Step-by-step explanation:

Answer:

at first find the slope of the line

by using this formula...

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

again..

find the equation of line by using the formula

[tex]y - y1 = m(x - x1)[/tex]

and u will get ans

Answer: Mr. Nut

Step-by-step explanation: Divide the price by the amount of oz. are in each brand to find the price of one oz of nuts. Round it to the nearest 100th because we're talking about money, Then compare the prices, then you have your answer! If my calculations are correct.

Answers:

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

Explanation:

Parallel lines always have equal slopes, but different y intercepts. For example, the two lines y = 3x+5 and y = 3x+7 have a slope of 3. Refer to y = mx+b where m is the slope. Parallel lines never intersect.

-----------

For perpendicular lines, the two slopes always multiply to -1 assuming neither line is vertical nor horizontal. Consider the two linear equations

y = (1/2)x+5

y = -2x-7

The slopes 1/2 and -2 multiply to -1 which is enough to show that they are perpendicular lines. The two lines meet at a 90 degree angle.

To go from one slope to the other, we apply the negative reciprocal. That means we...

Applying the first step to 1/2 gets us 2/1 or 2. Then changing the sign has us go from 2 to -2. This process can be reversed.

-----------

For some of these equations, you'll need to rearrange things into either point-slope form or slope intercept form. This will allow you to read off the slope.

Point slope form is y-y1 = m(x-x1)

Slope intercept form is y = mx+b

For either case, all we care about is the variable m.

I'll show how problem 14 transforms into slope intercept form

x+2y = 14

2y = -x+14

y = (-x+14)/2

y = (-x/2) + (14/2)

y = (-1/2)x + 7

We see that m = -1/2 here. Anything parallel to this will have the same slope. The perpendicular slope is 2 after applying the negative reciprocal operation. Problems 13, 15, 16, 17, and 18 are going to follow similar steps.

Answer:

(-4)(3+7)=-40

‌‌‌‌ ‌ ‌ ‌ ‌ ‌ ‌ ‌‌ ‌ ‌ ‌ ‌‌‌‌ ‌ ‌‌‌ ‌ ‌ ‌ ‌‌ ‌ ‌ ‌ ‌‌

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

According to above diagram :

RT = RS + ST

that is :

now, RT = 2x + 75

hence , RT = 31 units

Answer:

RT = 31

Solve for x:

[tex]x=-22[/tex]

Step-by-step explanation:

==>> The sum of the line is RST

[tex]4x+107+12=RST[/tex]

==>> Since [tex]RST = 2x + 75[/tex], the equation will newly become [tex]4x+107+12=2x+75[/tex]

--

To find [tex]4x+107[/tex], we need to find the x.

==>> [tex]x=-22[/tex]

-- Lets check our work

==>> [tex]4(-22) = -88[/tex]

[tex]-88 + 107 = 19 [RS = 19][/tex]

[tex]RS + ST = 19 + 12 =[/tex] 31

--

[tex]2(-22) = -44[/tex]

[tex]-44 + 75 =[/tex] 31

31 = 31

Answer:

x = 32

<1 = 102 degrees

<2 = 78 degrees

Step-by-step explanation:

3x + 6 + 2x + 14 = 180

5x + 20 = 180

5x = 180 - 20

x = 160/5

x = 32

3(32) + 6 = 102 degrees

180 - 102 = 78 degrees

The proportional relationship is given by y = 8.5x

Two variables are said to be proportion if an increase/decrease in one variable causes an increase/decrease in the other variable.

Let x represent the movie tickets and y represent the cost.

Since x and y are proportional, hence:

y ∝ x

y = rx

Where r is the constant of proportionality.

From the table to find x, when y = 17, x = 2, hence:

17 = 2r

r = 8,5

y = 8.5x

The proportional relationship is given by y = 8.5x

Find out more at: https://brainly.com/question/17178834

Answer:

67 tickets (with $5 extra)

Step-by-step explanation:

1000÷15= Number of tickets

Answer:

96 strawberries (c)

Step-by-step explanation:

the ratio from strawberry to tart:

4:1

the ratio if we have 24 tarts:

?:24

from multiplying the tart by 24 we must multiply the strawberries by 24 making the ratio:

96:24