Using the properties of exponents and logarithms, find the value of x in 19+2 in x=25

Answer:

The value of a4 is 6

Step-by-step explanation:

* Lets revise the rule of the geometric series

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)  

* General term (nth term) of a Geometric series:

- a1 = a  ,  a2 = ar  ,  a3  = ar2  ,  a4 = ar3  ,  a5 = ar4

- an = ar^n-1, where a is the first term , r is the constant ratio

  between each two consecutive terms  and n is the position

  of the number in the series

* Now lets solve the problem

- The rule of the series is  2/9 (3)^n - 1

∴ a = 2/9 and r = 3

- To find a4 put n = 4

∴ a4 = 2/9 (3)^(4 - 1) = 2/9 (3)³ = 2/9 (27) = 6

∴ The series is 2/9 , 2/3 , 2 , 6 , ........

* The value of a4 is 6

Answer:

r

Step-by-step explanation:

(–1,4)

Shapes are congruent if you can turn one into the other by moving, rotating or flipping. We can use this symbol [tex]\cong[/tex] to show that two things are congruent. Two triangles are congruent if and only if all the corresponding legs are congruent. The only point that makes the corresponding legs to be congruent is [tex](-1,4)[/tex]. Why? because we can match these two triangles by flipping the red one two times and moving it into the blue one.

Answer:

(–1,4)

Step-by-step explanation:

Answer:

The 3rd problem on mondays answer is 2:1

The 4th problem on monday answer is it is not long enough he needs to make it 4 inches longer.

The 5th problem on monday is 41

The 6th problem on monday is 13,12,11

Can't read the whole problem for the 7th question on monday

the 8th problem on monday is 55 and 8/15

That is the answers for monday hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Z score is the number of standard devations above the mean.

For example if z=1, the data value is 1 st. dev. above the mean.

So, z=1.95, so the player's heigh is 1.95 st. dev. above the mean.

Answer:

[tex]0.056\ \frac{miles}{second}[/tex]

Step-by-step explanation:

we know that

The rate is equal to

[tex]200\ \frac{miles}{hour}[/tex]

Remember that

[tex]1\ hour=3,600\ seconds[/tex]

substitute

[tex]200\ \frac{miles}{hour}=(200/3,600)\ \frac{miles}{seconds}=0.056\ \frac{miles}{second}[/tex]

Answer:

3 ft, 5ft, 6ft

Step-by-step explanation:

To build a kennel of my dog, I would try to make it the largest possible with what I have.

So, I would go with the 3 longest planks: 3ft, 5ft and 6ft.

By looking at the length, I see I could make something very close to a right triangle since I could use the 6ft as an hypotenuse, and have the two other sides as 3ft and 5 ft  (6² is almost 3²+5², which equal 34).

That means my corner angle would be slightly over 90 degrees.

Answer:

3,5,6

Step-by-step explanation:

because i said so

Answer:

A

Step-by-step explanation:

Madison's expression equals 8z and so does the answer.

Answer:

Answer: A

Step-by-step explanation:

This is an example of the associative property of multiplication. The general way it is written is (a*b)*c = a*(b*c) It means that the order of multiplication does not matter.

The one that looks like that for your question is

(z*2)(4) = z * (2 * 4)

Both give an answer of 8z

A

Answer:

If sine theta = .3090 then arc sine theta =

18 degrees

Then we look up csc 18 degrees which = 3.2361

Step-by-step explanation:

Answer:

cscΘ ≈ 3.2362

Step-by-step explanation:

Using the trigonometric identity

• cscx = [tex]\frac{1}{sinx}[/tex] , then

cscΘ  = [tex]\frac{1}{0.3090}[/tex] ≈ 3.2362

32

1024/2=528(~512)/2=256/2=128/2=64/2=32

Answer:

0 and -4

Step-by-step explanation:

We have been given the following functions;

f(x) = 1/x

g(x) = x^2 + 4x

The first step would be to evaluate the composite function fºg.

fºg = f[g(x)]. We substitute g(x) in place of x in f(x)

fºg = [tex]\frac{1}{g(x)}=\frac{1}{x^{2}+4x}[/tex]

This is clearly a rational function which will be defined everywhere except where the expression in the denominator will be equal to 0.

We solve for x;

[tex]x^{2}+4x=0\\\\x(x+4)=0\\x=0\\x=-4[/tex]

Therefore, the two numbers that are not in the domain of fºg are 0 and -4

For this case we have the following equations:

[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2 + 4x[/tex]

We must find (f_ {o} g) (x):

By definition of composition of functions we have to:

[tex](f_ {o} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {o} g) (x) = \frac {1} {x ^ 2 + 4x}[/tex]

We must find the domain of [tex]f (g (x)).[/tex] The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.

[tex]x ^ 2 + 4x = 0\\x (x + 4) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = - 4[/tex]

The domain is given by all real numbers except 0 and -4

Answer:

x other than 0 and -4

Answer:

The correct answer is first option  6 units

Step-by-step explanation:

From the figure we can see a rectangle was mediated to crerate A'B'C'D'

To find the value of AB

AB = ?

A'B' = 15 units

BC = 3.8 units

B'C' = 9.5 units

From the figure we can write,

A'B'/AB = B'C'/BC

15/AB = 9.5/3.8

AB = (15 * 3.8)/9.5 = 6 units

Therefore the correct answer is first option 6 units

Answer:

414

Step-by-step explanation:

12 times 7, 12 times 15, 7 times 15

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

So it seems you were able to eliminate a and c. Good job. :)

y= x/2  is the same as y= 1/2 * x + 0 (this is now in the form y= mx +b.)

y= x+ 2 is already in (y=mx+b) form, with m being 1.

now what you can do is look at the individual parts of these equations.

the b is the y intercept. So when x is 0, y is b. in the y= 1/2 x + 0 equation, we know when x= 0, y= 0.

for the y=x + 2, we know that when x= 0, y= 2. Since this is not a point on the line shown, we know that it is not correct. Therefore, your answer would be y= 1/2 x, or y= x/2.

You could also find this using slope, but the y- intercept (b) was simpler to explain and find. :)

Answer:

A- control group

Since group A is tested under normal condition, it is the control group. Control group is separated from other groups so that the independent variable being tested cannot influence the result.

Answer:

x = - 5

Step-by-step explanation:

A line with an undefined slope indicates that the line is vertical and parallel to the y- axis.

The equation of a vertical line is

x = c where c is the value of the x- coordinates the line passes through.

The line passes through (- 5, 2) with x- coordinate -5, hence

x = - 5 ← equation of line

The equation of a line that passes through the point (-5, 2) and has an undefined slope is x = -5.

i.e y-axis.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

We have,

The equation of a line passes through the point (-5, 2)

The equation of a line has an undefined slope.

Now,

An undefined slope means,

The line is parallel to the y-axis.

There is only one point on the x-axis.

Slope = Change in y-axis / Change in the x-axis

Slope= Change in y-axis / 0

Slope = undefined

If the slope of a line is undefined there is no y-intercept.

The equation of  the line is:

y = mx + c

y = (1/0)x + 0

0 = x

x = 0

This means the y-axis.

The equation of the line passes through the point (-5, 2) so,

x = -5

Thus,

The equation of a line that passes through the point (-5, 2) and has an undefined slope is x = -5.

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Answer:

36

Step-by-step explanation:

This figure is a trapeoid.

Turning the figure sideways,

A = 1/2 (b1+b2) *h  where b1 and b2 are the top and bottom and h is the height

b1 and b2 are the  top and bottom so b1 =6 and b2=12  and h is the height so h = 4

A = 1/2 (6+12)*4

A = 1/2 (18)*4

   = 9*4

   = 36 in^2

The area of the irregular figure is 36 sq. in.

Given is an irregular figure with dimensions 6 in, 4 in and 12 in, we need to find the area of the irregular figure,

To find the area of the given figure, we will break the figure into two regular figures,

a) Triangle [base = 4 in and height = 12-6 = 6 in]

b) Parallelogram [base = 4 in and height = 6 in]

Area of a triangle = 1/2 × base × height

Area of a parallelogram = base × height

Therefore,

Area of the irregular figure = [1/2 × 4 × 12] + 4 × 6

= 24 + 12

= 36

Hence the area of the given figure is 36 in².

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Answer:

Its a 25% chance you choose the correct answer

Also 1/4 odds

1/4 (or 25%)

There are four possible outcomes, so the denominator of the fraction is 4.

There is only one correct answer, so the numerator of the fraction is 1.

This means the probability is 1/4, or 25%.

Answer:

B  II

Step-by-step explanation:

Answer:quad 1

Step-by-step explanation:

-90 is clockwise and 90 is counter like whatttttttt

Answer:

The answer is 48    NOT   12

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

By using theorem of intersecting secant and tangent at a point outside a circle.

PB × PA = (PQ)²

Since, PB = 2 units

PA = (PB + AB)

     = (2 + 6)

     = 8 units

PQ = x units

Therefore, by substituting these values,

2 × 8 = x²

[tex]x^{2} = 16[/tex]

Therefore, Option (2) will be the correct option.

ANSWER

Converges

[tex]S_{ \infty } = 68[/tex]

EXPLANATION

The guy sequence is

17 + 12.75 + 9.5625 + ...

The common ratio is:

[tex] \frac{9.5625}{12.75} = \frac{12.75}{17} = \frac{3}{4} = r[/tex]

Since

[tex] |r| < 1[/tex]

the series converges.

The sum to infinity of this sequence is :

[tex]S_{ \infty } = \frac{a}{1 - r} [/tex]

where a=17 is the first term of the series.

[tex]S_{ \infty } = \frac{17}{1 - \frac{3}{4} } [/tex]

[tex]S_{ \infty } = \frac{17}{ \frac{1}{4} } = 68[/tex]

Answer:

B

Step-by-step explanation:

Margin of Error is simply a range, an amount that is allowed for in case of miscalculation or change of circumstances. The margin of error is 5%.

1. Find the 5% of 3.20 = .16

2. Subtract and add .16 to 3.20 to get rid of that margin of error

    3.20 + .16 = 3.36 and 3.20 - .16 = 3.04

3. 3.04 and 3.36

Answer:

b 3.04 to 3.36

Step-by-step explanation:

First we need to find 5% of 3.20

.05*3.20 = .16

To find the lower value, subtract 16 cents from 3.20

3.20-.16 = 3.04

To find the upper value, add 16 cent to 3.20

3.20 + .16 = 3.36

The range is 3.04 to 3.36

ANSWER

129

EXPLANATION

The given expression is:

[tex]4^2×2^3- (14-16)÷2[/tex]

Deal with the parenthesis first.

[tex]4^2×2^3- ( - 2)÷2[/tex]

[tex]4^2×2^3 + 2÷2[/tex]

Deal with exponents,

[tex]16×8+ 2÷2[/tex]

Divide now

[tex]16×8 + 1[/tex]

Multiply

[tex]128 + 1 [/tex]

You can now add to get

[tex]129[/tex]

The order of operations is PEDMAS

Answer:

Miguel

Step-by-step explanation:

Since the pie is round it is a circle, and all circles have 360 degrees in total. Miguel cut 1/4 of the pie and 1/4 x 360 = 90. 90 is greater than 60.

Answer:

Miguel

Explanation:

Think of the 1/4 as 90 degrees.

An entire circle is 360 degrees. A quarter of that is 90 or 1/4.

Hope this picture helps.

Answer:

$2,239.66

Step-by-step explanation:

To find the amount of reimbursement, convert miles to km by multiplying 1564 by 1.609 since 1 mile = 1.609 km.

He drive 1564(1.609)=2,516.476 km.

Multiply this distance by $0.89 per km.

2516.476(0.89)=$2,239.66

Answer:

2 13/15

Step-by-step explanation:

2.26/ 1 X 100/100 = 226/100

226/100 Dived by 2 ( both top and bottom ) = 113/50

113/50 = 2 13/50

2.26 = 2 13/50

Side length of cube = 9 feet

The side length of the cube is 9 feet. Thus, the third option is correct.

To find the side length of a cube when given its volume, we can use the formula for the volume of a cube:

Volume = side length³

In this case, we know that the volume of the cube is 729 cubic feet.

Let's substitute this value into the formula:

729 = side length³

To find the side length, we need to take the cube root of both sides of the equation:

∛729 = ∛(side length³)

Simplifying:

9 = side length

Therefore, the side length of the cube is 9 feet.

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Answer:

2/3 is the slope and

-1 is the y intercept

Step-by-step explanation:

y = 2/3 x -1

This is in the form y = mx+b where m is the slope and b is the y intercept

2/3 is the slope and

-1 is the y intercept

Answer:

2/3 slope, -1 y intercept.

Step-by-step explanation:

Equations in y=mx+b forms follow these rule- y is the dependent variable, and x is the independent variable; m is the slope and b is the y intercept.

This means that the m, or slope is 2/3, and the y intercept is -1.

3n -10 ≥ 2

Add 10 to each side:

3n ≥ 12

Divide both sides by 3:

n ≥12/3

n≥4

The dot would be solid and located on the number 4, with the line and arrow moving/ pointing to the right.

1. n >2

2. n≤3

3. n<4

4. n≥5

Answer:

1/5

Step-by-step explanation:

Since there are 2 red marbles and since there are a total of 10 marbles, the probability is 2/10. This simplifies to 1/5. So the probability of picking a red marble is 1/5.

The probability of randomly picking out a red marble is 1/5

To determine the probability of randomly picking out a marble and it being red, we need to consider the total number of marbles and the number of red marbles.

Total marbles = 5 green + 3 blue + 2 red = 10 marbles

Red marbles = 2

So, we have

Probability = (Number of favorable outcomes) / (Total possible outcomes)

This gives

Probability = (Number of red marbles) / (Total marbles)

By subsituition

Probability = 2/10 = 1/5

Hence, the probability of randomly picking out a marble and it being red is 1/5

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Answer:

24 and 8

Step-by-step explanation:

The formula for the perimeter of the rect. is P = 2W + 2L.

Here, L = 2W + 8, so the area formula becomes:

P = 2W + 2(2W + 8) = 64

Dividing all terms by 2 reduces this to:

         W + 2W + 8 = 32, or 3W = 24, or W = 8.

Then:  L = 2W + 8 = 2(8) + 8 = 24

Check:  does 2W + 2L = 64 when these values for W and L are substituted?

              Is 2(8) + 2(24) = 64   true?  Yes

The length and width are 24 and 8 respectively.

The length of rectangle will be 8 units.

The width of rectangle will be 24 units.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is eight more than twice the width.

The perimeter is 64.

Now,

Let the width of rectangle = x

Then, The length of rectangle = 2x + 8

Here, The perimeter is 64.

So, We get;

2 (length + width) = 64

2 (2x + 8 + x) = 64

2 (3x + 8) = 64

3x + 8 = 64/2

3x + 8 = 32

3x = 32 - 8

3x = 24

x = 8

Thus, The width of rectangle = x

                                            = 8

Then, The length of rectangle = 2x + 8

                                              = 2 × 8 + 8

                                              = 24

Therefore, The length of rectangle will be 8 units.

The width of rectangle will be 24 units.

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