Determine if each infinite geometric series is convergent or divergent.

[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]

notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.

Answer: Hope This Helps!

Step-by-step explanation:

Changes in air pressure are determined by a variety of forces, including the density and temperature of air masses. When air moves from between areas of high pressure and low pressure, wind directions and speeds may change. The driving force behind changes in air pressure and therefore the creation of wind is gravity.

Answer:

we have:

∆BDE is similar to ∆BAC

so their side are proportional :

BD/BD=BE/BC

2/BD=4/(6+4)

BD=2×10/4

BD=5

again

BE/BC=DE/AC

4/10=5/AC

AC=5×10/4

AC=25/2

Now,

AC=25/2 or 12.5.

AD=BA-BD=5-2=3.

is your answer.

Answer:

AC = 12.5, AD = 3

Step-by-step explanation:

A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is

[tex]\frac{BD}{BE}[/tex] = [tex]\frac{AD}{CE}[/tex] , substitute values

[tex]\frac{2}{4}[/tex] = [tex]\frac{AD}{6}[/tex] ( cross- multiply )

4 AD = 12 ( divide both sides by 4 )

AD = 3

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

Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is

[tex]\frac{DE}{AC}[/tex] = [tex]\frac{BD}{BA}[/tex] , substitute values

[tex]\frac{5}{AC}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )

2 AC = 25 ( divide oth sides by 2 )

AC = 12.5

Answer:

55

Step-by-step explanation: i think

Answer:

Step-by-step explanation:

it would be 55 because he does 11 each minute.

As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.

A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Based on how quickly iterations rise as input increases, fair and unreasonable algorithms can be distinguished. Since the algorithm does not grow exponentially, we can infer that it completes in an acceptable amount of time.

assessing the mathematical function that represents the algorithm's growth rate when input is added;

200 = 10k, where k is the proportionality constant.

k = 200/10

k = 20

The function that represents the number of iterations is as a result:

I = input size; n = 20i; represents the number of iterations.

As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.

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Answer:

x<5/2

Step-by-step explanation:

hope this helps :)

Answer:

[tex]x < \frac{5}{2} [/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable. Hope it helps :)

Answer:

B. y ≤ –3x + 5

Step-by-step explanation:

Its B, all y-values are less than -3x+5. also consider root by setting -3x+5=0

x=5/3 is positive so its the second one

...................................................................................................................................................

Answer:

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area below the solid line (the gray area)

The slope of the solid line is negative

The y-intercept of the solid line is positive

The equation of the solid line is equal to  

therefore

the equation of the inequality is equal to

The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:

$60.

Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.

The amounts of each item are given as follows:

36, 48 and 24.

Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:

36 - 48 - 24|2

18 - 24 - 12|2

9 - 12 - 6|3

3 - 4 - 2

Hence:

gcf(36, 48, 24) = 2² x 3 = 12.

Which is the number of packages. As each package sells for $5, the amount earned is given as follows:

12 x 5 = $60.

Each package is composed by:

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Answer: $3.06

Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.

2 is not a polynomial root of  [tex]x^{3} + 4x^{2} + 3x[/tex] . A polynomial is an equation that employs addition, subtraction .

A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients that uses solely the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that employs addition, subtraction, multiplication, and division of numbers to combine variables, constants, and exponents (No division operation by a variable).

given

[tex]x^{3} + 4x^{2} + 3x[/tex]

= [tex]2^{3} + 2^{2} + 3(2) = 0\\8 + 4 + 6 = 0 \\18= 0[/tex]

Consequently, 2 is not a polynomial root of  [tex]x^{3} + 4x^{2} + 3x[/tex] .

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Answer:

[tex]x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]

Step-by-step explanation:

[tex]y = x^2-2x+5\\\\6=x^2-2x+5\\\\x^2-2x-1=0\\\\\\\frac{-b+-\sqrt{b^2-4ac} }{2a} = x\\a = 1, b = -2, c = -1\\\\\frac{2+-2\sqrt{2} }{2\\}\\\\x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]

The value of the x is -0.4 when y = 6 and the graph is drawn on the left.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The quadratic equation,

y = x² – 2x + 5

To find the value of x:

When y = 6.

So,

x² – 2x + 5 = 6

x² – 2x - 1 = 0

Comparing the quadratic equation with standard quadratic equation,

ax²+ bx +c = 0

We get,

a = 1, b = -2 and c = -1

So,

x = {-b ±√(b²-4ac)}/2a

Substituting the values,

x = (2±√8)/2

x = 1 ± √2

x = 2.41421 and x = −0.414214

And the graph is drawn on the left so x = −0.414214 = -0.4 to one decimal place.

Therefore, the value of the x is -0.4.

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Answer:

97.53 in³

Step-by-step explanation:

The cylindrical birthday cake has a diameter (d) of 14 inches and a height (h) of 6 inches.

The radius of the cake (r) = diameter / 2 = 14 inches / 2 = 7 inches.

The volume of the full cake = πr²h = π(7²)6 = 924 in³

Since only a part of the cake was cut and given to Myong. The total measure of the cake is 360°, but the part given to her was 38°. Hence the volume of her slice is given as:

Volume of her slice = (38 / 360) * volume of the full cake = (38 / 360) * 924 = 97.53 in³

Volume of her slice = 97.53 in³

Answer:

45

Step-by-step explanation:

Step-by-step explanation:

there is nothing its just a dark screen?

Answer:

1/2

Step-by-step explanation:

A line that is perpendicular to another has an opposite reciprocal slope. In this case, we can see that the slope of the given line is -2, so the perpendicular line would have a slope of 1/2.

Answer:

1/2

Step-by-step explanation:

The slope of a line perpendicular to any given line is the negative reciprocal of the given line's slope:

[tex]m_\perp = \dfrac{1}{m}[/tex]

In this problem, the slope of the given line is [tex]\dfrac{-2}{1}[/tex] (rise over run).

So, to find the slope of a line that is perpendicular to it, we simply flip the given line's slope and change its sign.

[tex]m_\perp = \dfrac{1}{2}[/tex]

So, a line which is perpendicular to the given line would have a slope of 1/2.

Answer:

A to #4

B to #3

C to #1

D to #2

Step-by-step explanation:

A. 7 + 3² = 16

B. 5 - 2²=1

C. 2 · 2³ = 2^4

D. 3^4/3^1=27

Answer:

B) 2 + 3x = 8

Step-by-step explanation:

Option B is not an expression as expressions do not have equal signs.

Answer:

(9,-3)

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

Just if you divide any to congruent sides you will find the ratio to be 2

Solve for the missing side

Answer:

No triangle

Step-by-step explanation:

Since [tex]4+4=8[/tex], the side lengths fail to satisfy the triangle inequality theorem. Thus, no such triangle exists.

Answer:

90 is your answer i hope this helps

Step-by-step explanation:

Answer:

55.2049%

Step-by-step explanation:

R², the coefficient of determination, is the proportion of the variation in the dependent variable that is predictable from the independent variable.

In this case, if we square our correlation coefficent r=0.743, we get R²=0.552049, which means that 55.2049% of the variation in the number of yearly boaters can be explained by differences in lake sizes

Answer:

2. $1,100 in clothing sales gives Rachel a $260 paycheck

3 $.2,200 in clothing sales gives Rachel a $370 paycheck

5. $10,800 in clothing sales gives Rachel a 1,230 paycheck

Step-by-step explanation:

Here is the complete question :

Rachel works for a clothing store. She is $150 paid every week plus a 10% commission on any clothes that she sells. Which of the following is true in regards to Rachel's weekly paycheck? Chose three correct answers.

1. $100 in clothing sales gives Rachel a $250 paycheck

2. $1,100 in clothing sales gives Rachel a $260 paycheck

3 $.2,200 in clothing sales gives Rachel a $370 paycheck

4. $ 4,200 in clothing sales gives Rachel a $420 paycheck

5. $10,800 in clothing sales gives Rachel a 1,230 paycheck

6. $ 16,000 in clothing sales gives Rachel a 1,450 paycheck

The equation representing Rachel's paycheck = amount she earns every month + commission

If she makes  $100 in clothing sales, her paycheck = $150 + (0.1 x 100) = $160

If she makes  $1100 in clothing sales, her paycheck = $150 + (0.1 x 1100) = $260

If she makes  $2200 in clothing sales, her paycheck = $150 + (0.1 x 2200) = $370

If she makes  $4200 in clothing sales, her paycheck = $150 + (0.1 x 4200) = $570

If she makes  $10800 in clothing sales, her paycheck = $150 + (0.1 x 10800) = $1230

If she makes  $16000 in clothing sales, her paycheck = $150 + (0.1 x 16000) = $1750

thus the correct options are 2,3,5

Answer:

20 feet per second

Step-by-step explanation:

130/6.5 = 20

the correct answer is D, 8.

Answer:

the answer is 42,000

Step-by-step explanation:

obviously because if you carry the one and than divide by the denominator, you get four oranges. and when life gives you lemons, you give it back

Answer:

$4088.5

Step-by-step explanation:

Given data

Price a =  $6500

Rate of depreciation r= 14.3%

Time x= 3 years

The exponential function Decay is described as

y= ab^x

For decay

b= 1-r

a.

Hence the exponential function that model the value of the computer is

y=a(1-r)^x

b.

y= 6500(1-0.143)^3

y= 6500*(0.857)^3

y= 6500*0.629

y=$4088.5

Hence the value of the computer after 3 years is $4088.5

Answer:

46080

Step-by-step explanation:

multiply all of them

Answer: might be 150 sq ft if the problem is of the irregular figure

Answer:

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

The product of 7/9 and 6 is:

Answer:

[tex]\textsf{C)} \quad 4\frac{2}{3}[/tex]

Step-by-step explanation:

To find the product of two numbers, multiply them.

[tex]\implies \dfrac{7}{9} \times 6[/tex]

To multiply a fraction by a whole number, first rewrite the whole number as a fraction by dividing it by 1:

[tex]\implies \dfrac{7}{9} \times \dfrac{6}{1}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{a \times b}{c \times d}[/tex]

[tex]\implies \dfrac{7 \times 6}{9 \times 1}[/tex]

Simplify:

[tex]\implies \dfrac{42}{9}[/tex]

Reduce the fraction by dividing the numerator and denominator by the common factor of 3:

[tex]\implies \dfrac{42 \div 3}{9 \div 3}[/tex]

[tex]\implies \dfrac{14}{3}[/tex]

Divide the numerator by the denominator:

[tex]\implies 14 \div 3=4\;\rm remainder\;2[/tex]

The mixed number answer is the whole number and the remainder divided by the denominator:

[tex]\implies 4\frac{2}{3}[/tex]