The 3rd term of a geometric sequence is -2 and the 7th is -32. Find the common ratio,the first term, the explicit formula, and the 10th term.

Answer:

a=-4, b=-4. (-4, -4).

Step-by-step explanation:

-3a+7b=-16

-9a+5b=16

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

-3(-3a+7b)=-3(-16)

-9a+5b=16

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

9a-21b=48

-9a+5b=16

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

-16b=64

b=64/-16

b=-4

-3a+7(-4)=-16

-3a-28=-16

-3a=-16+28

-3a=12

a=12/-3

a=-4

Answer:

They both are equal to -4.

Step-by-step explanation:

Just took the test and got it right hope this helps. :)

Answer:

6,561

Step-by-step explanation:

3x3=9

9x9=81

81x81=6,561

Final answer:

Georgia received 3 dimes on Tuesday, 9 on Wednesday, and 81 on Thursday, following a trend of tripling the amount each day. Continuing this pattern, she would receive 243 dimes on Friday.

Explanation:

The question involves identifying and extending a mathematical pattern. Here, we notice that the number of dimes Georgia receives each day is being multiplied by 3 to get the number of dimes for the next day. On Tuesday she received 3 dimes, on Wednesday this was multiplied by 3 to get 9 dimes, and on Thursday it was multiplied again by 3 to get 81 dimes. So, to find out how many dimes Georgia received on Friday, we simply continue this pattern and multiply Thursday's amount by 3.

3 dimes (Tuesday) * 3 = 9 dimes (Wednesday

9 dimes (Wednesday) * 3 = 81 dimes (Thursday)

81 dimes (Thursday) * 3 = 243 dimes (Friday)

Therefore, if this trend continued, Georgia would have received 243 dimes on Friday.

Answer:

-75x + 45

Step-by-step explanation:

-15(5x - 3)

-75x + 45

Answer: -75x + 45

Step-by-step explanation: Let's simplify this problem using the distributive property.

Let's first change the minus in front of the 3 to plus a negative.

Now we can distribute or multiply this -15 times each of the terms inside the set of parentheses.

So we get -15 (5x) + -15 (-3) and this simplifies to -75x + 45

The exponential expression 3^1/2 can be converted to radical form as √3. This is because the fractional exponent 1/2 equates to a square root and the base of the expression, 3, becomes the number under the square root symbol.

The expression 3^1/2 can be expressed in radical form by understanding that the exponent 1/2 represents a square root, which means the value inside the square root is being multiplied by itself to get the original number. Therefore, we rewrite this exponential term in radical form by placing the base, which is 3, under a square-root symbol, so 3^1/2 can be expressed as √3 in radical form. This is because the root, which corresponds to the denominator of the fractional exponent, is 2 (hence square root), and the radicand, which corresponds to the numerator of the fractional exponent, is 3.

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To convert the expression 3^1/2 to radical form, we need to find the square root of 3, which is represented as √3 or 3^(1/2).

Exponential expressions involve a base raised to an exponent. They are written in the form a^n, where "a" is the base and "n" is the exponent. These expressions represent repeated multiplication, where the base is multiplied by itself "n" times. Exponential functions play a crucial role in various mathematical and scientific contexts.

To convert the expression 3^1/2 to radical form, we need to find the square root of 3.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In this case, the square root of 3 is represented as √3 or 3^(1/2).

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Answer:

Odds for = Odds against = 1/2

Step-by-step explanation:

In a fair die, we have {1, 2, 3, 4, 5, 6} and [tex]$ n(S) = 6 $[/tex]

{1, 4, 5} and {2, 3, 6} constitute the entire sample space.

So, Probability of getting a 1 or a 4 or a 5

= Probability of getting a 1 +

Probability of getting a 4 +

Probability of getting a 5

= [tex]$ \frac{1}{6} + \frac{1}{6} + \frac{1}{6} $[/tex]

=[tex]$ \frac{3}{6} = \frac{1}{2} $[/tex]

Therefore, Odds for 1 or 4 or 5 = [tex]$ \frac{1}{2} $[/tex].

Since, Probability of getting a number between 1 and 6 is 1 and Probability of getting a number from 2 or 3 or 6 = [tex]$ \frac{1}{2} $[/tex], we have:

Probability of not getting a 1 or 4 or 5 = 1 - [tex]$ \frac{1}{2} $[/tex]

= [tex]$ \frac{1}{2} $[/tex]

Hence, odds for and odds against = [tex]$ \frac{1}{2} $[/tex]

Answer:

Option C. 4(20-16y): Each side measures 20-16y units.

Step-by-step explanation:

we know that

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the length side of the square

we have

[tex]P=(80-64y)\ units[/tex]

substitute the given value in the formula

[tex](80-64y)=4b[/tex]

solve for b

Divide by 4 both sides

[tex](20-16y)=b[/tex]

Rewrite the expression

[tex]b=(20-16y)\ units[/tex]

Alternative Method

we have

[tex]P=(80-64y)\ units[/tex]

Factor 4

[tex]P=4(20-16y)\ units[/tex]

so

Each side measures (20-16y) units.

Answer:

*From what I'm getting, many of the blanks have multiple numbers that would work.*

No Solutions:

First Blank: 7

Second Blank: Any number but 5

One Solution:

First Blank: Any number but 7

Second Blank: Any number

Infinitely Many Solutions:

First Blank: 7

Second Blank: 5

For no solutions, the equation could be 7x + 5 = 7x + 6. For one solution, the equation could be 7x + 5 = 7x + 6. For infinitely many solutions, the equation would be 7x + 5 = 7x + 5.

The given problem is an algebraic expression which needs to be manipulated appropriately to yield No Solutions, One Solution and Infinitely Many Solutions.

Let's simplify the left-hand side expression first: 2x + 5 + 2x + 3x = 7x + 5.

For No Solutions, you would need the constant term on the right-hand side to not be equal to 5, and the coefficient of x not equal to 7, for example, 7x + 6 would yield no solutions, because there's no value of x which would make 7x + 5 equal to 7x + 6.

For One Solution, you need to make sure the right-hand side and left-hand side aren't identical. For example, 7x + 6 = 7x + 5 has one solution, x = -1.

For Infinitely Many Solutions, the equation on the right-hand side should be the same as the left-hand side. So, it would be 7x + 5 = 7x + 5 as for every real number x, these two expressions will be equal.

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Answer:

8+6n

Step-by-step explanation:

First, distribute the 2 into the parenthesis.

2(6)+2(3n)-4

Then, multiply the numbers.

12+6n-4

Now add(subtract in this case) the common multiples.

12-4= 8

8+6n

Since you can no longer simplify the equation, this is the answer..

8+6n

Answer:

[tex]2,400\pi[/tex] cubic units

Step-by-step explanation:

Given the cylinder has a base radius of 10 units.

And slant length of 26 units.

The formula for volume of an oblique cylinder is [tex]\pi r^2h[/tex]

Where [tex]r[/tex] is the radius and [tex]h[/tex] is the height of cylinder.

We will now find height of cylinder using following equation.

[tex](slant\ length)^2=(radius)^2+(height)^2[/tex]

[tex]26^2=10^2+(height)^2\\\\676=100+(height)^2\\\\676-100=(height)^2\\\\576=(height)^2\\\\\sqrt{576}=\sqrt{(height)^2}\\ \\24=height[/tex]

Now, the volume of cylinder would be

[tex]=\pi r^2h\\=\pi(10)^2\times24\\=\pi 100\times24\\=2400\pi[/tex]cubic units

The volume of the cylinder is 2,400pi cubic units

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where:

r is the radius = 10units

h is the height

Since the cylinder is oblique, hence:

h² = 26² - 10²

h² = 676 - 100

h² = 576

h = 24 units

V = 22/7(10)² * 24

V = 2400 pi cubic units

Hence the volume of the cylinder is 2,400pi cubic units

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Answer:

1/3 cup of water.

Step-by-step explanation:

Answer:

Two quarters (50 cents)

Two dimes (20 cents)

Four pennies (4 cents)

Step-by-step explanation:

Guess and check.  

Rachel has two quarters (50 cents), two dimes (20 cents) and four pennies (4 cents) that amounts to 74 cents.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

A current medium of exchange in the form of coins and banknotes.

Given that, Rachel has 8 coins.

The amount of her coins is 74 cents.

Let us split 74 cents into 8 coins as follows

Two quarters (50 cents)

Two dimes (20 cents)

Four pennies (4 cents)

Therefore, Rachel has two quarters (50 cents), two dimes (20 cents) and four pennies (4 cents).

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Answer:

16

Step-by-step explanation:

4*(1/2)^2-3*(-5)

4*1/4+15

1+15=16

Answer:

Step-by-step explanation:

[tex]\text{Put the values of }\ x=\dfrac{1}{2}\ \text{and}\ y=-5\ \text{to the expression}\ 4x^2-3y:\\\\4\left(\dfrac{1}{2}\right)^2-3(-5)\qquad\text{use PEMDAS}\\\\=4\left(\dfrac{1}{2}\right)\left(\dfrac{1}{2}\right)+(-3)(-5)\\\\=4\!\!\!\!\diagup\left(\dfrac{1}{4\!\!\!\!\diagup}\right)+15\\\\=1+15\\\\=16[/tex]

Answer:

[tex]r_Y=\frac{3}{\pi}[/tex]

Step-by-step explanation:

Circumference has the formula:

C = 2πr,

Where

C is the circumference

and

r is the radius

Given Circle Y has Circumference of 6, we can find the radius:

C = 2πr

6 = 2πr

r = 6/2π

r = 3/π

So, the radius (r_y) of Circle Y is 3/π, the first choice is right.

Answer:

Population: The entire number of students present in town’s high school.

Sample: Identical number of students across various categories of freshers, senior students and juniors.  

Step-by-step explanation:

Population is the large set of the people who are present during the experiment. Sample is a smaller subset from the population who become a part of the experiment. In this question, samples are the students who are either new joiners to the college, the senior students or the juniors. It will help Alan to come to a possible conclusion using the survey

Answer:

Sample Response-bThe population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the composition of two functions F(G(x)), substitute the value of G(x) into F(x). The result for F(G(x)) in this case is -10x + 38.

This question pertains to the mathematical concept of functions. Specifically, you are being asked to find the composition of two functions, F(x) and G(x).

To find F(G(x)), you substitute the value of G(x) into the function F(x). Recall that G(x) = -2x + 9. So, you need to replace 'x' in F(x) = 5x -7 by the value of G(x). Thus, F(G(x)) = 5(-2x+9) - 7 = -10x + 45 - 7 = -10x + 38.

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Answer: -3/6 (reduced is -1/2)

Step-by-step explanation:

distribute the 6

-18 = 9 + 6y - 24

combine like terms on one side

-18 = -15 + 6y

get all like terms on one side

-3 = 6y

divide by 6

-3/6 = y

if you need to simplify or reduce the answer is -1/2.

Answer:

[tex]\large\boxed{y=-\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

[tex]-18=9+6(y-4)\qquad\text{use the distributive property}\\\\-18=9+6y+(6)(-4)\\\\-18=9+6y-24\qquad\text{combine like terms}\\\\-18=6y+(9-24)\\\\-18=6y-15\qquad\text{add 15 to both sides}\\\\-3=6y\qquad\text{divide both sides by 6}\\\\\dfrac{-3}{6}=\dfrac{6y}{6}\\\\-\dfrac{3:3}{6:3}=y\to y=-\dfrac{1}{2}[/tex]

Answer:

The number of hot dogs sold was 35 and the number of sodas sold  was 52

Step-by-step explanation:

Let

x ----> the number of hot dogs sold

y ----> the number of sodas sold

we know that

[tex]x+y=87[/tex]

[tex]x=87-y[/tex] ----> equation A

[tex]1.50x+0.50y=78.50[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]1.50(87-y)+0.50y=78.50[/tex]

solve for y

[tex]130.50-1.50y+0.50y=78.50[/tex]

[tex]1.50y-0.50y=130.50-78.50[/tex]

[tex]y=52\ sodas[/tex]

Find the value of x

[tex]x=87-52=35\ hot dogs[/tex]

therefore

The number of hot dogs sold  was 35 and the number of sodas sold  was 52

Answer:

Step-by-step explanation:

Here two equation of straight lines are given.

Two equations can intersect each other at a point.

The given equations are,

Equating both 1 and 2 we get,

[tex]10 - 5x = 3x + 2\\8x = 8\\x = 1[/tex]

Hence, from 1 we get, [tex]y = 3+2 = 5[/tex]

Answer:

[tex]y-3=-2(x+4)[/tex]

Step-by-step explanation:

The complete question is

The given line passes through the points (−4, −3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3)?

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

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

we have

(−4, −3) and (4, 1)

substitute the values

[tex]m=\frac{1+3}{4+4}[/tex]

[tex]m=\frac{4}{8}[/tex]

[tex]m=\frac{1}{2}[/tex]

step 2

Find the slope of the perpendicular line to the given line

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=\frac{1}{2}[/tex] ---> slope of the given line

so

[tex]m_2=-2[/tex] ---> slope of the perpendicular line to the given line

step 2

Find the equation in point slope form

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

we have

[tex]m=-2[/tex]

[tex]point\ (-4,3)[/tex]

substitute

[tex]y-3=-2(x+4)[/tex] ----> equation in point slope form

Answer:

A

Step-by-step explanation:

did the edge quiz

Answer:

4

Step-by-step explanation:

The soil is 4 inches deep in the pot, calculated by dividing the volume of soil (48 cubic inches) by the area of the pot's base (length times width).

Ian put 48 cubic inches of soil into a flower pot. The length of the pot is 4 inches, and the width of the pot is 3 inches. To find out how many inches deep the soil is, we can use the formula for the volume of a rectangular prism, which is Volume = length times width times height. In this case, we have the volume and the dimensions for length and width, so we can solve for the height (or depth).

The formula would be:

Therefore, the soil is 4 inches deep in the pot.

Answer:

22%

Step-by-step explanation:

Given: Profit this year= $245000

           Profit last year= $315000

Now, lets find the percentage decrease in profit this year.

Profit percentage= [tex]\frac{\textrm{difference in profit}}{\textrm{last years profit}} \times 100[/tex]

Profit percentage= [tex]\frac{\$ 315000-\$ 245000}{\$ 315000} \times 100[/tex]

⇒ Profit percentage= [tex]\frac{70000}{315000} \times 100[/tex]

⇒ Profit percentage=~[tex]\frac{7000}{315} =  22.22\%[/tex] ≅ 22% (nearest whole percent)

∴ Percent decrease in profit is 22%

Answer:

22%

Step-by-step explanation:

Answer:

  (a)   -3/4

  (b)  -0.75

  (c)  -0.75

Step-by-step explanation:

It's a bit hard to tell what constitutes an "iteration" when using the bisection method to approximate a polynomial root. For the purpose here, we'll say one iteration consists of ...

Thus, the result of the iteration consists of a bracketing interval and the choice of one of the interval's ends as the solution approximation.

__

(a) We observe that the graphs intersect in the interval (-1, 0). For the first iteration, we evaluate f(x)-g(x) at x=-1/2. This tells us the solution is in the interval (-1, -1/2). The x-value closest to the root is x=-1/2.

For the second iteration, we evaluate the function f(x)-g(x) at x=-3/4. This tells us the solution is in the interval (-1, -3/4). The x-value closest to the root is x=-3/4.

For the third iteration, we evaluate the function f(x)-g(x) at x=-7/8. This tells us the solution is in the interval (-7/8, -3/4). The x-value closest to the root is x=-3/4.

__

(b) The graph tells us the solution is approximately 0.7549. Rounded to 2 decimal places, the solution is approximately 0.75.

__

(c) The above solution found after 3 iterations rounded to 2 decimal places is exactly 0.75.

__

See the attached table for function values.

_____

Comment on bisection iteration

Since you cut the interval containing the root in half with each iteration, you gain approximately one decimal place for each 3 iterations. When the function value is very nearly zero at one of the interval endpoints, it can take many more iterations to achieve a better result.

Here, it takes 4 more iterations before an x-value becomes closer to the solution (x≈-97/128). And it takes one more iteration to move the end of the interval away from -3/4. After these 5 more iterations (8 total), the solution is known to lie in the interval (-97/128, -193/256). The corresponding solution approximation is -193/256. It is still only correct to 2 decimal places.

Answer:

(0.5, 2)

Step-by-step explanation:

substitution method is when you substitute a variable for another

so, it is given that y=2x+1 and y=6x-1. so we know the 'y' value is equal since they are the same thing

hence:

y=2x+1

y=6x-1

2x+1=6x-1

4x=2

x=1/2

y=2

Answer:

The second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A function is where one x value only matches up to one y value.

Answer:

Step-by-step explanation:

Answer:

6.5 yards total

Step-by-step explanation:

1.

Find the least common multiple (LCM) for the denominators. Because you have to make the denominators the same before you add the fractions, find a common multiple that they share. Then choose the lowest one. In this case the LCM is 6

2. Multiply the numerator and denominator to get like denominators. You'll need to multiply the entire fraction to make the denominator become the least common multiple. In this case multiply 2/3 by 2 = 4/6

3. Add the two fractions and the whole numbers

In this case: 2+ 3 =5

4/6 + 5/6 = 9/6

4. Now you have

5 + 9/6

5. Simplify 9/6 to 1 3/6 = 1 1/2

6. Add 5 + 1 1/2 = 6 1/2

Kristin has approximately 4 yards of plaid ribbon and 3 yards of polka-dot ribbon after rounding fractions to the nearest whole number, which totals to about 7 yards of ribbon in all. This estimation method is reasonable for handling fractions.

We are asked to estimate the total amount of ribbon Kristin has by adding together 3 2/3 yards of plaid ribbon and 2 5/6 yards of polka-dot ribbon. To estimate, we round each fraction to the nearest whole number. The 2/3 in 3 2/3 rounds up to 1, making it approximately 4 yards. The 5/6 in 2 5/6 rounds up to 1, making it approximately 3 yards. Adding these estimates together gives us 4 yards of plaid ribbon plus 3 yards of polka-dot ribbon, which equals to about 7 yards of ribbon in total.

Our estimate is reasonable because we rounded each fraction up to the nearest whole number, making for easy addition. It's also a common method to simplify calculations and get a sense for the magnitude of the sum. Since our original fractions were more than 1/2 (3/2 is 1 1/2, and 5/6 is nearly 1), rounding up provides a reasonable overestimate likely very close to the actual sum.

See explanation

Step-by-step explanation:

Given that Crystal sold b balloons, Aliya sold 2 more balloons than Crystal and Shamika sold twice as many balloons as Crystal then forming the expressions;

If Crystal sold b number of balloons then;

a) Number of balloons Aliya sold is 2 more than Crystal's .This means Aliya sold two more balloons added to what Crystal sold.mathematically, it will be = 2+b

b) Number of balloons Shamika sold is twice Crystal's.This means Shamika sold double the number of balloons Crystal sold.If Crystal sold b balloons, twice this number is =2b

c)Total number of balloons sold will be presented by the expression;

=b+2+b+2b=4b+2

The expression for total cost will be;

$2*(4b+2) =$900----------------------expression

d) solving the expression for total cost as

   2(4b+2)=900

    8b+4=900

     8b=900-4

     8b=896 -------divide both sides by 8 to get b

    b=896/8 =112 balloons  ----------value of variable b

e)

Crystal sold  b  balloons = 112 balloons

Shamika sold, 2b, =2*112 = 224 balloons

Aliya sold , 2+b balloons = 2+112 =114 balloons

f)By solving the expression for total cost , you obtain the value of variable b which represents the number of balloons sold by Crystal. Using the value of b, you can calculate the number of balloons for Shamika and Aliya using their expressions which represent number of balloons they sold.

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Answer:

The graph in the attached figure

see the explanation

Step-by-step explanation:

we have

[tex]y=\sqrt{-x-3}[/tex]

we know that

The radicand must be greater than or equal to zero

so

[tex](-x-3)\geq 0[/tex]

solve for x

Adds 3 both sides

[tex]-x\geq 0+3[/tex]

[tex]-x\geq 3[/tex]

Multiply by -1 both sides

Remember that, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

[tex]x\leq -3[/tex]

so

The domain of the function is the interval (-∞,-3]

For x=-3 ---> the value of y=0

The range is the interval {0,∞)

therefore

The graph in the attached figure

Answer:

0.97

Step-by-step explanation: i used a calculator to divide and then rounded to the nearest hundredth.

Answer:

25x^2

Step-by-step explanation: