In the box, type in the number that will correctly complete the sentence.

Jane has a debt of $63. She owes equal amounts to seven different people. Her debt to each person can be expressed as Answer
dollars.

The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]

Step-by-step explanation:

The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex] , where

∵ The sequence is [tex]\frac{-2}{3}[/tex] , -4 , -24 , -144 , .......

∵ The 1st term is [tex]\frac{-2}{3}[/tex]

∵ The 2nd term is -4

∴ [tex]\frac{-4}{\frac{-2}{3}}=6[/tex]

∵ The 3rd term is -24

∴ [tex]\frac{-24}{-4}=6[/tex]

∵ The 4th term is -144

∴ [tex]\frac{-144}{-24}=6[/tex]

∵  [tex]\frac{a_{2}}{a_{1}}[/tex] = [tex]\frac{a_{3}}{a_{2}}[/tex] =  [tex]\frac{a_{4}}{a_{3}}[/tex] = 6

∴ There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

∵ The formula of the nth term of the geometric sequence is [tex]a_{n}=a(r)^{n-1}[/tex]

∵ a = [tex]\frac{-2}{3}[/tex]

∵ r = 6

∴ The formula of the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]

The formula can be used to describe the sequence is [tex]a_{n}=\frac{-2}{3}(6)^{n-1}[/tex]

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Answer:

c - f(x) = -2/3(6)^x − 1

Step-by-step explanation:

Edge 2020

Answer:

A if you're subtracting amount grown from amount cut

C if your subtracting husband's gain from wife's loss,

E for sure. 100%. a sum or 1.5 is reached through addition

& F if you're subtracting amount used from amount bought.

Step-by-step explanation:

Please comment & ask for further explanation if you would like it :)

Answer: they are A C E and F

Step-by-step explanation:

My siblings explained it to me

These rates are not in proportion. Juan walked faster.

Explanation:

First, we want to make these ratios to have the same denominator so we can compare the numerators. To do this, do 3x5 and 8x5 to get 40:15. Then, we do 5x3 and 14x3 to get 42:15. Now we can just compare the numbers 40 and 42, and since 42 < 40, we know Juan walked faster.

The rates of 8/3 miles per hour and 14/5 miles per hour are not in proportion.

To determine whether the rates of Anna and Juan are in proportion, we can compare the rates of their walking speeds by forming a ratio and seeing if the ratios are equivalent. Anna walked 8 miles in 3 hours, which gives us a rate of 8/3 miles per hour. Juan walked 14 miles in 5 hours, resulting in a rate of 14/5 miles per hour.

To check the proportion, we set up a ratio of Anna's speed to Juan's speed: (8/3) / (14/5). If these rates are proportional, the cross-products of the ratios will be equal. However, when you cross-multiply, you get 8 * 5 = 40 and 3 * 14 = 42. Since 40 is not equal to 42, the rates are not in proportion.

Answer:

The number is 50.

Step-by-step explanation:

1.12x=56

x=56/1.12

x=50

Answer: 40 000

Step-by-step explanation:

Population doubles in first 55 years =

5000 * 2 = 10 000

In 220 years from now, 220/55 = 4

Hence, 10 000 * 4 = 40 000 population

Answer:

[tex]y =  \frac{22-x}{2}[/tex]

For width = 2 ft, the length of the flower bed = 10 ft.

For width = 3 ft, the length of the flower bed = 9.5 ft.

For width = 4 ft, the length of the flower bed = 9 ft.

Step-by-step explanation:

Here, the Perimeter of the flower garden is given as

22 = 2 y + x

: where, y : Length of the garden

and x : Width of the garden .

Now, solving for y in the above expression,we get

22 = 2 y + x  ⇒    22 - x = 2 y

or, [tex]y =  \frac{22-x}{2}[/tex]

Now, when the width (x) = 2 feet

Length of the flower  bed [tex]y =  \frac{22-x}{2}  = \frac{22-2}{2}  = \frac{20}{2}  = 10[/tex]

or, x = 10 ft

⇒For, the width = 2 ft, the length of the flower bed = 10 ft.

when the width (x) = 3 feet

Length of the flower  bed [tex]y =  \frac{22-x}{2}  = \frac{22-3}{2}  = \frac{19}{2}  = 9.5[/tex]

or, x = 9.5 ft

⇒For, the width = 3 ft, the length of the flower bed = 9.5 ft.

when the width (x) = 4 feet

Length of the flower  bed [tex]y =  \frac{22-x}{2}  = \frac{22-4}{2}  = \frac{18}{2}  = 9[/tex]

or, x = 9 ft

⇒For, the width = 4 ft, the length of the flower bed = 9 ft.

Answer:

45

Step-by-step explanation:

45 is constant, because no mater how many miles you drive, you will always be charged $45. It stays the same

Answer:

45

Step-by-step explanation:

your equation would be y= 45+22x and no matter what x equals, you will always have the set $45, so that is your constant.

For this case we must solve the following quadratic equation:

[tex]3x ^ 2-2x + 5 = 0[/tex]

Where:

[tex]a = 3\\b = -2\\c = 5[/tex]

The roots are given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting the values we have:

[tex]x = \frac {- (- 2) \pm \sqrt {(- 2) ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {- (- 2) \pm \sqrt {(- 2) ^ 2-4 (3) (5)}} {2 (3)}\\x = \frac {2 \pm \sqrt {4-60}} {6}\\x = \frac {2 \pm \sqrt {-56}} {6}[/tex]

By definition we have to:

[tex]i ^ 2 = -1\\x = \frac {2 \pm \sqrt {56i ^ 2}} {6}\\x = \frac {2 \pm i \sqrt {56}} {6}\\x = \frac {2 \pm i \sqrt {2 ^ 2 * 14}} {6}\\x = \frac {2 \pm 2i \sqrt {14}} {6}\\x = \frac {1 \pm i \sqrt {14}} {3}[/tex]

We have two complex roots:

[tex]x_ {1} = \frac {1+ i \sqrt {14}} {3}\\x_ {2} = \frac {1- i \sqrt {14}} {3}[/tex]

Answer:

[tex]x_ {1} = \frac {1+ i \sqrt {14}} {3}\\x_ {2} = \frac {1- i \sqrt {14}} {3}[/tex]

Answer:

x=2, y=4. (2, 4).

Step-by-step explanation:

x+y=6

3x-2y=-2

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

y=6-x

3x-2(6-x)=-2

3x-12+2x=-2

5x-12=-2

5x=-2+12

5x=10

x=10/5

x=2

y=6-(2)=6-2=4

Answer:

81

Step-by-step explanation:

Answer:

Step-by-step explanation:3(180-x)=8(90-x)

540-3x=720-8x

540=720-5x

-180=-5x

36=x

x=36

the angle is 36,supplement is 144,complement is 54.

The angle is 36, the supplement is 144, complement is 54.

Two angles whose sum is 180° are called supplementary angles.

Two angles whose sum is 90° are called complementary angles.

Given;

The three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle.

So, 3(180-x)=8(90-x)

Solve for x;

540-3x=720-8x

540=720-5x

-180=-5x

36=x

x=36

Hence, the angle is 36, the supplement is 144, complement is 54.

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Answer:

  12/5

Step-by-step explanation:

The tangent ratio is the ratio of the opposite side (GH) to the adjacent side (FG). The mnemonic SOH CAH TOA can help you remember this:

  Tan = Opposite/Adjacent

In this triangle, ...

  tan(F) = GH/FG = 12/5

Final answer:

The sale price of the television, after a 35% discount on the original price of $1,800, is $1,170.

Explanation:

To calculate the sale price of the television that was originally priced at $1,800 and now has a 35% discount, we need to determine what 35% of the original price is and subtract it from the original price.

Step-by-Step Calculation

Find 35% of $1,800:
(35/100) × $1,800 = $630.

Subtract the discount from the original price:
$1,800 - $630 = $1,170.

Therefore, the sale price of the television is $1,170.

Answer:

4

Step-by-step explanation:

If we were to work backwards, 4 would be the 2 part in the equation, already done. 2x2=4. so that means that the other number must also be multiplied by 2, making the number 6. 6+4 is 10, meaning ten gallons. message me with any remaining questions!

There are 4 gallons of yellow paint are needed to mixed with the ten gallons of green paint.

To calculate how many gallons of yellow paint must be used to mix with blue paint in order to make ten gallons of green paint, using a ratio of 3 parts blue to 2 parts yellow, we first need to understand the total ratio parts. The ratio given is 3:2, which means there are 3 + 2 = 5 parts in total. Since we want to mix ten gallons of green paint, we need to split these ten gallons according to the ratio.

First, we calculate the value of one part by dividing the total gallons of green paint by the total number of parts:

10 gallons / 5 parts = 2 gallons per part

Now, since we have 2 parts yellow, we need:

2 parts  imes 2 gallons per part = 4 gallons

Therefore, to make ten gallons of green paint with the given ratio, 4 gallons of yellow paint must be used.

Answer:

10

Step-by-step explanation:

To solve this, we have to do 4 divided by 2/5, because there are stops every 2/5 mile of a 4-mile track.

To make dividing easier, you can write 4 as a fraction, which would be 4/1

Now, divide:

4/1 ÷ 2/5

Remember that when you divide a fraction by another fraction, you can multiply the first fraction by the reciprocal of the second fraction and get the same fraction.

The reciprocal of 2/5 is 5/2.

So 4/1 x 5/2 = 20/2, which can be simplified as 10.

So there are 10 stops. ^-^

Answer:

A) -4

Step-by-step explanation:

f(x)=10-2x

f(7)=10-2(7)

f(7)=10-14

f(7)=-4

fx)= 10-2x

f(7)=10-2(7)

do the bracket first

-2(7)=-14

f(7)=10-14

f(7)=-4

answer:

-4

[tex]\( \cos(2x) = \frac{1}{2} \).[/tex]

Given that [tex]\( \sin(x) = -\frac{1}{2} \) and \( \tan(x) \)[/tex] is negative, we can find \[tex]( \cos(2x) \)[/tex]using the trigonometric identities.

First, let's find the value of [tex]\( \cos(x) \)[/tex] using the Pythagorean identity:

[tex]\[ \cos^2(x) = 1 - \sin^2(x) \][/tex]

Given [tex]\( \sin(x) = -\frac{1}{2} \),[/tex] we have:

[tex]\[ \cos^2(x) = 1 - \left(-\frac{1}{2}\right)^2 \][/tex]

[tex]\[ \cos^2(x) = 1 - \frac{1}{4} \][/tex]

[tex]\[ \cos^2(x) = \frac{3}{4} \][/tex]

Taking the square root of both sides, since [tex]\( \cos(x) \)[/tex] is positive in the first and fourth quadrants:

[tex]\[ \cos(x) = \pm \frac{\sqrt{3}}{2} \][/tex]

Given that [tex]\( \tan(x) \)[/tex] is negative, we know that ( x ) lies in either the second or fourth quadrant. In the second quadrant, both [tex]\( \sin(x) \) and \( \cos(x) \)[/tex] are negative. In the fourth quadrant, [tex]\( \sin(x) \)[/tex] is negative but [tex]\( \cos(x) \) i[/tex]s positive.

Since [tex]\( \cos(x) = \pm \frac{\sqrt{3}}{2} \),[/tex] we conclude that [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \)[/tex]  (since [tex]\( \cos(x) \)[/tex] is negative in the second quadrant).

Now, using the double angle identity for cosine:

[tex]\[ \cos(2x) = 2\cos^2(x) - 1 \][/tex]

Substituting [tex]\( \cos(x) = -\frac{\sqrt{3}}{2} \):[/tex]

[tex]\[ \cos(2x) = 2\left(-\frac{\sqrt{3}}{2}\right)^2 - 1 \][/tex]

[tex]\[ \cos(2x) = 2\left(\frac{3}{4}\right) - 1 \][/tex]

[tex]\[ \cos(2x) = \frac{3}{2} - 1 \][/tex]

[tex]\[ \cos(2x) = \frac{3}{2} - \frac{2}{2} \][/tex]

[tex]\[ \cos(2x) = \frac{1}{2} \][/tex]

So, [tex]\( \cos(2x) = \frac{1}{2} \).[/tex]

Answer:

1/15 of a kilogram

Step-by-step explanation:

Answer:1/15 of a kilograms

Step-by-step explanation:

1/5 divided by three is the same as 1/5*1/3. 1*1 =1 and 5*3 =15

Answer:

4/7

Step-by-step explanation:

32/56=4/7

Answer:

The number of boys = 32

The number of girls = 56

therefore, to fine the possible ratio, you divided 32 and 56 to their lowest terms.

i.e 32: 56. 32÷8 : 56÷8 = 4:7

Answer:

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

Step-by-step explanation:

Given:

The range is 4 less than half of the domain.

The domain of a function is its input values represented by 'x'. The range of a function is its output values represented by 'y' values.

Domain is 'x'. So, half of domain is [tex]\frac{1}{2}x[/tex].

Now, range is 4 less than half of domain. Hence,

[tex]y=\frac{1}{2}x-4[/tex]

So, the correct option is the last option.

Answer:

[tex]y=0.95x+2.5[/tex]

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

Find the slope

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

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

take the points

(0,2.5) and (100,97.5)

substitute in the formula

[tex]m=\frac{97.5-2.5}{100-0}[/tex]

[tex]m=\frac{95}{100}[/tex]

[tex]m=0.95[/tex]

Find the y-intercept b

we have

[tex]m=0.95[/tex]

[tex]point\ (0,2.5)[/tex]

substitute i the linear equation  [tex]y=mx+b[/tex]

[tex]2.5=0.95(0)+b[/tex]

solve for b

[tex]b=2.5[/tex]

Note It was not necessary to calculate the value of b because the value is given in the table

Remember that the y-intercept is the value of y when the value of x is equal to zero (the y-intercept is the point (0,2.5))

The linear equation is

[tex]y=0.95x+2.5[/tex]

To write the equation of a linear relationship in slope-intercept form, find the slope and y-intercept. Use the formula y = mx + b, where m is the slope and b is the y-intercept. Calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b.

To write the equation of the linear relationship in slope-intercept form, we need to find the slope (m) and the y-intercept (b). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Choosing any two points from the given data, we can calculate the slope.

Let's use the points (0, 2.5) and (100, 97.5):
m = (97.5 - 2.5) / (100 - 0) = 95 / 100 = 0.95

Next, we can substitute the slope and one set of coordinates into the slope-intercept form equation and solve for b:

2.5 = 0.95(0) + b
b = 2.5

Therefore, the equation of the linear relationship is: y = 0.95x + 2.5

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Answer:

x=2

Step-by-step explanation:

x/6=3/9

simplify 3/9 into 1/3

x/6=1/3

cross product

6*1=3x

6=3x

x=6/3=2

x=2

The number 0.251 is a rational number because it can be expressed as the fraction 251/1000, which has both integers as its numerator and denominator, with the denominator not being zero.

To determine whether 0.251 is a rational number, one must understand the definition of rational numbers.

Rational numbers include all numbers that can be expressed as a fraction where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not zero.

The number 0.251 meets this criterion because it can be written as the fraction 251/1000, where 251 and 1000 are both integers, and 1000 is not zero.

If we look at different numerical expressions, such as ones resulting from operations on fractions or converting numbers into scientific notation, the underlying principle is that the operations maintain equality and the representations still refer to rational numbers as long as they can be expressed as a ratio of integers.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-6})\qquad W(\stackrel{x_2}{x+2}~,~\stackrel{y_2}{y+3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{(x+2)-2}{2}~~,~~\cfrac{(y+3)-6}{2} \right)\implies \left( \cfrac{x}{2}~~,~~\cfrac{y-3}{2} \right)[/tex]

Answer:

multiply 35(26)

Step-by-step explanation:

35(26)=910

and 910/26=35 ,

so w=910

Answer:

910

Step-by-step explanation:

Your equation is w ÷ 26 = 35

To solve for 'w,' you have to get 'w' alone on one side. To do that, you multiply both sides by 26, getting rid of the '÷ 26' on the left side of the equation.

w ÷ 26 = 35

w = 910

So your answer is 910  ^-^

Step-by-step explanation:

the segments are equal to each other because O is the midpoint of the segment

Answer:

x-intercept = 1 and y-intercept = -3

Step-by-step explanation:

The graph of the function is attached with this answer.

I have used some computer program to draw graph but you can draw a rough graph manually on a graph sheet. For that

To Calculate Some Important Points :

These are the points where the the first derivative of the function becomes zero. This means that at these points the graph takes turn, if it was increasing behind this point then it will start decreasing after this point or the other way. The second derivative of the function at these points are either positive or negative (positive for local minima and negative for local maxima).

To calculate the x-intercept, first you need to analyse the graph to know how many x-intercepts are there. According to this graph only one intercept is there, it means that only one real root of this cubic equation is there (a cubic equation has 3 roots in which either one is real and two are imaginary or all the three are real). To calculate roots of a cubic equation there is no specific way. Generally, the first root is through hit and trial method. So, let's start with the simplest number which is x=0

[tex](0)^{3}+2(0)^{2}-3 \neq 0[/tex]

∴ 0 is not a root.

Now, let x=1

[tex](1)^{3}+2(1)^{2}-3=0[/tex]

∴ 1 is a root.

Since 1 is the only real root of the equation, therefore (1,0) is the only x-intercept of the graph.

To calculate y-intercept, simply put x=0 in the equation which is

[tex]f(0)=(0)^{3}+2(0)^{2}-3=-3\\\therefore f(0)=-3[/tex]

Therefore the y intercept is (0,-3).

* Cubic Polynomial : Polynomials which have a degree (highest power of the variable) of 3 are called cubic polynomials.

** Local Maxima : Points at which the left and right neighbours have less function value are called local maxima.

*** Local Minima : Points at which the left and right neighbours have more function value are called local minima.

Answer:

x = 1 and the y = -3

Step-by-step explanation:

here below hope this helps

Answer:

The truck have travelled 345.5 inches after 5 rotations of the tires

Step-by-step explanation:

Given:

Diameter of the tyre= 22 inches

Number of rotations= 5

To find:

Distance travelled after 5 rotations=?

Solution:

We have given with diameter,

So let radius be r

r= [tex]\frac{diameter}{2}[/tex]

[tex]r=\frac{22}{2}[/tex]

r=11 inches

The distance covered by one rotation is given by circumference

Circumference =[tex]2\pi r[/tex]

Substituting the values, we get

Circumference =[tex]2\times\pi\times r[/tex]

Circumference =[tex]2\times\pi\times 11[/tex]

Circumference =[tex]2\times\3.14\times 11[/tex]

Circumference =[tex]6.28\times 11[/tex]

Circumference = 69.11

Now for 5 rotation,

Distance travelled = [tex]5\times(\text{circumference value})[/tex]

Distance travelled = [tex]5\times(69.11)[/tex]

Distance travelled = [tex]5\times(69.11)[/tex]

The truck will travel 345.5 inches.

The explicit formula for the sequence 1/2, -4, 32, -256 is an = 1/2 * (-8)^(n-1), where n represents the position of each term in the sequence.

To find an explicit formula for the sequence 1/2, -4, 32, -256, we need to look for a pattern in the sequence. Upon examination, we notice that each term is obtained by multiplying the previous term by -8.

The first term, a1, is 1/2. The second term, a2, is 1/2 times -8, which is -4. If we continue this pattern, the nth term of the sequence can be described by the formula an = 1/2 * (-8)^(n-1).

Therefore, the explicit formula for the nth term of this sequence is an = 1/2 * (-8)^(n-1).

Final answer:

The explicit formula for the sequence 1/2, -4, 32, -256 is an = 1/2 × (-8)(n-1), where n represents the nth term. This is derived from the pattern that each term is -8 times the previous term, indicating a geometric sequence.

Explanation:

To find an explicit formula for the sequence 1/2, -4, 32, -256, we need to look for a pattern in the terms of the sequence. Upon inspection, we see that each term is -8 times the previous term. This is a geometric sequence with a common ratio of -8.

The formula for the nth term of a geometric sequence is given by an = a1 × r(n-1), where a1 is the first term and 'r' is the common ratio.

Applying this to the given sequence with a1 = 1/2 and r = -8, the explicit formula for the nth term (an) is: