What is the first term of the quotient of the following division problem ? (X^3-1)

Answer:

2. n = 11

4. g = -2

6. t = 21

8. n = 4

10. y = -1

Step-by-step explanation:

2. 63  = -3(1 - 2n)

Dividing both the side by negative 3 we get

[tex]-21=1-2n\\2n=1+21\\2n=22\\n=\frac{22}{2} \\\therefore n=11[/tex]

4. -g + 2(3 + g) = -4(g + 1)

First we will open the bracket by distributive property A( B +C) = AB + AC

[tex]-g+2\times 3 + 2\times g = -4\times g + -4\times 1\\-g+6+ 2g=-4g-4\\\textrm{we will take all the g term the left side and the constant to the right side}\\4g-g+2g=-6-4\\5g=-10\\g=\frac{-10}{5}\\\therefore g=-2[/tex]

6.-3(t +5 ) + (4t + 2) = 8

Using distributive property A( B +C) = AB + AC we get

[tex]-3\times t + -3\times 5 + 4t + 2=8\\-3t-15+ 4t + 2=8\\t=8+15-2\\t=21\\\therefore t=21\\[/tex]

8. -8 - n = -3(2n -4)

Using distributive property A( B +C) = AB + AC we get

[tex]-8 - n = -3\times 2n - -3\times4\\-8-n=-6n+12\\\textrm{all the n terms to the left inside and the constant of the right-hand side}\\6n-n=8+12\\5n=20\\n=\frac{20}{5}\\ \therefore n= 4[/tex]

10. -4( 2 - y) + 3y = 3(y - 4)

Using distributive property A( B +C) = AB + AC we get

[tex]-4\times 2 --4\times y + 3y = 3\times y -3\times 4\\-8+4y+3y =3y-12\\\textrm{all the y terms to the left side and the constant to the right side}\\4y+3y-3y=-12+8\\4y=-4\\y=\frac{-4}{4}\\ \therefore y=-1[/tex]

Answer:

Step-by-step explanation:

The expanded form of the number 234.567 written using exponential notation  would be ...

  2×10² +3×10¹ +4×10⁰ +5×10⁻¹ +6×10⁻² +7×10⁻³

Note that exponents decrease going left to right (or increase going right to left). The exponent associated with the "ones" place is 0.

Apparently, you're supposed to write the negative powers as fractions, so you would have ...

  6.19 = 6×10^0 + 1×(1/10^1) + 9×(1/10^2)

Answer:

No

Step-by-step explanation:

because one can be 5 by 5 and the other can be 7 by 7.

I know it's to short but this is what I got.

Answer:

5 by 5 and 7 by 7. Really hope this helped :)

Step-by-step explanation:

The value of k will be 3 if the function is transformed by compression factor of 3

Step-by-step explanation:

The horizontal stretch or compression for a function f(x) is given by  g = f(bx) where b is a constant. If b> 0 then the graph of function is compressed.

As it is given in the question that he function is transformed by a compression factor of 3.

Given function

[tex]f(x) = 7^x+1\\To\ transform\\g = f(bx)\\g = 7^{3x}+1[/tex]

The value of k will be 3 if the function is transformed by compression factor of 3

Keywords: Functions, Transformation

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Answer:

=40/33

8/11 divide 3/5 -> 8/11 x 5/3 and multiply 8x5 then 11x3 then u got your answer! :)

Hope this worked :D

Answer:

Your answer is 40/33

Step-by-step explanation:

8/11 * 3/5

flip the fraction

8/11* 5/3

Multiply

V = π·r²·h/3 = π·81·6/3 = 2·81·π = 162π cm³

Answer:

1.69

Step-by-step explanation:

well to find out the unit rate that would be a pound now we need to find out how much it would cost for 1 lb which would be 3.38 / 2 which would be 1.69 as your answer

Answer:

$1.69 per pound

Step-by-step explanation:

3.38/2=1.69

Step-by-step explanation:

10. |-41|= 41

12. -|1.5|= -1.5

Answer:

A.) 41

B.) -1.5

Step-by-step explanation:

Absolute value means to make whatever that is inside positive

10.) The absolute value of negative 41 would simply be positive 41

11.) Since the negative sign is on the outside of the absolute value, you do the absolute value of everything inside then apply a negative sign. Absolute value of 1.5 is just 1.5 because it's already positive. Then apply the negative sign, which would make it -1.5

Answer:

The answer is y = 6.

Step-by-step explanation:

Given:

RS = [tex]3y+41[/tex], ST = [tex]18y-76[/tex] and RT = 91.

Now, to find the [tex]y[/tex].

According to question add the equations:

RS + ST = RT

[tex]3y+41+18y-76=91[/tex]

Adding the numbers and variables in L.H.S.

[tex]3y+18y-76+41=91[/tex]

[tex]21y-35=91[/tex]

Adding 35 on both sides:

[tex]21y-35+35=91+35[/tex]

[tex]21y=126[/tex]

Dividing both sides by 21:

[tex]21y\div 21=126\div 21[/tex]

[tex]y=6[/tex]

Therefore, the answer is y = 6.

Answer:

[tex](150+21m)\ miles[/tex]

Step-by-step explanation:

we know that

[tex]1\ week=7\ days[/tex]

Remember that the speed is equal to divide the distance by the time

Let

s ---> the speed in miles per day

d ---> the distance in miles

t ---> the time in days

[tex]s=\frac{d}{t}[/tex]

[tex]d=st[/tex]

we have

[tex]s=m\ miles/day[/tex]

[tex]t=3\ weeks[/tex]

Convert to days

[tex]t=3(7)=21\ days[/tex]

Find the distance covered in the trip

[tex]d=st[/tex] ----> [tex]d=m(21)=21m\ miles[/tex]

To find out the mileage on Jim’s car after his trip, sum the mileage before his trip (150 miles) plus the mileage of the trip

[tex](150+21m)\ miles[/tex]

Answer:

The restaurant Manager can afford 6 employees for the day.

Step-by-step explanation:

Manager can spend at most of $400.

Total Money ≤ $400

Cost to operate bank = $100

Cost for each employee = $50

Let number of employees for the day be[tex]x[/tex]

Hence the equation will become;

[tex]50x + 100 \leq 400[/tex]

Solving this equation we get;

[tex]50x + 100 \leq 400\\50x \leq 400-100\\50x \leq 300\\x\leq \frac{300}{50}\\\\x\leq 6[/tex]

Hence, The restaurant Manager can afford 6 employees for the day.

Answer:

x < = 10

Step-by-step explanation:

i did it on photo math so yah

Answer:

169/100

Step-by-step explanation:

93 + 76/100 = 169/100

Answer: 169/100

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-2+4(-x+4)=10\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\-2+(4)(-x)+(4)(4)=10\\\\-2-4x+16=10\qquad\text{combine like terms}\\\\-4x+(-2+16)=10\\\\-4x+14=10\qquad\text{subtract 14 from both sides}\\\\-4x+14-14=10-14\\\\-4x=-4\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{-4}{-4}\\\\x=1[/tex]

Answer:

1

Step-by-step explanation:

Using the rule of exponents

[tex]a^{0}[/tex] = 1

Any expression raised to the power of zero will equal 1

Given

[tex](3/7)^{0}[/tex] = 1

Answer:

18.55, lines m and n are parallel and t is the transversal. If ∠1 = 130o, find the measures of the other angles and give reasons.

Step-by-step explanation:

The measure of angle 8 will be 130° since it corresponds to angle 1, and their measures are equal because lines m and n are parallel.

To find the measure of angle 8 when lines m and n are parallel, and the measure of angle 1 is 130°, it's important to understand the concept of corresponding angles in the context of parallel lines. Corresponding angles are equal when two lines are parallel. Given that angle 1 is 130°, and assuming that angle 1 and angle 8 are corresponding angles (since the question does not specify their positions), the measure of angle 8 is also 130°.

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Answer:

The answer is C.

Step-by-step explanation:

Just failed hah stream fancy

Answer:

Answer is a^8/b^10

Option C

Step-by-step explanation:

((a²b-³)/(a-²b²))² where b and a are not equal zero

To solve this equation we start solving the equation from inside the bracket. And for simplicity we solve the numerator and solve the denominator before dividing them with each other. Now let get started

((a²b-³)/(a-²b²))²

Recall from indices that

a ^ -b = 1/a^b

I.e b-³ = 1/b³... We will apply this here.

((a²b-³)/(a-²b²))²

=((a²* 1/b³)/(b²*1/a²))²

=((a²/b³)/(b²/a²))²

Also recall that

(a/b) / (c/d) = (a/b) * (d/c)

Therefore

=((a²/b³)/(b²/a²))²

=(a²/b³ * a²/b²)²

Recall that: a^b * a^c = a^(b+c)

= (a ^ (2+2) / b ^ (2+3))²

= (a^4/b^5)²

Recall that: (a^b)^c = a^(b+c)

Therefore:

=™(a^4/b^5)²

=(a^(4*2)/b^(5*2))

= a^8/b^10

1 An integer is a number that has no fractional part, and no digists after the decimal point. An integer can be positive, negative or zero. example 12, 34,-4,0 etc.

2. A natural number is a number that occurs commonly and obviously in nature. As such it is a whole, non -negative number. The set of natural numbers, denoted N, can be defined in either of two ways : N = (0,1,2,3,.......)

Natural numbers include 1, 2, 3, 4...; they are numbers you normally count and will go onto infinity and beyond. ZERO IS NOT A NATURAL NUMBER BECAUSE IT IS NEUTRAL.

Integers are all negative and positive counterparted whole numbers; e.g.... −4, −3, −2, −1, 0, 1, 2, 3, 4,...

I am joyous to assist you anytime.

Final answer:

To find the previous year's total revenue, divide the current year's revenue by 1.34 since the current revenue is 34% higher than the previous year. The calculation shows that the previous year's revenue was $25,000.

Explanation:

The question asks us to find the total revenue of a small business for the previous year, given that the current year's revenue is 34% higher. To do this, we let x represent the revenue from the previous year. Since this year's revenue is 34% more than last year's, we have the equation:

1.34x = 33,500

To find the value of x, we divide both sides of the equation by 1.34:

x = 33,500 / 1.34

x = 25,000

Therefore, the total revenue for the previous year was $25,000.

Answer:

126

Step-by-step explanation:

621 - x = 495

Subtract 621 from both sides.

-x = -126

Divide by -1

x = 126

Final answer:

To find the angle of elevation, we can use the concept of tangent. The angle of elevation is approximately 67.7 degrees.

Explanation:

To find the angle of elevation, we can use the concept of tangent.

Tan(Angel of Elevation) = Opposite/Adjacent

Here, the opposite side is the height of the fair, which is 1800 meters, and the adjacent side is the height of the station, which is 700 meters.

Tan(Angel of Elevation) = 1800/700

Angel of Elevation = tan-1(1800/700)

Using a calculator, the angle of elevation is approximately 67.7 degrees.

Answer:

C

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x) by c units

• If c > 0 then shift c units up

• If c < 0 then shift c units down

The red graph is a vertical translation f(x) of 3 units down

Thus

y = f(x) - 3 ( add 3 to both sides )

y + 3 = f(x) ← equation of red graph

Answer:

the 1st & last paras are fixed.

that leaves 3 to be put in any order

there are 3 choices for the 1st,

2 choices left for the 2nd

and just 1 choice for the last

multiply to get

3*2*1

= 6 ways

We want to find the total number of orders in which we can order the given sentences.

We will see that there are 120 different orders.

There are 5 sentences, let's define them as:

We know that we can order these in any order, so we can think of the situation as 5 empty slots, in each slot, we can put one of the previous statements.

Let's count the number of options for each one of these slots.

On the first one, we have 5 options (5 sentences)

On the second one we have 4, because we already used one on the first slot.

On the third, we have 3 options.

On the fourth, we have 2 options.

On the fifth, we have 1 option.

The total number of combinations is given by the product of these numbers of options.

Combinations = 5*4*3*2*1 = 120

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Answer:

17/8

Step-by-step explanation:

2/1=2

11-2-6-7/8

9-6-7/8

3-7/8

24/8-7/8

17/8

The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y) ⇒ 1st answer

Step-by-step explanation:

Let us revise some words in the operations of mathematics problems

∵ The algebraic expression is " 3 times the sum of 2 and y "

∵ Sum is the answer of add

∴ add 2 and y

∴ The sum of 2 and y = 2 + y

∵ 3 times means multiply by 3

∴ 3 times the sum

∴ Multiply the sum by 3

∵ The sum = 2 + y

∴ Multiply (2 + y ) by 3

∴ 3(2 + y)

∴ 3 times the sum of 2 and y = 3(2 + y)

The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y)

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Answer:

a

=

Step-by-step explanation:

uo[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

Answer:

The next two terms for the geometric sequence are - 108 and - 324.

Step-by-step explanation:

1. Let's find the next two terms for the geometric sequence which first three terms are as follows:

- 4, 12, - 36.....

Aₓ = Aₓ₋₁ * 3 ; A₁ = - 4

A₁ = - 4

A₂ = A₁ * 3 = - 4 * 3 = - 12

A₃ = A₂ * 3 = - 12 * 3 = - 36

A₄ = A₃ * 3 = - 36 * 3 = - 108

A₅ = A₄ * 3 = - 108  * 3 = - 324

The next two terms for the geometric sequence are - 108 and - 324.

The homing pigeon will minimize its flying time by flying straight across the river, then directly to its nest. The time to fly this route would be 142.5 seconds.

The homing pigeon's path that will minimize its flying time would-be one where it flies straight across the river and then flies directly to its nest. The total time can be calculated by adding the time it flies over water and the time it flies over land. Initially, calculating the flying time over water, if the river is 500 meters wide, the time will be the distance divided by speed which equals 500m/8m/s = 62.5s . Now the land distance is the total distance minus the width of the river, so it would be 1300m – 500m = 800m. The time to cross this distance will be 800m/10m/s = 80s. Hence, adding both times, total flying time will be 62.5s + 80s = 142.5s. Therefore, the shortest path is firstly, flying straight across the river, and then straight towards its nest.

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The recursive formula for given sequence is:

[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]

Step-by-step explanation:

Given sequence is:

-16, 4, -1, ...

First of all, we have to find the common ratio. common ratio is the ratio between two consecutive terms of a geometric sequence

Here

[tex]a_1 = -16\\a_2 = 4\\a_3 = -1\\Now\\r = \frac{a_2}{a_1} = \frac{4}{-16} = -\frac{1}{4}\\r = \frac{a_3}{a_2} = \frac{-1}{4} = -\frac{1}{4}[/tex]

The recursive of geometric sequence is:

[tex]a_n = r * a_{n-1}[/tex]

Putting the value of r

[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]

Hence,

The recursive formula for given sequence is:

[tex]a_n = -\frac{1}{4}a_{n-1}[/tex]

Keywords: Geometric sequence, Recursive formula

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Because the equation contains an absolute value, the shape of the graph would be a V,.

The Y intercept is -1, so this would be the lowest point on the graph.

Replace X with 1 and solve:

y = 2(1) -1 = 2-1 = 1, so another point would be (1,1) and another point would be (-1,1)  ( Absolute value would use both -1 and 1 as the same).

Make 3 points on the graph:

(-1,1) (1,1) ans (0,-1) and draw lines through them.

See attached picture:

Answer:

y=3x/2

Step-by-step explanation:

first you want to get the -2y alone so you move the 3x. since it's adding now the opposite of addition is subtraction. now your left with -2y= -3x. since your trying to solve for y now you divide -2 on both sides and your gonna be left with y= -3x/-2. since their both negatives it turns to postive. that's why the answer would be y= 3x/2.

Step-by-step explanation:

this line will cross the origin

to help I'm just going to explain something real quick.

make it into y intercept form (y=mx+b)

-2y=0-3x

y=3/2x +0

the m (3/2) is the slope

and b (0) is the y intercept

if you want to check it then imput a point on the line into the x and y variables

The correct sequence is a. 17, 26, 37.

To determine the next three terms in the sequence, we must first identify the pattern governing the sequence. Let's examine the differences between consecutive terms:

- The difference between the second term (2) and the first term (1) is 1.

- The difference between the third term (5) and the second term (2) is 3.

- The difference between the fourth term (10) and the third term (5) is 5.

- The difference between the fifth term (17) and the fourth term (10) is 7.

We can see that the differences between consecutive terms are increasing by 2 each time. This suggests that the sequence is generated by adding consecutive odd numbers to the previous term. To find the next terms, we continue this pattern:

- The sixth term will be the fifth term (17) plus the next odd number (9), which is 17 + 9 = 26.

- The seventh term will be the sixth term (26) plus the next odd number (11), which is 26 + 11 = 37.

- The eighth term will be the seventh term (37) plus the next odd number (13), which is 37 + 13 = 50.

Therefore, the next three terms of the sequence are 26, 37, and 50, confirming option a as the correct answer.