ASSIGN #1: Object A is moving 12 feet per second (ft/sec). Object B is moving 5 miles per
R.A. hour (mila/hr). Which object is moving faster

From the inequality given by 8x + 15 > 9x - 26, x is less than 41.

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

Solving the inequality,

8x + 15 > 9x - 26

Combine like terms in one side and the constants in the other side.

8x - 9x > -26 - 15

-x > -41

Divide both sides by -1.

x > 41

Note that when we multiply or divide by a negative number

we must reverse the inequality.

x < 41

Therefore, x is less than 41.

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The equation in point-slope form of the line having the given slope m = 2 that contains the given point (4, -9) is 2x - y = 17

It is given that,

Slope is the measure of the steepness of a line.

Equation is the mathematical statement made up of two expressions joined together by the equal sign. For instance 3x - 5 = 16

The slope of a one point line = m = 2

The point through which the line passes = (4, -9)

We need to find the,

The equation in point-slope form of the line having the given slope that contains the given point

The formula which will be used,

(y-y1) = m(x-x1)

where, (x1,y1) = (4, -9) and m = 2

putting the values in the formula, we get

[y - (-9)] = 2. (x-4)

y + 9 = 2x - 8

y - 2x = -17

2x - y = 17

Hence, the equation in point-slope form of the line having the given slope that contains the given point is 2x - y = 17

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I and IV only are statements that are true out of all the statements.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

I. -(-6)=6 and -(-4)>-4

⇒ 6 = 6 and 4 > -4

IV. 17>2 or 6<9

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Answer:

First Section:4km per hour

Second Section:0km per hour

Third Section:1.5km per hour

Step-by-step explanation:

From the first section to the second section the distance remains the same therefore he didn't travel at all that's why it is 0km. For the third section he has to travel 6 kilometers in 4 hours which is 1.5.

The interval notation that expresses the expression is (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)

The expression is given as:

x ≤ 3 and x ≠ -1 or 4 ≤ x

In inequality, "and" is represented with ∩, while "or" is represented with ∪

The above can be represented as:

x ≤ 3 ∩ x ≠ -1 ∪ 4 ≤ x

As an interval notation, we have (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)

Hence, the interval notation that expresses the expression is (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)

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Answer:

the answer should be 5 sorry if wrong

Answer:

5

Step-by-step explanation:

y=xx5

The ratio of the radius of the small sphere with a volume of 36π cubic centimeters to the radius of the large sphere having a volume of 288π cubic centimeters is 1/2.

Given two spheres having volumes of 36π cubic centimeters and 288π cubic centimeters, solve for the radius of each sphere using the formula for the volume of sphere given by:

V = 4/3πr^3

smaller sphere :

36π cubic centimeters = 4/3πr^3

r^3 = 27

r = 3 centimeters

larger sphere :

288π cubic centimeters = 4/3πr^3

r^3 = 216

r = 6 centimeters

Getting the ratio of the radius of the small sphere to the radius of the large sphere:

ratio = radius of the small sphere / radius of the large sphere

ratio = 3 centimeters / 6 centimeters

ratio = 1/2

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Answer:

The value of x is 12 if the value of f^-1(x) = 2.

Step-by-step explanation:

It is given that f(x) = 4(x + 1), which is an inverse function.

Now,

First of all, let us understand what is a function and an inverse function;

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

On the other hand;

A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.

Now, let us consider the first part of the question;

We have to calculate the value of x when f^-1(x) = 2 given that f(x) = 4(x+1) is the function;

=> f(x) = 4(x + 1)

=> 4(y + 1) = x

=> x = 4y + 4

=> y = (x - 4)/4

=> f^-1(x) = (x - 4)/4

Hence, f^-1(x) = (x - 4)/4 is the inverse of f(x).

Now, let us put the value of f^-1(x) = 2 in the equation so obtained;

=> f^-1(x) = (x - 4)/4  

=> 2 = (x - 4)/4

=> 8 = (x - 4)

=> x = 12

Hence, the value of x is 12 if the value of f^-1(x) = 2.

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Answer:

7.519*10 power 3 is the answer.

The dimensions are 3 inches, 10 inches, and 13 inches.

It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.

Therefore,

(2x + 6)²

4x²+ 24x + 36

Reduce to lowest term

x² + 6x + 9

x² + 3x + 3x + 9

x(x + 3) - 3(x + 3)

(x - 3) = 0

x = 0 + 3 = 3

Therefore x = 3

Therefore the dimensions will be:

x = 3

2x + 4 = 2(3) + 4 = 10

2x + 6 = 2(3) + 6 = 12

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Answer:1/15

Step-by-step explanation:

Assuming it is multiplication, multiply the numerators: 3 * 2 = 6

Multiply the denominators: 10 * 9 = 90

Put them together for 6/90 and simplify for 1/15

hi

slope formula is :    y2-y1 / x2-x1  

you can reverse it if you want.   :    y1-y2 / x1 -x2

m =   0- (-2)  / 3 - (-1) =  2/ 4 = 1/2

The explicit formula for a geometric sequence is [tex]a_{n}[/tex] =[tex]a_{1}^{r-1}[/tex]

The sequence is:

  1, 2, 4, 8..........

The formula for a geometric sequence,

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

                   a, ar, [tex]ar^{2}[/tex], [tex]ar^{3}[/tex]

r = common ratio

n = number of sequences in a series.

Let us understand by the sequence,

Here r = 2 , a = 1

Therefore by putting these values in the equation we get,

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

   = a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex], ........

   1, 2, 4, 8 .........

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The percentage is the hundredth of any digit or value between 1 to 100 so 35% of 900 will be 315.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The x percentage of any random y digit is given as;

⇒ (x/100) × y

Therefore,

35% of 900 →

(35/100) × 900

⇒ 35 × (900/100)

⇒ 35 × 9

⇒ 315

Hence " The 35% percentage of the amount 900 will be 315".

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The given question is not in English, English translation follows;

What is 35% of 900?

These sites are on a line with a -5 degree slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the y-intercept for the equation y = 3x - 7 is (0, 7) and the slope is 3.

In response to the query, I see the points as

(x ,y)

(13, 11)

(14, 6)

(15, 1)

(16, -4)

(13, 11) , (14, 6), (15, 1), and (16, -4)

slope =  (6 - 11) / (14 - 13)

= - 5/-1

 = -5

try again:   (1 - 6)/(15 -14)

= -5/1

= -5

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2x and 72

Step-by-step explanation:

pls don't use this I don't want you to get a bad grade if it is wrong

Answer: 4x+24

Step-by-step explanation: 8x+40-4x-16

The equation when the accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes is 120 + 40h.

From the information, it should be noted that the

accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes.

Let the number of hours be represented by h.

Therefore, the expression to describe the problem will be:

= 120 + (40 × h)

= 120 + 40h

The equation is 120 + 40h.

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Answer:  Theorem 4 says that the columns of B do NOT span R4. Further, using Theorem 4, since 4(c) is false, 4(a) is false as well, so Bx = y does not have a solution for each y in R4.

Step-by-step explanation:

Yes, the column b span r4. Yes, the equation has a solution for each y in r4.

Matrix is defined as a set of numbers consisting of rows and columns elements.

It consists of rows and columns.

The dimensions of the matrix are determined by m×n.

Given matrix,

[tex]\begin{bmatrix} &1 &3 &-2 &2\\ &0 &1 &1 &-5\\ &1 &2 &-3 &7\\ &-2 &-8 &2 &-1\\\end{bmatrix}[/tex]

R3  → R1

R3→R4+2R1

[tex]\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-1 &1 &5 \\ &0 &-2 &-2 &3\\\end{bmatrix}[/tex]

R3→R3+R2

R4→R4+2R2

[tex]\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-0 &2 &0 \\ &0 &-0 &0 &7\\\end{bmatrix}[/tex]

This is the row echelon form of B. It has four independent columns and the dimension of r4 is 4.

column of B spans r4.

Row of matrix = 4

No of columns of matrix = No of rows of the matrix.

and the columns of B span r4.

thus we can conclude that the columns of b span r4 and the equation

bx =d y have a solution for each y in r4.

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The probability that the card drawn has a composite number written on it is 1/2

The sample space is given as

S  = {1, 2....3}

The list of composite numbers from 1 to 12 is 4, 6, 8, 9, 10, 12

So, we have

Composite = 6

The probability that the card drawn has a composite number written on it is

P = Composite/Sample size

So, we have

P = 6/12

Simplify

P = 1/2

Hence, the probability that the card drawn has a composite number written on it is 1/2

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Using the distance formula, the distance between the pair of points C(11,-12) and D(6,2) is 14.86 units

Given,

The points = C(11,-12) and D(6,2)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(6-11)^{2}+(2--12)^{2} }[/tex]

[tex]=\sqrt{(-5)^{2}+14^{2} } \\=\sqrt{25+196}\\ =\sqrt{221}[/tex]

=14.86 units

Hence, Using the distance formula, the distance between the pair of points C(11,-12) and D(6,2) is 14.86 units

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Answer: the third option

Step-by-step explanation: 0.66666666666 is it in decimal form, the line above the single six just means its the same number over and over again

Answer:

.67 (See explanation for why)

Step-by-step explanation:

2/3

in order to turn this into a whole number, we are going to multiply the bottom number until it becomes any number starting with 1 and ending with a zero. this isnt possible Because 3 is a number that cannot do that.

So instead, we will multiply the number by 333

2*333 = 666

3*333 = 999

666/999 = 2/3

999 is nearly 1000, so lets write the decimal point 3 spaces inwards

.666

which can become

.66

The longer decimal for this(when using a calculator)

would give you

.6666666667

And if we round,

7 is higher than 5, so it becomes .666666667

continue...

Until you have .67

Hope this helps! ^^

You find a book that costs $16.75 and you must pay 4% sales

tax. You use a $25 gift card then only $7.58 is left on the gift card after you buy the book.

A sales tax is a government-imposed consumption tax levied on the purchase of goods and services. A traditional sales tax is assessed at the point of sale, collected by the retailer, and passed on to the government. A firm is liable for sales taxes in a given jurisdiction if it has a nexus there, which can be a physical location, an employee, an affiliate, or some other presence, depending on the rules in that country.

We must 4% sales tax on $16.75 book

Sales tax = 16.75 × 0.04

               = 0.67

The total cost = 16.75  + 0.67

                       = $17.42

He uses a $25 gift card, so he is left with

= 25 - 17.42

= 7.58

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a. The square roots and square cancel each other so 5 × 3 = 15

b. The cube roots and cubes cancel each other so 9 × 30 = 270

For math students, especially those in class 8, the square root and cube root concepts are the most crucial. In order to get the square root of any integer, we must first identify a number that, when multiplied twice by itself, equals the original number.

Similar to this, we must locate a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any number.

The cube root is represented by the sign "√," whereas the square root is represented by the symbol "∛."

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Answer:

F

Step-by-step explanation:

Wrong answers

A. current price not doubled

B. price before is 150%, not current price

C. price is reduced by 33.3%, not 25%

D. price is 66.6% of price before

E. price before is 1.5 times greater, not current price

G. price is now 66.6% of price before

H price is 66.6%, not 75%

Using scientific notation and subtraction between two amounts, the difference between the payrolls is given by:

B. 2.5753 x 10¹¹ dollars.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For any generic amounts a and b, to find how much an amount a is more than an amount b, we subtract a by b.

For this problem, the budgets are given as follows:

Hence the difference is given by:

2.6 x 10¹¹ - 2.47 x 10^9

To subtract two numbers in scientific notation, they must have the same exponent, hence:

2.47 x 10^9 = 0.247 x 10^10 = 0.0247 x 10¹¹.

Then the difference is:

2.6 x 10¹¹ - 0.0247 x 10¹¹ = 2.5753 x 10¹¹ (to subtract two numbers in scientific notation, we subtract the bases and keep the exponents).

The difference between the payrolls is given by:

B. 2.5753 x 10¹¹ dollars.

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and

Find amount of tax against each paycheck:

Answer:

= 0.25m/s

Step-by-step explanation:

The formula of finding the speed, v is given by

[tex]v \: = \frac{change \: in \: distance \: d}{change \: in \: time \: t} [/tex]

The change in distance from the graph is

∆d = (8 - 6)

= 2 m

The change in time from the graph is

∆d = (20 - 12)

= 8s

Substituting to our formula, we have

[tex]v \: = \frac{2m}{8s} \\ = \frac{1}{4} \frac{m}{s} \\ = 0.25 {m}s^{ -1 } [/tex]

Therefore, the speed v, of the journey between 12 and 20 second is 0.25m/s.