[tex]-\sqrt[4]{324}[/tex]

Answer:

x² - 6x + 4

Step-by-step explanation:

Hello!

Factor each term completely:

Common factors that are shown in all 3 terms are x and 3.

Divide each term by 3x:

Combine the terms: x² - 6x + 4

The 58 m/s initial velocity of the arrow with height, y = 58•t - 0.83•t², gives;

(1) 55.925 m/s

(2) 56.257 m/s

(3) 56.3317 m/s

(4) 56.33917 m/s

(b) 56.34 m/s

Initial velocity of the arrow = 58 m/s

Height of the arrow is; y = 58•t - 0.83•t²

The above kinematic equation can be analyzed as follows;

(1) The height at t = 1 is found as follows;

y = 58 × 1 - 0.83 × 1² = 57.17

Height at t = 1.5 s. is y = 58×1.5 - 0.83×1.5² = 85.1325

Which gives;

Average velocity = (85.1325-57.17)/(1.5-1) = 55.925

The average velocity in the interval [1, 1.5] is therefore;

(2) [1, 1.1]

Height at t = 1.1 s. is y = 58×1.1 - 0.83×1.1² = 62.7957

Which gives;

Average velocity = (62.7957-57.17)/(1.1-1) = 56.257

(3) [1, 1.01]

Height at t = 1.01 s. is y = 58×1.01 - 0.83×1.01² = 57.733317

Which gives;

Average velocity = (57.733317-57.17)/(1.01-1) = 56.3317

The average velocity is 56.33 m/s

(4) [1, 1.001]

Height at t = 1.01 s. is y = 58×1.001 - 0.83×1.001² = 57.22633917

Which gives;

Average velocity = (57.22633917-57.17)/(1.001-1) = 56.33917

(b) The equation for the instantaneous velocity is found as follows;

v = dy/dt = 58 - 2×0.83•t

After 1 second, we have;

t = 1

v = 58 - 2×0.83 × 1 = 56.34

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Answer:

9

Step-by-step explanation:

Answer:

  14

Step-by-step explanation:

You want the number of my cats when that number is "one-half of my cats plus seven".

Let the number of cats be represented by c. Then the description of the number of cats is ...

  c = c/2 +7

Multiplying by 2 gives ...

  2c = c +14

  c = 14 . . . . . . . subtract c

The nemesis has 14 cats.

The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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The graph of the parabola is given at the end of the answer.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the range and the symmetry line, the vertex of the function is at (-1,-4) and:

h = -1, k = -4.

Hence:

y = a(x + 1)² - 4.

It has a y-intercept of -3, that is, when x = 0, y = -3, hence we use it to find a as follows.

-3 = a - 4

a = 1.

Hence the function is:

y = (x + 1)² - 4.

The graph of this function is given at the end of the answer.

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Answer:625

Step-by-step explanation:(2+3)^4

5^4

Answer: -40

Step-by-step explanation:

Answer:

-1/40

Step-by-step explanation:

-3/8x -11+11=4+11

-3/8x=15

-3/8x x=15x

-3/8=15x

15x/15= -3/8/15

x=-1/40

Hope this helps!^^

Answer:

x = 4 - 2y

Step-by-step explanation:

4x + 8y = 16

or, x + 2y = 4

or, x = 4 - 2y

Answer:4-2y

Step-by-step explanation:

Answer:

−55x+750=0

Step-by-step explanation:

Answer:

perpendicular slope = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 3x + 4y = 7 ( add 3x to both sides )

4y = 3x + 7 ( divide through by 4 )

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex]

The perimeter of the given figure for the given values is equal to 24units.

As given in the question,

Given values of the figure,

AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm

HG = AB - (EF + CD)

      = 8- (3 +1)

      = 4 units

AH = (BC-DE)+FG

     = (3-2)+1

     =2units

Perimeter of the given figure

= AB + BC+ CD+ DE+ EF+ FG+ GH+ HA

= 8+ 3+ 1+ 2+ 3+ 1+ 4+ 2

=24 units

Therefore, the perimeter of the given figure for the given values is equal to 24units.

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Answer:

I'll answer the question in the picture first.

log(6) = 1.788

log(8) = 2.079

ln(6) = 1.792

ln(8)= 2.08

How to use a scientific calculator?

There are many different types of scientific calculators, so it is difficult to give a single answer to this question. However, most scientific calculators have a variety of buttons that perform different functions. Typically, there are buttons for the four basic operations ( addition, subtraction, multiplication, and division), as well as buttons for more complex functions such as square roots and exponential operations. To use a scientific calculator, simply press the buttons corresponding to the operations you want to perform.

Step-by-step explanation:

Answer:

D [tex] \frac{1}{3} x - \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] f(x) = 3x + 2[/tex]

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

Answer:

This is not proportional.

Step-by-step explanation:

If there was no meal delivery cost than it would be proportional.

Answer:

x + 7

___________________________________________________
What are variables?

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common symbols used for variables!

How do we describe variables in word form?

When we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable).

In this case "The sum of a number" has no definite correlation to a number, therefore, it is automatically considered a variable.

Then, since it says "The sum" we know we are adding. Adding what? We are adding an unknown term to the number 7.

Henceforth, the answer is x + 7.
___________________________________________________
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(a) 45 tens is equal to 450. :- True

(b) 12.3 is equal to 123 ones. :- True

(c) 80 tens is greater than 6 hundreds. :- True

(d) 43,200 is less than 50 thousands. :- True

(e) 60 hundreds = 6,000 :- True

Consider the first statement,

45 tens are equal to 450

So, 45 tens mean 45 times 10 is written as:

45 × 10 = 450

Hence, it's true.

Consider the second statement,

12.3 is equal to 123 ones.

Now, 123 ones is equal to 123 times 1.

123 × 1 = 123

Hence, the statement is true.

Consider the third statement,

80 tens is greater than 6 hundreds.

Now 80 tens = 80 × 10 = 800

Now, 6 hundreds = 6 × 100 = 600

Now, 800 > 600

Hence, the statement is true.

Consider the fourth statement.

43,200 is less than 50 thousands.

Now, 50 thousands = 50 × 1000 = 50,000

We know,

50,000 > 43,200

Therefore, the statement is true.

Consider the fifth statement,

60 hundreds = 6000

Now, 60 hundreds = 60 × 100 = 6000

Therefore, the statement is true.

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Answer:

y = x - 11

Step-by-step explanation:

5y + 22 = 5x - 33

5y = 5x - 33 - 22

5y = 5x - 55

y = x - 11

Answer: Domain: -2<=x<=2

Range: -2<=y<=2

Not a function

Step-by-step explanation:

Domain: x goes from -2 to 2

-2<=x<=2

Range: y goes from -2 to 2

-2<=y<=2

Not a function since there are several y-coordinates that have the same x-coordinate, so the graph doesn't pass the vertical line test. Example: (0, -2) and (0, 2).

The number that is six less than the product of three and the difference of the number and eight is; 15

The verbal expression of the equation in the word problem is presented in mathematical form as follows;

Expanding the left hand side gives;

3•x - 3×8 = x + 6

3•x - 24 = x + 6

3•x - x = 24 + 6 = 30

2•x = 30

x = 30/2 = 15

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The money James needs to invest as his principal in order to achieve this goal is $ 5, 197. 67

The formula for simple interest is expressed as;

Simple Interest, I = PRT/100

Where:

Substitute the values

8388 = P × 7. 34 × 22/ 100

cross multiply

161. 48 P = 838800

Make 'P' the subject of formula

P = 838800/ 161. 38

Divide through

P = $ 5, 197. 67

Thus, the money James needs to invest as his principal in order to achieve this goal is $ 5, 197. 67

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The last year's salary is found as 33078.43.

Divide the value by the total value as well as multiply the result by 100 to get the percentage. (amount/total amount), the formula for determining the percentage is 100%.

A percentage is defined as a portion of the whole expressed in the form of 100. There are two ways to calculate a percentage:

As per the given question;

The salary for the current year is given as  37,740.

There is the increase in 2%.

Let the last year's salary be x.

Then 2% of x will be;

x + 2%of x = 37,740

x + 2x/100 = 37,740

x + 0.02x = 37,740

1.02x = 37,740

x =  37,740/1.02

x = 33500

Therefore, the value of last year's salary is was 33,500.

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Answer:

  zero real solutions

Step-by-step explanation:

You want the number of real roots of 3x² -5x +4 = 0 and determined by using the discriminant.

The discriminant of a quadratic equation ax²+bx+c=0 is ...

  d = b² -4ac

When d < 0, both roots are complex. When d = 0, there is one (repeated) real root. The number of real solutions is 2 when d > 0.

For this equation, a=3, b=-5, c=4, so the discriminant is ...

  d = b² -4ac = (-5)² -4(3)(4) = 25 -48 = -23

This means both roots are complex. There are no real solutions.

__

Additional comment

As confirmation, we can look at the graph. It does not cross the x-axis, so there are no (real) values of x that make the value of the quadratic be zero.

The function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600

The given parameters are

Fixed cost = 16600

Variable cost = 67 per toilet

Cost of toilet = 157 per toilet

Let the number of toilets be x

So, the cost function is

C(x) = Fixed cost + Variable cost * Number of toilets

This gives

C(x) = 16600 + 67x

Also, we have the revenue function to be

R(x) = Cost of toilet  * Number of toilets

This gives

R(x) = 157x

The function P(x) for the total profit from the production and sale of x toilets is

P(x) = R(x) - C(x)

So, we have

P(x) = 157x - 16600 - 67x

Evaluate

P(x) = 90x - 16600

Hence, the function P(x) for the total profit from the production and sale of x toilets is P(x) = 90x - 16600

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Using translation concepts, the coordinates of the vertices after a rotation 180º clockwise around the origin is:

S': (-4,-10), R'(-4,-3), U'(-8,-3) and T'(-8,-10).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the coordinates (x,y) of the vertices are given as follows:

S(4,10), R(4,3), U(8,3), T(8,10).

The rule for a rotation 180º clockwise around the origin is:

(x,y) -> (-x,-y).

Hence the vertices of the rotated image will be given as follows, applying the above rule:

S': (-4,-10), R'(-4,-3), U'(-8,-3) and T'(-8,-10).

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Answer:

Step-by-step explanation

it is true

Answer: 58 sq ft

Step-by-step explanation:

2 * 2 = 4

9 * 6 = 54

54+4=58

[tex]s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} [/tex]

The shaded region represents 1.5 grids

[tex]1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} [/tex]

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

The product or overall change in time for 8 weeks will be 29.33 minutes.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

After one week, Greg's watch has lost 11/3 minutes. If the watch continues to lose time at the same rate, we can say that the change in time is 11/3 minutes per week.

According to given question we have

(11/3 minutes/week) x (8 weeks) = 29.33 minutes

Therefore, the product or overall change in time for 8 weeks will be 29.33 minutes.

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