Write this number using digits:
twenty-eight thousand, nine hundred twenty-seven

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.

Answer:

x + 7

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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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Answer:625

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

5^4

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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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:

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 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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[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! :)

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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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:

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]

0.166 is the standard form of that

Answer: 58 sq ft

Step-by-step explanation:

2 * 2 = 4

9 * 6 = 54

54+4=58

Answer:

y = x - 11

Step-by-step explanation:

5y + 22 = 5x - 33

5y = 5x - 33 - 22

5y = 5x - 55

y = x - 11

Answer:

B.

Step-by-step explanation:

233% = 2.33

2 2/3 = 2.6

All work and the answer is provided in the screenshot that is attached! :)

Have a great day!

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

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:

The correct area is 25 square units.

His mistake was that he found the perimeter instead of the area.

Step-by-step explanation:

Area = Length x Width

Area= 5 x 5= 25

His mistake:

Perimeter = length + length + width + width

Perimeter = 5 + 5+ 5+ 5 = 20

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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(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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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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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 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:

This is not proportional.

Step-by-step explanation:

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

The greatest common factor of 38 and 30 is 2.

It should be noted that thw first step to this method of finding the Greatest Common Factor of 30 and 38 is to find and list all the factors of each number.

Let’s take a look at the factors for each of these numbers, 30 and 38:

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Factors of 38: 1, 2, 19, 38

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 30 and 38 would be 2.

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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]

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.

Greater because a meter is greater than a millimeter.

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