Denise is going to shop with the $250.00 that she earned from doing chores. She wants to save
20% of her money to put into a savings account. She buys a pair of jeans for $75.00 and a new
leather coat for $110.00, with 5% sales tax on both items. Does Denise still have the amount of
money she planned to put into her savings account?

Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation

v = √(16d)

a wave forms in water with a depth of 300 feet,

therefore d = 300 ft

so, we get,

velocity = √(16*300)

             = 4√300

             =4*17.32

             =69.28

Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

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Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer:

486 square feet

Step-by-step explanation:

To calculate the area of the path, first find the dimensions of the garden, including the path. Then find the area of this larger outer rectangle and subtract the area of the inner rectangle (the garden without the path).

The garden measures 28ft by 47ft.

The path is 3ft wide, so it adds a total of 6ft to the length (3ft on each side) and 6ft to the width.

The dimensions of the garden, including the path:

Length: 47ft + 6ft = 53ft

Width: 28ft + 6ft = 34ft

Find the area of the outer rectangle (including the path):

Area_outer = Length * Width = 53ft * 34ft = 1802 sq ft

Find the area of the inner rectangle (the garden without the path):

Area_inner = 28ft * 47ft = 1316 sq ft

Now subtract the area of the inner rectangle from the area of the outer rectangle to find the area of just the path:

Area_path = Area_outer - Area_inner = 1802 sq ft - 1316 sq ft = 486 sq ft

So, the area of the path is 486 square feet.

Answer: 486 square feet;

Step-by-step explanation:

Area of the garden = 28 x 47 = 1316ft.²

-

Length of the garden and path = Length of the garden + 3 ft. on both sides

Length of the garden and path = 28 + 3 + 3 = 34 ft.

-

Width of the garden and path = Width of the garden + 3 ft. on both sides

Width of the garden and path = 47 + 3 + 3 = 53ft.

-

Area of the garden and path = Length x Width

Area of the garden and path = 34 x 53 = 1802 ft²  

-

Area of the path = Area of the garden and path - Area of the garden

Area of the path = 1802 - 1316 =  486ft²

-

Answer: 486ft²

Answer:

2

Step-by-step explanation:

(3/4)/(9/2)=1/6 tank of gas used every hour.

1/6*12=2 tanks of gas used in 12 hours.

By using the unitary method we will get 2 tanks of gas will anna use after 12 hours.

The unitary method is a method of determining the value of a single unit and based on that value you can find the value for the number of units you need.

Let the volume of the tank of gas  be x units

Volume of the tank of gas  uses for  9/2 hours = 3/4 of total volume

                                                         = 3/4 x

Volume of the tank of gas uses after 1 hour = 3/4 x ÷ 9/2

                                                                         = 3/4 x × 2/9

                                                                          = x/6

Volume of the tank of gas uses after 12 hours =x/6  x× 12 = 2x

Here, 2x  shows that 2 tanks of gas will anna use after 12 hours.

Therefore , 2 tanks of gas will be used by anna.

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Answer:

13/2 or 6 1/5 or 6.5

Step-by-step explanation:

\(\frac{7+6}{2}\)x 1

13/2 x 1

6.5x1

The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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The third ordered pair positive integers that satisfies the equation is (123, 369).

The given parameters;

The third ordered pair of the equation can be determined by using general equation of a circle;

\(a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}\)

The radius of the circle is calculated as;

\(r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96\)

The value of a can be obtained by randomly choosing numbers less than the radius as values of b.

\(b < r\\\\b < 388.96\)

\(a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)\)

Thus, the third ordered pair positive integers that satisfies the equation is (123, 369).

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The base 10 representation of the number 142 base 5 as required to be determined in the task content is; 47.

Since, the conversion of numbers from any base to base 10 requires imaginary exponents to represent place value in such number as follows;

142₅ can therefore be written as follows; 1²4¹2⁰₅.

On this note the evaluation is carried out by summing the product of each digits and 5 to the corresponding power as follows;

1²4¹2⁰₅ = (2 × 5⁰) + (4 × 5¹) + (1 × 5²)

= (2 × 1) + (4 × 5) + (1 × 25)

= 2 + 20 + 25.

= 45.

Ultimately, the base 10 representation of the number 142 base 5 as required to be determined in the task content is; 47.

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Answer: a=mx+b

Step-by-step explanation:

Answer: -1 Is the answer.

Answer:

D

Step-by-step explanation:

21,871 x 0.96 = 20,996

Answer:

x = 5

Step-by-step explanation:

5 x 5 = 25

25 - 7 = 18

Answer:

Use the given functions to set up and simplify  

f

e

e

t

=

f

e

2

t

A

⋅

81

=

81

A

B

⋅

100

=

100

B

C

⋅

120

=

120

C

Step-by-step explanation:

Answer:

1/3, 1/2, .52, 55%

Step-by-step explanation:

Let:

• t, be the time that the colony has spent growing (in days)

• f(t) ,the number of bacteria after ,t, days

The function that describes the situation is:

For t = 20,

You would have 9720 bacteria.

Consequently, there are 5 elements in A B'.

Given the following definitions:

U = {1, 2, 3, 4, 5, 6, 7}A = {1, 2, 4, 5}B = {1, 3, 5, 7}

The complement of a set B is the set of all elements that belong to the universal set U but not to B.

A’ = {x | x ∈ U and x ∉ A} = {3, 6, 7}B’ = {x | x ∈ U and x ∉ B} = {2, 4, 6}

The union of sets A and B is the set of all elements that belong to set A or set B, or both.

A ∪ B = {x | x ∈ A or x ∈ B}

= {1, 2, 3, 4, 5, 7}A ∪ B'

= {x | x ∈ A or x ∈ B’}

= {1, 2, 4, 5, 6}

Therefore, the number of elements in A ∪ B' is 5.

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Answer:

x=4

Step-by-step explanation:

5+2x=13

-5 on both sides

2x=8

÷2 on both sides

x=4

Hope this helps :)

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

Given: (x+3)^2

Expand the given

(x+3)^2 → (x+3)(x+3)

Do the FOIL method

(x+3)(x+3)

= (x)(x) + (3)(x) + (3)(x) + (3)(3)

Simplify

= x^2 + 3x + 3x + 9

= x^2 + 6x + 9

Therefore, (x+3)^2 is equal to x^2 + 6x + 9

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

\(\hrulefill\)

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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We need to find the y-intercept of the equation.

For this, we need to use the slope-intercept form:

Where m represents the slope and b the y-intercept.

Now, to get the form, we need to solve the equation for y:

Then:

Solving for y:

Add both sides 5x:

Divide both sides by 3

We can rewrite the expression as:

Where 5/3x represents the slope and 10 represents the y-intercept.

The y-intercept represents when the graph of the equations intersects with the y-axis, therefore, it can be written as the ordered pair (0,10).

Answer:

5(x + 2)

Step-by-step explanation:

5x + 10 ← factor out 5 from each term

= 5(x + 2)

Answer:

a circle

Step-by-step explanation: