need help asap ..! please and thank you

Hey there!

-7x + 21 > -14

SUBTRACT 21 to BOTH SIDES

-7x + 21 - 21 > -14 - 21

SIMPLIFY IT!

NEW EQUATION: -7x > -35

DIVIDE -7 to BOTH SIDES

-7x/-7 > -35/-7

SIMPLIFY IT!

x < 5

Therefore, your answer is: x < 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Isolate the term of x from one side of the equation.

First, subtract by 21 from both sides.

-7x+21-21>-14-21

Solve.

Add or subtract the numbers from left to right.

-14-21=-35

Rewrite the problem down.

-7x>-35

Then, multiply by -1 from both sides.

\(\sf{\left(-7x\right)\left(-1\right) < \left(-35\right)\left(-1\right)}\)

Solve.

7x<35

Divide by 7 from both sides.

7x/7<35/7

Solve.

Divide the numbers from left to right.

35/7=5

x<5

I hope this helps! Let me know if you have any questions.

The minimum number of cards which must be drawn to get atleast 3 cards of aces is 4.

According to the given question.

We have a deck of cards.

As, we know that

The total numbers of cards in a deck = 52

Since, we have to find the minimum number of cards to be drawn so that we will get atleast 3 cards of aces.

As they have used atleast in the question so the cards can be more also so we have to reach at minimum number of cards to be drawn to guarantee atleast 3 cards of aces.

Number of suits in a  standard deck= 4 (Clubs, Hearts, Diamond,  Spades)

Number of aces in a suit = 1

We need atleast three cards of aces. Which means that we have 4*1 =4 cards from each suit.

Thereofre, the minimum number of cards which must be drawn to get atleast 3 cards of aces is 4.

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Answer:

Step-by-step explanation:

jjj

Answer:

1244

Step-by-step explanation:

real answer is 1244.07

Answer: 1244.07 cubic meters

Step-by-step explanation:

Diameter x height

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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The height at which the air pressure equals 65% of the air pressure at the surface of the earth is -ln(0.65P0)/0.0012 meters.

An equation is a mathematical statement that shows the equality of two expressions. It can be written in a variety of forms, including an equation with an equals sign, an inequality with a greater than or less than sign, or a system of equations with multiple variables. Equations can be used to solve problems, model real-world scenarios, and explore relationships between different quantities.

To solve this problem, we can rearrange the equation to find the height h, given the pressure P. The rearranged equation is h=-ln(P/P0)/0.0012. Substituting 65% of the surface pressure for P, we get h=-ln(0.65P0)/0.0012. Therefore, the height at which the air pressure equals 65% of the air pressure at the surface of the earth is -ln(0.65P0)/0.0012 meters.
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(a) the height of the ball when it is launched is 5 feet.

(b) the ball hits the ground at approximately t = 4.32 seconds.

(c)the height of the ball is 20 feet at approximately t = 1.04 seconds and t = 3.46 seconds.

(d)the maximum height of the ball is approximately 31.88 feet.

a) When the ball is launched (at t = 0), we can find the height by substituting t = 0 into the equation h(t) = -16t^2 + 40t + 5.

h(0) = -16(0)^2 + 40(0) + 5 = 5

Therefore, the height of the ball when it is launched is 5 feet.

b) To determine when the ball hits the ground, we need to find the value of t when the height h(t) is equal to 0.

-16t^2 + 40t + 5 = 0

We can use a graphing calculator to find the roots or solve the quadratic equation using the quadratic formula.

Using the quadratic formula, t = (-b ± √(b^2 - 4ac)) / (2a), where a = -16, b = 40, and c = 5, we can calculate the values of t.

t = (-40 ± √(40^2 - 4(-16)(5))) / (2(-16))

t = (-40 ± √(1600 + 320)) / (-32)

t = (-40 ± √(1920)) / (-32)

t ≈ 4.32 or t ≈ 0.18

Since time cannot be negative, we discard the negative value.

Therefore, the ball hits the ground at approximately t = 4.32 seconds.

c) To find when the height of the ball is 20 feet, we set h(t) = 20 and solve for t.

-16t^2 + 40t + 5 = 20

-16t^2 + 40t - 15 = 0

Using the quadratic formula, we can solve for t.

t = (-40 ± √(40^2 - 4(-16)(-15))) / (2(-16))

t = (-40 ± √(1600 + 960)) / (-32)

t = (-40 ± √(2560)) / (-32)

t ≈ 1.04 or t ≈ 3.46

Therefore, the height of the ball is 20 feet at approximately t = 1.04 seconds and t = 3.46 seconds.

d) The maximum height of the ball can be determined by finding the vertex of the parabolic equation. The vertex form of a quadratic equation is given by h(t) = a(t - h)^2 + k, where (h, k) represents the coordinates of the vertex.

In this case, a = -16. To find the vertex, we use the formula h = -b / (2a) and substitute the values.

h = -40 / (2(-16))

h ≈ 1.25

To find the maximum height, we substitute t = 1.25 into the equation.

h(1.25) = -16(1.25)^2 + 40(1.25) + 5

h(1.25) ≈ 31.88

Therefore, the maximum height of the ball is approximately 31.88 feet.

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The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 can be found through the following.

Recognize that the logarithm function is increasing.

Minimize the argument of the logarithm, i.e., (x - 5)² + 3.

Observe that (x - 5)² is always non-negative since it is a square of a real number.

The minimum value of (x - 5)² occurs when x = 5 (in this case, (x - 5)² = 0).

However, x cannot be equal to 5 because the interval is -5 < x < 5.

Since the interval is open, find the minimum value for (x - 5)² in this interval, which occurs when x is as close to 5 as possible within the given interval. This would be x = 4.999.

Substitute this value of x into the function:

h(x) = log[(4.999 - 5)² + 3] = log[0.001² + 3] ≈ log[3.000001].

Hence, the minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

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Answer:

109 - -37 = 146

Step-by-step explanation:

Answer:

146

Step-by-step explanation:

Answer:

x = 1 y = 6

Step-by-step explanation:

x + 2y = 13

-x + y = 5

3y = 18

y = 6

-x + 6 = 5

-x = -1

x = 1

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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The ratio of 30% to 60% she should mix is; 3:2

From the task content;

Let the volume of 30% sulphuric acid

solution and 60% sulphuric acid solution to be mixed be x and y respectively.

Hence, it follows that;

By solving simultaneously, it follows that;

Therefore, Ratio x/y = 6/4 = 3/2

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The simplest terms of the expression given above would be = -7/8

The simplest terms of a given expression is defined as the reduced form of the expression after carrying out the necessary calculations.

The given term:

-10(9v-2v+7)-10v

Open the brackets by multiplying through with -10;

= -90v + 20v -70 -10v

Bring the like terms together;

= -90v + 20v -10v -70

= -80v -70

80v = -70

V = -70/80

V = -7/8

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Answer:

k, m,  m mm

Step-by-step explanation:

1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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1) Looking at the first table, we can see that this is a proportional relationship given by y=8.5x

So Anna charges:

Number of hours (x) | Amount (y)

1 8.5

2 17

5 42.5

8 68

11 93.5

a) The expression for her earnings in 11 hours:

y=8.5(11) ⇒ y = 68

$68

b) She'll earn $29.75. We can get it by plugging into that formula.

3 1/2 = 3.5

y= 8.5(3.5)

y=29.75

$29.75

c) To know how long, we plug 51 for y. Since x is for hours.

y=8.5x

51=8.5x Divide both sides by 8.5

x=6

She'll take 6 hours to get $51.00 working as a baby sitter.

Answer: 1110

Step-by-step explanation:

Answer:

1,110

Step-by-step explanation:

1. Multiply to the powers(?)

10 x 10 x 10 = 1000

10 x 10 = 100

10 = 10

2. Add

1000 + 100 + 10 = 1110

The dimensions of the picture size to fit in the frame are 14 inches by 11 inches.

It is known the frame is 17 inches tall but this includes 1.5 inches of the wooden frame. This means that 3 inches of the frame (1.5 inches x 2) do not count for the size of the picture.

We already know the picture can be 14 inches tall and the total area is 238 square inches including the 1.5 wooden frame.

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Answer:

The last year value of the house will be $230,000.

Step-by-step explanation:

GIVEN: Decrease in house price = 20%

            Current house price = $184,000

TO FIND: Value of the house last year

SOLUTION:

If the value of the house decreased by 20% during last year, this means the value of the house this year is 80% of last year's value.

Let the value of the house last year be 'x'.

If the value of the house today is  $184,000, then:

                           \(80/100 * x = 184,000\\\\0.8x = 184,000\\\\x = 184,000/0.8\\\\x = 230,000\)

Therefore, the last year value of the house will be $230,000.

Sets (a) and (d) are equivalent, while sets (b) and (c) are not equivalent.

a. {12,10,25} and {10,25,12}:

These sets are equivalent because the order of elements does not matter in a set. Both sets contain the same elements: 12, 10, and 25.

b. {10,12,15} and {12,15,20}:

These sets are not equivalent because they have different elements. The first set includes 10, 12, and 15, while the second set includes 12, 15, and 20. They do not have the same elements.

c. {20,30,25} and {20,30,35}:

These sets are not equivalent because they have different elements. The first set includes 20, 30, and 25, while the second set includes 20, 30, and 35. They do not have the same elements.

d. {10,15,20} and {15,20,25}:

These sets are equivalent because they contain the same elements, though in different orders. Both sets include 10, 15, and 20.

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Answer:

a = 4 b = 2 c = 6

Step-by-step explanation:

4 + b = c

b & c are any even numbers between 2 and 9 (2, 4, 6, 8)

c > 4 ( 6, 8)

b < 6 (2, 4)

b can't be the same number, so b is 4 meaning c is 6

Answer:

b=2, c=6

Step-by-step explanation:

If Carmen paid a total of $49.50 for 3 CD's, then the price of each CD before the tax is $15.80.

The "Sales-Tax" is $0.70 per CD, which is added to the original price of each CD to arrive at the total cost of the CDs including sales tax

Let the price of each CD before tax be = "x",

Carmen bought 3 CDs, so the total cost of the CDs without tax would be 3x.

The "Sales-Tax" on each CD is $0.70, and Carmen bought 3 CDs,

The "total-sales" tax will be = 3 × $0.70 = $2.10,

So, the "total-cost" of the CDs including sales tax is "3x + $2.10", and

We know this total cost is = $49.50,

The equation to represent the cost is written as :

⇒ 3x + $2.10 = $49.50

Now, Solving for "x", the price of each CD before tax.

⇒ 3x = $49.50 - $2.10

⇒ 3x = $47.40

⇒ x = ($47.40)/3,

⇒ x ≈ $15.80

Therefore, the price of each CD is $15.80.

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Answer:

I'm sorry but which ones are the x, y, and z, like (x, z, y)?

Step-by-step explanation:

By the way I promise you respond back and answer just making sure I know which variables are what so I can answer with the correct answer.

The function f(x) - g(x) is an illustration of a composite function

Leanne's end result of f(x) - g(x) = -1/2x + 9 is correct

The functions are given as:

f(x) = 1/2x + 6

g(x) = x - 3

The function f(x) - g(x) is calculated using:

f(x) - g(x) = 1/2x + 6 - x + 3

Collect like terms

f(x) - g(x) = 1/2x - x + 6  + 3

Evaluate the like terms

f(x) - g(x) = -1/2x + 9

By comparing the above solution to the students' response, we can see that:

Leanne's end result of f(x) - g(x) = -1/2x + 9 is correct

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The transformation from f(x) = -7|x| + 7 to  g(x) =  7|x|- 7 is-

The graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)

What is rotation?

The mathematical transformation which turns a geometrical figure about a fixed point is called rotation. The fixed point is called center of rotation.

f(x)= –7|x|+7

g(x) =  7|x|- 7

At first the graph of f(x) has been moved 14 units down. Then it is rotated upwards to get the graph of g(x)

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