Solve the inequality 4x - 6 > 6x - 20


A.) x > 7

B.) x < 7

C.) x < 2

D.) x > 2

Nadia gave Pete 11 postcards to balance the numbers as described. This means Pete ended up with 2 more postcards than Nadia after the exchange.

To find out how many postcards Nadia gave to Pete, let's set up some equations based on the information given.

First, let's define the number of postcards Pete has as P.

Since Nadia has 20 more postcards than Pete, we know:

N = P + 20

Now, let's define the number of postcards Nadia gives to Pete as x.

After Nadia gives x postcards to Pete, Nadia will have N - x postcards and Pete will have P + x postcards.

According to the problem, after the exchange, Pete has 2 more postcards than Nadia: P + x = (N - x) + 2

Substitute the first equation (N = P + 20) into the second equation: P + x = ((P + 20) - x) + 2

Simplify the equation:

P + x = P + 20 - x + 2

P + x = P + 22 - x

Now, isolate x on one side of the equation by subtracting P from both sides:

x + x = 22

2x = 22

Divide both sides by 2: x = 11

Answer:

X=3

Step-by-step explanation:

We have two linear functions which intersect at a point. This point is shown in the attached graph. Linear functions are lines which are made of points that satisfy the function or relationship.  This means at the intersection, this point (3,-1), both functions have the same values. An input of x=3 produces y=-1 in both functions.

Final answer:

To find the input value that yields the same output for both functions f(x) = -2/3x + 1 and g(x) = 1/3x - 2, we set the functions equal, combine like terms, and solve for x, getting the result x = 3.

Explanation:

The question asks which input value produces the same output value for the two functions f(x) = -2/3x + 1 and g(x) = 1/3x - 2. To find this value, we need to set the two functions equal to each other and solve for x.

Here are the steps to find the input value:

Set f(x) equal to g(x):
  -2/3x + 1 = 1/3x - 2

Combine like terms:
  -2/3x - 1/3x = -2 - 1

Combine the x coefficients on the left side and constants on the right side:
  -1x = -3

Divide both sides by -1 to solve for x:
  x = 3

Therefore, the input value that produces the same output value for both functions is x = 3.

Answer: 8

Step-by-step explanation:

2/3 divided by 1/12

2/3 * 12/1

24/3=8

hope i helped angel!

Answer:

I think it would be 8

Step-by-step explanation:

Divide 2/3 by 1/12.

(2/3) / (1/12) = 2/3 * 12/1 = 24/3 = 8

Answer:

461 adults and 864 students

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 1,325 tickets were purchased, then s+a=1325.

We also know that a total of $3,169 was collected and adult tickets cost $5 each and students cost $1 each. We can write 1s+5a=3169.

We will solve by substituting one equation into the other. We first solve the first equation for s which is s=1325-a. Substitute s=1325-a into 1s+5a=3169. Simplify and isolate the variable a.

1(1325-a)+5a=3169

1325-a+5a=3169

1325+4a=3169

1325-1325+4a=3169-1325

4a=1844

a=461

This means that 461 adults attended and 864 students attended since 864+461=1325.

Answer:

The function [tex]p(x) = 0.1x+1[/tex] ,   where  x is the depth in meters.

Step-by-step explanation:

As per the statement: The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases.

Then, we have the two points i,e (0, 1) and (23, 3.3).

An equation of the line is in the form of y=mx+b where m is the slope or rate of the line and b is the y-intercept.

Let x represents the depth in meters and p(x)= y represents the pressure in atmosphere.

Calculate slope of the line:

Slope of line(m) is given by:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given point we have;

[tex]m = \frac{3.3-1}{23-0} = \frac{2.3}{23} = 0.1[/tex]

Then, our equation of line become:

y = 0.1x + b                           .....[1]

To solve for b;

Substitute the point (0, 1)  in [1];

[tex]1 = 0.1(0)+b[/tex]

[tex]1 = b[/tex]

Our equation for this line become: y = 0.1x +1

Now, we write this for x as a function of p,

i.e, p(x) = 0.1x + 1

Then, the function formula become;

[tex]p(x) = 0.1x+1[/tex] where x is the depth in meters.

Answer: Option 'B' is correct.

Step-by-step explanation:

since we have given that

Group radii of fertilized tomatoes is given by

[tex]0.8, 1.1, 0.9, 0.8, 1.0, 1.2, 0.9, 1.1, 1.0, 1.2[/tex]

Group radii of unfertilized tomatoes is given by

[tex]1.4, 1.6, 1.3, 1.5, 1.1, 1.5, 1.6, 1.2[/tex]

So, we will first find the mean of both the group i.e.

Mean radii of fertilized tomatoes is given by

[tex]=\frac{0.8+1.1+0.9+0.8+1.0+1.2+0.9+1.1+1.0+1.2}{10}\\\\=1[/tex]

Similarly,

Mean radii of unfertilized tomatoes is given by

[tex]\frac{1.4+1.6+1.3+1.5+1.1+1.5+1.6+1.2}{8}\\\\=\frac{11.2}{8}\\\\=1.4[/tex]

So, the difference between the mean radii of fertilized and unfertilized tomatoes will be

[tex]1.4-1=0.4\ cm[/tex]

Hence, Option 'B' is correct.

Answer:

value of y is 2√2

C is the correct option.

Step-by-step explanation:

We can use Pythagoras theorem to find the value of y.

In triangle ABC, using Pythagoras theorem

BC² = AB² + AC²

(8+1)² = 3² + z²

9² = 9 + z²

z² = 81-9

z² = 72

Now, apply Pythagoras theorem in triangle ADC

AC² = AD² + DC²

z² = y² + 8²

Plugging the value of z

72 = y² +64

y² = 72 -64

y² = 8

y = 2√2

Therefore, value of y is 2√2

C is the correct option.

Answer:

[tex]\dfrac{3}{5}[/tex] of the height makes up the height.

Step-by-step explanation:

The length of an aquarium, which has the form of a rectangular solid, is [tex]5\ dm[/tex]

The width is [tex]\dfrac{4}{5}[/tex] of the length, so teh width is,

[tex]=5\times \dfrac{4}{5}=4\ dm[/tex]

Let us assume the height is 'h' dm.

So the volume will be,

[tex]=\text{Length }\cdot \text{ Width }\cdot\text{ Height}[/tex]

[tex]=5\times 4\times h[/tex]

[tex]=20h\ dm^3[/tex]

As 1 liter of water occupies volume of  1 dm³, so volume of 40 liters of water will be,

[tex]=40\times 1=40\ dm^3[/tex]

This [tex]40\ dm^3[/tex] is the [tex]\dfrac{2}{3}[/tex]th of total volume.

Hence total volume will be,

[tex]=\dfrac{40}{\frac{2}{3}}=40\times \dfrac{3}{2}=60\ dm^3[/tex]

Therefore,

[tex]\Rightarrow 20h=60[/tex]

[tex]\Rightarrow h=3\ dm[/tex]

So the part of length makes up to the height will be,

[tex]=\dfrac{3}{5}[/tex]

Answer:

2(x + 3)^2 - 22

Step-by-step explanation:

2x^2 + 12x - 4

Start by making your "a" value equal to 1 by factoring the 2 from the first 2 terms in the standard form equation.

2(x^2 + 6x) - 4

Complete the square by using the formula (b/2)^2. Identify your "b" value, which is 6. Now you can complete the square.

((6)/2)^2 = 9

After completing the square, add 9 inside the parentheses and subtract 9 outside the parentheses. Since the 9 inside the parentheses is also being multiplied by 2, multiply the subtracted 9 by 2 as well.

2(x^2 + 6x + 9) - 4 - 9(2)

Factor the terms inside the parentheses by using the product/sum factoring method. This is where you find two of the same terms that multiply to "c" (9) and add to "b" (6).

In this case, positive 3 multiplies to 9 and adds to 6, so we will use the factors (x + 3)(x + 3), which is the same as (x + 3)^2.

2(x + 3)^2 - 4 - 9(2)

To finish off the problem, combine the like terms outside of the parentheses by multiplying 9 times 2 first and then subtracting -4 by 9(2).

[tex]\boxed{2(x + 3)^2 - 22 }[/tex]

The system that models the situation relates to the weights of peanuts and almond mixture.

The solution to the system can be determined by substituting the values of peanuts and mixture into the equations and checking if they hold true.

(a) The system that models this situation is:

p + m = 5

0.6p + 0.2m = 5 * 0.6

(b) To determine if a solution is valid, we need to substitute the values of p and m into the equations and check if the equations are true. For the solution 2 lb peanuts and 3 lb mixture:

p + m = 5

2 + 3 = 5 (true)

0.6p + 0.2m = 5 * 0.6

0.6(2) + 0.2(3) = 3 (true)

Therefore, 2 lb peanuts and 3 lb mixture is a valid solution.

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Answer:

Step-by-step explanation: answer should be 360

Answer: 990

Step-by-step explanation:

10: 2 * 5

22: 2 * 11

99: 3 * 3 * 11

GCF: 1

LCM: 2 * 5 * 11 * 3 * 3

     = 990

The Least Common Multiple (LCM) of the numbers 10, 22, and 99 is found by prime factorization and taking the highest power of all prime factors that appear, which results in an LCM of 990.

To find the Least Common Multiple (LCM) of the numbers 10, 22, and 99, we need to prime factorize each number and then take the highest power of all the prime factors that appear.

Prime factorization of 10 = 2 x 5

Prime factorization of 22 = 2 x 11

Prime factorization of 99 = 32 x 11

Now, identify the highest powers of all prime factors, which are 2, 32, 5, and 11. Then, multiply these together:

LCM = 2 x 32 x 5 x 11 = 2 x 9 x 5 x 11 = 990

Therefore, the LCM of 10, 22, and 99 is 990.

If the manager buys 2 or more chairs then he saves 31.99 dollars on each chair.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A manager needs to buy chairs for his office the price for 1 chair is 79.99 dollars.

If the manager buys 2 or more chairs then he get's a 40% discount on each chair.

Therefore, He saves 40% of the original cost of 1 chair which is,

= (40/100)×79.99.

= 31.99 dollars.

So, The manager saves 31.99 dollars on each chair if he buys 2 or more at a time.

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Three-point Turns

Three-point turns are typically used to reverse direction on narrow, two-lane roads. They are tricky due to the narrowness of the road and the fact that your car completely blocks all traffic flow during part of the procedure.

Two-point turns (left side)*

If we’re going to get technical, then I must put a qualifier to these types of turns. Many driver’s ed professionals call these two-point turns and I have to agree albeit with an asterisk. Most professionals reserve three point turns for those turns which reverse direction on narrow streets without the aid of a side street. Therefore, any turn that reverses direction with the aid of a side street would be a two-point turn.

Step-by-step explanation:

We are told that the music club is having a bake sale as a fundraiser. They sell x brownies at $5 each and y cookies at $8 each. They will sell at least 26 brownies and 15 cookies.

We can represent this information as:

[tex]x\geq 26[/tex]

[tex]y\geq 15[/tex]

They need to make at least $250. We can represent this information as:

[tex]5x+8y\geq 250[/tex]

Therefore, our system of inequalities will be:

[tex]x\geq 26[/tex]

[tex]y\geq 15[/tex]

[tex]5x+8y\geq 250[/tex].

The equation [tex]\(14,000 = 8 \cdot 2^{x+y}\)[/tex] correctly represents the area of the wildfire in terms of x and y (option C).

How to find the correct equation for the area in terms of x and y?

The initial size of the wildfire is 8 square feet.

It doubles its width every x hours, so the width grows by a factor of [tex]\(2^{\frac{1}{x}}\)[/tex] each hour.

It doubles its length every y hours, so the length grows by a factor of [tex]\(2^{\frac{1}{y}}\)[/tex] each hour.

The area (A) of a rectangle is given by the formula [tex](A = \text{length} \times \text{width}\))[/tex].

So, after a period of time, the area of the wildfire is given by:

[tex]A = 8 \times 2^{\frac{1}{x}} \times 2^{\frac{1}{y}}[/tex]

Combine the exponents:

[tex]A = 8 \times 2^{\frac{1}{x} + \frac{1}{y}}[/tex]

Now, if the area is 14,000 square feet, we can set up the equation:

[tex]14,000 = 8 \times 2^{\frac{1}{x} + \frac{1}{y}}[/tex]

To make it match one of the given options, we can express 8 as 2³:

[tex]\[ 14,000 = 2^3 \times 2^{\frac{1}{x} + \frac{1}{y}} \][/tex]

Combine the exponents again:

[tex]\[ 14,000 = 2^{3 + \frac{1}{x} + \frac{1}{y}} \][/tex]

So, the correct equation that represents the area of the wildfire in terms of x and y is:

[tex]\[ 14,000 = 8 \times 2^{x+y} \][/tex]

Therefore, option C. [tex]\(14,000 = 8 \cdot 2^{x+y}\)[/tex] is the correct representation.

Answer:

$18.15

Step-by-step explanation:

We have been given that in Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at \$220$220 before tax.

To find total sales tax paid by Yuki for her handbag purchase we will find 4.6% of $220 and 3.65% of $220 and add amount of both taxes.  

[tex]\text{Total sales tax amount}=\text{State sales tax amount+ County sales tax amount}[/tex]

[tex]\text{States sales tax amount for handbag}=\frac{4.6}{100}*220[/tex]

[tex]\text{States sales tax amount for handbag}=0.046*220[/tex]

[tex]\text{States sales tax amount for handbag}=10.12[/tex]

Now let us find county sales tax for handbag purchase.

[tex]\text{County sales tax amount for handbag}=\frac{3.65}{100}*220[/tex]

[tex]\text{County sales tax amount for handbag}=0.0365*220[/tex]

[tex]\text{County sales tax amount for handbag}=8.03[/tex]

Now let us add both amount to get total tax paid by Yuki.

[tex]\text{Total sales tax}=10.12+8.03[/tex]

[tex]\text{Total sales tax}=18.15[/tex]

Therefore, Yuki paid $18.15 sales tax for her handbag purchase.    

Answer: 12x^2 - 13x - 14

Choice D

==========================================

Work Shown:

Let y = (3x+2)

Replace (3x+2) with y and we go from (3x+2)(4x-7) to y(4x-7)

Distribute this y through: y(4x-7) = 4xy - 7y

--------------

Now replace y with (3x+2), distribute again, and simplify

4xy - 7y

4x(3x+2) - 7(3x+2)

4x(3x)+4x(2) - 7(3x) - 7(2)

12x^2 + 8x - 21x - 14

12x^2 - 13x - 14

Answer:

Alternative D

Step-by-step explanation:

(3x + 2)(4x - 7)

12x² - 21x + 8x - 14

12x² - 13x - 14

I hope I helped you.

Answer:

He did not calculate correctly.

Answer:

$450.40

Step-by-step explanation:

well 5630 times .04 = 225.2 times it by 2 = 450.40

Answer:

The interest earned is $450.40

Step-by-step explanation:

We are given the formula

I =PRT

where I is the interest, p is the principal, r is the rate and t is the time

p = 5630,

r = 4 % which we convert to a decimal = .04

t = 2 years

Substitute these into the equation

I = 5630 * .04 * 2

450.40

The interest earned is $450.40

Answer:

154 square cm (choice B)

Step-by-step explanation:

The diameter is 14 cm, so the radius is half that at 7 cm. Let r = 7

Use the formula

A = pi*r^2

to find the area of the circle. Let pi = 3.14 be the approximation for pi

So,

A = pi*r^2

A = 3.14*7^2

A = 3.14*49

A = 153.86

A = 154

Answer: B.

Step-by-step explanation:

3.14*r2

3.14*7(2)

153.9

Answer:

x=-1.8

Step-by-step explanation:

When x = 0, we look at the graph and the point (0,5)

The value of the function at x=0 is 5, so we want to find the point (x,0)

Looking around the graph, we find it at (-1.8, 0)

The function f(x) is =0 at x= -1.8

Answer:

A:-1.8

Step-by-step explanation:

how because its me i'm always right

Answer:

the diagonal measurement from corner A to corner B=15 inches

Step-by-step explanation:

as we know that the loptop has the shape of a rectangle that means all it's angles are right angles. so we can use the pythogoras theorem to find out the diagonal of the rectangle.

let us denote the diagonal of rectangle by D and the sides of rectangle be denoted by X=12 and Y=9

so by using pythogoras theorem we have,

[tex]D^{2} =X^{2} +Y^{2}[/tex]

[tex]D^{2}[/tex]=225

D=15

Hence the diagonal measurement from corner A to corner B is 15 inches.

Answer:

The diagonal measures 15 inches

Step-by-step explanation:

The diagonal of the Marcy's rectangular laptop forms a right angle triangle with its width and length.

We can use the Pythagoras Theorem to write the following equation,

[tex]|AB|^2=12^2+9^2[/tex]

This implies that,

[tex]|AB|^2=144+81[/tex]

We simplify the right hand side to obtain,

[tex]|AB|^2=225[/tex]

We take the positive square root of both sides to obtain,

[tex]|AB|=\sqrt{225}[/tex]

[tex]|AB|=15inches[/tex]

Hence the diagonal of Marcy's laptop measures 15 inches.

Sounds like "exponential decay" is the answer your teacher is looking for

Expressions of the form y = a*b^x are considered decay equations or exponential decay equations if 0 < b < 1. So b can be between 0 and 1, but not equal to either endpoint.

Example: y = 3*0.5^x means we start off with 3 as the initial value, and then cut it in half repeatedly as x increases by 1 (eg: x = 0, x = 1, etc). This graph goes downhill as you read it from left to right.

Answer:

A) (-2, 12)

Step-by-step explanation:

Just multiplied the second equation by -1

then eliminated the y

Then solved for x  and you get x = -2

then you plug in x = -2 and figure out y

and you get y = 12

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w - width

3w - 1 - length

54 in - perimeter

w + w + (3w - 1) + (3w - 1) = 8w - 2 - perimeter

The equation:

8w - 2 = 54      add 2 to both sides

8w = 56     divide both sides by 8

w = 7

3w - 1 = 3(7) - 1 = 21 - 1 = 20

The perimeter of the rectangle is twice the sum of the length and the width.The length of the rectangle is 20 inches long.

Given information-

The length of a rectangle is one inch less than three times its width.

The perimeter of the rectangle is 54 inches.

The perimeter of the rectangle is the boundary by which the rectangle is covered. The perimeter of the rectangle is twice the sum of the length and the width.

It can be given as,

[tex]P=2(a+b)[/tex]

Here,[tex]a[/tex] is the length of the rectangle and [tex]b[/tex] is the width of the rectangle.

Now it is given that the length of a rectangle is one inch less than three times its width. Suppose the length of the rectangle is [tex]x[/tex] inches long. Thus the width [tex]y[/tex] of the rectangle is,

[tex]=\dfrac{x+1}{3} =\dfrac{x}{3} +\dfrac{1}{3}[/tex]

Thus the perimeter of the rectangle is,

[tex]\begin{aligned}\\P&=2(x+\dfrac{x}{3}+\dfrac{1}{3} )\\54-\dfrac{2}{3} &=2\times\dfrac{3x+x}{3} \\\dfrac{160}{3} &=\dfrac{8x}{3}\\160&=8x\\x&=20\\\end[/tex]

Hence the length of the rectangle is 20 inches long.

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Answer:

option A) New cars and used cars is correct option.

Step-by-step explanation:

loan Interest rate can be defined as the percentage of a loan paid by borrowers to lenders. For most loans, interest is paid in addition to principal repayment in order to compound over time.

since new cars have  more price than old cars that's why new cars have more greater loan interest than old cars

hence option a is correct

There is generally a significant difference in loan interest rates between new cars and used cars, with new cars usually having lower rates. Institutions regard new cars as less risky than used or refinanced cars, hence, they tend to offer lower interest rates to encourage new car loans.

There is typically a significant difference in loan interest rates between new cars and used cars. This is mainly because new cars tend to have lower interest rates than used cars. Financial institutions, such as banks and credit unions, usually perceive new cars as less risky because they have not been subjected to any wear and tear compared to used cars which could potentially have mechanical issues. Consequently, these institutions lower the interest rates for new car loans to encourage more borrowers.
Whereas, in the case of used cars and refinanced cars, the interest rates are significantly higher due to the increased risk that the lender has to take on.

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