How to work this out ?

Answer:

Only options a ,b,d have the same solution as [tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]

Step-by-step explanation:

Given:

An equation:  [tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]    ....[1]

Like terms states that contain the same variables raised to the same power.

Combine like terms on left hand side in equation [1] we get,

[tex]\frac{3}{5}x+x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

[tex]\frac{8}{5}x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

we get option (a) as the same solution.

Using LCM(Least Common ) to change each fraction to make their denominators the same as the least common denominator

Taking LCM both sides in Equation (1) ,

[tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]

As LCM(3,5)=15 and LCM(2,5)=10 we have,

[tex]\frac{9x+10+15x}{15}= \frac{5-2x}{10}[/tex]

On simplifying we get,

[tex]10(9x+10+15x)= 15(5-2x)[/tex]=

Dividing both sides by 5 we get,

[tex]\frac{10(9x+10+15x)}{5} =\frac{15(5-2x)}{5}[/tex]

On simplify:

[tex]2(9x+10+15x)=3(5-2x)[/tex]

∴ [tex]18x+20+30x=15-6x[/tex]

which is same solution as given in option (b).

Now,

Use Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.

Further, using the above property add 6x both sides  in  [tex]18x+20+30x=15-6x[/tex] we get,

[tex]18x+20+30x+6x=15-6x+6x[/tex]

On simplifying we get,

[tex]18x+20+30x+6x=15[/tex]

Subtract 20 from both the sides we get,

[tex]18x+20+30x+6x-20=15-20[/tex]

Simplify:

[tex]18x+30x+6x=-5[/tex]

or, [tex]24x+30x=-5[/tex] which is same solution  as given in option(d)

But, options c and e equation doesn't have same solution as [tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]

To calculate the total value of Eve's stamps, multiply the number of stamps (24) by the value of each stamp ($24.75), resulting in a total value of $594.00.

The question involves calculating the total value of stamps using multiplication. Eve has 24 stamps, each valued at $24.75. To find the total value, we multiply the number of stamps by the value of each stamp.

Here is the calculation:

Therefore, the total value of Eve's stamps is $594.00.

Answer:

The answer is A

Step-by-step explanation:

(the product of one-fourth and a number plus seven)

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is D, the product of one-fourth and a number plus seven.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

2x + 3 is an example of a variable mathematical expression. Every variable must have a coefficient, which is a number multiplied by the variable. The coefficient of x in the formula 2x + 3 is the number 2, and it signifies 2 times x plus 3.

The given algebraic expression 1/4d+7 can be represented as a phrase as the product of one-fourth and a number plus seven.

Hence, the phrase that represents the algebraic expression 1/4d+7 is the product of one-fourth and a number plus seven.

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Note that point-slope equation is: (y - y₁) = m(x - x₁)

Also note that f(x) = y

Isolate the y. Subtract 7 from both sides:

y + 7 = –(x + 6)

y + 7 (-7) = -(x + 6) - 7

y = -(x + 6) - 7

Note that the equation is really: y = -1(x + 6) - 7

Distribute -1 to all terms within the parenthesis

y = -1(x + 6) - 7

y = -x - 6 - 7

Simplify. Combine like terms

y = -x - 13 ; or f(x) = -x - 13, which is none of the above.

Please check and verify your choices.

hope this helps

Answer:

[tex]9.67[/tex] per hour

Step-by-step explanation:

Rate per hour can be calculated by sing following equation,

Rate per hour = Total amount paid / Total number of hours worked

By substituting values to the above equation we can get the  rate per hour,

Rate per hour = [tex]\frac{232}{24}[/tex] per hour

                       = [tex]9.67[/tex] per hour

Step 1: reflected across the line y=x

Step 2: reflected across the x axix

Since all 3 shapes are still the same size and shape:

Because the transformations are both rigid , the pre-image and image are congruent

The sequence of 3 letters "a,b,c" is repeating.

[tex]40=3\cdot13+\boxed{1}[/tex]

So it will be the letter at the 1st position, which is a.

The Answer Is 196

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Answer:

it should be c 14 to the power 2

Step-by-step explanation:

Answer:

It will take 4.5 hours for Naomi and Clair to paint an equal number of square feet

Explanation:

 Let the time in hour it will take for Naomi and Clair to paint an equal number of square feet be t hours.

Naomi paints 16.5 square feet of a mural at a rate of 2 square feet per hour, so after t hours the are painted by Naomi = 16.5 + 2 * t

Clair paints 7.5 square feet of the mural at a rate of 4 square feet per hour, so after t hours the are painted by Clair = 7.5 + 4 * t

We know that after hours the area painted by them are equal, so we have

           16.5 + 2 * t = 7.5 + 4 * t

            2 * t = 16.5 - 7.5 = 9

                t = 4.5 hours.

  So it will take 4.5 hours for Naomi and Clair to paint an equal number of square feet.                          

If Naomi and Clair continue to paint at their current rates, it will take approximately 4.5 more hours for both to have painted an equal amount of the mural.

First, let's calculate how much Naomi and Clair have already painted. Naomi has painted 16.5 square feet and Clair has painted 7.5 square feet. Now, calculate the difference which is 9 square feet.

Every hour, Naomi paints 2 square feet and Clair paints 4 square feet. However, since Clair needs to catch up by 9 square feet, we need to consider the extra square feet Clair paints per hour, which is 2 (4 - 2).

So, to find out how many more hours it will take for them to paint an equal number of 2 square feet, simply divide the difference (9 square feet) by the extra square feet Clair paints per hour (2). So, it would take Clair 4.5 more hours to paint an equal amount of mural to Naomi.

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Answer:

1/6

Step-by-step explanation:

The student's question pertains to calculating fuel economy, which is found by dividing the distance traveled by the amount of fuel used. We find that the first vehicle gets 24 mpg and the second one gets 25.33 mpg. This calculation is useful for comparing vehicle efficiency and managing fuel costs.

The question involves calculating fuel economy, which is a mathematical concept generally taught in high school Algebra or Applied Math classes. Fuel economy is calculated by dividing the distance traveled by the amount of fuel used. For example, for the first vehicle that traveled 96 miles on 4 gallons, the fuel economy is calculated as follows:

Divide the total miles by the gallons used: 96 miles / 4 gallons = 24 miles per gallon (mpg).

Similarly, for the second vehicle that traveled 380 miles on 15 gallons, we calculate fuel economy like this:

Divide the total miles by the gallons used: 380 miles / 15 gallons = 25.33 mpg.

This practice of tracking fuel economy is useful for comparing the efficiency of different vehicles, as shown in the examples of the Toyota Prius and Ford Fusion hybrid. Additionally, knowing your vehicle's fuel economy and the average fuel cost can help you budget for fuel purchases more effectively

Answer:

Reactive power is 1.152 VARs

Step-by-step explanation:

We are given that in a parallel circuit,[tex]E_{T}=240V[/tex],R=47kΩ and [tex]X_{L}[/tex]=50kΩ.

reactive power means the dissipating power resulting from inductive and capacitive loads measured in volt-amperes reactive(VAR).Since our circuit has inductor only, reactive power will be power dissipated from inductor.

Current through inductor=[tex]\frac{E_{T}}{X_{L}} =\frac{240}{50}=4.8[/tex]milli amps=0.0048 A

Reactive power = (current flowing through inductor)X (Voltage across inductor)

Hence reactive power = 0.0048 X 240=1.152 VARs

In six seconds,a total of 3 waves crash onto the shore of the beach .

The distance between each wave crest on the water is 8 meters.

Wave length is the length between two wave crests that is the distance between two wave crests.

We know distance between each wave crest is 8 meters

Total of 3 wave crests, the distance between first and second wave crest is 8 meters

the distance between second and third wave crest is 8 meters

So wave length = 8+8 = 16 meters

[tex]2y-3 > -1\ \ \ \ |\text{add 3 to both sides}\\\\2y > 2\ \ \ \ |\text{divide both sides by 2}\\\\y > 1\\\\5-y > 4\ \ \ \ |\text{add y to both sides}\\\\5 > 4+y\ \ \ \ |\text{subtract 4 from both sides}\\\\1 > y\to y < 1[/tex]

Answer: d.   (all real numbers without 1).

To solve the quadratic equation 48x^2 + 44x = 60, one can rearrange it to the standard form, use the quadratic formula, attempt factoring if it is factorable, or multiply by a common factor to simplify. The most common method is the quadratic formula which provides a systematic way to find the solutions.

To solve the equation 48x^2 + 44x = 60, we can use several methods that are commonly used to solve quadratic equations. First, we need to rearrange the equation into the standard quadratic form, which is ax^2 + bx + c = 0. By subtracting 60 from both sides of the equation, we get 48x^2 + 44x - 60 = 0.

One way to solve for x is by using the quadratic formula, which is x = (-b ± √(b^2 - 4ac))/(2a), where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0. In this situation, a = 48, b = 44, and c = -60. By plugging these values into the quadratic formula, we can find the two possible solutions for x.

Alternatively, we can try to factor the quadratic if it can be expressed as a product of two binomials. In some cases, like when the quadratic is a perfect square or can be easily factored, this is a simpler solution. However, if factoring is complicated or not apparent, the quadratic formula can always be used as a reliable method.

Additionally, if the equation has coefficients that are not integers or are difficult to work with, we can multiply both sides by a common factor to simplify the equation into a more manageable form with integer coefficients, after which we can proceed to use the quadratic formula or factor the quadratic, if possible.

The correct expression to find solutions is [tex]\(4(4x + 3)(3x - 5)\)[/tex], as it correctly factors the given quadratic equation.

To find the solutions to the given quadratic equation [tex]\(48x^2 + 44x = 60\)[/tex], we can use factoring. The equation needs to be rearranged to set it equal to zero:

[tex]\[48x^2 + 44x - 60 = 0\][/tex]

Now, we can factor the quadratic expression. The correct factorization is:

[tex]\[4(4x + 3)(3x - 5)\][/tex]

To verify this, distribute the factors:

[tex]\[4(4x + 3)(3x - 5) = 48x^2 + 36x - 60x - 45\][/tex]

Combine like terms:

[tex]\[48x^2 - 24x - 45\][/tex]

This matches the original quadratic expression, confirming the correct factorization.

Therefore, the correct expression that could be used to find the solutions to the given equation is [tex]\(4(4x + 3)(3x - 5)\)[/tex].

Complete Question:

Answer:

Average temperature at night -140°C.

Step-by-step explanation:

To find the average temperature at night we have to deduct the drop in temperature from the average temperature at noon.

Average temperature at night = Average temperature at noon - drop in temperature.

                                                  =112°C -  252°C

                                                  = -140°C

The average temperature on the moon's surface at night is -140 degrees Celsius, as calculated by subtracting the temperature drop at night (252 degrees Celsius) from the daytime temperature (112 degrees Celsius).

Your question involves finding out the average temperature on the Moon's surface during the night. The temperature on the Moon at noon is 112 degrees Celsius. However, the temperature drops by 252 degrees Celsius at night. To find the temperature at night, you subtract the drop in temperature from the daytime temperature.

So, let's do the calculation: 112 degrees Celsius (noon temperature) - 252 degrees Celsius (temperature drop) = -140 degrees Celsius. Therefore, the average temperature on the Moon's surface during the night is -140 degrees Celsius.

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The length of the segment is 22 units

y = 11 units

The total length of the segment will be expressed as:

L = x + y

Note that x = y

Substituting into the total length

L = y + y

L = 2y

L = 2(11)

L = 22 units

Hence the length of the segment is 22 units

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Paula = 6 video games

Myles = 1 video game + Paula(6 video games)

P + M = Total video games

M = 1 + P

P = 6

P + M = 6  + 1 = 7

Final answer:

To find the total number of video games Paula and Myles have, add Paula's 6 games to Myles's 7 games (since he has one more than Paula), which equals 13 games.

Explanation:

To find out how many video games Paula and Myles have in total, we can use a simple addition equation based on the information given. Paula has 6 video games, and Myles has 1 more video game than Paula. Therefore, we can express the number of video games Myles has as 6 games + 1 game, which equals 7 games.

Next, we add the total number of games Paula has to the total number of games Myles has:

Paula's video games: 6 games
Myles's video games: 7 games
Total video games: 6 games + 7 games = 13 games

By adding the two amounts together, we can find the total number of video games they have combined.

3. definition of supplementary angles

5. defintion of congruency

6. substitution (refer to statements 3 and 5)

[tex]-\dfrac{2}{3}\left(2x-\dfrac{1}{2}\right)\leq\dfrac{1}{5}x-1\ \ \ \ \text{use distributive property}\\\\-\dfrac{4}{3}x+\dfrac{1}{3}\leq\dfrac{1}{5}x-1\ \ \ \ \ |\cdot15\\\\-5(4x)+5\leq3x-15\\\\-20x+5\leq3x-15\ \ \ \ \ |-5\\\\-20x\leq3x-20\ \ \ \ |-3x\\\\-23x\leq-20\ \ \ \text{change the signs} \\\\23x\geq20\ \ \ \ \ \ |:23\\\\\boxed{x\geq\dfrac{20}{23}}\to x\in\left[\dfrac{20}{23},\ \infty\right)[/tex]

Final answer:

Gabe needs to give 25 hours of piano lessons in a month to earn a profit of $326, calculated by setting up an equation that factors in his earnings per hour and the monthly cost of renting the piano.

Explanation:

To find out how many hours of lessons Gabe must give to earn a profit of $326, we need to set up an equation that represents his earnings and costs. Given that Gabe earns $15 per hour giving piano lessons, and his fixed cost for renting the piano is $49 per month, we can create the following equation:

Profit = (Earnings from lessons) - (Cost of renting the piano)

Let h represent the number of hours he teaches. His earnings from giving lessons would be 15h (because he earns $15 for each hour of lessons). The cost of renting the piano is a fixed $49 per month. Therefore, we have:

Profit = (15h) - 49

To make a profit of $326, we substitute this into the equation:

326 = (15h) - 49

Now we solve for h to find out how many hours he needs to teach:

326 + 49 = 15h

375 = 15h

h = 375 / 15

h = 25

Gabe needs to give 25 hours of lessons in a month to earn a profit of $326.

Answer: 275 Miles

Step-by-step explanation: 55 x 5 = 275

Answer:

275 Miles

Step-by-step explanation:

55 mph * 5hours= 275 Miles

-3x+9 = -3(2x+3) + 3(x-4)+1

distribute

-3x+9 =-6x-9+3x-12+1

add like terms

-3x+9= -3x-20

add 3x to each side

9 = -20

there are no solutions because 9 does not equal -20

Answer:

Step-by-step explanation:

[tex]x^2 + 2x - 15=\\\\x^2-3x+5x-15=\\\\x(x-3)+5(x-3)=\\\\(x+5)(x-3) \Rightarrow \text{D}[/tex]

Answer:

$48.66

Step-by-step explanation: