c. Will bought a tennis racket on sale for $24.60. If the sale was 20% off,
how much was the tennis racket originally?

Scientific notation exists as a method of writing very large or very small numbers. The expression as a number in scientific notation is 6.4 × [tex]$$10^4[/tex].

Utilizing scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

To express exceedingly high numbers in a shorter manner, scientists have created a shorthand. Scientific notation is the name of this technique. The foundation of scientific notation is the base-10 powers. The coefficient is defined as the initial number, 1.23.

Given: (8 ×10²) × (3.2 ×[tex]$$10^5[/tex])/4 × 10³

simplifying the above equation, we get

= 800 × 320000/4000

= 64000

= 6.4 × [tex]$$10^4[/tex]

Therefore, the expression as a number in scientific notation is 6.4 × [tex]$$10^4[/tex].

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Answer:

6.4 x 10^4

Step-by-step explanation:

Answer:

129

Step-by-step explanation:

75% of 516 is 387 so we just need to subtract 387 from 516. The answer will be 129. Please mark as brainiest

The solution of the system of equations involving 3x + 7y = 15 and 5x + 2y = -4 is  (-2 , 3).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

3x + 7y = 15     (equation 1)

5x + 2y = -4     (equation 2)

Using the first equation, find the value of one variable, lets say x, in terms of the other.

3x + 7y = 15     (equation 1)

3x = 15 - 7y

x = 5 - (7/3)y

Substitute the equation of x to the second equation.

5x + 2y = -4     (equation 2)

5[5 - (7/3)y] + 2y = -4

25 - (35/3)y + 2y = -4

Combining all terms containing the variable y on one side and the constants on the other side of the equality, and solving for y.

25 - (35/3)y + 2y = -4

- (35/3)y + 2y = -4 - 25

-(29/3)y = -29

y = 3

Substitute the value of y in the equation of x.

x = 5 - (7/3)(3)

x = 5 - 7

x = -2

Hence, the solution of the given system of equations is (-2 , 3).

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The simplification of each sum or difference of the given expression [tex]\frac{1}{2x} +\frac{1}{2x}[/tex] is equal to 1/x. Restriction on the variables is given by x≠ 0.

As given in the question,

Given expression is [tex]\frac{1}{2x} +\frac{1}{2x}[/tex]

Simplify the given expression by taking the least common multiple,

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

Restriction on the variables is given by x≠ 0.

Therefore, the simplification of each sum or difference of the given expression [tex]\frac{1}{2x} +\frac{1}{2x}[/tex] is equal to 1/x. Restriction on the variables is given by x≠ 0.

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The new function is g(x) =-1(1/-x) +2.

The transformation of function f(x) to function g(x) is given by g(x)=A f(Bx+ H)+K. where the constant A scales the function vertically. (A negative A reflects the function about the x-axis B scales the function horizontally. (A negative B reflects the function on the y-axis.) H shifts the function horizontally, and K shifts the function vertically.

Convert f(x) to g(x)

where the conversion is g(x)=f(x)+2.

A perpendicular line has negative reciprocal slopes, so for g(x) to be perpendicular to f(x), we need to get the negative reciprocal of -x, which is -1(1/-x)

So, f(x)=-x-2  ; m = -1

From the above information, we get g(x) as follows.

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

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hope the picture makes sense. I think it's right (no expert) if u want me to explain just ask. the answer is circled. usually the question would ask you to round so i wrote the full version

Answer:

Part1: 4.25 + 4.00x = 12.25
Part2: 2 lbs. of potato salad. The customer bought 2 lbs because you subtract 4.25 from 12.25 and are left with $8. You would then divide 8$ by 4 and end up with 2

For the domain -1 <  x < ∞ and -∞ <  x < -1, the function y= |x+1| is increasing and decreasing, respectively.

It must be identified for which domain intervals the function y= |x+1| increases or decreases, as stated in the question.

Since,

Accoding to the question of the given function, y= |x+1|

Assigned functions  is an absolute functions,

Whose domain is all real numbers from negative infinity to positive infinity

And Plotting the function's graph reveals that it decreases from -∞  to -1 and grows from -1 to ∞ .

Thus, For the domain -1 <  x < ∞ and -∞ <  x < -1, the function y= |x+1| is increasing and decreasing, respectively.

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Answer: x = - 2

Step-by-step explanation:

3 ( x + 4 ) + 3 =9

multiply into the brackets

3x + 12 + 3 = 9

3x = 9 - 12 -3

3x = -6

x = -6/3

x = - 2

Answer:

new position is 360 feet below sea level.

Step-by-step explanation:

see picture for reference.

The expression representing the amount remaining will be 45 - 2.50x.

Table of values

At x = 1 Amount = 42.50

At x = 2 Amount = 40.

From the information, Malika uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and the original amount of money on the gift card was $45.

Therefore, the expression representing the amount remaining will be:

A = 45 - (2.50 × x)

A = 45 - 2.50x

At x = 1 Amount remaining will be:

= 45 - 2.50

= 42.50

At x = 2

A = 45 - 2.50x

A = 45 - 2.50(2)

= 40

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The slope of the line 3x - 2y = -12  is 3/2 .

The equation of a straight line can be written as follows,

y = mx + c                                         equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 3x - 2y = -12 .

To get the slope of this given equation we need to convert the given equation in the format of equation of a straight line i.e., equation1. So now we will rearrange the given equation as,

  3x - 2y = -12

⇒ 2y = 3x + 12

Now on dividing this equation by 2 on both sides, we will get

⇒ y = (3/2)x + 6                                               equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 3/2.

Intercept = c = 6

The slope of the line 3x - 2y = -12  is 3/2 .

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Step-by-step explanation:

what is B in your question ? you did not tell us.

since you mention "fraction", I assume B is the slope of a line ?

if that is the case, please remember, the slope is (y coordinate change / x coordinate change) when going from one point of the line to another.

the way you phrased it I assume the slope was originally negative.

that means either the y difference or the x difference was negative (but not both, otherwise it would have been a positive fraction again).

let's look at what happens, when things get reflected across the y axis :

things go from the left side (negative x values) to the right side (positive x values) of the y axis or vice versa.

and things stay on the same side of the x axis (either above the x-axis with positive y values, or below the x-axis with negative y values).

so, that reflection causes the x values to flip their sign, but the y values stay the same.

so, if y was originally negative, then x must have been positive. after the reflection x is now negative too, that makes the y/x fraction -/- = +/+ positive.

if y was originally positive, then x must have been negative. after the reflection x is now positive too, that makes the y/x fraction +/+ positive.

therefore, in every case, the reflected slope fraction must be positive.

Answer: x=24

6:9,    16 is to x = 16:x

6/9=16/x

multiply both sides by x

6x/9=16

multiply both sides by 9

6x=144

divide by 6

x=24

Answer:

6 motorcycles/ 9 hours = 16 motorcycles/x hours

to complete a proportion you need to multiply the cross products

9(16)=6x

144=6x

144/6=6/6 x

24=x

it will take 24 hours to produce 16 motorcycles

The solution of the given linear equation in one variable 0.2(x+3)-4(2 x-3)=0.9 is at x = 1.5.

According to the given question.

We have a linear equation in one variable.

0.2(x+3)-4(2 x-3)=0.9

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofore, the solution of the linear equation in one variable 0.2(x+3)-4(2 x-3)=0.9 is given by

0.2(x+3)-4(2 x-3)=0.9

⇒ 0.2x + 0.6 -8x + 12 = 0.9

⇒ -7.8x + 12.6 = 0.9

⇒ -7.8x  = 0.9 - 12.6

⇒ -7.8x = -11.7

⇒ x = -11.7/(-7.8)

⇒ x = 1.5

Hence, the solution of the given linear equation in one variable 0.2(x+3)-4(2 x-3)=0.9 is at x = 1.5.

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Answer:

The variable m is not a solution of the equation -2(2m-8)=-2(-6m-8);m=0. Give brainly if I helped!

Step-by-step explanation:

28 m is the approximate perimeter of the rectangle patio.

What is a rectangle, exactly?

p = 2w + 2l

therefore, p = 8.39 * 2 + 5.4 * 2

p = 16. 78 + 10.8

p = 27.58

perimeter = 28 meters

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The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In a triangle, if the angle is small then the opposite side will be short, and if the angle increases then the side also increases.

The sides of the triangle are in ascending order, then we have

WY < YZ < WX < XY < XZ

Then the sequence of the angles is given as,

∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ

The sequence of the angles from least to biggest is ∠WXY < ∠YXZ < ∠WYX < ∠XZY < ∠XYZ.

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It should be noted that Tyler writing the equation x = y/65 is correct and matches the information.

It should be noted that speed is calculated as:

= Distance / Time

In this case, the car is going 65 miles per hour down the highway

x = the time traveled, in hours

y = the distance traveled,

Therefore, time = Distance / Speed

Therefore, Tyler wrote the equation x = y/65, this is correct and matches the information.

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A car is going 65 miles per hour down the highway. Tyler wrote the equation x = y/65, with x representing the time traveled, in hours, and y representing the distance traveled, in miles. Explain why Tyler's equation matches the story.

Answer:

The length is 120 yards, the width is 60 yards.

Step-by-step explanation:

[tex]l = 2w[/tex]

[tex]2(w + 2w) = 360[/tex]

[tex]3w = 180[/tex]

[tex]w = 60[/tex]

[tex]l = 120[/tex]

Answer:

х=8/3 solution on screen

Step-by-step explanation:

Good luck

  The algebraic expression or sigma (summation) notation is given by:

∑ = 10(-3 - 30)/2

And its value is ∑ = -165

 The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

  The equation for this type of problem is:

∑ = n(a1 + an)/2

  Our values are:

(-3)+(-6)+(-9)+. . . . . . +(-30)

∑ = 10(-3 - 30)/2

∑ = 10(-33)/2 = 5(-33)

∑ = -165

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The result of the expression [tex]-k^{2}-(3k+5n)+4n[/tex] for the variable k= -1 and n= -2 is -16

Given,

The expression =[tex]-k^{2}-(3k-5n)+4n[/tex]

We know

k= -1

n= -2

Substitute the values in the expression

[tex]-(-1)^{2}-(3(-1)-5(-2))+4(-2)[/tex]= -1-(-3+10)-8

=-1-(7)-8

=-1-7-8

=-16

Hence, The result of the expression [tex]-k^{2}-(3k+5n)+4n[/tex] for the variable k= -1 and n= -2 is -16

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The cylinder's total surface area includes the area of the curving surface as well as the areas of the two circle-shaped bases of the cylinder.

The area of the two bases and the area of the curved surface are added to determine the cylinder's total surface area. Consequently, the following is the formula for the cylinder's total surface area:

Area of the two bases plus the area of the curved surface equals the cylinder's total surface area. Due to the cylinder's round bottoms, their combined area will be equal to r2 + r2. We already know that a cylinder's curved surface area is 2rh.

(r2 + r2 + 2rh) is the cylinder's total surface area.

⇒ 2πr2 + 2πrh

Total surface area of cylinder = 2πr(r+h)

where,

r = radius of the cylinder

h = height of cylinder

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Answer:

156

Step-by-step explanation:

1. cross multiply

2. Divide both sides

i hope i helped

Answer: Substitute the value of the variable into the equation and simplify.

22743

v

a

2

l

u

e

2

−

1083

Step-by-step explanation:

Answer:

8004

Step-by-step explanation:

8000+4

= 8004

Answer: [tex]=2\circ \:3[/tex]

Step-by-step explanation:

[tex]\mathrm{For}\:\frac{\left(5x^2\right)^3+16y}{4y,\:x}\circ \:y\:\mathrm{substitute}\:\frac{\left(5x^2\right)^3+16y}{4y,\:x}\:\mathrm{\:with\:}\:2,\:y\:\mathrm{\:with\:}\:3[/tex]

[tex]=2\circ \:3[/tex]

The maximum allowable weight for a disc with circumference 66.92 centimeters Round to the nearest tenth is 176.9 grams.

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

the maximum weight, w of a disc in grams is 8.3 times the diameter, d in centimeters

⇒ w ≤ 8.3d

and  the maximum allowable weight for a disc with circumference 66.92 centimeters

So, Circumference = πd   [∵ d = 2r]

∴ 66.82 = πd

⇒ d = 66.82π

Thus,  w ≤ 8.3*66.82π grams

⇒ w ≤ 176.89 grams

Round to the nearest tenth, w ≤ 176.9 grams

Thus, the maximum allowable weight for a disc with circumference 66.92 centimeters Round to the nearest tenth is 176.9 grams.

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