Which expression is the completely factored form of x6−64y3 ?

Answer:

Hypotenuse, AB = 7.61 cm

Step-by-step explanation:

In the given figure it is given that, ABC is a right angled triangle with base length BC = 3 cm and perpendicular distance AC = 7 cm. We have to find the length of hypotenuse i.e. AB

The length of hypotenuse is solved using Pythagoras theorem. The mathematical expression for the Pythagoras theorem can be written as :

[tex]AB^2=AC^2+BC^2[/tex]

[tex]AB^2=7^2+3^2[/tex]

[tex]AB^2=58[/tex]

AB = 7.61 cm

So, the length of the hypotenuse of the triangle is equal to 7.61 cm    

Answer:

x=-39

Step-by-step explanation:

subtract 23 from both sides

-16 - 23= -39

therefore x=-39

Let x and y be the two numbers.  

x = y - 4  

2y = 5x - 10  

solve the system of equations:  

2y = 5(y - 4) - 10  

2y = 5y - 20 - 10  

-3y = -30  

y = 10  

x = 10 - 4 = 6

I will try my best...

Let x and y be the two numbers.  

x = y - 4  

2y = 5x - 10  

Now, we solve the system of equations:  

2y = 5(y - 4) - 10  

2y = 5y - 20 - 10  

-3y = -30  

So...

y = 10  

x = 10 - 4 = 6

Answer:

B) Kara's highest speed was between 30 and 35 minutes.

Step-by-step explanation:

A zero slope (horizontal line) means a stopped car with zero speed.

The higher the slope, the steeper the line, the higher the speed.

Let's look at the options.

a) The car was stopped between 10 and 15 minutes, not 20. False.

b) Between 30 and 35 min, the graph shows the steepest slope, so this statement is True.

c) False, since here slope is not steepest.

d) Between 5 and 10 minutes, the graph is a straight line, so speed was constant. False.

Answer:

i realy need help with this one

Step-by-step explanation:

Hey there!!

Multiply both the sides with 4/3.

Then we get

x = 5 ^ 4/3

x = 8.5 ( avg. )

Hope it helps!

bi(two)...sector(section).  Bisector cuts the segment into two equal sections.  

BC = CD             definition of perpendicular bisector

BC + CD = BD    segment addition postulate

CD + CD = BD   substitution

2CD = BD          added like terms

2CD = 16           substitution

  CD = 8            division property of equality

CD = y + 3         given per graph

y  + 3 = 8           transitive property

  y = 5               subtraction property

Answer: 5

They wash a car for $5, so 5 represents the cost of washing one car. to find out how much they will earn by washing x cars, we can multiply 5 by any number to find the total cost of the washed cars. For example 5×2=10 which means the cost of washing 2 cars is $10 and 5×3=15 means the cost of washing 3 cars is $15 and also 5×4=20 means the cost of washing 4 cars is $20. Basically the cost of the washed cars will increase by $5 each time the number of cars increase.

The probability that all seven arrows will not hit the bullseye is 1 2/5

Probability calculate how likely it is for an event to occur. The chances of an event occurring is between 0 and 1. The value of the event is one if the event happens and zero if the event does not happen.

For example the probability that it would rain everyday of the week lies between 0 and 1. If it rains, a value of 1 would be attached to the event and if it does not rain all the days of the week a value of zero would be attached to the event.

Probability all seven arrows does not hit the bullseye = number of arrows x probability of one arrow not hitting the bullseye

Probability that one arrow does not hit the bullseye = 1 - 4/5

5/5 - 4/5 = 1/5

Probability = 1/5 x 7 = 7/5 = 1 2/5

To learn more about probability, please check: https://brainly.com/question/23044118?referrer=searchResults

If the point (a, b) is in Quadrant IV of a coordinate plane, then the x-coordinate of (a, b) will be positive and the y-coordinate will be negative.

EX: (5, -5)

Final answer:

The point (a,b) is in Quadrant IV, where 'a' is positive and 'b' is negative. Switching the coordinates to (b,a) places it in Quadrant II, where 'b' is now the x-coordinate (negative), and 'a' is the y-coordinate (positive).

Explanation:

Given that the point (a,b) is in Quadrant IV of a coordinate plane, where 'a' is the x-coordinate, and 'b' is the y-coordinate. In Quadrant IV, x-coordinates (a) are positive, and y-coordinates (b) are negative, hence a > 0 and b < 0. When we consider the point with coordinates (b,a), we switch the positions of 'a' and 'b'. Since 'a' is positive and 'b' is negative, the point (b,a) would then be in Quadrant II, where x-coordinates are negative and y-coordinates are positive. To recap, in the Cartesian coordinate system, a point's location is determined by the signs of its x and y values, which change across different quadrants, affecting the point's location accordingly.

Just like you drew those dotted lines. You know how to find the areas of rectangles which is A=length x width

The answer would be 20cm^2+6cm^2+18cm^2=44 cm^2

You would divide it into smaller shapes and then find the area then add them all up.

4*5=20

3*2=6

3*6=18

20+6+18=34cm^2

Answer,

42

Explanation,

18/3 = 6

6 x 7 = 42

Hope this helps :-)

1) Divide both sides by 3

3(5x+3)=114

2) Move constant to the right side and change it's side

5x+3=38

3) Subtract the numbers

5x=38-3

4) Divide by sides by 5

5x=35

5) The answer is x=7

Hope I could help! :)

Hey mate !!

Answer

= 5x +3=114/3

Simplify 114/3 to 38

= 5x+3=38

Subtract 3 from both sides

=5x=38-3

Simplify 38-3=35

5x=35

Divide both sides by 5

X= 35/5

Simplify 35/5 to 7

X=7

Answer confirmed = x=7

Hope this helps you!

Answer:

D.)  (12 + 11 + 20) ÷ 3

Step-by-step explanation:

Step 1: Line up the equations so that the variables are lined up vertically.

Step 2:  Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same.

Step 3:  Subtract the two equations.

Step 4:  Solve the one variable system.

Step 5:  Put that value back into either equation to find the other equation.

Step 6:  Reread the question and plug your answers back in to check.

Final answer:

To solve systems of equations, one can use methods like graphing, substitution, or elimination, and check the solution by substituting it back into the original equations. For inequalities, graph the lines, decide where to shade by testing a point, and find the overlap of the shaded regions for the solution.

Explanation:

Steps to Solving Systems of Equations and Inequalities

The process of solving systems of equations and inequalities involves several steps. To solve a system of equations, you can use methods such as graphing, substitution, or elimination. When solving inequalities, additional considerations such as shading the solution region are necessary. Here's a step-by-step approach for both equations and inequalities:

For Equations:

Choose a suitable method (graphing, substitution, elimination).

Apply the selected method to find the point of intersection, which represents the solution to the system.

Check your solution by substituting it back into the original equations.

For Inequalities:

Graph the lines or curves that represent the inequalities, using dashed or solid lines.

Determine where to shade the region by testing a point not on the line.

Find the overlap of the shaded regions if there is more than one inequality.

It's important to practice these steps with different systems to become proficient in solving them. Remember to pay close attention to the signs of the inequalities when graphing and shading the solution regions.

If you plug in h, the answer would be 13-9 which is 4.

h(13)=13-9=4,inlocuiesti x cu 13 si calculezi.

Charges per load = $5.25

Total money = $31.50

As the situation says that charges are 5.25 and one has a total money of 31.50 so lets suppose the total load one has be 'w'

so equation becomes:

[tex]5.25w\leq31.50[/tex]

solving it we get, [tex]w\leq6[/tex]

So, option C is the correct answer.

The question is about simplifying an algebraic expression, specifically 3x - 1/2y + 2 2/3y - 5/6x. This can be achieved by first consolidating like terms and performing multiplication and addition/subtraction to get the simplified expression 2 1/6x + 2 1/6y.

This question appears to be about simplifying algebraic expressions. The expression at hand is 3x-1/2y +2 2/3y -5/6x. To simplify this, you should first consolidate your like terms. The 'like terms' in this case, are the X terms (3x and -5/6x) and the Y terms (-1/2y and +2 2/3y).

Secondly, perform the operations necessary for the terms – which involve multiplication and addition/subtraction. Thus, the sum of 3x and -5/6x is 2 1/6x (or 2.167x if we want it in decimal form). Similarly, the sum of -1/2y and +2 2/3y is 2 1/6y (or 2.167y in decimal form).

Finally, to complete the simplification, you should combine these totals. The simplified algebraic expression for 3x - 1/2y + 2 2/3y - 5/6x is therefore 2 1/6x + 2 1/6y.

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So if you let x and y be the two numbers...

the sum of the two means you add them together... so you get:

x+y=56 : the difference means you subtract them.. so

x-y = 16

now you have two equations and two unknowns... which you can solve with a variety of methods... you can use elimination, substitution, or trial and error.

x+y=56

x-y = 16

I will use the elimination method: Because there is a plus y and a negative you cancel that out and you add the 2x's. Therefore:

2x=72

x=36

Now, you can plug in 36 into one of your original equation:

36+y=56

y=20

Those are your two numbers!

The product of the numbers is 720.

Simplify fractions by cancelling all the common factors from both the numerator and the denominator and writing the fraction in its lowest/simplest form.

Given that, the sum of two numbers is 56. the difference of the 2 numbers is 16.

Let the numbers be x and y,

x+y = 56

x-y = 16

On solving, we get,

x = 36 and y = 20

x*y = 36*20 = 720

Hence, The product of the numbers is 720.

For more references on simplification, click;

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it could be 460-490 to round to 500

Answer:

450-549

Step-by-step explanation:

you can round up or down

the answer is B. hope i helped!

Correct answer:

2.32 x 10^8

10^8 + 6 - 6 = 10^8

and

(1.6)(5.8)

(4)

= 9.28

4

= 2.32

thus,

2.32 x 108

mark Brainliest?

Answer:

She did not get the correct answer because she did not put the decimal in the correct spot. The correct answer should be 428.206.

Step-by-step explanation:

17.06×25.1=428.206

Answer:

The n-th term for the sequence will be:  [tex]n^2+4n+2[/tex]

Step-by-step explanation:

Given sequence is:  7, 14, 23, 34, 47. 62, 79, ........

The n-th term of a quadratic sequence is:  [tex]t_{n}=an^2 +bn+c[/tex]

For [tex]n=1[/tex]....

[tex]t_{1}=a(1)^2+b(1)+c\\ \\ a+b+c=7 .............................(1)[/tex]

For [tex]n=2[/tex]....

[tex]t_{2}=a(2)^2+b(2)+c\\ \\ 4a+2b+c=14 .............................(2)[/tex]

For [tex]n=3[/tex]....

[tex]t_{3}=a(3)^2+b(3)+c\\ \\ 9a+3b+c=23 .............................(3)[/tex]

Subtracting equation (1) from equation (2), we will get......

[tex]3a+b=7..........................(4)[/tex]

Subtracting equation (2) from equation (3), we will get.......

[tex]5a+b=9..........................(5)[/tex]

Now, subtracting equation (4) from equation (5)...........

[tex]2a=2\\ \\ a=\frac{2}{2}=1[/tex]

Plugging this  [tex]a=1[/tex] into equation (4), we will get....

[tex]3(1)+b=7\\ \\ 3+b=7\\ \\ b=7-3=4[/tex]

Now, plugging [tex]a=1[/tex] and [tex]b=4[/tex] into equation (1) .........

[tex]1+4+c=7\\ \\ 5+c=7\\ \\ c=7-5=2[/tex]

Thus, the n-th term for the sequence will be:  [tex]n^2+4n+2[/tex]

To find the nth term of a quadratic sequence, we can follow these steps:

Step 1: Find the first difference.
To do this, we calculate the difference between the consecutive terms of the sequence.

14 - 7 = 7
23 - 14 = 9
34 - 23 = 11
47 - 34 = 13
62 - 47 = 15
79 - 62 = 17

Now we have the first difference sequence: 7, 9, 11, 13, 15, 17.

Step 2: Find the second difference.
If it's a quadratic sequence, the second difference should be constant. That is, the difference of the first difference sequence should be the same. Let's calculate it.

9 - 7 = 2
11 - 9 = 2
13 - 11 = 2
15 - 13 = 2
17 - 15 = 2

Great, our second difference is constant and equal to 2.

Step 3: Create the general quadratic formula.
Quadratic sequences are defined by the formula:
a_n = an^2 + bn + c

Since the second difference is constant and equal to 2, we know that 2a should be equal to the second difference. Therefore, a is half of the second difference.

a = 2/2 = 1
So our sequence has the form:
a_n = n^2 + bn + c

Step 4: Find b and c.
We use the given terms from the sequence to find the values of b and c. We know that the first term (when n=1) is 7.

a_1 = 1^2 + b(1) + c = 7
1 + b + c = 7
b + c = 6 ... [1]

We also know that the second term (when n=2) is 14.
a_2 = 2^2 + b(2) + c = 14
4 + 2b + c = 14
2b + c = 10 ... [2]

At this point, we have two equations with two variables. We can resolve this system of equations to find b and c.

Step 5: Solve the system of equations.
We can subtract equation [1] from equation [2] to find the value of b.

(2b + c) - (b + c) = 10 - 6
2b - b + c - c = 4
b = 4

Plug the value of b into either equation [1] or [2] to find c.

b + c = 6
4 + c = 6
c = 6 - 4
c = 2

Step 6: Write down the nth term formula with the found coefficients a, b, and c.
a_n = n^2 + 4n + 2

Therefore, the nth term of the quadratic sequence 7, 14, 23, 34, 47, 62, 79 is a_n = n^2 + 4n + 2.

we have

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

Combine like terms in both sides

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

we know that

[tex](\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x[/tex]

substitute in the expression above

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

Multiply equation A by [tex]5*3*2=30[/tex] both sides

[tex]30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)[/tex]

[tex]48x+20=15-6x[/tex] ---------> equation B

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]48x+6x=15-20[/tex]

[tex]54x=-5[/tex] ---------> equation C

Solve for x

[tex]x=-\frac{5}{54} =-0.09[/tex]

We are going to proceed to verify each case to determine the solution.

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

the case a) is equal to the equation A

so

the case a) have the same solution that the given equation

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

Combine like terms in left side

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

[tex](48x)+20=15-6x[/tex]

the case b) is equal to the equation B

so

the case b) have the same solution that the given equation

Case c) [tex]18x+20+x=15-6x[/tex]

Combine like terms in left side

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

[tex](19x)+20=15-6x[/tex]

[tex]19x+6x=15-20\\25x=-5\\x=-0.20[/tex]

[tex]-0.20\neq -0.09[/tex]

therefore

the case c) not have the same solution that the given equation

Case d) [tex]24x+30x=-5[/tex]

Combine like terms in left side

[tex]54x=-5[/tex]

the case d) is equal to the equation C

so

the case d) have the same solution that the given equation

Case e) [tex]12x+30x=-5[/tex]

Combine like terms in left side

[tex]42x=-5[/tex]

[tex]x=-5/42=-0.12[/tex]

[tex]-0.12\neq -0.09[/tex]

therefore

the case e) not have the same solution that the given equation

therefore

the answer is

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

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

case d) [tex]24x+30x=-5[/tex]

Answer:

Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

Step-by-step explanation:

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

We have to use  properties to rewrite the given equation and check which are correct from thee given options,

Consider the given equation,

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

Applying commutative property of addition , [tex]a+b=b+ a[/tex]

Equation becomes,

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

Now adding x terms on right side , we get,

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

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

Thus, obtained option (a).

Again consider given equation ,

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

Taking LCM both sides, we get,

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

Solving , we get,

[tex]\frac{9x+10+15x}{3}= \frac{5-2x}{2}[/tex]

Cross multiply, we get,

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

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

Thus, obtained option (b).

Taking like terms together,

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

[tex]\Rightarrow 24x+30x=-5[/tex]

Thus, obtained option (d).

Thus, Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]