[tex](\sqrt[3]{7x^6})^5[/tex]

How would I rewrite this using rational exponents? I know the answer is [tex]7^\frac{5}{3}x^{10}[/tex] , but I don't know how to get the [tex]x^{10}[/tex].

Final answer:

The product of 5/12 multiplied by 7 is equal to 35/12.

Explanation:

The product of 5/12 multiplied by 7 is equal to 35/12. To multiply fractions, you multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Therefore, (5/12) x 7 = (5 x 7) / (12 x 1) = 35/12.

It will take 3 hours 6 minutes 40 seconds for the cars to be 420 miles apart.

Step-by-step explanation:

Step 1; The cars are traveling in the opposite direction at different speeds. One is going north at a speed of 75 mph while the other is going 60 mph. So for every hour, the cars are traveling they increase the distance between in between themselves by 75 miles + 60 miles = 135 miles.

Step 2; Assume that in x hours the distance between them is 420 miles. To calculate x we divide the distance to be traveled by the distance being traveled every hour.

x = distance to be covered / distance being traveled every hour

= 420 / 135 = 3.11 hours

We multiply the 0.11 hours with 60 to convert it into minutes. 0.11 × 60 = 6.66 minutes and if we do the same for seconds, 0.66 minutes × 60 = 40 seconds.

Answer:

look at the picture ahown

Answer:

14

Step-by-step explanation:

Answer: Area = 14 [tex]units^{2}[/tex]

Step-by-step explanation:

The formula for calculating the area of Triangle is given by :

Area = [tex]\frac{1}{2}[/tex] x base x height

From the given triangle

base = 4

height = 7

substituting into the formula

Area = [tex]\frac{1}{2}[/tex] x 4 x 7

Area = [tex]\frac{1}{2}[/tex] x 28

Area = 14 [tex]units^{2}[/tex]

Answer: If you want mx + b= y form and you want the y intercept, then the answer would be 2x/7 - 12/7 = y. The y intercept is b, so it is 12/7.

Step-by-step explanation: 2x - 7y = 12

Move -7y to the other side: 2x= 12 + 7y

Subtract 12 to the left side: 2x - 12 = 7y

Then divide 7 into everything: 2x/7 - 12/7 = 7y/7

The 7s in the right side cancel out, so the equation is now: 2x/7 - 12/7 = y

The y intercept is b, which is the second term in the equation, so the

Y Equals : 12/7

I hope this is what you are looking for!  

Answer:

y =  − 12 /7  +  2 x /7

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

In the y intercept formula which is y=Mx+b the b in the formula represents the y intercept

Answer:

D) 0,6,12,18,24

Step-by-step explanation:

Answer:

The graph in option 3 will be the correct one.

Step-by-step explanation:

We have to choose the graph from the given options that shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes.

Now, the graph in option 3 will be the correct one.

On a coordinate plane, the x-axis shows elapsed time in minutes (t) and the y-axis shows total volume of water (V). A straight line with a positive slope begins at point (0, 4) and ends at point (6, 16). (Answer)

Answer:

C

Step-by-step explanation:

Answer:

85%

135%

Step-by-step explanation:

34/40=.85

.85 times 100= 85%

54/40=1.35

1.35 times 100=135%

sorry if its wrong!

Answer:

391

Step-by-step explanation:

product of 49and 13= 49x13

sum of 92 and 164 =92+164

the difference of them =

49x13-(92+164)

=49x13-256

=637-256

=381

Answer:

y=(x-2)^2+4

Step-by-step explanation:

The quadratic function that represents the parabola is y = - (x - 4)² + 4.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

From the graph of the function, the parabola intersects the x-axis

at 0 and 4, and we also know when a parabola opens downwards the equation is negative.

So, The required equation is y = - (x - 0)(x - 4).

y = - (x² - 4x).

y = - {x² - 4x + 4 - 4}.

y = - { (x - 2)² - 4}.

y = - (x - 4)² + 4.

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Answer:

78

Step-by-step explanation:

40 x 76 is the equation by 4x4 of 86 and the 36

Answer:28×5=$140.00

Step-by-step explanation:

Answer:

It is proved that AB = 2 × DE.

Step-by-step explanation:

The three vertices of triangle ABC are A(-2,6), B(8,-2) and C(-8,-4).

So, the mid point of AC (say D) has coordinates [tex](\frac{- 2 - 8}{2},\frac{6 - 4}{2}) = (-5,1)[/tex].

And the mid point of BC (say E) has coordinates [tex](\frac{8 - 8}{2}, \frac{- 2 - 4}{2}) = (0, - 3)[/tex].

Now, the length of DE will be [tex]\sqrt{(- 5 - 0)^{2} + (1 + 3)^{2}} = \sqrt{41}[/tex] units.

Again, the length of AB will be [tex]\sqrt{(- 2 - 8)^{2} + (6 + 2)^{2}} = 2\sqrt{41}[/tex] units.

So, it is proved that AB = 2 × DE. (Answer)

Answer:

x < 3

Step-by-step explanation:

4x +6 < 18

add and subtract 6 from both sides

4x + 6 - 6 < 18 -6

4x < 12

x< 12/4

X < 3

Answer:

x < 3

Step-by-step explanation:

I took the test its, the right answer, trust me.

Answer:

1 13/32

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = mx + b....in this form, the slope will be in the m position and the y int will be in the b position

so ur equation is : y = 2/3x - 7

Answer:

3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

y=3

Step-by-step explanation:

Step 1: Subtract from both sides

3y+39-16y=16y-16y

-13y+39=0

Step 2: Subtract 39 from both sides

-13y+39-39=0-39

-13y=-39

Step 3: Divide Both sides by -13

-13y/-13=-39/-13

y=3

A system of equations to represent the situation with Sparkles the Clown is: 2p + 2g = 12 for Jenny's party and 4p + 5g = 27 for Roger's party. We can use substitution or elimination methods to solve for 'p' and 'g' to determine the number of balloons needed for each animal.

To write a system of equations based on the given situation with Sparkles the Clown, we will let 'p' represent the number of balloons needed for a poodle and 'g' represent the number of balloons needed for a giraffe. From Jenny's party, we know that 2 poodles plus 2 giraffes used a total of 12 balloons. From Roger’s party, we learn that 4 poodles plus 5 giraffes used a total of 27 balloons. Therefore, our system of equations to represent this situation is:

To solve this system of equations, we could use methods such as substitution or elimination to find the values of 'p' and 'g' which would tell us how many balloons are required for each balloon animal.

Final answer:

To find out how many balloons are required for each balloon animal, we set up a system of equations with p representing the number of balloons for a poodle, and g for a giraffe. The system is based on the balloon usage at two parties, resulting in the equations 2p + 2g = 12 and 4p + 5g = 27.

Explanation:

To solve the problem of how many balloons Sparkles the Clown needs for each type of balloon animal, we need to set up a system of linear equations based on the given information. We will let p represent the number of balloons needed for a poodle, and g represent the number for a giraffe.

From Jenny's party, we have the first equation:

2p + 2g = 12

From Roger's party, we have the second equation:

4p + 5g = 27

Now, we have established our system of equations:

1) 2p + 2g = 12

2) 4p + 5g = 27

Solving this system will give us the number of balloons needed to make each type of balloon animal.

To calculate the distance by which a laser beam misses its target on the moon due to an angular error, one can use the tangent function with the Earth-moon distance. For an error of 1 degree, it would miss by approximately 4,080 miles, and for an error of 30 arcseconds, by about 34 miles.

To find out how far a laser beam directed toward the center of the moon misses its target by 1 degree, we can use a simple trigonometric calculation. Since we are dealing with a right-angled triangle with the Earth-moon distance as one leg (the adjacent leg in this case), and we want to find the opposite leg which represents the distance on the moon's surface from the intended target, we can use the tangent function.

For an error of 1 degree:

Convert the degree to radians, because trigonometric functions in calculators usually use radians. There are π radians in 180 degrees, so 1 degree is (π/180) radians.

Use the formula distance = tangent of the angle in radians × Earth-moon distance. So distance = tan(1° × (π/180)) × 234,000 miles.

Calculate the tangent of 1° in radians (approximately 0.01745) and multiply by 234,000 miles.

The result is approximately 4,080 miles.

For an error of 30 arcseconds (30″):

There are 60 arcseconds in 1 arcminute and 60 arcminutes in 1 degree, hence 30 arcseconds is 30/60/60 degrees, which equals 1/120 degrees.

Convert 1/120 degrees to radians similarly as before.

Use the same tangent formula: distance = tan((1/120)° × (π/180)) × 234,000 miles.

Calculate the tangent of (1/120)° in radians (approximately 0.000145444) and multiply by 234,000 miles.

This results in approximately 34 miles from the assigned target.

Answer:

The problem does not work.

Step-by-step explanation:

The plane with speed of 31 mph will cover 640 miles in [tex]\frac{640}{31} = 20.64[/tex] hours.

Now, it burns 5 gallons of gas every 3 minutes i.e. 0.05 hours.

So, it will burn in 20.64 hours [tex]\frac{5 \times 20.64}{0.05} = 2064[/tex] gallons.

Now, the helicopter with speed of 45 mph will cover 640 miles in [tex]\frac{640}{45} = 14.22[/tex] hours.

Now, it burns 7 gallons of gas every 5 minutes i.e. 0.083 hours.

So, it will burn in 14.22 hours [tex]\frac{7 \times 14.22}{0.083} = 1194.48[/tex] gallons.

But both of them starts with only 80 gallons of fuel.

Therefore, the problem does not work. (Answer)

Answer:

|SQ|=5

Step-by-step explanation:

If S is the median, then OP is a median of triangle OMN.

This implies that:

|MP|=|NP|

[tex]3x-4=x+4[/tex]

We group like terms and solve for x.

[tex]3x-x=4+4[/tex]

[tex]\implies 2x=8[/tex]

[tex]\implies x=4[/tex]

Now we know that: MN:SQ=2:1

But MN=2x+2

This implies that:

2x+2:SQ=2:1

Put x=4

2(4)+2:SQ=2:1

10:SQ=2:1

Therefore |SQ|=5

Answer:

The ball would be at its peak at 8 feet from the basket.

Step-by-step explanation:

The basketball should be at its maximum height when it is 10 feet away from the player.

We have,

In a standard basketball shot, the path of the ball follows a parabolic arc. The maximum height is reached at the peak of this arc, which occurs halfway between the player and the basket.

The distance at which the basketball should be at its maximum height is half the distance between the player and the basket.

Half of 20 feet is 10 feet.

Therefore,

The basketball should be at its maximum height when it is 10 feet away from the player.

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Answer:

Option A.) is correct  [tex]\triangle XYZ \sim \triangle WVZ[/tex]  by AA similarity. There are two angles that are congruent given by [tex]\angle ZXY = \angle ZWV \hspace{0.2cm} and\hspace{0.2cm} \angle ZYX = \angle ZVW[/tex].

This is because both pairs represent alternate interior angles formed by lines intersecting two parallel lines.

Step-by-step explanation:

From the given figure we can say that

i) Option A.) is correct  [tex]\triangle XYZ \sim \triangle WVZ[/tex]  by AA similarity. There are two angles that are congruent given by [tex]\angle ZXY = \angle ZWV \hspace{0.2cm} and\hspace{0.2cm} \angle ZYX = \angle ZVW[/tex].

This is because both pairs represent alternate interior angles formed by lines intersecting two parallel lines.

Subtract 3x on both sides: 6x-3x-9=3x-3x+4 which is 3x-9=4

Add 9 to both sides: 3x+9-9=4+9 which is 3x=13

Divide both sides by 3 to get x=13/3 or 4 1/3

Hope this helped!

Answer:

 x = 13/3 = 4.333

Step-by-step explanation:

   6*x-9-(3*x+4)=0  

Step  1  :

Solving a Single Variable Equation :

  Solve  :    3x-13 = 0  

Add  13  to both sides of the equation :  

                     3x = 13

Divide both sides of the equation by 3:

                    x = 13/3 = 4.333

Answer:

(-1/2,2)

Step-by-step explanation:

2(4x+y=0)=8x+2y=0

8x+2y=0

-(8x-y=6)

3y=6

Divide both sides y=2

4x+2=0

4x=-2

divide both sides x=-1/2

To solve the system of equations, we can use the matrix tool. The solution to the system of equations is (1, 1.5) as an ordered pair.

To solve the system of equations using matrices, you can represent the coefficients and constants as matrices and then use matrix operations. The system of equations can be represented in matrix form as:

[A] [X] = [B],

Where:

[A] is the coefficient matrix,

[X] is the variable matrix (containing x and y),

[B] is the constant matrix.

For the given system of equations:

4x + y = 0

8x - y = 6

The coefficient matrix [A], variable matrix [X], and constant matrix [B] are:

[A] = [[4, 1],

[8, -1]]

[B] = [[0],

[6]]

Now, to solve for [X], you can use matrix multiplication:

[A] [X] = [B]

[X] = [A]⁻¹ [B]

First, calculate the inverse of [A]:

[A]⁻¹ = [[-1/12, -1/12],

[1/4, 1/4]]

Now, multiply [A]⁻¹ by [B]:

[X] = [[-1/12, -1/12],

[1/4, 1/4]] [0, 6]

[tex][X] = [(-1/12 \times 0 + -1/12 \times 6),[/tex]

[tex](1/4 \times 0 + 1/4 \times 6)][/tex]

Simplify:

[X] = [-(-1), 1.5)]

[X] = [1, 1.5]

So, the solution to the system of equations is (1, 1.5) as an ordered pair.

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Check the picture below.

well, then we know that (3x-5) + (4x+10) = 180, so

[tex]\bf (3x-5)+(4x+10)=180\implies 7x+5=180\implies 7x=175 \\\\\\ x = \cfrac{175}{7}\implies x = 25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \measuredangle BEC}{3x-5\implies 3(25)-5\implies 70} \\\\\\ \stackrel{~\hfill \measuredangle ABE}{180 - (x-5)\implies 180-(25-5)\implies 180-20\implies 160}[/tex]

Answer:

r= -45

Step-by-step explanation:

trust on this one

Answer:

-189

Step-by-step explanation: