4x - 3 ( x - 2 ) = 21

Answer:

The dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

Step-by-step explanation:

The formula for the perimeter of a rectangle = 2(L + W)

= 2L + 2W

The perimeter = 46 mm

L = 3x + 3

W = x - 4

P = 2L + 2W

46mm = 2(3x + 3) + 2(x - 4)

46 = 6x + 6 + 2x - 8

Collect like terms

46 +8 -6 = 6x + 2x

48 = 8x

x = 48/8

x = 6

Since the Length = 3x + 3

= 3(6) + 3

= 18 + 3

= 21mm

Since the Width = x - 4

= 6 - 4

= 2mm

Therefore, the dimension of this rectangle = 2mm by 21mm

Where 2 mm = Width of the rectangle

21 mm = Length of the rectangle.

Answer:

3y-7

Step-by-step explanation:

-4y + 7y - 10 + 3

Combine like terms

-4y + 7y      - 10 + 3

3y              -7

Answer:

12x -28

Step-by-step explanation:

4(5x - 6) - 4(2x + 1)

Distribute

20x -24  -8x -4

Combine like terms

12x -28

Answer:

I think the value of x might be 127°

Answer:

ABC = 36 , DBC = 44

Step-by-step explanation:

(7x+2) + (7x -6) = 8=

14x -4 = 80

14x = 84

x = 6

Answer:

w = 9

Step-by-step explanation:

We can use ratios to solve

2        3

---- = ------

6         w

Using cross products

2w = 3*6

2w = 18

Divide by 2

w = 9

Answer:

See below

Step-by-step explanation:

See attached table

Regular polygon with n sides can map onto itself n times

It will rotate 360°/n about its center every time and will map onto itself

Examples are in the attached table

Answer:

PLATO

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Answer:

(5,10)

Step-by-step explanation:

So we have the system of equations:

[tex]y=x+5\\3x+y=25[/tex]

To solve, we can use substitution.

Substitute the first equation into the second:

[tex]3x+y=25\\3x+(x+5)=25[/tex]

Combine like terms:

[tex]4x+5=25[/tex]

Subtract 5:

[tex]4x=20[/tex]

Divide by 4:

[tex]x=5[/tex]

Now, substitute this into the first equation:

[tex]y=x+5\\y=5+5[/tex]

Add:

[tex]y=10[/tex]

So, our answer is (5,10)

And we are done :)

[tex]x=2y+1[/tex]

what is [tex]10y-5x[/tex]?

all you gotta do is substitute the value of [tex]x[/tex] in the equation:

[tex]x=2y+1\\10y-5(2y+1)[/tex]

now solve for [tex]y[/tex]:

[tex]10y-5(2y+1)\\10y-10y-5=-5[/tex]

so the value of [tex]10y-5x =[/tex] [tex]\boxed{-5}[/tex]

Answer:

It is a rational integer.

Step-by-step explanation:

'-3' is rational. It could be written as [tex]\frac{-3}{1}[/tex].

It is also a integer. Integers include all whole numbers and negative numbers without a fraction or a decimal.

Whole and natural numbers are only positive values. And since '-3' could be written as a fraction, it is not irrational.

'-3' is a rational number and an integer.

Hope this helps.

Answer:

x > 23

Step-by-step explanation:

5x – 1 < 7x - 47​

Add 1 to -47, you get -46.

5x < 7x - 46

Subtract 7x from 5x.

-2x < -46

Multiply both sides to reverse the inequality.

2x > 46

Divide both sides by 2.

x > 23

Answer:

this is all I could find

Answer:

1000 tennis balls will produce the minimum  cost

Step-by-step explanation:

Daily cost equation of tennis ball : [tex]C(x)=200-10x+0.01x^2[/tex]

Where C(x)  is the  total cost in dollars

x is the number of tennis balls produced

We are supposed to find number of tennis balls will produce the minimum

cost.

Lead coefficient = 0.01

The lead coefficient is positive, the parabola opens up.

Thus ,the minimum is at the vertex.

[tex]x=\frac{-b}{2a}[/tex]

So, [tex]x= \frac{10}{0.01}\\x=1000[/tex]

Substitute the value of x in given equation:

C(x)=200-10(1000)+0.01(1000)^2

C(x)=200

Hence 1000 tennis balls will produce the minimum  cost

Answer:

The answer is C in my opinion and it is one of confusing question i have ever seen

Step-by-step explanation:

If he scored 351 points last years and he plays 18 games this year and if we want to know the points that he need to beat last year score in thsi year we need to divide 351÷18=19.5 so he will need to have no morethan 20 points because 19.5 is also enough to get the score

I hope u like it

Answer:

z = -8

Step-by-step explanation:

I'm guessing you want to find out what z is equal to, so here you go.

2z - 1 = -9 + z

2z = -8 + z

z = -8

Answer:

z = -8

Step-by-step explanation:

let's simplify the equation by getting the like terms together.

2z-1 = -9+z

first get the z's on the same side:

2z-z-1 = -9

z-1 = 9

then the constants:

z = -9+1

z = -8

Given :

Monthly practice time , T=35 hours .

This month, he has practiced 8.5 hours in week 1, 12 hours in week 2, and 5.5 hours in week 3.

To Find :

Many more hours of practice time does Jason need to complete .

Solution :

Number of hours he practice in week 1 , [tex]t_1=8.5\ hours[/tex] .

Number of hours he practice in week 2 , [tex]t_2=12\ hours[/tex] .

Number of hours he practice in week 3 , [tex]t_3=5.5\ hours[/tex] .

Now , number of hours left is :

[tex]t=T-t_1-t_2-t_3\\\\t=35-(8.5+12+5.5)\ hours\\\\t=8\ hours[/tex]

Hence , this is the required solution .

Step-by-step explanation:

Hey, there!!

Given,

cos theta = 0.5

To convert it into angle, you have to take cos to right side making it (cos inverse).

Therefore, theta = cos inverse (0.5)

= 60°.

Hope it helps......

Answer:

B and D

Step-by-step explanation:

5% of 35 can be represented as 5% [tex]\cdot35[/tex].

To find equations that make this work, we need to find different ways to represent 5%.

5% can be represented as fraction - over 100. The percentage over 100 will be equal to the percent.

So, [tex]\frac{5}{100}[/tex]. Multiplying by 35 gets us [tex]\frac{5}{100}\cdot35[/tex]

This means that Choice B is correct.

Another way to represent 5% is as a decimal.

We already know that the fraction form of 5% is [tex]\frac{5}{100}[/tex]. This means that in the decimal, the number 5 will be two place values to the right of the decimal place.

0.05

So the decimal expansion of 5% is 0.05. Multiplyin by 35 get us [tex]0.05\cdot35[/tex], so choice D works too.

Hope this helped!

Answer:

Step-by-step explanation:

To find the the value of the percentage of a number divide the percentage by 100 and multiply it by the number

So we have

5 percent of 35 is written as

[tex] \frac{5}{100} \times 35 \\ = \frac{1}{20} \times 35 \\ = \frac{7}{4} [/tex]

We have the answer as

1.75

From the options the one that has the same value as the above answer are

0.05 × 35 and 5/100 × 35

Hope this helps you

Answer: 10 Feet by 15 Feet

Step-by-step explanation:

Answer:

1=27

2=34

Step-by-step explanation:

1)9y power 2÷3

or, y=9 power 2÷3

or, y=9×9÷3

or, y=81÷3

or, y=27

2) (8x power 2+4x)÷2

=(8x×8+4x)÷2

=(64x+4x)÷2

=68x÷2

or, x=68÷2

or, x=34

Answer:

A Blue Viper

Step-by-step explanation:

A Blue Viper can travel 18 2/5 miles on 4/5  tank of gas.

It can travel on full tank:

A Red Rocket can travel 17 2/5 miles on 3/4 tank of gas.

It can travel on full tank:

A Blue Viper can travel further as:

Answer:

Step-by-step explanation:

[tex]4+3\left(15-2^3\right)\\\\3\left(15-2^3\right)=21\\\\=4+21\\\\=25[/tex]

Answer:

25

Step-by-step explanation:

4+3(15-2^(3)

4+3(15-(2*2*2)

4+3(15-8)

4+3(7)

4+21=25

Answer: yes

Step-by-step explanation:

Answer:

I think so

Step-by-step explanation:

I think all numbers are technically natural

Answer:

Step-by-step explanation:

The real part is everything that does not multiply i. The imaginary part is everything that does multiply i.

Conventionally, the real part is written first:

  z = -32 +73i

Re(z) = -32

Im(z) = 73