A number pattern was created by dividing the previous term by 3. If the starting value for the pattern was 135, which of the following shows the resulting pattern?
A.
135, 45, 30, 5...
B.
135, 45, 15, 5...
C.
135, 45, 15, 2...
D.
135, 45, 30, 25...

Answer:

a) [tex]( -[/tex]∞[tex], -\frac{4}{3}[/tex][tex])[/tex] ∪ [tex](-\frac{4}{3}[/tex] , ∞[tex])[/tex]

b) [tex][-\frac{5}{2} ,[/tex] ∞)

Step-by-step explanation:

The domain of a function is known as the input. We need to find whatever set of numbers can be plugged into every x of a function so that the result is a real number.

a) This problem is a fraction alone, so we need to find out what input of x will make the denominator zero - that will be the number we "skip" when writing out the domain. This is because if the denominator were zero, then it would be 1 divided by 0, which would be undefined and therefore not a real number.

To find this number, we can just take the denominator and solve for x:

[tex]3x + 4 = 0[/tex]

[tex]3x = -4\\x = -\frac{4}{3}[/tex]

Therefore [tex](-[/tex]∞, [tex]-\frac{4}{3}[/tex]) ∪ [tex](-\frac{4}{3},[/tex] ∞[tex])[/tex] is our answer.

b) This problem is just a square root alone, so we need to find out what input of x will make the number inside the square root negative - that number, and the numbers less than it, will be the numbers that we "skip." This is because if the number inside the square root was negative, then it would produce an imaginary answer and not a real one.

A simple trick to find the domain would be to set the terms inside the square root greater than or equal to 0 then solve for x:

[tex]2x + 5\geq 0 \\2x \geq -5\\\\x \geq \frac{-5}{2}[/tex]

Thus, the domain would be any number greater than or equal to [tex]-\frac{5}{2}[/tex], which in interval notation would be written [tex][-\frac{5}{2} ,[/tex] ∞).

Answer:

-0.1, -0.02, [tex]\frac{5}{6}[/tex], [tex]|\frac{9}{8}|[/tex], 10

Step-by-step explanation:

Answer:

x = [tex]\sqrt{3}[/tex]/6

Step-by-step explanation:

30-60-90 triangles have legs in the ratio of 1 : [tex]\sqrt{3}[/tex] : 2

create a proportion:  (6 ÷[tex]\sqrt{3}[/tex]) = (1÷x)

cross-multiply:  6x = [tex]\sqrt{3}[/tex]

divide by 6

                                          Question No 7

Answer:

Please check the explanation.

Step-by-step explanation:

Show that 4x - x² - 7 is always negative.

Given

4x - x² - 7

4x - x² - 7 is always negative because:

Hence, 4x - x² - 7 is always negative

For example,

let suppose we enter x = 1

[tex]4(1)-1^{2} -7\\=4-1-7\\=4-8\\=-4[/tex]

let suppose we enter x = -1

[tex]4(-1)-(-1)^{2} - 7\\= -4 - 1 - 7\\= -12[/tex]

Answer:

New Coordinates W(-4, 5), X(-5, 6), (-8, 8), 2(-8,6)

Answer:

12

Step-by-step explanation:

Answer:

P=104

Step-by-step explanation:

-212+316=104

therefore p=104

Answer:

5y

Step-by-step explanation:

Answer:

m∠C = 44°

Step-by-step explanation:

In ΔCDE,

m∠C=(4x−16) ∘

m∠D=(6x−1) ∘

m∠E=(4x−13) ∘ .

The sum of angles in a triangle = 180°

Step 1

We solve for x

m∠C + m∠D + m∠E

(4x−16)° + (6x−1)° + (4x−13)° = 180°

4x - 16 + 6x - 1 + 4x - 13 = 180°

4x + 6x + 4x -16 - 1 - 13 = 180°

14x - 30 = 180°

14x = 180+ 30

14x = 210

x = 210/14

x = 15

Step 2

Find m∠C

m∠C = (4x−16)°

m∠C = (4 × 15 - 16)°

m∠C = (60 - 16)°

m∠C = 44°

Answer:

0.7>0.54

Step-by-step explanation:

Answer:

A. parallel lines

You can also use the app desmos to help you graph equations.

Answer:

The length of the first piece is 0.51 m

The length of the second piece is 0.31 m

The length of the third piece is 0.28 m

Step-by-step explanation:

The question is a simultaneous equation with word problem

The total length of the wood = 0.9 m

The number of pieces the wood is cut into = 3

The length of the first piece = 0.2 m + The length of the second piece

The length of the third piece = The length of the second piece - 0.23 m

Let "y" represent the length of the second piece, let "x" represent the length of the first piece, and let "z" represent the length of the third piece, we have;

x = 0.2 + y...(1)

z = y - 0.23...(2)

x + y + z = 0.9...(3)

Therefore, by substitution, we have;

0.2 + y + y + y - 0.23 = 0.9

3·y - 0.03 = 0.9

3·y = 0.9 + 0.03 = 0.93

y = 0.93/3 = 0.31

y = 0.31

The length of the second piece = y = 0.31 m

From equation (1), we have;

x = 0.2 + y = 0.2 + 0.31 = 0.51

x = 0.51

The length of the first piece = x = 0.51 m

From equation (2), we have;

z = y - 0.23

z = 0.51 - 0.23 = 0.28

z = 0.28

The length of the third piece = z = 0.28 m.

Answer:

no

Step-by-step explanation:

linear functions have straight lines

so this is not a linear function

Answer:

y=-3.571

Step-by-step explanation:

To get rid of the x's make the other x cancel out the other.

5x-y=25+(-5(x+4y=-10)=-21y=75= -3.571

Answer:

x+4y =10

5x-y =25

Step-by-step explanation:

x=10-4y

5(10-4y)-y =25

50-20y-y =25

50-21y = 25

-21y = 25-50

-21y =-25

y =25/21

Substitute y =25/21 in equation 1

x + 4(25/21) = 10

x +100/84 =10

x=10-100/84

Answer:

Lower bound = 3.835

Upper bound = 3.844

Step-by-step explanation:

Given,

A number rounded to 2 decimal place = 3.84

In other to obtain the least and greatest number, we are mostly concerned about the third digit after the decimal point.

Knowing that numbers 5 and above are rounded to 1 while numbers below 5 are rounded to Zero.

Hence, the lower bound should have its original hundredth value as (4 - 1) such that it becomes 4 when the thousandth value is rounded to 1.

Lower bound = 3.835

The upper bound should have its thousandth value as one which is rounded to Zero, just a point below 5

Upper bound = 3.844

Answer:

Step-by-step explanation:

yes his work looks good

step 1   multiply both side by 2

step 2 subtract both side by 6

step 3 divide both side by 5

:)

Answer:

the second one

Step-by-step explanation:

Answer:

y

Step-by-step explanation:

Answer: I don't know I'm sorry

Answer:

a) [tex]5\sqrt{3} + 3\sqrt{5}[/tex]

b) [tex]4(\sqrt{2} + \sqrt{7})[/tex]

Step-by-step explanation:

a) [tex]9\sqrt{3} - 4\sqrt{3} +\sqrt{5} + 2\sqrt{5}[/tex]

Taking √3 & √5 common respectively,

[tex]=> \sqrt{3} (9 - 4) + \sqrt{5} (1 + 2)[/tex]

[tex]=> 5\sqrt{3} + 3\sqrt{5}[/tex]

b) [tex]10\sqrt{2} + 4\sqrt{7} - 6\sqrt{2}[/tex]

Taking √2 common ,

[tex]=> \sqrt{2} (10-6) + 4\sqrt{7}[/tex]

[tex]=> 4\sqrt{2} + 4\sqrt{7}[/tex]

Taking 4 common ,

[tex]=> 4(\sqrt{2} + \sqrt{7})[/tex]

Answer:

Top Right Problem: PACKAGE #2 and $0.80

Bottom left: BAND and $0.05

Bottom Right: PEPSI and $0.05

Answer:

x=35

Step-by-step explanation:

A pentagon's sum of interior angles is 540 degrees.

Now, we can set up an equation.

(4x - 57) + (3x + 15) + 4x + (2x - 3) (3x + 25) = 540

Combine similar terms

16x - 20 = 540

16x = 560

x = 35

Answer:

= 12n + 19

Step-by-step explanation:

Answer:

10/16

Step-by-step explanation:

Find the common factor between both

5/8 = 10/16

10/16 > 3/16

Answer:

b. – 0.4(x + 1.6) = 1.6

Step-by-step explanation:

The equation with negative solution is -

- 0.4(x + 1.6) = 1.6

Given are the equations as shown in the question.

The equation with the negative solution are -

- 0.4(x + 1.6) = 1.6

- 0.4x - 0.64 = 1.6

- 0.4x = 1.6 + 0.64

- 0.4x = 2.24

x = - (2.24/0.4)

Therefore, the equation with negative solution is -

- 0.4(x + 1.6) = 1.6.

To solve more questions on algebraic expressions, visit the link below-

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