Daniel had 1,868 in his bank account before he left for North Carolina. He wrote a check for $710 to pay his monthly truck payment. He also wrote a check for $224.89 to Farm Bureau Insurance Company for his truck insurance. When he got home from North Carolina he deposited his paycheck in the amount of $4,020.67. What was the balance in his bank account after he deposited his paycheck?

Solution:

[tex]\text G\text i\text v\text e\text n\ \text e\text x\text p\text r\text e\text s\text s\text i\text o\text n: 20x^{3} + 34x^{2} + 6x[/tex]

Step-1: Find the GCF of the terms.

[tex]20x^{3} \ \ \ = \ \ \ 2 \times 2 \times 5 \times x \times x \times x \\34x^{2} \ \ \ = \ \ \ 2 \times 17 \times x \times x \\ 6x \ \ \ \ \ \ = \ \ \ 2 \times 3 \times x[/tex]

GCF = 2x

Step-2: Factor the expression using the GCF.

[tex]20x^{3} + 34x^{2} + 6x \\\\ {2x(10x^{2} + 17x + 3)}[/tex]

Step-3: Further factorize.

[tex]{2x(10x^{2} + 17x + 3)}[/tex]

[tex]2x(2x + 3)(5x + 1)[/tex]

Thus, the factorized expression is [tex]2x(2x + 3)(5x + 1)[/tex].

Answer: 121 meters

Step-by-step explanation:

In picture

Answer:

If the * is supposed to be multiplication, then my answer is : 2(x-y)/(x^2+y^2-xy)

Step-by-step explanation:

Answer:

Length = 45m

Breadth = 15m

Step-by-step explanation:

Dimensions of Rectangular field:

Let the breadth (B)=BC = x m

Length (L) = AB = 3x m

width of the road (w) = 5 m

Dimensions of inner rectangle:

length (l) = EF = L-2w

= 3x - 2×5

= (3x-10) m

breadth (b)=EH = B-2w

= (x-10) m

Given ,

Area of the path =500 m²

=> Area of ABCD - Area of EFGH = 500

=> L×B - l×b=500

=> (3x)× x - (3x-10)(x-10)=500

=> 3x²-(3x²-30x-10x+100)=500

=> 3x²-3x²+30x+10x-100=500

=> 40x=500+100

=> 40x = 600

=> x = 600/40

=> x = 15

Therefore,

Length (L) = 3x = 3×15 = 45m

Breadth (B) = x = 15m

Mark me as brainliest if it was helpful

Answer:

-2.8 or -14/5

Step-by-step explanation:

To divide one fraction by another, there is a really cool method called Keep Change Flip

Keep the first fraction

Change the division sign to multiplication

Flip the numbers on the last fraction

Let's try it out.

Keep the 1/5

Change the ÷ to a ×

Flip the -1/14 to a -14/1

1/5 × -14/1

Multiply the top numbers by each other first

1 × -14 = -14

Now the bottom numbers

5 × -1 = -5

The fraction we have now is -14/5

It can also be written as -2.8

Answer:

2,5

Step-by-step explanation:

since radius is 5

each point lies on the circumference that has 5 or -5 in its y coordinates must have -3 in its x coordinate because -3 is the center

then option number 1 is incorrect

second option is correct , -3 + ( -5 ) = -8

third option is correct, -3 + 5 = 2

fourth is correct, -3 is the center and 5 steps on y axis

fifth is the same as fourth but opposite direction

so the first one is the exception

3m + 8 = 15 is not a quadratic equation. quadratic equation must have the power of 2 in the quadratic term.

Answer:

Definitely not.

Step-by-step explanation:

3m+8=15

A quadratic equation needs to consist of these values:

x^2+x+y

In this case x can be followed by any coefficient but needs to end with a variable to the power of 2. The second part of this question needs to have that variable- but to no power. Finally, the third part is just a regular integer. We can tell 3m+8=15 is not a quadratic because while it has a variable and integer, it does not have a variable to the power of two.

please mark me as brainliest....................

==========================================

Work Shown:

f(x) = x^3 - x^2 + x - 1

f ' (x) = 3x^2 - 2x + 1

f ' (2) = 3(2)^2 - 2(2) + 1

f ' (2) = 9

In step 2, I used the power rule [tex]\frac{d}{dx}x^n = nx^{n-1}[/tex]

Answer:

Multiplicative Identity

Step-by-step explanation:

This is what they all basically mean:

Additive Identity - addition

Associative Property - simplifying

Distributive Property - multiplying brackets, or expanding

Multiplicative Identity - multiplication

In this equation, you first expand 16(4x-1) which uses multiplication but only has one bracket meaning, you use multiplicative identity first.

Answer:

Karen: 16

Justin :18
Austin:36

Step-by-step explanation:

you don’t need one- I’m smart soooo-

Answer:

83, acute

Step-by-step explanation:

49 + 48 + x = 180

97 + x = 180

x = 83

All angles are smaller than 90 so they all are acute and that makes this trinagle an acute triangle. So cute! :)

Have a great day!!

Please rate and mark brainliest!!

Answer:

[tex]-2b^2+17b-15[/tex]

Step-by-step explanation:

Given expression:

[tex](b^2+13b-9)-(6-4b+3b^2)[/tex]

Apply rule [tex](a)=a[/tex]:

[tex]=b^2+13b-9-(6-4b+3b^2)[/tex]

Apply the distributive law  [tex]-(a-b)=-a+b[/tex] :

[tex]=b^2+13b-9-6+4b-3b^2[/tex]

Subtract the numbers:

[tex]=b^2+13b-15+4b-3b^2[/tex]

Group like terms:

[tex]=b^2-3b^2+13b+4b-15[/tex]

Combine like terms:

[tex]=-2b^2+17b-15[/tex]

Answer:The solution is in the attached file

Step-by-step explanation:

Answer:

14 hours

Step-by-step explanation:

Find the rate of what he earns per hour.

150 ÷ 4 = $37.50

Divide $525 with the rate:

525 ÷ 37.50 = 14

It would take him 14 hours

Answer:

True, the diameter=2in and the circumference=6.28

Step-by-step explanation:

The circumference, C, of a circle is found by the following equation: C = 2 x pi x r where r equals the radius of the circle (or half its diameter) and pi = 3.14159 (a constant).

Thus, 6.28 = 2 x pi x r

Solving for r: 6.28/(2 x pi) = r

or: 6.28/(2 x 3.14) = 6.28/6.28 = r

thus r = 1 and since the diameter equals 2 x r, the diameter is 2.

Answer:

25.12 feet

.............................

Answer:

C = 25.12 Ft.

Step-by-step explanation:

Formula: C = 2πr

C = 2π (4)

C = 8π

C = 8 (3.14)

C = 25.12 Feet

Answer:

11

Step-by-step explanation:

Because it's +5 every number

Answer:

11

Step-by-step explanation:

-9 +5=-4

-4+5=1

1+5=6

6+5=11

Answer: 40 degrees

Step-by-step explanation:

Answer:

q=13

Step-by-step explanation:

First, you can multiply to distribute 2 over -9 and 4.

-18=2(-q+4)

-18=-2q+8

Then, you can subtract 8 from both sides.

-18=-2q+8

-26=-2q

Finally, you can divide -2 on both sides.

13=q

Now, you can check by plugging in 13 for the value of q in the original equation.

-18=2(-(13)+4)

-18=2(-13+4)

-18=2(-9)

-18=-18

Hope this helps you! :)

Answer:

This matrix is amplified by exponential sequencing

Answer:

Step-by-step explanation:

Answer:

(-3, 7)

Step-by-step explanation:

The rotation of an object turns the object around a fixed point called the center of rotation.  

Positive rotations are counterclockwise.

Negative rotations are clockwise.

Therefore, rotation of 90° about the origin means a 90° rotation counterclockwise with (0, 0) as the center of rotation.

The rule for rotation of 90° about the origin is:

(x, y) → (-y, x)

Therefore  (7, 3) → (-3, 7)

The rule of 90° rotation about the origin is

Here given point is

The new point is

Answer:

41

Step-by-step explanation:

You do 50% of 82 which is 41.

Answer: 41 empty barrels

Step-by-step explanation:

if Jack rolled 82 total barrels and 50% of them were empty, that is the same as taking 82 times .5, which gives us 41. This is how we know he rolled 41 empty barrels onto the ships deck.

Answer:

yes

Step-by-step explanation:

Answer:

x= -7              x= 5

Step-by-step explanation:

2x + 1 = -13

    -1      -1

2x    =   -14

/2           /2

x       =    -7

x + 2 + 4 = 11

x + 6 = 11

  -6    -6

x      =   5

hope this helps (:

The solutions of the given linear equations are:  x = 7, - 13; x = 6, - 7; x = 5, - 9, respectively.

A linear equation is an equation that has on or multiple variables with the highest power of the variable is 1.

Given equations are:

1. |3x + 9| = 30

⇒ ( |3x + 9| )² = (30)²

⇒ 9x² + 54x + 81 = 900

⇒ 9x² + 54x + 81 - 900 = 0

⇒ 9x² + 54x - 819 = 0

⇒ 9(x² + 6x - 91) = 0

⇒ (x² + 6x - 91) = 0

⇒ (x + 13)(x - 7) = 0

⇒ x = 7, - 13

2. |2x+1| = - 13

⇒ (|2x+1|)² = (- 13)²

⇒ 4x² + 4x + 1 = 169

⇒ 4x² + 4x - 168 = 0

⇒ 4(x² + x - 42)= 0

⇒ (x² + x - 42)= 0

⇒(x - 6)(x + 7) = 0

⇒ x = 6, - 7

3. |x + 2| + 4 = 11

⇒ |x + 2| = 7

⇒ (|x + 2|)² = 7²

⇒ x² + 4x + 4 = 49

⇒ x² + 4x - 45 = 0

⇒ (x - 5)(x + 9) = 0

⇒ x = 5, - 9

Learn more about linear equation here: https://brainly.com/question/17038547

#SPJ3

Answer: 50 cents per can

Step-by-step explanation: you do 2.50 divided by 5

Answer:

50 cents per can

Step-by-step explanation:

use a calculator and divide 2.50 by 5

The mean of the data set is 6.8.

Mean is the average value of the given set of observations. In statistics, we also come across different types of mean such as Arithmetic, Geometric and Harmonic mean.

Given

The data set is 14, 7, 2, 8, 3.

The mean of the data set is given by;

[tex]\rm Mean = \dfrac{Sum \ of \ all \ data}{Number \ of \ data}\\\\Mean =\dfrac{14+7+2+8+3}{5}\\\\Mean = \dfrac{34}{5}\\\\Mean=6.8[/tex]

Hence, the mean of the data set is 6.8.

To know more about mean value click the link given below.

https://brainly.com/question/4209766