Fisher Auto Parts is running a 45% clearance sale on batteries. One battery cost $149.99. If the consumer purchases 2 batteries. What would be the final cost?
Sales tax is 5%.

Step-by-step explanation:

the original side length is x.

the volume of a block is length × width × height.

so, for a cube with all sides being equal, the volume in our case is x³ (x × x × x).

now, with the same formula but with every side shortened by 1 cm we get

(x-1)(x-1)(x-1) = x³ - 91 (the original volume minus 91)

now, we have to do the multiplications.

(x-1)(x-1) = x² - 2x + 1

(x²-2x+1)(x-1) = x³ - x² - 2x² + 2x + x - 1 = x³ -3x² + 3x -1

x³ - 3x² + 3x - 1 = x³ - 91

-3x² + 3x = -90

-x² + x = -30

x² - x = 30

x² - x - 30 = 0

the general solution to such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -1

c = -30

x = (1 ± sqrt((-1)² - 4×1×-30))/(2×1) =

= (1 ± sqrt(1 + 120))/2 = (1 ± sqrt(121))/2 =

= (1 ± 11)/2

x1 = (1 + 11)/2 = 12/2 = 6

x2 = (1 - 11)/2 = -10/2 = -5

a negative number does not make any sense for a side length, so our solution is x = 6 cm.

the original side length of the cube is 6 cm.

to check :

6³ = 216

(6-1)³ = 5³ = 125

216 - 125 = 91

perfect.

Answer:

10.38 = 0.60b + 1.74p

Step-by-step explanation:

Let's see

[tex]\\ \rm\rightarrowtail (fog)(x)=f(g(x))[/tex]

[tex]\\ \rm\rightarrowtail f(5x-4)=20x+p[/tex]

[tex]\\ \rm\rightarrowtail 4(5x-4)+3=20x+p[/tex]

[tex]\\ \rm\rightarrowtail 20x-16+3=20x+p[/tex]

[tex]\\ \rm\rightarrowtail -13=p[/tex]

Answer:

[tex]\sf p = -13[/tex]

Step-by-step explanation:

Given functions:

[tex]\sf f(x)=4x+3[/tex]

[tex]\sf g(x)=5x-4[/tex]

[tex]\sf fg(x)=20x+p[/tex]

[tex]\sf fg(x)=f[g(x)][/tex]

This means g(x) is substituted for x in f(x).

[tex]\sf \implies f[g(x)]=4[g(x)]+3[/tex]

                 [tex]\sf =4(5x-4)+3[/tex]

                  [tex]\sf= 20x-16+3[/tex]

                  [tex]\sf =20x-13[/tex]

[tex]\sf f[g(x)]=f[g(x)][/tex]

[tex]\sf \implies 20x+p=20x-13[/tex]

[tex]\sf \implies p=-13[/tex]

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: log_{4}(39.2) [/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{4}( {2}^{3} \times {7}^{2} \times 10 {}^{ - 1} ) [/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{4}( {2}^{3} ) + log_{4}( {7}^{2} ) + log_{4}(10 {}^{ - 1} ) [/tex]

[tex]\qquad \sf  \dashrightarrow \: log_{ {2}^{2} }( {2}^{3} ) + log_{ {2}^{2} }( {7}^{2} ) + log_{ {2}^{2} }(10 {}^{ - 1} ) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{3}{2} log_{2}(2) + \frac{2}{2} log_{2}(7) - \frac{1}{2} log_{2}(10) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \frac{3}{2} + a - \frac{b}{2} [/tex]

That's the required result ~

also you can take it's LCM and write it as :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2a - b + 3}{2} [/tex]

Answer:

Im confused w ur question or i dont know maybe im just dum.b

Step-by-step explanation:

The length of the side AB and side CD of kite abcd which is shown in the figure is 15 units and 20 units respectively.

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

Let the intersection point of dignoals is O. The figure of the kite ABCD, is attached below. The sides of the kite ABCD, are,

[tex]AO=12\\OB=9\\CO=12\\OD=16[/tex]

In the triangle AOB using the pythagours theorem,

[tex]AB=\sqrt{(AO)^2+(OB)^2}\\AB=\sqrt{(12)^2+(9)^2}\\AB=\sqrt{225}\\AB=15[/tex]

Similarly, in the triangle DOC using the pythagours theorem,

[tex]CD=\sqrt{(CO)^2+(OD)^2}\\CD=\sqrt{(12)^2+(16)^2}\\CD=\sqrt{400}\\CD=20[/tex]

Thus, the length of the side AB and side CD of kite abcd which is shown in the figure is 15 units and 20 units respectively.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

Answer:

its B

Step-by-step explanation:

Answer:

The student spent 48 minutes and 45 seconds playing basketball.

Answer:

[tex]\frac{5}{36}[/tex]

Step-by-step explanation:

the total number of possible combinations of rolling two dice is 36 because a side has 6 sides and [tex]6^{2}=36[/tex]

and possible combinations that sum to 8 are

which are 5 possible combinations which gives [tex]\frac{5}{36}[/tex]

The volume of the larger cone is about 18.8 cubic inches greater than the volume of the small cone

The volume of a cone is calculated as:

For the small cone, we have the following parameters:

Diameter = 3 inches

Height = 3.5 inches

Diameter = 4.5 inches

Height = 5.1 inches

So, the volume of the large cone is:

Calculate the difference of both volumes

Hence, the volume of the larger cone is about 18.8 cubic inches greater than the volume of the small cone

Read more about volumes at:

brainly.com/question/8994737

Answer:

127

Step-by-step explanation:

Given :

On differentiating,

At x = 2

First differentiate

So

[tex]\\ \rm\Rrightarrow \dfrac{d}{dx}(30x^2+7x)[/tex]

[tex]\\ \rm\Rrightarrow 60x+7[/tex]

Put x=2

Answer: 6 units squared.

Step-by-step explanation: The equation for area of a triangle is 1/2 * length of base * the length of the height.

The length of the base is D to E, which is 3 units.

The length of the height is from F to the base of the triangle, which is 4 units.

Therefore, the area of the triangle would be 1/2 * 3 * 4 = 6 units squared.

Answer:

1 and 7

Step-by-step explanation:

let me know if this is helpful!

[tex]a = 6(4) - 3 = 24 - 3 = 21[/tex]

Answer:

44.5 percent is shaded.

from whole model, 44.5% is shaded of 100%

Answer:  "How do u calculate the diameter of a circle"?

Step-by-step explanation:  Calculating diameter is easy you just need the radius, the circumference, or the area. Even if you don't have any of those dimensions, you can still find the diameter if you have a drawing of the circle.

Answer:

14/23

Step-by-step explanation:

There are 253 tokens in all. Since 77 are blue and 77 are green, the probability of selecting either a blue token or a green token is 154/253, which reduces to 14/23.

Answer:

11. b

10.d

9.c

7.b

1.d

the rest I can't see clearly

please give brainiest

Step-by-step explanation:

11.

3/x-4=7/x

*cross multiply

3x=7 (x-4)

3x=7x-28

28=7x-3x

28=4x

x=7

10.

SOHCAHTOA

Cos☆=11/14

cos^-1 (11/14)

☆=38.21 degrees

9.

MLN CONGRUENT TO WBN

ML/WB=LN/BN=MN/WN

LN/BN=10/6

ML/WB

24/x=10/6

24x6=10x

144÷10

=14.4

6^2+14.4^2

=243.36

squareroot

=15.6

The explicit rule formula an = -2n + 8 is an arithmetic progression

The value of a11 is -14

The explicit rule formula is given as:

an = -2n + 8

Substitute 11 for n to calculate a11

a11 = -2 * 11 + 8

Evaluate the product

a11 = -22 + 8

Evaluate the sum

a11 = -14

Hence, the value of a11 is -14

Read more about explicit rules at:

https://brainly.com/question/12119793

Answer:

the decimal is 1.75 and  The percentage is 175%

Step-by-step explanation:

Answer:

2x + y = 5

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = - 2x + 5 ( add 2x to both sides )

2x + y = 5 ← in standard form

Answer:

 y=-2x+5 as standard form is 2x+y=5

Answer:

year boy built an igloo =3/4

year3 girl built same igloo=3/7

To find out all together how much have built =3/4+3/7

if we take alceam

4×7=28

in fraction down we need to make 28

so 3/4 we multiply by 7 and 3/7we multiply by 4

3×7/4×7+3×4/7×4=21/28+12/28=21+12/28

33/28

to find out we divide fraction we will know what left .

1,5/28

5is left.

Answer: 26 degrees

Step-by-step explanation:

An interior angle and its exterior angle are supplementary.

Answer:

C, D, and E are the answers.

Answer:

118.25

Step-by-step explanation:

Answer:

8:20 or if you want it simplified 2:5

Step-by-step explanation:

[tex]\displaystyle \int csc^2(9x) dx \\\\=\dfrac 19\displaystyle \int \csc^2 u ~du~~~~~~~;\left[\text{Let}~u= 9x \implies dx = \dfrac{du}9\right]\\\\=-\dfrac 19 \cot u + C\\\\=-\dfrac 19 \cot(9x)+C[/tex]

Answer:

a)0.012 kg

b)0.007kg

c)35.015kg

d)0.675kg

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

10% = 15.30

40%=61.20

1% = 1.53

2%=3.06

61.20+3.06=64.26

153+ 64.26=217.26