MATHEMATICS COLLEGE

If log(x+3)-log(x-5)=log2What is the value of x?

Please answer with explanation and process

Answers

Answer 1
Answer: We use log(x) - log(y) = log(x/y) and log(x) = log(y) ⇔ x = y

\displaystyle\log(x+3) - \log(x-5) = \log 2 \implies \log\left( (x+3)/(x-5) \right) = \log 2 \implies \n \n (x+3)/(x-5) = 2 \impliesx+3 = 2(x-5) \n \nx = 13

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Jarvis works in a garage for $9 an hour. If he works on saturday he is paid time and a quarter. if he works on sunday he is paid time and three quarters. Last weekend jarvis worked for four hours on Saturday and four hours on Sunday. -How much was Jarvis paid last week all together?
-Hours paid Saturday=
-Hours paid Sunday=
-Total Hours paid=

Answers

Answer:

Total Earned Saturday: $45

Total Earned Sunday: $63

Total: $108

Step-by-step explanation:

Time and a quarter means that you divide his normal rate by 4 and add that to his normal rate:

9/4 = 2.25     2.25 + 9 = 11.25

Jarvis makes $11.25 an hour on Saturdays. Since he worked 4 hours, you multiply 11.25 x 4 = 45.

Time and three quarters means that you multiply his normal rate by 3/4 and add that to his normal rate:

9x0.75 = 6.75     6.75 + 9 = 15.75

Jarvis makes $15.75 an hour on Sundays. Since he worked 4 hours, you multiply 15.75 x 4 = 63.

To get the total, you add his earnings on Saturday and earnings on Sunday:

45 + 63 = 108.

I hope this helped you. If it did, please feel free to rate and press thanks! Have a splendid day.

Answer:

72

Step-by-step explanation:

If he worked on saturday for four hours  he got 36 dollars and worked the same time on sunday he 36+36=72 dollars

Which of the following constants can be added to x2 + x to form a perfect square trinomial?

Answers

Answer:

x^2+x + 1/4

Step-by-step explanation:

x^2+x

Take the coefficient of x

1

divide by 2

1/2

Square it

(1/2)^2 = 1/4

Add this to make a perfect square trinomial

At swim practice, several swimmers take turns, swimming 100 meters each. The total distance they swim is less than 1,200 meters. Which inequality can be solved to determine, s, the possible number of swimmers?1,200 greater-than 100 s
1,200 less-than 100 s
1,200 s greater-than 100
1,200 s less-than 100

Answers

Answer:

1,200 greater-than 100 s

Step-by-step explanation:

Each swimmer swims 100m.

So the total distance they swim is given by:

T = 100s.

The total distance they swim is less than 1,200 meters.

This means that:

T < 1200

So

100s < 1200

Or

1200 greater than 100s.

So the correct answer is:

1,200 greater-than 100 s

Answer:

A

Step-by-step explanation:

You buy six pens for $2.99 each, and sales tax is 10%. How much change should you receive from a clerk if you give her a $20 bill?

Answers

Answer:

$2.06

Step-by-step explanation:

$2.99 x 6 = $17.94

$20.00 - $17.94 = $2.06

Hope this helps

Answer: $0.26

Step-by-step explanation:

Cost of 6 pens

= 2.99 x 6

= 17.94

Add sales tax at 10%,

= 17.94 x 1.1

= 19.74

Change due to me

= 20 - 19.74

= 0.26

If a sphere fits snugly inside a cube with 34-in edges. What’s is the approximate volume of the space between the sphere and cube

Answers

The volume of the space between the sphere and cube is equal to the volume of the sphere subtracted from the volume of the cube:

V_{}=V_(cube)-V_(sphere)

The volume of a cube is:

V=s^3

s is the length of each edge in the cube

The volume of a sphere is:

V=(4)/(3)\pi\cdot r^3

The diameter of the sphere is equal to the edge of the cube, then, its radiusr is:

r=(s)/(2)

Then, the volume of the space between the sphere and cube is:

V=s^3-(4)/(3)\pi\cdot((s)/(2))^3

s is 34 in

\begin{gathered} V=(34in)^3-(4)/(3)\pi\cdot((34in)/(2))^3 \n \n V=39304in^3-(4)/(3)\pi\cdot(17in)^3 \n \n V=39304in^3-(4)/(3)\pi\cdot4913in^3 \n \n V=39304in^3-(19652\pi)/(3)in^3 \n \n V\approx18724.47in^3 \end{gathered}Then, the approximate volume of the space between the sphere and cube is 18724,47 cubic inches

Drag each figure to show if it is similar to the figure shown or why it is not similar

Answers

Answer:

In the given shapes above, we can see that all shapes have four sides.

Above geometrical shapes could be named as Rectangles, parallelogram or quadrilateral.

First two shapes are Rectangles.

Third is a parallelogram.

Fourth and fifth shapes are Rectangles again.

Also we can say all those shapes with four side as quadrilaterals. (Note: A quadrilateral has four sides.)

Below shown shape has only three sides in it.

It is called a triangle when a shape has three sided close figure.

So, we could drag : Not similar - Different Type of shape.
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