11. The temperature was 81°F at 4PM and steadily decreased 3° each hour. What was the
temperature at 8PM?

Answer:

Step-by-step explanation:

Apply the natural log to both sides we have

[tex](-(2/3)x -1 ) \ln 2 = (3-2x)\ln 3\\-x(2/3)\ln 2 + 2x\ln 3 = 3\ln 3 -\ln 2\\x\left(\frac{-2}{3}\ln 2 +2\ln 3\right)=\ln (27/2)\\x\left(\ln 9 -\ln \sqrt{8}) =\ln(27/2)\\\\x\ln (9/\sqrt{8})=\ln(27/2)\\\\x= \ln(27/2) / \ln(9/\sqrt{8})[/tex]

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

Explanation:

The changes of this number are

The overall net change is -0.4+0.008+20 = 19.608

We'll be adding this net change to the original number

143.351 + 19.608 = 162.959

This value is exact and hasn't been rounded.

Answer:

Base: 24 and height:6

Step-by-step explanation:

Answer:

Base: 24

Height: 6

Step-by-step explanation:

The question says a scale factor of 1/2 so divide by 2. It says scale back

so you know as well that your answer is going to get bigger.

Original Base = 48/2 or (48)x(1/2)

Original Height = 12/2 or (12)x(1/2)

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 4

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

y -  [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~~~

m = - [tex]\frac{1}{2}[/tex]

( - 10, 1 )

y - 1 = - [tex]\frac{1}{2}[/tex] [ x - ( - 10 )]

y - 1 =  - [tex]\frac{1}{2}[/tex] x + ( - [tex]\frac{1}{2}[/tex] )(10)

y = - [tex]\frac{1}{2}[/tex] x - 4

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

Explanation:

Think of unwrapping a present and doing so without any unnecessary tearing. That means there aren't any little small pieces thrown away. There are many ways to unwrap a 3D box, and this diagram shows one of many ways. This flat layout is the 2D version of the 3D surfaces.

To find the surface area of the 3D figure, we simply need to find the area of each rectangle in this 2D flat net. Once we know all the little areas, we add them up to get the surface area.

------------------------------

The lowest rectangle is 3 cm by 5 cm, so its area is 3*5 = 15 cm^2. Let A = 15 so we can use it later.

Let's move to the middle row of four rectangles. From left to right, we have these four rectangular areas

I'll call these results B,C,D,E in the order given above. So B = 21, C = 35, etc.

The rectangle up top has area of 3*5 = 15 cm^2. I'll let F = 15

Lastly, we'll add up the sub-areas to get the grand total

A+B+C+D+E+F = 15+21+35+21+35+15 = 142 cm^2 is the surface area

------------------------------

Another pathway to the answer:

If you can picture how this flat diagram would fold up, then you would see that we'd get a 3D block with the following dimensions

The order of L,W,H doesn't really matter.

Then we can use the 3D block surface area formula like so

SA = 2*(LW + LH + WH)

SA = 2*(7*5 + 7*3 + 5*3)

SA = 2*(35 + 21 + 15)

SA = 2*71

SA = 142 cm^2 is the surface area

As you can see from the third step, we have "35", "21" and "15" show up again. The 2 out front is because we have 2 copies of each item mentioned.

Answer:

ALU stands for arithmetic logic unit. which is part of the central processing unit of a computer which performs arithmetic and logical operations.

I hope this helps

Answer:

In computer science: Architecture and organization. …of a control unit, an arithmetic logic unit (ALU), a memory unit, and input/output (I/O) controllers. The ALU performs simple addition, subtraction, multiplication, division, and logic operations, such as OR and AND.

Step-by-step explanation:

Answer:

50000 5000 200 20 2

Step-by-step explanation:

Step-by-step explanation:

Given line y=1/3x-4

slope of given line m=1/3

Slope of required line :

m=1/3

As lines are parallel then slope of lines are equal.

Using point slope form:

y-y1=m(x-x1)

p(x1,y1)=(9,8)

y-8=1/3(x-9)

3y-24=x-9

x-3y-9+24=0

x-3y+15=0

Note:if you need to ask any question please let me know.

An ordered pair is simply the x-coordinate and the y-coordinate of a point.

The ordered pair of the bullseye is (4,-2.5)

From the given image (see attachment), we have:

[tex](x_1,y_1) = (9,3)[/tex]

[tex](x_2,y_2) = (-1,-8)[/tex]

The bullseye is at the midpoint of these two points.

So, the ordered pair of the bullseye is calculated using the following midpoint formula.

[tex](x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

So, we have:

[tex](x,y) = (\frac{9-1}{2},\frac{3-8}{2})[/tex]

[tex](x,y) = (\frac{8}{2},\frac{-5}{2})[/tex]

[tex](x,y) = (4,-2.5)[/tex]

Hence, the ordered pair of the bullseye is (4,-2.5)

Read more about ordered pair at:

https://brainly.com/question/13688667

The answer is 56. work is shown below.

Step 1: apply 2nd power to everything inside parentheses

(7 - 1)² = 7² - 1²

Step 2: apply exponents (remember, exponents are a shorter way to express a number multiplied by itself a number of times).

1 x 1 = 1

7 x 7 = 49

Step 3: subtract

49 - 1 = 48

Step 4: apply exponent

2 x 2 x 2 x 2 = (2 x 2) x (2 x 2)

2 x 2 = 4

2 x 2 = 4

4 x 4 = 16

2⁴ = 16

Step 5: add

48 + 16 = 64

Step 6 (final step): subtract

64 - 8 = 56

final answer: 56

Step-by-step explanation:

Steps are in the picture above.

Answer:

3

Step-by-step explanation:

[tex]log(3x^{3}) - log(x^{2}) = log(\frac{3x^{3}}{x^{2}})\\log(27) - log(x) = log(\frac{27}{x} )\\[/tex]

therefore,

[tex]\frac{3x^{3} }{x^{2} } = \frac{27}{x} \\3x=\frac{27}{x} \\3x^{2} =27\\x= +3\\x=-3[/tex]

however, since logarithms cannot have negative arguments, x can only be +3

i.e. log(-3) is impossible, and will return MATH ERROR on a calculator.

Answer:

Answer is 4 I think!!

Answer:

-4x+1-10

Step-by-step explanation:

-2(2x+5)=0

-4x-10=0

-4x+1-10=0

-4x-9=0

-4x=9

x=9/-4

x=-2,25

please inform if wrong

Answer:

C

E

Step-by-step explanation:

Answer:

54.895

Step-by-step explanation:

hopes it's help you

Answer:

27

Step-by-step explanation:

3(5+1+3) distribute

15+ 3+ 9 add

27

Answer:

It is 1/10

Step-by-step explanation:

One decade has 10 years

[tex]{ \sf{1 \: decade = 10 \: years}} \\ { \sf{ \frac{1}{10} \: decade = 1 \: year}}[/tex]

Answer:

10% , 1/10, or 10/100

Step-by-step explanation:

There are 10 years in a decade

1/10 represents the 1 year out of the 10!

[tex](2a - 5)(4a - 7)[/tex]

[tex]2a(4a - 7) - 5(4a - 7)[/tex]

[tex]8 {a}^{2} - 14a - 20a + 35[/tex]

[tex]8 {a}^{2} - 34a + 35[/tex]

Step-by-step explanation:

( 2a - 5 ) ( 4a - 7 )

2a ( 4a - 7) - 5 ( 4a - 7 )

8a² - 14a - 20a + 35

8a² -34a + 35

Answer:

a = 5, b = - 13

Step-by-step explanation:

The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)

Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.

2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0

2(- 8) + 4a - 2b - 30 = 0

- 16 + 4a - 2b - 30 = 0

- 46 + 4a - 2b = 0 ( add 46 to both sides )

4a - 2b = 46 → (1)

----------------------------------------------------

Similarly when f(x) is divided by (cx - a) the remainder is f([tex]\frac{c}{a}[/tex] )

The remainder on dividing by (2x - 1) is - 35, then by substituting x = [tex]\frac{1}{2}[/tex]

2([tex]\frac{1}{2}[/tex] )³ + a([tex]\frac{1}{2}[/tex] )² + [tex]\frac{1}{2}[/tex] b - 30 = - 35

2([tex]\frac{1}{8}[/tex] ) + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b - 30 = - 35 ( add 30 to both sides )

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b = - 5 ( multiply through by 4 to clear the fractions )

1 + a + 2b = - 20 ( subtract 1 from both sides )

a + 2b = - 21 → (2)

Solve (1) and (2) simultaneously )

Add (1) and (2) term by term to eliminate b

5a = 25 ( divide both sides by 5 )

a = 5

Substitute a = 5 into (2)

5 + 2b = - 21 ( subtract 5 from both sides )

2b = - 26 ( divide both sides by 2 )

b = - 13

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Using the remainder theorem we can write,

f(x) = 2x³+ ax² + bx - 30

f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0

-16 + 4a - 2b - 30 = 0

4a - 2b = 46   ........ equation 1

f(x) = 2x³+ ax² + bx - 30

f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35

(1/4) + a(1/4) + b(1/2) = -35 + 30

(1+a+2b)/4 = -5

1 + a + 2b = -5 × 4

a + 2b = -21   .......... equation 2

Adding the two equations,

4a + 2b + a - 2b = 46 - 21

5a = 25

a = 25/5

a = 5

Substitute the value of a in any one of the equation,

a + 2b = -21

5 + 2b = -21

2b = -21 - 5

2b = -26

b = -26/2

b = -13

Hence, the value of a and b are 5 and -13, respectively.

Learn more about the Remainder Theorem here:

https://brainly.com/question/13264870

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Answer:

the function is always increasing

Step-by-step explanation:

if you look at the graph, as x increases, y increases, no matter how small the increase

Answer:

y=2 x=4

Step-by-step explanation:

Substitute x with 2y so the second equation is 2y+y=6

Then simplify your new equation:

3y=6

y=2

If y=2 and x=2( 2) then x=4

Answer:

Step-by-step explanation:

t=2g+3.

Answer:

a=2 and b=2...............

Step-by-step explanation:

x=y

x+2y=6

y+2y=6

3y=6

y=2

Step-by-step explanation:

x=y

x+2y=6

y+2y=6

3y=6

y=2

Answer:

6.25 or 6 2/8 or 6 R2

Step-by-step explanation:

Answer: Yes it is.

Step-by-step explanation:

Mixed to proper

7/3 = 2 1/3