Simplify the following expression in Scientific Notation. (1.8x10⁹) (6.7 x 10¹²)
a x 10^b
a=?
b=?​

Value of the given function f(x) = 5x +2 , g(x) = 8 -3x for the following condition:

a. g(f(-2)) =32

b. f(g(x)) =42 -15x

As given in the question,

Given function:

f(x) = 5x + 2

g(x) = 8 - 3x

Value of the function for the following condition:

a. g(f(-2))

f(x) = 5x + 2

⇒f(-2) = 5(-2) + 2

⇒f(-2) = -8

g(f(-2))= g(-8)

         = 8 - 3(-8)

         = 32

b. f(g(x)) = f(8-3x)

             = 5(8 -3x) + 2

             =42 -15x

Therefore, value of the given function f(x) = 5x +2 , g(x) = 8 -3x for the following condition:

a. g(f(-2)) =32

b. f(g(x)) =42 -15x

The complete question is :

Given function  f(x) = 5x + 2 and g(x) = 8 - 3x, find the following value.

a. Find g[f(-2)].

b. Find f(g(x)).

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The distance between two points [tex](x_{1}, y_{1} )[/tex] and [tex](x_{2} ,y_{2})[/tex] is given by

[tex]d = \sqrt{ (x_{2} -x_{1})^{2} +(y_{2} -y_{1})^{2} }[/tex]                   …(1)

Given points are:

C = (7,-4) = [tex](x_{1}, y_{1} )[/tex]

D = (-8,-5) = [tex](x_{2} ,y_{2})[/tex]

Substituting the values in equation (1), we get

[tex]CD = \sqrt{ (-8-7)^{2} +(-5-(-4))^{2} }[/tex]    

[tex]CD = \sqrt{ (-15)^{2} +(-1)^{2} }[/tex]

[tex]CD = \sqrt{{ 225} +1 }[/tex]

[tex]CD = \sqrt{{ 226 }[/tex]

[tex]CD = 15.03}[/tex]

After Rounding it to nearest tenth, we get

CD = 15 units

Hence, the distance between the points (7,-4) and (-8,-5) is 15 units.

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In the given triangle , ∠n = 50° and ∠m = 35°

In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can also say that the angle is a figure formed by two rays with having same initial point. The rays are also known as the sides of the angle. A angle can have two rays.

Some common terms related to angles :

In the given question mark the triangle as ABC and the mid line as point D.

that means,

∠A = ∠n

∠B = ∠m

and, in ΔABC

∠C = 60 + 35 =95

now, as ΔCDB is isosceles triangle therefore,

∠m = ∠C = 35°

Also, as sum of all angle of triangle is 180

Therefore, ∠A + ∠B + ∠C = 180

=> ∠n + ∠m + 95 = 180

=> ∠n + 35 + 95 = 180

=> ∠n = 180- 130

=>∠n = 50

Hence in the triangle given , ∠n = 50 and ∠m = 35

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Answer:

3.8439141e+15

Answer:

A=l×b

A=20×14

A=280

tan(90)=14/aq

aq×tan(90)=14/aq×as

aqtan(90)=14

aqtan(90)/tan(90)=14/tan(90)

aq=0.16

The quadratic equation with a repeated root is:

8*x^2 - 32*x  +32

And the repeated root is x = 2

For a quadratic equation:

0 = a*x^2 + b*x + c

We define the discriminant as:

D = b^2 - 4ac

If D = 0, we have only one real root (or two repeated roots). Then we just need to see which of the given quadratic equations has a discriminant of zero.

1) -x^2 + 18x + 81

The discriminant is:

D = 18^2 - 4*(-1)*81 = 648

2) 3x^2 - 6x + 9

The discriminant is:

D = (-6)^2 - 4*3*9 = -72

3) 8*x^2 - 32*x  +32

The discriminant is:

D = (-32)^2 - 4*8*32 = 0

So this is the one with a discriminant of zero.

The roots are given by:

8*x^2 - 32*x  +32 = 0

Using Bhaskara's formula we will get:

x = (- (-32) ± √( (-32)^2 - 4*8*32))/(2*8)

x = (32/16) = 2

The repeated root is x = 2

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Answer:

p) zero

q) 10,559.5

r) from $37,001 to $87,000

Step-by-step explanation:

p) zero

q) Tax = 3,572 + (58,500 - 37,000)(0.325)

= 3,572 + 6,987.5

= 10,559.5

r) from $37,001 to $87,000

Check the picture below.

The difference of the algebraic expression is 2. 7m² - 4n² - 8. 2m

To represent the difference in standard form is leave in the power or exponent of a variable or number.

Given the expression

(2.7m^2 - 3.1n) - (4n^2 + 5.1m)

First, expand the brackets

2. 7m² - 3.1 m - 4n² - 5. 1m

Then, collect like terms

2. 7m² - 4n² - 3.1m - 5. 1m

Subtract like terms, we have

2. 7m² - 4n² - 8. 2m

The difference of the algebraic expression gives 2. 7m² - 4n² - 8. 2m

Thus, the difference of the algebraic expression is 2. 7m² - 4n² - 8. 2m

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Answer:

(-13, -10)

Step-by-step explanation:

Your original point is (-17, -13)  The instruct tell you to move the point 4 units to the right and down 7 units.

-17 + 4 = -13

-3 - 7 = -10

The change in the temperature is 11°.

Temperature is the physical quantity which describes, how much hot is something? Or we can say it is the quantity which measures the hotness and coldness of something. There are two main quantity values to measure the temperature which are Celsius and Fahrenheit.

Mathematically we can write :

1° Celsius = 32 Fahrenheit

Suppose if we have temperature of two difference time space then we can easily find the difference between the two by simply subtracting them.

For the given question,

last year temperature = 82 degree

temperature today = 71 degree

therefore the change in the temperature in one year is :

82 - 71 = 11 degree.

Thus , the change in temperature is 11 degree.

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Answer:

75

Step-by-step explanation:

Each placemat is .15 cents

500 x .15

Answer: the first table with all 2s as its y values

Step-by-step explanation: the first table shows that no matter what the x value is, the graph is staying still at y=2. Its rise/run is 0 since it is not rising at all.

Answer:

The first column of the first chart due to the repetition of the numbers! hope this helps!

Answer:6.5m

Step-by-step explanation:

The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

The given parameters are:

Number of hours = at least 30 hours a week

This means that

x + y ≥ 30

Also, we have:

The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).

This means that

y ≤ 2x

Substitute y ≤ 2x in x + y ≥ 30

x + 2x ≥ 30

This gives

3x ≥ 30

Divide

x ≥ 10

Substitute x ≥ 10 in y ≤ 2x

y ≤ 2 x 10

Evaluate

y ≤ 20

Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

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The factor of its area less than the initial area is 1/4

The given parameters can be represented as:

Second sheet = 1/2 * The first sheet

Assume the sheet is rectangular, the area of the sheet is calculated as:

Area = Length * Width

So, the area of the second sheet is

Second sheet = 1/2Length * 1/2Width

This gives

Second sheet = 1/4(Length * Width)

So, we have:

Second sheet = 1/4 * First sheet

Hence, the factor of its area less than the initial area is 1/4

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The total kilowatt-hours of electricity used during these two years is (6.03 x 10^9)+(4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11) = 4.3603 x 10^11 using arithmetic operations.

Addition is the sum of two or more numbers or values to get a new number. The addition symbol is the plus sign (+).

Multiplication is the repeated addition of a number. If we multiply m by n, that means m is repeatedly added to itself for n times. The symbol for multiplication is ‘×’.

Given that the use of electricity in the US in 1902 was 6. 03 x 10^9 kilowatt-hours and in 1950, it was 4. 3 x 10^11 kilowatt-hours.

To find the total kilowatt-hours of electricity used during these two years, we must add the kilowatt-hours of electricity used in 1902 and 1950.

6. 03 x 10^9 kilowatt-hours can also be written as 0.0603 x 10^11 kilowatt-hours.

This implies, (6.03 x 10^9) + (4.3 x 10^11) = (0.0603 x 10^11) + (4.3 x 10^11)

= (0.0603+4)10^11

= 4.3603 x 10^11 kilowatt-hours

Therefore, the total kilowatt-hours of electricity used during these two years is 4.3603 x 10^11.

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The cost of 11 cans of dog food will be equal to $10.12.

What is unitary method ?

The unitary method is a method in which , you first determine the value of a single unit before determining the value of the required quantity of units.

It is given that the cost of 20 cans of dog food at store B is $18.40.

We need to find cost of 1 can of dog food and that can be calculated by dividing the cost of cans of dog food by total no. of cans.

i.e.,

Cost of 1 can of dog food = $ 18.40 ÷ 20

So ,

The cost of 1 can of dog food will be :

= $0.92

Now , the cost of 11 cans of dog of food will be calculated by multiplying cost of 1 can of food to 11 cans of dog food which will be :

= 11 × $ 0.92

= $10.12

Therefore , the cost of 11 cans of dog food will be equal to $10.12 .

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The measure of angle JKN is 108 degrees

From the figure, we have the following parameters

Angle 1 equals Angle 2

Where

Angle 1 = Angle JKP = 3r + 12

Angle 2 = Angle PKN = 4r - 2

Recall that

Angle 1 equals Angle 2

So, we have

3r + 12 = 4r - 2

Evaluate the like terms

r = 14

Substitute r = 14 in Angle 1 = Angle JKP = 3r + 12 and Angle 2 = Angle PKN = 4r - 2

Angle 1 = Angle JKP = 3 * 14 + 12 = 54

Angle 2 = Angle PKN = 4 * 14 - 2 = 54

The measure of angle JKN is calculated as

Angle JKN = Angle 1 + Angle 2

So, we have

Angle JKN = 54 + 54

Evaluate

Angle JKN = 108

Hence, the measure of angle JKN is 108 degrees

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Answer:  49   &  82

Step-by-step explanation:

*the total degrees for each triangle is 180 degrees

9)  Start with the triangle furthest left- subtract 71 and 57 both from 180.  That leaves you with 52 degrees for that third angle.  The angles that all make a straight line or straight angle add up to 180 degrees as well.  Now, subtract the 52 and 65 from 180, which leaves you with 63 degrees for the first angle in the second triangle.  Now subtract the 63 and 68 from 180, which leaves you with 49 degrees for that answer.

10)  For this one, you will start with the triangle further right, since it already has two angles shown.  Subtract the 85 and 35 from 180, which gives you 60 degrees for that third angle.  Then, you can use the vertical angles to fill in its opposite angle in the first triangle (vertical angles are equal).  This means that the first triangle has angles of 38 and 60 degrees, so subtract those both from 180, giving you 82 degrees for that answer.

Answer:

Shapes S and D are congruent because they are both parallel to the line. Shapes M and S have the same area since they both cover 6 triangles.

Step-by-step explanation:

Answer is 7/3

Step-by-step explanation:

Answer:

[tex]\frac{23}{6}[/tex] or 3.833333...

Hope this helps

Step-by-step explanation:

[tex]4+(-\frac{1}{2} *\frac{1}{3} )\\\\4+ (-\frac{1}{6} )\\\\4-\frac{1}{6} \\\\\frac{24}{6} -\frac{1}{6} \\\\\frac{23}{6}[/tex]

Answer:33.1

Step-by-step explanation: 3.61 × 10-3 =33.1

Step-by-step explanation:

429 × 10⁷

hopefully it will help you

The measurements can be explained as low accuracy and high precision.

Accuracy is how close or far off a given set of measurements are to their true value.

Precision is how close or dispersed the measurements are to each other.

Given,

His height = 5 feet 3 inches

Friend measures you three times and gets these results =5 ft 10 in, 5 ft 9.5 in and 5 ft 10.5 in

Here, the measurements are closely dispersed but the measurements are far from actual measurement.

Hence, the measurements can be explained as low accuracy and high precision.

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Answer:

1. true

2. false

3. false

4. true

Step-by-step explanation:

If the length of a rectangle is 3 more than twice the width and the perimeter is 36 inches, then the area of the rectangle is equal to 65 in².

The length and width of the rectangle can be determined by using the formula for the perimeter of the rectangle,

P = ( L + W ) × 2

P = 2L + 2W

Here L is equal to the length of the rectangle and W is the width of the rectangle.

As the length is 3 more than twice the width, we can write the length of the rectangle as,

L = 3 + 2W

Putting L = 3 + 2W in the equation of perimeter,

P = 2L + 2W

As P = 36

36 = 2( 3 + 2W) + 2W

36 = 6 + 4W + 2W

6W = 30

W = 30 ÷ 6

W = 5

The length of the rectangle can be found by putting W = 5 in the equation,

L = 3 + 2W

L = 3 + 2(5)

L= 3 + 10

L = 13

Therefore, the length and width of the rectangle are equal to 13 and 5 respectively

As, area = width × length

area = 5 × 13

area = 65

Hence, the area of the rectangle is equal to 65 square inches.

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The three arithmetic means between 12 and 44 are -

20, 26, 36.

We have two numbers 12 and 44.

We have to determine the three arithmetic mean between these numbers.

Assume that x, y and z are in AP, then -

y - x = z - y

2y = x + z

y = (x + z)/2

Here -  y is called the arithmetic mean of x and z.

According to the question -

Assume that the three arithmetic means between the two numbers are -

12, a, b, c, 44

Then -

12 , 12 + d, 12 + 2d, 12 + 3d, 44

will be an AP with common difference 'd'.

Now, we have -

a[5] = 44

Using the formula for nth term of an AP, we get -

a + (n - 1)d = 44

12 + 4d = 44

4d = 32

d = 8

Therefore, the three arithmetic means are -

12 + 8 = 20

12 + 2 x 8 = 26

12 + 3 x 8 = 36

Hence, the three arithmetic means between 12 and 44 are -

20, 26, 36

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