a survey was conducted to study the relationship between the annual income of a family and the amount of money the family spends on entertainment. data were collected from a random sample of 280 families from a certain metropolitan area.

Answer:

Proved!

Step-by-step explanation:

Given Problem:

a(cosB+cosC-1)+b(cosC+cosA-1)+c(cosA+cosB-1) = 0​

Solution:

Let ABC be any triangle.

1) Consider the L.H.S  (left hand side) of the given equation:

LHS =

We know that,

Projection formula:

= 0 =RHS

(2) Consider the LHS of the given equation:

Hence Proved!!

Answer:

$6 in each group

Step-by-step explanation:

$5.20+$4.64+$2.16=12

12/2=6

According to the solving the value of a and b of the X² - 4X - 21 equation are:

a = -2

b= -25

A quadratic problem is a sort of problem in mathematics that deals with either a variable multiplied by itself – a process known as squares. The area of a square is defined as its side length multiplied by double itself in this language.

 In everyday life, we employ quadratic formulas to calculate areas, determine the profit of a product, or calculate the velocity of an object. Furthermore, quadratic equations are defined as equations with at least one squared variable.

X² - 4X - 21

Expand to check:

For a.

(X - 2)² - 4 - 21 = (X - 2)² - 25

                       = X² - 4X + 4 - 25

                       = X² - 4x -21

                       =  (X - 2)² - 25

a = -2 , b = -25

For b.

X² - 4X - 21 = (X - 2)² - 25 due to part a we can say that:

(X - 2)² - 25 = 0

X - 2 = ± 25

x  = 7 , X = -3

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The remaining weight seashells that Jonathon has is 7/4 kg or  [tex]1\frac{3}{4}[/tex] kg.

A fraction is a percentage of a whole. This entire sentence could be referring to a single location or a collection of locations. The English word "fraction" derives from the Latin word "fractio," which means "to break." As the first civilization to comprehend fractions, the Egyptians used fractions to solve a number of mathematical problems, including the distribution of food and resources and the absence of a metal currency.

Weight of the remaining sea shells = [tex]4\frac{1}{2}[/tex] - [tex]2\frac{3}{4}[/tex]

Weight of the remaining sea shells = 9/2 - 11/4

Weight of the remaining sea shells = 18-11/4

Weight of the remaining sea shells = 7/4 kg

Weight of the remaining sea shells = [tex]1\frac{3}{4}[/tex] kg

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The weight of the remaining sea shells Jonathan has is 1¾ kg.

So, the weight of the remaining sea shells: 4½ - 2¾

Now, solve the above fraction operation for the weight of remaining sea shells.

Therefore, the weight of the remaining sea shells is 1¾ kg.

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The point on the number line which is closest to  √130 is 11

According to the question we need to find the number closest to the √130

We know that the √130 = 11.4

And 11.4 number lies between 11 and 12 . That is

               11< 11.4 <12

But as we see on the number line 11 is much closest than the number 12 on the number line.

Also the

         distance between 11 and 11.4 is 0.4

  and distance between 11.4 and 12 is 0.6 .

Thus distance between 11 and 11.4 is small.

Hence 11 is closest point to √130 on the number line.

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Answer: 2044.444444444 repeating

Step-by-step explanation:

divide 18400/9 and that's what you get in long division

The result of simplifying the number 64³.⁵ using the exponent rules is

1.24x10^27

To solve this exercise we have to resolve algebraic operations following the exponent rules.

Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

(64³)⁵

64 ⁽³*⁵⁾ =

64¹⁵ =

1.24x10^27

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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4y +5x = 8

y= -3x+5

The slope-intercept form of the equation of the line through the given points =  1) through: (0, 2) and (4, -3)

              2 ) through: (0, 5) and (2, -1)

The general formula for slope-intercept form is y = mx + b, where m represents the slope of the line, and b represents the y-value of the line's y-intercept. The slope-intercept form of a linear equation makes it easier for us to identify how steep a line is and where it crosses the y-axis.

1) through: (0, 2) and (4, -3)

m = y2-y1 /x2-x1

m= -3-2/4-0

m=-5/4

y = mx

y-y1 = m(x-x1)

y- 2 = -5/4(x-0)

y-2= -5x/4

4(y-2) = -5x

4y -8 = -5x

4y +5x = 8

2 )  through: (0, 5) and (2, -1)

m = y2-y1 /x2-x1

m= -1-5/2-0

m= -6/2

m= -3

y = mx

y-5 = m(x-0)

y-5 = -3(x)

y-5 = -3x

y= -3x+5

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Answer: 11 hours :)

Step-by-step explanation: 1215-445=770, 770 divided by 70=11 so 11 days

The error in solving for the equation in the question was that m was not appropriately converted from a negative number.

The equation is:

-m/3 = -4

Solving gives:

3 x (-m/3) = 3 x -4

m is a negative and should remain so. The next step is:

-m = -12

m = -12 / -1

m = 12

m is therefore 12 and not -12.

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Answer:

20

Step-by-step explanation:

multiples of 4 (4,8,12,16,20....)

multiples of 10 (10,20....)

Answer: 10.8 cm

Following are the calculation to find the x:

Given:

Assuming the triangle is ABC:

then

∠A = 81∘

∠B = 40∘

A = 7cm

To find:

x=?

Solution:

To find the x value we use the Law of sine:

Putting the given value:

Answer:f

(

x

+

2

)

=

3

x

+

2

Step-by-step explanation:

If the function f(x) = 4 - 2√x  then the inverse function be [tex]x^{2}[/tex] −8x+18 = f(x)

An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.

Assume that the function is [tex]f(x) = 4 + \sqrt{x-2}[/tex] and f(x) = 4+x−2

​where the x − 2 is under the radical sign.

The first step is to swap the f(x) and x.

The new function would be

[tex]$x = 4 + \sqrt{f(x) -2}x=4+ f(x)-2[/tex]

To solve the value of f(x) in the new function

x = 4 + [tex]\sqrt[2]{f(x)-2}[/tex]

x - 4 = [tex]\sqrt{f(x)-2}[/tex]

simplifying the above equation, we get

[tex](x -4^{} )^{2}[/tex] = f(x) − 2

[tex]x^{2}[/tex] − 8x +16 = f(x) − 2

[tex]x^{2}[/tex] − 8x + 18 = f(x)

The inverse of the function f(x) = 4 - 2√x is [tex]x^{2}[/tex] −8x+18 = f(x)

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The equation of the line in slope-intercept form is: y = 6.

Given that the points, (-4,6) and (4,6) lie on a line, the steps below shows how to write the equation of the line in slope-intercept form.

Step 1: Find the slope of the line:

Slope (m) = change in y / change in x = (6 - 6)/(-4 - 4)

Slope (m) = 0/-8

Slope (m) = 0

Step 2: Substitute m = 0 and (x, y) = (4, 6) into y = mx + b to find the value of b

6 = 0(4) + b

6 = 0 + b

6 = b

b = 6

Step 3: Substitute m = 0 and b = 6 into y = mx + b

y = 0(x) + 6

y = 0 + 6

y = 6

In conclusion, the equation of the line in slope-intercept form is: y = 6.

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The interval in which the function has positive average rate of change is x > √3

The function is given as

f(x) = x^3 - 9x

Differentiate the above function to determine the average rate of change

So, we have

f'(x) = 3x^2 - 9

Set the function to greater than 0

So, we have

3x^2 - 9 > 0

Add 9 to both sides

3x^2 > 9

Divide by 3

x^2 > 3

Take the square root of both sides

x > √3

Hence, the interval in which the function has positive average rate of change is x > √3

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Answer:

firstg one

Step-by-step explanation:

two x's

Answer:

CosW =0.28

explaination:

first find value of the Hypotenuse side,

then find value of Cos W as recalled from

Cos W =Adjacent side/Hypotenus side

Answer:

The answer to that question is 58

The written description of the relationship between the variables as discussed in the task content is; Choice C; You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before.

According to the task content, the time (hours) is plotted on the x-axis while the distance (miles) is plotted on the y-axis.

Since the graph is described by a line, it follows that it's slope is constant and consequently, its distance covered increases to 2 hours. This signifies driving.

Also, since the distance covered is constant through 3 hours, it follows that no distance is covered in that time and hence, speed is zero which signifies a stop.

Ultimately, when the distance increases through 6 hours, it follows that although the speed is constant, it is slower than the first 2 hour distance.

Therefore, Choice C correctly represents the interpretation of the relationship between the variables.

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Answer: The length of the cell in stand form is 5.4x10-6 m = 0.000000054 m

Step-by-step explanation:

It is given by that the size of a bacterial is 0.000000054 m , which can be with in as 5.4x10-6 m in standard form

We need to find the value of m.

Clearly the standard form of

0.000000054 = 5/10000000

                         = 5 x 1/10000000

                         = 5 x 1/[tex]10^{6}[/tex]

0.000000054 = 5 x [tex]10^{-6}[/tex]

Therefore,

                      5 x [tex]10^{-m}[/tex] = 5 x [tex]10^{6m}[/tex]

and the value of m = 6

So,

The length of the cell in stand form is 5.4x10-6 m = 0.000000054 m

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The expression that is equivalent to the given expression is -2x/15 + 2. The correct option is the third option-  negative two over fifteen times x plus two

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

1/5(3x +10) - (11/15)x

Clear the parentheses by applying the distributive property

1/5(3x) + 1/5(10) - (11/15)x

3x/5 + 2 - 11x/15

Collect like terms

3x/5 - 11x/15 + 2

(9x - 11x)/15 + 2

-2x/15 + 2

Hence, the expression that is equivalent to the given expression is -2x/15 + 2. The correct option is the third option-  negative two over fifteen times x plus two

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the verified answer is wrong.

Answer:

y = 1/2 x + 1.

Step-by-step explanation:

A line perpendicular to a line with slope m will have a slope of -1/m.

The line y = -2x - 7 will have a slope of -1/ -2 = 1/2.

Using the point-slope form of a straight line

y - y1 = m(x - x1)

Here m = 1/2 and (x1, y1) = (4, 3).

So, y - 3 = 1/2(x - 4)

y = 1/2x - 2 + 3

y = 1/2 x + 1.

Answer:

-25

Step-by-step explanation:

First, write an equation to represent the situation. To get -87, a number (lets say x) is first tripled, and then 12 is subtracted from the result.

So: -87 = 3x - 12

Then, solve for x by first adding 12 to both sides:

-87 = 3x - 12 ----> -75 = 3x

Finally, divide both sides by 3 to get x by itself:

-75 = 3x ----> -25 = x

Answer: Transporting substances in a cell.

Step-by-step explanation: Transporting substances in a cell producing and storing energy.

Answer:

137174211/100000000000

Step by Step Explanation:

First, find the answer of 9^(-3), which would be 0.00137174211. Then, convert that into fraction form. Which would be 137174211/100000000000. Then simplify, which in order to simplify a fraction, there must be: 1. A number that will divide evenly into both the numerator and denominatior so it can be reduced. No such number exists for 137174211 and 100000000000. or 2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. 137174211 is not greater than 100000000000, also meaning, this fraction is in it's simplest form.

Answer:

-5/14

Step-by-step explanation:

common denomatior is 14

-9/14 + 4/14 (since 2/7 and 4/14 are the same thing)

numerator: -9+4=-5

denominator stays the same.

-5/14 is your answer

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

These fractions have denominators in common, so let's find them!

7 x 2 = 14, so 2/7 also equals 4/14.

9/14 + 4/14 = 13/14

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

Have a wonderful day/night! :)

(Please consider leaving a Brainliest as it will be greatly appreciated!)

~pinetreee

The exponential decay function for 24 mg sample is given as  

[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex])   and 0.64mg carbon - 14 will remain after 30 millennia.

Exponential function that represent the decay is given as :

           [tex]F(t) = a (0.5)^{\frac{t}{h} }[/tex]       (1)

where,   F(t) = amount remaining after time t

               a = amount of sample is decayed

               t = time in years

               h = half life years

The values that we have been given are :

       a = 24 mg sample

       h = 5730 years

Putting the required values in equation (1) we get

          [tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex]     (2)

 Now we need to find how much carbon-14 remains after 30 millennia.

That is we have to find F(t) for t = 30 millennia = 30000 years

      [As 1 millennium = 1000 years]

Putting the required values in equation (2) we get

        [tex]F(t) = 24 (0.5)^{\frac{30000}{5730} }[/tex]

       [tex]F(t) = 24 (0.5)^{5.236}[/tex]

        F(t) = 24*0.027

       F(t) = 0.64 mg

Thus 0.64mg carbon - 14 will remain after 30 millennia.

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Answer:

h=-2

Step-by-step explanation:

17+4h+2=1−5h

19+4h=1-5h

4h=-18-5h

9h=-18

h=-2