13-9-x/11=3x/22+121/2

Final answer:

The average rate of change of the function g(x) = 3(2^x) - 6 over the interval [0,3] is 7. This is found by evaluating g(x) at x = 0 and x = 3 and then dividing the difference by the interval length.

Explanation:

Calculating Average Rate of Change

The average rate of change of a function over an interval is the change in the function's values divided by the change in the independent variable (often x) over that interval. For the function g(x) = 3(2^x) - 6 over the interval [0,3], we first find the values of g(x) at the endpoints of the interval: g(0) and g(3). We then use the formula for average rate of change:

[tex]\[\text{Average Rate of Change} = \frac{g(3) - g(0)}{3 - 0}\][/tex]

Let's compute:

Now we can substitute these values into the formula:

[tex]\[\frac{18 - (-3)}{3 - 0} = \frac{21}{3} = 7\][/tex]

So, the average rate of change of the function g(x) over the interval [0,3] is 7.

Answer:

(set up a ratio)

54/x = 18/100

(cross multiply)

18x = 5400

(solve for x)

x = 300 miles

Step-by-step explanation:

Answer:

Average = 96

Step-by-step explanation:

Average = sum of terms/ number of terms

sum of terms = number of burgers sold

number of terms = number of visitors

d =  number of days since Monday which is 7

burgers sold = 200d^3 + 542d^2 + 179d + 1605 substituting d with 7

burgers sold = 200(7)³ +542(7)² + 179(7) +1605

burgers sold =68600 + 26558 + 1253 + 1605

burgers sold =98016

number of visitors= 100d + 321

number of visitors= 100(7) + 321

number of visitors= 700+321

number of visitors= 1021

Average = 98016/1021

Average = 96

Answer:

It’s B if you dont want to read all that.

Step-by-step explanation:

The equation of f(x) is f(x) = -8(4x).

The equation of the reflected function f(x) can be obtained by changing the sign of the coefficient of g(x), which is 8.

So, the equation of f(x) is f(x) = -8(4x).

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Answer:

[tex]\frac{11}{5}[/tex]

Step-by-step explanation:

Using the section formula

[tex]y_{P}[/tex] = [tex]\frac{3(5)+7(1)}{3+7}[/tex] = [tex]\frac{15+7}{10}[/tex] = [tex]\frac{22}{10}[/tex] = [tex]\frac{11}{5}[/tex]

Answer:

52

Step-by-step explanation:

65 dollar is price so it has 20 percent discount so,

65× 20% = 13

so,

65- 13

52 dollars

Problem 1

-7+9 is the same as 9+(-7) or 9-7. All of which simplify to 2.

On the other hand, -9+7 is the same as 7+(-9) or 7-9, which simplifies to -2.

Therefore the equation -7+9 = -9+7 becomes 2 = -2, and we can see this is a false equation.

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

Problem 2

Your second question has some weird typo errors going on. Please update.

From given,

Final solution is 260 liter

Let x be the liters of 40 % dye solution

Then, (260 - x) is the liters of 53 % dye solution

Therefore, according to question,

x liters of 40 % dye solution is mixed with (260 - x) liters of 53 % dye solution to get 260 liters of 50 % dye solution

40 % of x + 53 % of (260 - x) = 50 % of 260

Solve for "x"

[tex]\frac{40}{100} \times x + \frac{53}{100} \times (260-x) = \frac{50}{100} \times 260\\\\0.4x+ 0.53(260-x) = 0.5 \times 260\\\\0.4x + 137.8 - 0.53x = 130\\\\0.13x = 137.8 - 130\\\\0.13x = 7.8\\\\Divide\ both\ sides\ by\ 0.13\\\\x = 60[/tex]

Thus 60 liters of 40 % dye solution is used

Then, (260 - x) = 260 - 60 = 200

Thus 200 liters of 53 % dye solution is used

Answer:

2:25

Step-by-step explanation:

Answer:

Step-by-step explanation:

3:05

Answer:

A grand total of 50 dimes

Step-by-step explanation:

The option (D) (r + s) × 5 is correct if the expression is 5 times as much as the sum of r and s.

It is defined as the combination of constants and variables with mathematical operators.

We have a statement about the expression:

The expression is 5 times as much as the sum of r and s

We can frame the expression as follows:

= 5(r + s)

or

= (r + s) × 5

Thus, the option (D) (r + s) × 5 is correct if the expression is 5 times as much as the sum of r and s.

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Answer:

  see below for a graph

Step-by-step explanation:

It is convenient to use a point-slope form of the equation of a line for graphing, since we know the slope is -12 m/min and the point is (30, 0) at sea level.

The horizontal axis is minutes; the vertical axis is meters above sea level. The graph cannot extend below -413 meters from sea level, as that is the lowest place on earth.

Answer:

87.5%

Step-by-step explanation:

35/40=7/8=0.875=87.5%

The complete factorized form for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]

Step-by-step explanation:

Step 1: Given expression:

              [tex]81 x^{8}-1[/tex]

Step 2: Trying to factor as a Difference of Squares

Factoring [tex]81 x^{8}-1[/tex]

As we know the theory that the difference of two perfect squares, [tex]A^{2}-B^{2}[/tex]  can be factored into (A+B) (A-B)

from this, when analysing, 81 is the square of 9, [tex]x^{8}[/tex] is the square of [tex]x^{4}[/tex]. Hence, we can write the given expression as,

            [tex]\left(9 x^{4}\right)^{2}-1^{2}[/tex]

By using the theory, we get

           [tex]\left(9 x^{4}+1\right)\left(9 x^{4}-1\right)[/tex]

Again, we can further factorise the term [tex]\left(9 x^{4}-1\right)[/tex]

[tex]9 x^{4}[/tex] is the square of [tex]3 x^{2}[/tex]. Therefore, it can be expressed as below

           [tex]\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]

Now, we can not factorise further the term [tex]\left(3 x^{2}-1\right)[/tex]. Because it will come as [tex]\sqrt{3} x[/tex] (3 is not a square term). Thereby concluding that the complete factorisation for the given expression is [tex]\left(9 x^{4}+1\right)\left(3 x^{2}+1\right)\left(3 x^{2}-1\right)[/tex]

Step-by-step explanation:

BOTH TRIANGLES ARE SIMILAR BY THE AA SIMILARITY POSTULATE.

In first triangle:

Remaining angle = 180° - (70° + 30°)= 80°

In second triangle:

Remaining angle = 180° - (80° + 30°)= 70°

Hence, all the angles of first triangle are congruent to the corresponding angles of the second triangle.

Thus, both the triangles are similar by

THE AA SIMILARITY POSTULATE

Answer:

The length of the diagonal x is  13.9 cm

Step-by-step explanation:

Given:

Side of the cube =  8 centimetres

To Find:

The length of the diagonal  = ?

Solution:

The  length of the diagonal is = [tex]\sqrt{3}a[/tex]

where a is the side of the cube

On substituting the values

Diagonal  x = [tex]\sqrt{3}(8)[/tex]

Diagonal x  =  [tex]1.73 \times 8[/tex]

diagonal x =  13.856

Diagonal  x  =  13.9 cm

Answer: proved

Step-by-step explanation:

-2x+8=3

-2x=3-8

-2x= -5

2x= 5

x=5/2

Answer:

formula for sum of interior angles is (n-2)*180 - for a regular polygon

divide that by the number of sides

so 6-2 = 4*180 =720 degrees

720/6 = one angle(angle a) =120

Answer:

D. 120 degrees.

Step-by-step explanation:

We nee to find the measure of the interior angle in a regular hexagon.

The exterior angle = 360 / 6 = 60 degrees.  ( In all convex polygons the sum of the exterior angles = 360 degrees).

So α = 180 - 60 = 120 degrees    (adjacent angles add up to 180 degrees).

Answer:

an equations which can be used to find the answer.

Answer: must be found.

Step-by-step explanation:

Equation is y = 6x - 4

Step-by-step explanation:

⇒ m = (2 - -4)/(1 - 0) = 6

⇒ y = 6x - 4

Answer:

3*(5*x-7)-(15*x-21)=0

Step-by-step explanation:

3 • (5x - 7) -  (15x - 21)  = 0

Step  2  :

Equation at the end of step  2  :

 0  = 0

Step  3  :

Equations which are always true :

Answer:

The y-intercept is where an equation's graph hits the y-axis. It represents the constant value, when x=0, the intercept is the constant

Step-by-step explanation:

The y-intercept indicates the vertical position where the line or curve intersects the y-axis

The y-intercept refers to the point where a line or curve intersects the y-axis on a graph.

It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the equation of a line in slope-intercept form (y = mx + b), where m represents the slope of the line and b represents the y-intercept, the y-intercept is the constant term (b).

The y-intercept represents the value of the dependent variable (y) when the independent variable (x) is not present or equal to zero.

It is the initial value or starting point of the function or graph.

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Answer:

−2k=k−7−8

−2k=k+−7+−8

−2k=(k)+(−7+−8)(Combine Like Terms)

−2k=k+−15

−2k=k−15

Step 2: Subtract k from both sides.

−2k−k=k−15−k

−3k=−15

Step 3: Divide both sides by -3.

−3k

−3

=

−15

−3

k=5

Step-by-step explanation:

Answer:

Part 1) [tex]\frac{5}{2}[/tex]  or  [tex]5:2[/tex]

Part 2) [tex]\frac{8}{1}[/tex]  or  [tex]8:1[/tex]

Step-by-step explanation:

Write the ratio as a fraction in simplest form

Part 1) 15 girls to 6 boys

we know that

To find out the ratio, divide the number of girls by the number of boys

so

[tex]\frac{15}{6}[/tex]

Simplify

Divide by 3 both numerator and denominator

[tex]\frac{5}{2}\ \frac{girls}{boys}[/tex]

Part 2) 24 plays for 3 teams

we know that

To find out the ratio, divide the number of plays by the number of teams

so

[tex]\frac{24}{3}[/tex]

Simplify

Divide by 3 both numerator and denominator

[tex]\frac{8}{1}\ \frac{plays}{team}[/tex]

Final answer:

To simplify the ratios 15 girls : 6 boys and 24 plays : 3 teams, find the greatest common factor and divide both parts of the ratio by it, resulting in the simplest forms  rac{5}{2} and 8, respectively.

Explanation:

To write the ratios as fractions in simplest form for the given scenarios:

For the ratio of 15 girls to 6 boys, the fraction would be  rac{15}{6}. To simplify, divide both the numerator and the denominator by their greatest common factor (GCF), which is 3. Thus, the simplest form is  rac{15 \/ 3}{6 \/ 3} =  rac{5}{2}.

For the ratio of 24 plays for 3 teams, the fraction is  rac{24}{3}. Again, to simplify, divide both the numerator and the denominator by the GCF, which is 3 in this case. The simplest form is  rac{24 \/ 3}{3 \/ 3} =  rac{8}{1}, which can also be written simply as 8 since a denominator of 1 implies the value is a whole number.

Answer:

yes

Step-by-step explanation:

Answer:

no i believe its an irrational number

Step-by-step explanation:

Answer:

Step-by-step explanation:

let x be the width.

length =  x +2

Perimeter = 36 ft

2*( x +2 + x ) =36

2x + 2 = 36/2

2x + 2 = 18

2x = 18 -2 = 16

x = 16/2

x = 8 ft

Width =  8 ft

Length = 8 + 2 = 10 ft

Answer:

The best estimate of the solution ordered pair from the graph is [tex](\frac{1}{2},0)[/tex].

Step-by-step explanation:

See the attached graph to this question.

The graph of two straight lines are shown in the graph.

Now, the two straight lines intersect on the x-axis, so the solution ordered pairs should have y-value equals to zero.

But, there are two ordered pairs with y-value zero and they are [tex](\frac{1}{2},0)[/tex] and [tex](\frac{1}{3},0)[/tex].

The best estimate of the solution ordered pairs from the graph is [tex](\frac{1}{2},0)[/tex].

So, this is the solution. (Answer)

Yo sup??

we can simply try option verification for this problem.

when x=0 we get,

1 and 1≠5 therefore x=0 is not a solution.

when x=1 we get

√6-1≠5 therefore x=1 is not a solution.

when x=16 we get

9-4=5 therefore x=16 is a solution

Hence the correct answer is option C

Hope this helps.

Answer:

One real solution (which is x = 2)

Step-by-step explanation:

8-4x = 0

8 = 4x

8/4 = 2

x=2

Can be solved with no different solution