Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^x + 2 intersect are the solutions of the equation 8^x = 2^x + 2. (4 points)

Part B: Make tables to find the solution to 8^x = 2^x + 2. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 8^x = 2^x + 2 graphically? (2 points)

Answer:

Important note: "of" means to multiply!
22% of 150 is 33

Step-by-step explanation:

[tex]Y = P\% \times X\\Y = 22\% \times 150\\P = 22\%\div100 = 0.22\\Y = 0.22 \times 150\\Y = 33[/tex]

Hope this helps!

Step-by-step explanation:

He added 8 to each number on the left column to get the number on the right column

So that

X 1, 2, 3, 4, 5, 6,

Y 1+8 = 9

Y 2 + 8 = 10

Y 3+8 = 11

Y 4 + 8 = 12

Y 5 + 8 = 13

Y 6 + 8 = 14

Answer:

x = 1, x = 3

Step-by-step explanation:

Given function:

[tex]f(x)=\left(\log(3x)-2 \log(3)\right) \cdot \left(x^2-1\right)[/tex]

The roots of the function are when f(x) = 0:

[tex]\begin{aligned}f(x) & = 0\\ \implies \left(\log(3x)-2 \log(3)\right) \cdot \left(x^2-1\right) & = 0\\\\ \textsf{Therefore,} \:\:\:\log(3x)-2 \log(3) & = 0\\ \textsf{and }\:\:\:x^2-1 & = 0 \end{aligned}[/tex]

Case 1

[tex]\begin{aligned}\left(\log(3x)-2 \log(3)\right) & = 0\\\log(3x) & = 2 \log(3)\\ \log(3x) & = \log (3)^2\\ \log(3x) & = \log (9)\\ 3x & = 9\\ x & = 3\end{aligned}[/tex]

Case 2

[tex]\begin{aligned}\left x^2-1\right & = 0\\x^2 & = 1\\ x & = \pm 1\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = 1 only.

Therefore, the roots of the given function are: x = 1, x = 3

Answer:

b) -8

c) 11

d) {x is a member of all real numbers | except for 2}

Answer:

(a) Choice C is correct

(b) f(x) = -8  Point is (1, -8)

(c) x =11  Point is at (11,2)

(d) Domain of f is x is [tex]\:x < 2\quad \mathrm{or}\quad \:x > 2\:[/tex]  
    In interval notation [tex]\:\left(-\infty \:,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]

(e)  x intercept is at x = -7

(f) y-intercept is at [tex]-\frac{7}{2} = -3.5[/tex]

Step-by-step explanation:

(b) Plug in x = 1 into the equation [tex]\:\:\frac{x+7}{x-2} = \frac{1+7}{1-2} = \frac{8}{-1} = -8[/tex]

(c) If f(x) = 2 then we get [tex]2 = \:\:\frac{x+7}{x-2}[/tex]  

==> 2(x-2) = x + 7

==>   2x - 4 = x + 7

==> 2x - x = 7 +4 =11

==>  x = 11

(d) Domain of f is all values of x -∞ < x < ∞ except at x = 2 since at x = 2 the denominator is 0 and division by zero is undefined; So we can say the domain is x < 2 or x  >2

(e) To get the x-intercept set y = 0 and solve for x
We get (x+7)/(x-2) = 0

x+7 = (x-2)(0) = 0

x = -7 and the x intercept is at point (-7, 0)

(f) [tex]y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0[/tex]

Substitute for x = 0 to get y = (0+7)/(0-2) = -7/2

Answer:

[tex]x=\pm \sqrt{\frac{y-c}{a}}[/tex]

Step-by-step explanation:

[tex]y=ax^2 + c \\ \\ ax^2 =y-c \\ \\ x^2=\frac{y-c}{a} \\ \\ x=\pm \sqrt{\frac{y-c}{a}}[/tex]

Using a system of equations, it is found that she uses 700 ml of Solution B.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

She uses 400 milliliters less of Solution A than Solution B, hence:

x = y - 400.

Solution A is 20% alcohol and Solution B is 17% alcohol. The esulting mixture has 179 milliliters of pure alcohol, hence:

0.2x + 0.17y = 179.

Since x = y - 400, we have that:

0.2(y - 400) + 0.17y = 179.

0.37y = 259

y = 259/0.37

y = 700.

She uses 700 ml of Solution B.

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Answer:2 x^2 + 7 x + 15

Step-by-step explanation:

Answer:

-2x^2-7x-5 or -(x+1)(2x+5)

Step-by-step explanation:

We combine -2x and 5x which becomes a -5x equaling to -7x

And then we add -10 and 5 to get -5.

Correct answer is D. The statement that shows Sam's purpose for making the investment,  is; Sam wants an investment that offers a higher return than stocks.

Sam desires an investment that delivers a larger return than stocks, which is the phrase that best demonstrates his motivation for making the investment.

Bonds are a sort of investment that may be held for a time in the hopes of earning returns, as is common knowledge. The two most popular forms of investments traded on the stock market are bonds and stocks. Buyers just hold them in the belief that they will generate returns.

Bonds, however, are often safer investments than stocks. In actuality, stocks are a type of investment that is excessively volatile.

Sam desires an investment that delivers a larger return than stocks, which is the phrase that best describes his motivation for making the investment.

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Answer:

Sam wants a steady income from his investment.

Step-by-step explanation:

Got it right on edmentum

Given the length of the perpendicular height and base length, the hypotenuse of the right triangle is 2√74 ft.

Hence option a)2√74 ft is the correct answer.

The Pythagoras theorem can be expressed as;

c = √( a² + b² )

Where c is hypotenuse, a and b are the other two sides of the right triangle.

Given the data in the image;

Plug the given values into the above equation and solve for the hypotenuse 'c'.

c = √( a² + b² )

c = √( (14)² + (10)² )

c = √( 196 + 100 )

c = √( 296 )

296 can be written as 4 × 74, and 4 can further be written as 2²

Hence

c = √( 2² × 74 )

c = 2√74 ft

Given the length of the perpendicular height and base length, the hypotenuse of the right triangle is 2√74 ft.

Hence option a)2√74 ft is the correct answer.

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Step-by-step explanation:

= 25/100 = 1/4

60% to fraction = 60/100 = = 12/20 further division gives 3/5

30% to fraction = 30/100 = 3/10

6% to fraction= 6/100 = 3/50

55% to fraction= 55/100 = 11/20

22% to fraction = 22/100 = 11/50

45% to fraction = 45/100 = 9/20

Answer:

the vector is 24 OVER 67

Step-by-step explanation:

and never the less the vector is the number u Will have total of 67 and 24

The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).

In accordance with geometry, three points are collinear if and only if these points lie on the same line. Then, the geometric system is represented by the following model:

AC = AB + BC

If we know that AB = x + 4, BC = 2 · x - 1 and AC = 4 · x - 7, then the value of x and the lengths of the line segments are, respectively:

4 · x - 7 = (x + 4) + (2 · x - 1)

4 · x - 7 = 3 · x + 3

x = 10

AB = 10 + 4

AB = 14

BC = 2 · 10 - 1

BC = 20 - 1

BC = 19

AC = 4 · 10 - 7

AC = 40 - 7

AC = 33

The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).

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Inscribing a circle means to draw a circle inside a shape. the correct option is the last option

An inscribed figure is a shape drawn inside another shape. For example, if a circle is drawn inside a square, the circle is said to inscribed inside the square.

Likewise,

If a triangle is drawn inside a circle, the triangle is said to be inscribed inside the circle.

A cyclic quadrilateral is an example of a quadrilateral that is inscribed inside a circle.

Then,

We can conclude that inscribing a circle means to draw a circle inside another shape

Hence, inscribing a circle means to draw a circle inside a shape. the correct option is the last option

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Answer:

15

Step-by-step explanation:

x(x + 2) = 27 + 6(x + x + 2)

x^2 + 2x = 27 + 6(2x + 2)

x^2 + 2x = 27 + 12x + 12

x^2 + 2x - 12x - 12 - 27 = 0

x^2 -10x - 39 = 0

(x + 3)(x - 13) = 0

x + 3 = 0

x = -3 (extraneous solution)

x - 13 = 0

x = 13

x + 2 = 15

The gas tank holds 60 quarts.

What is quarts?

The quart is an English volume unit equivalent to one-quarter gallon. There are now three types of quarts in use: the liquid quart and dry quart of the US customary system, as well as the imperial quart of the British imperial system. All of them are essentially equivalent to one liter. It is split into two pints or four cups (in the United States). The exact size of the quart has historically fluctuated with the varying values of gallons over time and in relation to different commodities.

1 US gallon = 4 US quarts

so, 15 US gallons = 15 x 4 = 60 quarts

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Using angle sum property for angles For, the given triangle, the value of x = 23°

The angle sum feature is a characteristic shared by all varieties of triangles. Triangles have an angle sum property of 180 degrees. This indicates that a triangle's internal angles add up to 180 degrees.

The angle 135 ,makes a linear pair with the line

So, the angle will be -

180 - 135

= 45°

Using angle - sum property,

x + 45 + 112 = 180

x + 157 = 180

x = 180 - 157

x = 23

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Answer:

2/9y(3y−4/7)

Use the distributive property to multiply  

9

2

​

y by 3y−

7

4

​

.

9

2

​

y×3y+

9

2

​

y(−

7

4

​

)

Multiply y and y to get y

2

.

9

2

​

y

2

×3+

9

2

​

y(−

7

4

​

)

Express  

9

2

​

×3 as a single fraction.

9

2×3

​

y

2

+

9

2

​

y(−

7

4

​

)

Multiply 2 and 3 to get 6.

9

6

​

y

2

+

9

2

​

y(−

7

4

​

)

Reduce the fraction  

9

6

​

 to lowest terms by extracting and canceling out 3.

3

2

​

y

2

+

9

2

​

y(−

7

4

​

)

Multiply  

9

2

​

 times −

7

4

​

 by multiplying numerator times numerator and denominator times denominator.

3

2

​

y

2

+

9×7

2(−4)

​

y

Do the multiplications in the fraction  

9×7

2(−4)

​

.

3

2

​

y

2

+

63

−8

​

y

Fraction  

63

−8

​

 can be rewritten as −

63

8

​

 by extracting the negative sign.

3

2

​

y

2

−

63

8

​

y

Step-by-step explanation:

Drawing a "blue 2" will be represented by the event (or combination of events):

B ∧ O.

We know that we have the following events:

So, if we draw a card with a number 2, like in this case, the event "E" is true.

And also happens for event "B", because our card is a blue card.

Then a "blue 2" will be represented by the event (or combination of events):

B ∧ O.

Where the symbol in the middle, ∧, means "and".

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The value of the account at the end of 1 year is $10,500

The value of the account at the end of 2 years is $11,025

The value of the account at the end of 3 years is $11,576.25

If the amount of interest that is added into the account at the end of the year. Both the initial amount in the account and the interest that has already been earned would increase in value each year. This is known as compound interest.

The formula that can be used to determine compound interest is:

FV = P (1 + r)^n

Where:

FV = Future value

P = Present value

R = interest rate

N = number of years

Value of the account at the end of 1 year: 10,000 x (1.05) = $10,500

Value of the account at the end of 2 years: 10,000 x (1.05²) = $11,025

Value of the account at the end of 3 years: 10,000 x (1.05³) = $11,576.25

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Answer:

Step-by-step explanation:

7 days= 1 week

42 days= 42/7 = 6 weeks

For 1 week 1 bag of food

For 6 weeks 6 bags of food

Answer:

Step-by-step explanation:

Alberto was in the shelter with his friends for four days how many Ligias were they?

Values of x and y in the given equations by elimination method are 5 and 7 respectively. that is, x=5 and y=7.

In the elimination method, the aim is to entirely remove one of the unknown variable which would eventually make it easier to calculate be other unknown. However, it is important to note that this method is most effective when neither of the coefficients is equal to 1. The coefficient of either of the two variables will be made the same in both equations and by subtracting one from the other, it would be eliminated. It is a non-graphical methods of solving simultaneous linear equations.

consider the equations as (1) and (2),

-9x+10y=25..........................(1)

   7x-4y=7............................(2)

Now, multiply equation (1) by 4 and equation (2) by 10

Let the equations we get now be (3) and (4),

-36+40y=100......................(3)

70x-40y=70........................(4)

We can see that the coefficient of y in both equations is same that is 40

Now, add equation (3) and (4)

-36+40y+70x-40y=100+70                ( y terms cancel out)

By evaluating we get,

-34x=170

x=-170/34

x=5

To find the value of y, substitute value of x in equation (2)

7x-4y=7

7*5-4y=7

35-4y=7

35-7=4y

28=4y

y=28/4

y=7

Therefore, we can conclude that the values of x and y in the given equations -9x+10y=25 and 7x-4y=7 by elimination method are 5 and 7 respectively. that is, x=5 and y=7.

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Answer:

35 volunteer hours

Step-by-step explanation:

1.25*7=8.75(in a week)

8.75*4=35

120 and 90 are Partial product of 3×1,342. Hence, option C is correct.

A Partial product is what we get when we multiply already multiplicand by the first digit of a multiplier that has multiple digits. We split the number into smaller parts in order to multiply. Further, each piece is multiplied separately, and after that, it is added.

In simple terms Partial products are mathematical operations that multiply each digit of one number by each digit of another number while maintaining the place value of each digit. For example, the place value of 4 in the number 43 would be 40.

Model for multiplication of incomplete products.

A model that breaks down data into its individual components. or position values in easy place value to make multiplication easier.

Thus, option C is correct.

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Answer:

yes. we can write it as a fraction= 56214/100000

it is terminating because it has a stop and its not repeating

Based on the number of days that the health inspector and the fire inspector visits, the table for their next 4 visits is:

Number of visits        Health Inspector visits           Fire inspector visits

          1                                             7                                          12

          2                                            14                                        24

          3                                             21                                        36

           4                                            28                                       48

The number of days till both inspectors visit on the same day is 84 days.

The model that would be best to use and solve the problem of the number of days till both inspectors visit is the Lowest Common Multiple.

This shows the number of days till both inspectors would visit based on their visiting interval.

The lowest common multiple of 7 and 12 is 84 which means that the health and fire inspectors would visit after 84 days on the same day.

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The in the canoe race, Dallas paddles faster than Mason.

According to the statement

We have to find that the Speed of the .

So, For this purpose, we know that the

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

From the given information:

Mason and Dallas are in a canoe race. Mason paddles 7/8 mile in 1/4. Dallas paddles 9/5 miles in 1/3 hour.

Then

The Mason paddles 7/8 mile in 1/4 hour.

We calculate the Speed = Distance/Time

Speed = (7/8)/(1/4)

Speed = (7/8) × (4/1)

Speed = 7/2

Speed = 3.5 miles per hour

And Dallas paddles 9/5 miles in 1/3 hour.

Speed = Distance/Time

Speed = (9/5)/(1/3)

Speed = (9/5) × (3/1)

Speed = 27/5

Speed = 5.4 miles per hour.

So, The in the canoe race, Dallas paddles faster than Mason.

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Answer:

5 2/5 is GREATER THAN  3 1/2, so DALLAS paddles faster.

Answer:

10:30 On the Next day

Step-by-step explanation:

This Is a Answer