Instructions: For the following quadratic functions, write the function in factored form and then find the -intercepts, axis of symmetry, vertex, and domain and range.

It is given that the price of the box increases from R17.99 to R19.99.

It is required to find the inflation rate for the period.

Recall the formula for the Inflation Rate:

Substitute the given prices:

Answer:

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 12 on the left side and the dividend 155 on the right side like this:

 1 2 ⟌ 1 5 5

Step 2:

The divisor (12) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

       0    

 1 2 ⟌ 1 5 5

Step 3:

Multiply the divisor by the result in the previous step (12 x 0 = 0) and write that answer below the dividend.

       0    

 1 2 ⟌ 1 5 5

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

       0    

 1 2 ⟌ 1 5 5

     - 0    

       1    

Step 5:

Move down the 2nd digit of the dividend (5) like this:

       0    

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

Step 6:

The divisor (12) goes into the bottom number (15), 1 time(s). Therefore, put 1 on top:

       0 1  

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

Step 7:

Multiply the divisor by the result in the previous step (12 x 1 = 12) and write that answer at the bottom:

       0 1  

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

       1 2  

Step 8:

Subtract the result in the previous step from the number written above it. (15 - 12 = 3) and write the answer at the bottom.

       0 1  

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

     - 1 2  

         3  

Step 9:

Move down the last digit of the dividend (5) like this:

       0 1  

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

     - 1 2  

         3 5

Step 10:

The divisor (12) goes into the bottom number (35), 2 time(s). Therefore put 2 on top:

       0 1 2

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

     - 1 2  

         3 5

Step 11:

Multiply the divisor by the result in the previous step (12 x 2 = 24) and write the answer at the bottom:

       0 1 2

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

     - 1 2  

         3 5

         2 4

Step 12:

Subtract the result in the previous step from the number written above it. (35 - 24 = 11) and write the answer at the bottom.

       0 1 2

 1 2 ⟌ 1 5 5

     - 0    

       1 5  

     - 1 2  

         3 5

     -   2 4

         1 1

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 155 divided by 12 calculated using Long Division is:12

11 Remainder

Answer

a) The plotted graph is shown in the Explanation below.

b) a = 12, b = 2

Explanation

n = a(b^m)

Taking the logarithm of both sides

log n = log [a(b^m)]

log n = log a + log (b^m)

log n = log a + m log b

So, to first plot the graph, we know we need to rewrite this equation to match the equation of a straight line. Equation of a straight line is

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

log n = (log b) m + log a

y = mx + b

y-axis = log n

slope = log b

x-axis = m

intercept = log a

So, we need to plot log n (on the y-axis) against m (on the x-axis)

m | n | log n

1 | 24 | 1.38

2 | 48 | 1.68

3 | 96 | 1.98

4 | 192 | 2.28

5 | 384 | 2.58

The values for log n are then plotted against the corresponding value of m

The image is presented below.

From the graph, we can easily see that

Intercept = 1

To obtain the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

Using the two farthest points,

(x₁, y₁) and (x₂, y₂) = (1, 1.38) and (5, 2.58)

b) Intercept = log a = 1.08

a = log⁻¹ (1.08) = 12

Slope = log b = 0.3

b = log⁻¹ (0.3) = 1.995 = 2

n = 12 (2^m)

We can test this by putting values of m in the expression looking to get n

when m = 1,

n = 12 (2^1)

n = 12 (2) = 24

when m = 5

n = 12 (2^5)

n = 12 (32) = 384

So, our model works!!!

Hope this Helps!!!

The change after buying the calculators is $204.12

Ms. Wood has a class of 18 students

She wants to spend $20 on each of her students

The total money she can spend can be calculated as follows

= 18 × 20

= 360

She buys the calculators for her students, everything costs $155.88

The money she has left to spend can be calculated as follows

= 360 - 155.88

= 204.12

Hence she has $204.12 left as the change she can spend on her students

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In a population of values having a normal distribution with (μ = 62.9) and (σ = 25.8), and we intend to draw a random sample of size (n = 22),

(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is 0.2476

(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is (0.0007)

As per the question statement, a population of values has a normal distribution with (μ = 62.9) and (σ = 25.8) and we intend to draw a random sample of size (n = 22).

We are required to calculate:

(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3)

(ii) The probability that a sample of size (n = 242) is randomly selected less than 45.3 [P(M < 45.3)].

Let us assume that, a random variable "X" follows normal distribution with mean (μ = 62.9), standard deviation (σ = 25.8) and a sample size of (n = 22).

(i) The probability that a single randomly selected value is less than 45.3 [P(X < 45.3) is,

P (X < 45.3) = P[{(X - μ)/σ} < {(45.3 - 62.9)/25.8}]

= [P{Z < (-0.6822)}]

=0.247556247343...[Using Excel Function "NORMSDIST (-0.6822)]

≈ 0.2476

(ii) The probability that a sample of size (n = 22) is randomly selected with a mean less than 45.3 [P(M < 45.3)] is,

P(M < 45.3) = P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/25.8/√22)}]

= P[{(M - μ)/(σ/√n)} < {(45.3 - 62.9)/5.5006}]

=P[Z < (-3.19965)]

= (0.000687972836)...[Using Excel Function "NORMSDIST (-1.49)]

≈ 0.0007

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Answer: Heather: $10, Kareem: $19, Tom: $57

Step-by-step explanation:

Given the expressions:

these two expressions are not equivalent, since one is thrice a number and the other is a cubic number. We can see this if we write completely each expression:

thus, the expressions are not equivalent

D: {-5, -2, 1, 2}

R: {-4, 0, 3}

The relation is a function

Given:

5) Ordered pairs on a coordinate plane

To find:

the domain, range, and the type of relation

To determine the domain and range, we will list the ordered pairs:

(-5, 3), (-2, -4), (1, 0), (2, 3)

The first number in each pair represents the x values (domain), while the 2nd number in each pair represents the y values (range)

The domain: {-5, -2, 1, 2}

The range: {3, -4, 0, 3}

Rearranging and picking one of the repetitions:

The range: {-4, 0, 3}

For a relation to be a function, each input will have only one output.

None of the inputs appears more than once. Hence, each input has only one output. It is a function

As it is a proportional relationship then this relationship can be described by a line. To find the equation of the line that passes through the points shown in the table, you can first find the slope and then use the point-slope formula.

The result of the expression -8w times -w is [tex]8w^{2}[/tex]

The expression is -8w times -w

Expressions is the mathematical statements that have a minimum of two terms containing numbers or variables, connected by an operator in between. The operator maybe addition, subtraction, division or multiplication.

Here the expression is -8w times -w

Here -8w times -w means, we have to multiply the -8w by -w

Therefore the expression is

-8w × -w

We know when we multiply the a negative number by negative number the result will be positive number

-8w × -w = [tex]8w^{2}[/tex]

Hence, the result of the expression -8w times -w is [tex]8w^{2}[/tex]

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Given data:

The first point on the graph is (0,20,000).

The second point on the graph is (40,0).

The equattion of the line is,

(y-20,000)/(x-0)=(0-20,000)/(40-0)

(y-20,000)/(x)=-500

y-20,000=-500x

y=-500x+20,000

Thus, the equation of the line is y=-500x+20,000

The cations and Anions for the given compounds are;

1) CuS: Cation; Cu²⁺ and Anion: Su²⁻

2) (NH₄)₂O; Cation; NH₄⁺ and Anion: O²⁻

3)Mn₃(PO₄)₂; Cation; Mn²⁺  and Anion: PO₄³⁻

4) VBr₅; Cation; V⁵⁺ and Anion: Br⁻

Cations are defined as Positively charged ions that are formed by loss of electrons by an atom. In a cation, number of electrons are less than number of protons.

Anions are defined as Negatively charged ions that are formed by gaining of electron by an atom. In anions, number of electrons are more than the number of protons.

Thus;

1) CuS

Cation; Cu²⁺

Anion: Su²⁻

2) (NH₄)₂O

Cation; NH₄⁺

Anion: O²⁻

3) Mn₃(PO₄)₂

Cation; Mn²⁺

Anion: PO₄³⁻

4) VBr₅

Cation; V⁵⁺

Anion: Br⁻

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Answer:

100 is the number

Step-by-step explanation:

For this equation, it may be helpful to replace words with symbols.
The question is:
if 6% of x is the same as 5% of 120, then what is x?

The comma splits the sentence into two parts

if 6% of x is the same as 5% of 120 is the main focus, and the second part requires you to find x.

In the question "if 6% of x is the same as 5% of 120"
the word "of" can be replaced with " * ", and the words "is the same as" can be replaced with "=". The if can be dropped

The question becomes:

6% * x = 5% * 120

This equation can be easily solved.

6% = 0.06
5% = 0.05

So,

0.06x=0.05*120

0.06 x = 6

x = 6 / 0.06

x = 100

Simple interest is the cost of borrowing money without accounting for the effects of compounding.12672 is the size of Kathleen’s total interest when she retires.

Simple interest is the cost of borrowing money without accounting for the effects of compounding.

Given that Kathleen begins working and at age 32 she invests $6000.00 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65.

Let us calculate the age or time

65-32 =33 years

A=P(1+rt)

A= Final Amount

P=Principle amount=6000

r = rate of interest=6.4%

t is time =33 years

Substitute these values in Formula.

Convert 6.4% to decimal number by dividing with 100.

A=6000(1+0.064(33))

A=6000(1+2.112)

A=6000(3.112)

A=18672

The final Amount she got is 18,672.

To find the interest amount we have to substitute initial amount from final amount.

18672-6000

=12672

Hence 12672 is the size of Kathleen’s total interest when she retires.

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C

1) Writing down the data gathered from that :

lbs number of fishes

18 2

19 1

20 1

26 1

31 3

34 1

2) Examining the steam and plot graphs we can state that the best represents those collected data is the option C

Note how many times those data are enlisted, and you can conclude that. On the left the tens and on the right the units, just like the "key" displays.

3) Hence, the answer is C

The length of the longest side of the metal triangle is 7.8 inches

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Answer:

Domain: [tex](-\infty, \infty)[/tex]

Range: [tex][0, \infty)[/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

Option C: Square root of 74

Step-by-step explanation:

Use the distance formula

The approximate surface area of the right triangular prism is 141.5 cm².

The surface area of a triangular prism can be found as follows;

surface area of a triangular prism = (perimeter × length) + (2 × base area)

Therefore,

perimeter of the triangular base = 5 + 5 + 5

perimeter of the triangular base = 15 cm

length = 8 cm

The base area = 1 / 2 bh

where,

The base area = 1 / 2 × 4.3 × 5

The base area = 1 / 2 × 21.5

The base area = 10.75 cm²

Hence,

surface area of a triangular prism = (15 × 8) + 2(10.75)

surface area of a triangular prism = 21.5 + 120

surface area of a triangular prism = 141.5 cm²

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Answer:

Step-by-step explanation:

The average rate of change of the function f(x) on the interval−6≤x≤2 is  -0.5

This is further explained below.

Generally, The average rate of reaction is referred to as the change in concentration of any of the reactants or any of the products per unit of time during a specific period of time. This change may occur at any point throughout the reaction.

A single rate is applicable to property that is located in more than one place and that is calculated by weighting the separate rates that are calculated for each location.

In conclusion, The average rate of change on x e(a, b)

[tex]\begin{aligned}m &=\frac{f(b)-f(a)}{b-a} \\\\m &=\frac{f(2)-f(-6)}{2-(-6)} \\\\&=\frac{2-(-(-6))}{8}=\frac{6}{2} \\\\=-0.5\\\\\end{aligned}[/tex]

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Answer : r = 3%

Answer:

C. 6 + 6 + 10 + 10 + 15 + 15

Explanation:

The surface area of a rectangular prism can be calculated as:

Surface Area = lw + lw + wh + wh + lh +lh

Where l is the length, w is the width, and h is the height.

So, replacing l by 3, w by 2, and h by 5, we get:

Surface Area = 3(2) + 3(2) + 2(5) + 2(5) + 3(5) + 3(5)

Surface Area = 6 + 6 + 10 + 10 + 15 + 15

Therefore, the expression that can be used to find the surface area is:

Surface Area = 6 + 6 + 10 + 10 + 15 + 15

  A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the points A, B, C, D, and E in the aforementioned figures are vertices.

Fill in the square for 2 x ² + 8 x + 7.

To continue, tap...

2 ( x + 2 ) 2 − 1 Set y to the newly created right side.

y = 2 ( x + 2 ) 2 − 1

Find the values of a, h, and k using the vertex form, y = a (x h ) 2 + k. a = 2 h = 2 k = 1

Find the (h,k) vertex. ( 2, 1 ) .

2 x ² + 8 x - 7

Discover the initial derivative.

4 x + 8

Solve the problem 4 x + 8 = 0 by setting the first derivative to 0.

To continue, tap... x = − 2

Locate the values at which the derivative is ambiguous.

All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number.

At each x value where the derivative is 0 or undefined, evaluate 2 x 2 + 8 x 7.

( − 2 , − 15 ).

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Answer: 16.9 feet.

Step-by-step explanation:

The person's shadow is 1.3 times its shadow, which was found by dividing 5.2 by 4. Once we have the proportion, we can multiply the tree's shadow by 1.3 and get 16.9 feet.

originally, the cost was to be divided among all members

Where m is the number of members and x was the cost per person originally

When 5 people decided not to go, x was increased $14 and m decreased 5...

Now, we have two equations that we need to solve...

if we subtract the two expressions, we get the above

Now, we simplify...

Now, we solve for m

we obtain that m=25, meaning there are 25 members, so 25-5=20, this is, 20 people went to the expedition

The number of pounds of doughs available is given as:

The fraction of a pound used for one medium is given as:

Let m be a glass of milk and s be a snack bar.

3 glasses of milk and 4 snack bars have a total of 80 carbohydrates. So, the expression is,

4 glasses of milk and 3 snack bars have a total of 81 carbs.

The above equation can be rewritten as,

Put equ (3) in (1) to find s.

Now, put 11 for s in equ (1) to find m.

So, there are

The probability of winning is 1/200.

The probability of losing is 199/200.

The gain of winning is

($90 - $6) that is $90 of the winning ticket minus the $6 ticket cost.

The loss of lossing is -$6 that is a player loses $6 for the ticket.

The expected value therefore is calculated as

Therefore, the expected value for a ticket in this lotter is -$5.55 or an average loss of $5.55.