4(2x + 3) = 3x + 3 + 2x

Answer:

-x² - x + 2

Step-by-step explanation:

We are given the following expression:

(2x-3) + (2x²- 3x) – (3x²- 5).

To simplify, we first need to remove the parenthesis. If there is a negative sign before the parenthesis, we change the signal of everything that is inside(+ goes to -, - goes to +). So

(2x-3) + (2x²- 3x) – (3x²- 5) = 2x - 3 + 2x² - 3x - 3x² + 5

Now we need to combine the like terms:

With x²: 2x² - 3x² = -x²

With x: 2x - 3x = -x

Independent: -3 + 5 = 2

Now adding these terms, we get the simplified expression, which is:

-x² - x + 2

Given: A seventh-degree polynomial function has zeros of -6, 0 (multiplicity of 2), 1, and 4 (multiplicity of 3).

Required: To determine the behavior of the graph at the zeros.

Explanation: The given seventh-degree polynomial can be represented as

Now, the graph will cross straight through at x=-6 and x=1.

We have an odd multiplicity at x=4; hence the graph will cross through while hugging.

We have an even multiplicity at x=0; therefore, the graph will be tangent.

Here is the graph of the given function-

Final Answer: The graph will cross straight through at x=-6 and x=1,

the graph will cross through while hugging at x=4,

the graph will be tangent at x=0.

Given:

To Determine: Using the increament method the rate of change of y with respect to x

Substitute for y

Hence, the rate of change of y with respect to x is

A=$88,000

P=$70,586

r=9.8% (0.098)

Divide both sides by 70,586:

Find ln of both sides:

Divide both sides by 0.098:

Given the equation :

The first step is to add 5 to both sides

so,

The selling price after adding the profit to the dealer’s cost is $17628

The dealership averages 13% profit on new car sales

If the dealership pays $15,600 for a Rancho Turbo,

The profit is 13% of the dealership

profit =(13/100) 15600

profit = 2028

Selling proce =  cost price + profit

= 15600 + 2028

= 17628

Therefore, the selling price after adding the profit to the dealer’s cost is $17628

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The values of x and y vary directly. Hence, we can write

Here, k is the constant of proportionality.

Substitute x=0.1 and y=0.9 in the above equation and solve for k.

Put the value of k in y=kx.

Therefore, y=9x.

Since Angle AED is congruent to angle CFD and angle EDA is congruent to angle FDS, we can use the midpoint theorem to get the following:

therefore, by the ASA postulate (angle,side,angle), we have that triangle AED is congruent to triangle CFD

The sides of a triangle can be determined if the trigonometric ratios and angles are given. The missing sides of the given triangle are 6 and 8 respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

The diagram for the given triangle is given below,

Since, sin(x) = (The side opposite to angle x) / Hypotenuse

Apply the above trigonometric ratio in triangle 1 to get,

Sin(21°) = x / 16

=> x = 16 × Sin(21°)

=> x = 16 × 0.36

=> x = 5.76

Which is approximately 6 when taken as nearest to tenth.

Similarly for triangle 2, it can be written as,

Sin(40°) = x / 12

=> x = 12 × Sin(40°)

=> x = 12 × 0.64

=> x = 7.68

Which is approximately 8 when taken as nearest to tenth.

Hence, the missing sides for the given triangles are 6 and 8 approximately.

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Answer:

5:13

Explanation:

Given that the probability of the box having a toy = 13/18

Therefore, the probability of the box not having a toy:

The odds against an event is given as the ratio of the Number of unfavorable outcomes to number of favorable outcomes.

• Number of Unfavourable Outcomes = 5

• Number of favourable Outcomes = 13

Thus, the odds against the box having a toy is 5:13.

Now the total interest for 42 months will be:-

So the total amount he has to pay after 42 months will be = 9000+4095

= $13095

So

So his monthly installment will be $ 311.79

So $ 311.79 is the correct option.

From the table, to transform points in rectangle ABCD into A'B'C'D', we have to apply the next rule: (x, y) → (x+1, y-3). That is,

A(2, 4) → (2+1, 4-3) → A'(3, 1)

C(2, -1) → (2+1, -1-3) → C'(3, -4)

D(-6, -1) → (-6+1, -1-3) → D'(-5, -4)

Then, if we want to transform a point in A'B'C'D', the rule is: (x,y) → (x-1, y+3). Applying this rule to point B', we get:

B'(-5, 1) → (-5-1, 1+3) → B(-6, 4)

As the first step, let us say that the velocity of the boat in relation to a fixed point in the map of this travel is equal to its velocity in relation to the water PLUS the water velocity in relation to the fixed point WHEN it is in the same direction (travel downstream), and MINUS when traveling in the opposite direction (upstream).

From this, we will remember the definition of velocity by:

The ΔS is the distance ran by the boat, which is 60 miles. Δt is 4h for the upstream case, and 3h for the downstream case.

From this, we say that the value of V is for the boat in relation to the water (which is what we need here) and v for the water. Now, we have the following system of equations.

Now, to proceed with the solution, we will sum up the equations, which will result in the following:

We want to find the value of the expression:

Since 2 is a common factor of both numerator and denominator, we divide by 2s:

The answer is 4. (Option A)

Answer:

The slope of the line is;

Explanation:

Given the attached graph.

Recall that the formula for calculating the slope m of a line is;

From the graph, let us select two points on the line;

We have;

The slope can then be calculated by substituting this points into the formula;

Therefore, the slope of the line is;

We have two similar triangles.

They will have proportional sides and equal measures.

Then, if we have to evaluate Then, we can write:

Knowing x, we can calculate m[tex]\begin{gathered} m\angle A=3x+18 \\ m\angle A=3\cdot16+18=48+18=66\degree \end{gathered}[/tex]Answer: the measure of A is 66º

Answer: C. 7

Explanation

When the exponent of a natural logarithm has an exponent, we can do the following:

Additionally, we are given a natural logarithm, and the base for the natural logarithm is the mathematical constant e. When the argument of the logarithm is equal to the base, then it is equal to 1:

Given:

Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year.

The general equation of the growth is:

Given rate = r = 69% = 0.69

After 1 year, P = 9000

Substitute to find the initial number of Lionfish

So,

Part (A), we will write an explicit formula f(n) that represents the number of lionfish after n years

so, the formula will be:

Part (B): we will find the number of lionfish after 6 years

so, substitute with n = 6 into the equation of part (a)

So, after 6 years, the number of lionfish = 124,073

Part (C): The scientists remove 1400 fish per year after the first year

So, we the number of lionfish:

Then after 2 years, the number of lionfish

After 3 years:

So, after (n) years:

Since we want the total amount, we first can add the red and green ribbon:

Martha has 15 feet of ribbon.

To converto to yards, we can just divide the amount in feet by 3. So, in yards:

So

Martha has 5 yards of ribbon.

If R is between Q and T, we can conclude:

QR + RT = QT

Where:

QR = 10

RT = 4

therefore:

10 + 4 = QT

QT = 14

The graph that represents the theoretical probability distribution of Jeremiah's total points is given by:

Graph A.

The probability of an event in an experiment is calculated as the absolute frequency of the desired outcomes in the experiment divided by the total number of outcomes in the experiment.

The probability distribution gives the probability of all possible events in the context of the problem.

For Jeremiah to make zero points, he needs to:

Hence:

P(X = 1) = 0.2 x 0.5 x 0.7 = 0.07 = 7%.

For Jeremiah to make one point, he needs to:

Hence:

P(X = 1) = 0.8 x 0.5 x 0.7 = 0.28 = 28%.

For Jeremiah to make two points, he needs to:

Hence:

P(X = 2) = 0.2 x 0.5 x 0.7 = 0.07.

For Jeremiah to make three points, he needs to either:

Or:

Hence:

P(X = 3) = 0.2 x 0.5 x 0.3 + 0.8 x 0.5 x 0.7 = 0.31.

For Jeremiah to make four points, he needs to:

Hence:

P(X = 4) = 0.8 x 0.5 x 0.3 = 0.12.

For Jeremiah to make five points, he needs to:

Hence:

P(X = 5) = 0.2 x 0.5 x 0.3 = 0.03.

For Jeremiah to make six points, he needs to:

Hence:

P(X = 6) = 0.8 x 0.5 x 0.3 = 0.12.

Hence Graph A is correct, as it contains these probabilities.

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WE can find the sides if the triangle by apply the Sine rule :

where, a,b & c are the sides of triangle

For eg :

Consider an triangle with one side AB = 5

and angles A = 60, angle B = 45 and angle C= 75

So, substitute the value in the expression of Sine

The sides : AB = 5, AC = 3.66 & BC = 4.4

Define an exponential function, h(x), which passes through the points (1,16) and

(5, 1296). Enter your answer in the form axb^x

the equation is of the form

we have

point (1,16)

so

For x=1, y=16

substitute

isolate the variable a

Point (5,1296)

For x=5, y=1,296

substitute

substitute equation 1 in equation 2

solve for b

Find the value of a

a=16/3

therefore

the equation is

see the attached figure to better understand the problem

Solution

Step 1:

Let find the slope

His answer and these calculations are correct because he followed all the steps correctly to findtwo points' slope.

Step 2; First we need to determine how many different slopes there are on the given graph. Assume time is represented in minutes and distance is represented in meters. There are three in this graph, one goes from 0 minutes to 120 minutes and the second one is from 120 minutes to 150 minutes. The final one goes from 150 to 180 minutes. To calculate the speed of traveling we convert the distance traveled into a constant period of time i.e. an hour.

Question1

What does the slope tell you about the rate of change in elavation during Ryan’s uphill climb?

The first slope(line) tell us that Ryan travels from 300 meters to 1,500 meters from 0 minutes to 120 minutes.

meaning he traveled 1200 meters in 120 minutes which is equal to 600meters per hour or 0.6km/h.

In the second line, Ryan's travels no distance from 120 minutes to 150 minutes. So he was at rest and did not travel in this period of time.

In the third line (slope) , Ryan travels from 1,500 meters to 300 meters from 150 minutes to 180 minutes. So he traveled 1,200 meters in 30 minutes. This equals 2,400 meters per hour, which is 2.4 kilometers per hour.

Final answer

The slope tell you about the rate of change in the elevation during Ryan's uphill climb that:

Ryan ascends at a speed of 0.6 kilometers per hour for the two hours, takes rest for half an hour and then descends at 2.4 kilometers per hour for the half-hour.

Question 2

What is the total elevation change?

Elevation gain is the total amount you will climb in a day, and elevation loss is the total amount you will descend in a day. For example, if you climb 1000 feet, descend 500 feet, and then climb an additional 300 feet, the elevation gain would be 1300 feet and the elevation loss would be 500 feet.

From the graph?

Elevation gain = 1200 feet

Elevation loss = 1200 feet

Answer: 194 degrees

From the given figure, we can see a transversal forming between the pairs of parallel lines.

Let us focus on the lines n, a, and e. Here, we can see a pair of parallel lines a and e, cut by a transversal n.

We are given a measurement for angle 4, which is 97. Then we are asked to find the sum of angle 2 and angle 4.

One theorem with respect to transversals that we must be familiar with is the Alternate Interior Angles Theorem which states that:

When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

With this, we can see from the figure that angle 2 and angle 4 are actually alternate interior angles.

Since they are alternate interior angles, and they are congruent, this would mean that angle 2 also measures 97.

With this, we can now add the two measurements, and that would give us:

The sum of angle 2 and angle 4 is 194 degrees.

Answers: IQR and standard deviation

Explanation:

2/3 ---->8/12

7/12 ----> 7/12

1) Equivalent fractions have the same value proportionally, so let's find out equivalent fractions:

2) To find equivalent fractions and sum those fractions, let's factorize 3 and 12 dividing them only by Prime Numbers, when one of those numbers can't be divided then we repeat it below:

As we can see on the first line, 12 can be divided by 2 and 3 cannot.

So we repeat 3 on the line below.

We then picked 6 and divided by 2, and then repeated below 3.

Then divided3 by 3

3) Now we can rewrite 2/3 + 7/12 as:

So using the Least Common Denominator we have 2/3 (8/12) and 7/12 (7/12) as their equivalent fractions. Note that 7/12 in this case is equivalent to itself.

Step 1:

Write the equation

Step 2:

Write the trigonometric inverse identity

Step 3:

Substitute in the equation

Final answer

Since the amplitud of the function is 5 and it starts on (0,9) we can say that the function is:

y=5cos(pi/80x)+4