Can someone please help. Will you graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. In your final answer, include a copy of the graph.
y = 2x^2 + 7
y = 5^(x-4)

The solution to the first algebraic equation is x = 7, and the solution to the second equation is x = -3. Both problems involve setting up and solving algebraic equations to find the value of the unknown number.

To solve the problems stated, we need to set up algebraic equations and solve for the unknown number x.

For the first one:

Fourteen less than five times a number is three times the number: 5x - 14 = 3x.

After simplifying, we get 2x = 14.

Divide both sides by 2 to find x = 7.

For the second one:

Twelve more than seven times a number equals the number less six: 7x + 12 = x - 6.

Rearrange to find 6x = -18.

Divide both sides by 6 to find x = -3.

We have found that the unknown number in the first equation is 7 and in the second equation, it is -3.

Answer:

1,802,862.

Step-by-step explanation:

We have been given that the population of state is 1,821,000 decreasing by 0.2% every year. We are asked to find the population of state after 5 years.

We will use exponential decay function to solve our given problem.

[tex]y=a\cdot b^x[/tex], where,

y = Amount left after x years,

a = Initial amount,

b = For decay b is in form (1-r) where r represents decay rate in decimal form.

x = Number of years.

Let us convert our given rate in decimal form.

[tex]0.2\%=\frac{0.2}{100}=0.002[/tex]

Upon substituting our given values in above formula we will get,

[tex]y=1,821,000 \cdot(1-0.002)^5[/tex]

[tex]y=1,821,000 \cdot(0.998)^5[/tex]

[tex]y=1,821,000 \cdot 0.990039920079968[/tex]

[tex]y=1,802,862.69[/tex]

Since we can not have 0.69 of a person, therefore, we will round down our answer.

[tex]y=1,802,862.69\approx 1,802,862[/tex]

Therefore, the population of state after 5 years will be 1,802,862.

Answer:(-2.7,2.1)

Step-by-step explanation:

Answer:

The inequality would be r/7 ≤ 18 and the solution would be r ≤ 126

Step-by-step explanation:

We start by writing the inequality

r/7 ≤ 18

We know to use division between r and 7 since it asks for the quotient and we know to use a ≤ sign since it says "is no more than"

To solve, simply multiply both sides by 7

r ≤ 126

The inequality will be r/7 ≤ 18

Since it's a quotient, we'll need to divide the expression and this will be:

= r/7 ≤ 18

Now the value of r will be gotten thus:

r/7 ≤ 18

Cross multiply.

r ≤ 18 × 7

r ≤ 126

Therefore, this mean that the value of r will be 126 or numbers lower than 126

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[tex] p\%=\dfrac{p}{100}=p:100\\\\21\dfrac{1}{4}\%=\dfrac{21\cdot4+1}{4}=\dfrac{85}{4}\%=\dfrac{85}{4}:100=\dfrac{85}{4}\cdot\dfrac{1}{100}=\dfrac{85}{400}=\dfrac{85:5}{400:5}=\dfrac{17}{80} [/tex]

Answer:

the answer is 17/80 hope this helps

To convert 1559 cm to inches, divide by 2.54, and the result should be reported with the same number of significant figures as the given measurement, which is four. Thus, 1559 cm is equal to 613.8 inches.

To convert 1559 cm to inches using the conversion factor 1 inch = 2.54 cm, we divide 1559 by 2.54. The number 1559 has four significant figures because all non-zero digits are considered significant. Since the conversion factor 2.54 cm per inch is exact and does not limit the number of significant figures, the result should also be reported with four significant figures.

The calculation would be as follows:

The measurement of ∠y = ∠DBC will be 40°.

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given is ∠ABC = 110°

Let ∠ABD = x , ∠DBC = y, ∠CBE = z

∠ABD + ∠DBC + ∠CBE = 180°

x + y + z = 180°

and

∠ABD + ∠DBC = 110°

x + y = 110°

Then -

z = 180° - (x + y)

z = 180 - 110

z = 70°

Since DB and EC are equally inclined -

x = z = 70°

Then -

x + y = 110°

y = 110° - 70°

y = 40°

Therefore, the measurement of ∠y = ∠DBC will be 40°.

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Answer:

The value of A is 4.

Step-by-step explanation:

Consider the provided quadratic equation.

[tex]4x^2-20x+3=0[/tex]

Subtract 3 from both sides.

[tex]4x^2-20x+3-3=-3[/tex]

[tex]4x^2-20x=-3[/tex]

Now take 4 common from the left side of the above equation.

[tex]4(x^2-5x)=-3[/tex]

Compare the above equation with [tex]A(x^2 - 5x) = -3[/tex]

By the comparison it is clear the value of A is 4.

Hence, the value of A is 4.

Answer-

The best-fit quadratic equation is  [tex]y=14.9786x^2+3.1057x+56.2771[/tex] and the game cost in 2010 will be $1586

Solution-

Plotting a table taking year as input variable and cost as output variable.

X= year - 2000    

Y= cost in dollar.

Quadratic equation formula,

[tex]y=ax^2+bx+c[/tex]

[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]

Where,

[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]

[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]

[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]

[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]

[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]

Putting the values, we get

[tex]a=14.9786,b=3.1057,c=56.2771[/tex]

Putting these in the quadratic equation,

[tex]y=14.9786x^2+3.1057x+56.2771[/tex]

In order to  get the cost of game in 2010, we can put x=10 to get the value of y or the cost of game.

[tex]y(10)=14.9786(10)^2+3.1057(10)+56.2771=1585.1941 \approx 1586[/tex]

0-9 = 10 numbers

 1st digit can be 1 0f 10

2nd digit can be 1 of 9

3rd digit can be 1 of 8

4th digit can be 1 of 7

10 * 9 *8*7 = 5040 different combinations

The number of different possible passwords are possible

Given that each digit can be used once, then:

So, the number of passwords is:

n = 10 * 9 * 8 * 7

Evaluate the products

n = 5040

Hence, there are 5040 different possible passwords

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$27 / 4 = 6.75 dollars per hour

4 / 24 = 0.148 = 0.15 hours per dollar

Answer is A

Complementary angles add up to 90 degrees. Angle b can be found by subtracting the measure of angle a from 90 degrees.

The question states that angle a and angle b are complements, and that the measure of angle a is 36 degrees. In mathematics, complementary angles are two angles whose measures add up to 90 degrees. So, if angle a is 36 degrees, angle b can be found by subtracting 36 from 90, which gives us 54 degrees. Therefore, angle b is 54 degrees.

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"To create a box and whisker plot and calculate the Q1, Q3, and IQR for the given set of quiz grades, we must first organize the data in ascending order:

58, 60, 69, 71, 78, 78, 85, 85, 86, 87, 88, 91, 93, 95, 95, 95, 96, 98, 100, 100

Next, we find the median (Q2), which is the middle value in the ordered list. Since there are 20 scores, the median will be the average of the 10th and 11th scores:

Q2 = (87 + 88) / 2 = 175 / 2 = 87.5

Now, we need to find the first quartile (Q1), which is the median of the first half of the data (excluding the median if the number of data points is odd). Since we have an even number of scores, we take the first 10 scores and find their median:

Q1 = (71 + 78) / 2 = 149 / 2 = 74.5

For the third quartile (Q3), we take the median of the second half of the data (excluding the median if the number of data points is odd). Again, we have an even number of scores, so we take the second set of 10 scores and find their median:

Q3 = (95 + 96) / 2 = 191 / 2 = 95.5

Finally, the interquartile range (IQR) is calculated by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 95.5 - 74.5 = 21

Therefore, the Q1, Q3, and IQR for the fifth period Coordinate Algebra class quiz grades are:

Q1 = 74.5

Q3 = 95.5

IQR = 21

These values are essential for constructing the box and whisker plot and for understanding the spread of the middle 50% of the quiz scores."

Answer:

C. Circumcenter.

Step-by-step explanation:

We have been given an image of a triangle KLM  and we are asked to choose the term that describes point N.

We can see that point N is the point where perpendicular bisector of our given triangle are intersecting.

Since the point where the perpendicular bisectors of a triangle intersect is called circumcenter, therefore, point N is the circumcenter of our given triangle KLM nad option C is the correct choice.  

False, the given equation of hyperbola is vertical hyperbola.

What is hyperbola?

Hyperbola is defined as a conic section, two-branched open curve, produced by the intersection of a circular cone.

[tex]\frac{(y-2)^2}{16} -\frac{(x+1)^2}{144}=1[/tex]

Simplify each term in the equation in order to set the right side equal to 1

The standard form of an ellipse or hyperbola requires the right side of the equation be 1

This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.

[tex]\frac{(y-k)^2}{a^2} -\frac{(x-h)^2}{b^2}=1[/tex]

Match the values in this hyperbola to those of the standard form. The variable

h represents the x-offset from the origin,

k represents the y-offset from origin, a.

a=4

b=12

k=2

h=−1

c, the distance from the center to a focus  4√10

The foci is (−1,2+4√10),(−1,2−4√10)

Hence, the hyperbola is vertical.

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To solve this problem, we use the z statistic.  The z formula is:

z = (x – u) / s

where x is lakers score = 101.7, u is Celtics score = 99.2, s is standard dev = 10.5

z = (101.7 – 99.2) / 10.5 = 0.24

using the normal distribution table at z = 0.24, the P value is:

P (z = 0.24) = 0.5984 = 59.84% 

To find the proportion of games in which the Boston Celtics scored more than the Los Angeles Lakers' mean score, we need to standardize the Lakers' mean score, find the z-score, and then find the proportion from the standard normal distribution table.

To find the proportion of games in which the Boston Celtics scored more than the Los Angeles Lakers' mean score, we need to find the area under the normal distribution curve to the right of the Lakers' mean. First, we need to standardize the Lakers' mean score by finding the z-score using the formula:

z = (x - μ) / σ

where x is the mean score, μ is the mean of the Celtics' scores, and σ is the standard deviation of the Celtics' scores. Substituting the given values, we have:

z = (101.7 - 99.2) / 10.5 = 0.2381

Next, we find the proportion of scores greater than the Lakers' mean in the standard normal distribution table or using a calculator. Looking up the z-score of 0.2381 in the table, we find the proportion to be approximately 0.4069, or 40.69%.