Convert each equation from slope-form to standard form

The value of x in (8^x/5) (8^x/4)=8^4 is 80/9

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

The equation;(8^x/5) (8^x/4)=8^4

LHS=(8^x/5) (8^x/4)

=(8^x/5) (8^x/4)

=8^(x/5+x/4)

=8^((4x+5x)/20)

=8^(9x/20)

Now, by comparing LHS to RHS

We will get;

9x/20=4

9x=80

x=80/9

Therefore the answer of the equation will be 80/9

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.

The correct option is C.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

We have a graph that has a slope of negative three halves and a y-intercept of 3.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁).

A). Line passing through the points (0, 2) and (3, 0).

y - 2 = 2/3(x)

y = 2/3(x) + 2.

This is not a required line.

B). Line passing through the points (0, 2) and (2, -1).

y - 2 = -3/2(x)

y = -3/2(x) + 2.

This is not a required line.

C).  Line passing through the points (0, 3) and (2, 0).

y - 3 = -3/2(x)

y = -3/2(x) + 3.

This is a required line.

D). Line passing through the points (0, 3) and (3, 1).

y - 3 = -2/3(x)

y = -2/3(x) + 3.

This is not a required line.

Therefore, y = -3/2(x) + 3 is a required line.

To learn more about the slope;

brainly.com/question/3605446

#SPJ1

Answer:

The line y = -3/2(x) + 3 has a slope of negative three halves and a y-intercept of 3.

The correct option is C.

Step-by-step explanation:

The simplest polynomial function having integer coefficients with the given zeros is: x⁴ -2x³ + 14x² - 32x - 48

The polynomial is of degree 4

We have the values as 4i, 3 , -1

Hence we would have the following in brackets

for 4i = (x - 4i) (x + 4i)

for 3 = (x - 3)

for - 1 = (x + 1)

We would have to multiply these

(x - 4i) (x + 4i) (x - 3) (x + 1)

f(x) = x² + 4ix - 4ix (-4i)² (x² + x - 3x - 3)

f(x) = (x²  + 16)(x² - 2x - 3)

This can also be expanded to standard form if you wish

x⁴ - 2x³ - 3x² + 16x² - 32x - 48

properly arrange

x⁴ -2x³ + 14x² - 32x - 48

Read more on polynomials here: https://brainly.com/question/2833285

#SPJ1

where A is a real integer and A ≠ 0.

f(x) = A(x2 + 16)(x - 3)(x + 1)

Laverne said the number 222 before Shirley flees

It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.

To solve this exercise we are going to apply the formula of the arithmetic sequence:

S = (n/2)[a1 + a1 + d(n - 1)]

Where;

Information about the problem:

Clearing the (n) variable we get:

S = (n/2)[ 7 +  7 + 5(n-1) ] > 5000

(n/2) [ 9 + 5n ]  > 5000

n[ 9 + 5n  ] > 10000

5n^2 + 9n - 10000 > 0

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 9 ± √ [9² - (4* 5*-10000)]} / (2 * 5)

x= {- 9 ± √ (81+ 200000)} / 10

x= {- 9 ± √200081} / 10

x= (- 9 ± 447.30) / 10

x = 43.83

n > 43 then n = 44

Calculating the 44th term, we get:

aₙ= a + d*(n-1)

a44 = [ 7 +5(44 - 1) ]

a44 =  [ 7 +5(43) ]

a44 = 222

Learn more about arithmetic sequence at: brainly.com/question/6561461

#SPJ4

Answer:

12

Step-by-step explanation:

Assuming that $300 and $50 are the respective cost(s) of the premium and discount tickets, if we didn't buy any premium tickets, we could afford to buy 12 discount tickets at $50 because 12($50) = $600 

It is not a triangle.

Does given feet is a triangle or not?

The Triangle Inequality theorem states that in a triangle, , where  and  are shorter side lengths and  is the longest side length.

Given that  5+9<15, the given side lengths do not compose a valid triangle.

To learn more about triangle refers to:

https://brainly.com/question/17335144

#SPJ1

At a large museum, there are 60 people in each tour group. so that the ordered pairs are 1 - 60 peoples, 2 - 120 peoples, 3 - 180 peoples, 4 - 240 peoples, 5 - 300 peoples, 6 - 360 peoples etc.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

In order to understand a point visually, it can be helpful to position it on the Cartesian plane.

An ordered pair's numerical values may be fractions or integers.

Given that, at a large museum, there are 60 people in each tour group.

In 1 group there are 60 peoples.

In 2 group there are 2 * 60 = 120 peoples.

In 3 group there are 3 * 60 = 180 peoples.

like this the correct ordered pairs are 1 - 60 peoples, 2 - 120 peoples, 3 - 180 peoples, 4 - 240 peoples, 5 - 300 peoples, 6 - 360 peoples etc.

To learn more about ordered pair visit:

brainly.com/question/1528681

#SPJ1

Answer: 77 degrees

Step-by-step explanation:

Ratio of the angles = 5 : 7 : 9 = 5x : 7x : 9x

5x + 7x + 9x = 21x

180 = 21x

x = 180/21

Largest angle = 9x,

= 9 * 180/21

= 540/7

540/7 = 77.14285...

Which is rounded to 77 degrees :>

The result of an average of more than 100% in a survey of tenants on cleaning chores in shared apartments is likely due to social desirability bias.

The average tenant response of more than 100% in a study about cleaning duties in shared apartments is probably the product of social desirability bias. Social desirability bias occurs when respondents give answers that they think are socially acceptable or desirable, rather than their true opinions or behavior.

In this case, tenants may have overstated their contribution to cleaning the apartment, in order to appear more helpful or responsible, leading to an average percentage higher than 100%.

To learn more about average here:

https://brainly.com/question/24057012

#SPJ4

When it comes to baking bread, Jennifer has an absolute advantage. But when it comes to making cookies, Janet has an absolute advantage.

Absolute advantage is used when there is efficient production.  It is used to describe the ability of a person, place, business, or nation to produce a lot of goods or services with the same amount of inputs in a given amount of time.

Here, a loaf of bread baked by Jennifer takes about 2 hours but it takes about 3 hours for Janet to bake a loaf of bread. So, Jennifer has an absolute advantage in baking a loaf of bread.

Also, Jennifer takes about 1 hour to bake 12 cookies but it only takes 3/4 hours or 45 minutes for Janet to bake cookies 12 cookies. So, Janet has an absolute advantage in baking a dozen cookies.

To know more about absolute advantage:

https://brainly.com/question/12291750

#SPJ4

Hi There!

Your Answer could be 8 don't trust me i might be wrong

Answer: Your GCF would be 1!

Step-by-step explanation:

First you need to:

Factor 10x² as shown - 2 · 5 · x · x

Factor 21x as shown - 3 · 7 · x

Factor 49 as shown: 7 · 7

GCF = 1

I hope this helps!

If Neil uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend , then the number of 41 cent stamp used is 3  and number of 6 cent stamps used is 12 .

Let number of 41 cents stamps used be = x ;

and let number of 6 cents stamps used be = y ;

converting amount 41-cents in dollars is = $0.41  ;

and converting amount 6-cents in dollars is = $0.06  ;

the amount for which Neil used 41-cent stamps , 6-cent stamps is = $1.95 ;

this situation in equation form is written as ⇒ 0.41x + 0.06y = 1.95

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 195  ;

⇒ y = (195 - 41x)/6 ;

We will test this equations for values of x and y , the number of stamps must be whole numbers .

If x = 1 , then value of y is = 25.66

If x = 2 , then value of y is = 18.833

If x = 3 , then value of y is = 12

If x = 4 , then value of y is = 5.166 .

the only value of x and y which shows a whole number as an output is : If x = 3 , then y = 12 .

Therefore , Neil used "3" 41-cents stamps and "12" 6-cent stamps .

Learn more about Equations here

https://brainly.com/question/14532602

#SPJ4

The possible side length of the third side is 16 inches

It is important to note that the Pythagorean theorem states that the square of the hypotenuse side is the sum of the square of the other two sides, they are the opposite and adjacent sides.

This is represented as;

a² = b² + c²

Given that;

Note: 1 feet = 12 inches

Substitute the values into the formula, we get;

20² = 12² + c²

Find the squares

400 = 144 + c²

collect like terms

c² = 256

Find the square root

c = 16 inches

Hence, the value is 16 inches

Learn about triangles on:

https://brainly.com/question/17335144

#SPJ1

The trigonometric function that accurately fits the data is as follows:       y = 1.87sin(–0.29x + 4.79) + 6.13. So the option D is correct.

The following is the trigonometric function that best represents the data:

y = 1.87sin(-0.29x + 4.79) + 6.13

Check the values in the table using the aforementioned equation;

At x = 1

y = 1.87sin(-0.29 x 1  + 4.79) + 6.13

y = 1.87sin(4.5 rad) + 6.13

y = 4.3

At x = 2

y = 1.87sin(-0.29 x 2  + 4.79) + 6.13

y = 1.87sin(4.21 rad) + 6.13

y = 4.49

At x = 4

y = 1.87sin(-0.29 x 4  + 4.79) + 6.13

y = 1.87sin(3.63 rad) + 6.13

y = 5.2

At x = 7

y = 1.87sin(-0.29 x 7  + 4.79) + 6.13

y = 1.87sin(2.76 rad) + 6.13

y = 6.8

At x = 9

y = 1.87sin(-0.29 x 9  + 4.79) + 6.13

y = 1.87sin(2.18 rad) + 6.13

y =7.7

At x = 10

y = 1.87sin(-0.29 x 10  + 4.79) + 6.13

y = 1.87sin(1.89 rad) + 6.13

y = 7.9

At x = 13

y = 1.87sin(-0.29 x 13  + 4.79) + 6.13

y = 1.87sin(1.02 rad) + 6.13

y = 7.72

At x = 17

y = 1.87sin(-0.29 x 17  + 4.79) + 6.13

y = 1.87sin(-0.14 rad) + 6.13

y = 5.9

At x = 20

y = 1.87sin(-0.29 x 20  + 4.79) + 6.13

y = 1.87sin(-1.01 rad) + 6.13

y = 4.6

To learn more about trigonometric function link is here

brainly.com/question/6904750

#SPJ4

The complete question is:

Review the table showing wind speed, y, in miles per hour, measured x hours after midnight. Which trigonometric function best models this data?

Hours after Midnight                          Wind Speed (mph)

              1                                                      4.3

              2                                                     4.2

              4                                                      5

              7                                                      6.8

              9                                                      8

              10                                                     8.1

              13                                                     7.2

              17                                                     6

              20                                                    5.1

y = 1.87sin(0.29x + 6.13) + 4.79

y = 1.87sin(0.29x + 4.79) + 6.13

y = 1.87sin(–0.29x + 6.13) + 4.79

y = 1.87sin(–0.29x + 4.79) + 6.13

The domain of the function is the set of all real numbers

From the question, we have the following parameters that can be used in our computation:

f(x)=^3radx+2-2

Express properly

So, we have the following representation

f(x) = ∛(x + 2) - 2

The above function is a cubic function

A cubic function has no restriction on its input value

This implies that the domain is the set of all real numbers

Read more about domain at

https://brainly.com/question/2264373

#SPJ1

If value of Kensington's car decreases in Value according to the exponential decay function "V = Pe^(-0. 12t)" , then value of Kensington car after 8 years is = $7658     .

The value of the Kensington car is decreasing according to the function ;

the exponential decay function is : V = Pe^(-0. 12t) ;

the purchase Price(P) of the car is = $20000  ;

we have to find the value of Kensington's car in 8 years ;

So , we substitute the value of P = 20000 and t = 8 years in the exponential decay function ,

we get ;

V  = 20000 × e^(-0. 12 × 8)

V = 20000 × e^(-0.96)

V = 20000/e^(0.96)

Simplifying further ,

V = 7657.8577 ,

V ≈ $7658 .

Therefore , the value of the car after 8 years is $7658  .

Learn more about Exponential Decay Function here

https://brainly.com/question/12889747

#SPJ4

Answer:

5

Step-by-step explanation:

(1) last season, the new york yankees played 160 games

(2) last season, the new york yankees scored

4 runs per game in exactly 1/5 of their games,  1/5*160 =32 games

5 runs per game in exactly 3/4 of their games, 3/4*160 =120 games

9 runs per game in exactly 1/20th of their games 1/20*160 = 8 games

total runs 4*32+ 5*120 + 9 *8 = 128+600+72 =800

total games 160

average: 800/160 =5

Jennifer's monthly gross pay will be $4,589.08

Figures used to determine Jennifer's monthly gross compensation

Calculate the overall tax percentage deductions as a first step.

Using this equation

State tax + City tax + Social Security + Medicare = Total tax percentage deductions

Let's enter the formula.

Total tax deductions as a percentage equal: 3.5% + 2.5% + 6.2% + 1.45%

Total tax deductions as a percentage equal 13.65%

Now let's calculate the monthly gross pay

Total tax percentage deductions = 2.5% +1.2% +6.2% +1.45%

Total tax percentage deductions = 11.35%

Now let's calculate the monthly gross pay

Monthly gross pay= ($3,981.22 +87)/(1-11.35%)

gross pay= ($3,981.22 +87)/0.8865

Monthly gross pay=$4,068.22/0.8865

Monthly gross pay= $4,589.08'

Know more about Monthly gross pay

https://brainly.com/question/25273589

#SPJ4

Answer:

A function is concave downward if its second derivative is negative. To find the values of x for which the graph of y = x^4 - 6x^2 + x is concave downward, we need to find the values of x for which the second derivative of y is negative.

The second derivative of y = x^4 - 6x^2 + x is y'' = 12x^2 - 12x

To find the values of x for which y'' is negative, we need to find the roots of the equation 12x^2 - 12x = 0.

We can factor the equation as: 12x(x-1) = 0

which gives us x = 0 and x = 1 as the roots.

Now, we need to test the sign of the second derivative in the intervals between the roots.

In the interval (0,1)

y'' = 12x^2 - 12x is positive, therefore the function is not concave downward in this interval.

In the interval (-infinity,0)

y'' = 12x^2 - 12x is negative, therefore the function is concave downward in this interval.

In the interval (1,infinity)

y'' = 12x^2 - 12x is negative, therefore the function is concave downward in this interval.

Therefore, the values of x for which the graph of y = x^4 - 6x^2 + x is concave downward are all values of x less than 0 or greater than 1.

The inequality equations is

a) The point ( -9 , 4 ) lies on the inequality relation

b) The point ( 6 , -2 ) lies on the inequality relation

c) The point ( 0 , -4 ) does not lie on the relation

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

a)

Now , let the first point be represented as P ( -9 , 4 )

The shaded region is below 4 in the y axis and less than -4 in the x axis

So , the point ( -9 , 4 ) does lies on the inequality equation graph

b)

Now , let the first point be represented as Q ( 6 , -2 )

The shaded region is below -8 in the y axis and less than 8 and more than 4  in the x axis

So , the point ( 6 , -2 ) does lies on the inequality equation graph

c)

Now , let the first point be represented as R ( 0 , -4 )

The shaded region is above -8 in the y axis and more than -4 in the x axis and less than -1

So , the point ( 0 , -4 ) does not lie on the inequality equation graph

Hence , the inequality equations is solved

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

The length of x in the triangle is 8 units.

A midsegment is the line segment connecting the midpoints of two sides of a triangle.

The midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it

Therefore, DE is the mid segment of the triangle ABC. The value of x can be found as follows:

Using the mid segment principle,

BE = EC

BD = DA

Therefore,

x = 8 units

learn more on midsegment here: brainly.com/question/20841801

#SPJ1

The mean is 24.2 and the standard deviation is 8.7.

The mean amount of revenue each car generates can be calculated by multiplying the mean number of hours parked by the cost per hour. To find the mean number of hours parked, we need to multiply each possible number of hours by its probability and add them up.

E(X) = (1 * 0.229) + (2 * 0.113) + (3 * 0.114) + (4 * 0.076) + (5 * 0.052) + (6 * 0.027) + (7 * 0.031) = 4.84 hours

So, the mean revenue is 4.84 * 5 = 24.2 dollars

The standard deviation of the revenue can be calculated by finding the standard deviation of the number of hours parked and then multiplying by the cost per hour.

SD(X) = sqrt( (1^2 * 0.229) + (2^2 * 0.113) + (3^2 * 0.114) + (4^2 * 0.076) + (5^2 * 0.052) + (6^2 * 0.027) + (7^2 * 0.031) - (4.84)^2) = 1.74 hours

So, the standard deviation of the revenue is 1.74 * 5 = 8.7 dollars.

To learn more about mean here:

https://brainly.com/question/30112112

#SPJ4

Answer:

To factor the equation y = x^2 + 6x + 8, we can use the method of finding the factors of the constant term (8) that add up to the coefficient of the x term (6).

In this case, the factors of 8 are 1 and 8, and -1 and -8. But only -1 and -8 add up to 6, so we can factor the equation as:

(x + 8)(x + 1) = 0

So the solutions are x = -8 and x = -1.

The ratio of the volume of the figure is 3:1.

The term called volume in math is defined as the space occupied within the boundaries of any three-dimensional solid

Here we know that the cylinder and a cone are having equal radii of their bases and heights.

Then let us consider that radius of the cone is equal to radius of the cylinder is defined as r and Height of the cone and height of the cylinder is defined as h.

Then their volume is written as,

=> Volume of cylinder /volume of cone

=> πr²h/ (1/3)πr²h

When we simplified this on, then we get the fraction as,

=> 3/1

Then the resulting ratio is 3:1.

To know more about Volume here.

https://brainly.com/question/11168779

#SPJ4

If you had only 5 and 11 cent stamps, it would be impossible to make a postage stamp for any amount less than 16 cents.

This is because 16 cents is the smallest amount that can be made with those two denominations of stamps.

To prove this, let's start by looking at the possible combinations of 5 and 11 cent stamps that can be used to make a postage stamp:

5 cent stamps x 11 cent stamps

1 x 0 = 0

1 x 1 = 11

2 x 0 = 10

2 x 1 = 16

As you can see, the smallest possible combination of 5 and 11 cent stamps is 2 five cent stamps and 1 eleven cent stamp, which totals 16 cents. Therefore, it is impossible to make a postage stamp for any amount less than 16 cents using only 5 and 11 cent stamps.

To learn more about stamps, click here:

https://brainly.com/question/22056874

#SPJ4

Answer:

c. non-linear and increasing

Step-by-step explanation:

The cost of each raffle ticket is thus $14.50, and the cost of 90 tickets is $1305.

In multiplication, the numbers being multiplied are referred to as factors, and the end result is referred to as the product. In division, the dividend is the number being divided, the divisor is the number dividing it, and the quotient is the outcome of the division.

Given that the equation to find the cost of a single ticket is:

1218 ÷ 84 = x

x = 14.5

The cost of each raffle ticket is thus $14.50.

The cost of 90 tickets is given by:

90 × 14.50 = y

y = 1305.

Hence, the cost of 90 tickets is $1305.

Learn more about division here:

https://brainly.com/question/1292482

#SPJ1