Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.

[tex]Solution,\:solve\:for\:x,\:\frac{5}{6}x=\frac{10}{3}\quad :\quad x=4[/tex]

[tex]Steps[/tex]

[tex]\frac{5}{6}x=\frac{10}{3}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}6,\\6\cdot \frac{5}{6}x=\frac{10\cdot \:6}{3}[/tex]

[tex]\mathrm{Simplify}:\\\\6\cdot \frac{5}{6}x,\\\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c},\\\frac{5\cdot \:6}{6}x,\\\mathrm{Cancel\:the\:common\:factor:}\:6,\\x\cdot \:5\\\\\frac{10\cdot \:6}{3},\\\mathrm{Multiply\:the\:numbers:}\:10\cdot \:6=60,\\\frac{60}{3},\\\mathrm{Divide\:the\:numbers:}\:\frac{60}{3}=20,\\\\5x=20[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}5,\\\frac{5x}{5}=\frac{20}{5}[/tex]

[tex]\mathrm{Simplify},\\x=4[/tex]

[tex]\mathrm{The\:Correct\:Answer\:is\:x=4}[/tex]

[tex]\mathrm{Hope\:This\:Helps!!!}[/tex]

[tex]\mathrm{Please\:Mark\:Brainliest!!!}[/tex]

[tex]\mathrm{-Austint1414}[/tex]

Final answer:

To solve the equation 5/6x = 10/3, multiply both sides by the reciprocal of 5/6 (i.e., 6/5), then simplify the resulting equation to find that x = 4.

Explanation:

Solving the Equation 5/6x = 10/3

To solve for x in the equation 5/6x = 10/3, we aim to isolate x on one side of the equation. First, we would multiply both sides of the equation by the reciprocal of the fraction that is multiplied with x, which is 6/5. Multiplying both sides by 6/5 will cancel the 5/6 on the left side and leave us with x alone.

Here are the steps for the solution:

Multiply both sides of the equation by 6/5: (6/5) imes (5/6)x = (6/5) imes (10/3).

Simplify the left side: x = (6/5) imes (10/3).

Multiply the numerators and the denominators: x = (6 imes 10) / (5 imes 3).

Simplify the multiplication: x = 60 / 15.

Divide 60 by 15: x = 4.

Therefore, the value of x is 4.

Answer: 12x^2 - 13x - 14

Choice D

==========================================

Work Shown:

Let y = (3x+2)

Replace (3x+2) with y and we go from (3x+2)(4x-7) to y(4x-7)

Distribute this y through: y(4x-7) = 4xy - 7y

--------------

Now replace y with (3x+2), distribute again, and simplify

4xy - 7y

4x(3x+2) - 7(3x+2)

4x(3x)+4x(2) - 7(3x) - 7(2)

12x^2 + 8x - 21x - 14

12x^2 - 13x - 14

Answer:

Alternative D

Step-by-step explanation:

(3x + 2)(4x - 7)

12x² - 21x + 8x - 14

12x² - 13x - 14

I hope I helped you.

Answer: 5/14 which is choice B

================================================

How I got this answer:

Define the following events

A = event of picking a red paper clip on the first selection

B = event of picking a red paper clip on the second drawing

Replacement is not made.

Now onto the probabilities for each

P(A) = 2/5 = 0.4 is given to us as this is simply the probability of picking red on the first try

P(A and B) = probability of both events A and B happeing simultaneously = 1/7

P(B|A) = probability event B occurs, given event A has occured

P(B|A) = probability of selecting red on second selection, given first selection is red (no replacement)

P(B|A) = P(A and B)/P(A)

P(B|A) = (1/7) / (2/5)

P(B|A) = (1/7) * (5/2)

P(B|A) = (1*5)/(7*2)

P(B|A) = 5/14

So if event A happens, then the chances of event B happening is 5/14

------------------

A more concrete example:

If we had 15 paperclips, and 6 of them were red, then

P(A) = (# of red)/(# total) = 6/15 = 2/5

P(B|A) = (# of red left)/(# total left) = (6-1)/(15-1) = 5/14

P(A and B) = P(A)*P(B|A) = (2/5)*(5/14) = 10/70 = 1/7

Answer: B

Step-by-step explanation:

Draw 1 (red)     and     Draw 2 (also red)     =   Both red

        [tex]\dfrac{2}{5}[/tex]                *                    x                    =         [tex]\dfrac{1}{7}[/tex]

Solve the equation to find the probability:

[tex]\dfrac{2}{5}x = \dfrac{1}{7}[/tex]

[tex](\dfrac{5}{2})\dfrac{2}{5}x = (\dfrac{5}{2})\dfrac{1}{7}[/tex]

[tex]x = \dfrac{5}{14}[/tex]

Answer:

See attachment

Step-by-step explanation:

We graph equations by drawing a number line and placing an open circle on the two values. We fill in the circles if we have [tex]\leq or \geq[/tex]. Since we don't, we leave it open. We then shade between the two.

Answer:

you spend a total of $60 and save $20

Step-by-step explanation:

The measure of the smaller angle, when it is one-fourth the measure of the other supplementary angle, is 36 degrees.

The student is asking about the measures of two supplementary angles where one angle is four times the measure of the other angle. In Mathematics, supplementary angles are two angles whose sum is 180 degrees. Let's call the smaller angle 'x' and the larger angle '4x'. The equation we need to solve is:

x + 4x = 180

This equation simplifies to '5x = 180', meaning that 'x', the smaller angle, is equal to '180 / 5', which calculates to be 36 degrees. Therefore, the measure of the smaller angle is 36 degrees.

Answer:

It is equal to that area because 120 times 3 is equal to 360, which is the area of a circle

Step-by-step explanation:

To find this, you simply multiply 120 by 3, the 3 is from 1/3. That gives you ur answer

Answer:

154 square cm (choice B)

Step-by-step explanation:

The diameter is 14 cm, so the radius is half that at 7 cm. Let r = 7

Use the formula

A = pi*r^2

to find the area of the circle. Let pi = 3.14 be the approximation for pi

So,

A = pi*r^2

A = 3.14*7^2

A = 3.14*49

A = 153.86

A = 154

Answer: B.

Step-by-step explanation:

3.14*r2

3.14*7(2)

153.9

Answer:

b - 60

Step-by-step explanation:

Let the number of books in the library be b.

The number of books in the library minus the 60 checked out is translated into a variable expression as b - 60

Answer:

[tex]b-60[/tex]

Step-by-step explanation:

We are given that the number of books in the library minus the 60

We have to translate the phrase into a variable expression.

We are given that a letter ''b'' is used for the number of books in the library.

Number of books in the library=b

According to question

[tex]b-60[/tex]

Hence, the required expression is given by

[tex]b-60[/tex]

Answer:

2(x + 3)^2 - 22

Step-by-step explanation:

2x^2 + 12x - 4

Start by making your "a" value equal to 1 by factoring the 2 from the first 2 terms in the standard form equation.

2(x^2 + 6x) - 4

Complete the square by using the formula (b/2)^2. Identify your "b" value, which is 6. Now you can complete the square.

((6)/2)^2 = 9

After completing the square, add 9 inside the parentheses and subtract 9 outside the parentheses. Since the 9 inside the parentheses is also being multiplied by 2, multiply the subtracted 9 by 2 as well.

2(x^2 + 6x + 9) - 4 - 9(2)

Factor the terms inside the parentheses by using the product/sum factoring method. This is where you find two of the same terms that multiply to "c" (9) and add to "b" (6).

In this case, positive 3 multiplies to 9 and adds to 6, so we will use the factors (x + 3)(x + 3), which is the same as (x + 3)^2.

2(x + 3)^2 - 4 - 9(2)

To finish off the problem, combine the like terms outside of the parentheses by multiplying 9 times 2 first and then subtracting -4 by 9(2).

[tex]\boxed{2(x + 3)^2 - 22 }[/tex]

Answer:

value of y is 2√2

C is the correct option.

Step-by-step explanation:

We can use Pythagoras theorem to find the value of y.

In triangle ABC, using Pythagoras theorem

BC² = AB² + AC²

(8+1)² = 3² + z²

9² = 9 + z²

z² = 81-9

z² = 72

Now, apply Pythagoras theorem in triangle ADC

AC² = AD² + DC²

z² = y² + 8²

Plugging the value of z

72 = y² +64

y² = 72 -64

y² = 8

y = 2√2

Therefore, value of y is 2√2

C is the correct option.

Answer:

[tex]2K+12L\geq87[/tex]

Step-by-step explanation:

Let K be the number of kites made by Min-young and L be the number of lamps made by Min-young.

We are told that it takes 2 wooden sticks to make a kite, so number of sticks used to make K kites will be 2K.

We are also told that it takes 12 wooden sticks to make a lamp, so number of sticks used to make L lamps will be 12L.

As Min-Young wants to make kites and lamps using at least 87 wooden sticks, so the total number of sticks used in making K  kites and L lamps will be greater than or equal to 87.

We can represent this information in an inequality as:

[tex]2K+12L\geq87[/tex]

Therefore, the our required inequality will be [tex]2K+12L\geq87[/tex].

An inequality based on the number of wooden sticks needed for making kites and lamps is 22K + 12L ≥ 87, where K represents the number of kites and L represents the number of lamps.

To determine the inequality that represents the condition based on the number of wooden sticks for making kites and lamps, we need to use the given data. It takes 22 wooden sticks to make a kite and 12 wooden sticks to make a lamp. Min-Young wants to use at least 87 wooden sticks.

The inequality will be formed by considering the number of kites (K) and the number of lamps (L) she wants to make. The total number of sticks used will be equal to 22 times the number of kites plus 12 times the number of lamps. This sum must be at least 87, the minimum number of sticks Min-Young wants to use. Therefore, the inequality can be written as 22K + 12L≥ 87.

Answer:

the diagonal measurement from corner A to corner B=15 inches

Step-by-step explanation:

as we know that the loptop has the shape of a rectangle that means all it's angles are right angles. so we can use the pythogoras theorem to find out the diagonal of the rectangle.

let us denote the diagonal of rectangle by D and the sides of rectangle be denoted by X=12 and Y=9

so by using pythogoras theorem we have,

[tex]D^{2} =X^{2} +Y^{2}[/tex]

[tex]D^{2}[/tex]=225

D=15

Hence the diagonal measurement from corner A to corner B is 15 inches.

Answer:

The diagonal measures 15 inches

Step-by-step explanation:

The diagonal of the Marcy's rectangular laptop forms a right angle triangle with its width and length.

We can use the Pythagoras Theorem to write the following equation,

[tex]|AB|^2=12^2+9^2[/tex]

This implies that,

[tex]|AB|^2=144+81[/tex]

We simplify the right hand side to obtain,

[tex]|AB|^2=225[/tex]

We take the positive square root of both sides to obtain,

[tex]|AB|=\sqrt{225}[/tex]

[tex]|AB|=15inches[/tex]

Hence the diagonal of Marcy's laptop measures 15 inches.

Answer:

144 people.

Step-by-step explanation:

Let n be the vertices, where cars are located.

We have been given that the sum of the measures of the angles' vertices is 6120°.

Let us find the number of vertices using formula:

[tex]\text{Sum of all interior angles of a polygon with n sides}=180(n-2)[/tex].

Upon substituting the given sum of the measures of the angles in this formula we will get,

[tex]6120=180(n-2)[/tex]

Using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex]6120=180n-360[/tex]

Adding 360 to both sides of our equation we will get,

[tex]6120+360=180n-360+360[/tex]

[tex]6480=180n[/tex]

Upon dividing both sides of our equation by 180 we will get,

[tex]\frac{6480}{180}=\frac{180n}{180}[/tex]

[tex]36=n[/tex]

As the cars are located on the vertices of regular polygon, so there will be 36 cars in the ride.

We are told that each car holds a maximum of 4 people, so the number of maximum people who can ride at one time will be equal to 4 times 36.

[tex]\text{Maximum number of people who can be on the ride at one time}=4\times 36[/tex]

[tex]\text{Maximum number of people who can be on the ride at one time}=144[/tex]

Therefore, the maximum number of people who can be on the ride at one time is 144 people.

The maximum number of people who can be on the ride at one time is 144, given that each car holds a maximum of four people.

Step 1

To find the maximum number of people who can be on the ride at one time, we need to determine the number of cars first, which is equal to the number of vertices in the regular polygon.

We know that the sum of the measures of the angles at the vertices of a polygon is given by the formula [tex]\(180^\circ \times (n - 2)\)[/tex], where n is the number of sides of the polygon.

Given that the sum of the measures of the angles' vertices is 6120°, we can set up the equation as follows:

[tex]\[180^\circ \times (n - 2) = 6120^\circ\][/tex]

Step 2

Solving for n:

[tex]\[n - 2 = \frac{6120^\circ}{180^\circ}\][/tex]

[tex]\[n - 2 = 34\][/tex]

[tex]\[n = 36\][/tex]

So, there are 36 cars on the ride. Since each car holds a maximum of four people, the maximum number of people who can be on the ride at one time is [tex]\(36 \times 4 = 144\)[/tex] people.

Answer:KL

Step-by-step explanation:

Answer: cotθ

Step-by-step explanation:

 tanθ * cos²θ * csc²θ

=  [tex]\dfrac{sin\theta}{cos\theta} * \dfrac{cos\theta*cos\theta}{} *\dfrac{1}{sin\theta*sin\theta}[/tex]

= [tex]\dfrac{cos\theta}{sin\theta}[/tex]

= cotθ

Answer: B

Step-by-step explanation:

The parent graph is y = x²

The new graph y = -x² + 3 should have the following:

Answers:

Explanation:

[tex]\dfrac{17\pi}{6} - \dfrac{12\pi}{6} = \dfrac{5\pi}{6}[/tex]

a) Quadrant 2 is: [tex]\dfrac{\pi}{2} < \theta < \pi[/tex]

b) In Quadrant 2, cos is negative and sin is positive, so tan is negative

c) [tex]\pi-\dfrac{5\pi}{6}[/tex] = [tex]\dfrac{\pi}{6}[/tex]

d) the reference line is above the x-axis so it is negative -->  [tex]-tan\dfrac{\pi}{6}[/tex]

e) [tex]tan(\dfrac{5\pi}{6})=\dfrac{1}{-\sqrt{3}}=-\dfrac{\sqrt{3}}{3}[/tex]

Answer:7.50(x) + 24 is the answer

Step-by-step explanation:

Answer:

VARIABLES

Step-by-step explanation:

in a proportional relationship graph, an equation that relates the distance y and the time x is y = kx.

In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:

y = kx

Where:

In this context, we can logically deduce that the constant of proportionality or speed (k) that relates the distance (y) and the time (x) can be modeled as follows:

Constant of proportionality, k = y/x

Therefore, the required linear equation is given by;

y = kx

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Answer:

$450.40

Step-by-step explanation:

well 5630 times .04 = 225.2 times it by 2 = 450.40

Answer:

The interest earned is $450.40

Step-by-step explanation:

We are given the formula

I =PRT

where I is the interest, p is the principal, r is the rate and t is the time

p = 5630,

r = 4 % which we convert to a decimal = .04

t = 2 years

Substitute these into the equation

I = 5630 * .04 * 2

450.40

The interest earned is $450.40

Answer:

Andy bought = 13 cakes.

Betty bought = 52 cakes.

Colin bought = 16 cakes.

Step-by-step explanation:      

We are told that Andy buys x cakes. Betty buys 4 times as many cakes as Andy. So number of cakes bought by Betty will be 4*x.

We are also told that Colin buys 3 more cakes than Andy. So number of cakes bought by Colin will be x+3 cakes.

Each cake costs 65 p. The total cost of the cakes is $52.65. We can represent this information as:

[tex]0.65(x+4*x+x+3)=52.65[/tex]

[tex]0.65(2x+4*x+3)=52.65[/tex]

[tex]1.3x+2.6x+1.95=52.65[/tex]  

Let us combine like terms.

[tex](1.3+2.6)x+1.95=52.65[/tex]

[tex]3.9x+1.95=52.65[/tex]

[tex]3.9x=52.65-1.95[/tex]

[tex]3.9x=50.7[/tex]

[tex]x=13[/tex]

Therefore, Andy bought 13 cakes.

Let us find number of cakes bought by Betty by substituting x=13 in expression 4*x.

[tex]\text{Cakes bought by Betty}=4*13[/tex]

[tex]\text{Cakes bought by Betty}=52[/tex]

Therefore, Betty bought 52 cakes.

Now we will find number of cakes bought by Colin by substituting x=13 in expression x+3.

[tex]\text{Cakes bought by Colin}=13+3[/tex]

[tex]\text{Cakes bought by Colin}=16[/tex]

Therefore, Colin bought 16 cakes.

Andy bought 13 cakes, Betty bought 52 cakes, and Colin bought 16 cakes.

Let's break down the given information and solve the problem step by step:

Let the number of cakes bought by Andy be x.

Betty buys 4 times as many cakes as Andy, so she buys 4x cakes.

Colin buys 3 more cakes than Andy, so he buys (x+3) cakes.

The total cost of the cakes is €52.65, and each cake costs 65p.

Now, we can create the equation to find the value of x:

x*(65p) + 4x*(65p) + (x+3)*(65p) = £52.65

Simplifying the equation:

65x + 260x + 65x + 195 = 5265

390x + 195 = 5265

390x = 5070

x = 13

So, Andy bought 13 cakes, Betty bought 4x13 = 52 cakes, and Colin bought (13+3) = 16 cakes.

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Answer:

Add 9 to each side of the equation.

Step-by-step explanation:

To complete the square, we need to add (b/2) ^2 to each side, where b is the coefficient of the x terms.

The coefficient of the x terms is -6

so we need to add (-6/2) ^2 = (-3)^2 = 9.  

Add 9 to each side of the equation.

Answer:

The coefficient of the x terms is -6

so we need to add (-6/2) ^2 = (-3)^2 = 9.    

Add 9 to each side of the equation.

Step-by-step explanation:

Answer:

Given:

Principal  (P) = $20,000 , interest rate compounded annually (r) = 5.2% = [tex]\frac{5.2}{100} = 0.052[/tex] ; n = 1 , t = 3 years.

Using formula :

[tex]A = P(1+\frac{r}{n})^{nt}[/tex]

where

A is total return

P is the Principal ,

r is interest rate ,

n is the number of times interest is compounded per year

t is the time in year.

Substitute the given values we have;

[tex]A = 20,000(1+\frac{0.052}{1})^{1 \cdot 3}[/tex]

[tex]A = 20000(1.052)^{3}[/tex]

Simplify:

A = $23285.05216

Therefore, your total return is, $23285.05216

Answer:

D. 13.267 m

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem

a^2 + b^2 = c^2

where a and b are the legs and c is the hypotenuse

7^2 + b^2 = 15^2

49 + b^2 = 225

Subtract 49 from each side

b^2 = 225-49

b^2 =176

Take the square root of each side

sqrt(b^2) = sqrt(176)

b = sqrt(176)

b = 13.266

Let x equal Thomas' age.  Then Huilan's age is 2x.  Set up an equation to model this situation:

x+2x=78

*Combine like terms*

3x=78

*Divide both sides by 3*

x=26

Hope this helps!!

Answer:

A) (-2, 12)

Step-by-step explanation:

Just multiplied the second equation by -1

then eliminated the y

Then solved for x  and you get x = -2

then you plug in x = -2 and figure out y

and you get y = 12

Hope this helped and plz mark as brainliest!

Sounds like "exponential decay" is the answer your teacher is looking for

Expressions of the form y = a*b^x are considered decay equations or exponential decay equations if 0 < b < 1. So b can be between 0 and 1, but not equal to either endpoint.

Example: y = 3*0.5^x means we start off with 3 as the initial value, and then cut it in half repeatedly as x increases by 1 (eg: x = 0, x = 1, etc). This graph goes downhill as you read it from left to right.

Answer:

Step-by-step explanation:

Remark

You need 2 facts.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

Givens

Solution

Perimeter

P = 4s

You don't need the area. The answer is D

Area

For a square with a diagonal length of 11in, the side length is 11√2/2. The area of the square is then 60.5 square inches and the perimeter is 22√2 inches.

To find the perimeter and area of a square with a given diagonal length, we need to firstly understand the relation between the diagonal and sides of the square. A square's diagonal divides it into two equal right triangles, and according to Pythagoras' theorem, the diagonal, being the hypotenuse in these right triangles, is equal to the square root of the sum of the squares of the sides. But since all sides of a square are equal, let's say the side length is 'a', then the diagonal would be 'a√2'.

Given that the diagonal length is 11in, we then have:

11 = a√2 or a = 11/√2

It's common to rationalize the denominator which gives: a = 11√2/2

Area of a square is a², therefore, Area = (11√2/2)² = 121/2 = 60.5 square inches.

The Perimeter of a square is 4a, therefore, Perimeter = 4 * (11√2/2) = 22√2 inches.

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