[tex]y= 4\\y = \frac{8}{3} x - 4\\[/tex]

Answer:

[tex]\textsf{a)} \quad y=1.8(3.2)^x[/tex]

[tex]\textsf{b)} \quad y=5(7)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given ordered pairs:

The y-intercept is the y-value when x = 0.

Therefore, as the y-intercept is 1.8, a = 1.8.

[tex]\implies y=1.8b^x[/tex]

Substitute point (1, 5.76) into the equation and solve for b:

[tex]\begin{aligned} y&=1.8b^x\\\implies 5.76&=1.8 \cdot b^1\\5.76&=1.8b\\b&=\dfrac{5.76}{1.8}\\b&=3.2\end{aligned}[/tex]

Therefore, the exponential equation is:

[tex]\boxed{y=1.8(3.2)^x}[/tex]

To complete the given table, simply substitute the values of x into the found equation:

[tex]\begin{array}{c|l}x&\phantom{189}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{18}1.8\\\vphantom{\dfrac12}}1&\phantom{18}5.76\\\vphantom{\dfrac12}}2&\phantom{1}18.432\\\vphantom{\dfrac12}}3&\phantom{1}58.9824\\\vphantom{\dfrac12}}4&188.74368\end{array}[/tex]

Given ordered pairs:

The y-intercept is the y-value when x = 0.

Therefore, as the y-intercept is 5, a = 5.

[tex]\implies y=5b^x[/tex]

Substitute point (2, 245) into the equation and solve for b:

[tex]\begin{aligned} y&=5b^x\\\implies 245&=5 \cdot b^2\\49&=b^2\\b&=\sqrt{49}\\b&=7\end{aligned}[/tex]

Therefore, the exponential equation is:

[tex]\boxed{y=5(7)^x}[/tex]

To complete the given table, simply substitute the values of x into the found equation:

[tex]\begin{array}{c|l}x&\phantom{11}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{1111}5\\\vphantom{\dfrac12}}1&\phantom{111}35\\\vphantom{\dfrac12}}2&\phantom{11}245\\\vphantom{\dfrac12}}3&\phantom{1}1715\\\vphantom{\dfrac12}}4&12005\end{array}[/tex]

13000 divided by 3000 = 4.33 repeating meaning the 33 keps going like 4.33333333333333333333333333333333333333333333333333

Answer:

HL

Step-by-step explanation:

the two triangles are right and have the same hypotenuse (the diagonal side) and one congruent leg (the horizontal side)

Answer:7

Step-by-step explanation:

Yes, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

In the scientific form, we write a number in the form of base×10ⁿ.

Where 0 ≤ base < 10 and n can be any rational number.

Given,

Humans can distinguish up to 18,400,000 individual dots called pixels on a typical computer display

We need to check whether human distinguish pixels on a same sized HDTV with 2 x 10 to the 6th power pixels

2×10⁶ pixels.

= 2000000 pixels.

As  2000000 < 18400000

Hence, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.

To Learn more on Scientific Notation click:

https://brainly.com/question/16936662

#SPJ1

The answer is x = -70.

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Multiply all terms by the same value to eliminate fraction denominators

/7 = −10

7⋅/7 = 7(−10)

Cancel multiplied terms that are in the denominator

7⋅/7 = 7 (−10)

x =7(-10)

Multiply the numbers

=7(−10)

=−70.

Hence The answer is x = -70.

Learn more about the X value question at :

https://brainly.com/question/25117861?

The value of numerical expression 4(16)³ / 10³ will be 16.384.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 4(16)³ / 10³

Simplify the expression, then we have

⇒ 4(16)³ / 10³

⇒ 4 x 4096 / 1000

⇒ 16384 / 1000

⇒ 16.384

The value of numerical expression 4(16)³ / 10³ will be 16.384.

More about the value of the expression link is given below.

https://brainly.com/question/23671908

#SPJ1

The zeros of the quadratic equation: h(x) = x^2 - 2x - 35

are -5 and 7, thus the correct option is B.

Here we have the quadratic equation:

h(x) = x^2 - 2x - 35

Using the quadratic formula we will get the two solutions:

[tex]x = \frac{2 \pm \sqrt{(-2)^2 - 4*1*-35} }{2*1} \\\\x = \frac{2 \pm 12 }{2} \\\\[/tex]

The solutions are:

x = (2 + 12)/2 = 7

x = (2 - 12)/2 = -5

Then the factors of the quadratic are (x - 7) and (x + 5), the correct option is B.

Learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Answer:

  (c)

Step-by-step explanation:

You want the graph that has a domain of x ≥ 5.

The domain of a function is the set of x-values for which the function is defined. A domain of x ≥ 5 means the function is defined for x-values at least 5. The graph of the function will extend from x=5 indefinitely to the right.

Graph C is like that.

Answer: x = 1/0 in exact form. x = 0.1 in decimal form.

First step, distribute:

[tex]-6x-3 = 4x-4[/tex]    

Next, isolate x to one side :

[tex]-6x - 4x=-4+3[/tex]

[tex]-10x=-1[/tex]

Last step, divide both sides by -10:

[tex]x=\frac{1}{10}[/tex]

Thus, the answer is [tex]\frac{1}{10}[/tex]

Hope this helped :)

Answer:

Step-by-step explanation:

option 2 since it equals 14/4

Answer:500 I hope this helpful

Step-by-step explanation:

3000 divided by 48 times 8

To make the calculation easier, first multiply the numbers that result in multiples of 10

24000 divided by 48

Divide the numbers
=500

Answer:

250

Step-by-step explanation:

If we follow the rules of PEMDAS, we go from left to right. Therefore, first, do 3,000 divided by 48.

3,000/48=62.5

Now, multiply 62.5 by 4.

62.5x4= 250

250 is your answer :D

Hope this helps and have a wonderful day!

Answer: C

Step-by-step explanation:

38520 *.12 = $4,622.40

78.9 kg.

To convert 78,900 grams to kilograms, we can divide the number of grams by 1,000. Since 1 kilogram is equal to 1,000 grams, dividing the number of grams by 1,000 will give us the equivalent number of kilograms.

Therefore, 78,900 grams is equivalent to 78,900 / 1,000 = 78.9 kilograms.

Answer: 7

Step-by-step explanation:

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

9-6+4

=7

With the help of similar triangles the height of Flagpole is 15.13 feet

what is similar triangle?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.

solution:

let C is the point of reflection in triangle ABC and EDC

∠ ABC = ∠ EDC ( 90 Degree)

∠ ACD = ∠ ECD ( Reflective angle )

By symmetry,

AB/ED = BC/CD

5.6/ x  = 7.4 / 20

       x  =  15.13 feet

Hence the height of flagpole is 15.13 feet

To learn more about similar triangle from the given link

https://brainly.com/question/14285697

#SPJ1

Answer: D

Step-by-step explanation:

Answer:

Part A: The bill is $27.32

Part B: The percentage is 19%

My work:

Part A

   ?                   8

---------     =    ---------

25.30             100

equals 2.02400

then round to get the tax amount which is $2.02

to find the bill cost we need to add the tax and the cost of the meal:

2.02 + 25.30 = 27.32

Part B

to find the tip we need to subtract the bill from the total lunch cost:

27.32 + t = 4.92                              (t = tip)

32.24 - 27.32 = 4.92

So now that we know the tip we can figure out how much percentage that is of the cost of the meal:

4.92              ?

--------    =   --------

25.30         100

which equals 19.4466403/100

the percentage is 19%

Sarah spends reading 30 min + [tex]0.05 min^{2}[/tex].

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

The problem is in a mathematical expression.

30 min+3s min did Sarah spend reading

Convert s to min

.30min+3s min× 1min/60s

Cancel the common units and simplify.

Cross-cancel units.

30 min + [tex]0.05 min^{2}[/tex]

To learn more about mathematical expression, click

https://brainly.com/question/1703934

#SPJ1

Answer:

C

Step-by-step explanation:

(√2) can be interpreted as 2^(1/2) and the second term can be interpreted as 2^(1/3). The law of exponents tells us that we must add the exponents when multiplying two numbers with the same base. 1/2 + 1/3 is 3/6+2/6 = 5/6 so the final answer would be 2^(5/6)

Answer:x=-9

Step-by-step explanation:-12/4=-3 then do 3*-3=-9

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

If two lines intersects, then the opposite angle of the line will be congruent to each other.

In ΔBAE and ΔCDE,

AB = DC, (Given)

∠BAE = ∠CDE, (Right angle)

∠BEA = ∠DEC, (Opposite angle)

The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Answer:

-8/3

Step-by-step explanation:

The Largest Angle has a measure of 100 degrees and measure of other two angles is 40 degrees each.

What is angle sum property of a triangle?

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

According to the given question:

In triangle ABC, angle ABC equals to angle ACB and BAC is the largest angle.

Let angle measure of ABC and ACB angles be x degree then, measure of third angle BAC will be x + 60 degrees.

Since sum of all angles of any triangle is 180 degree.

      x  + x + (x + 3) = 180

       3x  = 180 - 60

        3x = 120

         x = 40 degrees

So, First angle = 40 degree

Second angle = 40 degree

Third Angle = 100 degree.

The Largest Angle angle has a measure of 100 degrees.

To know more about angle sum property visit

https://brainly.com/question/24311162

#SPJ1

Answer:

21.64 % probability of rain at a random year

Step-by-step explanation:

79/365 * 100

21.64 %

When the figure passed through the transformations the image formed is similar to the image at B as attached

The figure is in the second quadrant

clockwise rotation 90degrees about the origin will being the figure to the first quadrant

Translation 9 units down will bring an image to the -6 of the y direction in the fourth quadrant

reflection over the y axis will create a mirror image of the figure and make the image at the third quadrant

The option B correctly shows the final image

Learn more about transformation here:

https://brainly.com/question/29321312

#SPJ1

Answer:

Below

Step-by-step explanation:

830 to 1130   is 3 hours

Hours per gallon =    3hrs / 2100 gal

3 hr / 2100 gal    * 3500 gal =   5hrs to fill from 830 = 13:30   ( 1:30 PM)

The percentage increase in the number of cars from hour 2 to hour 3 is 16.7%

In this question, we have the given figures that can be used in our computation:

Hour 1 = 22 cars

Hour 2 = 30 cars

Hour 2 = 35 cars

We want to calculate the percentage increase in the number of cars

So, we make use of only the following parameters

Hour 2 = 30 cars

Hour 2 = 35 cars

These figures can be represented as

Initial amount = 30

Final amount = 35

The percentage of the increase of the cars is then calculated using the following percentage equation

Increase percentage = (Final amount - Initial amount)/Initial amount * 100%

Substitute the known values in the above equation, so, we have the following representation

Increase percentage = (35 - 30)/30* 100%

Evaluate

Increase percentage = 16.7%

Hence, the increase percentage is 16.7%

Read more about percentage increase at

https://brainly.com/question/11360390

#SPJ1