What is the exponential function that best models the number of gnats the scientists have
gathered after the number of hours listed in the table below?

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4}{y - 6} + \cfrac{5}{y + 3} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4(y + 3) + 5(y - 6)}{(y - 6)(y + 3)} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{4y + 12 + 5y - 30}{ {y}^{2} + 3y - 6y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{9y - 18}{ {y}^{2} - 3y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 9y - 18 = 7y - 4[/tex]

[ denominator is same, so numerator must have same value to be equal ]

[tex]\qquad \sf  \dashrightarrow \: 9y - 7y = - 4 + 18[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2y = 14[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 7[/tex]

The type of model that best fits the given situation is; A linear equation  Model

Right inside the local reservoir we will have an initial amount of water A.

Now, for every hour that passes by, the amount of water in the reservoir decreases by 500 gals.

Thus, after t hours, the amount of water in the reservoir is expressed as:

W = A - 500gal * t

This is clearly a linear equation model and so we can conclude that the model that fits best in the given situation is a linear model.

The domain of this model is restricted because we can't have a negative amount of water in the reservoir,  and as such the maximum value of t accepted is: W = 0 = A - 500gal*t

t = A/500 hours

Therefore, the domain of this linear relation is: t ∈ {0h, A/500 }

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Answer:

10

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]4x=2x+20 \\ \\ 2x=20 \\ \\ x=10[/tex]

Answer:

$149.25

Step-by-step explanation:

The discount is 15% of $995

[tex]15\%\times995[/tex]

Note that percentages can also be written as that number over 100.

[tex]\frac{15}{100}\times995[/tex]

Simplify the fraction

[tex]\frac{3}{20}\times995=\frac{2985}{20}=149.25[/tex]

Therefore the discount is $149.25.

Answer:

$149.25

Step-by-step explanation:

Answer:

 [tex]h(x)=7(1.3)^x[/tex]

Step-by-step explanation:

Since this is an exponential equation we will use

[tex]h(x)=a(b)^x[/tex]

[tex]a[/tex] Is your starting value, 7

[tex]b[/tex] Is your percentage of change, remember its not 0.3, as that would hint the population is decreasing by thirds exponentially, instead we will use 1.3 as our percent of change, as the 1 maintains the original value and the 0.3 adds 30%, now all we have to do is put it all together!

[tex]h(x)=7(1.3)^x[/tex]

He is using Access 2016 Database tools are the tab that should he use for the add a query for multiple tables in his database.

Databases and a desk is hard and fast of records elements (values) the usage of a version of vertical columns (identifiable with the aid of using the name) and horizontal rows, the cell being the unit wherein a row and column intersect.

Tables are database gadgets that incorporate all of the records in a database. In tables, records is logically prepared in a row-and-column layout much like a spreadsheet.

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The above question is incomplete:

Marcus needs to add a query for multiple tables in his database. He is using Access 2016. Which tab should he use

to add the query?

Home

External data

Create

Database tools

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Answer:

Step-by-step explanation:

Area of circle:

area = π · r · r

Radius=  [tex]\frac{16}{2}[/tex]= 8

[tex]3.14\times { 8 }^{ 2 }[/tex] = 200.96 [tex]cm^2\\[/tex]

If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

Answer:

Step-by-step explanation:

A= π(5)²

 = 3.14(5)²

 = 3.14(25)

 = 78.5 ans

The solution to the inequality 4 ≥ b is represented in the graph

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

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Inequality shows the non equal comparison between two or more numbers and variables.

Given the inequality:

4 ≥ b

Rearranging gives:

b ≤ 4

The solution to the inequality 4 ≥ b is represented in the graph

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The equivalent expression of the radical expression ∛1080 is 6∛5

The radical expression is given as

∛1080

Express 1080 as 216 * 5

∛1080 = ∛(216 * 5)

Split the factors

∛1080 = ∛216 * ∛5

Evaluate the cube root of 216

∛1080 = 6 * ∛5

Evaluate the product

∛1080 = 6∛5

Hence, the equivalent expression of the radical expression ∛1080 is 6∛5

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The angle the pole makes with the tent is 39.7°.

Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.

Let θ represent the angle the pole makes with the tent.

Using trigonometric ratios:

Therefore, the angle the pole makes with the tent is 39.7°.

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The solution to the system of inequalities y > 2x + 4 and x + y ≤ 6 on the coordinate plane is the darker region shown in the graph.

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

Inequalities is an expression that shows the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities y > 2x + 4 and x + y ≤ 6 on the coordinate plane is the darker region shown in the graph.

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Answer:

Resistance

Step-by-step explanation:

Answer:

x=2.5

Step-by-step explanation:

Solve for x in this systems of equations, we already have two values which equal y so half the work is finished for us.

Starting with the equation:

[tex]x+12=17-x[/tex]

Add x to both sides to remove the negative x on the right side of the equation:

[tex]2x+12=17[/tex]

Subtract 12 from both sides to remove the 12 on the left side of the equation:

[tex]2x=5[/tex]

Divide both sides by 2 to cancel out the x coefficient

[tex]x=2.5[/tex]

Answer:

(28.36)

Step-by-step explanation:

a. altitude = CE

b. bisector = BD

c. exterior angle = ∠ABE

d. median = CF

e. remote interior angles = ∠BCE and ∠CEB

From the question, we are to fill in the blanks

In ΔBCE, we have that ∠BCE is a right angle

Thus,

a. altitude = CE

Also, we have that

∠EBD ≅ ∠CBD

Thus, BD is a bisector

b. bisector = BD

The exterior angle of the triangle is ∠ABE

c. exterior angle = ∠ABE

From the given information,

BF ≅ EF

∴ F is the midpoint of BE

NOTE: Median is a line segment joining the vertex of one side of the triangle to the midpoint of its opposite side.

The median of the triangle is CF

d. median = CF

The remote interior angles of the triangle are ∠BCE  and ∠CEB

e. remote interior angles = ∠BCE and ∠CEB

Hence,

a. altitude = CE

b. bisector = BD

c. exterior angle = ∠ABE

d. median = CF

e. remote interior angles = ∠BCE and ∠CEB

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Answer: 3

Step-by-step explanation:

We can solve this problem by recognizing that z is the geometric mean of 9 and 9+4. This property is outlined in the following formula:

[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]

where hypotenuse is the longest side of the triangle, leg is the side of the triangle we are calculating for, and part is the part of the hypotenuse on the side of the leg.

Here, the hypotenuse is 13, or 4 + 9. The leg is z, as it is the side of the triangle we are trying to find. Finally, the part is 9. It is the part of the hypotenuse that is on the side of the leg.

Let's plug in these values:

[tex]\frac{13}{z}=\frac{z}{9}\\117=z^2\\z=\sqrt{117}[/tex]

117 is the product of 9 and 13. Since 9 is a perfect square, we can take it out from the square root.

[tex]z=\sqrt{9*13}\\z=\sqrt{9}*\sqrt{13}\\z=3\sqrt{13}[/tex]

The "?" must be a 3.

Step-by-step explanation:

3 meters = 300 cm

anyway, the ratio tells us that the whole ribbon can be seen as the combination of 3 + 2 = 5 equally long parts.

one such part is then

3 m / 5 = 0.6 m or 60 cm

the shorter piece is 2 of these parts long :

2 × 0.6 = 1.2 m or 120 cm

Answer:

Exact Form:

61/12

Decimal Form:

5.083 with 3 repeating

Mixed Number Form:

5   1/12

Step-by-Step Explanation:

-5/3×3/8 = -5/8

-5/8+3/8= -1/4

-1/4+6/9=5/12

5/12+14/3=61/12

The roots of the given polynomials exists

[tex]$x=8+\sqrt{10},[/tex]  and [tex]$ x=8-\sqrt{10}[/tex]

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]

simplifying the equation, we get

[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]

[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]

[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are

[tex]$x=8+\sqrt{10},[/tex]  and [tex]$ x=8-\sqrt{10}[/tex].

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The domain of the function is:

h > 0, only integers.

Then the correct option is the first one.

For a function f(x), we define the domain as the set of the possible values of x that we can use as inputs in the given function.

Here the function is:

f(h) = 6*h + 12

Where h is the number of packages that you buy.

Then h can be only integers larger than zero (as you can't buy half a package or something like that).

Then we conclude that the correct option is the first option.

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Answer:

5 and 5

Step-by-step explanation:

[tex]AB = BC =\sqrt{(4-0)^2+(3-0)^2}=5[/tex]

Answer:

AB = 5

BC = 5

Step-by-step explanation:

The formula to find the distance between two points is: [tex]\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

AB: 5

The two points are A(-4,0) and B(0,3).

In the formula, it will be expressed as:

[tex]\sqrt{(0-(-4))^2+(3-0)^2}[/tex]

-->  [tex]\sqrt{4^2+3^2}[/tex] .

-->  [tex]\sqrt{16+9}[/tex]

-->  [tex]\sqrt{25}[/tex]

--> 5

BC: 5

The two points are: B(0,3) and C(4,0)

In the formula, it will be expressed as:

[tex]\sqrt{(4-0)^2+(0-3)^2}[/tex]

-->  [tex]\sqrt{(4)^2 + (-3)^2}[/tex]

-->  [tex]\sqrt{16 + 9}[/tex]

-->  [tex]\sqrt{25}[/tex]

--> 5

So both AB and BC is 5.

Answer:

x-int: (4, 0)

Step-by-step explanation:

First, we need to find the equation of the line.

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

Thus, we need to find the slope first by using the slope formula:

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } \\[/tex] or change in y / change in x

So we have: [tex]\frac{3-2}{1-2}=\frac{1}{-1}=-1=m[/tex]

We must plug in the slope to find the y-intercept:

[tex]3=-1(1)+b\\3=-1+b\\4=b[/tex]

So the equation of the line is y = -x + 4

The x-intercept means that the y coordinate is 0 so we can use the equation:

[tex]0=-x+4\\-4=-x\\4=x[/tex]

Answer:

0.6kg

Step-by-step explanation:

first roses share becomes 2:5

then you change the kilograms into grams for an easier working

then you multiply 2:5 by 1500g to get roses share

Answer:

336

Step-by-step explanation:

They can place 1 of 8 frags on the bottom.

Now they have 7 flags left.

They can place 1 of 7 flags in the middle.

Now they have 6 flags left.

The can place 1 of 6 flags on top.

8 × 7 × 6 = 336

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.

Distance equals speed multiplied by time.

Distance between Alice and Bob=1000 feet.

Distance between the bird and Bob=1000 feet.

Speed of Alice and Bob=10 feet per second.

The combined speed of Alice and Bob=20 feet per second.

Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)

The time covered at the meeting point=20 second (1000/50)

Speed of the bird=20 feet per second.

The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).

Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.

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The y-intercept of the linear equation that models the data indicates that:

There was 1 inch of water on the tub when the water was turned on.

A linear function is modeled by:

y = mx + b

In which:

In this problem, when x changes by 1, y changes by 2, hence the slope is of 2. Hence, since when x = 1, y = 3, when x = 0, y = 3 - 2 = 1, which means that the y-intercept is of 1, and the correct interpretation is:

There was 1 inch of water on the tub when the water was turned on.

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