The graph of y<3x+5 is the half plane below the line y=3x+5. True or False?

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer:

3x-3

Step-by-step explanation:

3x has a variable attach, because no other numbers have a variable attached leave it alone.

2+(-5) are like terms so combine these two. 2+(-5)=-3

now put back in the equation

3x-3

Answer:

Step-by-step explanation:

Okay, so first of all, when a slope is negative, the line goes down from left to right, not up from left to right. Then, plot the Y intercept as -2. Finally, either go up 2 and left 3 or down 2 and right 3.

Answer:

Graph attached.

Step-by-step explanation:

As we have been given the slope and the y-intercept, we can create a linear equation using the slope-intercept form.

Slope-intercept form of a linear equation:

\(y=mx+b\)

where:

Substitute the given values into the formula to create an equation for the line:

\(\implies y=-\dfrac{2}{3}x-2\)

Now we have an equation for the line, find at least two points on the line by inputting values of x into the found equation:

\(x=0 \implies y=-\dfrac{2}{3}(0)-2=-2 \implies (0,-2)\)

\(x=3 \implies y=-\dfrac{2}{3}(3)-2=-4 \implies (3,-4)\)

\(x=-6 \implies y=-\dfrac{2}{3}(-6)-2=2 \implies (-6,2)\)

Plot the found points and draw a straight line through them (see attachment).

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

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The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

t = 6.67 seconds

Step-by-step explanation:

Given that,

The distance of Moon from Earth, \(d=2.4\times 10^5\ miles\)

The speed of the spacecraft, \(v=3.6\times 10^4\ miles/hour\)

We need to find the time it take this spacecraft to fly to the moon from earth. Let the time is t.

We know that,

Speed = distance/time

\(t=\dfrac{d}{v}\\\\t=\dfrac{2.4\times 10^5}{3.6\times 10^4}\\\\t=6.67\ s\)

So, the required time is equal to 6.67 seconds.

The area and perimeter of 2D shape of Rectangle is 6.8448cm and 11.04cm repectively. The area and perimeter of 2D shape of circle is 5.0761cm and 8.0028cm respectively.

2D shape of Rectangle with dimensions of Length is3.72 cm and Width is 1.84 cm. we can find the area of rectangle with formula Area = length x width and the formula of perimeter is Perimeter = 2(length + width).

Area = length x width = 3.72 cm x 1.84 cm = 6.8448 square cm (rounded to four decimal places)

Perimeter = 2(length + width) = 2(3.72 cm + 1.84 cm) = 11.04 cm

2D shape of Circle with dimension of diameter of 2.54 cm. we can find the area with formula Area = πr^2 and circumference with formula Circumference = 2πr

Radius = diameter / 2 = 2.54 cm / 2 = 1.27 cm

Area = πr^2 = π(1.27 cm)^2 = 5.0761 square cm (rounded to four decimal places)

Circumference = 2πr = 2π(1.27 cm) = 8.0028 cm (rounded to four decimal places)

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____The given question is incomplete, the complete question is given below:

Calculating area and circumference or perimeter of a 2D shape. Use your measurements to calculate the area and circumference of the circle and to calculate the area and perimeter of the rectangle. Rectangle Length: 3.72 cm Width: 1.84 cm  Circle : 2.54 cm Diameter of circle

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

x = n - m

Step-by-step explanation:

To solve for x we have to isolate it.

\(x^{2} \\\) + \(m^{2}\) = \(n^{2}\)

First, let's subtract  \(m^{2}\) from both sides of the equation:

\(x^{2} \\\) + \(m^{2}\) -  \(m^{2}\) = \(n^{2}\) -  \(m^{2}\)

Now the equation looks like this: \(x^{2} \\\) =  \(n^{2}\) -  \(m^{2}\)

Now we have apply a square root to both sides to remove the exponent from the x: \(\sqrt{x^2}\) = \(\sqrt{n^2 - m^2}\)

The square root and the exponents cancel out on both sides and you're left with: x = n - m

To solve for x the equation is: x = n - m

I hope this helps! :)

day 1  4 cm

day 2  8 cm

day 3  12 cm

day 4  16 cm

day 5  20 cm

day 6  24 cm

day 7  28 cm

????

Answer:

No, because 3 (domain) has two different ranges: -1 and 4.

Also, apply the vertical line rule.

Step-by-step explanation:

Answer:

Let the 'cart' total is x and total payment is y.

The sales tax is 5.6% added to the 'cart' amount and then shipping and handling fee added.

There are three intervals as below and function added accordingly:

y = 89.20, this is close to the number we got in part B and we assume it is same - the middle interval.

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Answer: the largest possible volume (in cm³) of the box is 108,000 cm³

Step-by-step explanation:

first lets rep each side of the base by x cm; and height by y cm

now

Surface Area(SA) = base area + four sides area [open at top]

SA = x² + 2y(x + x)

= x² + 4xy = 10800 cm²

y = {10800 - x²} / 4x

y = 2700/x - x/4

now

Volume (V) = (x²) × (2700/x - x/4)

= 2700x - (x³)/4

by Differentiation

V' = 2700 - (3/4) × (x²)

Setting V' = 0,

2700 - (3/4) × (x²)  = 0;

Solving x = +/- 60 cm

As dimension cannot be negative, so - 60 is rejected.

As well V" = (-3/2) × (x)

At x = -60,

V" = 90, which is > 0; so volume is minimum;

while at x = 60,

V" = -90, which is < 0; so volume is maximum.

Therefore for maximum volume x = 60 cm

⇒ height y = 30 cm

Therefore the largest possible volume (in cm³) of the box

= 60 x 60 x 30 = 108,000 cm³

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

They will meet after four hours

Step-by-step explanation:

The boat moving at 2.5 mph will have travelled 10 miles after 4 hrs, and the boat moving at 5 mph will have travelled 20 miles after 4 hrs

Answer:

y=3

Step-by-step explanation:

y + 3 = - y + 9

y + y = 9 - 3

2y = 6

y = 6/2

y =3

Answer:

 -2 °C.

Step-by-step explanation:

Usa el signo + para representar temperaturas arriba de cero y el signo – para representar temperaturas bajo cero.

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

The surface area of the cube is equal to 216 cm².

General Formulas and Concepts:
Geometry

Surface Area Formula [Cube]:
\(\displaystyle \text{SA} = 6a^2\)

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 6 cm

Step 2: Find Surface Area

∴ we have found the surface area of the cube to be 216 cm².

---

Topic: Geometry

The surface area of a 3D figure is the sum of the area of its faces.

We know the following:

Since all faces in a cube have the same area, the surface area of a cube is:

\(\boxed{(\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})x^{2} = 6(\text{side})^{2}}\)

Therefore, the surface area of a cube must be known as 6(side)².

\({\text{Given side length of cube:} \ |\text{6 centimeters}|\)

Substitute the side length in the surface area formula and simplify:

\(\implies 6(6)^{2}\)

\(\implies 6(6)(6)\)

\(\implies \boxed{216 \ \text{cm}^{2}}\)

Therefore, the surface area of the cube is 216 cm².

\(\overline{===============================================}\)

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Answer:

y - 4 = -(x - h)^2

Step-by-step explanation:

We begin with the stock function y = x^2.  Its graph is a parabola with vertex at (0, 0) and opening up.  The more general vertex form of the graph is

y - k = a(x - h)^2, where the point (h, k) is the vertex and 'a' determines the direction of opening as well as by how much the parabola is stretched vertically.

In this problem the vertex is (6, 4); that is, the vertex is shifted to the right by 6 units and upward from there by 4 units.  The coefficient 'a' is -1, indicating that the graph opens downward.

So we have the equation y - 4 = -(x - h)^2.  Without more information we cannot tell whether the graph is stretched vertically or not.

Answer:

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.

a) The sample space is given as:

Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.

b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.

{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}

c) find the set b corresponding to the event number of dots in the first toss is 6.

{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

e) a does not imply b or does b imply a.

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The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.

What is Critical value?

In statistics,  critical value is  value that is used to determine whether to reject  null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting  true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.

To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.

Using a t-distribution table with 21 degrees of freedom (n-1), we find that  critical value for a 99% confidence level is approximately 2.819.

Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).

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33.85 or 32.75 sorry if I am wrong

Step-by-step explanation:

for this one you have you multiply 17 by itself like this 17x17=289 but you also have to do it with the 28 to like this 28x28=784, now what you do it add up the 289+784=1,073 then you square root 1,073 which gives you 32.75 round it to the nearest tenth of needed so your will be between 33.85 or 32.75

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)

For the given condition of choosing president and treasurer from the 10 board members on the Community Arts Council , the total number of outcomes president and treasurer can be chosen as

Combination ; 45 ways.

As given in the question,

Total number of board members in the Community Arts Council = 10

Number of people to be chosen from Community Arts Council (president and treasurer) = 2

Total number of ways to choose a president and treasurer is calculated using combination of selecting 2 people is equal to

= ¹⁰C₂

= ( 10 )! / ( 2! ) ( 10 - 2 )!

= ( 10 × 9 × 8! ) / ( 2 × 1 ) ( 8! )

= 90 / 2

= 45

Therefore, for the given condition of choosing president and treasurer from the 10 board members on the Community Arts Council , the total number of outcomes president and treasurer can be chosen as

Combination ; 45 ways.

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Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40