Apply the first derivative test to classify stationary point(s) of () =
1
3

3 − 9 + 2

The slope of the line having points (3,135), (5,225), and (7,315) is 45

Slope:

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

The formula of slope for a line(m)=[tex]\frac{y2-y1}{x2-x1}[/tex]

Given the points  (3,135) , (5,225) and (7,315)

Consider any two points, Let's say  (3,135) and (5,225).

Slope=[tex]\frac{225-135}{5-3}[/tex]

Slope=45

Therefore, The slope of the line having points (3,135), (5,225), and (7,315) is 45

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Answer:

[tex]2x^{4} - 3x^{2} + 7x[/tex]

Step-by-step explanation:

Answer:

1 cm : 12.5 m

Step-by-step explanation:

Answer: 1250000:1

Step-by-step explanation:

Scale factor: 50 km/4 cm=25 km/2 cm

25 km/2 cm=

(25 * 1000 m)/(2 * 1/100 m)=   ==> convert to common measurement which is meters.

(25000 m)/(2/100 m)=

(25000*100 m)/(2*100/100 m)=

2500000 m/2 m=1250000/1

Answer:

x - intercept; (80, 0)

y - intercept; (0, ∞)

Step-by-step explanation:

Let Week be w and Amount be A;

We see an inverse proportionality;

[tex]{ \rm{w \: \alpha \: \frac{1}{A } }} \\ \\ { \rm{w = \frac{m}{A} }}[/tex]

m is a constant of proportionality;

When w is 1, A = 68

[tex]{ \rm{ 1 = \frac{m}{68} }} \\ \\ { \rm{m = 68}}[/tex]

Therefore;

[tex]{ \tt{w = \frac{68}{A} + c }} \\ [/tex]

c is a constant;

When w is 0, A is 80

[tex]{ \rm{0 = \frac{68}{80} + c}} \\ \\ { \rm{c = - \frac{17}{20} }}[/tex]

Overall equation:

[tex]{ \rm{y = \frac{68}{x} + \frac{17}{20} }} \\ [/tex]

For x-intercept, y = 0

[tex]{ \rm{ \frac{17}{20} = \frac{68}{x} }} \\ \\ { \rm{x = 80}}[/tex]

For y-intercept, x = 0

y = ∞

Based on the numbers given, we can say that 51 is a multiple of 3.

51 is not a prime number which means that it has factors and it is a multiple of several numbers.

The factors of 51 include:

1, 3, 17, and 51

Out of the numbers given of 2,3,5,6,9,10, it therefore means that 51 is a multiple of only one number which is 3. When 3 is multiplied by 17, it gives 51.

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Answer:

One pen is $4.25 and one pencil is $1.85.

Step-by-step explanation:

Let cost of pens be x and cost of pencils be y.

1. 4x+3y=22.55

2. 3x+2y=16.45

Sub. 1.-2.,

x+y=22.55-16.45

x=6.1-y

Sub. x=6.1-y into 1.,

y=1.85

x=4.25

Answer:

Cost of a box of pens = $4.25

Cost of a box of pencils = $1.85

Step-by-step explanation:

Given information:

Define the variables:

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad 4x + 3y = 22.55[/tex]

[tex]\textsf{Equation 2}: \quad 3x + 2y = 16.45[/tex]

Multiply Equation 1 by 3:

[tex]\implies 3 \cdot 4x + 3 \cdot 3y = 3 \cdot 22.55[/tex]

[tex]\implies 12x + 9y = 67.65[/tex]

Multiply Equation 2 by 4:

[tex]\implies 4 \cdot 3x + 4 \cdot 2y = 4 \cdot 16.45[/tex]

[tex]\implies 12x + 8y = 65.80[/tex]

Subtract the equations to eliminate the term in x:

[tex]\begin{array}{r rr}& 12x+9y = &67.65\\- & 12x+8y = &65.80\\\cline{2-3} & y = & 1.85\end{array}[/tex]

Substitute the found value of y into one of the equations and solve for x:

[tex]\implies 3x + 2y = 16.45[/tex]

[tex]\implies 3x + 2(1.85) = 16.45[/tex]

[tex]\implies 3x + 3.7 = 16.45[/tex]

[tex]\implies 3x =12.75[/tex]

[tex]\implies x=4.25[/tex]

Solution

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Answer: 1/2 * n

1 hour of practice in 2 days

2 hours of practice in 4 days

5 hours of practice in 10 days

Step-by-step explanation:

60 minutes=1 hour

30 minutes * 1 hour/60 minutes=

30*1/60=

30/60=1/2 hour.

1/2 * n

1/2 * 2 = 1 hour of practice in 2 days

1/2 * 4 =

4/2 = 2 hours of practice in 4 days

1/2 * 10=

10/2 = 5 hours of practice in 10 days

Answer:

Step-by-step explanation:try using quizlet

The direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is given that:

A mouse is trapped in a maze.

He walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.

Based on the data given:

tanA = 8/(-10+15) = 8/5

A = tan⁻(8/5)

A = 58 degrees

The direction will be 58 degrees east-north

Thus, the direction of the resultant vector is 58 degrees east-north if the mouse walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m.

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Simplifying the given polynomial expression is; -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)

We want to simplify the polynomial expression;

((1/2)x + 2)((1/2) - 2x) + ((1/4)x + (7/2))

Let us expand the first bracket to get;

((1/2)x * (1/2) + (2 * (1/2)) - ((1/2)x * 2x) - (2 * 2x))

⇒ (1/4)x + 1 - x² - 4x

⇒ 1 + (15/4)x - x²

Thus, our expression is now;

(1 + (15/4)x - x²)((1/4)x + (7/2))

This can be multiplied out to give;

(1/4)x + (15/16)x - (1/4)x³ + (7/2) + (105/8)x - (7/2)x²

= -(1/4)x³ - (7/2)x² + (107/8)x + (15/16)x + (7/2)

= -(1/4)x³ - (7/2)x² + (214/16)x + (7/2)

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Answer:

Student B

Step 1: the quantity 1 over sine theta end quantity minus sine theta over the quantity cosecant theta

Step 2: the quantity 1 minus sine squared theta end quantity over sine theta all over cosecant theta

Step 3: cosine squared theta over sine squared theta

Step 4: cot2 θ

Step-by-step explanation:

the other statements are.

For a conditional statement of the form:

If P, then Q

The other statements are:

Here the conditional is:

"if a figure is a rectangle with sides 2 cm and 3cm, then it has a perimeter of 10cm"

We can identify:

P = a figure is a rectangle with sides 2 cm and 3cm

Q = it has a perimeter of 10cm

Then the other statements are.

This clearly is false, as we can have a circle with a perimeter of 10 cm.

This is also false, the figure can be a rectangle with sides of 1cm and 4 cm for example.

This is true. if the figure does not have a perimeter of 10cm, then it can't be a rectangle with sides of 2cm and 3cm

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Answer:

[tex]p ≤6[/tex]

Step-by-step explanation:

Inequality: [tex] - 4p +36 ≥2p[/tex]

Collect like terms

→ [tex] - 4p - 2p≥ - 36[/tex]

→ [tex] - 6p≥ - 36[/tex]

Divide both sides by -6

→ [tex] \frac{ - 6p}{ - 6}≤\frac{ - 36}{ - 6} [/tex]

Therefore: [tex]p ≤6[/tex]

Answer:

to extend over or past and cover a part of The roof shingles overlap each other. 2 : to have something in common with Baseball season overlaps the football season in September. 1 : to occupy the same area in part The two towns overlap.

Step-by-step explanation:

The equation for the sentence 10 more than p is -3" will be B. p + 10 = -3.

It should be noted that an equation illustrates the relationship between the variables that are given.

In this case, the equation for the sentence 10 more than p is -3" will be:

p + 10 = -3

p = - 3 - 10

p = -13

The value of P is -13.

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Answer:

a) The probability that Jim wins is 0.56.

b) The probability that Henry wins is 0.44.

Step-by-step explanation:

Hope this helps!

i would need a photo of the lines to find the values of other angles

Answer:

[tex](1, -1)[/tex] and [tex](-\frac{1}{5}, \frac{7}{5})[/tex]

In decimal form this would be (1, -1) and (-0.2, 1.4)

Step-by-step explanation:

Basically here we are trying to solve a system of 2 equations. The first one is a straight line and the second is a circle. This can be done graphically and graph is attached. There will be two points where the line cuts the circle so two solution sets

The equations are

Line Equation [tex]y = 1 - 2x[/tex]    (1) and

Circle Equation [tex]x^2+ y^2 = 2[/tex]   (2)

[tex]y=1-2x[/tex]

Plug this value of y into the second equation for the circle
[tex]x^2 + (1-2x)^2= 2[/tex]

Apply the perfect squares formula [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]

[tex](1-2x)^2 = 1^2-2\cdot \:1\cdot \:2x+\left(2x\right)^2\\= 1-4x+4x^2\\\\[/tex]

So equation (2) becomes
[tex]1-4x+4x^2 +x^2 = 2 \\\\\\5x^2 -4x - 1 = 0[/tex]

Solve using the quadratic formula
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here a is the coefficient of x ², b is the coefficient of x and  c is the constant

So
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)}}{2\cdot \:5}[/tex]

Now,

[tex]\sqrt{\left(-4\right)^2-4\cdot \:5\left(-1\right)} = \sqrt{\left(-4\right)^2+4\cdot \:5\cdot \:1}[/tex]

= [tex]\sqrt{16+20} = \sqrt{36} = 6[/tex]

Therefore
[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \:6}{2\cdot \:5}[/tex]

[tex]x_1=\frac{-\left(-4\right)+6}{2\cdot \:5}[/tex] = [tex]\frac{-\left(-4\right)+6}{2\cdot \:5} =[/tex]  [tex]\frac{10}{2\cdot \:5}[/tex] [tex]= 1[/tex]

[tex]x_2 = \frac{-\left(-4\right)-6}{2\cdot \:5}[/tex] [tex]= \frac{4-6}{2\cdot \:5}[/tex] = [tex]-\frac{1}{5}[/tex]

To find corresponding values for [tex]y_1 y_2[/tex] plug these values of [tex]x_1, x_2[/tex] into the line equation

[tex]y_1 = 1- 2(1) = -1[/tex]
[tex]y_2 = 1 - 2(-\frac{1}{5}) = 1 + \frac{2}{5} = \frac{7}{5}[/tex]

So the two points of intersection are

[tex](1, -1)[/tex] and ([tex](-\frac{1}{5}, \frac{7}{5})[/tex].

In decimal form this would be (1, -1) and (-0.2, 1.4)

See attached graph

Answer:

Step-by-step explanation:

6.92

Answer:

Evan could be thinking of 200,000.

Step-by-step explanation:

The digit 2 in 328,907 has values 20,000 so in Evan's number it has the values 200,000.

Answer:

22 and 23

Step-by-step explanation:

The first step is to make an equation that models this problem. Since the two numbers are consecutive, make them [tex]x[/tex] and [tex]x+1[/tex].

Since it says three times the larger number is 47 more than the smaller number, that means

[tex]3 (x+1) = x+47[/tex]

[tex]3x+3 = x+47[/tex]

[tex]2x+3=47[/tex]

[tex]2x=44[/tex]

[tex]x=22[/tex]

The smaller number is 22, and the larger number is 23.

The sum of the expression in simplest form is 8( x + 2y)

Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc

Given the expressions;

(3x+9y) and (5x+7y)

Let's find the sum

3x + 9y + 5x + 7y

collect like terms

3x + 5x + 9y + 7y

8x + 16y

Find common factor

8( x + 2y)

Thus, the sum of the expression in simplest form is 8( x + 2y)

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Eli's strawberry milk has a stronger strawberry taste than Arjun.

According to the question we have been given that

Arjun ,       adds milk = 90ml

                in strawberry syrup = 20ml

Eli,             adds milk = 180ml

                in strawberry syrup = 45ml

We need to find whose strawberry milk has stronger strawberry taste that is we have to find the concentration of the solution.

The formula for the concentration is given as :

   Concentration of the solution = [tex]\frac{volume of solute}{volume of solution}[/tex]  * 100%

For Arjun,  

        Volume of solvent = 90ml

      Volume of solute = 20ml

     Volume of solution = 20+90 ml = 110 ml

Concentration = (20/110)*100%

                        = 18.18%

For Eli,

         Volume of solvent = 180ml

      Volume of solute = 45ml

     Volume of solution = 180+45 ml = 225 ml

Concentration = (45/225)*100%

                        = 20%

As we can see that the Eli's concentration of the solution is greater than Arjun's. Hence Eli's strawberry milk has a stronger strawberry taste.

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Answer:

30

Step-by-step explanation:

150/5 = 30

Answer: 30

Step-by-step explanation:

The number of cabinets that can be placed along the wall is 15.

It should be noted that in this scenario, we simply have to calculate the perimeter.

This will be:

= 2(length + width)

= 2(1 1/2 + 6)

= 2(7 1/2)

= 15

Therefore, the number of cabinets that can be placed along the wall is 15.

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first of all let's recall that on the negative side of the number line, the closer to 0, the greater, so -1 is much greater than -1,000,000.

well, let's simply try to convert both fractions to the same denominator by multiplying top and bottom by 1 or namely the same value, hmmm let's multiply -2/3 by 2/2 = 1, and -1/2 by 3/3 = 1

[tex]-\cfrac{2}{3}\cdot \cfrac{2}{2}\implies -\cfrac{4}{6}\hspace{5em}-\cfrac{1}{2}\cdot \cfrac{3}{3}\implies -\cfrac{3}{6}[/tex]

well, rats, no much wiggling room there, well, let's simply multiply them again by 1, in this case hmmmm 2/2 for both

[tex]-\cfrac{4}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{8}{12}}\hspace{5em}-\cfrac{3}{6}\cdot \cfrac{2}{2}\implies \boxed{-\cfrac{6}{12}} \\\\\\ \underset{-\cfrac{2}{3}}{\boxed{-\cfrac{8}{12}}}\hspace{5em} < \qquad -\cfrac{7}{12}\qquad < \hspace{5em} \underset{-\cfrac{1}{2}}{\boxed{-\cfrac{6}{12}}}[/tex]

In linear equation, S = x2 + 36/x  the surface area S of the box as a function of the length x of one of the sides.

What in mathematics is a linear equation?

Let x = length of the sides of the base, and h = the height.  The volume is given as 9 m3

Volume = area of base * height

9 = x2*h

So 9/x2 = h

The surface area, S, of the box is:

S = (Area of Base) + 4*(Area of a Vertical Side)

S = x2 + 4 * (xh)

Substitute 5/x2 in place of h:

S = x2 + 4 * x * (9/x2)

S = x2 + 36/x

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