find the equation of the tangent to the curve at x=3 for parametric equations

x = t + 1/t
y = t^2 + 1/(t^2) when t is greater than 0

There are 15 students in Ms. Jackson’s class

How many students are in Ms. Jackson’s class?

From the question, we have the following parameters that can be used in our computation:

The Venn diagram

Where, we have

Both = 5

None = 2

Using the above as a guide, we have the following:

Total students = (10 -5) + 5 + (8 -5) + 2

Evaluate

Total students = 15

Hence. there are 15 students in Ms. Jackson’s class

answer:

11.Quadrant 1 10.quadrant II 9. IV 13. IV 12. III 14. III 16: III 17: II 15 I

Step-by-step explanation:

this should help https://socratic.org/questions/what-is-the-order-of-quadrants-in-a-graph  just look at the coordinates x and y if they correspond to which quadrant.

Each point is placed in a quadrant based on its x and y values. Quadrant I contains points where both values are positive, Quadrant II where x is negative and y is positive, Quadrant III where both are negative and Quadrant IV where x is positive and y is negative

To determine which quadrant a point is located in, recognize that the x-y coordinate plane is divided into four sections called quadrants. The quadrants are numbered I through IV and progress counterclockwise, starting with quadrant I in the upper right corner.

Quadrant I: Both x and y are positive. Quadrant II: x is negative, y is positive. Quadrant III: Both x and y are negative. Quadrant IV: x is positive, y is negative.

With this in mind, let's carry out the following:

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Answer: About 4 movies

Step-by-step explanation:

1 2/3 times 4/1 = 28/5

28/5 converted to a mixed number is 5 3/5

so therefore it would be ABOUT 4 movies

To find the number of movies that can be downloaded, divide the total downloading time by the time it takes to download one movie. In this case, 15 movies can be downloaded.

To find the number of movies that can be downloaded, we need to divide the total downloading time by the time it takes to download one movie. First, convert the mixed number 5 1/4 to an improper fraction, which is 21/4. Then, multiply 21/4 by the reciprocal of 1 2/5, which is 5/7. This gives us a total of 15 movies that can be downloaded.

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Answer:

8.73

Step-by-step explanation:

Supplement of an angle measuring 50 degrees is 130 degrees

Step-by-step explanation:

Step 1 :

Given,

Measure of the angle = 50 °

We need to calculate the supplement of this angle

Step 2 :

2 angles are supplement to each other if the sum of their measures is 180°.

Hence the supplement of one angle can be computed by subtracting the value of that angle from 180°

Hence the supplementary angle to 50 ° is 180° - 50 ° = 130 °

Step 3:

Answer:

Supplement of an angle measuring 50 degrees is 130 degrees

Answer:

c = 57.5

Step-by-step explanation:

Since its 90 degree.

it would be 90 - 32.5 = c

Answer:

57.5

Step-by-step explanation:

It’s a 90 degree angle, which means the angles added together make 90. So if you want to get the missing angle, subtract the 32.5 angle to see what remains. That is your missing angle

There are 15 girls and 18 boys. Therefore, the ratio of girls to boys in the cafeteria is 15 : 18 (or 15/18). However, both sides can be divided by 3, which simplifies the ratio to 5 : 6 (or 5/6).

Hope this helps!! :)

Answer: The ratio would be 5 girls to every 6 boys.

Step-by-step explanation:

Find a common number both can be divided be which would be 3, so 15 by 3 is 5, and 18 by 3 is 6. So, there is 5 girls for every 6 boys which is the ratio.

Answer:

Step-by-step explanation:

Find the change in y over the change in x.

1. 123-62/2-1

2. Slope = 39x

Answer:

10.022

Step-by-step explanation:

Answers are bolded.

4 2/3 + 7/9 = 49/9

3.64 + 3/5 = 106/25

2.8+ 7.2 = 10.022

When you add two rational numbers, each number can be written as a  (Fraction)

The sum of two fractions can always  be written as a  (Fraction)

Therefore, the  sum of two rational numbers will always be (Rational)

Step-by-step explanation:

I got these questions correct

Answer:

C)x^2 - 6x-6

Step-by-step explanation:

-3(x + 2) + (x – 3)x=

-3x-6+x^2-3x=

x^2 - 6x-6

Answer:

C

Step-by-step explanation:

-3(x + 2) + (x – 3)x = -3*x + (-3)*2 +x*x - 3*x

                              = -3x - 6  +x² - 3x

                              = x² - 3x -3x - 6

                               = x² - 6x - 6

Answer:

2.1 gaallons of honey

Step-by-step explanation:

If you have to istrubute things then its obvous you need to divide something.  To get 19 equally into 9 containers you divide 19 by 9 an get 2.1

I hope this helped

Each jar will have approximately [tex]\( \boxd{2.111 \text{ gallons}} \)[/tex] of honey.

Step 1

To find out how much honey will be in each jar when Jill distributes all of the honey equally among 9 jars, we need to divide the total amount of honey by the number of jars.

Given:

Total amount of honey = 19 gallons

Number of jars = 9

So, to find out how much honey each jar will have, we divide the total amount of honey by the number of jars:

[tex]\[ \text{Amount of honey per jar} = \frac{\text{Total amount of honey}}{\text{Number of jars}} \]\[ \text{Amount of honey per jar} = \frac{19 \text{ gallons}}{9} \]\[ \text{Amount of honey per jar} = \frac{19}{9} \text{ gallons} \][/tex]

Step 2

Now, let's perform the division:

[tex]\[ \text{Amount of honey per jar} = 2.111111 \text{ gallons} \][/tex]

So, each jar will have approximately [tex]\( \boxd{2.111 \text{ gallons}} \)[/tex] of honey.

Answer:19

Step-by-step explanation:

30-(3x2)-5=9

Answer:

17.861 feet or 17.9 feet (3 sf)

Step-by-step explanation:

180 - 36 - 87 = 57

X/sin(87) = 15/sin(57)

X = 17.861 feet

Solution:

Given is:

[tex]f(x) = 2x^2 - 1[/tex]

We have to find the vertex and axis of symmetry

The general equation is given as:

[tex]f(x) = ax^2 + bx + c[/tex]

Comparing with given equation,

a = 2

b = 0

c = -1

The axis of symmetry is given as:

[tex]x = \frac{-b}{2a}[/tex]

[tex]x = \frac{0}{2(2)}\\\\x = 0[/tex]

Thus axis of symmetry is 0

The x coordinate of the vertex is the same

x coordinate of the vertex = 0

h = 0

The y coordinate of the vertex is:

k = f(h)

k = f(0)

[tex]f(0) = 2(0) - 1\\\\f(0) = 0 - 1\\\\f(0) = -1[/tex]

Thus, y coordinate of the vertex is -1

Therefore, vertex is (0, -1)

Answer:

4000

Step-by-step explanation:cause u add 3          

Answer:

Step-by-step explanation:

first you add all the numbers together-

15+16+20=51

you add them up as shown-

=51

and the divide by 3, because you added up 3 numbers-

51/3=17

so your answer is 17

Step-by-step explanation:

Let the required line bisects the segment joining the point (5,3) and (4,4) at point M (x, y).

Therefore, M is the mid point of segment joining the point (5,3) and (4,4).

Now by mid-point formula we have:

[tex]M = ( \frac{5 + 4}{2} \: \: \frac{3 + 4}{2} ) = ( \frac{9}{2} \: \: \frac{7}{2} ) \\ \\ \therefore \: M \: = ( 4.5 \: \: 3.5 ) = (x_1 \: \: y_1)\\ \\ \because \: Line \: makes \: 45 \degree \: angle \: with \: positive \: \\ \: \: \: \: \: direction \: of \: x - axis. \\ \\ \therefore \: Slope \: of \: line: \: \\ \: \: \: \: \: \: \: m = tan \: 45 \degree = 1 \\ \\ Equation \: of \: line \: in \: slope \: point \: form\\ \: is \: given \: as: \\ y-y_1 =m(x-x_1) \\ \therefore \: y - 3.5 = 1(x - 4.5) \\ \therefore \: y - 3.5 = x - 4.5 \\ \therefore \: y = x - 4.5 + 3.5 \\ \therefore \: y = x - 1\\ \huge \purple { \boxed{\therefore \: x - y - 1 = 0}} \\ [/tex]

is the equation of required line.

Answer:

The other x-intercept is the point (1,0)

Step-by-step explanation:

we have

[tex]y=x^2-3x+2[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]y=x^2-3x+2[/tex]

equate to zero

[tex]x^2-3x+2=0[/tex]

so

[tex]a=1\\b=-3\\c=2[/tex]

substitute in the formula

[tex]x=\frac{-(-3)\pm\sqrt{-3^{2}-4(1)(2)}} {2(1)}[/tex]

[tex]x=\frac{3\pm\sqrt{1}} {2}[/tex]

[tex]x=\frac{3\pm1} {2}[/tex]

so

[tex]x=\frac{3+1} {2}=2[/tex]

[tex]x=\frac{3-1} {2}=1[/tex]

therefore

The other x-intercept is the point (1,0)

The y-intercept can be used to discover the high which the ball must be to be intercepted

Step-by-step explanation:

if x represents the distance the ball traveled, y represent the height of the ball. you must use these two points in order to intercept the ball and catch it at the exact location just like a (x,y) graph.

Answer:

B) 0:15=0

Step-by-step explanation:

Answer:

[tex]\displaystyle \sqrt{15} = x[/tex]

Step-by-step explanation:

Be VERY careful. When it write out the equation that way, it will give the speculation of this:

[tex]\displaystyle 15 = x^2[/tex]

Now, in this case, since you were extra explanatory about this [what is written in parentheses], two factors I know of that multiply to 15 are these:

** [tex]\displaystyle 15 = 2 \times 7\frac{1}{2}[/tex]

I am joyous to assist you at any time. ☺️

Answer:

Slope=2/4 or 1/2

Y-Intercept=8

Step-by-step explanation:

-2x+4y=8

+2x both sides

4y=2x+8

/4

y=2/4x+8

Slope=2/4 or 1/2

Y-Intercept=8

The slope of the graph of the equation -2x + 4y = 8 is  [tex]\frac{1}{2}[/tex] , and the

y-intercept is 2.

To calculate the y-intercept and slope of the graph of the equation -2x + 4y = 8, to change the given equation in the general form of line. The general form of the line is y = mx + b, where m is the slope of the line and b is the y-intercept of the line.

Find the value of y from the given equation of graph.

Calculate y as:

[tex]-2x + 4y = 8\\4y = 2x + 8\\y=\dfrac{2}{4}x+2\\ y=\dfrac{1}{2}x +2[/tex]

Here, the slop of the graph m is  [tex]\dfrac{1}{2}[/tex]  and  y-intercept is 2

Therefore, the slope of the graph is 1/2, and the y-intercept is 2.

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Answer:

D

Step-by-step explanation:

Polynomials are closed under addition and subtraction because we will still get a polynomial

Polynomials are closed under multiplication because we still get a polynomial.

Polynomials are not closed under division because we can get   negative exponents

2x/ 4x^2 = 1/2x  This is not a polynomial

Answer:

D

Step-by-step explanation:

Quotient of 2 polynomials may not be a polynomial

Example:

(10x+5)/(5x²) = 2/x + 1/x²

= 2x^-1 + x^-2

which is not a polynomial because the power is negative

Answer:0

Step-by-step explanation:

-8 + 8 (opposite)

=0

Answer:

0

Step-by-step explanation:

the oppisite of -8 is 8 the sum of 8+(-8)

is the same as 8-8

Answer:

  c = V/((r^3)-72.25r)

Step-by-step explanation:

V is proportional to c, so you can simply divide by the coefficient of c.

  c = V/((r^3)-72.25r)

Option C:

[tex]2 g^{3}-5 g^{2}+6[/tex]

Solution:

Given expression:

[tex]$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}[/tex]

To find which expression is equal to the given expression.

[tex]$\frac{\left(5 g^{4}+5 g^{3}-17 g^{2}+6 g\right)-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right)}{g+2}[/tex]

Expand the term [tex]-\left(3 g^{4}+6 g^{3}-7 g^{2}-12\right):-3 g^{4}-6 g^{3}+7 g^{2}+12[/tex]

         [tex]$=\frac{5 g^{4}+5 g^{3}-17 g^{2}+6 g- 3 g^{4}-6 g^{3}+7 g^{2}+12}{g+2}[/tex]

Arrange the like terms together.

         [tex]$=\frac{5 g^{4}- 3 g^{4}+5 g^{3}-6 g^{3}-17 g^{2}+7 g^{2}+6 g+12}{g+2}[/tex]

         [tex]$=\frac{2 g^{4}- g^{3}-10 g^{2}+6 g+12}{g+2}[/tex]

Factor the numerator [tex]2 g^{4}-g^{3}-10 g^{2}+6 g+12=(g+2)\left(2 g^{3}-5 g^{2}+6\right)[/tex]

         [tex]$=\frac{(g+2)\left(2 g^{3}-5 g^{2}+6\right)}{g+2}[/tex]

Cancel the common factor g + 2, we get

         [tex]=2 g^{3}-5 g^{2}+6[/tex]

Hence option C is the correct answer.

Answer:

C.

Step-by-step explanation: