Given that the 10th term of an AP is 45 and that the sum
of the first 10 terms is 270 find
a) The first term
b) The common difference
c) The sum of the first 15 terms

Answer: A= 4.5 B=no C= 4.5

Step-by-step explanation:

Answer:

gradient is 0.35

Step-by-step explanation:

The gradient or slope of the line is 1/4.

The slope of a line indicates the direction and the steepness of the line. The formula for the slope of a line passing through the points (x₁,y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁).

The graph of the line is given.

Note that the line passes through the point (0,1) ad (4,2).

The gradient of the line is nothing but the slope of the line.

The slope of the line is:

m = (2-1)/(4-0)

m = 1/4

Hence, the gradient or slope of the line is 1/4.

To learn more about slopes, click here:

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Answer:

[tex]\frac{d}{dx}(-xcos3x)= 3x \ sin(3x)- cos(3x)[/tex]

Step-by-step explanation:

Use the Product Rule for derivatives, which states that:

In the function we are given, [tex]f(x)=-x \cos3x[/tex], we can break it up into two factors: -x is being multiplied by cos3x.

Now, we have the factors:

Before using the product rule, let's find the derivative of cos3x using the chain rule and the power rule.

Now let's apply the product rule to f(x) = -xcos3x.

Simplify this equation.

Multiply x and 3 together and remove the parentheses.

Therefore, this is the derivative of the function [tex]f(x)=-xcos3x[/tex].

Hi there!

[tex]\large\boxed{f'(x) = -cos3x + 3xsin3x}[/tex]

[tex]f(x) = -xcox3x\\\\\text{Use the product rule and chain rule to solve for the derivative:}\\\\\frac{dy}{dx}= -cos3x + (-x * (-sin3x) * 3)\\\\= -cos3x + 3xsin3x[/tex]

Answer:

sorry I don'tknow. ...answer

Answer:

15. Yes, it is larger than 14.

Step-by-step explanation:

In this problem,

[tex]\frac{3}{5}[/tex]×25,

25 is divided by 5 and the remainder is 5, So,

3×5 = 15,

Now,

15 > 14,

So, the product of ([tex]\frac{3}{5}[/tex] × 25) is greater than 14

Answer:

vudnfvd 3/5

Step-by-step explanation:

Answer:

7°

Step-by-step explanation:

If the temperature was -5 and it increased by negative 12, it's asking you to add -5 and 12

-5+12=7

Answer:

Step-by-step explanation:

1. Yes

2.No

3. No

4. No

To be a function, the x axis can only be used once so it will pass the vertical line test.

Answer:

Step-by-step explanation:

4) ΔSTW ≅ ΔBFN . So, corresponding parts of congruent triangles are congruent.

a) BN = SW                                        d) m∠W = m∠N

  BN = 9 cm                                           m∠W = 82°

b) TW = FN                                        e) m∠B = m∠S

TW = 14 cm                                            m∠B = 67°

c) BF = ST                                          f) m∠B + m∠N + m∠F = 180°

  BF = 17 cm                                                 67 + 82 + m∠F = 180

                                                                            149 + m∠F = 180

                                                                                     m∠F = 180 - 149

                                                                                      m∠F = 31°          

5) ΔUVW ≅ ΔTSR

UV = TS

12x - 7 = 53

   12x   = 53+7

   12x = 60

      x = 60/12

      x = 5

UW =TR

3z +14 = 50

    3z = 50 - 14

   3z = 36

     z = 36/3

    z = 12

SR =VW

5y - 33 = 57

     5y = 57 + 33

     5y = 90

       y = 90/5

       y = 18

7) ΔPHS ≅ ΔCNF

∠C = ∠P

4z - 32 = 36

      4z = 36 + 32

       4z = 68

        z = 68/4

       z = 17

∠H = ∠N

6x - 29 = 115

  6x     = 115 + 29

      6x = 144

        x = 144/6

       x = 24

∠P + ∠H + ∠S = 180   {Angle sum property of triangle}

36 +115 + ∠S = 180

      151   + ∠S = 180

                ∠S = 180 - 151

               ∠S = 29°

∠F = ∠S

3y - 1 = 29

   3y = 29 + 1

  3y = 30

    y = 30/3

    y = 10

8) ΔDEF ≅ ΔJKL

DE = 18    ;  EF = 23

DF = 9x - 23

JL= 7x- 11

DF = JL           {Corresponding parts of congruent triangles}

      9x - 23 = 7x - 11

9x  - 7x - 23 = -11

        2x - 23 = -11

               2x = -11 + 23

               2x = 12

                 x = 12/2

                x = 6      

JK   = DE           {Corresponding parts of congruent triangles}

3y - 21  = 18

       3y = 18 + 21

        3y = 39

         y = 39/3

        y = 13

Answer:

no it is not the same.

Step-by-step explanation:

it is not the same because 13/4 is smaller than 3/14. 3 1/4 includes a whole number, and 13/4 doesn't.

Answer: It will be needed 864 square feet of glass to cover the Skywalk floor.

Step-by-step explanation: The figure below shows the area in question.

Area of a circle is given by

[tex]A=\pi.r^{2}[/tex]

The walkway is a semicircle. Then, area will be:

[tex]A=\frac{\pi.r^{2}}{2}[/tex]

The area that will be covered with glass is the area between the outer and the inner circles. So, area is

[tex]A_{t}=A_{outer}-A_{inner}[/tex]

[tex]A_{t}=\frac{\pi.r_{o}^{2}}{2}- \frac{\pi.r_{i}^{2}}{2}[/tex]

[tex]A_{t}=\frac{\pi}{2}(32.5^{2}-22.5^{2})[/tex]

[tex]A_{t}=\frac{\pi}{2}(550)[/tex]

[tex]A_{t}=[/tex] 864

To cover the Skywalk floor is needed 864[tex]ft^{2}[/tex] of glass.

Answer: Quad IV

Step-by-step explanation:

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Absolute value.

so we get as,

let, y = 2 - 9i

so the absolute value is |y|

[tex] |y| = \sqrt{ {2}^{2} + {9}^{2} } [/tex]

so we get as,

|y| =

[tex] \sqrt{81 + 4} = \sqrt{85} [/tex]

so the absolute value is

[tex] \sqrt{85} [/tex]

Answer:

931.00

Step-by-step explanation: took the quiz

Answer:

Input is the number in the first column of the table. This is the number that you start with to follow the rule if the rule is given. You would also use this number to figure out what the rule is if it is not given.

Step-by-step explanation:

An input-output table, like the one shown below, can be used to represent a function. Each pair of numbers in the table is related by the same function rule. That rule is: multiply each input number (\begin{align*}x\end{align*}-value) by 3 to find each output number (\begin{align*}y\end{align*}-value).

Answer:

1.5lb/ounces

Step-by-step explanation:

Given:

Mass of dry ice Carmen uses  = 12lb

Mass of root beet  = 8ounces

Unknown:

Ratio/Proportional constant for number of pounds to number of ounces of root beer extract  = ?

Solution:

To solve this problem,

    Ratio = [tex]\frac{number of pounds of dry ice}{Ounce of root beer}[/tex]

    Ratio  = [tex]\frac{12lb}{8ounces}[/tex]   = 1.5lb/ounces

Answer:

d = -13

Step-by-step explanation:

Subtract 4.7 from both sides to get d by itself

-13 = d

Answer:

-13

Step-by-step explanation:

Subtract the total (-8.3) by the number that we know (4.7), to get -13 as the answer for the value of D.

(We can clarify by doing -13+4.7=-8.3)

Answer:

The answer is -9

Step-by-step explanation:

First we have to find the value for g(8) so that we can plug its solution into f(x).

So...

[tex]\frac{1}{8}[/tex](8) + 5

1 + 5

6

So now we plug in 6 into f(x) since 6 was our solution to g(x)

3 - 2(6)

3 - 12

-9

Answer:

Step-by-step explanation:

2 more tiles are added in the next figure so in figure 30 the tiles will be 61

Answer:

9 tiles

Step-by-step explanation:

So figure 3 is literally figure 2 but added 1 to each corner. If the pattern is to contiue there should be 9 for figure 4.

Answer:

I don't understand what should i answer.

The only thing I undrestood was that this is a relation which can be a function.

Answer:

can't see full thing dhbsvshshzhd

Answer:

2,400 minutes and its is 144,000 secods

Step-by-step explanation:

Answer:

x=6

y=-6

Step-by-step explanation:

Answer: The answer is true :)

Answer:

7/50

Step-by-step explanation:

7/50 is the reduced fraction form of 0.14.

Answer: 280

Step-by-step explanation:

4200/60 = 70

70*4 = 280

9514 1404 393

Answer:

  11.85 deciliters

Step-by-step explanation:

Your table tells you 1 cup is 0.237 liters. Then 5 cups is ...

  (5 cups)(0.237 L/cup) = 1.185 L = 11.85 dL

__

"deci-" is the SI prefix for 1/10. 1.1 liters is 11 tenths of a liter.

Answer:

Let the price of one senior citizen ticket be sc and the price of one student ticket be st.

Let's write equations using the information given and the variables above:

=> 5sc + 15st = $137.50

=> 20sc + 44st = $430

Hmm.. We can multiply 5sc by 4 to get 20sc.

=> 4(5sc) + 4(15st) = 4($137.50)

=> 20sc + 60st = $550

Now we can subtract the second equation from the first to determine the price of a student ticket.

  20sc + 60st = $550

-  20sc + 44st = $430

=> 16st = $120

=> st = $7.5

So, the price of a student ticket is $7.5.

Answer:

33/10

Step-by-step explanation:

I used a calculator sorry if I am wrong

Answer:

3 3/10.

Step-by-step explanation:

The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''.

Answer:

its 10y

Step-by-step explanation:

hope this helps (*^▽^*)

Answer: -10y

Step-by-step explanation: [tex]2x-7y-2x-3y\\-7y-3y[/tex]