10.The sum of first 16 terms of the AP: 10, 6 ,2, ....is



− 320− 320

320320

640640

 − 352 − 352


​

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids.

A sphere is a solid shape.

Given data

radius of sphere = 17 units

The volume of a sphere can be expressed as below

[tex]volume = \frac{4}{3}\pi r^3[/tex]

Substituting our data into the expression we have

[tex]volume = \frac{4}{3}*3.142*17^3[/tex]

[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]

The volume of the sphere is given as

20582.195 units

Answer:

18 inches by 36 inches.

Step-by-step explanation:

Since we have given that

The generic version was basedOn the brand name and was 2/3

And given Dimensions of generic version is given by 12inches ×24inches

If we use the first dimensions of 12inches we have

12=2/3 × brand

12×3/2 = brand

=18inches= brand

we use the first dimensions of 24 inches we have

24=2/3 × brand

24×3/2 = brand

=36 inches= brand

brand= 36 inches

Therefore,the dimensions of brand name will be 18 inches by 36 inches.

Answer:

18

Step-by-step explanation:

3⋅6−2+2​

Use PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction

First we multiply, then add or subtract so,

18 - 2 + 2

Now we subtract,

16 + 2

Now we add,

18

Answer:

Area : 14+10+40=64 square unit

Step-by-step explanation:

the area of the top rectangle with sides  2 and 7

A=2*7=14 square unit

the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5

Area=5*2=10 square unit

the bottom rectangle : sides 10 and 4

Area=10*4=40

add the areas : 14+10+40=64 square unit

Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation:

Answer:

5 cm

Step-by-step explanation:

The volume (V) of milk in the container is calculated as

V = 8 × 15 × 12 = 480 cm³

After change of position with depth d then

8 × 15 × d = 480

120d = 480 ( divide both sides by 120 )

d = 4 cm

Answer:

perimeter is  4 sqrt(29) + 4pi  cm

area is 40 + 8pi cm^2

Step-by-step explanation:

We have a semicircle and a triangle

First the semicircle with diameter 8

A = 1/2 pi r^2 for a semicircle

r = d/2 = 8/2 =4

A = 1/2 pi ( 4)^2

  =1/2 pi *16

  = 8pi

Now the triangle with base 8 and height 10

A = 1/2 bh

  =1/2 8*10

  = 40

Add the areas together

A = 40 + 8pi cm^2

Now the perimeter

We have 1/2 of the circumference

1/2 C =1/2 pi *d

         = 1/2 pi 8

        = 4pi

Now we need to find the length of the hypotenuse of the right triangles

using the pythagorean theorem

a^2+b^2 = c^2

The base is 4 ( 1/2 of the diameter) and the height is 10

4^2 + 10 ^2 = c^2

16 + 100 = c^2

116 = c^2

sqrt(116) = c

2 sqrt(29) = c

Each hypotenuse is the same so we have

hypotenuse + hypotenuse + 1/2 circumference

2 sqrt(29) + 2 sqrt(29) + 4 pi

4 sqrt(29) + 4pi  cm

Step-by-step explanation:

First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.

2pi4 so the perimeter for the half circle would be 8pi/2.

The area of that half circle would be piR^2 so 16pi/2.

Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2

16+100=C^2

116=C^2

C=sqrt(116)

making the perimeter of this triangle 2×sqrt(116)

The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.

We than just need to add up the perimeters and areas for both the half circle and triangle.

The area would be equal to 8pi+40

The perimeter would be equal to 4pi+4(sqrt(29))

Answer:

The answer is (3×7) + (12×2) .

[tex](3 \times 7) + (12 \times 2)[/tex]

[tex] = 21 + 24[/tex]

[tex] = 45[/tex]

Answer:

288.4m

Step-by-step explanation:

This track is split into a rectangle and two semi-circles.

We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].

[tex]2\cdot3.14\cdot30\\188.4[/tex]

However this is half a circle, so:

[tex]188.4\div2=94.2[/tex].

There are two semi-circles.

[tex]94.2\cdot2=188.4[/tex]

Since there are two legs of 50m each, we add 100 to 188.4

[tex]188.4+100=288.4[/tex]m

Hope this helped!

Answer:

Step-by-step explanation:

To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.

For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.

15 * 2π ≈ 94.2477796077

We add that to 100m and get:

194.2477796077

Answer:

When x = -4 and y = -6, p = 37.75

Step-by-step explanation:

Given that p = x² - y²/x² + x·y, we have;

p = (x² × x² -y² + x·y×x²)/x²

p = (x²⁺² - y² + x¹⁺² × y)/x²

p = (x⁴ - y² + x³·y)/x²

Therefore, p in the simplest form is given as follows;

[tex]p = \dfrac{x^4 - y^2 + x^3 \cdot y }{x^2}[/tex]

To find the value of p when x = -4 and y = -6, we plug in the value of x and y into the above equation to get the following equation;

[tex]p = \dfrac{(-4)^4 - (-6)^2 + (-4)^3 \cdot (-6) }{(-4)^2} = 37.75[/tex]

Therefore, the value of p when x = -4 and y = -6 is equal to 37.75.

Answer:

? = 4.73

Step-by-step explanation:

Since this is a right triangle we can use trig functions

sin theta = opp / hyp

sin 25 = 2 / ?

? sin 25 = 2

? = 2 / sin 25

? =4.732403166

To the nearest hundredth

? = 4.73

Answer:

m = -9

Step-by-step explanation:

2m-10=44+8m

Subtract 2m from each side

2m-2m-10=44+8m-2m

-10 = 44+6m

Subtract 44 from each side

-10-44 = 44-44+6m

-54 = 6m

Divide by 6

-54/6 = 6m/6

-9 = m

Answer:

solve by solving the salvation for equation don't be a slave get educated from what's gave

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer:

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

Step-by-step explanation:

Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:

Speed = distance / time

The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.

For running:

Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:

5 = p / x

p = 5x

For biking:

Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:

12 = q / y

q = 12y

The total distance ran and biked by Suzette (d) = Distance biked + distance ran

d = p + q

80 = p + q

80 = 5x + 12y                 (1)

The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run

t = x + y

9 = x + y                         (2)

Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:

7y = 35

y = 35/7

y = 5 hours

Put y = 5 in equation 2:

9 = x + 5

x = 9 -5

x = 4 hours

a) Suzette ran for 4 hours

b) Suzette biked for 5 hours

Answer:

A

Step-by-step explanation:

Find the vertex form of the quadratic function below.

y = x^2 - 4x + 3

This quadratic equation is in the form y = a{x^2} + bx + cy=ax  

2

+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…

y = a(x - h)^2 + k

This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.

Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.

STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.

STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).

STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.

Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.

STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.

After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).

Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.

Example 2: Find the vertex form of the quadratic function below.

The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a  



​  

=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.

STEP 1: Factor out 22 only to the terms with variable xx.

STEP 2: Identify the coefficient of the xx-term or linear term.

STEP 3: Take that number, divide it by 22, and square.

STEP 4: Now, I will take the output {9 \over 4}  

4

9

​  

 and add it inside the parenthesis.

By adding {9 \over 4}  

4

9

​  

 inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(  

4

9

​  

)=  

2

9

​  

 to the entire equation.

Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.

STEP 5: Since I added {9 \over 2}  

2

9

​  

 to the equation, then I should subtract the entire equation by {9 \over 2}  

2

9

​  

 also to compensate for it.

STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.

It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)  

2

+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(  

2

−3

​  

,  

2

−11

​  

).

Example 3: Find the vertex form of the quadratic function below.

Solution:

Factor out - \,3−3 among the xx-terms.

The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}  

4

1

​  

 inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(  

4

1

​  

)=  

4

−3

​  

 is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}  

4

3

​  

 outside the parenthesis.

Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(  

2

1

​  

,  

4

11

​  

).

Example 4: Find the vertex form of the quadratic function below.

y = 5x^2 + 15x - 5  

Solution:

Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}  

4

9

​  

.

Add {9 \over 4}  

4

9

​  

 inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(  

4

9

​  

)=  

4

45

​  

 is the number that we need to subtract to keep the equation unchanged.

Express the trinomial as a square of binomial, and combine the constants to get the final answer.

Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}  

2

−3

​  

,  

4

−65

​  

.

Answer:

(x - 1 )^2 - 3

Step-by-step explanation:

( x - 1 )^2 + ( -3)

x^2 - 2x + 1 - 3

x^2 - 2x - 2

Greetings from Brasil...

a - whole number

FALSE

3/5, for example isnt a whole number

b. natural number

FALSE

0,457888..., for example isnt a natural number

c. integer

FALSE - like a

d. real number

TRUE

The set of real numbers contains the set of rational numbers

ℝ ⊃ ℚ

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Answer:

Step-by-step explanation:

Volume = 1/3πr²h

Surface Area = πr(r+√(h²+r²))

V = 1/3π(10)²(34) = 3560 .5 cm³

SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²

Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21

Answer:

-3=x <13

Step-by-step explanation:

[tex] - 9 = \frac{2x}{3} - 7 < 5[/tex]

Multiply through by 3

[tex] - 27 = 2x - 21 < 15[/tex]

Add 21 to all sides

[tex] - 6 = 2x < 36[/tex]

Divide through by 2

[tex] - 3 = x < 18[/tex]

The solutin set is

[tex]{- 3 = x < 18}[/tex]

Answer:

p= 25/100 = 180/x

Step-by-step explanation:

In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.

Answer:

0.75p=p-180

Step-by-step explanation:

0.75p=p-180 is your answer

Answer:

h = 10

Step-by-step explanation:

Given

[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]

Multiply through by 14 to clear the fractions

6 = h - 4 ( add 4 to both sides )

10 = h

Answer:

10

Step-by-step explanation:

We start out with 3/7 = h/14 - 2/7

add 2/7 to both sides:

(5/7) = h/14

Multiply both sides by 14 to get rid of the fraction:

h = 10

===================================================

Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

Read more about non-linear graphs at:

https://brainly.com/question/16274644

#SPJ5

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer:

Step-by-step explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]

Perimeter:

P = 4s = 4•17 = 68 cm

Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.