Can someone help me with all these? .

Given:

The sum of third and seventh terms of an AP is 20.

To find:

The sum of the first nine ​ terms.

Solution:

We have, the sum of third and seventh terms of an AP is 20.

[tex]a_3+a_7=20[/tex]        ...(i)

nth term of an AP is

[tex]a_n=a+(n-1)d[/tex]

where, a is first term and d is common difference.

[tex]a_3=a+(3-1)d[/tex]

[tex]a_3=a+2d[/tex]       ...(ii)

[tex]a_7=a+(7-1)d[/tex]

[tex]a_7=a+6d[/tex]       ...(iii)

Using (i), (ii) and (iii), we get

[tex](a+2d)+(a+6d)=20[/tex]

[tex]2a+8d=20[/tex]         ...(iv)

Now, the sum of first n terms of an AP is

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Put n=9 to find the sum of first 9 terms of an AP.

[tex]S_n=\dfrac{9}{2}[2a+(9-1)d][/tex]

[tex]S_n=\dfrac{9}{2}[2a+8d][/tex]

[tex]S_n=\dfrac{9}{2}[20][/tex]           [Using (iv)]

[tex]S_n=\dfrac{180}{2}[/tex]

[tex]S_n=90[/tex]

Therefore, the sum of the first 9 terms is 90.

Step-by-step explanation:

Since x is equal to -5, you would need to substitute that value for x in the equation x^2 + y^2 = 25. So....

-5^2 + y^2 = 25

(-5)*(-5) + y^2 = 25

25 + y^2 = 25

y^2 +25 - 25 = 25 - 25

y^2 = 0

y = 0

(x, y) = (-5, 0)

To check the answer....

x^2 + y^2 = 25

-5^2 + 0^2 = 25

25 + 0 = 25

25 = 25

The answer should be correct, if not i am extremely sorry

Hope this helps!!!

Answer:

The equation of the straight line passing through the point ( 3,1 )

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

Step-by-step explanation:

Step(i):-

The equation of the straight line passing through the point ( 3,1 )

                      [tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]

                     [tex]\frac{3}{a} + \frac{1}{b} = 1[/tex]

                    3b + a = ab ...(i)

Given the difference of length is  4

                      a-b = 4

                       b =  a - 4 ...(ii)

Step(ii):-

substitute b=a-4 in equation (i) , we get

                3( a-4 ) + a = a (a-4)

               3a - 12+ a =  - 4 a + a²  

                 a² - 8 a + 12 =0

Find the factors of 'a'

                 a² - 6a -2a +12 =0

                a (a-6) -2(a-6) =0

             a =2 and a=6

                  we know that a-b =4

             put       a = 2

                          2 - b =4

                            b = -2

The equation of the straight line whose intercepts on the axes

                    [tex]\frac{x}{a} + \frac{y}{b} = 1[/tex]

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

The equation of the straight line

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

Verification:-

The equation of the straight line passing through the point (3,1)

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

Put x =3 and y=1

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

                 1 = 1

∴  The point (3,1) is satisfies the equation

Answer:

x=34

Step-by-step explanation:

a^2 + b^2 = c^2

16^2 + 30^2 = c^2

256 + 900 = c^2

1156 = c^2

sqrt1156 = c

34 = c

34 = x

Checked work with a calculator. Hope this helps. Have a nice day. May it be filled with joy and happiness. Please, be safe and wash your hands. Happy Holidays.

Answer:

x = 34

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to find the missing side.

Step 2: Identify Variables

Leg a = 30

Leg b = 16

Hypotenuse c = x

Step 3: Solve for x

Answer:

[tex]G' = (1,4)[/tex]

[tex]H' = (-4,5)[/tex]

[tex]I = (-8,2)[/tex]

Step-by-step explanation:

Given

[tex]G = (4,1)[/tex]

[tex]H = (5,-4)[/tex]

[tex]I = (2,-8)[/tex]

Reflection: [tex]y = x[/tex]

Required

Determine the coordinates of G'H'I'

The following applies when a line A is reflected over [tex]y = x[/tex]

[tex]A = (x,y)[/tex]

[tex]A' = (y,x)[/tex]

i.e, we simply swap the positions of x and y

So, for:

[tex]G = (4,1)[/tex]

[tex]H = (5,-4)[/tex]

[tex]I = (2,-8)[/tex]

The reflections are:

[tex]G' = (1,4)[/tex]

[tex]H' = (-4,5)[/tex]

[tex]I = (-8,2)[/tex]

See attachment

Answer:

I'm pretty sure its -11

Answer:

f(3) = -11

Step-by-step explanation:

Substitute 3 in wherever you see an x:

f(3) = -4 * 3 + 1

f(3) = -12 + 1

f(3) = -11

Answer:

13

Step-by-step explanation:

The length of the line segment is 13 unit.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.

(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)

We are given that coordinate plane shows Line A B.

We need to find the length of the line segment.

We can see that the graph has 1 unit equal to 1 cm.

Then the coordinate for Point B is (5, 13)

The length of the line segment is 13 unit.

Learn more about line segment here:

https://brainly.com/question/14186383

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Answer:

sorry to tell you this but you will be measuring for a while

Step-by-step explanation:

go to walmart get a 2/3 measuring cup and measure out 8 cups i guess. get me some chips while your there plss. <3

Answer:

complementary means that their measures add up to 90 degrees. since they're also congruent, they have to be the same measure.

90/2= 45 degrees which is your answer

Step-by-step explanation:

I hope this helps :)

Answer:

45 degrees

Step-by-step explanation:

i just took the test on edge

Answer:

19.9 is the answer

Step-by-step explanation:

10 percent of 199 is 19.9

Answer:

18 students

Step-by-step explanation:

Now think of it in this form. 12 students wanna learn french which is 24% and in this problem we have to find 24% of "x" is 12. The answer is obviously 50. Now go to German and you can see that 18% want to learn German. All you have to do is find 50% of 18 to get your answer which is 9. Now follow that same pattern with the Spanish one. If 36% want to learn Spanish, just find 50% of it or half of it and that could be done by doing 36 divided by 2 to get 18 as your answer. Another way to do it is my turning 50% into 0.5 and multiplying it by 36 to get your answer. As a result, your answer is 18 students want to learn Spanish.

Answer:

Step-by-step explanation:

2) They distributed an x out of the term with out one.  that is the 8

so the expression should be  5x +8

3) They didn't follow order of operations and took 2 away from the 7 before they distributed the 7  :O  very bad of them

the expression should be  7x + 54

4) They distributed out the y but didn't leave a 1 so the problem lost a term.

the expression should be -6x + 7y

Answer:

sin A= 3/5

sin C= 4/5

cos A= 4/5

cos C= 3/5

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

for the first one the answer is .50 . for the second one you put for every .50 there is 3.50 and for number 3 for 7 is 49

2x-2y+1

Step-by-step explanation:

you will add ir subtarct like terms only

Answer:

2x - 6y

Step-by-step explanation:

u have to divide

Answer:

3 dollars

Step-by-step explanation:

5 cans= 15 dollars

1 can = 15/5= 3

3 dollars

Answer:   The height is 3  units.

Step-by-step explanation:

By using the give figure we can form right angle out of the whole figure  with a base of  4  and an hypotenuse of 5.

By using this information we can use the Pythagorean Formula to find the height

a^2 + b^2 =c^2     a= base, b = height and c will be the hypotenuse.

4^2 + b^2 = 5^2     Solve for B

16  + B^2 = 25  

-16               -16

    b^2 = 9    

    b = [tex]\sqrt{9}[/tex]  

  b  = 3

The height, h, of the triangular prism is 3 units.

Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.

Given that, vertical cross-section of the triangular prism shown in the given figure is an isosceles triangle.

Here, equal sides of an isosceles triangle is 5 units and base of the isosceles triangle is 8 units.

By using Pythagoras theorem,

5²=h²+4²

25=h²+16

h²=9

h=3

Therefore, the height, h, of the triangular prism is 3 units.

To learn more about an isosceles triangle visit:

https://brainly.com/question/10147636.

#SPJ7

Answer:

17 units

Step-by-step explanation:

Distance between points [tex](a,b)\,,\,(c,d)[/tex] is given by [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

The trail starts at P(−2, 2) and goes to Q(5, 2).

Take [tex](a,b)=(-2,2)\,,\,(c,d)=(5,2)[/tex]

[tex]PQ=\sqrt{(5+2)^2+(2-2)^2}=\sqrt{7^2}=7[/tex] units

It goes from Q to R(5, −5)

Take [tex](a,b)=(5,2)\,,\,(c,d)=(5,-5)[/tex]

[tex]QR=\sqrt{(5-5)^2+(-5-2)^2}=\sqrt{(-7)^2}=7[/tex] units

It goes from R to S.

Take [tex](a,b)=(5,-5)\,,\,(c,d)=(8,-5)[/tex]

[tex]RS=\sqrt{(8-5)^2+(-5+5)^2}=\sqrt{3^2}=3[/tex] units

[tex]PQ+QR+RS=7+7+3=17[/tex] units

I believe it would be 60, 60 is the only multiple for 6.

Answer: choices for the number in hundreds place =  7 , 8, 9,0

Step-by-step explanation:

Given: Dinesh wrote a number greater than 4699 and less than 5100.

Numbers greater than 4699 = 4700, 4701,.....

Numbers less than 5100 = 5099, 5098 , .....

From 4700 to 5099 , the possible values for hundreds place = 7 , 8, 9,0

So, the choices for the number in hundreds place =  7 , 8, 9,0

Answer:

multiply by 1.81

Step-by-step explanation:

Answer:

9 1/2

Step-by-step explanation:

i think think this may be the anwser

Answer:

m = 3

Step-by-step explanation:

Pick two points from the table.

(-1, 1) and (1, 7)

Apply the slope formula.

[tex]m=\frac{7-1}{1+1}=\frac{6}{2}=\boxed{3}[/tex]

Hope this helps.

Answer:

Han's mixture tastes stronger, because...

Han's uses 6 2/3 cups of water for every 1 cup of orange juice concentrate.

Clare uses 7 1/2 cups of water for every 1 cup of orange juice concentrate.

Step-by-step explanation:

Claire

Cups of water = 2 1/2 cups

Cups of orange juice = 1/3

Cups of water for every cup of orange juice = 2 1/2 ÷ 1/3

= 5/2 × 3/1

= 15/2

= 7 1/2

Han:

Cups of water = 1 2/3 cups

Cups of orange juice = 1/4 cups

Cups of water for every cup of orange juice = 1 2/3 ÷ 1/4

= 5/3 × 4/1

= 20/3

= 6 2/3

Step-by-step explanation:

y = -5x² + 2x - 3 and y = -3x - 3.

=> -5x² + 2x - 3 = -3x - 3

=> 5x² - 5x = 0

=> 5x(x - 1) = 0

=> x = 0 or x = 1.

When x = 0, y = -3(0) - 3 = -3.

When x = 1, y = -3(1) - 3 = -6.

The solutions are (0,-3) and (1,-6).

Answer:

1,155 miles in a year.

Step-by-step explanation:

Assuming there are 4 weeks per month, that would mean there are a total of 48 weeks. If she takes 6 weeks off then that would leave 42 weeks. We know need to find how many minutes are in 11 hours by multiplying 11 by 60min.

11 * 60 = 660min

Now we need to divide 660min by the 24min it takes to walk 1 mile which will also give us the number of miles she walks per week

660 / 24 = 27.5 miles per week

Finally, we need to multiply the number of miles by the number of weeks in the year.

27.5 miles * 42 weeks = 1,155 miles in a year.

Answer:

Step-by-step explanation:

J is correct.. that function can never be less than 2

Answer:

2.25

Step-by-step explanation:

2/5 is equal to 4/10

(9/10)/(4/10)

(9/10)*(10/4)

90/40

9/4 = 2.25

(Can be checked if you multiply 4 by 2.25)