If the 12th term of the arithmetic sequence is 15 and the 11th term is 10, find the common difference of the sequence.​

Answer:

(1, 7 )

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Then the equations of the 2 lines are

y = 4x + 3 → (1)

y = 6x + 1 → (2)

Substitute y = 6x + 1 into (1)

6x + 1 = 4x + 3 ( subtract 4x from both sides )

2x + 1 = 3 ( subtract 1 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Substitute x = 1 into either of the 2 equations for corresponding value of y

Substituting into (1)

y = 4(1) + 3 = 4 + 3 = 7

Point of intersection = (1, 7 )

Answer:

it's 5

Step-by-step explanation:

Answer:

r = 5

Step-by-step explanation:

if x and y are proportional then 'y = rx' where 'r' is the constant of proportionality

35 = 7r

60 = 15r

100 = 20r

'r' is 5

Answer:

A. 2 lines

Step-by-step explanation:

Just did it on Acellus

Figure constitute 2 lines.

A line is a part of line that is bounded by two distinct end point, and contains every point on the line is between its endpoint.

option d) 2 lines will be described in  the figure

PQ is already a line . Since , a point let say R is 4 unit away from that line , then this will constitute another line which is 4unit away from PQ.

Hence , figure constitute 2 lines.

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Answer:

(1,3)

Hope this helps! :)

Answer:

A and D are true.

Step-by-step explanation:

A function is a relationship that maps elements from one set (the domain, set of the inputs) into elements from another set (the range, set of the outputs), such that each element from the domain can be mapped into only one element from the range.

So, if the inputs are represented in the horizontal axis, and the outputs are represented in the vertical axis, when we draw a vertical line in any given point, this line can not intersect the graph more than once (because that would mean that a given input has two different outputs). This is known as the vertical line test. Note that two different values from the domain can be mapped into the same value in the range.

Also, we define a function as one-to-one if each output is mapped from only one input.

(so here we can not have two different inputs mapped into the same output).

Here we can do a similar test to the one above, this time we should use the horizontal line test to verify if the function is one-to-one or not.

So, here the correct options are:

A and D.

Option B is false.

And for option C, a sequence is a function where the variable is a set of natural numbers, so option C is also false.

Answer:

A and B is correct

Step-by-step explanation:

Answer:

Perimeter = 30

Area = 30

Step-by-step explanation:

[tex](x+8)^2 -x^2 = 12^2[/tex]

[tex]x^2 +16x +64 - x^2 = 144[/tex]

[tex]16x+64=144[/tex]

[tex]16x = 80[/tex]

[tex]x = 5[/tex]

Double check:

[tex]\sqrt{12^2 + 5^2} = (5+8)\\\sqrt{12^2 + 5^2} = 13\\13 = 13[/tex]

Perimeter:

[tex]12+5+13=30[/tex]

Area([tex]\frac{1}{2}bh[/tex]):

[tex]\frac{1}{2}[/tex] × 12 × 5 = 30

According to Pythagorean theorem,

Δ  (Hypotenuse)² = (1st Leg)² + (2nd Leg)²

⇒  (x + 8)² = x² + 12²

⇒  x² + 64 + 16x = x² + 144

⇒  16x = 80

⇒ x = 5

Hypotenuse = (x + 8) = (5 + 8) = 13

1st Leg = 5

2nd Leg = 12

We know that : Perimeter is the Sum of all sides of the Triangle

⇒  Perimeter = Hypotenuse + 1st Leg + 2nd Leg

⇒  Perimeter = 13 + 5 + 12

⇒  Perimeter = 30

We know that :

[tex]\bigstar \ \ \boxed{\sf{\textsf{Area of a Triangle is given by} : \dfrac{1}{2} \times Base \times Height}}[/tex]

Base = 1st Leg

Height = 2nd Leg

[tex]\implies \sf{\textsf{Area of the Triangle} = \dfrac{1}{2} \times 5 \times 12}[/tex]

[tex]\implies \sf{\textsf{Area of the Triangle} = 30}[/tex]

Answer:

4/10 + 5/100=  9/20

Step-by-step explanation:

Answer:

9/20

Step-by-step explanation:

reduce the fraction with 2

4/10+5/100

2/5+5/100

2/5+1/20

write all numerators above the least common denominator 20

8+1/20

8+1=9

9/20

Answer:

C

Step-by-step explanation:

Plug in two different numbers in the x coordinate and see if the y coordinate matches up with the same line.

Answer:

1.  1/2(700 + 20)  

2. 12(50 -20)  

3. There are infinite expressions with fractions and decimals, and even if you dont enclude those its quite a large number

Step-by-step explanation:

Eight faces!!!

In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices.

Hope this helps! :D

Answer:

Replace all the (x) values with the Values "-1, 0, 2" to get your answers

Step-by-step explanation:

        4(-1)+4  (-1) < 0

f(-1)=  4(-1)+4  (-1) > 0

f(-1)= 4x+4 x < 0

f(0)= 4x +8 x>/_ 0

f(2)= 4x +8 x>/_ 0

Answer:

42.4 foot

Step-by-step explanation:

Please check the attached image for a diagram explaining the question

We would use sine to determine the required side

Sin 45 = opposite / hypotenuse

0.7071 = opposite / 60

60 x 0.7071 = 42.4 foot

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

[tex]Distance = \sqrt{89}[/tex]

Step-by-step explanation:

[tex]Let \ (x_1 , y_1) = \ ( 7, 2 ) \ and \ (x_2 , y _2) \ = ( -1 , - 3) \\\\\\Distance = \sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}\\\\[/tex]

               [tex]= \sqrt{(-1 - 7)^2 + ( -3 -2)^2}\\\\=\sqrt{(-8)^2 + ( -5)^2}\\\\=\sqrt{ 6 4 + 25 } \\\\=\sqrt{89}[/tex]

Answer:

[tex]5\sqrt{10}[/tex] when simplified and added this is what i got and when redone too over check i got it again hopefully this helps.

Answer:

22/24

ALL TOGETHER there is 24 donuts.

take half of 24, or 24 divided by 2, and you get 12.

so we know 12 of the donuts are vanilla with sprinkles.

then 2 had strawberry frosting and the rest had chocolate and sprinkles.

we took 12 away so we only have twelve left and if 2 of those 12 are strawberry with no sprinkles and the rest are chocolate WITH sprinkles, this means 10 are chocolate with sprinkles.

so 10 chocolate and sprinkles +12 vanilla and sprinkles=22 donuts with sprinkles out of 24 donuts total

Answer:

22/24

Step-by-step explanation:

Answer:

11:7 or 11/7

Step-by-step explanation:

Since your asking for the ratio 11 goes first as the problom states red apples to green apples and there are 7 green apples so the corect answer is 11:7

Answer:

The answer would be : 7,500 <-- (rounded)

Step-by-step explanation: How i got this answer is, i just multiplied all of the sides together since thats what you do with area's. ( 21 x 21 x 17= 7,497)

Now, the last step is to just round the number off. As we see, the "497" is much more closer to the number "500". So we can just simply round "497" to "500". So your final number for the area would be (7,500) ft.

~hope this helped you out in any way, have a gr8 day/night my friend!~

Answer:

part A: 30,000 is more

Step-by-step explanation:

Answer:

More people ordered processed than produce

Step-by-step explanation:

They are comparing [tex]\frac{1}{5} and \frac{19}{91}[/tex]

First we have to find the least common multiple (lcm)

The lcm is 455

[tex]\frac{1}{5} x \frac{91}{91} = \frac{91}{455}[/tex] (produce)

[tex]\frac{19}{91} x \frac{5}{5} =\frac{95}{455}[/tex] (processed)

[tex]\frac{91}{455} < \frac{95}{455}[/tex]

More people ordered processed than produce.

Answer:

Arc CB is equals to 160

Step-by-step explanation:

Add all of those numbers and subtracted by 360

Answer:

Step-by-step explanation:

Remark

Be very careful that you understand which arc you are asking for. Arc CB could be the arc made up of 53 + 79 + 68 = 200.

Somehow I get the idea that is not what you want. You want the arc that is not divided up so it is

Arc CB = 360 - Sum of the minor arcs

Arc CB = 360 --  200

Arc CB = 160

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

Explanation:

The top and bottom semicircles can be joined to form a full circle. The same can be said about the left and right semicircles. Each circle has diameter 3 and radius 1.5

The area of one circle is

A = pi*r^2

A = 3.14*(1.5)^2

A = 7.065

So two circles doubles to 2*7.065 = 14.13 square meters in area.

Then the last step is to add on the area of the 3 by 3 square (area 3*3 = 9) to get 14.13+9 = 23.13

This area is approximate because pi = 3.14 is approximate. Use more decimal digits in pi to get a more accurate area. However, your teacher wants you to use this specific value so it's best to stick with 23.13

Answer:

23.14

Step-by-step explanation:

The shape is basically two equal-sized circles and a square.

Find the area of the square: 3 x 3 = 9

9 is the area of the square

The formula for finding the area of a circle is pi x radius squared.

3.14 x 1.5 squared = 7.06858

Round to 7.07 and multiply by 2 = 14.14

14.14 (area of both circles) + 9 (area of square) = 23.14

Answer:

4th option

Step-by-step explanation:

Given

B (- 5, 3 ) → B' (2, 1 )

The change in the x- coordinates are - 5 → 2 , that is + 7

The change in the y- coordinates are 3 → 1 that is - 2

Then the translation rule is

(x, y ) → (x + 7, y - 2 )

If translation moves point B (-5,3) to point B’ (2,1).  Then (X+7, y-2) is the image of (x,y) under this translation

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

A translation moves point B (-5,3) to point B’ (2,1).

We need to find the image of  (x,y) under this translation

A graph is translated k units horizontally by moving each point on the graph k units horizontally.

Which means to get B' which translation is used.

B (- 5, 3 ) and  B' (2, 1 )

If we add +7 to x coordinate we will get 2.

When we subtract 2 from B we will get 1

So the translation rule is

(x, y ) → (x + 7, y - 2 )

Hence (X+7, y-2) is the image of (x,y) under this translation

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Answer:

I don't know this answer

Answer:

28.27 inches ^2

Step-by-step explanation:

Answer:

(1, 4)

Step-by-step explanation:

4x + 3y = 16

5x - y = 1

20x + 15y = 80            (Subtract the equations)

20x - 4y = 4

19y = 76

y = 4

Substitute into any of the original equations:

4x + 3(4) = 16

4x + 12 = 16

4x = 2

x = 1

x = 1, y = 4

Answer:

x = 1 and y = 4

Step-by-step explanation:

4x + 3y = 16

5x - y = 1

→ Rearrange the second equation to make y the subject

y = 5x - 1

→ Substitute this into the first equation

4x + 3 ( 5x - 1 ) = 16

→ Expand

4x + 15x - 3 = 16

→ Simplify

19x - 3 = 16

→ Add 3 to both sides

19x = 19

x = 1

→ Substitute this solution into 5x - y = 1

( 5 × 1 ) - y = 1

→ Simplify

5 - y = 1

→ Minus 5 from both sides

-y = -4

→ Multiply both sides by -1

y = 4

Answer:

A = 2000(1.04)^t

Step-by-step explanation:

Using the compound interest formula;

A = P(1+r)^t

P is the principal = $2000

r is the rate = 4% = 0.04

On substituting

A = 2000(1+0.04)^t

A = 2000(1.04)^t

Hence the required expression is A = 2000(1.04)^t

Answer:

No solution

Step-by-step explanation:

15x+5y=20 8-3x

substitute one unknown quantity into the elimination

15x+5(8-3x)=20

solve the equation

nosolution

Answer:

$1,608

Step-by-step explanation:

I think you have to do $70 x 24

Answer:

$1680

Step-by-step explanation:

For 1 ticket price=$70

For 24 ticket price=$70 x 24

=$1680