simplify 7y + 2x + 3x + 2y

9514 1404 393

Answer:

  A. d = ∑[k=1,n] (4.5+0.5k)

  B. 9

Step-by-step explanation:

A) The series has first term 5 and common difference 0.5. The general term is given by ...

  an = a1 +d(n -1)

  an = 5 + 0.5(n -1) . . . . substitute numbers for this series

  an = 4.5 +0.5n . . . . . . simplify

The sum is the sum of these terms:

  [tex]\displaystyle \boxed{d_n=\sum_{k=1}^n(4.5+0.5k)}[/tex]

__

B) The sum of terms of an arithmetic series is the average of the first and last, multiplied by the number of terms. We want to solve for n to make the sum greater than 60.

  [tex]\displaystyle d_n=\frac{n}{2}(5 +4.5 +0.5n)\\\\\dfrac{n}{2}(9.5+0.5n)>60\\\\n(19+n)>240\qquad\text{multiply by 4}\\\\n^2+19n+9.5^2>240+9.5^2\qquad\text{complete the square}\\\\n+9.5>\sqrt{330.25}\qquad\text{square root}\\\\n>18.17-9.5=8.67\qquad\text{positive root, subtract 9.5}[/tex]

Melissa's total distance will first exceed 60 miles the 9th time she trains.

Answer:

 A. d = ∑[k=1,n] (4.5+0.5k)

 B. 9

Step-by-step explanation:

A) The series has first term 5 and common difference 0.5. The general term is given by ...

 an = a1 +d(n -1)

 an = 5 + 0.5(n -1) . . . . substitute numbers for this series

 an = 4.5 +0.5n . . . . . . simplify

Answer:

Step-by-step explanation:

m∠ 1  =  180 - 117

m∠ 1  = 63

m∠2 = the same as m∠ 1

m∠2 = 63

m∠3 is also the same b/c of the same length of the "legs" of the triangle

m∠3 = 63

Answer:

3.33

Step-by-step explanation:

each cube represents 1, so each flat represents 0.1 and each unit represents 0.01. so if there are 3 of each, it would be 3+0.3+0.03 which equals 3.33

Answer:

3.33

Step-by-step explanation:

Each cube in this picture is equal to 1 unit as the diagram in the upper right corner shows.

We have 3 cubes so -> 1 + 1 + 1 = 3

We also have 3 squares that are 1/10th of a cube.

1/10 * 1 = 0.1  so each square is equal to 0.1 unit.

We have 3 squares so it would be 0.1 + 0.1 + 0.1 = 0.3

We have 3 tiny squares that are 1/100th of a cube.

1/100 * 1 = 0.01 so each tiny square is equal to 0.01 unit.

We have 3 tiny squares so it would be 0.01 + 0.01 + 0.01 = 0.03

Add everything up: 3 + 0.3 + 0.03 = 3.33

Answer:

the answer is option (A) . (-4) + 8

[tex] - \frac{4 {m}^{2} }{1 + {m}^{4} + {m}^{8} } [/tex]

is your answer

Answer:

jshdgdhdhdhdhdhdhd English project work

Answer:

0

Step-by-step explanation:

The 2 lines never intersect so there are 0 solutions

Answer:

The distance between the two points is 6.3 units

Step-by-step explanation:

Here, we want to find the distance between the two points

We have the equation to find this as follows;

D = √((x2-x1)^2 + (y2-y1)^2

where (x1,y1) = (-4,2) and (x2,y2) = ((2,4)

so we have the length calculated as follows;

D = √(2-(-4))^2 + (4-2)^2

D = √6^2 + 2^2

D = √36 + 4

D = √40

D = 6.3 units

Answer:

25

Step-by-step explanation:

50-25=25

Answer:

6 and 9

Step-by-step explanation:

6 x 9 = 54

Answer:

The answer would be 14 units.  

Step-by-step explanation:

Count each of the units to find the height and base.

Height - 4 units

Base - 7 units.

Then use the formula A = 1/2*h*b

A = 1/2*7*4

A = 1/2*28

A = 14 units.

The area of the given triangle is 14 units².

Use the concept of the triangle defined as:

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

And area of triangle = (1/2)x base x height

In the given triangle:

Width  = 5 units + 2 units

Width  = 7 units

Height = 2 units + 2 units

Height = 4 units

Put the values into the above formula of area,

Area of triangle = (1/2)x 7 x 4

Area of triangle = 14 unit²

Hence,

The area of the given triangle is 14 units².

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ6

Answer:

Step-by-step explanation:

Answer:

i think its 18(DONT TRUST ME)

Step-by-step explanatioN:

6 x 3                

Answer:

45

Step-by-step explanation:

Since the lines of hypotenuse are parallel,the triangles are similar

20/8 = x/18

cross multiplication

8x = 20x18

8x=360

x=45      

Answer:

20 + 0.10t

Step-by-step explanation:

The 20 is the flat rate, the .10 is the per minuet rate meaning the answer is 20 + 0.10t. plz 5 str and thx, and brailiest.

28ft

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whats the question....?

Answer:

First of all, is it the ratio cats to dogs or dogs to cats?

Step-by-step explanation:

?????

Answer:

y=-2(x+8)²-7

Step-by-step explanation:

Given: y=-2x²+5

After transformations: y=-2(x+8)²-7

Vertex would be (h,k) -> (-8,-7) instead of (0,5)

Answer:

Surface area of cylinder = 50.26 unit² (Approx.)

Step-by-step explanation:

Given:

Radius of base r = 2 units

Width of lateral rectangle = 4 units

Length of lateral rectangle = 6.28 units

Find:

Surface area of cylinder

Computation:

Surface area of cylinder = 2[Area of base] + Area of lateral rectangle

Surface area of cylinder = 2[πr²] + [l][b]

Surface area of cylinder = 2[(22/7)(2)²] + [6.28][4]

Surface area of cylinder = 2[(22/7)(4)] + 25.12

Surface area of cylinder = 25.14 + 25.12

Surface area of cylinder = 50.26

Surface area of cylinder = 50.26 unit² (Approx.)

Consider we need to find f(n).

Given:

Achilles ordered a pizza with 16 slices.

Every hour, he ate half of the remaining slices.

To find:

The function f(n) that is the number of slices Achilles ate in the hour since he got home.

Solution:

Initial number of slices = 16

Every hour, he ate half of the remaining slices. So, the number slices Achilles ate in the hour since he got home are:

8, 4, 2, 1, ...

It is a geometric sequence with first term 8 and common ratio [tex]\dfrac{1}{2}[/tex].

The explicit formula for a geometric sequence is:

[tex]f(n)=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Substituting [tex]a=8,r=\dfrac{1}{2}[/tex], we get

[tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex]

Therefore, the  function f(n) that is the number of slices Achilles ate in the hour since he got home is [tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex].

Answer:

True, since 1 is 1/1, which is 100%

Hope that helps! :)

Step-by-step explanation:

Answer:

The length of the base of the rectangle is 7 inches

Step-by-step explanation:

The Area of the rectangle can be found out by multiplying length with the breadth

Area= length *  breadth

35 squared inches= x *5

5x= 35

x= 35/5

x= 7inches

Hence the length of the base of the rectangle is 7 inches.

If the area and one side are known then we can simply find the 2nd side by simply substituting x in its place and solving the equation.

Answer:

O The numerical value of the circumference is less than the numerical value of the area.

Step-by-step explanation:

as pi>2, therefore, only 'the numerical value of the circumference is greater than the numerical value of the area. The numerical value of the circumference is less than the numerical value of the area' is correct.

Answer:

[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

Step-by-step explanation:

Since the required hyperbola has its vertex at (5,0), its transverse axis is on the x-axis and center at (0,0).

So, we use the equation in standard form

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex]

Also, since the path of the space probe gets closer to y = -x, this is the asymptote to the hyperbola.

Our standard asymptote equation is y = ±bx/a taking the negative sign and comparing with y = -x,

-bx/a = -x ⇒ b/a = 1 ⇒ a = b

Also, the coordinate of the vertex (c, 0) = (5, 0) and c² = a² + b²

substituting c = 5 and a = b into the equation, we have

c² = a² + b²

5² = a² + a²

25 = 2a²

a² = 25/2

a = √(25/2)

a = ±5/√2

rationalizing, we have

a = ±5/√2 × √2/√2

a = ±5√2/2

Since a = b, b = ±5√2/2

Inserting a and b into the equation for the hyperbola, we have

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\\\frac{x^{2} }{(\frac{5\sqrt{2} }{2} )^{2} } + \frac{y^{2} }{\frac{5\sqrt{2} }{2} ^{2} } = 1\\\frac{x^{2} }{\frac{25 X 2 }{4} } + \frac{y^{2} }{\frac{25X2 }{4} } = 1\\\frac{x^{2} }{\frac{25}{2} } + \frac{y^{2} }{\frac{25}{2} } = 1\\\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

So, the required equation is

[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

Answer:

Both volumes are the same

Step-by-step explanation:

Volume of cylinder = [tex]\pi[/tex][tex]r^{2} h[/tex]

r = radius

h = height

Since area of the circle is given on top,

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

We know the area is 12

12 = [tex]\pi[/tex][tex]r^{2}[/tex] (we need to find r)

r = [tex]\sqrt{\frac{12}{\pi} }[/tex]

r = 1.954

Now we can find the cylinder's volume:

Volume of cylinder = [tex]\pi[/tex][tex](1.954)^{2}[/tex] (6)

Volume of cylinder = 72

To find the volume of the cuboid, we use

Volume of cuboid = lwh

l = length

w = width

h = height

Volume of cuboid = 6 x 4 x 3

Volume of cuboid =  72

This proves that both the volumes are the same.

Divide total price by number of cookies:

1.92/12 = 0.16

Each cookie cost $0.16

Answer:

Step-by-step explanation:

16 cents each cookie :3

Answer:

8.62

Step-by-step explanation:

Use the Pythagorean theorem.

b= [tex]\sqrt{c^{2}-a^{2} }[/tex]

b=[tex]\sqrt{10.5^{2}-6^{2} }[/tex]

b= [tex]\sqrt{110.25-36[/tex]

b=[tex]\sqrt{74.25}[/tex]

b= 8.62

Answer:

5

Step-by-step explanation:

divide the figure as a triangle and a rectangle first.

take away the rectangle part and if you just look at the triangle part,

you can get x using Pythagorean theorem.

Pythagorean theorem is a^2 + b^2 = c^2,

so 3^2 + 4^2 = x^2.

If you calculate it, x should be root 25, which equals 5.

So, the answer is 5.

Answer:

343

Step-by-step explanation:

[tex]\frac{(7^4)^2}{7^5}[/tex]

[tex]=\frac{7^4^*^2}{7^5}[/tex]

[tex]=\frac{7^8}{7^5}[/tex]

[tex]=7^8^-^5[/tex]

[tex]=7^3[/tex]

[tex]=7*7*7[/tex]

[tex]=343[/tex]