Order the following in ascending order. ​

Answer:

large = 12

medium = 18

Step-by-step explanation:

L + M = 30 => L = 30-M

4L+3M =102

substitute : L with M

=> 4(30-M)+3M =102

120-4M+3M = 102

- M = 102-120

-M = -18

=========> M = 18, L = 12

Given:

[tex]a_n[/tex] is an arithmetic sequence.

To find:

The value of [tex]\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}[/tex].

Solution:

We have,

[tex]\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}[/tex]

It can be written as:

[tex]=\dfrac{d}{d}\left[\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\right][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{d}{a_1a_2}+\dfrac{d}{a_2a_3}+...+\dfrac{d}{a_{39}a_{40}}\right][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{a_2-a_1}{a_1a_2}+\dfrac{a_3-a_2}{a_2a_3}+...+\dfrac{a_{40}-a_{39}}{a_{39}a_{40}}\right][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_2}+\dfrac{1}{a_2}-\dfrac{1}{a_3}+....+\dfrac{1}{a_{39}}-\dfrac{1}{a_{40}}\right][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_{40}}\right][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{a_{40}-a_1}{a_1a_{40}}\right][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{a_1+(40-1)d-a_1}{a_1a_{40}}\right][/tex]       [tex][\because a_n=a_1+(n-1)d][/tex]

[tex]=\dfrac{1}{d}\left[\dfrac{39d}{a_1a_{40}}\right][/tex]

[tex]=\dfrac{39}{a_1a_{40}}[/tex]

Therefore, the value of given expression is [tex]\dfrac{39}{a_1a_{40}}[/tex].

Answer: D) f(z) = 7 to the power of 2.

Answer:

A(an)   altitude    of a prism is a perpendicular segment that joins the planes of the bases. (The height h is the length of one.)

Step-by-step explanation:

AN ALTITUDE -  An altitude of a triangle is a line segment that passes through a vertex and is perpendicular to (i.e. forms a right angle with) the base line (the side opposite the vertex). The expanded base of the altitude is the line that contains the opposing side. The foot of the altitude is the point where the extended base meets the altitude. The area of a triangle can be calculated using altitudes: one half of the product of an altitude's length and its base's length equals the triangle's area. As a result, the longest altitude is perpendicular to the triangle's shortest side. Through trigonometric functions, the heights are also connected to the triangle's sides.

Hence , the answer is an altitude .

Answer:

The surface area increases at 12/7 square inches per minute

Step-by-step explanation:

Given

[tex]l = 7[/tex] --- side length

[tex]\frac{dV}{dt} = 3in^3/min[/tex] --- Rate at which volume increases

Required

The rate at [tex]which[/tex] the [tex]surface[/tex] area [tex]increases[/tex]

The volume of a cube is:

[tex]V = l^3[/tex]

Differentiate with respect to time

[tex]\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}[/tex]

When [tex]l = 7[/tex] and [tex]\frac{dV}{dt} = 3in^3/min[/tex]

The expression becomes:

[tex]3 = 3 * 7^2 \cdot \frac{dl}{dt}[/tex]

Divide both sides by 3

[tex]1 = 7^2 \cdot \frac{dl}{dt}[/tex]

[tex]1 = 49 \cdot \frac{dl}{dt}[/tex]

Divide both sides by 49

[tex]\frac{dl}{dt} = \frac{1}{49}[/tex]

The surface area is calculated as:

[tex]A= 6l^2[/tex]

Differentiate with respect to time

[tex]\frac{dA}{dt} = 12l\frac{dl}{dt}[/tex]

Substitute: [tex]\frac{dl}{dt} = \frac{1}{49}[/tex] and [tex]l = 7[/tex]

[tex]\frac{dA}{dt} = 12 * 7 *\frac{1}{49}[/tex]

[tex]\frac{dA}{dt} = 12 *\frac{1}{7}[/tex]

[tex]\frac{dA}{dt} = \frac{12}{7}[/tex]

The surface area increases at 12/7 square inches per minute

Answer:

g= 1

Step-by-step explanation:

-3+5+6g=11-3g

-3+5=11-9g

-3-11+5=-9g

-9=-9g

1=g

you want to first isolate the variables on one side. from there you calculate all the real numbers together. then you divide the number being multiplied with teh variable by the number that was calculated on the other side.

Once you have a singluar amount of the variable, you know you have your answer.

Answer:

D. He should survey all the students in all the history classes to make sure he collects enough data.

Step-by-step explanation:

correct on edge 2021

Answer:

x=19

Step-by-step explanation:

okay so all those angles there are pretty simple. because of the vertical angles theorem, the angles that go across from each other are equal to each other. On a thing like this those intersections are congruent. So knowing this we can assume that (6x+4)=118. so if you solve the basic algebra for that (you can use mathpapa or smt if you really need the work for that) then it comes out as x=19 which you can check.

6x+4=118

subtract 4 from both sides

6x=114

divide by 6 on both sides

x=19

Hope this helps!

Answer:

Problem 1:

Width of the larger version = 2.99 in.

Problem 2:

Friday = 5⅞ miles

Step-by-step explanation:

Problem 1:

Since the cell-phones are similar in shape and the width and length of both are proportional, therefore:

Width of the bigger phone/Width of the smaller phone = length of the bigger phone/length of the smaller phone

Width of smaller phone = 2.6 in.

Length of smaller phone = 5.4 in.

Width of bigger phone = x = ? in.

Length of bigger phone = 6.21 in.

Therefore:

6.21/5.4 = x/2.6

Cross multiply

5.4 × x = 2.6 × 6.21

5.4x = 16.146

Divide both sides by 5.4

x = 16.146/5.4

x = 2.99

Width of the larger version = 2.99 in.

Problem 2:

Jen's goal for the 5 days = 22 miles

The number of miles she ran Mon to Thursday was given.

To meet her goal, let's find the number of miles she has to run to meet her goal.

Thus:

Number of miles to run on Friday = 22 - (4¾ + 5⅛ + 0 + 6¼)

Change to improper fraction

= 22 - (19/4 + 41/8 + 0 + 25/4)

= 22 - ((38 + 41 + 0 + 50)/8)

= 22 - 129/8

= (176 - 129)/8

= 47/8

= 5⅞ miles

Step-by-step explanation:

[tex]volume =\pi {r}^{2}h[/tex]

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

remember

[tex]\pi = 22 \div 7[/tex]

So, we will just place the area and equate it to the unknown volume including the height

1004.80 = 22/7 × 10× 10 × h

1004.80 = 314.26h

h = 3.197

Answer: The Answer Is 54 ft2

Answer:

54

Step-by-step explanation:

A=1/2(b)(h)

Answer:

allen= y=3/2+2  billy= y= 3/2+4

Step-by-step explanation:

ok both of the equation are (almost) the same except for the y intercepts.

y=mx+b... you are learning about that hopefully!

so. each of their trees are growing by 3... feet I'll just say feet. that means the slope is three because they are each going up that much. you also have to pay attention to the fact that the year is going up by two, so your tree is actually growing by 1.5 (3 halves) feet each year. now you have to find the y intercept by back tracking. remember that the y intercept is where y is zero and x is whatever it is.

if you go back three on allen, the y intercept is 2 and if you go back on billy, the y intercept is 4.

as for the second question, the lines are parallel. they have the exact same slope so that means that they will never cross  because billy's line is higher then allens, billy's tree will always be higher

Answer:

_7 + 3 = 3 + 7 : commutative property,[if something is added or subtracted]

0 +5 _ = 5 is it: identity property.[if 0 is added or subtracted]

2 + (6 + 8) =(2 + 6)+ _8 associated property

[if added or multiplied]

Answer:

C   19.2

Step-by-step explanation:

Corresponding parts have the same proportion

x/24 = 20.8/26

multiply both sides by 24

x = 20.8/26 * 24

x = 19.2

Answer:

C

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{AC}{DF}[/tex] = [tex]\frac{AB}{DE}[/tex] , substitute values

[tex]\frac{x}{24}[/tex] = [tex]\frac{20.8}{26}[/tex] ( cross- multiply )

26x = 499.2 ( divide both sides by 26 )

x = 19.2 → C

Answer:

The formula for the volume of a triangular prism is:

V=(l)(w)(h)

Where l is the length of the triangle, w is the width of the triangle, and h is the height of the prism

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm.

Please mark as brainliest if answer is right

Have a great day, be safe and healthy  

Thank u  

XD  

Answer:

The stone will hit the water after 3 seconds

Step-by-step explanation:

Given

[tex]y = -5x^2 + 10x +15[/tex]

Required

At what time will the stone enter the water

When the stone enters the water;

[tex]y = 0[/tex]

So, we have:

[tex]-5x^2 + 10x +15 = 0[/tex]

Divide through by -5

[tex]x^2 -2x -3 = 0[/tex]

Expand

[tex]x^2 +x -3x -3 = 0[/tex]

Factorize

[tex]x(x +1) -3(x +1) = 0[/tex]

Factor out x + 1

[tex](x -3) (x +1) = 0[/tex]

Solve for x

[tex]x - 3 = 0\ or\ x + 1 = 0[/tex]

[tex]x = 3\ or\ x = -1[/tex]

x (time) cannot be negative.

So:

[tex]x = 3[/tex]

Answer:

5-x

Step-by-step explanation:

you will simplify the eq. it will be (x+8)-(x+8)(x-4)

taking (x+8) as common(1-x+4)

(x+8)(5-x)

Answer:

3

Step-by-step explanation:

Answer:

r = 0

1.

    25-6r=25

                          −6r+25=25

2.    

        − 6r+25 = 25

                                    − 6