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3 years ago

Prove that for any arithmetic sequence a7+a10=a8+a9

Mathematics

1 answer:

vodka [1.7K]3 years ago

5 0

Answer: a3+a6=a4+a5

Step-by-step explanation: since both of those sides there = a17, you can do the same for any other number.

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Find the lateral area for the prism. L.A. =<br> Find the total area for the prism. T.A. =

Ksivusya [100]

The lateral area of the prism is given by:
LA=[area of the two triangles]+[area of the lateral rectangles]
hypotenuse of the triangle will be given by Pythagorean:
c^2=a^2+b^2
c^2=6^2+4^2
c^2=52
c=sqrt52
c=7.211'
thus the lateral area will be:
L.A=2[1/2*4*6]+[6*8]+[8*7.211]
L.A=24+48+57.69
L.A=129.69 in^2

The total are will be given by:
T.A=L.A+base area
base area=length*width
=4*8
=32 in^2
thus;
T.A=32+129.69
T.A=161.69 in^2

6 0

4 years ago

Read 2 more answers

Does anyone know What is x+7=-7x-8

rjkz [21]

Answer:

$x=-\frac{15}{8}$

Step-by-step explanation:

$x+7=-7x-8$

Add 7x to both sides:

$8x+7=-8$

Subtract 7 from both sides:

$8x=-15$

Divide both sides by 8:

$x=-\frac{15}{8}$

3 0

4 years ago

If the volume of a cube is increased by a factor of 10 (so that the new volume is 10 times the size of the original volume), by

Alexeev081 [22]

Answer:

surface area of cube $10^{\frac{2}{3} }$ time

Step-by-step explanation:

given data

new volume = 10 time original volume

to find out

what factor surface area change

solution

we consider here side of cube is a

and volume is V

we consider here a is 2

then volume will be v1 = a³ = 2³ = 8

and surface area = 6a² = 6(2)² = 24 ..........1

so if volume increase 10 time

than

V = 10 × v1

a³ = 10 × 8

a³= 80

a = 2 × ∛10

and

surface area increase here

surface area = 6a²

surface area = 6( 2 × ∛10 )²

surface area = 24 × $10^{\frac{2}{3} }$ ............2

so from equation 1 and 2

surface area / surface area = 24 × $10^{\frac{2}{3} }$ / 24

surface area = $10^{\frac{2}{3} }$

so here surface area of cube will be $10^{\frac{2}{3} }$ time

5 0

4 years ago

Mathematics pls solve i need to check my answers bcs my teacher is sucky

Lilit [14]

If H is the circumcenter, then each of EH, FH, and GH are perpendicular bisectors of the legs BC, CD, and DB, respectively. So, for instance, EH cuts BC in half so that BE and EC have the same length.

Also, BH, CH, and DH are radii to the circumcircle of the triangle, so they all have the same length.

(1) CD = CF + FD = 2 • FD = 2 • 32 = 64

(2) CE = BE = 26

(3) HD = HC = 33

(4) GD = 1/2 • BD = 1/2 • 58 = 29

(5) By the Pythagorean theorem,

HG² + GD² = HD²

HG = √(33² - 29²) = 2 √(62)

(6) Similar to (5); by the Pythagorean theorem,

HF² + FD² = HD²

HF = √(33² - 32²) = √(65)

5 0

3 years ago

A section in a stained glass window is shaped like a trapezoid. The top base is 1 centimeter and the bottom base is 3.5 centimet

LUCKY_DIMON [66]

I don't know if it's right but this is what I did. the rounding might be a little different.

$(1 + 3.5) \div 2 \times x = 8.1$
$4.5 \div 2 = 2.3$
$2.3x = 8.1$
$8.1 \div 2.3 = 3.5$
x=3.5 cm.

5 0

4 years ago