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3 years ago

Determine the sum of the following arithmetic series: 3, 10, 17, 24, 498

Mathematics

1 answer:

shepuryov [24]3 years ago

6 0

Answer:

552

Step-by-step explanation:

when the sum of 3+10+17+24+498 is done it becomes 552

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Ricky, Sam, and Timothy cycles from Airy Town to Brightvale which was 9km apart. Ricky cycles at a constant x km/h. Sam cycled a

Semmy [17]

12.15 km /h

Step-by-step explanation:

Step 1 :

Given

Distance between Airy Town to Brightvale = 9 km

Speed of Ricky = x km/h

Step 2:

Speed taken by Sam = x + y km/h

Time taken by Sam = 40 min = 40/60 hrs = 2/3 hrs

so we have (x+y) 2/3 = 9

Step 3:

Speed taken by Timothy = x - y km / h

Time taken by Timothy = 50 min = 50/60 = 5/6 hrs

= > (x-y) 5/6 = 9

Step 4 :

Solving the 2 equations

(x+y) 2/3 = 9 and (x-y) 5/6 = 9 we have

(2/3)x + 2/3(y) = 9 = > 2x + 2 y = 27

5/6(x) - 5/6(y) = 9 = > 5 x - 5 y = 54

Multiplying the first equation by 5 and the second by 2 we have ,

10 x + 10 y = 135 and 10 x - 10y = 108

Adding both,

20 x = 243 => x = 12.15.

This gives speed of Ricky as 12.15 km /h

3 0

3 years ago

Can you please help me

Ket [755]

Answer:

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is $\frac{3}{4}$ ⇒ B

Step-by-step explanation:

In similar rectangles, their corresponding dimensions are proportional, which means $\frac{L_{1} }{L_{2}}$ = $\frac{W_{1} }{W_{2}}$ , where L is the length and W is the width

∵ Rectangle ABCD is similar to rectangle MNOP

∴ Their dimensions are proportional

∵ The dimensions of rectangle ABCD are 6 m, 14 m

∴ L $_{1}$ = 14 and W $_{1}$ = 6

∵ The dimensions of rectangle MNOP are 4.5 m, 10.5 m

∴ L $_{2}$ = 10.5 and W $_{2}$ = 4.5

∵ The rectangle MNOP is the image of rectangle ABCD after dilation

→ To find the scale factor of dilation find the ratio between the

corresponding dimensions in the two rectangles (image/pre-image)

∵ $\frac{L_{2} }{L_{1}}$ = $\frac{10.5}{14}$ = $\frac{3}{4}$

∵ $\frac{W_{2} }{W_{1}}$ = $\frac{4.5}{6}$ = $\frac{3}{4}$

∴ The scale factor for the dilation is $\frac{3}{4}$

The scale factor for the dilation of rectangle ABCD to rectangle MNOP is $\frac{3}{4}$

6 0

3 years ago

3x-5y=-6 -9x-5y=18 whats the answer

Firlakuza [10]

$\left \{ {{3x-5y=-6\ \ | *3} \atop {-9x-5y=18}} \right. \\\\ \left \{ {{9x-15y=-18} \atop {-9x-5y=18}} \right. \\+----\\add\ both\ equations\\\\
-20y=0\ \ \ | divide\ by \ -20\\\\
y=0\\\\
3x-5y=-6\ \ \ \ add\ 5y\\\\
3x=-6+5y\ \ \ | divide\ by\ 3\\\\
x=\frac{-6+5y}{3}=\frac{-6+0}{3}=-2\\\\ x=-2\\ y=0$