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2 years ago

Need the answer asapp with the working out please thanks :)

Mathematics

1 answer:

patriot [66]2 years ago

7 0

Hi,

The two numbers should be 12 and 30. 12=2x2x3 while 30=2x3x5.

Their HCF is 2x3=6 and their LCM is 2x3x2x5. Because of their HFC, we know that they are both multiple of 6. Also, the question says they both are GREATER than 6, so they can’t be 6 but are 6 times “something”. Thanks to the LCM, we know that “something” is equal to 2 for the first number and to 5 for the second one, the numbers hence being 12 and 30.

I hope this helps. If I was not clear enough or if you’d like further explanation please let me know. Also, English is not my first language, so I’m sorry for any mistakes.

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PLEASE HELP!<br>Calculate $40^{13} \pmod{85}.$

SVEN [57.7K]

In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85

Notice

40*40*40=64,000

so we check how many time does 85 fit into 64,000:

64,000/85=752.94

85*753=64,005; 64000-64,005=-5

this means that

$40^{3} =-5\pmod{85}$

thus

$40^{13} =40^{3*4+1}={(40^{3})}^{4}*40=(-5)^{4}*40 \pmod{85}=\\\\625*40\pmod{85}=(7*85+30)*40\pmod{85}=30*40\pmod{85}\\\\=1200\pmod{85}=(14*85+10)\pmod{85}=10\pmod{85}$

Answer: 10 (mod85)

Remark, the set of all solutions is:

{......-75, 10, 95, .....}, that is 85k +10

7 0

3 years ago

Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hy

vladimir1956 [14]

Answer:

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

In the right triangle XYZ

$cos(Y)=\frac{ZY}{XY}$ ---> adjacent side divided by the hypotenuse

substitute the values

$cos(30\°)=\frac{ZY}{4}$

Remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

substitute

$\frac{\sqrt{3}}{2}=\frac{ZY}{4}$

$ZY=(4)\frac{\sqrt{3}}{2}$

$ZY=2\sqrt{3}\ units$

step 2

$sin(Y)=\frac{XZ}{XY}$ --> opposite side divided by the hypotenuse

substitute the values

$sin(30\°)=\frac{XZ}{4}$

Remember that

$sin(30\°)=\frac{1}{2}$

$\frac{1}{2}=\frac{XZ}{4}$

$XZ=2\ units$

step 3

$tan(Y)=\frac{XZ}{ZY}$ --> opposite side divided by adjacent side

substitute the values

$tan(Y)=\frac{2}{2\sqrt{3}}$

$tan(Y)=\frac{1}{\sqrt{3}}$

Simplify

$tan(Y)=\frac{\sqrt{3}}{3}$

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

7 0

2 years ago

Read 2 more answers

What is the mean of 65.9, 80.8, 60.8, 46.5, and 64.3

vladimir2022 [97]

Answer:

63.66

Step-by-step explanation:

Mean=(65.9+80.8+60.8+46.5+64.3)/5

Mean=63.66

7 0

2 years ago

Choose all the numbers that 810 is divisible by.

Aleks04 [339]

810/2= 405

810/3= 270

810/4= 202.5 (not this one)

810/5= 162

810/6= 135

810/7= 115.71 ( not this one)

810/8= 101.25 (not this one)

810/9= 90

810/10= 81

810/11= 73.63 (not this one)

I hope this helps you!

3 0

3 years ago

How many 2-digit numbers can be formed using only the digits 2, 3, 5 and 6, if the numbers are not repeated within a number?

larisa [96]

(1) Repetition allowed : There are 4 choices for both positions, so 4 × 4 = 16 2-digit numbers can be formed. (2) Repetition not allowed : There are 4 options for tens position, and three options for ones position. Therefore, 4 × 3 = 12 2-digit numbers can be formed.

8 0

2 years ago