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Andrew [12]
3 years ago
10

A sixth grade math student made this conjecture: every prime number can be expressed as the product of two prime numbers. Do you

agree with the conjecture? Why or why not?
Mathematics
1 answer:
iren [92.7K]3 years ago
5 0

Answer:

No, I do not agree with the conjecture because 1 is not a prime number.

Step-by-step explanation:

A prime number is one that can be divided by 1 and itself only. Thus it can be expressed in 2 factors only, 1 and the number itself.

Examples are; 2, 3, 5, 13, 19 , 23 etc.

So, 2 = 1 x 2

      3 = 1 x 3

     23 = 1 x 23

Prime numbers must be expressed as the product of 1 and the number.

The conjecture that every prime number can be expressed as the product of two prime numbers is false. Because 1 is not a prime number, since it has no 2 factors.

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Sara would like to open a bank account. What will she need to do this? Check all that apply.
svet-max [94.6K]
Where are the examples?
4 0
3 years ago
Read 2 more answers
I am offering another 100 points
Ivahew [28]

Answer:

\sf Since \;\sqrt{\boxed{64}}=\boxed{8}\;and\;\sqrt{\boxed{81}}=\boxed{9}\; \textsf{it is known that $\sqrt{75}$ is between}\\\\\sf \boxed{8}\;and\;\boxed{9}\;.

Step-by-step explanation:

<u>Perfect squares</u>: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...

To find \sf \sqrt{75} , identify the perfect squares immediately <u>before</u> and <u>after</u> 75:

  • 64 and 81

\begin{aligned}\sf As\;\; 64 < 75 < 81\; & \implies \sf \sqrt{64} < \sqrt{75} < \sqrt{81}\\&\implies \sf \;\;\;\;\;8 < \sqrt{75} < 9 \end{aligned}

\sf Since \;\sqrt{\boxed{64}}=\boxed{8}\;and\;\sqrt{\boxed{81}}=\boxed{9}\; \textsf{it is known that $\sqrt{75}$ is between}\\\\\sf \boxed{8}\;and\;\boxed{9}\;.

See the attachment for the correct placement of \sf \sqrt{75} on the number line.

6 0
1 year ago
Read 2 more answers
A. Solve for y.<br> B. What is the measure of the missing angles?
Alik [6]
Answer: A.) y = 15 B.) (5y + 3)° = 78° (4y + 8)° = 68° and 34°

Steps:
180° - 146° = 34°

180 = 34 + (5y + 3) + (4y + 8)
180 - 34 = (5y + 3) + (4y + 8)
146 = (5y + 3) + (4y + 8)
146 = 5y + 3 + 4y + 8
146 = 9y + 11
146 - 11 = 9y
135 = 9y
135/ 9 = y
15 = y

(5y + 3)
5(15) + 3
75 + 3
78
(5y + 3) = 78

(4y + 8)
4(15) + 8
60 + 8
68
68 = (4y + 8)

Check:
68 + 78 + 34 = 180
180 = 180 ✅
5 0
2 years ago
PLEASE HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Bond [772]

Answer:

R = \frac {3ST}{2S + T}

Step-by-step explanation:

Given the equation;

\frac {3}{R} - \frac {1}{S} = \frac {2}{T}

Rearranging the equation, we have;

\frac {3}{R} = \frac {2}{T} + \frac {1}{S}

Lowest common multiple (LCM) of S and T is ST.

\frac {3}{R} = \frac {2S + T}{ST}

Cross-multiplying, we have;

3ST = R(2S + T)

Making R, the subject of formula;

R = \frac {3ST}{2S + T}

8 0
3 years ago
Triangle ptg has side lengths of 18 27 cm and 13 cm what type of triangle is it
diamong [38]
Angle PTG = arccos((18^2 + 13^2 - 27^2) / (2 x 18 x 13)) = arccos(-236 / 468) = arccos(-0.5043) = 120 degrees.

The triangle is an obtuse triangle (because one of the angles is greater than 90 degrees) and a scalene triangle (because all the sides are not equal).
6 0
3 years ago
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