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3 years ago

St 2

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

3 0

Answer:

$5.5

Step-by-step explanation:

6 * N (notebook) + 3 * P (pen) = 27

n = 1.5 +P

6 * (1.5 + P) + 3 * P = 27

9 +6p +3p = 27

9p = 18

p (pen): $2

N (notebook): $3.5

combined cost of 1 pen and 1 notebook: $2 + $ 3.5 = $ 5.5

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In the right ΔABC, AN is the altitude to the hypotenuse. Find BN, AN, and AC, if AB=2√5 in and NC= 1 in.

kipiarov [429]

Answer:

$BN=4\ \text{in}$

$AN=2\ \text{in}$

$AC=\sqrt{5}\ \text{in}$

Step-by-step explanation:

Let $BN=x$

$BC=c$

$NC=y=1\ \text{in}$

$AB=a=2\sqrt{5}\ \text{in}$

$AC=b$

We have the relation

$\dfrac{BC}{AB}=\dfrac{AB}{BN}\\\Rightarrow \dfrac{c}{a}=\dfrac{a}{x}\\\Rightarrow c=\dfrac{a^2}{x}\\\Rightarrow x+1=\dfrac{a^2}{x}\\\Rightarrow x^2+x=20\\\Rightarrow x^2+x-20=0\\\Rightarrow x=\frac{-1\pm \sqrt{1^2-4\times 1\times \left(-20\right)}}{2\times 1}\\\Rightarrow x=4,-5$

$\boldsymbol{BN=4\ \text{in}}$

$h=\sqrt{a^2-x^2}\\\Rightarrow h=\sqrt{(2\sqrt{5})^2-4^2}\\\Rightarrow h=2\ \text{in}$

$\boldsymbol{AN=2\ \text{in}}$

$b=\sqrt{h^2+y^2}\\\Rightarrow b=\sqrt{2^2+1^2}\\\Rightarrow b=\sqrt{5}\ \text{in}$

$\boldsymbol{AC=\sqrt{5}\ \text{in}}$

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2 years ago

How do I get this question started

vampirchik [111]

Answer:

you can search up apps that give you answers and there are apps that can help you

Step-by-step explanation:

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2 years ago

Read the above and answer

svetlana [45]

Answer:

Linear Pair:

∠ 1 and ∠ 2

Vertical Angles:

∠ 1 and ∠ 3

Supplementary Angles:

∠ 7 and ∠ 6

Step-by-step explanation:

Linear Pair:

A linear pair of angles is formed when two lines intersect.

Two angles are said to be linear if they are adjacent angles formed by two intersecting lines.

The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Example

∠ 1 and ∠ 2 ∠ 8 and ∠ 5 ,etc

Vertical Angles:

The angles opposite each other when two lines cross.

They are always equal.

Example

∠ 1 and ∠ 3 ∠ 8 and ∠ 6 ,etc

Supplementary Angles:

Two Angles are Supplementary when they add up to 180 degrees.

Examples two angles (140° and 40°)

All Linear pair are Supplementary angles

Example

∠ 7 and ∠ 6 ∠ 8 and ∠ 5 ,etc

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2 years ago

The probability that a student has a Visa card (event V) is .76. The probability that a student has a Master card (event M) is .

Rufina [12.5K]

Answer:

The Probability of both happening is <u>0.304</u>.

Step-by-step explanation:

P(A) × P(B)

= 0.76 × 0.4

= <u>0.304</u>

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1 year ago

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

iren [92.7K]

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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