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3 years ago

Evaluate each expression. Name the property used in each step.

Mathematics

1 answer:

IRINA_888 [86]3 years ago

4 0

1. (1 / 5)5 * 14 = 14 because 1/5 multplied by 5 is equal to 1. I believe this is called reciprocals.

2. 6 + 4 (19 - 5) = 6 + 4(19) - 4(5) = 6 + 76 - 20 = 62. This is called the distributive property.

3. 5 (14 - 5) + 6 (3 + 7) = 5(14) - 5(5) + 6(3) + 6(7) = 70 - 25 + 18 + 42 = 105. We also used the distributive property in this question.

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Descried how to derive the quadratic formula from a quadratic equation in standard form

Aleks [24]

Answer:

The standard form of a quadratic equation is:

$ax^2+bx+c=0$ , $a\neq 0$

Quadratic Formula Derivation:

$ax^2+bx+c=0\\$

$x^2+\frac{b}{a}x+\frac{c}{a} =0$

$x^2+\frac{b}{a}x = -\frac{c}{a}$

Completing the Square:

$x^2+\frac{b}{a}x +\frac{b^2}{4a^2} = \frac{b^2}{4a^2}-\frac{c}{a}$

$( x+\frac{b}{2a} )^2 = \frac{b^2-4ac}{4a^2}$

Square Root property:

$x+\frac{b}{2a} = \pm \sqrt{ \frac{b^2-4ac}{4a^2}}$

$x = -\frac{b}{2a} \pm { \frac{\sqrt {b^2-4ac}}{2a}}$

$x = \frac{-b\pm\sqrt{b^2-4ac}} {2a} }$

8 0

2 years ago

Please me in math<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%20%2B%201%7D%7Ba%20-%201%7D%20%20%2B%20%20%5Cfrac%7B%20%7B

PIT_PIT [208]

Step-by-step explanation:

hope this helps you thank you

5 0

2 years ago

Read 2 more answers

What is the following number in decimal form?

aleksley [76]

8.8 because you need to multiply 1.68 by 10 which is 16.8-8=8.8

6 0

2 years ago

What is the area of triangle DEF

kolezko [41]

Answer:

76.5 cm²

Step-by-step explanation:

Given the triangles are similar , then

ratio of sides = a : b , so

ratio of areas = a² : b²

Here ratio of sides = 9 : 13.5 = 2 : 3

ratio of areas = 2² : 3² = 4 : 9

let x be the area of Δ DEF and using proportion

$\frac{4}{34}$ = $\frac{9}{x}$ ( cross- multiply )

4x = 306 ( divide both sides by 4 )

x = 76.5

The area of Δ DEF = 76.5 cm²

3 0

2 years ago

Suppose that 95% of the fasteners pass the initial inspection. Of those that fail the initial inspection, 20% are defective. Of

hichkok12 [17]

Answer

Step-by-step explanation:

Let x be the fasteners

95% of x passed, and 5% of x failed

20% of the 5% which failed are defective, remaining the 80% of the failed 5%.

Now 40% of this 80% of the 5% which failed are scrapped, meaning only the remaining 60% passed second inspection.

Thus

a). The proportion ;

60% of 80% of 5% of x

mathematically

= 60/100 × 80/100 × 5/100

= 0.024 or 2.4%

b) initially 95% passed and later on 2.4% pass again. Therefore total that passed = 95%+2.4%=97.4%

c) probability that it passed on first inspection is 95/100

Percentage that went through recrimping = 80% of 5% = 80/100 × 5/100 = 1/25 or 0.04 or 4%

Thus probability of passing and not going through recrimping

= 1 - (1/25) = 0.96 or 96%

7 0

2 years ago