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3 years ago

Factorize 5z squared +3z

Mathematics

1 answer:

loris [4]3 years ago

5 0

Answer:

Step-by-step explanation:

Given ,

5z² + 3z

We need to factorize above expression:

So , Let f(z) = 5z² + 3z

Taking out z, we get

or f(z) = z(5z + 3) , This is the factorize form

if we plug f(z) =0

i.e z(5z + 3) = 0

z = 0 , 5z+ 3 = 0

or z = 0, z = -3/5

Hence z =0 and z= -3/5 are the roots of f(z).

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Brainliest will be given to the correct answer!

IrinaK [193]

Answer:

A) The height of the trapezoid is 6.5 centimeters.

B) We used an algebraic approach to to solve the formula for $b_{1}$ . $b_{1} = \frac{2\cdot A}{h}-b_{2}$

C) The length of the other base of the trapezoid is 20 centimeters.

D) We can find their lengths as both have the same length and number of variable is reduced to one, from $b_{1}$ and $b_{2}$ to $b$ . $b = \frac{A}{h}$

Step-by-step explanation:

A) The formula for the area of a trapezoid is:

$A = \frac{1}{2}\cdot h \cdot (b_{1}+b_{2})$ (Eq. 1)

Where:

$h$ - Height of the trapezoid, measured in centimeters.

$b_{1}$ , $b_{2}$ - Lengths fo the bases, measured in centimeters.

$A$ - Area of the trapezoid, measured in square centimeters.

We proceed to clear the height of the trapezoid:

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})$ Definition of division.

3) $2\cdot A\cdot (b_{1}+b_{2})^{-1} = (2\cdot 2^{-1})\cdot h\cdot [(b_{1}+b_{2})\cdot (b_{1}+b_{2})^{-1}]$ Compatibility with multiplication/Commutative and associative properties.

4) $h = \frac{2\cdot A}{b_{1}+b_{2}}$ Existence of multiplicative inverse/Modulative property/Definition of division/Result

If we know that $A = 91\,cm^{2}$ , $b_{1} = 16\,cm$ and $b_{2} = 12\,cm$ , then height of the trapezoid is:

$h = \frac{2\cdot (91\,cm^{2})}{16\,cm+12\,cm}$

$h = 6.5\,cm$

The height of the trapezoid is 6.5 centimeters.

B) We should follow this procedure to solve the formula for $b_{1}$ :

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $A = 2^{-1}\cdot h \cdot (b_{1}+b_{2})$ Definition of division.

3) $2\cdot A \cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot (b_{1}+b_{2})$ Compatibility with multiplication/Commutative and associative properties.

4) $2\cdot A \cdot h^{-1} = b_{1}+b_{2}$ Existence of multiplicative inverse/Modulative property

5) $\frac{2\cdot A}{h} +(-b_{2}) = [b_{2}+(-b_{2})] +b_{1}$ Definition of division/Compatibility with addition/Commutative and associative properties

6) $b_{1} = \frac{2\cdot A}{h}-b_{2}$ Existence of additive inverse/Definition of subtraction/Modulative property/Result.

We used an algebraic approach to to solve the formula for $b_{1}$ .

C) We can use the result found in B) to determine the length of the remaining base of the trapezoid: ( $A= 215\,cm^{2}$ , $h = 8.6\,cm$ and $b_{2} = 30\,cm$ )

$b_{1} = \frac{2\cdot (215\,cm^{2})}{8.6\,cm} - 30\,cm$

$b_{1} = 20\,cm$

The length of the other base of the trapezoid is 20 centimeters.

D) Yes, we can find their lengths as both have the same length and number of variable is reduced to one, from $b_{1}$ and $b_{2}$ to $b$ . Now we present the procedure to clear $b$ below:

1) $A = \frac{1}{2} \cdot h \cdot (b_{1}+b_{2})$ Given.

2) $b_{1} = b_{2}$ Given.

3) $A = \frac{1}{2}\cdot h \cdot (2\cdot b)$ 2) in 1)

4) $A = 2^{-1}\cdot h\cdot (2\cdot b)$ Definition of division.

5) $A\cdot h^{-1} = (2\cdot 2^{-1})\cdot (h\cdot h^{-1})\cdot b$ Commutative and associative properties/Compatibility with multiplication.

6) $b = A \cdot h^{-1}$ Existence of multiplicative inverse/Modulative property.

7) $b = \frac{A}{h}$ Definition of division/Result.

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4 years ago

I don’t get this may someone help me

aksik [14]

First count the fully shaded boxes than count each half knowing two halfs equal one

1)32
2)22
3)22
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3 years ago

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A landscaper charges you $102 to plant 8 bushes in front of your office building. If you decide to put 12 much of the same bushe

Korolek [52]

$102/8=$12.75 per bush
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3 years ago

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gtnhenbr [62]

Answer:

See Below

Step-by-step explanation:

Lets look at our numbers:

The balloon is at 1000 feet.

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How long will it take to get to 215ft, in seconds, s.

Lets see, if you were to subtract 1000-215, you will get 785.

The balloon needs to drop 785ft to get to 215ft above the ground.

The question asks how long will it take to get below 215ft.

Lets do the math for the descending feet. We calculated that it takes 785ft to hit 215ft above the ground, so, you need to divide 785ft by 4 1/2 to see how many seconds it takes. The answer for this is 174.4, we can make this 174 4/9.

**VERY IMPORTANT** If you use 174 4/9, this equals 215 seconds, it asks for below this, so you can use ANY number for this that it above this number.

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3x+4y=2 4x-4y=12 by using elimination

Sidana [21]

(+3x+4y=2)
(+4x-4y=12)
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4 years ago