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3 years ago

What is

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

6 0

Answer:

Standard form of the equation is:

∴ $3x+y=23$

Step-by-step explanation:

Given equation:

$y-2=-3(x-7)$

To convert the given equation to standard form of equation:

$A(x)+B(y)=c$

Using distribution.

$y-2=(-3x)+(-3\times-7)$

$y-2=-3x+21$

Adding 2 both sides.

$y-2+2=-3x+21+2$

$y=-3x+23$

Adding $3x$ to both sides.

$3x+y=3x-3x+23$

∴ $3x+y=23$

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Simplify completely x^2+4x-45 / x^2+10x+9

S_A_V [24]

Answer: x - 5/x + 1

Step-by-step explanation:

This algebraic fraction

The task to be performed here is factorisation and simplification. Now going by the question,

x² + 4x - 45/x² + 10x + 9, the factorisation of

x² + 4x - 45 = x² + 9x - 5x - 45

= x(x + 9 ) - 5(x + 9 )

= ( x + 9 )(x - 5 ), don't forget this is the algebraic fraction's Numerator

The second part

x² + 10x + 9 = x² + x + 9x + 9

= x(x + 1) + 9( x + 1 )

= ( x + 9 )( x + 1 ), this is the algebraic denominator.

Now place the second expression which is the denominator under the first expression which is the numerator.

( x + 9 )( x - 5 )/( x + 9 )( x + 1 ).

You can see that, ( x + 9 )/( x + 9 ) divide each other , therefore therr then cancelled and left with

x - 5/x + 1

4 0

3 years ago

Birth Weights Babies born after a gestation period of 32-35 weeks have a mean weight of 2600 grams and a standard deviation of 6

lukranit [14]

Answer:

The z-score for the 34-week gestation period baby is 0.61

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score,

μ is the population mean

σ is the population standard deviation.

We are told in the question that:

Babies born after a gestation period of 32-35 weeks have a mean weight of 2600 grams and a standard deviation of 660 grams. Also, we are supposing a 34-week gestation period baby weighs 3000grams

The z-score for the 34-week gestation period baby is calculated as:

z = (x-μ)/σ

x = 3000, μ = 2600 σ = 660

z = 3000 - 2600/660

= 400/660

=0.6060606061

Approximately, ≈ 0.61

6 0

2 years ago

What is the domain of the function y= square root of X plus 4

kumpel [21]

Answer: all real numbers

Step-by-step explanation:

the domain for any function is always, all real numbers or in other words, negative infinity to positive infinity.

5 0

3 years ago

Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do

ivanzaharov [21]

Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter

Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l (1)

Part A.
The area is
A = w*l
= (2 - l)*l
A = 2l - l²
This is a quadratic function or a parabola.

Part B.
Write the parabola in standard form.
A = -[l² - 2l]
= -[ (l -1)² - 1]
= -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.

The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).

Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.

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3 years ago

Is 3.14 a Rational, Whole Number, Integer, or Irrational number?

IrinaVladis [17]

Answer:

the answer is a rational number

7 0

2 years ago

Read 2 more answers