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3 years ago

7(4 + 3x) = 45(x - 3) - 3(2x -12)

Mathematics

1 answer:

Bezzdna [24]3 years ago

4 0

7(4 + 3x) = 45(x - 3) - 3(2x - 12)

Distribute:

28 + 21x = 45x - 135 - 6x + 36

Collect like terms:

28 + 21x = 39x - 99

Rearrange terms to get them all on one side (add 99 to both sides):

28 + 99 + 21x = 39x - 99 + 99

Simplify:

127 + 21x = 39x

Subtract 21x from both sides:

127 + 21x - 21x = 39x - 21x

Simplify:

127 = 18x

Divide by 18 on both sides to isolate the x variable and solve the expression:

127/18 = 18x/18

Simplify:

x = 127/18

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3 years ago

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

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3 years ago

Segment DE has endpoints at D(2, - 8) and E(-4, 4) . If it is dilated about the origin by a factor of 4, which of the following

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Answer:

answer 2) 24 $\sqrt{5}$

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after the dilation pt D is (8,-32)

after the dilation pt E is (-16,16)

if you use the distance formula for these two points you get $\sqrt{2880}$ which simplifies to 24 $\sqrt{5}$

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3 years ago

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3 years ago

Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probabili

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Answer:

(a) The mean and the standard deviation for the numbers of peas with green pods in the groups of 36 is 27 and 2.6 respectively.

(b) The significantly low values are those which are less than or equal to 21.8. And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is significantly low value.

Step-by-step explanation:

We are given that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods.

Assume that the offspring peas are randomly selected in groups of 36.

The above situation can be represented as a binomial distribution;

where, n = sample of offspring peas = 36

p = probability that a pea has green pods = 0.75

(a) The mean of the binomial distribution is given by the product of sample size (n) and the probability (p), that is;

Mean, $\mu$ = n $\times$ p

= 36 $\times$ 0.75 = 27 peas

So, the mean number of peas with green pods in the groups of 36 is 27.

Similarly, the standard deviation of the binomial distribution is given by the formula;

Standard deviation, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{36 \times 0.75 \times (1-0.75)}$

= $\sqrt{6.75}$ = 2.6 peas

So, the standard deviation for the numbers of peas with green pods in the groups of 36 is 2.6.

(b) Now, the range rule of thumb states that the usual range of values lies within the 2 standard deviations of the mean, that means;

$\mu - 2 \sigma$ = 27 - (2 $\times$ 2.6)

= 27 - 5.2 = 21.8

$\mu + 2 \sigma$ = 27 + (2 $\times$ 2.6)

= 27 + 5.2 = 32.2

This means that the significantly low values are those which are less than or equal to 21.8.

And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is a significantly low value because the value of 15 is less than 21.8 which is represented as a significantly low value.

5 0

3 years ago