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3 years ago

Tamara says she used the GCF to factor the expression 21x + 56xy as 7(3x + 8xy). Is she correct? Explain.

Mathematics

1 answer:

coldgirl [10]3 years ago

6 0

Answer:

Tamara incorrectly factored the whole expression.

Step-by-step explanation:

Note that

•21x=3·7·x;

•56xy=2·2·2·7·x·y.

Mark in bold all common factors, then GCF(21x,56xy)=7·x=7x.

Thus,

21x+56xy=7x(3+8y).

Hence, Tamara correctly found the GCF of numbers 21 and 56, but incorrectly factored the whole expression.

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a walking path BE in a park intersects intersects two sides of the park at their midpoints. You walk from point D to E, E to B,

bezimeni [28]

Answer:

Total distance covered = 436 yards

Step-by-step explanation:

Walking path BE joins the midpoints B and E of the sides AC and AD.

By midsegment theorem,

"Line joining midpoints of two sides of a triangle is parallel and measure half of the third side"

m(BE) = $\frac{1}{2}[m(CD)]$

CD = 2(BE)

CD = 2(74) = 128 yd

From starting point D,

DE = 107 yd

EB = 74 yd

BC = $\frac{254}{2}$

= 127 yd

CD = 128 yd

Total walking distance = DE + EB + BC + CD

= 107 + 74 + 127 + 128

= 436 yd

Total distance covered = 436 yards

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The answer is to this is 3/4

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If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal

lorasvet [3.4K]

Answer:

The percentage is

$P(x_1 < X < x_2 ) = 51.1 \%$

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Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 800$

The variance is $var(x) = 1600 \ kg$

The range consider is $x_1 = 778 \ kg \ x_2 = 834 \ kg$

The value consider in second question is $x = 900 \ kg$

Generally the standard deviation is mathematically represented as

$\sigma = \sqrt{var (x)}$

substituting value

$\sigma = \sqrt{1600}$

$\sigma = 40$

The percentage of a cucumber give the crop amount between 778 and 834 kg is mathematically represented as

$P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )$

Generally $\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)$

$P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )$

$P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)$

From the z-table the value for $P(z_1 < 0.85) = 0.80234$

and $P(z_1 < -0.55) = 0.29116$

$P(x_1 < X < x_2 ) = 0.80234 - 0.29116$

$P(x_1 < X < x_2 ) = 0.51118$

The percentage is

$P(x_1 < X < x_2 ) = 51.1 \%$

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$P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )$

substituting values

$P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )$

$P(X > x ) = P(Z >2.5 )$

From the z-table the value for $P(Z > 2.5 ) = 0.0062097$

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Alecsey [184]

<h3>Answer: 1/6</h3>

Work Shown:

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x = (1*15)/(6*15)

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