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3 years ago

If DE=4x+10, EF =2x-1, and DF=9x-15, find DF

Mathematics

2 answers:

Ket [755]3 years ago

8 0

Answer:

$DF=201$

Step-by-step explanation:

We have been given that segment $DE=4x+10$ , segment $EF=2x-1$ and $DF=9x-15$

From the given information, we can set an equation as:

$DF=DE+EF$

$9x-15=4x+10+2x-1$

Combine like terms:

$9x-15=6x+9$

$9x-15+15=6x+9+15$

$9x=6x+24$

$9x-6x=6x-6x+24$

$3x=24$

$\frac{3x}{3}=\frac{24}{3}$

$x=24$

$DF=9x-15$

$DF=9(24)-15$

$DF=216-15$

$DF=201$

Therefore, DF equals 201 units.

svetoff [14.1K]3 years ago

7 0

Answer:

Step-by-step explanation:

If DE = 4x+10,EF =2X -1, and DF= 9x - 15 find DF

(de + ef ) - df = 2e || 2e/2 = e || ed - e = d || ef - e = f || f + d = df

de + ef = 6x + 11 || (6x +11) - df = -3x -6 || 2e/2 = -3x/2 - 3 || (-3x/2 - 3) - de = x/2 + 7|| (- 3x/2 - 3) - ef = -x/2 - 1|| d + f = 6

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3 years ago

The number of square feet per house is normally distributed with a population standard deviation of 154 square feet and an unkno

11111nata11111 [884]

Answer: (1500.66,1599.34)

Step-by-step explanation:

Confidence interval for population mean:

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

,where $\overline{x}$ = Sample mean , n= Sample size, z* = critical two tailed z-value , $\sigma$ = population standard deviation.

As per given , we have

n= 16

$\sigma = 154$ square feet

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$\alpha= 1-0.80 = 0.20$

Critical z-value = $z_{\alpha/2}=z_{0.2/2}=z_{0.1}=1.2815$

Confidence interval for population mean:

$1550\pm (1.2815)\dfrac{154}{\sqrt{16}}\\\\ = 1550\pm (1.2815)\dfrac{154}{4}\\\\= 1550\pm 49.33775\\\\ =(1550-49.33775,\ 1550+49.33775)\\\\\approx (1500.66,\ 1599.34)$

Required confidence interval: (1500.66,1599.34)

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2 years ago