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2 years ago

3+

t="3+\sqrt{2}/4\sqrt{2}+2" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

tester [92]2 years ago

8 0

This is the answer unless the 2/4 is meaning divide the two if thats the case the answer is 48+√2 over 8

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Solve the equation for x∈Z -x² +8x -14 ≥ 0

kenny6666 [7]

$ax^2+bx+c=0\\\Delta=b^2-4ac\\if\ \Delta < 0\ then\ no\ solutions\\if\ \Delta=0\ then\ one\ solution:x=\frac{-b}{2a}\\if\ \Delta > 0\ then\ two\ solutions:x=\frac{-b\pm\sqrt\Delta}{2a}\\================================\\\\-x^2+8x-14\geq0\ \ \ \ |multiply\ both\ sides\ by\ (-1)\ \{change\ \geq\ on\ \leq\}\\\\x^2-8x+14\leq0\\\\a=1;\ b=-8;\ c=14\\\\\Delta=(-8)^2-4\cdot1\cdot14=64-56=8 > 0\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2$

$x_1=\frac{-(-8)-2\sqrt2}{2\cdot1}=\frac{8-2\sqrt2}{2}=\frac{8}{2}-\frac{2\sqrt2}{2}=\boxed{4-\sqrt2}\\\\x_2=\frac{-(-8)+2\sqrt2}{2\cdot1}=\frac{8+2\sqrt2}{2}=\frac{8}{2}+\frac{2\sqrt2}{2}=\boxed{4+\sqrt2}\\\\============================$

$ax^2+bx+c=0\\\\if\ a > 0\ then\ the\ parabola\ o pen\ up\\if\ a < 0\ then\ the\ parabola\ o pen\ down\\========================\\\\a=1 > 0-therefore\ o pen\ up\ (look\ at\ the\ picture)\\\\===============================\\\\Answer:x\in\left$

$Solutions\ in\ \mathbb{Z}:\\\\\sqrt2\approx1.4\\\\threfore:4-\sqrt2\approx4-1.4=2.6\ and\ 4+\sqrt2\approx4+1.4=5.4\\\\look\ at\ the\ second\ picture:x=3\ or\ x=4\ or\ x=5\ (x\in\{3;\ 4;\ 5\})$

6 0

3 years ago

Read 2 more answers

The length of a school bus is 12.6 meters. If 9 school buses park end to end with 2 meters between each one, what's the total le

weqwewe [10]

Answer:

129.4

Step-by-step explanation:

Calculation for what's the total length from the front of the first bus to the end of the last

First step is to multiply the given number of buses by the length of each one

Hence,

12.6 meters x 9 = 113.4 meters

Second step

Since there are 8 spaces in between we would multiply the 8 spaces by 2 meters

8 x 2 meters = 16

Now let calculate total length from the front of the first bus to the end of the last

16 + 113.4 meters =129.4

Therefore total length from the front of the first bus to the end of the last will be 129.4

7 0

3 years ago

Pring 2022

lutik1710 [3]

Answer:

c = 10 - 11(0.65)

Step-by-step explanation:

The equation is :

c = 10 - 11(0.65)

Change will be :

c = 10 - 7.15
c = $2.85

5 0

2 years ago

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Find the area. The figure is not drawn to scale. Please show work

Irina-Kira [14]

Answer:

13.8 square feet

Step-by-step explanation:

To find the area of a triangle you use the formula a = 1/2 bh

a = 1/2 (6.9) (4) = 13.8

(simplier to understand) a = 1/2 (6.9) (4) = 27.6 divided by 1/2 = 13.8

6 0

3 years ago

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A simple random sample of size nequals10 is obtained from a population with muequals68 and sigmaequals15. (a) What must be true

valentina_108 [34]

Answer:

(a) The distribution of the sample mean ( $\bar x$ ) is N (68, 4.74²).

(b) The value of $P(\bar X$ is 0.7642.

Step-by-step explanation:

A random sample of size n = 10 is selected from a population.

Let the population be made up of the random variable X.

The mean and standard deviation of X are:

$\mu=68\\\sigma=15$

(a)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Since the sample selected is not large, i.e. n = 10 < 30, for the distribution of the sample mean will be approximately normally distributed, the population from which the sample is selected must be normally distributed.

Then, the mean of the distribution of the sample mean is given by,

$\mu_{\bar x}=\mu=68$