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3 years ago

50 POINTS!!!!

Mathematics

2 answers:

Taya2010 [7]3 years ago

8 0

Answer:

D) x = 4, y = -2, z = 3

Step-by-step explanation:

x = 3z − 5

2x + 2z = y + 16

2(3z - 5) + 2z = y + 16

6z - 10 + 2z = y + 16

8z = y + 26 ---> (A)

7x − 5z = 3y + 19

7(3z - 5) - 5z = 3y + 19

21z - 35 - 5z = 3y + 19

16z = 3y + 54 ---> (B)

8z = y + 26

16z = 3y + 54

2(y + 26) = 3y + 54

2y + 52 = 3y + 54

y = -2

8z = -2 + 26

8z = 24

z = 3

x = 3(3) - 5

x = 4

garri49 [273]3 years ago

4 0

Answer:

The answer is D

x = 4

y = -2

z = 3

Step-by-step explanation:

Plug in the values of x and z into the first equation, and see that D is the only choice that is correct.

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7x-4y=20 for y when x=3

viktelen [127]

I think it is y=-.25
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3 years ago

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Answer: No, they are not collinear.

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3 years ago

drug sniffing dogs must be 95% accurate in their responses because their handlers don't want them to miss durgs and also don't w

GenaCL600 [577]

Answer:

95% Confidence interval: (0.8449,0.9951)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

Number of times the dog is right, x = 46

$\hat{p} = \dfrac{x}{n} = \dfrac{46}{50} = 0.92$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.92 \pm 1.96(\sqrt{\dfrac{0.92(1-0.92)}{50}})\\\\ = 0.92\pm 0.0751\\\\=(0.8449,0.9951)$

(0.8449,0.9951) is the required 95% confidence interval for the proportion of times the dog will be correct.

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3 years ago

Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s

Nataliya [291]

Answer:

$f(x)=\frac{1}{2}x^2-4x+5$

Step-by-step explanation:

A parabola is written in the form

$f(x)=a((x-h)^2+k)$ (1)

where:

$h$ is the x-coordinate of the vertex of the parabola

$ak$ is the y-coordinate of the vertex of the parabola

$a$ is a scale factor

For the parabola in the problem, we know that the vertex has coordinates (4,-3), so we have:

$h=4$ (2)

$ak=-3$

From this last equation, we get that $a=\frac{-3}{k}$ (3)

Substituting (2) and (3) into (1) we get the new expression:

$f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3$ (4)

We also know that the parabola contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

$-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6$

So we also get:

$a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}$

So the equation of the parabola is:

$f(x)=\frac{1}{2}((x-4)^2 -6)$ (5)

Now we want to rewrite it in the standard form, i.e. in the form

$f(x)=ax^2+bx+c$

To do that, we simply rewrite (5) expliciting the various terms, we find:

$f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5$

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3 years ago

Find a ⋅ b. a = <5, 2>, b = <4, 5>

cestrela7 [59]

Answer:

Step-by-step explanation:

For a = <xa, ya> and b = <xb, yb>, the dot product is the sum of products ...

a·b = (xa)(xb) + (ya)(yb)

Substituting the given information, you have ...

a·b = 5·4 + 2·5 = 20 + 10

a·b = 30

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Some graphing calculators can do such math. There are also dot product calculators available on the Internet. If you have quite a few of these to calculate, you can put the appropriate formula into a spreadsheet.

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3 years ago