Rewrite 3.47 • 10^5 in standard form

gtnhenbr [62]

So we want to solve 2x − 40 = 3y for x2x − 40 + 40 = 3y + 40(Add 40 to both sides!)2x = 3y + 40
Now divide both sides by 2!
 $\frac{2x}{2} = \frac{3y + 40}{2} \ \textgreater \ x = \frac{3}{2}y + 20$
Now substitute $\frac{3}{2}y + 20 for x in 2y = -4x + 48

$
$2y = -4( \frac{3}{2}y + 20) + 48$
Which then gives us..
2y = −6y − 32(Make sure to simplify both sides of the equation)2y + 6y = −6y − 32 + 6y(Now add 6y to both sides)8y = −32
Now divide both sides by 8
 $\frac{8y}{8} = \frac{-32}{8} \ \textgreater \ y = -4$
Now we have to substitute -4 for y in $x = \frac{3}{2}y + 20 \ \textgreater \ \frac{3}{2}(-4) + 20 \ \textgreater \ x = 14$
So we end up getting...
x = 14 and y = −4.
Hope this helps!

7 0

4 years ago

Which of the following does not factor as a perfect square trinomial?

Ede4ka [16]

Answer:

Option C. x^2-18x-81

Step-by-step explanation:

A. 16a^2-72a+81

x^2-2xy+y^2=(x-y)^2

x^2=16a^2→sqrt(x^2)=sqrt(16a^2)→x=sqrt(16) sqrt(a^2)→x=4a

y^2=81→sqrt(y^2)=sqrt(81)→y=9

2xy=2(4a)(9)→2xy=72a equal to the second term of the expression, then we can factor as a perfect square trinomial:

16a^2-72a+81=(4a-9)^2

B. 169x^2+26xy+y^2

a^2+2ab+b^2=(a+b)^2

a^2=169x^2→sqrt(a^2)=sqrt(169x^2)→a=sqrt(169) sqrt(x^2)→a=13x

b^2=y^2→sqrt(b^2)=sqrt(y^2)→b=y

2ab=2(13x)(y)→2ab=26xy equal to the second term of the expression, then we can factor as a perfect square trinomial:

169x^2+26xy+y^2=(13x+y)^2

C. x^2-18x-81

a^2+2ab+b^2=(a+b)^2

This expression does not factor as a perfect square trinomial because the third term is negative (-81).

D. 4x^2+4x+1

a^2+2ab+b^2=(a+b)^2

a^2=4x^2→sqrt(a^2)=sqrt(4x^2)→a=sqrt(4) sqrt(x^2)→a=2x

b^2=1→sqrt(b^2)=sqrt(1)→b=1

2ab=2(2x)(1)→2ab=4x equal to the second term of the expression, then we can factor as a perfect square trinomial:

4x^2+4x+1=(2x+1)^2

4 0

3 years ago

A simple random sample was taken of 44 water bottles from a bottling plant’s warehouse. The dissolvedoxygen content (in mg/L) wa

AleksAgata [21]

Answer:

a) $9.14-2.33\frac{2}{\sqrt{44}}=8.44$

$9.14+2.33\frac{2}{\sqrt{44}}=9.84$

b) The 98% confidence interval would be given by (8.44;9.84)

For this case we can conclude that we have 98% of confidence that the true mean for the oxygen content is between 8.44 and 9.84 mg/L

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=9.14$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=2$ represent the population standard deviation

n=44 represent the sample size

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=18-1=17$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.01$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$9.14-2.33\frac{2}{\sqrt{44}}=8.44$

$9.14+2.33\frac{2}{\sqrt{44}}=9.84$

Part b

The 98% confidence interval would be given by (8.44;9.84)

For this case we can conclude that we have 98% of confidence that the true mean for the oxygen content is between 8.44 and 9.84 mg/L

3 0

4 years ago

besides the 90 degree angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13

omeli [17]

Use sine cosine and tangent to find the answer. Sine=opposite/hypotenuse
Cosine= adjacent/hypotenuse tangent= opposite/adjacent. This should help you find your answers.

8 0

3 years ago

Read 2 more answers

help please!! Mark the following triangles so that they are congruent by the Side-Side-Side Postulate

Ivenika [448]

Hi!

If you want to show these are congruent, you make a single line through each of the sides. Just do this for both of the triangles.

See the screenshot for example

Hope this helps! :0)

7 0

3 years ago