At 0°C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by 225. Write an equation that represents the volume of the gas in terms of the temperature.

Answer:
The two positive numbers are 12 and 8. 

Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4

The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96

So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12

Now we plug each these pairs into the first equation to see if they satisfy the equation.

96 - 1 = 95               24 - 4 = 20
95 > 4                      20 > 4

48 - 2 = 46               16 - 6 = 10
46 > 4                       10 > 4

32 - 3 = 29               12 - 8 = 4
29 > 4                       4 = 4

Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ -1 &,& 2~) &&(~ 6 &,& 3~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-2}{6-(-1)}\implies \cfrac{3-2}{6+1}\implies \cfrac{1}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=\cfrac{1}{7}[x-(-1)]\implies y-2=\cfrac{1}{7}(x+1) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{1}{7}\implies y=\cfrac{1}{7}x+\cfrac{1}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{15}{7}[/tex]

Answer:

Step 1: Choose (x1, y1). (6,3)

Step 2: x2= -1 y2=2

Step 3: 1/7

Step 4: b= 15/7

What is the equation of the line in slope-intercept form?

B) y=1/7x+15/7

Step-by-step explanation:

The bold numbers are the answers.

( I need mo pts)

Answer:

So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1

Ans: [tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]

The standard form equation of a hyperbola with the center at the origin (0,0), a vertical axis, a vertex at (0, a), and a focus at (0, c) is given by:

[tex]\[\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\][/tex]

where [tex]\(c\)[/tex] is the distance from the center to the focus, and [tex]\(b\)[/tex] is related to [tex]\(a\) and \(c\)[/tex] by the equation [tex]\(c^2 = a^2 + b^2\)[/tex].

In your case, the center is at (0,0), the vertex is at (0,60), and the focus is at (0,-65). The distance from the center to the focus is [tex]\(c = 65\)[/tex], and the distance from the center to the vertex is [tex]\(a = 60\)[/tex]. Using the relationship [tex]\(c^2 = a^2 + b^2\)[/tex], we can find b:

[tex]\[65^2 = 60^2 + b^2\][/tex]

Solving for b:

[tex]\[4225 = 3600 + b^2\][/tex]

[tex]\[b^2 = 625\][/tex]

[tex]\[b = 25\][/tex]

Now, substitute [tex]\(a\), \(b\), and \((h, k) = (0, 0)\)[/tex] into the standard form equation:

[tex]\[\frac{y^2}{60^2} - \frac{x^2}{25^2} = 1\][/tex]

So, the equation of the hyperbola is:

[tex]\[\frac{y^2}{3600} - \frac{x^2}{625} = 1\][/tex]

[tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]

Answer:

13.

Step-by-step explanation:

The shape that best describes the cross-section cut perpendicular to the base of a right rectangular prism is a rectangle.

A cross-section cut perpendicular to the base of a right rectangular prism will always result in a rectangular shape.

This is because a rectangular prism has six faces, and the base of the prism is one of those faces.

When you make a cross-section cut perpendicular to the base, you are essentially slicing through the prism parallel to one of its other faces.

Since the base is a rectangle, the cross-section will also be a rectangle.

In summary, the cross-section cut of a right rectangular prism perpendicular to its base will consistently yield a rectangular shape due to the inherent geometry of the prism.

for such more questions on perpendicular

https://brainly.com/question/1091880

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Answer:

C.) 4

Step-by-step explanation:

we are given ABCD is an isosceles trapezoid

AB || CD

AB = m + 6

CD = 3m + 2

BC = 3m

AD = 7m - 16

Since, ABCD is an isosceles trapezoid

so, two sides must be equal

[tex]BC=AD[/tex]

now, we can plug values

[tex]3m=7m-16[/tex]

now, we can solve for m

[tex]3m-7m=7m-16-7m[/tex]

[tex]-4m=-16[/tex]

Divide both sides by -4

and we get

[tex]m=4[/tex]

Answer:

M= 4

Step-by-step explanation:

Answer:

The mean is 10.7 and the standard deviation is 5.6.

Step-by-step explanation:

To find the mean, add together all of the data and divide by the number of data points:

(6+7+19+7+18+7)/6 = 64/6 = 10.7

To find the standard deviation, subtract each data point from the mean, square them and find the sum:

(6-10.7)²+(7-10.7)²+(19-10.7)²+(7-10.7)²+(18-10.7)²+(7-10.7)²

=(-4.7)²+(-3.7)²+(8.3)²+(-3.7)²+(7.3)²+(-3.7)²

=22.09+13.69+68.89+13.69+53.29+13.69 = 185.34

Next divide this by 6, the number of data points:

185.34/6 = 30.89

Lastly, take the square root:

√30.89 = 5.6

Answer:

Interest rate - 9

Revenue - 3

Recovery - 7

Markdown - 6

Buyer's willingness to pay - 1

Markup - 10

Worker's wages - 5

2/10 net 30 - 4

Credit - 8

Rent - 2

Step-by-step explanation:

Just did this on odyssey

[tex] |\Omega|=25\cdot24\cdot23=13800\\
|A|=5\cdot4\cdot3=60\\\\
P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\% [/tex]

The probability of an event is calculated as = [tex] \frac{Favorable outcomes}{Total number of outcomes} [/tex]

Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles

So, total marbles = 25 marbles

Number of favorable or green marbles = 5 marbles

Probability of three green marbles if drawn with replacement = [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] ×[tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex] × [tex] \frac{Number of favorable or green marbles}{Total number of marbles} [/tex]

Probability of three green marbles if drawn with replacement = [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex] × [tex] \frac{5}{25} [/tex]

Probability of three green marbles if drawn with replacement = [tex] \frac{1}{125} [/tex]

Given point is (0, -2).

Given options are A(6, -2); B(-8, -2); C(0, -8); D(0, 4).

It says to select the options that are more than five units vertically away from the given point.

"Vertically away" means the x-coordinate would be same and y-coordinate would be shifted up or down.

Since it says to shift more than five units vertically away, so we must have :-

y > -2 + 5 or y < -2 - 5.  

Therefore, y > 3 or y < -7.

Hence, option C and D are correct i.e. (0, -8) and (0, 4).

the anser would be c fo it to be in scientific notation you have to have an exponet

Answer:

[tex]78\ million=7.80\times 10^7[/tex]

Step-by-step explanation:

A number N can be written in scientific notation as :

[tex]N=p{\circ}0\times 10^q[/tex]

Where

p is the any real number

q is any integer

Here, the given number is 78 million. Firstly, we must know meaning of 1 million.

Since, [tex]1\ million=10^6[/tex]

[tex]78\ million=78.0\times 10^6[/tex]

To convert the above number in scientific notation, we can shift the decimal before 8 such that,

[tex]78\ million=7.80\times 10^7[/tex]

Hence, this is the required solution.