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3 years ago

Through: (-3, -4) and (2, 1)

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

5 0

Answer:

y = 1x - 1

Step-by-step explanation:

$\frac{y2-y1}{x2-x1}\\\frac{1-(-4)}{2-(-3)}\\\frac{1+4}{2+3}\\\frac{5}{5}=1\\y=1x+b\\1=1(2)+b\\1 = 2 + b\\-1 = b\\y = 1x-1$

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If there are 30 boys and 50 girls in a room, fill out all of the possible ratios of boys to girls that could be made. They alrea

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3:5

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3 years ago

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$

Then

$\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.$

Answer 2: correct choice is D.

8 0

3 years ago

Read 2 more answers

Find the missing factor 4x^2+19x-5=(x+5)( )<br><br> NEED HELP PLEASE

S_A_V [24]

Answer:

4x^2+19x-5=(x+5)(4x -1)

Step-by-step explanation:

The given expression is 4x^2 + 19x - 5

The leading coefficient is 4 and last term is -5

Multiply them, we get -20

Now find the factors of -20 such that when you add the factors we have to get 19.

-1*20 = -20

20+ (-1) = 19

The right factors are -5 and 9.

4x^2 + 19x - 5 =4x^2 + 20x -1x - 5

= 4x(x + 5) -1(x + 5)

= (x + 5)(4x -1)

The missing factor is (4x -1)

Thank you.

4 0

3 years ago

The ratio of boys to girls in class is 4 : 5 <br> What fraction of the class are boys

Sav [38]

Answer:

The ratio of boys to girls is 4:5. So let 4x be the number of boys and 5x be the number of girls. Then 4x+5x = 9x is the total number of students. Then the fraction of boys in the class is 4x/9x = 4/9.

6 0

3 years ago

Help me this is the last question i just need to know what to use to solve the problem

Genrish500 [490]

Answer:

Not even one day

Step-by-step explanation:

I mean if it uses 4 bags a day . . .

2/5's wont last long at all

8 0

3 years ago