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3 years ago

Explain how the statement "there is 3/4 cup per serving" represents a rate.

1 answer:

7 0

There is 3/4 cup of whatever in one serving. If that serving amount changed to 2, then the 3/4 would be multiplied by 2. If there is half a serving, then it would be divided by 2. There is a constant change, and not one that is always changing.

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A cylindrical container contains some sand. If the diameter of the container is 10 inches and its height is 3 inches, about how

Mazyrski [523]

Answer:

251.33in²

Step-by-step explanation:

A cylindrical container contains some sand. If the diameter of the container is 10 inches and its height is 3 inches, about how much sand fits inside the container?

We solve the above question using the formula for Total surface area of a cylinder.

TSA = 2πr (h + r) Square units.

Where

h = Height of the cylinder

r = Radius of the cylinder

Diameter of the container is 10 inches

Hence, radius = Diameter/2 = 10/2 = 5 inches

Height is 3 inches.

Hence, Total surface area =

2 × π × 5 (5 + 3)

= 10π × (8)

= 251.32741229 in²

Approximately = 251.33 in²

Therefore, the amount of sand that can fit into the cylinder = 251.33 in²

6 0

3 years ago

The glee club has $90 to spend on pens and pencils. Each pen costs $0.75 and each pencil costs $0.15. Let x represent the number

Deffense [45]

Answer:

part a: answer b. 0.75x + 0.15y = 90

8 0

3 years ago

Read 2 more answers

The focus of a parabola is (-3,-5) The directrix of the parabola is y=2

cricket20 [7]

Check the picture below.

so the focus point is there, and the directrix is above it, meaning is a vertical parabola and is opening downwards, since the parabola opens up towards the focus.

now, the vertex is half-way between those two guys, at a "p" distance from either one, if we move over the y-axis from -5 to +2, we have 7 units, half-way is 3.5 units, and that puts us at -1.5 or -1½, as you see in the picture, so the vertex is then at (-3 , -1½).

so the distance from the vertex to the focus point is then 3½ units, however since the parabola is opening downwards, "p" is negative, thus "p = 3½".

$\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{using this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \begin{cases} h=-3\\ k=-\frac{3}{2}\\[0.7em] p=-\frac{7}{2} \end{cases}\implies 4\left( -\cfrac{7}{2} \right)\left[ y-\left(-\cfrac{3}{2} \right) \right]=\left[ x-\left( -3 \right) \right]^2 \\\\\\ -14\left( y+\cfrac{3}{2} \right)=(x+3)^2\implies y+\cfrac{3}{2} =-\cfrac{(x+3)^2}{14} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{14}(x+3)^2-\cfrac{3}{2}~\hfill$

4 0

3 years ago

Solve the in quality x plus 1<7

RUDIKE [14]

Answer:

x<6

Step-by-step explanation:

x+1 < 7

Subtract 1 from each side

x+1-1<7-1

x <6

7 0

3 years ago

Pythagorean theorem and its converse <br><img src="https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7B5%7D%5E%7B2%7D%

Anettt [7]

$x^2+25=225 \\ x^2=200 \\ \sqrt{x^2}= \sqrt{200} \\ x=14.14 \\ or \\ x=10 \sqrt{2}$
If
$c^{2} \ \textless \ a^2+b^2$ the triangle would be acute
If
$c^2=a^2+b^2$ the triangle would be right
If
$c^2\ \textgreater \ a^2+b^2$ the triangle would be obtuse
Hope this helps!

6 0

4 years ago