All categories

3 years ago

When resting, Tara’s heart beats 68 times a minute. Explain why this is an example of a unit rate?

Mathematics

2 answers:

Naily [24]3 years ago

6 0

(68 heart beats) and (minutes) so therefore it is an example

Eduardwww [97]3 years ago

4 0

There are two variables here, which are time (minutes) and the number of beats, and they both have a relationship (68 beats in one minute), therefore it is an example of a unit rate

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25 (a square) - 4 (b square) + 28bc - 49 (c square)

LUCKY_DIMON [66]

Answer:

(5a - [2b - 7c]) and (5a + [2b + 7c])

Step-by-step explanation:

Factor 25a^2 - 4b^2 + 28bc - 49c^2.

Note that - 4b^2 + 28bc - 49c^2 involves the variables b and c, whereas 25a^2 has only one variable. Thus, try to rewrite - 4b^2 + 28bc - 49c^2 as the square of a binomial:

- 4b^2 + 28bc - 49c^2 = -(4b^2 - 28bc + 49c^2), or

-(2b - 7c)^2.

Thus, the original 25a^2 - 4b^2 + 28bc - 49c^2 looks like:

[5a]^2 - [2b - 7c]^2

Recall that a^2 - b^2 is a special product, the product of (a + b) and (a - b). Applying this pattern to the problem at hand, we conclude:

Thus, [5a]^2 - [2b - 7c]^2 has the factors (5a - [2b - 7c]) and (5a + [2b + 7c])

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3 years ago

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alekssr [168]

Answer:

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Step-by-step explanation:

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Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.

CaHeK987 [17]

<u>Answer:</u>

$y=-\frac{1}{16} x^2$

<u>Step-by-step explanation:</u>

Equation of parabola with focus at (0,-4) and directrix is $y=4$ .

We know that parabola is the locus of all the points such that the distance from fixed point on the parabola to fixed line directrix is the same.

The parabola is opening downwards.

Let any point on parabola is (x,y).

Distance from focus(0,-4) to (x,y) = $\sqrt{(x-0)^2+(y-(-4))^2}=|y-4|$

$\sqrt{(x-0)^2+(y-+4)^2}=|y-4|$

$(x-0)^2+(y+4)^2=(y-4)^2$

$(x)^2+(y+4)^2=(y-4)^2$

$x^2+(y^2+4y+4y+16)=y^2-4y-4y+16$

$x^2+y^2+8y+16=y^2-8y+16$

$x^2+16y^2=0$

$16y=-x^2$

$y=-\frac{1}{16} x^2$

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Khalid invested $9500 in a savings account with a yearly interest rate of 3% for 8 years. How much simple interest did he earn?

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So simple interest, you don't compound anything, you will always add 3% from $9500 and it will not change. The equation will look like this:

9500*[1+(0.03*8)]
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Answer:

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Step-by-step explanation:

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