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3 years ago

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Algebra 2 Word Problem: Set up using 3 variables & 3 equations:

1 answer:

belka [17]3 years ago

7 0

A) The answer is
x + y + z = 24
3x + 2y + z = 53
x = y + z

x - the number of swimmers in the first place
y - the number of swimmers in the second place
z - the number of swimmers in the third place

<span>1. The e-mail states that 24 individuals placed: x + y + z = 24
2. </span>First place earned 3 points, second place earned 2 points, and third place earned 1 point, <span>earning a combined total of 53 points: 3x + 2y + z = 53
3. </span><span> There were as many first-place finishers as second and third-place finishers combined: x = y + z

The system of three equations is:
</span>x + y + z = 24
3x + 2y + z = 53
x = y + z

B) The answer is
12 swimmers in the first place
5 swimmers in the second place
7 swimmers in the third place

(i) x + y + z = 24
(ii) 3x + 2y + z = 53
(iii) x = y + z
______
Substitute y + z from the third equation into the first one:
(i) x + y + z = 24
(iii) x = y + z
______
x + x = 24
2x = 24
x = 24 / 2
<u>x = 12</u>
_____

x = y + z
x = 12
y + z = 12
z = 12 - y

3x + 2y + z = 53
3 * 12 + 2y + (12 - y) = 53
36 + 2y + 12 - y = 53
2y - y + 36 + 12 = 53
y + 48 = 53
y = 53 - 48
<u>y = 5</u>

z = 12 - y
z = 12 - 5
z = 7

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2-step equations Solve: 1/4n+7=10<br>show the steps

Bingel [31]

Answer:

$n = 12$

Step-by-step explanation:

$\frac{1}{4}n+ 7 = 10$

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Hope this helps :)

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3 years ago

Assume that the terminal side of thetaθ passes through the point (negative 12 comma 5 )(−12,5) and find the values of trigonomet

zmey [24]

Answer:

$\sin \theta = \dfrac{5}{13}$ and $\sec \theta = -\dfrac{13}{12}$

Step-by-step explanation:

Assume that the terminal side of thetaθ passes through the point (−12,5).

In ordered pair (-12,5), x-intercept is negative and y-intercept is positive. It means the point lies in 2nd quadrant.

Using Pythagoras theorem:

$hypotenuse^2=perpendicular^2+base^2$

$hypotenuse^2=(5)^2+(12)^2$

$hypotenuse^2=25+144$

$hypotenuse^2=169$

Taking square root on both sides.

$hypotenuse=13$

In a right angled triangle

$\sin \theta = \dfrac{opposite}{hypotenuse}$

$\sin \theta = \dfrac{5}{13}$

$\sec \theta = \dfrac{hypotenuse}{adjacent}$

$\sec \theta = \dfrac{13}{12}$

In second quadrant only sine and cosecant are positive.

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4 years ago

A circle has a circumference of 34 54 cm. What is the area of the circle to the nearest whole centimeter? Use 3.14

inysia [295]

Answer:

<h2>9498.5 m</h2>

Step-by-step explanation:

We know that the Circumference = 3454 cm

And we also know that the formula for the Circumference of Circle is,

$2\pi \times r$

So we can put the equation this way,

$3454 = 2\pi \times r$

So we can solve for 'r'

$3454 = 2 \times 3.14 \times r \\ 3454 = 6.28r \\ r = \frac{3454}{6.28} \\ r = 550$

Now we have radius and we can solve for the area of the circle,

$\pi \times {r}^{2}$

$3.14 \times 550 \times 550 \\ = 949850$

We can convert this to meter,

9498.5 m

I am not sure if this is correct just let me know thanks :)

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