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2 years ago

What is the value of k?

Mathematics

1 answer:

Flura [38]2 years ago

7 0

Answer:

k=10

Step-by-step explanation:

If you need me to explain, just comment below but heres my work:

180-115=65

(4k+5)+(6k+10)+65 = 180

10k+80=180

10k=100

k=10

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21. Randy owns a computer store. In 1990, he sold 150 monitors. In 2000, he sold 900

lutik1710 [3]

Answer:

$y=75x+150$

Step-by-step explanation:

Let $y$ represent the number of monitors sold.

Given:

$x$ is the number of years since 1990.

So, for the year 1990, $x=0$ .

For the year 2000, 10 years passed. So, $x=10$ .

Now, monitors sold in 1990 are 150. So, at $x=0,y=150$

Monitors sold in 2000 are 900. So, at $x=10,y=900$

Thus, the two points are $(0,150)$ and $(10,900)$ .

The slope of a line with points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given as:

Slope, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

For the points $(0,150)$ and $(10,900)$ , the slope is given as:

Slope, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\ m=\frac{900-150}{10-0}\\ m=75$

Now, the y-intercept is the point where $x=0$ . So, the point $(0,150)$ has $x$ value as 0.

So, the y-intercept is 150.

Equation of a line in slope-intercept form is given as:

$y=mx+b$

Where, $m$ is the slope and $b$ is the y intercept.

Here, $m=75$ and $b=150$ .

Therefore, the equation that represents the above data is given as:

$y=75x+150$

7 0

3 years ago

Prove the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Drag and drop the expressions to correctly complete the proof of the

Alex_Xolod [135]

Answer:

Step-by-step explanation:

Given expression is,

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

To prove this identity we will take the left hand side of the equation and will prove equal to the right side.

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)

4x² - 1 = (2x - 1)(2x + 1)

(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]

6 0

3 years ago

If Sin X equals .52" and cos X equals .85 what is cot X

Maslowich

Cot x = cos x / sin x = 0.85 / 0.52 = 1.6346

4 0

3 years ago

The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the tota

Dafna1 [17]

Answer:

a. The biomass weighs 2.30 * 10^7 kg after a year

b. It'll take 2.56 years to get to 4*10^7kg

Step-by-step explanation:

k = 0.78,K = 6E7 kg

Given

dy/dt = ky(1- y/K)

Make ky dt the subject of formula

ky dt = dy/(1-y/K) --- make k dt the subject of formula

k dt = dy/(y(1-y/K))

k dt = K dy / y(K-y)

k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides

kt + c = ln(y/(K-y))

Ce^(kt) = y/(K-y)

Substitute the values of k and K

Ce^(0.78t) = y/(6*10^7 - y) ----- (1)

Given that y(0) = 2 * 10^7kg

(1) becomes

Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)

Ce° = (2*10^7)/(4*10^7

C = 2/7

Substitute 2/7 for C in (1)

2/7e^0.78t = y/(6*10^7 - y) ---(2)

We're to find the biomass a year later

So, t = 1

2/7e^0.78 = y/(6*10^7 - y)

0.62 = y/(6*10^7 - y)

y = 0.62(6*10^7 - y)

y = 0.62*6*10^7 - 0.62y

y + 0.62y = 0.62*6*10^7

1.62y = 0.62*6*10^7

1.62y = 3.72 * 10^7

y = 2.30 * 10^7kg.

Hence, the biomass weighs 2.30 * 10^7 kg after a year

Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg

Substitute 4*10^7 for y in (2)

2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)

2/7e^0.78t = 4*10^7/2*10^7

2/7e^0.78t = 2

e^0.78t = (2*7)/2

e^0.78t = 2

t = 2 * 1/0.78

t = 2.56 years

Hence, it'll take 2.56 years to get to 4*10^7kg

8 0

3 years ago

Graph the image of the given triangle after the transformation with the rule (x, y)→(y, x). Select the "Polygon" button from the

VMariaS [17]

Answer:

Your coordinates would be:

(1,8) (1,5) (5,8)

Hope this helps!

5 0

3 years ago