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2 years ago

Find the values for a and b that would make the equality true. 4(ax^2 -5x+3)=8x^2 +bx+12

Mathematics

2 answers:

tankabanditka [31]2 years ago

5 0

Answer:

a 2 and b -20

Step-by-step explanation:

yawa3891 [41]2 years ago

4 0

Answer:

a = 2 and b = -20

Step-by-step explanation:

4(ax^2 -5x+3)=8x^2 +bx+12 should be multiplied out. Next, we equate the coefficients of the several powers of x:

4ax² - 20x + 12 = 8x² + bx + 12

Then 4a = 8, so a = 2

and -20 = b

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A line, y = mx +b, passes through the point (2,3) and is parallel to y = 2x + 3. What is the value of

diamong [38]

Answer:

The value of b is 3

Step-by-step explanation:

mx is the slope and b is the y intercept. I hope this helps!

4 0

2 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

Amy is buying ribbon for an art projectShe estimates that she will need 3.84 meters of ribbon. The store only sells ribbon by th

vodka [1.7K]

Answer:

3.90 meters.

Step-by-step explanation:

Since Amy needs ribbon for her art project, and she plans to buy 3.84 meters of that material, but the store only sells said product by the tenth of a meter, in order to get closer to the desired size she will have to buy 39 pieces of 10 cm (one tenth of a meter), that is, she must buy 3.90 meters, of which there will be 6 centimeters of the product left over.

4 0

2 years ago

Find a solution to the linear equation −2x−2y=8 by filling in the boxes with a valid value of x and y.Provide your answer below:

inna [77]

Given

$-2x-2y=8$

To find a solution for the linear equation, the first step is to write the equation in slope-intercept form:

-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of the equal sign:

$\begin{gathered} -2x+2x-2y=8+2x \\ -2y=2x+8 \end{gathered}$

-Divide both sides by -2:

$\begin{gathered} \frac{-2y}{-2}=\frac{2x}{-2}+\frac{8}{-2} \\ y=-x-4 \end{gathered}$

Once you have expressed the equation of the line in slope-intercept form, replace it with any value for x and calculate the corresponding value of y, for example, x=2

$\begin{gathered} y=-(2)-4 \\ y=-2-4 \\ y=-6 \end{gathered}$

One solution for the linear equation is x=2 and y=-6, you can check the solution by replacing the values on the original equation, with both values the result should be 8:

$\begin{gathered} -2x-2y \\ -2\cdot2-2\cdot(-6) \\ -4+12=8 \end{gathered}$

As you can see the values are a valid solution for the linear equation.

So the solution is:

$-2(2)-2(-6)=8$

6 0

10 months ago

Simplify the identity: tan cos/sin

xxMikexx [17]

I am going to simplify the top before simplifying the rest.

tan = sin/cos, so tan * cos simplifies down to sin in the numerator. which leaves sin/sin which equals 1.

to make a long story short the answer is 1

4 0

2 years ago