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3 years ago

Solve the quadratic equation 2x2 − 9x = 35 for x

Mathematics

2 answers:

Mrrafil [7]3 years ago

8 0

Answer:

Step-by-step explanation:

66666666666

tino4ka555 [31]3 years ago

6 0

Answer:

$x=7$ or $x=-5/2$

Step-by-step explanation:

The given equation in standard form can be written as

$2x^{2} -9x-35=0$

comparing with the standard equation $ax^{2} +bx+c=0$ ,

we observe that

$a=2$ , $b=-9$ , $c=-35$

putting the values of a, b and c in the quardatic formula

x=(-b± $\sqrt{b^{2}-4ac }$ )÷2a

x=(-(-9)± $\sqrt{(-9)^{2}-4(2)(-35) }$ )÷2(2)

x=(9± $\sqrt{81+280}$ )÷4

x=(9± $\sqrt{361}$ )÷4

x=(9±19)÷4

x=(9+19)÷4 or x=(9-19)÷4

x=28÷4 or x=-10÷4

x=7 or x=-5÷2

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A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

serious [3.7K]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

$0.5=e^{(24.5)r}$

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 3.

We solve with a calculator $\frac{ln0.5}{3} =r\\-0.23=r$

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is $A=6000e^{-0.23t}$

5 0

3 years ago

Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonome

ratelena [41]

Answer:

$x = 0.175\cdot (1-\cos 4\cdot \theta)$

Step-by-step explanation:

Let use the following trigonometric identities:

$\sin^{2}\theta = \frac{1-\cos 2\cdot \theta}{2} \\\cos^{2}\theta = \frac{1+\cos 2\cdot \theta}{2}$

Then, the equation is simplified by substituting its components:

$x = 1.40\cdot \left(\frac{1-\cos 2\cdot \theta}{2} \right)\cdot \left(\frac{1+\cos 2\cdot \theta}{2} \right)$

$x = 0.35\cdot (1-\cos^{2}2\cdot \theta)$

$x = 0.35\cdot \sin^{2}2\cdot \theta$

$x = 0.35\cdot \left(\frac{1-\cos 4\cdot \theta}{2} \right)$

$x = 0.175\cdot (1-\cos 4\cdot \theta)$

7 0

3 years ago

Read 2 more answers

How to solve this problem

rodikova [14]

$\bf \textit{circumference of a circle}\\\\
C=2\pi r\quad 
\begin{cases}
r=radius\\
-----\\
r=10
\end{cases}\implies C=2\pi 10\implies \boxed{C=20\pi }\\\\
-------------------------------\\\\$

$\bf \textit{let's converte 1km to inches}
\\\\\\
km\cdot \cfrac{1000m}{km}\cdot \cfrac{100cm}{m}\cdot \cfrac{in}{2.54cm}\implies \cfrac{1000\cdot 100\cdot in}{2.54}\approx 39370.079\ in\\\\
-------------------------------\\\\
\textit{how many times does }20\pi \textit{ go into }39370.079?\implies \boxed{\cfrac{39370.079}{20\pi }}$

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3 years ago

A school director Must randomly select 6 teachers to participate in a training session there are 30 teachers at the school in ho

Ede4ka [16]

Solution:

we are given that

A school director Must randomly select 6 teachers to participate in a training session there are 30 teachers at the schoo. The order of selection does not matter.

As we know

6 teacheras can be selected out of 30 teacher in ${30}_C_6$ ways.

${30}_C_6=\frac{30!}{6!24!}\\
\\ {30}_C_6=\frac{25*26*27*28*29*30}{1*2*3*4*5*6}\\
\\ {30}_C_6=593775$

Hence the required number of ways is 593775.

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2 years ago

Alejandro is flying a kite, holding his hands a distance of 3.5 feet above the ground

Lemur [1.5K]

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sin23/1=x/125

125sin23=x

x=48.841391... add 3.5 = 52.341391... round to 52.34

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2 years ago