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DochEvi [55]
3 years ago
15

Multiply and simplify : (4x -3)(-2x+1)​

Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0

Answer:

\boxed{ \bold{ \huge{ \boxed{ \sf{ - 8 {x}^{2}  + 10x - 3}}}}}

Option B is correct.

Step-by-step explanation:

\sf{(4x - 3)( - 2x + 1)}

Use the distributive property to multiply each term of the first binomial by each term of the second binomial

\dashrightarrow{ \sf{4x( - 2x + 1) - 3( - 2x + 1)}}

\dashrightarrow{ \sf{ - 8 {x}^{2}  + 4x + 6x - 3}}

Add like terms: 4x and 6x

\dashrightarrow{ \sf{ - 8 {x}^{2}  + 10x - 3}}

Hope I helped!

Best regards! :D

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1.73639 rounded to the nearest thousanth
Maurinko [17]
^ is in the thousadths place so look for the number before it, which is 3. 3 is less than 5 so 6 stays as is so it becomes 1.736
8 0
3 years ago
Barney has 14 dimes and quarters worth $2.15. write the system of equations
grigory [225]

Answer: 14 dimes and 3 quarters

Step-by-step explanation:

14x10=140+25=165+25=190+25=215 aka $2.15 meaning that there is 14 dimes and 3 quarters

5 0
3 years ago
Find the average rate of change of the function f(x)=(3/-3x-5), on the interval x ∈ [0,3]
Svet_ta [14]

Answer:

The average rate of change on the given interval is 9/70

Step-by-step explanation:

Here, we are to find the average rate of change of the function on the given interval

We proceed as follows;

on an interval [a,b] , we can find the average rate of change using the formula;

f(b) - f(a)/b-a

From the question;

a = 0

b = 3

f(0) = -3/5

f(3) = -3/14

Substituting the values, we have;

-3/14-(-3/5)/3-0

= 3/5-3/14/3

= (42-15)/70/3

= 27/70/3

= 27/70 * 1/3 = 9/70

4 0
2 years ago
The volleyball team and the wrestling team at Stamford High School are having a joint car wash today,
Sedbober [7]

Answer:

Money raised by each team = 94 + 11 = <em>$105</em>

Number of cars washed = <em>11</em>

Step-by-step explanation:

Money already present with volleyball team = $50

Money raised by washing each car by volleyball team = $5

Let the number of cars washed = x

Money raised by washing cars = $5x

Money already present with volleyball team = $94

Money raised by washing each car by volleyball team = $1

Money raised by washing cars = $1x = $x

Given that, both the teams have raised same amount of money:

50+5x=94+x\\\Rightarrow 44=4x\\\Rightarrow x=11

Money raised by each team = 94 + 11 = <em>$105</em>

Number of cars washed = <em>11</em>

4 0
3 years ago
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]

The left and right endpoints of the i-th subinterval, respectively, are

\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8

r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8

for 1\le i\le4, and the respective midpoints are

m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8

  • Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)

so that

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}

  • Midpoint rule

We approximate the area for each subinterval by

M_i=f(m_i)(\ell_i-r_i)

so that

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}

  • Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial p_i(x), where

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}

so that

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It so happens that the integral of p_i(x) reduces nicely to the form you're probably more familiar with,

S_i=\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))

Then the integral is approximately

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

3 0
3 years ago
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