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2 years ago

Select the expressions that are equivalent to 8 2/3

1 answer:

6 0

To change a mixed fraction, you'd multiply the number upfront, times the denominator, and then add that product to the numerator
that IS the new numerator, and you keep the denominator
thus $\bf 8\frac{2}{3}\iff \cfrac{8\cdot 3+2}{3}$

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(1-w-w²)⁶=64 prove thta

VLD [36.1K]

1−w−w2=64

Step 1: Simplify both sides of the equation.

−w2−w+1=64

Step 2: Subtract 64 from both sides.

−w2−w+1−64=64−64

−w2−w−63=0

For this equation: a=-1, b=-1, c=-63

−1w2+−1w+−63=0

Step 3: Use quadratic formula with a=-1, b=-1, c=-63.

w= −b±√b2−4ac /2a

w= −(−1)±√(−1)2−4(−1)(−63) /2(−1)

w= 1±√−251/ −2

7 0

1 year ago

Solve the equatuon<br><br> x/2-(2/(x+1))=1<br><br> x=?

Snezhnost [94]

$\frac{x}{2}-\frac{2}{x+1}=1$

We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.

Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)

$\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]$

Then shorten the fractions.

$\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)$

Distribute in all.

$x^2+x-4=2x+2$

We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.

$x^2+x-4-2x-2=0\\x^2-x-6=0\\$

We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)

$(x-3)(x+2)=0\\x=3,-2$

Thus, the answer is x = 3, -2

7 0

2 years ago

Carry out three steps of the Bisection Method for f(x)=3x−x4 as follows: (a) Show that f(x) has a zero in [1,2]. (b) Determine w

ELEN [110]

Answer:

a) There's a zero between [1,2]

b) There's a zero between [1.5,2]

c) There's a zero between [1.5,1.75].

Step-by-step explanation:

We have $f(x)=3^x-x^4$

A)We need to show that f(x) has a zero in the interval [1, 2]. We have to see if the function f is continuous with f(1) and f(2).

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(2)=3^2-(2)^4=9-16=(-7)$

We can see that f(1) and f(2) have opposite signs. And f(1)>f(2) and the function is continuous, this means that exists a real number c between the interval [1,2] where f(c)=0.

B)We have to repeat the same steps of A)

For the subinterval [1,1.5]:

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13$

f(1) and f(1.5) have the same signs, this means there's no zero in the subinterval [1,1.5].

For the subinterval [1.5,2]:

$f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(2)=3^2-(2)^4=9-16=(-7)$

f(1.5) and f(2) have opposite signs, this means there's a zero between the subinterval [1.5,2].

C)We have to repeat the same steps of A)

For the subinterval [1,1.25]:

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5$

f(1) and f(1.25) have the same signs, this means there's no zero in the subinterval [1,1.25].

For the subinterval [1.25,1.5]:

$f(x)=3^x-x^4\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13$

f(1.25) and f(1.5) have the same signs, this means there's no zero in the subinterval [1.25,1.5].

For the subinterval [1.5,1.75]:

$f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)$

f(1.5) and f(1.75) have opposite signs, this means there's a zero between the subinterval [1.5,1.75].

For the subinterval [1.75,2]:

$f(x)=3^x-x^4\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)\\\\f(2)=3^2-(2)^4=9-16=(-7)$

f(1.75) and f(2) have the same signs, this means there isn't a zero between the subinterval [1.75,2].

The graph of the function shows that the answers are correct.

6 0

2 years ago

Ramal filled 3 pages in a stamp album. This is one sixth of the pages in the album. How many pages are three in Ramal's stamp al

kumpel [21]

Let the total be x
1/6x=3
x/6=3
x=18
therefore Ramal's stamp has 18 pages

6 0

2 years ago

Determine the intercepts of the line.

Alina [70]

Answer:

x-intercept: (-250, 0)

y-intercept: (0, 100)

Step-by-step explanation:

Look for you the line intercepts the x-axis and y-axis. That's where the intercepts are located.

8 0

2 years ago

Read 2 more answers