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3 years ago

Which number is halfway between 1/2 and 2/3 ?

Mathematics

1 answer:

MariettaO [177]3 years ago

8 0

For example, 3/5.

3/5 = 0.6.

1/2 = 0.5
2/3 = 0.6666

0.5 -- 0.6 -- 0.66666666

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Find the unit rate. The unit rate is calories per serving.

aleksklad [387]

The unit rate is 120 calories per serving.

120 x 2 = 240
120 x 4 = 480
120 x 6 = 720
And so on..

6 0

2 years ago

Solve the following equations. log2(x^2 − 16) − log^2(x − 4) = 1

Alenkasestr [34]

Answer:

$x=\frac{4*(2+e)}{e-2}$

Step-by-step explanation:

Let's rewrite the left side keeping in mind the next propierties:

$log(\frac{1}{x} )=-log(x)$

$log(x*y)=log(x)+log(y)$

Therefore:

$log(2*(x^{2} -16))+log(\frac{1}{(x-4)^{2} })=1\\ log(\frac{2*(x^{2} -16)}{(x-4)^{2}})=1$

Now, cancel logarithms by taking exp of both sides:

$e^{log(\frac{2*(x^{2} -16)}{(x-4)^{2}})} =e^{1} \\\frac{2*(x^{2} -16)}{(x-4)^{2}}=e$

Multiply both sides by $(x-4)^{2}$ and using distributive propierty:

$2x^{2} -32=16e-8ex+ex^{2}$

Substract $16e-8ex+ex^{2}$ from both sides and factoring:

$-(x-4)*(-8-4e-2x+ex)=0$

Multiply both sides by -1:

$(x-4)*(-8-4e-2x+ex)=0$

Split into two equations:

$x-4=0\hspace{3}or\hspace{3}-8-4e-2x+ex=0$

Solving for $x-4=0$

Add 4 to both sides:

$x=4$

Solving for $-8-4e-2x+ex=0$

Collect in terms of x and add $4e+8$ to both sides:

$x(e-2)=4e+8$

Divide both sides by e-2:

$x=\frac{4*(2+e)}{e-2}$

The solutions are:

$x=4\hspace{3}or\hspace{3}x=\frac{4*(2+e)}{e-2}$

If we evaluate x=4 in the original equation:

$log(0)-log(0)=1$

This is an absurd because log (x) is undefined for $x\leq 0$

If we evaluate $x=\frac{4*(2+e)}{e-2}$ in the original equation:

$log(2*((\frac{4e+8}{e-2})^2-16))-log((\frac{4e+8}{e-2}-4)^2)=1$

Which is correct, therefore the solution is:

$x=\frac{4*(2+e)}{e-2}$

6 0

3 years ago

Pyramide-shaped gift boxes have square bases that measure 5 inches on each side.The slant height is 6.5 inches.How much cardboar

andrew-mc [135]

1. square base area= 25 inches

2. using the slanted 6.5
=1/2base , therefore 5/2=2.5 inches

3. then use pythagoras.... c=6.5, a=2.5
c^2=a^2 + b^2
(do this urself)

4. when u find what b is... that's the height of one of the triangle
base= 2.5 (look at step 2 if u don't understand this bit)
height=b (refer to step 3)

5. then work out the area of 1 triangle using that...
6. then have (the answer u work out in step 5 ) multiply 4
this will give u the area for the all of the 4 triangles...

7. Then add together the square based area in step 1..(25)
to the 4 triangular, area faces (i.e from step 6) - the total will be ur answer for the amount of cardboard!!

p.s don't forget the units!!!

5 0

3 years ago

[10 points] Let v1, v2 and v3 be three linearly independent vectors in R 3 . (a) Find the rank of the matrix A = (v1 − v2) (v2 −

MariettaO [177]

Answer:

The solution and complete explanation for the above question and mentioned conditions is given below in the attached document.I hope my explanation will help you in understanding this particular question.

Step-by-step explanation:

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3 years ago

I will make you brainlist

vichka [17]

Answer:

i think the aswer is b

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers