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malfutka [58]
3 years ago
12

Do 5/7 and 30/42 form a proportion

Mathematics
1 answer:
GREYUIT [131]3 years ago
4 0
5/7
6*5/6*7
30/42

30/42 = 30/42

Yes, 5/7 and 30/42 form a proportion.
You might be interested in
Hello, Can someone please explain on how to do this? thank you!
Marrrta [24]
Steps:

1) determine the domain

2) determine the extreme limits of the function

3) determine critical points (where the derivative is zero)

4) determine the intercepts with the axis

5) do a table

6) put the data on a system of coordinates

7) graph: join the points with the best smooth curve

Solution:

1) domain

The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0

=> x > 3 <-------- domain

2) extreme limits of the function

Limit log (x - 3) when x → ∞ = ∞

Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote

3) critical points

dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)

4) determine the intercepts with the axis

x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4

y-intercept: The function never intercepts the y-axis because x cannot not be 0.

5) do a table

 x                          y = log (x - 3)

limit x → 3+            - ∞

3.000000001        log (3.000000001 -3) = -9

3.0001                  log (3.0001 - 3) = - 4

3.1                       log (3.1 - 3) = - 1

4                          log (4 - 3) = 0

13                       log (13 - 3) = 1

103                     log (103 - 3) = 10

lim x → ∞             ∞

Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.
7 0
3 years ago
Read 2 more answers
PLEASE HELP QUICKLY 15 POINTS, WILL MARK BRAINLIEST
zhuklara [117]

Answer:

Binomial expansion also known as binomial theorem is a quick and easy way of expanding by multiplying binomial expression that has been raised to large power.

Step-by-step explanation:

A binomial is a polynomial with two terms. From the above definition given, if for instance an expression of (5x-4)²² was given, it wouldn't be that easy to multiply out by hand which is why the binomial theorem formula was created.

Another example to buttress this point is if we have (a³+2ab+b2)(a+b) expanding this will give a³+3a2b+b³ = a³+3a2b) +3ab²+b³)a+b = a⁴+ 4a³b+ 6a²b²+4ab³+b4..

This calculation could go on and on because it gets longer as we go but to make it easier and simpler, the best method to use here is the binomial theorem or expansion and the formula states thus:

n. n

(x+y)ⁿ = € {n}xⁿ-k*y^k

k=0 {k} = € {n} x^k*y^n-k

k=0 {k}

{n}

{k}. = binomial coefficient of each term

It should from the example given that we have index power(power raised)called exponent such that when an exponent is 0, we get 1 , i.e anything raised to power 0 =1

e.g (x+y)^0 = 1

And also when an exponent is 1, then the answer remain unchanged such that (x+y)¹= x+y. An exponent of 2 means to multiply given term by itself in two times and so on.

So to expantiate an expression like

a³+3a²b+3ab²+b³.. This expression has its index power(exponent) start with 3 such that .

The a goes down in the form.. 3,2,1,0 while the exponents of b go upwards in the form 0,1,2,3coeffiThe terms 0-n goes thus

k=0 k=1 k=2 k=3

a³ a² a 1

1 b. b² b³

which equals an-kbk.. This is confusing right. This is how it works

k=0 k=1 k=2 k= 3

an-kb^k. an-kb^k an-kb^k an-k^bk

a³-0b^0. a3-1b¹ a3-2b2 a3-3b3

a³ a²b. ab² b³

So when we put all this together we have: a³+a²b+ ab²+ b³. Actually this answer is correct but what we are missing here is the coefficient of n because we needs to include it.

So this becomes a³+3a²b +3ab²+b³ , the coefficient of n here is 3.

Now if we are to look at the result we got before from(a+b)^0 up to (a+b)³

And here that we have 3 as coefficient but where it is not shown we put 1 which is.

1

1a+ 1b

1a+2ab+ 1b²

1a³ +3a²b+3ab²+1b³... We solve this using pascal triangle.

1 This is solved by adding

1 1 each two numbers above

1 2 1 together to get the one

1 3 3 1 below.

1 4 6 4 1

This pascal pattern can be used for any exponents..1,2,3,5....60...120....n

Binomial theorem is basically the essence of this Pascal triangle pattern.

As stated earlier that the formula of binomial theorem is

n

€{n}a^n-kb^k

n-1 where €= summation

n= numbers given

k=coefficient of n

Now, let's to put into practical by solving this expression.

(x+y)ⁿ=€ⁿ {n}a^n-k* b^k

k=0 {k}

But before we solve this, its important we know the basis of Pascal triangle by using factorial to solve it with the formula n!/k!(n-k)! Such that

Factorial is n multiplied in descending order(i.e multiplying Numbers between 1-n)

K- coefficient of n

N- product of all the numbers between 1&n. For instance we are given this 4!/3!(4-3)! = 4!/3!*1!

= 4*3*2*1/3*2*1 *1 = 24/6 = 4

Now let's go back to the previous example of (x+y)ⁿ where n=4

(x+y)⁴= €⁴ {4} x^4-k*y^k

k=0 {k}

(x+y)⁴= €{4} (x^4-0)y^0 + {4} (x^4-1) *y¹

{0} {1}

+{4} (x^4-2)*y² + {4} (x^4-3)*y³

{2} {3}

+ {4} (x^4-4) * (y⁴)

{4}

= 1*x⁴y^0 + 4*x³y¹ + 6*x²y² +4*x¹y³ +1*x^0y⁴=

x⁴+4x³y +6x²y² + 4xy³ +y⁴(Final answer)

Please note that:

When solving binomial theorem expression, the easiest way to do this is by remembering the patterns below:

* first term's exponent start at n and go down

* second term's exponent start at 0 and goes up

* coefficient are solved with pascal triangle using n!/k!(n-k)!

5 0
2 years ago
Use the cofunction identities to find an angle x that makes each statement true.
Gekata [30.6K]

Answer:

x=20

Step-by-step explanation:

sin¢=cos90-¢

therefore; 3x-15+x+25=90

4x+10=90

4x=90-10=80

x=20

7 0
2 years ago
Read 2 more answers
I need help with this, I've never really understood linear stuff.
KonstantinChe [14]

You have several possible points (x,y). Any point that lies on the given line will have a y value that you obtain by plugging in the corresponding value of x into the equation of the line.

The line has equation y=-3x+7, so any point on the line will have the form (x,-3x+7).

Among the four given points, there are only 2 different values of x to check. We have

x=4\implies y=-3(4)+7=-12+7=-5

x=1\implies y=-3(1)+7=-3+7=4

which means the given line contains the points (4, -5) and (1, 4). So the answer is A.

4 0
3 years ago
Read 2 more answers
I have a question?.....Ms. Wallace makes soap to sell at craft fairs. The first bar of soap sells for $2, and each additional ba
Assoli18 [71]

Answer:

Has your teacher given you notes to practice?

Step-by-step explanation:

If no, then break the question down into pieces and write down what you know.

3 0
2 years ago
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