5 (a) Write the ratio 15:35 in its simplest form.​

Answer:

(5,-6) is a solution

Step-by-step explanation:

Given

[tex]6x + 3y = 12[/tex]

[tex]4x + y = 14[/tex]

Required

Tell whether (5,-6) is a solution

In (5,-6): x = 5 and y = -6.

Substitute these values in the given equations

[tex]6x + 3y = 12[/tex] becomes

[tex]6 * 5 + 3 * -6 = 12[/tex]

[tex]30-18 = 12[/tex]

[tex]12 = 12[/tex]

[tex]4x + y = 14[/tex] becomes

[tex]4 * 5 - 6 = 14[/tex]

[tex]20 - 6 = 14[/tex]

[tex]14 = 14[/tex]

Because both solutions are true, then (5,-6) is a solution

Answer:

680 girls and 850 boys

Step-by-step explanation:

the ratio of girls is 4/9

then we can find the number of girls (G) in the group of 1530 students using proportions:

4 / 9 = G / 1530

solving for G by multiplying both sides of the proportion by 1530, we get:

G = 4 * 1530 / 9 = 680

So there were:

680 girls and 1530 - 680 = 850 boys

Answer:

the answer will be

girls 680

boys 850

Answer:

[tex]600, 900, 1350[/tex]

Step-by-step explanation:

Given

[tex]a = 400[/tex] -- initial subscribers

[tex]b = 1.5[/tex] -- growth factor

Required

Determine the number of subscribers in the next three months

To do this, we make use of:

[tex]y = ab^x[/tex]

In this case:

x is the number of months

y is the number of subscribers

So:

when x = 1;

[tex]y = ab^x[/tex]

[tex]y = 400 * 1.5^1[/tex]

[tex]y = 400 * 1.5[/tex]

[tex]y = 600[/tex]

when x = 2

[tex]y = 400 * 1.5^2[/tex]

[tex]y = 400 * 2.25[/tex]

[tex]y = 900[/tex]

when x= 3

[tex]y = 400 * 1.5^3[/tex]

[tex]y = 400 * 3.375[/tex]

[tex]y = 1350[/tex]

So, the next three number of subscribers is:

[tex]600, 900, 1350[/tex]

Answer:

x = 3

Step-by-step explanation:

Using the triangle similarity theorem

x/x+3 = x+3/12

Cross multiply

12x = (x+3)(x+3)

12x = x²+3x+3x+9

12x =  x²+6x+9

x²+6x+9-12x = 0

x²-6x+9 = 0

Factorize

x²-3x-3x+9 = 0

x(x-3)-3(x-3) = 0

x - 3 = 0

x = 3 twice

Hence the value of x is 3

Answer:

Beck actually caught 45 fish

Step-by-step explanation:

System of Equations

We call the following variables:

x = number of fish Ally caught

y = number of fish Beck caught

They caught a total of 75 fish, thus:

x + y = 75      [1]

If Ally had caught twice as much fish as she actually did, and Beck had caught three times as many fish as he actually did, then Ally would have caught 75 fewer fish than Beck, thus:

3y = 2x + 75      [2]

From [1]:

x = 75 - y      [3]

Substituting in [2]:

3y = 2(75 - y) + 75

Operating:

3y = 150 - 2y + 75

Simplifying:

5y = 225

Dividing by 5:

y = 45

Beck actually caught 45 fish

Answer:

Beck caught 45 fish

Step-by-step explanation:

a = number of fish Ally caught

b = number of fish Beck caught

They caught a total of 75 fish, so we have:

b + a = 75  

From the facts in our question we know Ally would have caught 75 fewer fish than Beck.

3b = 2a + 75  

a = 75 - b

3b = 2(75 - b) + 75

3b = 150 - 2b + 75

5b = 225

5b ÷ 5 = 225 ÷ 5

b = 45

Beck caught 45 fish.

Answer:

The product of (k + 1) series starts with 3 (because k = 2) and you need 2 to be multiplied to this in order to get (n + 1)!

Therefore you need to multiply 2 and 1/2 to make it right. 2 completes the factorial and 1/2 remains.

Hope it was clear explanation.

Answer:

undefined

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

C its C hopes this helps

Answer:

20

Step-by-step explanation:

you just divid the number of points earned (14), by the percent earned (70). This gives you the total becuase you would divid 14 by the total to get 70.

Answer:

[tex]t = \frac{1}{4}\sqrt d[/tex]

Time to reach 100ft is 2.5 seconds

Step-by-step explanation:

Given

[tex]d = 16t^2[/tex]

Solving (a): Determine the inverse function

[tex]d = 16t^2[/tex]

Swap the positions of d and t

[tex]t = 16d^2[/tex]

Make d the subject

[tex]\frac{t}{16} = d^2[/tex]

Take positive square root of both sides

[tex]\sqrt{\frac{t}{16}} = d[/tex]

[tex]d = \sqrt{\frac{t}{16}}[/tex]

[tex]d = \frac{1}{4}\sqrt t[/tex]

Swap the positions of d and t

[tex]t = \frac{1}{4}\sqrt d[/tex] --- The inverse function

Solving (b): Find t when d =100

Substitute 100 for d in [tex]t = \frac{1}{4}\sqrt d[/tex]

[tex]t = \frac{1}{4}\sqrt {100[/tex]

[tex]t = \frac{1}{4}* 10[/tex]

[tex]t = \frac{1* 10}{4}[/tex]

[tex]t = \frac{10}{4}[/tex]

[tex]t = 2.5[/tex]

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = [tex]\frac{12!}{3! 3! 3! 3!}[/tex]

Now,

The Total number of ways in which Remaining cards are distributed = [tex]\frac{40!}{10! 10! 10! 10!}[/tex]

So,

Total number of ways of getting 3 picture card and remaining card = [tex]\frac{12!}{3! 3! 3! 3!}[/tex]× [tex]\frac{40!}{10! 10! 10! 10!}[/tex]

= [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = [tex]\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }[/tex]

∴ The probability = [tex]\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}[/tex]

                            = [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]×[tex]\frac{(13!)^{4} }{ 52! }[/tex]

                           = [tex]\frac{12! 40!}{(3!)^{4} (10!)^{4} }[/tex]×[tex]\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }[/tex]

                           = [tex]\frac{12!}{(3!)^{4} }[/tex]×[tex]\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}[/tex]

                           = [tex]\frac{479,001,600}{(6)^{4} }[/tex]×[tex]\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}[/tex]

                           = 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

Answer:

ayooo i'll take it

Step-by-step explanation:

thanks

Answer:

Ooh a couple more for 100 points!!

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

sides of triangle measure: 'x', '4x-2' and '4x-2' since isosceles means both legs are equal

perimeter is the sum of all sides, so set up equation:

95 = 4x - 2 + 4x - 2 + x

95 = 8x - 4 + x

95 = 9x - 4

99 = 9x

x = 11

Step-by-step explanation:

2. x =101

3. x= 120

4. x= 30

I am very confused in question no 1 and 5 th .

hope this will be helpful to you.

plz mark my answer as brainlist if you find it useful .

Answer:

Utiliza una cifra que pueda ser resultado de dividir 100:5 y eso a su vez nos dará el valor que debe aumentar en la escala

Step-by-step explanation:

4 + 8 + 3 + 5 + 5 + 7 + 6 + 4 divided 8

42 divided 8

5,25

cmiiw!

Answer: C. 254

Step-by-step explanation: All engineers is the population so this is stats and the number that chose math no matter what kind of engineer is 254

Answer:

Zach time of reading every weekend forms a sequence with these terms: 10, 20, 40, 80. On the other hand, that of Victoria forms a sequence with terms: 35, 50, 65, 80. By keenly observing the sequences, Zach's sequence is a geometric sequence with a common ratio equal to 2 and Victoria's sequence is an arithmetic or linear sequence with a common difference of 15. Thus, the answer is letter B.

Step-by-step explanation:

Answer:

-1.6 < √2 - 3 < -1.5

Step-by-step explanation:

√2  - 3 = -1.58

-1.5 is closer to 0 so it is larger than -1.5 and -1.6 is father from 0 than -1.58 and -1.5 so its less than

Answer:

See Explanation

Step-by-step explanation:

Required

Prove that Dexter is wrong

To prove that Dexter is wrong, we use the following numbers.

[tex]Number = 4[/tex]

The factors are:

[tex]Factor = 1,2\ and\ 4[/tex]

3 factors

Using a greater number:

[tex]Number = 5[/tex]

The factors are:

[tex]Factor = 1\ and\ 5[/tex]

2 factors

From the above analysis:

4 has 3 factors and 5 has 2 factors; which shows that 5 has fewer factors

This shows that Dexter is wrong

Answer:

8 is 10trillion and 7 is 1 million hope this helps!

Step-by-step explanation:

Answer:

f(x) = (1/10)x²

Step-by-step explanation:

This is the answer that  I think it is but I am not sure if it is right...

Hope this helps!

Answer:

No picture so I can’t answer the question

Step-by-step explanation:

Answer:

I believe the answer would be [tex]\sqrt{6}+\sqrt{2}[/tex] or 3.8637

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

A: (-4,1) QUAD 2

B: (-1, -3) QUAD 3

C: (2,5) QUAD 1

D: (5, -4) QUAD 4

Step-by-step explanation:

Answer:

A≈4536.46

Step-by-step explanation:

I hope this helps! ^^

☁️☁️☁️☁️☁️☁️☁️

Answer:

Radius 19

A ≈ 4536.46 .....ans

Answer:

y = 0.8x

Step-by-step explanation:

y = x-0.2x

y=x(1-0.2)

y=x(0.8)

hence y = 0.8x