MATHEMATICS HIGH SCHOOL

Angie has some red and blue beads. 40% of her beads were red. When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. How many beads did Angie have in the end?

Answers

Answer 1

Answer:

Step-by-step explanation:

Let x represent the total number of red and blue beads

Angie has some red and blue beads. 40% of her beads were red. This means that the total number of red beads is

40/100 × x = 0.4x

The number of blue beads would be

x - 0.4x = 0.6x

When she lost 50 blue beads, the number of blue beads was reduced by 1/3 its original number of beads. This means that

0.6x - 50 = 0.6x - 0.6x/3

0.6x - 50 = 0.6x - 0.2x = 0.4x

0.6x - 0.4x = 50

0.2x = 50

x = 50/0.2 = 250

The number of blue beads that Angie had initially is

0.6 × 250 = 150

The number of blue beads that Angie has left is

150 - 50 = 100 beads

The number of beads that Angie has in the end is

250 - 50 = 200 beads

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What is the prime factorization of 120? A.

22 • 3 • 5

B.

23 • 3 • 5

C.

23 • 5

D.

24 • 3

Answers

A is the answer hdndnbdbfb

he prime factorization of 120 is 2*2*2*3*5 .

it is 10 3\5 miles from Alston to Barton and 12 1/2 from Barton to Chester.the distance from Alston to Durban,via BARTON and Chester,is 35 miles.how far is it from Chester to Durban.

Answers

Answer:

Distance from Chester to Dublin is $11(9)/(10)$ miles

Step-by-step explanation:

Given :

Distance from Alston to Barton (A to B)= $10(3)/(5)=(53)/(5)$ miles

Distance from Barton to Chester (B to C)= $12(1)/(2)=(25)/(2)$ miles

Distance from Alston to Dublin via Barton and Chester(A to D) = 35 miles

Let the distance from Chester to Durban(C to D) = x

Refer the attached figure.

Therefore,

Total distance(A to D)= distance (A to B)+distance (B to C)+distance (C to D)

Putting values , we get

$35=(53)/(5)+(25)/(2)+x$

$35-(53)/(5)-(25)/(2)=x$

$35-10.6-12.5=x$

$11.9=x$

or $x=11(9)/(10)$

Distance from Chester to Dublin is $11(9)/(10)$ miles.

Final answer:

To find the distance from Chester to Durban, add the distances from Alston to Barton and Barton to Chester, and subtract this total from the given distance from Alston to Durban.

Explanation:

To find the distance from Chester to Durban, we need to determine the distance from Alston to Durban. We can start by finding the distance from Alston to Chester by adding the distances from Alston to Barton and from Barton to Chester. The total distance is 10 3/5 miles + 12 1/2 miles = 23 1/10 miles. Now, to find the distance from Alston to Durban, we subtract this total distance from the given distance from Alston to Durban via Barton and Chester: 35 miles - 23 1/10 miles = 11 9/10 miles. Therefore, it is 11 9/10 miles from Chester to Durban.

Learn more about Distance Calculation here:

brainly.com/question/34212393

#SPJ3

Which of the following is equivalent to 6x 2 + x - 12 ?A. (2x + 3)(3x - 4)
B. (2x - 3)(3x - 4)
C. (2x + 3)(3x + 4)
D. (6x + 3)(x - 12)
E. (x + 3)(2x - 12)
Please show me step by step how to solve this problem
Thanks

Answers

$6x^2+x-12=6x^2-9x+8x-12=3x(2x-3)+4(2x-3)\n\n=(2x-3)(3x+4)\n\nother\ method:\n\n6x^2+x-12\na=6;\ b=1;\ c=-12\n\Delta=b^2-4ac\to\Delta=1^2-4\cdot6\cdot(-12)=1+288=289\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(289)=17$

$x_1=(-1-17)/(2\cdot6)=(-18)/(12)=-(3)/(2);\ x_2=(-1+17)/(2\cdot6)=(16)/(12)=(4)/(3)\n\n6x^2+x-12=6(x+(3)/(2))(x-(4)/(3))=2\cdot3(x+(3)/(2))(x-(4)/(3))\n\n=2(x+(3)/(2))\cdot3(x-(4)/(3))=(2x+3)(3x-4)$

A salesman makes 5% commission on sales. What is his commission on $4,321 worth of sales?

Answers

So all you have to do here is,

Whats 5% of 4321

Witch = $216.05

He make $216.05 in commission

What's the game called thFind the volume of a cube whose surface area is 294 m2.at the kids are playing without August knowing?

Answers

Answer:

294cm² is the total area of the cube

area = 6c²

cubic side = 294/6c²

c²= 294/6=49

cubic side = √49=7m

the volume of the cube =c^3

Vcubed =7^3=343m^3

for the rest I don't know the game

Step-by-step explanation:

Expand and simplify: 1.(n-2)(3n+7)+2n(2n+3)

factor each expression fully:
2. 4xsquared-25

Answers

$1.\n(n-2)(3n+7)+2n(2n+3)\n\n=n\cdot3n+n\cdot7-2\cdot3n-2\cdot7+2n\cdot2n+2n\cdot3\n\n=3n^2+7n-6n-14+4n^2+6n\n\n=7n^2+7n-14$

==============================================================

$2.\n4x^2-25=(2x)^2-5^2=(2x-5)(2x+5)$

1.(n-2)(3n+7)+2n(2n+3)
We'll start with (n-2)(3n+7)
Use the FOIL method to simplify: First, Outside, Inside, Last.
Multiply the first numbers of each bracket (n and 3n), the outside numbers (n and 7), the inside numbers (-2 and 3n) and the last numbers (-2 and 7)
F= 3n×n= 3n²
O= n×7= 7n
I= -2×3n= -6n
L= -2×7= -14
Add them together, you get 3n² + n -14.
The second part is 2n(2n+3)
Multiply both numbers inside the bracket by 2n
2n×2n= 4n²
3×2n= 6n
Add these terms with the previous ones
7n² + 7n -14
Because they all have a common factor of 7, we can represent the equation as
7(n² + n -2)

2. 4x²-25
To factor this, we convert it into two expressions that we multiply together (like converting -9 into 3×-3)
2x × 2x= 4x²
5 × -5= -25
The answer is (2x+5)(2x-5)

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