MATHEMATICS HIGH SCHOOL

The sum of two numbers is 100. The sum of 8 and the larger number is equal to 5 times the smaller number. What is the smaller number?

Answers

Answer 1

Answer:

Answer:

The smaller number is 18

Step-by-step explanation:

Let the numbers be $x$ and $y$ where x is the smaller number; $y\:>\:x$ .

The sum of the numbers is 100.

$x+y=100...(1)$

The sum of 8 and the larger number is equal to 5 times the smaller number.

$y+8=5x$

$\Rightarrow y=5x-8...(2)$

Put equation (2) into equation (1).

$x+5x-8=100$

$x+5x=100+8$

$6x=108$

$x=18$

Answer 2

Answer:

Answer:

The smaller number is 18.

Step-by-step explanation:

We have given that

The sum of two numbers is 100. The sum of 8 and the larger number is equal to 5 times the smaller number.

Let x and y are two numbers.

Let y is the larger number.

x+y = 100 eq(1)

y+8 = 5x eq(2)

From eq(1), we have

y = 100-x

Putting above eq(3) into eq(2), we have

100-x+8 = 5x

108 = 5x+x

108 = 6x

x = 108/6

x = 18

Hence, the smaller number is 18.

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Please what is the vertex and the point of this graph k (×)=[2 (×+4)]^2+3

Answers

The vertex form of a quadratic is given by
y = a(x – h)^2 + k, where (h, k) is the vertex ;
In your case , ( - 4 , 3 ) is the vertex ;

k(x) = 2(x + 4)² + 3
k(x) = 2(x + 4)(x + 4) + 3
k(x) = 2(x² + 4x + 4x + 16) + 3
k(x) = 2(x² + 8x + 16) + 3
k(x) = 2(x²) + 2(8x) + 2(16) + 3
k(x) = 2x² + 16x + 32 + 3
k(x) = 2x² + 16x + 35
2x² + 16x + 35 = 0
x = -(16) +/- √((16)² - 4(2)(35))
2(2)
x = -16 +/- √(256 - 280)
4
x = -16 +/- √(-24)
4
x = -16 +/- 2i√(6)
4
x = -4 + 0.5i√(6)
x = -4 + 0.5i√(6) x = -4 - 0.5i√(6)
k(x) = 2x² + 16x + 35
k(-4 + 0.5i√(6)) = 2(-4 + 0.5i√(6))² + 16(-4 + 0.5i√(6)) + 35
k(-4 + 0.5i√(6)) = 2(-4 + 0.5i√(6))(-4 + 0.5i√(6)) + 16(-4) + 16(0.5i√(6)) + 35
k(-4 + 0.5i√(6)) = 2(16 - 2i√(6) - 2√(6) + 0.25i²√(36)) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 0.25i²(6)) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5i²) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-√(1²)) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-√(1 × 1)) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-√1) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) + 1.5(-1)) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16 - 4i√(6) - 1.5) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 2(16) - 2(4i√(6)) - 2(1.5) - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 32 - 8i√(6) - 3 - 64 + 8i√(6) + 35
k(-4 + 0.5i√(6)) = 32 - 3 - 64 + 35 - 8i√(6) + 8i√(6)
k(-4 + 0.5i√(6)) = 29 - 64 + 35 + 0i√(6)
k(-4 + 0.5i√(6)) = -35 + 35 + 0
k(-4 + 0.5i√(6)) = 0 + 0
k(-4 + 0,5i√(6)) = 0
(x, k(x)) = (-4 + 0.5i√(6), 0)
or
k(x) = 2x² + 16x + 35
k(-4 - 0.5i√(6)) = 2(-4 - 0.5i√(6))² + 16(-4 - 0.5i√(6)) + 35
k(-4 - 0.5i√(6)) = 2(-4 - 0.5i√(6))(-4 - 0.5i√(6)) + 16(-4) - 16(0.5i√(6)) + 35
k(-4 - 0.5i√(6)) = 2(16 + 2i√(6) + 2i√(6) + 0.25i²√(36)) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 0.25i²(6)) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5i²) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-√(1²)) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-√(1 × 1)) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-√(1)) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) + 1.5(-1)) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 2(16 + 4i√(6) - 1.5) - 64 - 8i√(6) + 35
k(-4 - 0.45i√(6)) = 2(16) + 2(4i√(6)) - 2(1.5) - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 32 + 8i√(6) - 3 - 64 - 8i√(6) + 35
k(-4 - 0.5i√(6)) = 32 - 3 - 64 + 35 + 8i√(6) - 8i√(6)
k(-4 - 0.5i√(6)) = 29 - 64 + 35 + 0i√(6)
k(-4 - 0.5i√(6)) = -35 + 35 + 0
f(-4 - 0.5i√(6)) = 0 + 0
f(-4 - 0.5i√(6)) = 0
(x, k(x)) = (-4 - 0.5i√(6), 0)

The point of the graph is (-4 + 0.5i√(6), 0), or (-4 + 0.5i√(6), 0) and (-4 - 0.5i√(6),0). The vertex of the graph is (-4, 3).

Joanne wants to put wallpaper in her daughter's room. Each wall measure 16.8 feet long by 12.9 feet wide. What is the area of one wall in her daughter's bedroom?

Answers

Answer: The area of one wall is 216.72 ft^2.

Step-by-step explanation:

16.8 * 12.9 = 216.72

5x+2y=7
7x+2y=5 i need it right

Answers

I solved it in the image below.

5x+2y=7 7x-2y=5 its subtract not add

Pleaaaaase help!!!!

Answers

Answer:

see below

Step-by-step explanation:

sqrt(20)

sqrt(4*5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(4) sqrt(5)

2 sqrt(5)

Answer:

We can factor down 20 with it's greatest prime GCF, which is 5. We get a 4. When we factor that down the same way, we get 2. If we repeat that process, we get 5, 2, and 2, which turns into $2√(5)$ .

3x^2-7x+4=0 solve for x. Write both solutions separated by a comma

Answers

$Hi \n \n 3x\²-7x+4 ~~--\ \textgreater \ \boxed{(-b\pm √(b\²-2ac) )/(2a) } \n a=3 \n b=-7 \n c=4 \n \n x= (7\pm √((-7)\²-2.3.4 ) )/(2.(3)) \n \n x= (7\pm5)/(6) \begin{cases}x_1= (7+5)/(6)=2 \n \n x_2= (7-5)/(6)= (1)/(3) \end{cases} \n \n \therefore~(2; (1)/(3)) \n \n \n$