MATHEMATICS HIGH SCHOOL

Abcd is a rectangle. Find the length of each diagonal. .AC= 3y/5 BD=3y-4

Answers

Answer 1

Answer:

Answer:

AC = BD = 1 unit

Step-by-step explanation:

Given : length of diagonal of rectangle ABCD $AC=(3y)/(5)$ and $BD=3y-4$

We have to find the length of diagonal.

We know In rectangle diagonal are of equal lengths.

Therefore, for rectangle ABCD diagonals AC= BD

Substitute the values, we get,

$(3y)/(5)=3y-4$

Cross multiply , we get

$3y=5(3y-4)$

On simplyfy , we get

$3y=15y-20$

Solve for y , we get

$15y-3y=20$

$12y=20$

Divide both side by 12, we get,

$y=(20)/(12)=(10)/(6)$

Thus, put the values of y in AC and BD to find the length of diagonals , we get,

$AC=(3y)/(5)=(3)/(5)*(10)/(6)=1$

Similarly for BC, we get,

$BD=3y-4=3((10)/(6))-4=5-4=1$

Thus, AC = BD = 1 unit

Answer 2

Answer: I hope this helps you

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The incorrect work of a student to solve an equation 2(y + 8) = 4y is shown below:Step 1: 2(y + 8) = 4y Step 2: 2y + 10 = 4y Step 3: 2y = 10 Step 4: y = 5 Which of the following explains how to correct Step 2 and shows the correct value of y? The equation should be y + 8 = 4y after division by 2; y = 4 The equation should be y + 8 = 4y after division by 2; y = 6 2 should be distributed as 2y + 16; y = 4 2 should be distributed as 2y + 16; y = 8

$2.50 per square foot. how much is that per square yard?

Answers

1 yard is 3ft, so just multiply 2.5 with 3 and that gives u 7.5.

Hello,

1yd=3ft ==>(1yd)²=(3ft)²=9ft² cost $2.5*9=$22.5

if the measure of angle one is "two-x minus nine" and the measure of angle two is "twenty seven minus four-x", solve for x.

Answers

$7x-9=27-4x\n\n7x+4x=27+9\n\n11x=36\ \ \ \ /:11\n\nx=(36)/(11)\n\nx=3(3)/(11)$

which has more volume a cube of sides measuring 4 units each or a sphere with a radius of 3 units

Answers

V cube = 4^3 = 64 $cm^(3)$
V sphere = 4*π*3^3/3 = 4*π*9 = 36*π≈113 $cm^(3)$
V sphere > V cube.

Solve for x. 3x^2-4x-2=0

Enter your simplified answers, as exact values, in the boxes

Answers

ANSWER

$x=\frac{2-√(10)} {3}$

or

$x=\frac{√(10)+2} {3}$

We have

$3x^2-4x-2=0$

Since we cannot factor easily, we complete the square.

Adding 2 to both sides give,

$3x^2-4x=2$

Dividing through by 3 gives

$x^2-(4)/(3)x= (2)/(3)$

Adding $(-(2)/(3))^2$ to both sides gives

$x^2-(4)/(3)x+(-(2)/(3))^2= (2)/(3)+(-(2)/(3))^2$

The expression on the Left Hand side is a perfect square.

$(x-(2)/(3))^2= (2)/(3)+(4)/(9)$

$\Rightarrow (x-(2)/(3))^2= (10)/(9)$

$\Rightarrow (x-(2)/(3))=\pm \sqrt{(10)/(9)}$

$\Rightarrow (x)=(2)/(3) \pm {(√(10))/(3)$

Splitting the plus or minus sign gives

$x=\frac{2- √(10)} {3}$

or

$x=\frac{√(10)+2} {3}$

Answer:

$x = (2)/(3) + (√(10) )/(3) , x = (2)/(3) - (√(10) )/(3)$

Step-by-step explanation:

Multiplying the coefficient of x by the constant to get:

3 x (-2) = -6

Find factors of -6 that equal the middle term -4.

Since, no such factors can be found so we can solve the equation by completing the square.

To complete the square, divide the equation by the coefficient of x^2 which is 3 to get:

$x^(2) - (4)/(3) x - (2)/(3) = 0$

$x^(2) - (4)/(3) x = (2)/(3)$

Now divide the coefficient of x by 2 and add the square of the result to both sides of the equation:

$x^(2) - (4)/(3) x + (-(2)/(3) )^(2) = (2)/(3) + (-(2)/(3) )^(2)$

$(x - (2)/(3) )^2 = (2)/(3) + (4)/(9)$

$(x - (2)/(3) )^2 = (4)/(9)$

$\sqrt{(x - (2)/(3) )^2} = \sqrt{(4)/(9) }$

$x - (2)/(3) = \sqrt{(10)/(9) }$ , $x - (2)/(3) = -\sqrt{(10)/(9) }$

$x = (2)/(3) + (√(10) )/(3) , x = (2)/(3) - (√(10) )/(3)$

What property does the statement show? ( 4 x 8 ) x 3 = ( 4 x 4 ) x 3

Answers

Answer: Associative property of multiplication.

Step-by-step explanation:

The property demonstrated by the statement "(4 x 8) x 3 = (4 x 4) x 3" is the associative property of multiplication.

The associative property of multiplication states that you can change the grouping of numbers in a multiplication expression without changing the result. In this case, both sides of the equation involve multiplication, and the numbers being multiplied are grouped differently but still yield the same result.

commutative property of multiplication

Example 1:For the function f(x) = x + 4, what is the ordered pair for the point on the graph when x = 3p?

Example 2:
If g(x) = 3(x − 2), find the value of x if g(x) = 6

The question is what is F(1) , what dose it equal?
@taskmasters @ShootingStar28 @ayah1

Answers

Simply substitute x by its value:

1)
f(x) = x + 4 ; x = 3p f(x) = x + 4 ;
f(3p) = 3p + 4 f(1) = 1 + 4
f(1) = 5
x = 3p (1,5)
y = 3p + 4

2) g(x) = 3(x-2) g(x) = 3(x-2)
g(x) = 6 g(1) = 3(1-2)
g(1) = 3 - 6
6 = 3x - 6 g(1) = -3
6+6 = 3x (1,-3)
12 = 3x
x = 4
g(4) = 3(4-2)
g(4) = 12 - 6
g(4) = 6

x = 4
y = 6

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