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1 year ago

24 red flowers and 18 white flowers will be equally divided into groups. Find the greatest number of groups that can be created

Mathematics

1 answer:

mariarad [96]1 year ago

4 0

Given:

The number of red flowers =24

The number of white flowers = 18

As flowers divided equally.

$\begin{gathered} 24=4\times6 \\ 18=3\times6 \end{gathered}$

The HCF ( highest common factor) of 24 and 18 is 6.

The largest number of group that can be created is 6.

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the equation is -2x² = 4-3 (x + 1) and the question is justify that it is a 2nd degree equation with the unknown x complete.

Serggg [28]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

-2x² = 4-3 (x + 1)

-2x² = 4-3x-3

-2x² = -3x -7

0 = 2x² -3x -7

We know that the degree of the equation is the highest power of x variable in the given equation.

In the equation 0 = 2x² -3x -7 the highest power of x variable in the given equation is 2.

Thus, the degree of the equation is 2.

Also in the equation 0 = 2x² -3x -7, the unknown variable is 'x'.

Let us determine the value 'x'

2x² -3x -7 = 0

Add 7 to both sides

$2x^2-3x-7+7=0+7$

$2x^2-3x=7$

Divide both sides by 2

$\frac{2x^2-3x}{2}=\frac{7}{2}$

$x^2-\frac{3x}{2}=\frac{7}{2}$

Add (-3/4)² to both sides

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{7}{2}+\left(-\frac{3}{4}\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{65}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{65}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solving

$x-\frac{3}{4}=\sqrt{\frac{65}{16}}$

$x-\frac{3}{4}=\frac{\sqrt{65}}{\sqrt{16}}$

$x-\frac{3}{4}=\frac{\sqrt{65}}{4}$

Add 3/4 to both sides

$x-\frac{3}{4}+\frac{3}{4}=\frac{\sqrt{65}}{4}+\frac{3}{4}$

$x=\frac{\sqrt{65}+3}{4}$

similarly solving

$x-\frac{3}{4}=-\sqrt{\frac{65}{16}}$

$x=\frac{-\sqrt{65}+3}{4}$

So the solution of the equation will have the values of x such as:

$x=\frac{\sqrt{65}+3}{4},\:x=\frac{-\sqrt{65}+3}{4}$

6 0

3 years ago

Pls Help asap thx alot

Novosadov [1.4K]

Answer: 52.5cm²

Step-by-step explanation:

Firs, you have to split this composite shape into two separate shapes; a rectangle and triangle.

To work out the area of the rectangle you would have to do 8x5=40.

To work out the area you would have to find out the height of it first. So, to do this you would have to do 1+2=3 then do 8-3=5. Now we know the height is 5.

Then you have to use the formula base times height divided by 2 (b×h/2). So 5×5=25 then 25÷2=12.5

To then find the total area of this composite shape you would have to add the two areas together. So 40+12.5=52.5cm²

Hope this helps :)

5 0

3 years ago

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

balandron [24]

Here you have 2 linear equations and are to solve this system. Both equations have already been solved for y, so you can set one of them = to the other one:

-2x+11 = -3x+21.

Then 3x-2x = 21 - 11, or x = 10 (answer)

Find y by subst. x = 10 into either of the given equations.

Solution is then (10, ? )

7 0

4 years ago

Find a polynomial with integer coefficients, with leading coefficient 1, degree 5, zeros i and 5- i, and passing through the ori

V125BC [204]

For a polynomial with real cofieints, if a+bi is a root, a-bi is also a root

zeros, i and 5-i

passes through origin means 0 is also a zero

get plus and minus of the roots

i, -1, 5-i, 5+i and 0 are roots

for a poly with roots, r1,r2,r3,r4,r5, the facotred form is

(x-r1)(x-r2)(x-r3)(x-r4)(x-r5)

sub the roots

(x-i)(x-(-i))(x-(5-i))(x-(5+i))(x-0)=

(x-i)(x+i)(x-5+i))(x-5-i))(x)=

x(x^2+1)(x^2-10x+26)=

x^5-10x^4+27x^3-10x^2+26x

the polynomial is f(x)=x^5-10x^4+27x^3-10x^2+26x

8 0

4 years ago

How many circles with a 3ft radius could fill a 100 square foot (10ft x 10ft) space without overlap?

Alborosie

Answer:

Step-by-step explanation:

Considering that the circle has radius of 3ft to mean its diameter is twice the radius hence 6 ft

Given that the length of the square is 10 ft

10÷6=1 ⅔ hence only 1 circle

10-6=4 ft

The space of 4ft can't allow another circle to fit without an overlap. Therefore, only one circle can fit

4 0

4 years ago