Order these number in order to least to greatest using less than or greater than signs

The sum of two numbers is 10 and their product is 24. Find the numbers.

irina [24]

Answer:

Step-by-step explanation:

$x,\ y-\text{the numbers}\\\\(1)\qquad x+y=10\\\\(2)\qquad xy=24\\\\==================\\\\(1)\qquad x+y=10\qquad\text{subtract}\ y\ \text{from both sides}\\(*)\qquad x=10-y\\\\\text{Substitute to (2):}\\\\(10-y)y=24\qquad\text{ue the distributive property:}\ a(b+c)=ab+ac\\10y-y^2=24\qquad\text{subtract 24 from both sides}\\-y^2+10y-24=0\qquad\text{change the signs}\\y^2-10y+24=0\\y^2-6y-4y+24=0\\y(y-6)-4(y-6)=0\\(y-6)(y-4)=0\iff y-6=0\ or\ y-4=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6\\\\y-4=0\qquad\text{add 4 to both sides}\\y=4$

$\text{Put the values of}\ y\ \text{to (*)}:\\\\\text{for}\ y=6:\\x=10-6=4\\\\\text{for}\ y=4:\\x=10-4=6$

8 0

4 years ago

To work out the area in m² of material required for a pair of curtains, a seamstress squares the height of the window in m and a

Kisachek [45]

Answer:

a. Area = 1.94m²

b. Area = (p² + 0.5)m²

c. Height = 1.5m

Step-by-step explanation:

Given

Let H represents Height and A represents Area

From the first and second statements, we have that:

$A = H^2 + 0.5$

a. Calculating Area When Height = 1.2

$A = H^2 + 0.5$

Substitute 1.2 for H

$A = 1.2^2 + 0.5$

$A = 1.44 + 0.5$

$A = 1.94$

Hence, the area is 1.94m²

b. Calculating Area When Height = p

$A = H^2 + 0.5$

Substitute p for H

$A = p^2 + 0.5$

Hence, the area is (p² + 0.5)m²

c. Calculating Height When Area = 2.75m²

$A = H^2 + 0.5$

Substitute 2.75 for A

$2.75 = H^2 + 0.5$

Subtract 0.5 from both sides

$2.75 - 0.5 = H^2 + 0.5 - 0.5$

$2.75 - 0.5 = H^2$

$2.25 = H^2$

Take Square Root of both sides

$\sqrt{2.25} = \sqrt{H^2}$

$\sqrt{2.25} = H$

$1.5 = H$

$H = 1.5$

Hence, the height is 1.5m

5 0

3 years ago

What does the slope of the line represent and what does the y-intercept of this function represent? HOW DO YOU GET THIS?!??!!

Gnoma [55]

Slope is the steepness of a line while the y-intercept is the point where the line crosses the y-axis.

6 0

4 years ago

Read 2 more answers

The diagram below shows the construction of the center of the circle circumscribed about .∆ABC.

Igoryamba

the medians to the sides of triangle ABC

4 0

3 years ago

Several shapes are cut out of a piece of cardboard. Two squares of length x, five rectangles of length x and width y and two cir

forsale [732]

The correct question in the attached figure

step 1
calculate the different volumes
a) Volume of prism square base=x*x*y=x²*y
b) Volume of the cylinder=π*(z²)*y

the combined volume of the two figures=[x²*y]+[π*z²*y]

the answer is [y*x²]+[π*y*z²]

6 0

3 years ago