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3 years ago

Lucy wants to make a table top pad for a square table that has a side of 3 feet. What is the area of the pad?

Mathematics

2 answers:

Butoxors [25]3 years ago

8 0

9 sq. ft.
because 3x3=9 as its a square

Sloan [31]3 years ago

4 0

Hey there!

3x3=9

the area is 9feet

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WARRIOR [948]

Answer:

$2\,(x-1)^2=4$

which is the first option in the list of possible answers.

Step-by-step explanation:

Recall that the minimum of a parabola generated by a quadratic expression is at the vertex of the parabola, and the formula for the vertex of a quadratic of the general form:

$y=ax^2+bx+c$

is at $x_{vertex}=\frac{-b}{2\,a}$

For our case, where $a=2\,\,, b=-4\,\,,\,\,and \,\,c=-2$ we have:

$x_{vertex}=\frac{-b}{2\,a}\\x_{vertex}=\frac{4}{2\,*\,2}\\x_{vertex}=1$

And when x = 1, the value of "y" is:

$y(x)=2x^2-4x-2\\y(1)=2(1)^2-4(1)-2\\y(1)=2-6\\y(1)=-4\\y_{vertex}=-4$

Recall now that we can write the quadratic in what is called: "vertex form" using the coordinates $(x_{vertex},y_{vertex)$ of the vertex as follows:

$y-y_{vertex}=a\,(x-x_{vertex})^2$

Then, for our case:

$y-(-4)=2\,(x-1)^2\\y=2\,(x-1)^2-4$

Then, for the quadratic equal to zero as requested in the problem, we have:

$y=2\,(x-1)^2-4=0\\2\,(x-1)^2-4=0\\2\,(x-1)^2=4$

5 0

3 years ago

Of the 423 students entering as freshmen at a small liberal arts school, 1 out of 3 will be participating in

Allisa [31]

Answer:

About 141 students would attend.

Step-by-step explanation:

423/3=141

4 0

1 year ago

Determine the converse of the conditional statement: If the lengths of the sides of a rectangle are 6 inches and 4 inches, the a

nlexa [21]

Answer:

If the area is 24 square inches, the lengths of the sides of a rectangle are 6 inches and 4 inches.

Step-by-step explanation:

If the lengths of the sides of a rectangle are 6 inches and 4 inches, the area is 24 square inches.

converse switches the statements

If the area is 24 square inches, the lengths of the sides of a rectangle are 6 inches and 4 inches.

5 0

3 years ago

a salesperson earns 9 commission on sales.the equation for the amount he or she earns in commission is c = 0.9s, where s is the

NNADVOKAT [17]

Answer:

c = $5,400

Step-by-step explanation:

Given:

c = 0.9s

where,

s = amount sold

c = commission on sales

How much commission will he or she earn if the amount sold is $6,000?

Find c when she = $6,000

c = 0.9s

= 0.9 × 6,000

= 5,400

c = $5,400

(c, s) (5400, 6000)

3 0

3 years ago

Solve the equation using the quadratic formula : x^2-10x+25=18

Sever21 [200]

$x^2-10x+25=18 \\ \\x^2-10x+25-18 = 0\\ \\ x^2-10x+ 7 =0 \\ \\a=1 , b = -10 , c= 7 \\ \\ \Delta = b^{2}-4ac = (-10)^{2}-4*1*7=100-28 = 72 \\ \\\sqrt{\Delta }=\sqrt{72}= \sqrt{2*36} =\sqrt{36}*\sqrt{2} =6\sqrt{2}$

$x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{10- 6\sqrt{2}}{2}=\frac{2(5-3\sqrt{2})}{2}= 5-3\sqrt{2}\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{10+ 6\sqrt{2}}{2}=\frac{2(5+3\sqrt{2})}{2}= 5+3\sqrt{2}$

$Answer : \ x= 5-3\sqrt{2} \ \ or \ \ x = 5+3\sqrt{2}$

8 0

3 years ago