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3 years ago

What is the nearest perimeter of rectangle ABCD, to the nearest tenth?

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

Answer: B

Step-by-step explanation:

Perimeter = 2(length+width)

'CD' = 20×cos(30) = 17.3205

width 'AD' = 20×cos(60) = 10

Perimeter = 2(17.3205+10)

= 2(27.3205)

= 54.641 =54.6

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Ken has a rectangular shaped vegetable garden that is 15 feet by 9 feet. He would like to increase the length and width by the s

tigry1 [53]

The current area is 15 x 9 = 135 square feet.

He wants to increase both the length and width by X:

Set up an equation:

(15 +x) * (9 +x) = 135 * 2

Simplify :

x^2 + 24x + 135 = 270

Subtract 270 from both sides:

x^2 + 24x - 135 = 0

Use the quadratic formula to solve for x:

-24 +/- √(24^2 - 4(1*-135) / 2*1

x = 4.7 or -28.7

The answer has to be a positive value, so x = 4.7 feet.

8 0

3 years ago

Which quadratic equation has roots –2 and 1/5?

AysviL [449]

Answer:

The equation $5x^2\:+\:9x\:-\:2\:=\:0$ has roots –2 and 1/5.

Hence, the option 'a' is the correct answer.

Step-by-step explanation:

Checking the equation

$5x^2\:+\:9x\:-\:2\:=\:0$

putting x = -2 in the equation

$5\left(-2\right)^2\:+\:9\left(-2\right)-\:2\:=\:0\:$

$2^2\cdot \:\:5-9\cdot \:\:2-2=0$

$2^2\cdot \:5-18-2=0$

$20-20=0$

$0=0$

L.H.S=R.H.S

putting x = 1/5 in the equation

$5\left(\frac{1}{5}\right)^2\:+\:9\left(\frac{1}{5}\right)-\:2\:=\:0\:$

$5\left(\frac{1}{5}\right)^2+9\cdot \:\frac{1}{5}-2=0$

$\frac{1}{5}+\frac{9}{5}-2=0$

$2-2=0$

$0=0$

L.H.S=R.H.S

As putting x = -2 and x = 1/5 satisfy the equation.

Therefore, the equation $5x^2\:+\:9x\:-\:2\:=\:0$ has roots –2 and 1/5.

Hence, the option 'a' is the correct answer.

4 0

3 years ago

Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.) Center at the origin

Elanso [62]

Answer:

The equation of circle is $x^2+y^2=65$ .

Step-by-step explanation:

It is given that the circle passes through the point (8,1) and center at the origin.

The distance between any point and the circle and center is called radius. it means radius of the given circle is the distance between (0,0) and (8,1).

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula the radius of circle is

$r=\sqrt{\left(8-0\right)^2+\left(1-0\right)^2}=\sqrt{65}$

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$ .... (1)

where, (h,k) is center and r is radius.

The center of the circle is (0,0). So h=0 and k=0.

Substitute h=0, k=0 and $r=\sqrt{65}$ in equation (1).

$(x-0)^2+(y-0)^2=(\sqrt{65})^2$

$x^2+y^2=65$

Therefore the equation of circle is $x^2+y^2=65$ .

5 0

3 years ago

Twenty percent of 150 is

Svetlanka [38]

20% of 150 is 30

Change the percentage into a decimal by dividing it over 100:

20 / 100 = 0.2

Multiply:

0.2 × 150 = 30

6 0

3 years ago

The local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16 bikes in the bike racks. What expression shows t

Step2247 [10]

44 that's a tricky question at first i thought it was -1 lol

5 0

3 years ago