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3 years ago

Will you help me?

Mathematics

1 answer:

Volgvan3 years ago

8 0

Answer:

The length side of the original square banner was 9 ft

Step-by-step explanation:

Let

x-----> the length side of the original square banner

we know that

The new area of the banner is equal to

$91=(x+4)(x-2)$

Solve for x

$91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0$

Solve the quadratic equation by graphing

The solution is x=9 ft

see the attached figure

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What is 2 times 2 times 2 times 2?

kolezko [41]

The answer 16 (sixteen)

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3 years ago

Read 2 more answers

Which point lies on a circle with a radius of 5 units and center at P(6,1)?

ryzh [129]

Answer:

Option B. $R(2,4)$

Step-by-step explanation:

we know that

If a ordered pair lie on the circle. then the ordered pair must satisfy the equation of the circle

step 1

Find the equation of the circle

we know that

The equation of the circle in center radius form is equal to

$(x-h)^{2}+(y-k)^{2}=r^{2}$

where

r is the radius of the circle

(h,k) is the center of the circle

substitute the values

$(x-6)^{2}+(y-1)^{2}=5^{2}$

$(x-6)^{2}+(y-1)^{2}=25$

step 2

Verify each case

case A) $Q(1, 11)$

substitute the value of $x=1, y=11$ in the equation of the circle and then compare the results

$(1-6)^{2}+(11-1)^{2}=25$

$25+100=25$ ------> is not true

therefore

the ordered pair Q not lie on the circle

case B) $R(2,4)$

substitute the value of $x=2, y=4$ in the equation of the circle and then compare the results

$(2-6)^{2}+(4-1)^{2}=25$

$16+9=25$ ------> is true

therefore

the ordered pair R lie on the circle

case C) $S(4,-4)$

substitute the value of $x=4, y=-4$ in the equation of the circle and then compare the results

$(4-6)^{2}+(-4-1)^{2}=25$

$4+25=25$ ------> is not true

therefore

the ordered pair S not lie on the circle

case D) $T(9,-2)$

substitute the value of $x=4, y=-4$ in the equation of the circle and then compare the results

$(9-6)^{2}+(-2-1)^{2}=25$

$9+9=25$ ------> is not true

therefore

the ordered pair T not lie on the circle

7 0

3 years ago

-10x + 3(8 + 8) = -6(x -4)

Tpy6a [65]

-10x + 48 = -6x+24
48 - 24 = -6x + 10x
24 = 4x
x = 24/4
x = 6

7 0

4 years ago

In FGH, the measure of H=90°, HF=91 feet, and GH = 50 feet. Find the measure of F to the nearest degree.

Rudik [331]

Given:

The angle of H=90°, HF=91 feet, and GH = 50 feet.

The objective is to find the measure of angle F.

In the given right angled triangle, the side opposite to the requierd angle is called opposite side, and the other smaller side is called adjacent side.

The trigonometry formula which relates with the opposite and adjacent side is,

$\tan \theta=\frac{opposite}{adjacent}$

Now substitute the value of opposite and adjacent in the above formula to find the value of angle F.

$\begin{gathered} \tan \theta=\frac{50}{91} \\ \theta=\tan ^{-1}(0.549) \\ \theta=28.787^0 \\ \theta\approx29^0 \end{gathered}$

Hence, the value of angle F is 29 degree.

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1 year ago

Convert the polar representation of this complex number into its standard form z=4(cos150+isin150).

Katen [24]

Answer:

Step-by-step explanation:

Using the exact values

cos150° = - cos30° = - $\frac{\sqrt{3} }{2}$

sin150° = sin30° = $\frac{1}{2}$

Given

z = 4(cos150° + isin150° ) , substitute values

= 4(- $\frac{\sqrt{3} }{2}$ + $\frac{1}{2}$ i )

= - 2 $\sqrt{3}$ + 2i , that is

(- 2 $\sqrt{3}$ , 2 ) → B

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3 years ago