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DENIUS [597]
3 years ago
12

What is -X - 29 = 15 - 3x

Mathematics
2 answers:
Inessa05 [86]3 years ago
5 0

Answer: x = 22

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Damm [24]3 years ago
5 0

Answer:

x =22

Step-by-step explanation:

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Find the area of each regular polygon. Round your answer to the nearest tenth if necessary​
Gnesinka [82]

Answer:

Step-by-step explanation:

13). Area of a square = (Side)²

                                   = (BC)²

     Since, diagonals of a square bisect each other at 90°,

     ΔBOC is a right triangle.

     By applying Pythagoras theorem in the given triangle,

     BC² = OB² + OC²

     BC² = 2(OB)²

     BC² = 2(7√2)²

     BC = \sqrt{196}

     Area of square ABCD = (BC)²

                                          = (√196)²

                                          = 196 units²

14). Measure of interior angles of the regular hexagon = 120°

     Area of the regular hexagon = \frac{3\sqrt{3}}{2}(\text{side})^2

      From the given picture,

      m∠BAC = m∠ABC = m∠ACB = 60°

      Therefore, ΔABC is an isosceles triangle.

      And all sides of this triangle will be equal in measure.

      AB = AC = BC = 9 units

      Area of the given regular hexagon = \frac{3\sqrt{3}}{2}(9)^2

                                                                 = 210.44 square units

                                                                 ≈ 210.4 square units

5 0
3 years ago
Two vertical poles of heights 60 ft and 80 ft stand on level ground, with their bases 100 ft apart. A cable that is stretched fr
Andreyy89

Answer:

Step-by-step explanation:

Given

height of two Poles are 60 and 80 ft

Distance between them is 100 ft

Let x be the distance of Pole of ht 80 ft from Point of stretch

thus length of rope is given by

L=L_1+L_2

L_1=\sqrt{80^2+x^2}

L_2=\sqrt{60^2+(100-x)^2}

L=\sqrt{80^2+x^2}+\sqrt{60^2+(100-x)^2}

differentiate w.r.t x we get

\frac{\mathrm{d} L}{\mathrm{d} x}=\frac{2x}{2\sqrt{80^2+x^2}}-\frac{2\left ( 100-x\right )}{\sqrt{60^2+\left ( 100-2x\right )^2}}

Put \frac{\mathrm{d} L}{\mathrm{d} x}=0 to get minimum value

\frac{2x}{2\sqrt{80^2+x^2}}=\frac{2\left ( 100-x\right )}{\sqrt{60^2+\left ( 100-2x\right )^2}}

squaring

x^2\left ( (100-x)^2+60^2\right )=(100-x)^2(80^2+x^2)

Rearranging

28x^2-1800x+640000=0

x=\frac{400}{7}

thus L_1=98.312 ft

L_2=73.73 ft

L=172.04 ft  

7 0
3 years ago
A manufacturer of shipping boxes has a box shaped like a cube. The side length is  (5a + 4b). What is the volume of the box in t
SVETLANKA909090 [29]

Answer:

125a^3 + 300a^2b + 240ab^2 + 64b^3

Step-by-step explanation:

The volume of a cube is the cube of the side length.

V = s^3

Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.

V = (5a + 4b)^3

V = (5a + 4b)(5a + 4b)(5a + 4b)

V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)

V = (25a^2 + 40ab + 16b^2)(5a + 4b)

V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3

V = 125a^3 + 300a^2b + 240ab^2 + 64b^3

8 0
3 years ago
There are 140 fruits in a bag if there are 24 more oranges than tangerines how many oranges are in a bag
SIZIF [17.4K]

Answer:

94 oranges

Step-by-step explanation:

Divide 140 by 2 and then add 24 to get the orange quantity

94 oranges

46 tangerines

8 0
3 years ago
Conver Mixed Number to an Improper Fraction<br> 63 and 2/5
PolarNik [594]

Answer:

The answer is 317/5

Step-by-step explanation:

8 0
3 years ago
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