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olga_2 [115]
3 years ago
8

Please Help the First Answer Will Get Brainliest!!!!!!!!

Mathematics
1 answer:
Tema [17]3 years ago
7 0

QUESTION 1

The area of a triangle is given by

Area=\frac{1}{2}\times base\times heigth

The length of the base of the triangle is 6\:in. and the vertical height is 8\:in..


We substitute these values into the formula to obtain,

Area=\frac{1}{2}\times 6\times 8


Area=3\times 8


Area=24\:in^2


The area of the triangle is 24 square inches.


The correct answer is A


QUESTION 2


The company logo is made up of three triangles and a square.


The length of the square is 7\:cm

The area of a square is given by

Area=l^2


\Rightarrow Area=7^2


\Rightarrow Area=49cm^2.


The area of one of the triangles is

Area=\frac{1}{2}\times base \times height


The height of the triangle is 4cm.

The base of the triangle is on one side of the square, so it is 7cm.


The area now becomes


Area=\frac{1}{2}\times 7 \times 4


\Rightarrow Area=7 \times 2


\Rightarrow Area=14cm^2.


Since there are three identical triangles, we multiply the area of one triangle by 3 to get area of the three triangles.

Area\:of\:the\:three\:triangles=3\times14=42cm^2


The area of the logo is equal to the area of the square plus the area of the three identical triangles.


Area\:of\:logo=49+42=91cm^2


Hence the area of the logo is 91cm^2


QUESTION 3


Since the figure is made up of two rectangles and two right triangles, we find their areas and sum them to get the area of the figure.

The area of a rectangle is given by

Area=l\times w


The width of the bigger rectangle is 5 and the length is 25.

Area\:of\:bigger\: rectangle=25\times 5


Area\:of\:bigger\: rectangle=125\:square\:units


The width of the smaller rectangle is 8.


The length of the smaller rectangle is 25-(6+6)=25-12=13.


Area\:of\:smaller\: rectangle=13\times 8


Area\:of\:smaller\: rectangle=104\:square\:units.


The two triangles are identical, so we find the area of one and multiply by 2

Area\:of\:triangle=\frac{1}{2}\times base \times heigth


Area\:of\:triangle=\frac{1}{2}\times 6 \times 8


Area\:of\:triangle=3 \times 8


Area\:of\:triangle=24\:square\:units


\Rightarrow Area\:of\:the\:two\:triangles=2\times24=48\:square\:units


The area of the figure is

=125+104+48=277\:sqaure\:units


The correct answer is C




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Values of c and d make the equation true are c=6, d=2

Equations

  • We must find the values of c and d that make the below equation be true

                                \sqrt[3]{162x^{c}y^{5}  }  = 3x^{2} y^{3} \sqrt[3]{6y^{d} }

  • cubing on both sides -

                               (\sqrt[3]{162x^{c}y^{5}  })^{3}   = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}

  • The left side just simplifies the cubic root with the cube:

                                 {162x^{c}y^{5}  }  = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}

  • On the right side, we'll simplify the cubic root where possible and power what's outside of the root:

                                  {162x^{c}y^{5}  }  = 27x^{6} y^{3}   ({6y^{d})

  • Simplifying

                                     {x^{c}y^{5}  }  = x^{6} y^{3}   ({y^{d})

                                     {x^{c}y^{5}  }  = x^{6} y^{3+d}

  • On equating,

                                   c = 6

                                   d = 2

To learn more about equations from the given link

brainly.com/question/14751707

#SPJ4

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