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2 years ago

5. Find the surface area of the prism. 13 cm 5 cm 4 cm 12 cm

Mathematics

1 answer:

erik [133]2 years ago

6 0

Answer:

162 sq. cm

Step-by-step explanation:

ph+ 2b

13 + 5 + 13 + 5 * 4 + 2 * 12

36 * 4 + 24

144 +24

168

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Saturday the low temperature was 56°F and the high temperature was 60° higher what was the high temperature on Saturday

leva [86]

116 degrees. It’s simple.

56 is what the low was, but the high was 60 more.
Therefore,
56+60=116

4 0

3 years ago

A string is 7 yards long. Jeff needs 2 feet and Lori needs 15 feet of string. If they both cut their string, how much is left?

Aleksandr [31]

$1\ yard=3\ feet\\\\7\ yard=3\cdot7=21\ feet\\\\21-2-15=4\\\\There\ are\ 4\ feet\ left$

5 0

2 years ago

Simplify each expression. Assume that all variables are positive.

kozerog [31]

Q1. The answer is $\frac{8x^{3}y^{6} }{27}$

$( \frac{16 x^{5} y^{10}}{81x y^{2} } )^{ \frac{3}{4} }= ( \frac{16}{81}* \frac{ x^{5} }{x}* \frac{ y^{10} }{y^{2}} )^{ \frac{3}{4} } \\ \\ 
 \frac{ x^{a} }{ x^{b} }= x^{a-b} \\ \\ 
( \frac{16}{81}* \frac{ x^{5} }{x}*\frac{ y^{10} }{y^{2}} )^{ \frac{3}{4} }}=( \frac{16}{81 }* x^{5-1}* y^{10-2})^{ \frac{3}{4} }=( \frac{16}{81 }* x^{4}* y^{8})^{ \frac{3}{4} }= \\ \\ = (\frac{16}{18} )^{ \frac{3}{4} }*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} }=$
$\frac{(16)^{ \frac{3}{4} }}{(18)^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} }=\frac{( 2^{4} )^{ \frac{3}{4} }}{( 3^{4} )^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} } \\ \\ 
 (x^{a} )^{b} = x^{a*b} \\ \\ 
\frac{( 2^{4} )^{ \frac{3}{4} }}{( 3^{4} )^{ \frac{3}{4} }}*(x^{4})^{ \frac{3}{4} }*(y^{8})^{ \frac{3}{4} } = \frac{ 2^{4* \frac{3}{4} } }{ 3^{4* \frac{3}{4} } } * x^{4* \frac{3}{4} } * y^{8*\frac{3}{4}} = \frac{ 2^{3} }{ 3^{3} } * x^{3} *y^{6} =$
$= \frac{8x^{3}y^{6} }{27}$

Q2. The answer is 1/16

$(-64) ^ \frac{-2}{3} =(-1* 2^{6} ) ^ \frac{-2}{3}=(-1)^ \frac{-2}{3} *(2^{6} ) ^ \frac{-2}{3} \\\\x^{-a} = \frac{1}{ x^{a} } \\\\(-1)^ \frac{-2}{3} *(2^{6} ) ^ \frac{-2}{3} = \frac{1}{(-1)^ \frac{2}{3}} *\frac{1}{(2^{6})^ \frac{2}{3}} \\ \\ (x^{a} )^{b}=x^{a*b} \\\\x^{ \frac{a}{b} = \sqrt[b]{ x^{a} } } \\ \\ 
$
$\frac{1}{(-1)^ \frac{2}{3}} *\frac{1}{2^{6*\frac{2}{3}}} = \frac{1}{ \sqrt[3]{(-1)^{2} } } * \frac{1}{ 2^{4} } = \frac{1}{ \sqrt[3]{1} } * \frac{1}{16} = \frac{1}{1} * \frac{1}{16}= \frac{1}{16}$

Q3. The answer is $a^{ \frac{7}{6} }$

$a^{ \frac{2}{3} } * a^{ \frac{1}{2} } \\ \\ 
 x^{a}* x^{b} =x^{a+b} \\ \\ 
a^{ \frac{2}{3} } * a^{ \frac{1}{2} }= a^{ \frac{2}{3} + \frac{1}{2} } =a^{ \frac{2*2}{3*2} + \frac{1*3}{2*3} }=a^{ \frac{4}{6} + \frac{3}{6} }=a^{ \frac{4+3}{6} }=a^{ \frac{7}{6} }$

7 0

2 years ago

jennifer bikes 7 miles south and then turns to bike 13 miles east how far away is she from where she started?

Marina CMI [18]

Answer:

She is about 14.765 miles ( $\sqrt{218}$ miles) from where she started

Step-by-step explanation:

There is a relation between the three sides of the right triangle

The side opposite to the right angle is called hypotenuse and it is the longest side

The other two sides called legs of the right angle

The relation between them is: (hypotenuse)² = (leg1)² + (leg2)²

∵ Jennifer bikes 7 miles south

∵ She turns to bike 13 miles east

∵ South and East are perpendicular

→ That means the distance from her start point to end point represents

a hypotenuse of a right triangle, whose legs are 7 and 13

∴ (hypotenuse)² = (leg1)² + (leg2)², where

hypotenuse is the distance between her start and end points

leg1 is her distance in south direction

leg2 is her distance in east direction

∵ Leg1 = 7 miles

∵ leg 2 = 13 miles

∴ (hypotenuse)² = (7)² + (13)²

∴ (hypotenuse)² = 49 + 169

∴ (hypotenuse)² = 218

→ Take √ for both sides

∴ hypotenuse = $\sqrt{218}$

∴ hypotenuse ≅ 14.76482306

∴ She is about 14.765 miles ( $\sqrt{218}$ miles) from where she started.

3 0

2 years ago

Solve.

rjkz [21]

123x - 23(-1 + x) = 14

Simplify.

123x + 23 - 23x = 14

Subtract 23 from both sides.

123x - 23x = 14 - 23

Simplify.

100x = - 9

Divide both sides by 100.

x = -9/100

~Hope I helped!~

6 0

3 years ago

Read 2 more answers