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2 years ago

Please help due today

Mathematics

1 answer:

alisha [4.7K]2 years ago

6 0

77.) x= {-5, 6}
78.) x= {-4, 9}
79.) x= {5/3, 2}
80.) x= {1/9, 3}
81.) x= {-6, 18}
82.) x= {-3√3 +4, 3√3 +4}
83.) x= {-7, -3}
84.) x= {-√85 +9 /2, √85 -9 /2}

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767 rounded to the nearest ten and hundred

soldi70 [24.7K]

767 rounded to the nearest ten is 770

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2 years ago

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Masha biked 20km 20 minutes faster than Dasha biked 20km. Find the speed of each cyclist if one biked 2km/h faster than the othe

motikmotik

Answer:

12 km/h and 10 km/h

Step-by-step explanation:

Let the speed of Masha = s, speed of Dasha = d

Distance = 20 km
Time difference = 20 min = 1/3 hr
Speed difference = 2 km/h

As per above info we get following equations:

s = d + 2
20/s + 1/3 = 20/d

Substitute s and solve for d:

20/(d + 2) + 1/3 = 20/d

Get rid of fraction by multiplying all terms by 3d(d + 2):

60d + d(d + 2) = 60(d + 2)
60d + d² + 2d = 60d + 120
d² + 2d = 120
d² + 2d + 1 = 121
(d + 1)² = 11²
d + 1 = 11
d = 10

Find s:

s = 10 + 2 = 12

The answer is

Masha's speed 12 km/h and Dasha's speed 10 km/h

3 0

2 years ago

Which of the following expressions is equivalent to a3 + b3?

lubasha [3.4K]

ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

${(a + b)}^{3} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3}$

Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

$(a + b)({(a + b)}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We expand the bracket on the left hand side to get,

$(a + b)( {a}^{2} + 2ab + {b}^{2} - 3ab ) = {a}^{3} + {b}^{3}$

We finally simplify to get,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = {a}^{3} + {b}^{3}$

5 0

2 years ago

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Solve the system of equations.

Alenkasestr [34]

Step-by-step explanation:

Step 1: Substitute x from the second equation into the second one

$2x - 9y = 14$