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Yanka [14]
2 years ago
15

Simplify this expression.

+\sqrt2)" alt="2\sqrt5(13+\sqrt2)" align="absmiddle" class="latex-formula">
Mathematics
2 answers:
andreyandreev [35.5K]2 years ago
5 0

Step-by-step explanation:

everything can be found in the picture

marin [14]2 years ago
3 0

Answer:

\small{\boxed{\tt{2 \sqrt{5} (13 +  \sqrt{2}  = 26 \sqrt{5}  + 2 \sqrt{10}  = 64.3}}}

Step-by-step explanation:

Given : Expression

2  \sqrt{5} (13 +  \sqrt{2} )

To find : Simplify the expression

Solution :

Step 1 - Write the expression

2 \sqrt{5} (13 +  \sqrt{2} )

Step 2 - Apply distributive property,

a(b + c) = a × b + a \times  c

= 2 \sqrt{5}  \times 13 + 2 \sqrt{5 }  \times  \sqrt{2}

Step 3 - Apply square root property,

\sqrt{x}  \times  \sqrt{y}  =  \sqrt{xy}

= 26 \sqrt{5}  + 2 \sqrt{10}

or to simplify more substitute the value of \sqrt{5}  = 2.23 and \sqrt{10}  = 3.16

Simplification-

= 26(2.23) + 2(3.16)

= 57.98  +  6.32

<h3>= 64.3</h3>
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The measure of the first angle in a right triangle is 10 less than the measure of the second angle.The third angle is the right
prohojiy [21]
Triangle angles add up to a total of 180 degrees.

X will substitute for the second angle.

(X - 10) will substitute for the first angle, which is 10 less than the second angle (x).

The third angle is a right angle which is 90 degrees.

The equation therefore, the summation of the angles:
90 + x + (x - 10) = 180

Join like terms:
80 + 2x = 180

Solve for x:
2x = 100
x = 50

This means that:
The second angle is 50.
The first angle is 50 - 10 which is 40.

We can double check by adding the angles 50, 40, and 90 together to get 180.
5 0
3 years ago
Choose the equation of the horizontal line that passes through the point (-2,-1)and has a slope of 5
nignag [31]
Y=mx+b
-1=5(-2)+b
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9=b
the equation is
y=5x+9
7 0
3 years ago
Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the sit
shutvik [7]

Answer:

\frac{6}{5} of an hour = 1 1/5 hour = 72 minutes

Step-by-step explanation:

\frac{1}{3} h + \frac{1}{2}h = 1\\\\\frac{2}{6} h + \frac{3}{6}h = 1\\\\\\\frac{5 }{6} h  =1\\\\h=\frac{6}{5}

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A recent poll of 1500 new home buyers found that 60% hired a moving company to help them move to their new home. Find the margin
Mrac [35]

Answer:

The margin of error M.O.E = 2.5%

Step-by-step explanation:

Given that;

The sample size = 1500

The sample proportion \hat p = 0.60

Confidencce interval = 0.95

The level of significance ∝ = 1 - C.I

= 1 - 0.95

= 0.05

The critical value:

Z_{\alpha/2} = Z_{0.05/2} \\ \\  Z_{0.025} = 1.96 (From the z tables)

The margin of error is calculated by using the formula:

M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}

M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}

M.O.E = 1.96 \times \sqrt{\dfrac{0.24}{1500}}

M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}

M.O.E = 0.02479

M.O.E ≅ 0.025

The margin of error M.O.E = 2.5%

8 0
3 years ago
An isosceles triangle has two angles both equal to x°. The third angle is 60° bigger than either of these. Find the value of x°.
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X+x+(x+60)=180
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3 years ago
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