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2 years ago

Find the length of side x in simplest radical form with a rational denominator.

Mathematics

1 answer:

Anni [7]2 years ago

8 0

9514 1404 393

Answer:

(4√3)/3

Step-by-step explanation:

You know the ratio of side lengths is ...

x : 4 = 1 : √3

Then ...

x = 4/√3

Multiply by (√3)/(√3) to rationalize the denominator:

x = (4√3)/3

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X+y=5 2x - y = 1 Need help

erma4kov [3.2K]

Answer:

y = 3

x = 2

Step-by-step explanation:

x+y=5 == -2x - 2y = -10

2x-y = 1 == 2x - y = 1 +

-------------------

-3y = -9

y = 3

x + y = 5

x + 3 = 5

x = 2

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3 years ago

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Rectangle J'K'L'M' shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applie

Y_Kistochka [10]

Answer:

The coordinates of T' will be T'(13,-1)

Step-by-step explanation:

step 1

Find the rule of the translation

take any point of rectangle JKLM (pre-image)

The coordinate of point k(-3,2)

The coordinate of point k'(4,7)

The rule of the transformation

k(-3,2) -----> k'(4,7)

is equal to

(x,y) ------> (x+7,y+5)

That means ----> the translation is 7 units at right and 5 units up

step 2

Apply the rule of the translation at the coordinate T of trapezoid STUV

we have

T(6,-6)

(x,y) ------> (x+7,y+5)

T(6,-6) ------> T'(6+7,-6+5)

T(6,-6) ------> T'(13,-1)

therefore

The coordinates of T' will be T'(13,-1)

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2 years ago

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2 years ago

Plz..... Solve this questions for me...

faust18 [17]

$6.\\\text{We know}\ 9=3^2.\ \text{Therefore}\\\\9^2=(3^2)^2\\\\\text{use}\ (a^n)^m=a^{nm}\\\\9^2=(3^2)^2=3^{2\cdot2}=3^4\\\\\boxed{3^4=9^2}\\=================$

$7.\\METHOD\ 1:\\\\\sqrt{7^4}=\sqrt{7^{2\cdot2}}\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(7^2)^2}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\boxed{7^2}\\\\METHOD\ 2:\\\\\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\\sqrt{7^4}=7^\frac{4}{2}=\boxed{7^2}\\=================$

$8.\\5^a\times5^b=5^{11}\\\\a)\\\text{use}\ a^n\times a^m=a^{n+m}\\\\5^a\times5^b=5^{a+b}\\\\5^{a+b}=5^{11}\Rightarrow a+b=11\\\\11\ \text{is odd. The sum of even and odd is odd. Therefore}\ a\ \text{and}\ b\ \text{can't be even.}\\--------------------\\\\b)\\5\ \text{solutions}\\\\11=5+6\\11=4+7\\11=3+8\\11=2+9\\11=1+10$

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The teachers had to transport 166 students by bus on a field trip. Each bus holds 65 students. How many buses do they need to or

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3 busses are needed for all of the kids

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3 years ago

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