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vazorg [7]
3 years ago
7

Complete the proportion 3 is to 4 as 75 is to...

Mathematics
1 answer:
kolezko [41]3 years ago
3 0

Answer: 100

Step-by-step explanation:

\frac{3}{4} = \frac{75}{x}

3 x 25 = 75

4 x 25 = 100

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The length of a rectangle is four times its width. if the area of the rectangle is 100 cm2 , find its perimeter.
sveticcg [70]
<u>Define x:</u>
Let the width be x.
width = x
Length = 4x

<u>Given the area, find Length and Width:</u>
The area is 100 cm²

Area = Length x Width
x(4x) = 100

Evaluate the Left Hand Side:
4x² = 100

Divide by 4:
x² = 25

Square root both sides:
x = 5

<u>Find the Width and the Length:</u>
Width = x = 5
Length = 4x = 4(5) = 20

<u>Find Perimeter:</u>
Perimeter = 2( 5 + 20) = 50 m

Answer: Perimeter = 50 m
7 0
3 years ago
Simplify this radical.<br> Square root of x to the 13th power
wlad13 [49]

Answer:

x^6\sqrt{x}

Step-by-step explanation:

we have:

\sqrt{x^{13}}

we can write:

\sqrt{x^{13}} :\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}

we know:

\sqrt{x^{2}} = x

so we have:

\sqrt{x^{13}} =\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}

we have:

\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}=

x^{6} \sqrt{x}

8 0
3 years ago
Read 2 more answers
Find the value of given expression <br><br>=》<br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B901%20-%205%20%2B%204%7D%20" id=
Hitman42 [59]

Step-by-step explanation:

Answer is 30 I hope this help you

6 0
3 years ago
Write 3.121*10^4 in standard form
Valentin [98]
3.121 * 10^4 is already in standard form i’m pretty sure
3 0
3 years ago
Find r'(t), r(t0), and r'(t0) for the given value of (t0). r(t) = (e^t, e²t), t0 = 0​
creativ13 [48]

Applying the differentiation rule, it can be obtained that:

r'(t)=(e^t,2e^{2t}), r(t_0)=(1,1) and r'(t_0)=(1,2).

<h3>What is the formula for differentiating an exponential function?</h3>

The exponential function exists a mathematical function designated by f(x)=\exp or e^{x}. Unless otherwise determined, the term generally directs to the positive-valued function of a real variable, although it can be extended to complex numerals or generalized to other mathematical objects like matrices or Lie algebras.

In mathematics, the derivative of a function of a real variable estimates the sensitivity to change of the function value affecting a change in its statement. Derivatives exist as a fundamental tool of calculus.

\frac{d}{dt}(e^{mt})=me^{mt}.

Given that r(t)=(e^t,e^{2t}).

So, differentiating r(t)=(e^t,e^{2t}) with respect to t, we get: r'(t)=\left(\frac{d}{dt}(e^t),\frac{d}{dt}(e^{2t})\right).

So, using the above formula \frac{d}{dt}(e^{mt})=me^{mt}, we get: r'(t)=(e^t,2e^{2t}).

Now, substituting t=t_0=0 in r(t)=(e^t,e^{2t}) and r'(t)=(e^t,2e^{2t}), we obtain:

r(t_0=0)=(e^0,e^{2\times 0})=(1,1) and r'(t_0=0)=(e^0,2e^{2\times 0})=(1,2).

Therefore, applying the differentiation rule, we get:

r'(t)=(e^t,2e^{2t}), r(t_0)=(1,1) and r'(t_0)=(1,2).

To know about the differentiation rule, refer:

brainly.com/question/25081524

#SPJ9

5 0
1 year ago
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