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In-s [12.5K]
3 years ago
14

What number makes the expressions equivalent? Enter your answer in the box.

Mathematics
1 answer:
pashok25 [27]3 years ago
7 0

– 0.7

Step-by-step explanation:

Given expression is  \frac{1}{2}(-1.4 m+0.4)

To simplify this expression \frac{1}{2}(-1.4 m+0.4)  we get equivalent expression.

Multiply and Divide the expression by two.

\Rightarrow\left(\frac{-1.4}{2} m+\frac{0.4}{2}\right)  

To simplify the expression again, we get,

⇒ (–0.7 m + 0.2)

So, we found the coefficient of m is –0.7.

The missing number is –0.7  

Hence, –0.7 makes the expression equivalent.

Therefore, \frac{1}{2}(-1.4 m+0.4)  = –0.7 m + 0.2.

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8, 1 and 7 are the digits you need ! :)
5 0
3 years ago
Read 2 more answers
An equivalent expression with a rational denominator is...
Whitepunk [10]

Given the expression,

(8x-56x^2)/(\sqrt{14x-2})

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]

If we have (\sqrt{a})(\sqrt{a}), we will get \sqrt{a^2} by multiplying them. And \sqrt{a^2} = a.

So here in the problem, we will get,

[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)

Now in the numerator we have (8x-56x^2). We can check 8x is common there. we will take out -8x from it, we will get,

-8x(-1+7x)

-8x(7x-1)

And in the denominator we have 14x-2. We can check 2 is common there. If we take out 2 from it we will get,

2(7x-1)

So we can write the expression as

[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]

(7x-1) is common to the numerator and denominator both, if we cancel it we will get,

(-8x)(\sqrt{14x-2})/2

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

(-4x)(\sqrt{14x-2})

(-4x)(14x-2)^(1/2)

So we have got the required answer here.

The correct option is the last one.

4 0
3 years ago
Negative two and three sevenths times 0.01
kirill [66]

Answer:

-0.02428571428

3 0
3 years ago
EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the
solong [7]

Answer:

<h2>a) f =  sin(yz)i + xzcos(yz)j + xycos(yz)k</h2><h2>b) -2</h2>

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

 

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

7 0
3 years ago
What is the area of a circle with a radius of 6 inches?
Vika [28.1K]

Answer:

The answer to your question is   113.04 in²

Step-by-step explanation:

To solve this problem substitute the values in the formula and simplify.

Data

Area = ?

radius = 6 in

π = 3.14

Formula

Area = π x r²

Substitution

Area = (3.14) x (6)²

Simplification

Area = 3.14 x 36

Result

Area = 113.04 in²

7 0
3 years ago
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