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Akimi4 [234]
3 years ago
8

Which decimal number is 17/21 equal to?

Mathematics
2 answers:
exis [7]3 years ago
8 0

It is equal to 0.8 five star please?

dangina [55]3 years ago
4 0

17/21 = 0.809524


This fraction equals to the decimal number 0.809524

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Find the distance from the point (1,4) to the line y = 1/3x - 3
Troyanec [42]

Answer:

Step-by-step explanation:

If I'm not mistaken, and I very well could be, this is a calculus problem(?). In order to find the distance without calculus you'd need a point on the given line to use to find the distance in the distance formula. But you don't have a point on the given line, so we can find the shortest distance between the point (1, 4) and the given line using the derivative of the polynomial formed when using the distance formula.

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} and we have the x and y for x2 (or x1...it doesn't matter which you choose to fill in):

d=\sqrt{(1-x)^2+(4-y)^2}

but what we find is that we have too many unknowns here, namely, the distance, the x coordinate, and the y coordinate. So we can replace the y coordinate with what y is equal to in terms of the linear equation:

d=\sqrt{(1-x)^2+(4-\frac{1}{3}x-3)^2 } and simplify:

d=\sqrt{(1-x)^2+(7-\frac{1}{3}x)^2 }

. No we'll expand each binomial by squaring:

d=\sqrt{(1-2x+x^2)+(49-\frac{14}{3}x+\frac{1}{9}x^2)  }

.  Combining like terms gives us

d=\sqrt{\frac{10}{9}x^2-\frac{20}{3}x+50  }

The distance between the point (1, 4) and the given line will be at a minimum when the polynomial above is at a minimum. We find the value of x for which the polynomial is at a minimum by finding its derivative, setting the derivative equal to 0, and then solving for x. The derivative of the polynomial is

\frac{20}{9}x-\frac{20}{3}

Setting equal to 0 and getting rid of the denominators gives us

20x - 60 = 0

Solving for x gives us

20x = 60 and x = 3.

That's the value of x that gives us the shortest distance between (1, 4) and the line y = 1/3x - 3. Sub into the distance formula that x value to find the distance:

d=\sqrt{(\frac{10}{9})(3)^2-(\frac{20}{3})(3)+50   }

which simplifies down, finally, to

x ≈ 6.325 units

8 0
3 years ago
Caitlyn needs to solve the equation: 2(3x+1)=3(2-x). after copying the problem correctly she uses the Properties of Algebra to s
astra-53 [7]

Answer:

x=49

Step-by-step explanation:

2(3x+1)=3(2−x)

Step 1: Simplify both sides of the equation.

2(3x+1)=3(2−x)

(2)(3x)+(2)(1)=(3)(2)+(3)(−x)(Distribute)

6x+2=6+−3x

6x+2=−3x+6

Step 2: Add 3x to both sides.

6x+2+3x=−3x+6+3x

9x+2=6

Step 3: Subtract 2 from both sides.

9x+2−2=6−2

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Step 4: Divide both sides by 9.

9x9=49

x=49

3 0
3 years ago
Read 2 more answers
What is the resulting equation when the expression for y in the second equation is substituted into the first equation?
Anni [7]

Answer: 3x + 6 -4x = 1

Simplify to -x + 6 = 1 because 3x - 4x = -1x

5 0
3 years ago
I need help with this question.
Citrus2011 [14]

Answer:

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Step-by-step explanation:

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2 years ago
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Tresset [83]

Answer:

digestive would be stomach, excretion is the big and small intestines

Step-by-step explanation:

stomach digests food, your intestines process whatever is left till you excrete

3 0
3 years ago
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