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12 days ago

Quadrilateral ABDE is a rectangle. DE = 4 in. and BD = 6 in. If the rectangle is rotated about a line through CF, cylinder Y is

created. If the rectangle is rotated about a line through GH, cylinder Z is created. Rectangle A B D E is shown. Point C is the midpoint of side D B, point G is the midpoint of side B A, point F is the midpoint of side E A, and point H is the midpoint of side D E. Side D E has a length of 4 inches and side B D has a length of 6 inches. What is the difference in the measures of the radii of cylinder Y and cylinder Z, in inches? 1 2 4 5

Mathematics

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Which number can each term of the equation be multiplied by to eliminate the fractions before solving? m – negative StartFractio

zzz [12365]

Answer: To remove fractions prior to solving, each term in the equation must be multiplied by $4$ .

Step-by-step explanation:

Consider the given expression:

$-\frac{3}{4}m-\frac{1}{2}=2+\frac{1}{4}m$

It is essential to simplify this before attempting to solve it.

Since the denominators differ, identifying the Least Common Denominator (LCD) is necessary.

Break down the denominators into their prime components:

$4=2*2=2^2\\2=2$

Select $2^2$ , as it possesses the greatest exponent. Thus:

$LCD=2^2=4$

Ultimately, to remove the fractions before solving, multiply both sides by 4:

$(4)(-\frac{3}{4}m)-(4)(\frac{1}{2})=(4)(2)+(4)(\frac{1}{4}m)\\\\-3m-2=8+m$

7 0

3 months ago

Which are the solutions of x2 = –5x + 8? StartFraction negative 5 minus StartRoot 57 EndRoot Over 2 EndFraction comma StartFract

tester [12383]

Answer:

$x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

Detailed solution:

Given:

The problem to solve is:

$x^2=-5x+8$

Convert the equation into the standard quadratic form $ax^2+bx +c =0$ , where $a,\ b,\ and\ c$ represent constants.

So, by adding $5x-8$ to both sides, we get:

$x^2+5x-8=0$

Note that $a=1,b=5,c=-8$ .

The roots of this quadratic are found by applying the quadratic formula given as:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute $a=1,b=5,c=-8$ into the formula and calculate for $x$ .

$x=\frac{-5\pm \sqrt{5^2-4(1)(-8)}}{2(1)}\\x=\frac{-5\pm \sqrt{25+32}}{2}\\x=\frac{-5\pm \sqrt{57}}{2}\\\\\\\therefore x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

Hence, the roots are:

$x=\frac{-5-\sqrt{57} }{2}\ or\ x=\frac{-5+\sqrt{57} }{2}$

4 0

3 months ago

Read 2 more answers

Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air

lawyer [12517]

The addition of the numbers can be done in any sequence.Step-by-step explanation:When determining the total time Colin spent traveling from home to the hotel, the sequence in which the numbers are added does not matter, since time is a scalar quantity that cannot be negative.A scalar quantity possesses only magnitude, without regard to direction. For instance, while temperature can be either positive or negative, time can only be positive, affirming its status as a scalar quantity.

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2 months ago

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Describe the set of points whose distance from the y-axis equals the distance from the xz-plane. a cone opening along the x-axis

tester [12383]

Response:

Detailed explanation:

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3 months ago