Condense log2 2 + 4 log2 as a single logarithm.

1 kilogram is roughly 2.2 pounds.

Paul [167]

Answer:

11 pounds

Step-by-step explanation:

1 k = 2.2 p

5 k = ?

2.2 x 5 = 11

5 k = 11 p

4 0

3 years ago

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HURRY I'LL PICK A BRAINLIEST PERSON!!!

Rzqust [24]

Answer:

The only options which are having same solution as the given equation is A, B and D.

Explanation:

Given the equation: $\frac{3}{5}x+ \frac{2}{3} +x =\frac{1}{2}- \frac{1}{5}x$ ......[1]

Like terms are terms whose variables are the same.

In the given equation [1],

Combine like terms of variable x on LHS; we have

$\frac{3x+5x}{5}+ \frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$

Simplify:

$\frac{8x}{5}+\frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$

or we can write this as;

$\frac{8}{5}x +\frac{2}{3} =\frac{1}{2}- \frac{1}{5}x$ .

LCM(Least Common Multiple) to change each fraction to make their denominators the same as the least common denominator.

Taking LCM to both sides of an equation [1] as;

LCM of 3, 5 on LHS is 15 and LCM of 2 , 5 on RHS is 10;

$\frac{9x+10+15x}{15} = \frac{5-2x}{10}$

By cross multiplication we get;

$10 \cdot (9x+10+15x) = 15 \cdot (5-2x)$

Divide both side by 5 we get;

$2 \cdot (9x+10+15x) = 3 \cdot (5-2x)$

Using distributive property on both sides of an equation (i.e, $a\cdot (b+c) =a\cdot b+a\cdot c$ )

we have;

$18x+20+30x = 15-6x$ ......[2]

Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.

Using additive property of equality:

Add 6x to both sides of an equation in [2];

$18x+20+30x+6x = 15-6x+6x$

Simplify;

$18x+20+30x+6x = 15$

Combine 18x and 6x we get;

$24x+20+30x= 15$ ......[3]

Subtraction Property of Equality states that allows one to subtract the same quantity to both sides of an equation.

Subtract 20 from both sides of an equation in [3] we get;

$24x+20+30x-20= 15-20$

Simplify:

$24x+30x= -5$

Therefore, from the given options only A, B and D have the same solution as $\frac{3}{5}x+ \frac{2}{3} +x =\frac{1}{2}- \frac{1}{5}x$

3 0

3 years ago

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How many times can 8 go into 329

tankabanditka [31]

8 can go into 329 wholly 41 times. However, there is a remainder of 0.125.

5 0

3 years ago

In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .