√4×√9 plz say the answer​

Given:

The logarithmic equation is:

[tex]\log x+\log (x-3)=1[/tex]

To find:

The value of x.

Solution:

Properties of logarithm used:

[tex]\log a+\log b=\log (ab)[/tex]

[tex]\log 10=1[/tex]

[tex]\log x[/tex] is defined for [tex]x>0[/tex].

We have,

[tex]\log x+\log (x-3)=1[/tex]

Using properties of logarithm, we get

[tex]\log [x(x-3)]=\log 10[/tex]

[tex]x^2-3x=10[/tex]

Splitting the middle term, we get

[tex]x^2-5x+2x-10=0[/tex]

[tex]x(x-5)+2(x-5)=0[/tex]

[tex](x-5)(x+2)=0[/tex]

[tex]x=5,-2[/tex]

In the given equation, we have a term [tex]\log x[/tex]. It means the value of x must be greater than 0 or positive. So, the only possible value of x is:

[tex]x=5[/tex]

Therefore, the value of x is 5.

Answer:

Real number

Rational number

Step-by-step explanation:

Answer:

Step-by-step explanation:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

Answer:

[tex]x = \frac{5a-2} {7+5a}\\[/tex]

Step-by-step explanation:

Given the expressions

[tex]x = \frac{5}{9y+5}....1\\y = \frac{5}{5a-2} ...2[/tex]

Substitute 2 into 1

[tex]x = \frac{5}{9(\frac{5}{5a-2} )+5} \\x = \frac{5}{(\frac{45}{5a-2} )+5} \\x = \frac{5}{\frac{45+5(5a-2)}{5a-2} } \\x= \frac{5}{\frac{35+25a}{5a-2} }\\x = \frac{5(5a-2)} {35+25a}\\x = \frac{5(5a-2)} {5(7+5a})\\\\x = \frac{5a-2} {7+5a}\\[/tex]

Sa Of Rectangular Prism - 65

Sa Of Pyramid - 85

TOTAL SURFACE AREA - 150

Answer:

0.44237 units

Step-by-step explanation:

Given

[tex]v(t) = e^t*sin(e^t)[/tex]

[tex]0 \le t \le \frac{\pi}{2}[/tex]

Required

The distance traveled in this interval

We have:

[tex]v(t) = e^t*sin(e^t)[/tex]

The distance is calculated as:

[tex]d(t) = \int\limits^a_b {v(t)} \, dt[/tex]

So, we have:

[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt[/tex]

Let:

[tex]u = e^t[/tex]

Differentiate

[tex]\frac{du}{dt} = e^t[/tex]

So:

[tex]dt = e^{-t} du[/tex]

So, we have:

[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(e^t)} \, dt[/tex]

[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t*sin(u)} \, e^{-t} du[/tex]

Rewrite as:

[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {e^t* e^{-t}*sin(u)} \, du[/tex]

[tex]d(t) = \int\limits^{\frac{\pi}{2}}_0 {sin(u)} \, du[/tex]

Integrate:

[tex]d(t) = -\cos(u)|\limits^{\frac{\pi}{2}}_0[/tex]

Substitute [tex]u = e^t[/tex]

[tex]d(t) = -\cos(e^t)|\limits^{\frac{\pi}{2}}_0[/tex]

Split

[tex]d(t) = -\cos(e^\frac{\pi}{2}) - [-\cos(e^0)][/tex]

[tex]d(t) = -\cos(e^\frac{\pi}{2}) +\cos(e^0)[/tex]

[tex]d(t) = -0.09793 + 0.5403[/tex]

[tex]d(t) = 0.44237[/tex]

The distance traveled in this interval is: 0.44237 units

dt =

d(t) = \int\limits^2_0 {e^t*sin(e^t)} \, dt

The Percentage increase in the purchase price each year is 4.5%.

The given function is:

[tex]V(t)=P(1.045)^t[/tex]

Where P is the purchase price of the baseball card and t is the time.

A function is a rule that establishes a relation between two variables.

[tex]V(1)=P(1.045)^1\\V(1)=1.045P[/tex]

[tex]V(2)=P(1.045)^2\\V(2)=1.092025P[/tex]

Percentage increase in the purchase price each year

=[tex]\frac{V(2)-V(1)}{V(1)} *100[/tex]

[tex]=\frac{1.092025P-1.045P}{1.045P} *100[/tex]

[tex]=4.5%[/tex]%

Hence, the Percentage increase in the purchase price each year is 4.5%.

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If we know the quadratic formula, the quadratic formula is

x = [-b ± √(b²- 4ac)] / 2a

Gosh! So overwhelming! But let's look at the composition of a quadratic equation:

ax² + bx + c = 0

And we have 6x² - 3x = 1. So, what do we do? We need to put this quadratic equation into an easy form to find the value of a, b, and c to plug in to the equation.

We can just minus one on both sides to get this:

6x² - 3x - 1 = 0

Is it in the form of ax² + bx + c? Yes! a = 6, b = -3, and c = -1. Now, all we have to do is plug it into the quadratic formula.

x = [-b ± √(b²- 4ac)] / 2a

x = [-(-3) ± √((-3)²- 4(6)(-1))] / 2(6)

     [3 ± √(9- 4(6)(-1))] / 12

     [3 ± √(9 + 24)] / 12

     [3 ± √(33)] / 12

At this point, we should just use a calculator, and recognize we have two answers because of the plus-or-minus sign! (or this sign: ±)

[3 ± √(33)] / 12

1) [3 + √(33)] / 12 = 0.73 approximately

2) [3 - √(33)] / 12 = -0.23 approximately

So, x=0.73 and x= -0.23.

Answer:

78732

Step-by-step explanation:

Answer:

120 yd²

Step-by-step explanation:

The solid has 5 faces.

Bottom: rectangle 6 yd by 3 yd

Left: rectangle 8 yd by 3 yd

Right: rectangle 10 yd by 3 yd

Front & Back: 2 triangles 6 yd base and 8 yd height

area = 6 * 3 + 8 * 3 + 10 * 3 + 6 * 8

area = 72 + 48

area = 120

Answer: 120 yd²

Answer:

V≈100.5

Step-by-step explanation:

V=πr2h=π·22·8≈100.53096

Answer:

D. 4 units to the left

The transformation of the function will be 4 units to the left. The correct option is D.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They've simply shifted in one or more directions.

Given that the functions are f(x) = x³ and g(x) = ( x + 4 )³. The translation of the function will be at 4 units to the left.

When the functions are plotted on the graph the translation is seen to the left of the origin at the coordinate (-4,0).

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Answer:

See solution below

Step-by-step explanation:

Given the expression

[tex]\frac{cos(x+30)-sin(x+60)}{sin(x)cos(x)} \\[/tex]

Recall that

cos x  = sin(90-x)

cos(x+30 ) = sin (90-(x+30)

= sin(90-x-30)

= sin(60-x)

Substitute

[tex]\frac{sin(60-x)-sin(x+60)}{sin(x)cos(x)} \\= \frac{sin60cosx-cos60sinx)-sinxcos60-cosxsin60)}{sin(x)cos(x)} \\= \frac{-2cos60sinx)}{sin(x)cos(x)} \\= \frac{-2(1/2)sinx)}{sin(x)cos(x)} \\= \frac{-1}{cos(x)}\\= \frac{1}{cos(x)}\\ \\= -sec(x) Proved[/tex]

Answer:

54°

Step-by-step explanation:

Because p and q are parallel, angle 3 equal to angle 6 as they are alternative angles.

So angle 6 is 54°.

Alternative

Line p and line q is parallel, so that the sum of a pair of interior angles (angle 3 and angle 5, angle 4 and angle 6) are equal to 180°.

So angle 4 + angle 6 = 180°.

Find angle 4 first:

180° - angle 3 = angle 4

180° - 54° = 126°

So the measure of angle 6 is

180° - 126° = 54°

Answer:

54 degrees

Step-by-step explanation:

Answer:

x=30

Step-by-step explanation:

x/5-16=-10

x/5=-10+16

x/5=6

x=6×5

x=30

Answer:

Angle AGC

Step-by-step explanation:

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees. ... For example, a 50-degree angle and a 40-degree angle are complementary; a 60-degree angle and a 120-degree angle are supplementary

Answer:

No

Step-by-step explanation:

A trapezoid is never a square. A trapezoid only has one pair of parallel lines and a square has two.

Answer:

y = -5x + 4/3

Step-by-step explanation:

m is the slope and b is the y intercept. m= -5 so -5 is the slope and b= 4/3 so 4/3 is the y intercept.

Answer:

378 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

The potential energy of a body can be found by using the formula

PE = mgh

where

m is the mass

h is the height

g is the acceleration due to gravity which is 9.8 m/s²

From the question we have

PE = 15 × 9.8 × 5

We have the final answer as

Hope this helps you

Answer:

2/6  or 33.3%

1/6 or 16.65%

3/6 or 50%

0/6 0r 0%

Step-by-step explanation:

Answer:

What is 2x times 3x

6x

Step-by-step explanation:

3•2=6

Answer:

4/7

Step-by-step explanation:

Answer:

2,827.43

Step-by-step explanation:

Answer:

110 square centimeters.

Step-by-step explanation:

The area for a trapezoid can be figured out with the equation (a + b)h/2.

(9 * 5) + (9 + 4)10/2 {Work inside the parentheses first.}

45 + (13)10/2 {Divide 10 by 2 to get 5.}

45 + 13(5) {Multiply 13 by 5 to get 65.}

45 + 65 {Add 45 & 65 to get 110.}

110 square centimeters.

The area of the figure is 110 square centimeters.

Answer:

1%

Step-by-step explanation:

.

Answer:

My dog getting smacked allot by my cat ( my cat was bullying my dog all day XD) 1 thanks = one less smack for the dog lol

Step-by-step explanation:

Me kat (cat) was mewing all day. Me go to market to buy his favourite food (fish).Me comes home. Me takes time to prepare fish. Me gives kat fish. He throw away fish and insult me with some more mews