q(t)= Q_0 e^-kt where Q represents the quantity remaining after t years and k is the decay constant 0.00043. How long will it take for 500g of radium to decay to 5g?

Answer:

59

Step-by-step explanation:

[tex] \sqrt{ {6}^{2} + {5}^{2} } = \sqrt{36 + 25} = \sqrt{61} [/tex]

[tex] \cos(p) = \frac{4}{ \sqrt{61} } [/tex]

[tex]p = {cos}^{ - 1} \frac{4}{ \sqrt{61} } = 59[/tex]

Make sure your calculator is in degree mode.

Answer:

2. All reals

Step-by-step explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

Answer:

Correct expression:

[tex]2x + 3y + 25[/tex]

Option C).

Answer:

21.5

Step-by-step explanation:

break the shape down to make two shapes: a triangle and rectangle.
triangle = A=bxh/2

3x5=15/2=7.5

Rectangle = A=bxh

2x7=14

7.5+14= 21.5

Hope this helps :)

Answer:

21.5

Step-by-step explanation:

(all steps provided in image attached)

Answer ya so  1 is the answer

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Given expression:

[tex]\sf \left(\dfrac{3a^{-2}b^6}{2a^{-1}b^5} \right)^2[/tex]

To find the value of the expression when a = 3 and b = -2, substitute these values into the expression:

[tex]\implies \sf \left(\dfrac{3(3)^{-2}(-2)^6}{2(3)^{-1}(-2)^5} \right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]

[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{3^2}\right)(-2)^6}{2\left(\dfrac{1}{3^1} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{3\left(\dfrac{1}{9}\right)(-2)^6}{2\left(\dfrac{1}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{3}{9}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right)(-2)^6}{\left(\dfrac{2}{3} \right)(-2)^5} \right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (2^6)}{\left(\dfrac{2}{3} \right) (-(2^5))} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1}{3}\right) (64)}{\left(\dfrac{2}{3} \right) (-32)} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\left(\dfrac{1 \times 64}{3}\right)}{\left(\dfrac{2 \times -32}{3} \right)} \right)^2[/tex]

[tex]\sf \implies \left(\dfrac{\dfrac{64}{3}}{\dfrac{-64}{3}} \right)^2[/tex]

When dividing fractions, flip the second fraction and multiply it by the first:

[tex]\implies \sf \left( \dfrac{64}{3} \times \dfrac {3}{-64} \right)^2[/tex]

[tex]\implies \sf \left( \dfrac{64 \times 3}{3 \times (-64)}\right)^2[/tex]

[tex]\implies \sf \left( \dfrac{192}{-192}\right)^2[/tex]

[tex]\implies \sf \left(-1\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad (-a)^n=a^n,\:\: \textsf{ if }n \textsf{ is even}[/tex]

[tex]\sf \implies 1^2=1[/tex]

The height of the tree is the man's height plus x.

[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]

So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]

Answer:

y = 2

Step-by-step explanation:

Y varies indirectly with x (as x gets bigger, y gets smaller)

You have to find k, the constant of proportionality.

y = [tex]\frac{k}{x}[/tex]

Plus in the x & y values you are given

58 = [tex]\frac{k}{9}[/tex]  Multiply both sides by 9 to solve for k

k= 522

Now plug in the new value of x to solve for y

y = [tex]\frac{522}{261}[/tex]

y = 2

The area of the kite ABCD will be 60 square millimeters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm

Then the area of the kite ABCD will be

Area = 2(area of triangle APB and area of triangle APD)

The side length of PB will be

AB² = AP² + PB²

PB² = AB² – AP²

PB² = 7.07² – 5²

PB² = 50 – 25

PB² = 25

 PB = 5 mm

Then the area will be

Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]

Area = 60 square mm

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Answer:

x = 10

Step-by-step explanation:

the ray is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is

[tex]\frac{x+4}{2x +1}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2(2x + 1) = 3(x + 4) ← distribute parenthesis

4x + 2 = 3x + 12 ( subtract 3x from both sides )

x + 2 = 12 ( subtract 2 from both sides )

x = 10

The volume of 10% solution will be 6 l and 9 litre of the 30 % solution will be taken.

Volume is the space occupied by a three dimensional object .

The concentration of solution required is 22% acid

The concentration of solution available is 10% and 30%

The total volume required is 15 liters

The formula for making a mixture is

Concentration = ( m₁x₁ +m₂x₂) / (x₁+x₂)

22 = (10 * x + 30 *(15 -x))/( 15)

10 x + 450 - 30x =330

-20x = -120

x = 6

The volume of 10% solution will be 6 l

and 9 litre of the 30 % solution will be taken.

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Answer:

congruent/alternate interior angles

Step-by-step explanation:

just took the quiz

Step-by-step explanation:

I have done it go and check it once

Answer:

Acute, right angle, obtuse, reflex

Step-by-step explanation:

Answer:

Acute

right angle

obtuse

reflex angle

Step-by-step explanation:

The linear inequality  [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality. the correct option is D.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

On a coordinate plane, a solid straight line has a negative slope and goes through (-2, 2) and (2, -8).

m = (-8 -2)/ (2 +2)

m = -10/ 4

m = -5/2

The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.

[tex]y \geq -5/2 (x-3)[/tex]

The linear inequality  [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality.

Thus, the correct option is D.

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Answer:

its b the guy above me is wrong

Step-by-step explanation:

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

Answer:

The factors are (x-7) and (x-4)

Step-by-step explanation:

We are finding the factors of a function from the zeros

The zeros are 7 and 4

We can use the zero product property which is

(x-b)(x-c) = 0  where b and c are the zeros

(x-7) (x-4) =0

The factors are (x-7) and (x-4)

[tex]3x ^{2} \: + \: {6x}^{3} \: - \: 9 {x}^{2} y[/tex]

[tex] \boxed{ \bold{3 {x}^{2} \: \times \: (1 \: + \: 2x \: - \: 3y)}}[/tex]

Answer:

[tex]\boxed{3x²(1 + 2x - 3y)}[/tex]

Step-by-step explanation:

3x squared + 6 x cube - 9x squared y

To factor

Solution:

A process when algebraic expression is expressed as a product of two or more expressions is factorisation.

ATP,

Square = a²

Cube = a³

We can see that 3x^2 is common in this expression.

So rewrite as:

Done!

To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:

[tex]y=a(x-r)(x-s)[/tex]

We're given:

[tex]y=a(x-r)(x-s)[/tex]

⇒ Plug in the given information:

[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]

[tex]a=-\dfrac{1}{2}[/tex]

Answer:

Each pizza was $12.55.

Step-by-step explanation:

et's take it piece by piece.

Salad and the tip together is 4.95 + 5 = 9.95, right?

47.60 - 9.95 = 37.65 spent on pizza

37.65/3 = 12.55

-5/7 x 1/5

-5 x 1 = -5

7 x 5 = 35

-5/35 = -1/7

Happy to help :P

A will have a value of 2. The value of A is found by the substitutional equation system.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation 1: [tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24}[/tex]

Equation 2: [tex]x+7y=8[/tex]

Rearrange equation 2 as;

x=8-7y

Substitute the value of x;

[tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24} \\\\ \frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24} \\\\ \frac{-21}{8} y+\frac{1}{3} = \frac{17}{24}-3 \\\\ \frac{-63y+8y}{24}=\frac{17-72}{24}\\\\ \frac{-55 \ y}{24} = - \frac{55}{24}\\\\ y= 1[/tex]

Substitute the value of y in equation 2 as;

x+7y=8

x+7(1)+8

x=8-7

x=1

The system of equations by substitution obtained the value of A is;

x + y = A

1+1=A

A=2

Hence the value of A will be 2.

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See below for the verification of ∠ACD =  ∠ABC + ∠BAC

The following proof works for both triangles.

The sum of angles in a triangle is 180 degrees.

So, we have:

∠ABC + ∠BAC + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ABC - ∠BAC

The sum of angles on a straight line is 180 degrees.

So, we have:

∠ACD + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ACD

Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC

180 - ∠ACD = 180 - ∠ABC - ∠BAC

Subtract 180 from both sides

- ∠ACD = - ∠ABC - ∠BAC

Multiply both sides by -1

∠ACD =  ∠ABC + ∠BAC

Hence, ∠ACD =  ∠ABC + ∠BAC has been verified

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Answer:

09

Step-by-step explanation:

34

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]

Factor out -1:

[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]

Divide both sides by -1:

[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]

Rearrange the terms:

[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]

[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]

Factor out the common term [tex](x^{98}-1)[/tex] :

[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]

Therefore, the solutions to the given equation are: x = 1 or x = -1

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-1000000 that is the answer

hope this helps!

Answer:

-14/15

Step-by-step explanation:

"of" means multiply, thus:

-8/15 * 21/12

-8 * 21 / 15 * 12

-2 * 7 / 15

-14/15

Answer:

-14/15

Step-by-step explanation:

So first you need to get rid of the negative sign. Don't worry you will add it back later!

So, you will do

-8/15×21/12

Once you cross cancel, you will have

-2/5x7/3

That would be equivalent to

-14/15

That's your answer!

Hope this helped :)

The equivalent expression of square root of -64 is 8i

We have:

square root of -64

Rewrite as:

√-64

Expand

√64 * √-1

Take the square root of 64

8√-1

In complex numbers

√-1  = i

So, we have:

8i

Hence, the equivalent expression of square root of -64 is 8i

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