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Answer:

The half-life of the substance is of 1600 years.

Step-by-step explanation:

Amount of the substance:

The amount of the substance after t years is given by the following equation:

[tex]C(t) = A(0.999567)^t[/tex]

In which A is the initial amount.

Find the half-life:

This is t for which [tex]C(t) = 0.5A[/tex], that is, the amount is half the initial amount. So

[tex]C(t) = A(0.999567)^t[/tex]

[tex]0.5A = A(0.999567)^t[/tex]

[tex](0.999567)^t = 0.5[/tex]

[tex]\log{(0.999567)^t} = \log{0.5}[/tex]

[tex]t\log{0.999567} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.999567}}[/tex]

[tex]t = 1600[/tex]

The half-life of the substance is of 1600 years.

Answer:

y=80

Step-by-step explanation:

when solve y-intercept let x=0

y= -16(0)2+64(0)+80

y=0+0+80

y=80

(0;80)

Answer:

x - 3

Step-by-step explanation:

Jenna picked x.

Josh picked 2x - 3.

The difference is:

2x - 3 - x

which simplifies to

x - 3

Answer: x - 3

Answer:

...........................I would be I don't know

Answer:

1/3

Step-by-step explanation:

3x -9y =4

To find the slope get the equation in slope intercept form ( y= mx+b where m is the slope and b is the y intercept)

Subtract 3x from each side

-9y = -3x+4

Divide each side by -9

-9y/-9 = -3x/-9 +4/-9

y = 1/3x -4/9

The slope is 1/3 and the y intercept is -4/9

Here,

3x -9y =4

To find the slope get the equation in slope intercept form ( y= mx+b where m is the slope and b is the y intercept)

Subtract 3x from each side

-9y = -3x+4

Divide each side by -9

-9y/-9 = -3x/-9 +4/-9

y = 1/3x -4/9

The slope is 1/3 and the y intercept is -4/9

[tex] \\ [/tex]

Answer:

Part A: x = y+45

Part B: 40 125-45 = 80, 80÷2 = 40

Part C: Yes, because 80+45 adds up to 125.

Hope this helps! :)

Answer:

Step-by-step explanation:

the second number be 2x. Therefore, the number 80 is divided in the ratio of 3:2 is, 48 and 32.

Answer:

y = 9x + (-7) should be the answer

Answer:

(C).

[tex]height = \sqrt{ {29}^{2} - {21}^{2} } \\ = \sqrt{400} \\ = 20 \: units[/tex]

Answer:

(x+5)(x-2)

Step-by-step explanation:

x^2 +3x-10

What two numbers multiply to -10 and add to 3

5*-2 = -10

5+-2 = 3

(x+5)(x-2)

Answer:

just subtract

Step-by-step explanation:

first go number by number and then subtract them and see the average rate of change and input that number

Answer:

2) slope=2

y intervept=2

3) slope=1/2

y intercept=-6

4)slope=2

y intercept=4

Answer:

B.  2(x+2)(x+1)

Step-by-step explanation:

[tex]\sf\purple{B. \:2(x + 2)(x+1) }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]2 {x}^{2} + 6x + 4[/tex]

Taking 2 as common factor, we have

[tex] = 2 \: ( {x}^{2} + 3x + 2) \\ =2 \: ( {x}^{2} + 2x + x + 2)[/tex]

Taking [tex]x[/tex] as common from first two terms and 1 from last two terms, we have

[tex] = 2 \:[x(x + 2) + 1(x + 2)][/tex]

Taking the factor [tex](x+2)[/tex] as common,

[tex] = 2(x + 2)(x + 1)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

35x^2-5x^4

Step-by-step explanation:

You have to multiply the numbers on the outside to the numbers on the inside.

For example, 5x^2 times 7 would be 35x^2.

Answer:

∠1 = 90°

∠2 = 66°

∠3 = 24°

∠4 = 24°

Step-by-step explanation:

Usually the diagonals of a rhombus bisect each other at right angles.

Thus; ∠1 = 90°

Since they bisect at right angles, then;

∠R1S = 90°

Now, sum of angles in a triangle is 180°

Thus;

66° + 90° + ∠4 = 180°

156 + ∠4 = 180

∠4 = 180 - 156

∠4 = 24°

Now, also in rhombus, diagonals bisect opposite angles.

Thus; ∠4 = ∠3

Thus, ∠3 = 24°

Similarly, the diagonal from R to T bisects both angles into 2 equal parts.

Thus; ∠2 = 66°

Answer:

False

Step-by-step explanation:

Step-by-step explanation:

YOU ARE CORRECT

[tex] {7}^{(1 \times 9)} = {7}^{5 + 5} \\ {7}^{9} \: \: \: \: \: \: \: \: \: \: \: {7}^{10} [/tex]

the equation is false

Answer:

There are two types of similar triangle problems; these are problems that require you to prove whether a given set of triangles are similar and those that require you to calculate the missing angles and side lengths of similar triangles. Subtract both sides by 130°. Hence; By Angle-Angle (AA) rule, ΔPQR~ΔXYZ.

Step-by-step explanation:

Answer:

Expression

Step-by-step explanation:

Given expression :

4a+3b-6cx9

So this is expression not equation because equation consist zero on the righ side

Example: ax+b=0 (This is equation )

And

ax+b (This is expression)

Step-by-step explanation:

answer is in the photo above

Answer:

[tex]\displaystyle p = \frac{16}{q + 1}[/tex].

Step-by-step explanation:

Factor out the coefficient of [tex]x^{2}[/tex]:

[tex]\displaystyle \frac{1}{q + 1}\, [(q + 1)\, x^2 - 8\, x + p] = 0[/tex].

[tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex].

Let [tex]m[/tex] denote the real root of this equation. By the Factor Theorem, this equation would have the factor [tex](x - m)[/tex] repeated for two times in total:

[tex](x - m)^{2} = 0[/tex].

Expand to obtain: [tex]x^2 - 2\, m\cdot x + m^{2} =0[/tex].

Compare this expression with [tex]\displaystyle x^2 - \frac{8}{q + 1} \, x + \frac{p}{q + 1} = 0[/tex]:

[tex]\displaystyle -\frac{8}{q + 1} = -2\, m[/tex] (for the coefficient of [tex]x[/tex].)

[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex] (for the constant.)

Rewrite the first equation to find an expression for [tex]m[/tex] in terms of [tex]q[/tex]:

[tex]\displaystyle m = \frac{4}{q + 1}[/tex].

Substitute this expression for [tex]m[/tex] into the second equation to find an expression for [tex]p[/tex] in terms of [tex]q[/tex]:

[tex]\displaystyle \frac{p}{q + 1} = m^2[/tex].

[tex]\displaystyle \frac{p}{q + 1} = \frac{4^2}{(q+1)^{2}}[/tex].

[tex]\displaystyle p = \frac{16}{q + 1}[/tex].

Verify that this expression for [tex]p[/tex] satisfies the requirements:

[tex]\displaystyle (q + 1) \, x^{2} - 8\, x + \frac{16}{q + 1} = 0[/tex].

[tex]\displaystyle x^2 - \frac{8}{q + 1} + \frac{16}{(q+1)^2} = 0[/tex].

[tex]\displaystyle x = \frac{4}{q + 1}[/tex] is the (repeated) real root of this quadratic equation.

Answer:

-9

Step-by-step explanation:

Find the common ratio by dividing one of the numbers in the sequence by the previous number:

117/-13

= -9

So, the common ratio is -9.

Answer:

43 units^2

Step-by-step explanation:

Area of a rectangle is

A = l*w

The bottom rectangle is 3 by 11 for an area of 33

The top rectangle is  2 by 5 for an area of 10

Add the areas together

33+10 = 43

Answer:

62.5

Step-by-step explanation:

Because there are 5 prime numbers so you have to divide 100 by 8 and then multiply by 5 so the answer is 62.5

Answer:

I think it's option B ...

Answer:

A.) F(x)=1/x-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Apply the Distributive Property of Multiplication.  Multiply each of the three terms inside parentheses by -(1/2):

(3/4)x - 3x - (1/2) - 3x, or

(3/4)x - 6x - 1/2

The first two terms can be combined, to obtain:

(-5 1/4)x - 1/2, or (-21/4)x - 1/2

Answer:

It does since lets say X and Y equal 10 it works

Step-by-step explanation:

Answer:

(8,-9)

Step-by-step explanation:

solve the equation for x

x=13/5-3/5y

7x+8y=-16

substitute the given value of x into the equation 7x+8y= -16

7(13/5-3/5y)+8y= -16

solve the equation for y

7(13/5-3/5)+8y= -16

y= -9

substitute the given value of y into the equation x=13/5-3/5y

x=13/5-3/5x(-9)

solve for x

x=8

the ordered pair is (8,-9)

Answer:

The solution to this system of equations is x = 8, and y = -9

Step-by-step explanation:

Firstly we need to use the first equation to represent "x" in terms of "y", so we do the following...

[tex]5x + 3y = 13\\5x = 13 - 3y\\x = \frac{13}{5} - \frac{3}{5}y[/tex]

Now we take the second equation and replace "x" with an equal value in terms of "y" which we know from the previous equation, and just solve for "y".

[tex]7x + 8y = -16\\7(\frac{13}{5} -\frac{3}{5} y) + 8y = -16\\\\18\frac{1}{5} - 4\frac{1}{5} y + 8y = -16\\\\3\frac{4}{5}y = -34\frac{1}{5} \\\\y = -34\frac{1}{5} / 3\frac{4}{5} \\y = -9[/tex]

After we found the value of "y" we can find the value of "x" by using any of the two equations, we just have put "-9" instead of "y". For example...

[tex]5x + 3y = 13\\5x + 3(-9) = 13\\5x - 27 = 13\\5x = 13 + 27\\5x = 40\\x = 40 / 5\\x = 8[/tex]

Now we know that the solution to this system of equations is x = 8, and y = -9

f(-3)=g(-4) 123456789012345