2a) What is the side length of the following square?*

Answer:

The function that models the mass of the carbon-14 sample remaining t years since the initial measurement is

M(t) = 741 e⁻⁰•⁰⁰⁰¹²¹ᵗ

with M(t) in grams and t in years.

Step-by-step explanation:

Radioactive reactions always follow a first order reaction dynamic

Let the initial concentration of Carbon-14 be M₀ and the concentration at any time be M

(dM/dt) = -kM (Minus sign because it's a rate of reduction)

(dM/dt) = -kM

(dM/M) = -kdt

 ∫ (dM/M) = -k ∫ dt 

Solving the two sides as definite integrals by integrating the left hand side from M₀ to M and the Right hand side from 0 to t.

We obtain

In (M/M₀) = -kt

(M/M₀) = e⁻ᵏᵗ

M(t) = M₀ e⁻ᵏᵗ

Although, we can obtain k from the information on half life.

For a first order reaction, the rate constant (k) and the half life (T) are related thus

T = (In2)/k

The half life is the time taken for the radioactive substance to decay to hAlf of its original amount, and according to the question, T = 5730 years

k = (In 2)/5730 = 0.000120968 /year. = 0.000121 /year

M(t) = M₀ e⁻ᵏᵗ

k = 0.000121 /year, M₀ = 741 grams

The equation then becomes

M(t) = 741 e⁻⁰•⁰⁰⁰¹²¹ᵗ

with M(t) in grams and t in years.

Hope this Helps!!!

Answer:

M(t)=741*(1/2)^t/5730

Answer:

844 is the ans

Step-by-step explanation:

512+4+1 -7 +343+9= 844

Answer: 844

Step-by-step explanation:

Answer:

15c +14b -22

Step-by-step explanation:

12c+14b+3c-22

Combine like terms

12c+3c+14b-22

15c +14b -22

Answer:

126

Step-by-step explanation:

squaring both sides

([tex]\sqrt{2x+4} ^{2} =16^{2}[/tex]

⇒2x+4=256

2x=252

x=252/2=126

Answer: A = x^2/16 + (5 - x/4)^2 > 20.5

Hope this helped.

Answer:

-180 is your answer.

Step-by-step explanation:

Answer: -180

Step-by-step explanation: I uh, used the calculator app on my phone.

Answer:

6

Step-by-step explanation:

Answer:

a1 = 0.5; common ratio = 5

Step-by-step explanation:

Let the common ratio = r

a2 = 2.5

a3 = 2.5r

a4 = 2.5r * r = 2.5r^2

We are told a4 = 62.5, so

2.5r^2 = 62.5

Divide both sides by 2.5

r^2 = 25

r = 5

a2 = a1 * r

a1 = a2/r = 2.5/5 = 0.5

Answer: a1 = 0.5; common ratio = 5

Answer:

kn=15

nm=20

Step-by-step explanation:

The lengths of sides KN and NM of the kite

KN =  15   units

NM =   20 units

A kite is a quadrilateral with four sides that may be divided into two neighboring pairs of equal length sides. A parallelogram, on the other hand, has two sets of equal-length sides, but they are opposed to one another as opposed to being adjacent.

Given:

KLMN is a kite.

According to the given kite,

KN = KL........ (1)  

and LM = NM........ (2)

From equation (1)

y + 10 = 2y + 5

y = 5.

Now,

3x -1 = 2x + 6

x = 7

We get,

LM = MN = 20

KN =  15   units

NM =   20 units

To learn more about the kite's shape;

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Answer:

-4,8

Step-by-step explanation:

If vertex A is located at (-1, 2) then the coordinates of A' is

A translation only moves a shape up, down, or from side to side; it has no effect on how it appears. One illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape. Every point in the shape is moved in the same direction and by the same amount.

We have,

The triangle is translated 6 units up and 3 units left.

If vertex A is located at (-1, 2).

To Translate 6 units up we have to add 6 to the y coordinate.

and, to translate 3 units left we have to subtract 3 from the x coordinates.

So, the coordinates after translation is

A (-1,2)  -->  A' (-4,8)

B (1,5)  -->  B' (-2,11)

Learn more about Translation here:

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Answer:

[tex]x=12\:mm[/tex]

Step-by-step explanation:

[tex]A=bh[/tex]

[tex]b \times h=120[/tex]

[tex]b \times 10=120[/tex]

[tex]b=120 \div 10[/tex]

[tex]b=12[/tex]

Answer:

31

Step-by-step explanation:

Each pizza had 24 slices so 2 pizzas had 24+24 or 24x2 = 48  slices

If only 17 remains, 48-17 = 31 slices got eaten

Answer:

31 eaten

Step-by-step explanation:

She started with 2 pizzas with 24 slices each

2*24 = 48

17 slices were left

48 - 17 = 31

That means 31 were eaten

Answer:

The last option is correct. (f*g)(x) = x² - 5

Step-by-step explanation:

Since is f * g you have to multiply them together.

x² - 2 * x - 3 (x)

Next ust simplify.

x² -5x

Answer:

A.

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] ÷ 5 = [tex]\frac{1}{3}*\frac{1}{5} =\frac{1}{15}[/tex]

Answer:

The answer is B.

Step-by-step explanation:

The shape form a Rectangular Pyramid.

Answer:

B, a Pyramid

Step-by-step explanation:

The net has a square base with 4 triangular faces. D, which is also a triangular prism, is not right as it has a triangular base, with every side being a triangle.

So B is the right answer.

Answer:

The measurements of the two angles are 67.5° and 112.5°

Step-by-step explanation:

We can set up the equation just like a normal equation when you are finding x. Once we know what x is, then we can use that number and multiply it to 3 and 5 to find the measurements of the angles.

3x + 5x = 180

Combine like terms.

8x = 180

Divide 180 by 8.

x = 22.5

Now, we plug in x to 3 and 5.

3 * 22.5 = 67.5

5 * 22.5 = 112.5

Just to make sure our work is correct, let's add these numbers together.

67.5 + 112.5 = 180

The measurement of the angle is 67.5 degrees and the measurement of the supplement of the angle is 112.5 degrees.

When the sum of the two angle are equal to the 180 degrees, then these angles are called the supplementary angle of each other.

The ratio of the measurement of an angle to its supplement is 3:5. Let, the ratio,

[tex]\dfrac{3}{5}=x[/tex]

As, these angles are supplementary to each other. Thus,

[tex]3x+5x=180\\8x=180\\\x=\dfrac{180}{8}\\x=22.5[/tex]

Thus, the measurement of the angle is,

[tex]3x=3\times22.5\\3x=67.5[/tex]

The measurement of the supplement of the angle is,

[tex]5x=5\times22.5\\5x=112.5^o[/tex]

Hence, the measurement of the angle is 67.5 degrees and the measurement of the supplement of the angle is 112.5 degrees.

Learn more about the supplementary angle here;

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Answer:

they would need 15 cases for 410 bag of chips

Step-by-step explanation:

410/7= about 15

Answer:

x = 7

Step-by-step explanation:

Since this is a right triangle, we can use a trig function

tan theta = opposite/ adjacent

tan 45 = 7/x

Multiply each side by x

x tan 45 = 7

Divide each side by tan 45

x = 7/ tan 45

x = 7

Answer:

7

Step-by-step explanation:

It is a 45 45 90 triangle

meaning that the side lenghts will be x, x, x root 2

the hypotenuse will be x root 2, so that means that the side length will be 7

Answer:

12

Step-by-step explanation:

Answer:

D) a horizontal stretch

Step-by-step explanation:

"A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis." Quoted from mathbitsnotebook.com.

Answer:

168, a little of both

Step-by-step explanation:

Make 14 out of 50, 14/50 simplified its 7/25, multiply it by 600 and you get 168 its a little of both because half the info we were given its experimental since it is not theorized, what we're being given (the question) and what we gave is theorized since we didn't actually perform an experiment to get a real answer

Answer

The answer is C. Trina is not correct because the two sides of the equation are equivalent.

Step-by-step explanation:

1.  solve for x

-8(x - 4) + 2x = -4(x - 8) -2x

-8x + 32 + 2x = -4x + 32 -2x

-6x + 32 = - 6x + 32

0 = 0

This equation has infinite solutions, any rational number fits as solution for x in this equation. And as we can see both sides of it are equivalent.

Therefore, the correct answer is C. Trina is not correct because the two sides of the equation are equivalent.

Hope This Helps :p

C. Trina is not correct because the two sides of the equation are equivalent

I just took the quiz on edge

Answer:

23 deg

Step-by-step explanation:

For angle x, 3 is the opposite leg.

sqrt(58) is the hypotenuse.

The trig ratio that relates the opposite leg and the hypotenuse is the sine.

sin x = opp/hyp

sin x = 3/sqrt(58)

sin x = 0.3939

x = sin^-1 0.3939 = 23 deg

Answer:

Step-by-step explanation:

surface area=4×5+2×1/2×3×4+5×5+3×6

=20+12+25+18

=75

Answer:

The answer is option 2.

Step-by-step explanation:

Given that the equation of a straight line is y = mx + c where m represents gradient and c is the y-intercept which touches the y-axis.

By looking at the graph, we know that it is a positive gradient and it touches -1 at y-axis.

Answer:

Answer:

The dilation is an enlargement, and the scale factor is 2.  So, the answer is B.  

Step-by-step explanation:

The dilation is an enlargement, and the scale factor is 2.  

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

The image of the object undergoing transformation is given.

From the attached object, we se that CP = 4.

Also CP' = 8

Thus; Scale factor is 8/4 = 2

Now, reduction is defined as reducing the dimensions while enlargement is increasing the dimensions by a scale factor.

Thus, the denominator of the scale factor is greater than the numerator, then there is a reduction.

The scale factor of the given dilation is; 2 and the dilation is a enlargement.

Read more about Transformations at;

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Answer:

I hope it helps . For any clarification , Please notify me through the comment section .

Step-by-step explanation:

[tex]f(x) = 3x-5\\g(x) = 2(x-1)\\ \\g(-3) = 2(-3-1)\\g(-3) = 2(-4)\\g(-3) = -8\\\\f[g(x)] = f(2(x-1)\\f[g(x)] = 3[2(x-1)]-5\\f[g(x)] = 3[2x-2]-5\\f[g(x)] = 6x-6-5\\f[g(x)] = 6x-11\\\\g[f(x)] = g[3x-5]\\g[f(x)] = 2[3x-5-1]\\g[f(x)] = 6x -10-2\\g[f(x)] = 6x -12[/tex]

Answer:

The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3

Step-by-step explanation:

- The shaved ice is modeled as a sphere.

- The half of the shaved ice sphere extends above the cup holder.

- The volume of sphere with radius r = diameter d / 2 :

- We are to calculate the volume of the extended part of the sphere with diameter d = 8 cm or radius r = 4 cm.

- The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3

                                             Hopes This Helps