URGENT AND EASY 8TH GRADE MATH

An equation that shows the relationship between the two angle measure is 3x + 2 = 180 and the value of x is 59.

Let us consider the two supplementary angles with measures (x + 1) and (2x + 1). Since they are supplementary angles, we know that their sum is equal to 180 degrees. We can write this relationship between the two angle measures as an equation:

(x + 1) + (2x + 1) = 180

Simplifying this equation, we get:

3x + 2 = 180

Now, we can solve for x by isolating it on one side of the equation. To do this, we can subtract 2 from both sides of the equation:

3x = 178

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 59.33

Therefore, we should round the value of x to the nearest whole number, which is 59.

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Answer:

120

Step-by-step explanation:

Given,

Solution A contains 2 parts salt to 8 parts water

Solution B contains 3 parts salt to 5 parts water

Target Mixture contains3 parts salt to 7 parts water:

Expressing the salt concentration in decimal form

Solution A: 2/(2 + 8) = 2/10 = 0.20 salt

Solution B: 3/(3 + 5) = 3/8 = 0.375 salt

Mixed Solution: s/(3 + 7) = 3/10 = 0.30 salt

Since target mixture is 280 quarts

If the amount of 0.375 salt present in mixed solution = x

Then, the amount of 0.20 salt, y = 280 – x

Using a typical mixture equation

0.375x + 0.20(280-x) = 0.30(280)

0.375x + 56 - 0.20x = 84

Subtract 56 from both sides of the equation

0.375x - 0.20x + 56 – 56 = 84 – 56

0.375x - 0.20x = 28

0.175x = 28

Divide both sides of the equation by 0.175

0.175x/0.175 = 28/0.175

x = 160

y = 280 – x

y = 280 – 160

y = 120

To apply the integral test, we need to check if the function f(x) = ln(x)/x^4 is continuous, positive, and decreasing for all x ≥ 1.

The function is positive and continuous for all x ≥ 1. To check if it is decreasing, we can take the derivative:

f'(x) = (1 - 4ln(x))/x^5

For x ≥ e^(1/4), the derivative is negative, which means that f(x) is decreasing for x ≥ e^(1/4). Since the function is positive, continuous, and decreasing for x ≥ 1, we can apply the integral test:

∫1^∞ ln(x)/x^4 dx = lim(t→∞) ∫1^t ln(x)/x^4 dx

Using integration by parts with u = ln(x) and dv = x^-4 dx, we get:

∫1^∞ ln(x)/x^4 dx = [-ln(x)/3x^3]1^∞ + (1/3) ∫1^∞ x^-4 dx

The first term evaluates to 0 since ln(1) = 0 and lim(x→∞) ln(x)/x^3 = 0. The second term evaluates to:

(1/3) ∫1^∞ x^-4 dx = (1/3) [(-1/3)x^-3]1^∞ = 1/9

Therefore, the series ∑n=1^∞ ln(n)/n^4 converges since the integral test confirms that its corresponding improper integral is finite. Thus, the answer is a. converges.

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a) The strength to weight ratio is 2/r. b) The nanotube's strength to weight ratio is 100 times greater than that of the flea's leg. 2) a) Resistance is (rho * L) / A = (2.44 × \(10^{-4\) Ω⋅m * 1.00 cm) / [\((1.00 cm)^2\)].

(a) The scaling relationship for the strength to weight ratio can be derived as follows. The strength of the object is proportional to its area, which for a cylinder can be expressed as A = 2πr(2r) = 4π\(r^2\). On the other hand, the weight of the object is proportional to its volume, given by V = π\(r^2\)(2r) = 2π\(r^3\). Therefore, the strength to weight ratio (S/W) can be calculated as (4π\(r^2\)) / (2π\(r^3\)) = 2/r.

(b) To compare the strength to weight ratio of a nanotube (r = 10 nm) and the leg of a flea (r = 100 μm), we substitute the respective values into the scaling relationship obtained in part (a). For the nanotube, the ratio becomes 2 / (10 nm) = 200 n\(m^{-1\), and for the flea's leg, it becomes 2 / (100 μm) = 2 × \(10^4\) μ\(m^{-1\). Therefore, the strength to weight ratio of the nanotube is 200 n\(m^{-1\) while that of the flea's leg is 2 × \(10^4\) μ\(m^{-1\). The nanotube's strength to weight ratio is 100 times greater than that of the flea's leg.

(a) To find the resistance of a cube of gold with side length L = 1.00 cm, we need to calculate the area and substitute the values into the resistance formula. The area of one face of the cube is A = \(L^2\) = \((1.00 cm)^2\). Given that the resistivity of gold (rho) is 2.44 × \(10^{-4\) Ω⋅m, the resistance (R) can be calculated as R = (rho * L) / A = (2.44 × \(10^{-4\) Ω⋅m * 1.00 cm) / [\((1.00 cm)^2\)].

(b) Similarly, for a cube of gold with side length L = 10.0 nm, the resistance can be calculated using the same formula as above, where A = \(L^2\) = \((10.0 nm)^2\) and rho = 2.44 × \(10^{-4\) Ω⋅m.

One application that utilizes the unique properties of nanomaterials is targeted drug delivery systems. In this application, nanomaterials, such as nanoparticles, play a crucial role. These nanoparticles can be functionalized to carry drugs or therapeutic agents to specific locations in the body. The small size of nanomaterials allows them to navigate through the body's biological barriers, such as cell membranes or the blood-brain barrier, with relative ease.

The particular property of nanomaterials that makes them suitable for targeted drug delivery is their large surface-to-volume ratio. Nanoparticles have a significantly larger surface area compared to their volume, enabling them to carry a higher payload of drugs. Additionally, the surface of nanomaterials can be modified with ligands or targeting moieties that specifically bind to receptors or biomarkers present at the target site.

By utilizing nanomaterials in targeted drug delivery, it is possible to enhance the therapeutic efficacy while minimizing side effects. The precise delivery of drugs to the desired site can reduce the required dosage and improve the bioavailability of the drug. Moreover, nanomaterials can protect the drugs from degradation and clearance, ensuring their sustained release at the target location. Overall, the unique properties of nanomaterials, particularly their high surface-to-volume ratio, enable efficient and targeted drug delivery systems that hold great promise in the field of medicine.

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Answer:

 . .

Step-by-step explanation:;

We are given two similar pyramids with base areas of 12.2 cm² and 16 cm². The surface area of the larger pyramid is 56 cm². We need to determine the surface area of the smaller pyramid.

The ratio of the surface areas of two similar solids is equal to the square of the ratio of their corresponding lengths. In this case, since the pyramids are similar, the ratio of their base areas is equal to the square of the ratio of their corresponding lengths. Let's denote the length ratio as x. We have (16/12.2)² = x², where x represents the ratio of the lengths of the corresponding sides of the pyramids. Simplifying the equation, we get (256/148.84) = x². Solving for x, we find that x ≈ 1.134. Now, we can calculate the surface area of the smaller pyramid. Since the surface area is proportional to the square of the length, we have (56/1.134²) = 59.8 cm². Therefore, the surface area of the smaller pyramid is approximately 59.8 cm².

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Answer:

- more people need extra large sweatshirts than large sweatshirts

Answer: C

Step-by-step explanation:

More people need extra large sweatshirts than large sweatshirts.

Answer:

3 sketch oads and 2 pencil

Step-by-step explanation:

I hope this can help you

Answer:

65/2

Step-by-step explanation:

3 1/4= 13/4

13/4(10)=65/2

Answer:

32 1/2

Step-by-step explanation:

first, convert both numbers into improper fractions. (10/1 and 13/4) then multiply the numerators to get 130 and the denominators to get 4. You get 130/4. Simplified, that would be 65/2 and as a mixed number, it would be 32 and 1/2.

If the difference between the total surface area and curved surface area of a hemisphere is 154 cm2, then its volume is 718.66 cm³

In general, the term "hemisphere" refers to the lower half of the earth, such as the northern or southern hemispheres. A hemisphere, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.

In everyday life, we encounter a variety of objects that have a hemisphere shape, such as a cherry that is shaped like a hemisphere when cut in half or a grapefruit that has a hemisphere shape when cut in half.

The difference between the total surface area and curved surface area of a hemisphere is 154cm.

Total Surface Area of Hemisphere = 3πr²

And Curved Surface Area of Hemisphere = 2πr²

It is Given that

Total Surface Area of Hemisphere - Curved Surface Area of Hemisphere. = 154.

Substituting the values, we get,

⇒ 3πr² - 2πr² = 154

⇒ πr² = 154

⇒ r² = 154/π

⇒ r² = 154 × (7/22)

⇒ r² = 7 × 7

⇒ r = 7.

Now, lets find the volume which is

Volume of Hemisphere = 2/3πr³

V = 2/3π(7)³

V = 2/3(22)(7)²

V = 2156/3

V = 718.66 cm³

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Answer:

5.5

Step-by-step explanation:

180/3 =60 (60/1 hr)

330/60 =5.5

Answer:

40

Step-by-step explanation:

We're given an angle that forms a linear pair, and we're given an isosceles triangle. The angle to the right of 110 is 70, since they have to add up to 180. Since this is an isosceles triangle (denoted by the two dashes), we know that the other base angle has to be 70. 70 + 70 = 140; all angles add up to 180 so 180 - 140 = 40 degrees.

Answer:

40 degrees

Step-by-step explanation:

Since this is an isosceles triangle the 2 bottom angles are congruent

The bottom angles will be 70 degrees bc the exterior angle is 110 and 180-110=70

Because a triangle adds up to 180 degrees you need to use the equation 70 + 70 + x = 180 and you should get x = 40 degrees

1. plug in the values

3(2) - (-1) = 7; true

2(2) + 3(-1) = 1

4 -3 = 1; true

yes, the point is true for the system. .

2.

the solution is referring to where both the lines intercept on the graph.

3. replace 'y' in the first equation with the second equation

3x + 6x + 1 = 10

9x + 1 = 10

9x = 9

x = 1

plug x = 1

y = 6(1) + 1

y = 7

(1,7)

4. elimiate the common terms which is 'n' which gives;

5m = -5

m = -1

plug in to find 'y' AKA 'n'

3(-1) - n = 2

-3 - n = 2

-n = 5

n = -5

I can futher explain if you'd like, let me know.

Answer: 7%

Step-by-step explanation: I did the test.

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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If you deposit $2,500 in a bank account that pays an APR of 3.55% and compounds interest monthly, after 6 years, the future value in the account will be $3,092.49.

The future value can be determined using the FV formula that compounds the present value using the FV factor as follows:

FV = PV (1 + r)^nt.

The future value can also be computed using an online finance calculator as follows:

N (# of periods) = 72 months (6 years x 12)

I/Y (Interest per year) = 3.55%

PV (Present Value) = $2,500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $3,092.49

Total Interest = $592.49

Thus, the initial deposit of $2,500 will become $3,092.49 in 6 years at 3.55% compounded monthly.

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Answer:

15.6

Step-by-step explanation:

SOH -CHA-TOA

Tan = opp / adj

Tan(60) = 27/x

x = 27/tan(60)

Answer:

x ≈ 5.4

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan60° = \(\frac{opposite}{adjacent}\) = \(\frac{MN}{LM}\) = \(\frac{9.3}{x}\) ( multiply both sides by x )

x × tan60° = 9.3 ( divide both sides by tan60° )

x = \(\frac{9.3}{tan60}\) ≈ 5.4 ( to the nearest tenth )

Answer:

Select all the expressions which have 3 as the greatest common factor of the terms.

b + 3 + 6c

27n + 66p

38 – 9j + 6k

12x + 75y + 21

–32 – 24z

Answer:

Please, I would appreciate it!

Answer:

A = 58.9 degrees

Step-by-step explanation:

straight line angles add up to 180 degrees

121.1 + A = 180

A = 180 - 121.1

A = 58.9 degrees

The unknown variables in parallelograms above include the following:

x = 8 units.

y = 27 units.

x = 20°

x = 9°

In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In this context, we have:

2x - 5 = 11

2x = 11 + 5

2x = 16

x = 8 units.

y + 1 = 28

y = 28 -1

y = 27 units.

Generally speaking, the opposite angles of a parallelogram are always congruent or equal and as such, we have the following:

(7x - 1)° = 139°

7x = 139° + 1°

7x = 140°

x = 140/7

x = 20°

For parallelogram b, we have:

(7x - 10)° = (6x - 1)°

7x - 6x = -1 + 10

x = 9°

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Answer:

h= -2

Step-by-step explanation:

Move the terms,

19 + 4h = 1 -5h

Combine like terms,

4h+5h=1-19

Divide both sides...

9h= -18

-18/9 = -2

Answer:

h=-2

Step-by-step explanation:

17+4h+2=1-5h

19+4h=1-5h

-1 -1

18+4h=-5h

-4h -4h

18=-9h

18/-9=-9h/-9

h=-2

hopefully this helps :)

Answer:

mf you are asking this in high school.

Step-by-step explanation:

Answer:

x=-16

Step-by-step explanation:

Ler the number be x.

Now we have,

\((5-x)/3=7\\5-x=21\\5-21=x\\x=-16\)

Hope it will help you.

Answer:

Now,By question,

Answer:

The coefficient of 6m is 6

Step-by-step explanation:

On solving thr provided question, by help of arithmetic progression, we got to know that a10 = 207

There are two approaches to define arithmetic progressions (AP):

The difference between any two successive terms in an arithmetic sequence must always be equal, and it is sometimes referred to as a series in which all terms except the first are created by adding a predetermined number to the preceding term.

9,15,25..............

15-9 = 6

25-15 = 10

a4 - 25 = 14 => a4 = 39

a5-39 = 18 => a5 = 57

a6-57 = 22 => a6 79

...

...

...

...

...

a10 - 169 = 38 => a10 = 207

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D   sin 85         sin 31

   ---------- =     ----------

     b                  9.3

We can use the law of sins

sin B        sin A         sin C

--------- = ----------- = ----------

b                   a            c

We do not know angle C, but we can calculate it

The angles of a triangle add to 180

A + B + C = 180

64+ 85 + C = 180

149 + C = 180

C = 180-149

C =31

sin B         sin C

--------- = ----------

b                  c

We know B =  85, C = 31, b = unknown and c = 9.3

sin 85         sin 31

---------- = ----------

b                  9.3

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Answer:

in ratio 4:14

Step-by-step explanation:

The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

maximize: z = c1x1 + c2x2 + ... + cnxn

subject to

a11x1 + a12x2 + ... + a1nxn ≤ b1

a21x1 + a22x2 + ... + a2nxn ≤ b2

am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i

In our case,

the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x

subject to:

x1 + x2 - x3 ≤ 5

6x1 + 5x2 - x4 ≤ 10

xi ≥ 0 for all i

We can rewrite the constraints as follows:

x1 + x2 - x3 + x5 = 5  (adding slack variable x5)

6x1 + 5x2 - x4 + x6 = 10  (adding slack variable x6)

Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:

x1 = x7

x2 = x8

x3 = x9

x4 = x10

The objective function becomes:

z = 36x7 + 30x8 - 3x9 - 4x10

Now we have the problem in standard form as:

maximize: z = 36x7 + 30x8 - 3x9 - 4x10

subject to:

x7 + x8 - x9 + x5 = 5

6x7 + 5x8 - x10 + x6 = 10

xi ≥ 0 for all i

To apply the simplex algorithm, we initialize the simplex tableau as follows:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |   0    |  36    |   30   |   -3   |   -4   |    0    |

---------------------------------------------------------------------------

x5|   0   |   1    |   0    |   1    |   1    |   -1   |   0    |    5    |

---------------------------------------------------------------------------

x6|   0   |   0    |   1    |   6    |   5    |   0    |   -1   |   10    |

---------------------------------------------------------------------------

Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:

Iteration 1:

1. Choose the most negative coefficient in the 'z' row, which is -4.

2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 5/0 = undefined, 10/(-4) = -2.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to

make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.4   |  36    |   30   |   -3   |   0    |   12    |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.2  |   1    |   1    |   -1   |   0    |   5     |

---------------------------------------------------------------------------

x10|   0  |   0    |   0.2  |   1.2  |   1   |   0    |   1    |   2.5   |

---------------------------------------------------------------------------

Iteration 2:

1. Choose the most negative coefficient in the 'z' row, which is -3.

2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).

3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.

Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5

4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.

5. Perform row operations to make all other elements in the pivot column zero.

After performing these steps, we get the updated simplex tableau:

  |  Cj   |   x5   |   x6   |   x7   |   x8   |   x9   |   x10  |    RHS  |

---------------------------------------------------------------------------

z |  0    |   0    |  0.8   |  34    |   30   |   0    |   4    |   0     |

---------------------------------------------------------------------------

x5|   0   |   1    |  -0.4  |   0.6  |   1    |   5   |   -2   |   10    |

---------------------------------------------------------------------------

x9|   0   |   0    |   1    |   6    |   5    |   0   |   -5   |   12.5  |

---------------------------------------------------------------------------

Iteration 3:

No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:

z = 0

x1 = x7 = 0

x2 = x8 = 10

x3 = x9 = 0

x4 = x10 = 0

x5 = 10

x6 = 0

Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.

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