What is the slope of the line represented by the equation y = 4/5x-3

\(5 + n = 12 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

The first integral to evaluate the volume of the tetrahedron is \(\int\limits\int\limits \int\limits R dV\). The integral that represents the volume in the order dx dy dz is \(\int\limits\int\limits \int\limits R dz dy dx\).

(a) Evaluating the integral ∫∫∫ R dV:

The limits of integration for z will be determined by the intersection of the plane and the coordinate axes. When x = 0 and y = 0, we have 12(0) + 4(0) + 3z = 12, which gives z = 4. When z = 0, we have 12x + 4y + 3(0) = 12, which gives 12x + 4y = 12. Dividing by 4, we get 3x + y = 3, which represents the line in the xy-plane.

To find the limits of integration for y, we need to consider the bounds of this line. When x = 0, we have y = 3; when x = 1, we have y = 0.

Finally, the limits of integration for x will be 0 to 1, as we are in the first octant.

So, the first integral to evaluate the volume is \(\int\limits^1_0 \int\limits^0_3 \, \int\limits^{({12-3x-4y} )}_4 \, dz dy dx.\)

(b) Writing the integral in the order dx dy dz:

The limits of integration for x will be determined by the intersection of the plane and the coordinate axes.

When y = 0 and z = 0, we have 12x + 4(0) + 3(0) = 12, which gives x = 1.

When x = 0, we have 12(0) + 4y + 3z = 12, which gives 4y + 3z = 12.

Dividing by 4, we get \(y + (\frac{3}{4})z = 3\), which represents the line in the yz-plane.

To find the limits of integration for y, we need to consider the bounds of this line. When z = 0, we have y = 3; when z = 4, we have y = 0.

Finally, the limits of integration for z will be 0 to 4, as we are in the first octant. Therefore, the integral that represents the volume in the order dx dy dz is:

\(\int\limits^1_0\int\limits^{4(1-(3/4)z}_{3}\int\limits^{12-4y-(3/4)z}_0 \, dx dy dz\).

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Answer:

cone: 157.08

cylinder: 502.65

sphere: 113.1

Step-by-step explanation:

Answer:

1000a+100b+10c+d

Step-by-step explanation:

place value of a =1000×a

place value of b=100×b

place value of c=10c

place value of d=1×d

Answer:

1000

Step-by-step explanation:

Answer:

x² - 3

This expression is not linear

Step-by-step explanation:

Let x = unknown number

The sum of a number and negative 3

Sum = addition

We are adding the unknown number "x" and -3

So we have x + (-3) or just x - 3

The sum of that is multiplied by the unknown number

So we get ( x - 3 ) x

We can then simplify this expression to get  x² - 3x

Any expression with an exponent is not linear. Refer to the attached image for more validation. A linear expression would create a straight line. The expression x² - 3x creates a curved line

This is because 3x-4 is a binomial consisting of the two terms 3x and -4

A monomial has only one term, which choices B through D reflect that.

The vertex and range of the function y = |x - 5| + 5 is (5, 4) and  [4, ∞) respectively

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

In the given function;

y = |x - 5| + 4

Using a graph, the lowest point of the function is at x = 5 and y = 4 is the vertex of this function.

vertex = (5, 4)

Range = [4, ∞)

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Answer:

b

Step-by-step explanation:

The amount of juice without orange juice will be 5.327 ounces.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that A fruit juice company includes 1.123 ounces of orange juice in a 6.45​-ounce bottle of mixed fruit juice.

The amount of orange juice will be calculated by subtracting the two values 6.45 and 1.123.

Juice = 6.45 - 1.123 = 5.327 ounces

Therefore, the amount of juice without orange juice will be 5.327 ounces.

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Answer:

  neither exponential nor linear

Step-by-step explanation:

A linear relationship will show a common difference between adjacent value. Here, the first differences between the first three values are 5 and 33. They are not the same, so the relation is not linear.

__

An exponential relationship will show first differences that are continuously increasing or decreasing by increasing or decreasing amounts (respectively).

As we showed, the difference between May 28 and May 27 is 33. This is more than the previous difference. However, the difference between May 30 and May 31 is only 28, which is less than a previous difference.

The relation is not exponential.

__

A graph points up the non-linearity of the relation.

Answer:

a and c are correct.

Step-by-step explanation:

In this arithmetic sequence, the first term is 3, and the common difference is 2. So a and c are correct.

a(n) = 3 + 2n for n>0 since a(0) = 3

c(n) = -1 + 2n for n>2 since c(2) = 3

Based on the information given in the problem, if you consider deposits as positive numbers and extractions as negative ones, you have the following expressions:

- Bill took $9.50

- 9.50

- Larry deposited twice the amount Bill took:

2*(9.50) = +19.00

- Chris deposited four times as much as Larry did:

4*(19.00) = +76.00

- Melinda took half the amount that Chris deposited:

- 1/2 * (76.00) = - 38.00

- Eddie took 9.50 less than Melinda:

- ( 38.00 - 9.50) = - (28.50) = -28.50

Then, by considering the signs of the different amounts of money you obtain:

-9.50 + 19.00 + 76.00 - 38.00 - 28.50 = 19.00

Hence, you can conclude that the amount of money in the safe increases by $19.00

There are 4 possible nitrogenous bases, so for each position in the DNA sequence there are 4 options to choose from. Therefore, in a single base position there are 4 possible mutations. In a double base position, there are 4 * 4 = 16 possible mutations. This means that for 11 double base positions, there are 11 * 16 = 176 possible double letter mutations.

DNA (Deoxyribonucleic Acid) is the genetic material that encodes the instructions for the development and function of all living organisms. DNA is made up of four nitrogenous bases: adenine (A), cytosine (C), guanine (G), and thymine (T).

The sequence of these nitrogenous bases is what determines the genetic information of an organism. Mutations are changes in the DNA sequence that can occur naturally or as a result of environmental factors.

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Answer:

Total weigh = 75g

a) so the mass of wheat and oats one protion = 75*(71/100) g = 53.25g

b) the mass of nuts in one serving = 75*(2.5/100) g = 1.875g

Step-by-step explanation:

Here I think mass = weigh, as it's not physics.

a) The relation is reflexive, symmetric, and transitive.

b) The relation is not reflexive, symmetric, or transitive.

a) For each watermelon x, x is related to x because the measured weight of x is at least the measured weight of x. Therefore, the relation is reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is also related to x (meaning the measured weight of y is at least the measured weight of x). Therefore, the relation is symmetric.

For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is related to z (meaning the measured weight of x is at least the measured weight of z). Therefore, the relation is transitive.

b) For each watermelon x, x is not related to x because no two watermelons have the same measured weight. Therefore, the relation is not reflexive.

For each watermelon x and y, if x is related to y (meaning the measured weight of x is at least the measured weight of y), then y is not related to x (meaning the measured weight of y is not at least the measured weight of x).

Therefore, the relation is not symmetric. For each watermelon x, y, and z, if x is related to y (meaning the measured weight of x is at least the measured weight of y) and y is related to z (meaning the measured weight of y is at least the measured weight of z), then x is not related to z (meaning the measured weight of x is not at least the measured weight of z).

Therefore, the relation is not transitive.

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Answer:

Question 1

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, or a right triangle)

Given:

⇒ BC² + 8² = 10²

⇒ BC² = 36

⇒ BC = 6 cm

Question 2

Given:

⇒ MB = AB - AM = 8 - x

As ΔABC ~ ΔMBN

⇒ AB : AC = MB : MN

⇒ 8 : 10 = (8 - x) : MN

\(\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}\)

\(\sf \implies \dfrac45=\dfrac{(8-x)}{MN}\)

\(\sf \implies MN=\dfrac54(8-x)\)

Question 3

D = (6, 8)

As ΔBAD ~ ΔMAP

⇒ AB : AD : BD = AM : AP : MP

⇒ 8 : 6 : 10 = x : AP : MP

\(\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}\)

\(\sf \implies AP=\dfrac34x\)

\(\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}\)

\(\sf \implies MP=\dfrac54x\)

Question 4

Perimeter of MNCDP = MN + NC + CD + PD + MP

As ΔABC ~ ΔMBN

⇒ AB : BC : AC = MB : BN : MN

⇒ 8 : 6 = (8 - x) : BN

\(\sf \implies \dfrac86=\dfrac{(8-x)}{BN}\)

\(\sf \implies BN=\dfrac34(8-x)\)

NC = BC - BN

\(\sf \implies NC=6-\dfrac34(8-x)\)

PD = 6 - AP

\(\sf \implies PD=6-\dfrac34x\)

Perimeter of MNCDP = MN + NC + CD + PD + MP

\(\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x\)

\(\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x\)

\(\sf \implies perimeter=10+8+6=24\)

Answer:

x = 112

Explanation:

The figure given is a pentagon; therefore, the sum of interior angles must add up to 540 degrees.

This means

Adding the angles on the left-hand side gives

Finally, subtracting 428 from both sides gives

which is our answer!

The value of Jenna's car would have been influenced by these factors, potentially increasing or decreasing its pound value in subsequent years.

In 2001, Jenna purchased a new car for £25000. The value of the pound fluctuated each year, leading to changes in the pound value of her car.

This means that the worth of her car in terms of pounds varied over time. The fluctuation in the pound's value could be due to factors such as inflation, economic conditions, or currency exchange rates.

As a result, the value of Jenna's car would have been influenced by these factors, potentially increasing or decreasing its pound value in subsequent years.

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Answer:

The dimensions have to be reduced by 2 inches

Step-by-step explanation:

Given that the dimensions are: 6 by 8 inches which means that the area is 48 square inches.

Let x be the amount to make a new photo which is half of the area that means

The new dimensions will be: (8-x) by (6-x) and as the area is half

The area of new photo will be: 48/2 = 24

Putting it mathematically

\((8-x)(6-x) = 24\\8(6-x)-x(6-x)=24\\48-8x-6x+x^2=24\\48-14x+x^2=24\\x^2-14x+48-24=0\\x^2-14x+24=0\\x^2-12x-2x+24=0\\x(x-12)-2(x-12)=0\\(x-2)(x-12)=0\\x-2=0 => x=2\\x-12=0 =>x=12\)

Subtracting 12 from both dimensions will make them negative so 12 cannot be the solution.

Hence,

The dimensions have to be reduced by 2 inches

We want to see by how much we must reduce the dimensions of the photograph in order to reduce its area to half. We will find that we must reduce each measure by 2 inches.

The original measures of the photograph are:

Then the area is:

A = (6 in)*(8 in)  = 48 in^2

Now we want to define a new length and a new width:

such that:

A' = L'*W' = 24 in^2

      (6 in - n)*(8in - n)  = 24 in^2

      48in^2 - n*14 in + n^2 = 24 in^2

    n^2 - n*14 in + 24in^2 = 0

This is a quadratic equation, we can solve this for n by using Bhaskara's formula, we will get:

\(n = \frac{14in \pm \sqrt{(-14)^2 - 4*1*24in^2} }{2*1} \\\\n = 7in \pm 5 in\)

The only solution that makes sense is:

n = 7in -  5in = 2in

This means that we need to reduce each measure by 2 inches.

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Based on the information given, the scale that's used by Harry for drawing the schoolyard will be 1:7000.

Firstly, it should be noted that

1 meter = 1000 milliliters

Therefore, 154 meters = 154,000 millimeters

Since the schoolyard is 154 meters long in real life but is 22 millimeters long in the drawing, then the scale will be:

= 22/154000

= 1/7000

Therefore, the scale is 1:7000.

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Answer:

A.) 10 to the 5th power

Step-by-step explanation:

because i'm ✨smart✨

The value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17

If 7x³ = 24, we can solve for x by taking the cube root of both sides:

\((7x^3)^{1/3} = (24)^{1/3} \\x = (24)^{1/3} \div7^{1/3}\)

To find the value of 5 - 4x, we can substitute the expression for x into the second equation:

5 - 4x = \(5 - 4(24)^{1/3} \div 7^{1/3\)

Simplifying, we get

5 - 4x = 5 - 4(2/3)

5 - 4x = 5 - (8/3)

5 - 4x = (15/3) - (8/3)

5 - 4x = 7/3

So the value of 5 - 4x is 7/3, which is equivalent to option (d) d. 17

The cube root of a number is a value that when multiplied by itself twice, produces the original number.

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An employee who is fired from his or her job because he or she lacks the skills required to accomplish the task, is part of structural unemployment.

Long-term unemployment known as structural unemployment is brought on by basic changes in an economy and made worse by unrelated elements like technology, rivalry, and public policy.

The type of unemployment you are referring to is called "structural unemployment."

Structural unemployment occurs when there is a mismatch between the skills possessed by job seekers and the skills demanded by employers. In this case, the employee lacks the necessary skills required to perform the job successfully, leading to their termination. Structural unemployment is a result of long-term changes in the economy, such as technological advancements or shifts in the structure of industries.

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If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch

The area of a triangle is 96 sq. inches

Let base be b

Its altitude is 2 inches greater than five times its base.

a=5b+2

ab/2=A

(5b+2)b/2=96

(5b+2)b=192

5b²+2b=192

5b²2+2b-192=0

On solving the quadrartic equation,

we get

b=6

a=32

Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs

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Answer:

Step-by-step explanation:

Let x represent the number of weeks

Let y represent the number of days in a week!

Answer:

C = 16pi or ≈50.24 units

Step-by-step explanation:

(x − 9)^2 + (y − 3)^2 = 64

This equation is in the form

(x-h)^2 + (y-k)^2 = r^2

The radius is 8

The circumference is given by

C = 2*pi*r

C = 2*pi*8

C = 16 pi

Using 3.14 as an approximation for pi

C = 16(3.14)

C ≈50.24

Answer: 20%

Step-by-step explanation:

Answer:

4.712 radians

Step-by-step explanation:

Answer: $8,500

Step-by-step explanation:I{Prt}