What index of m will equal to 1/m^2 ?

Answer:

x=1

Step-by-step explanation:

5x+37=-6(1-8x)

Distribute

5x+37 = -6 +48x

Subtract 5x from each side

5x+37 -5x = -6+48x-5x

37 = -6+43x

Add 6 to each side

37+6 = -6+43x+6

43 = 43x

Divide by 43

43/43 = 43x/43

1 =x

Answer:

x=1

Step-by-step explanation:

5x+37=-6(1-8×)

5x+37=-6(-7)

5x+37=6 x 7

5x+37= 42

5x+37-37=42-37

5x=5

5x/5 = 5/5

x = 1

Hope it Helps !!

The equation of line H in fully simplified slope-intercept form is y = 15x + 10.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (40 - 10)/(2 - 0)

Slope (m) = 30/2

Slope (m) = 15.

At data point (0, 10) and a slope of 15, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 = 15(x - 0)

y = 15x + 10

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

The given polynomial solved as same as RHS is x^3/3(x^2- 1/x^2)

Polynomial is defined as the sum of variable terms in the form of k×x^n, where k is constant and x variable and n is an integer.

we have given a polynomial,

(x-1/x)(x^4/3+x^2/3) = (x^3/3)(x²-1/x²)

Take LHS

⇒  (x-1/x)(x^4/3+x^2/3)

⇒  (x^2-1/x)×(x^4 + x^2/3)

⇒  (x^2-1/x) x^2(x^2+1/3)

⇒  x^2/3x (x^2-1)(x^2+1)

⇒​x^2/3x(x^4-1)                                  ∴(a^2-b^2 = (a+b)(a-b))

multiply numerator and denominator by x

⇒x^3/3 (x^4-1/x^2)

⇒x^3/3(x^2- 1/x^2) = RHS

Hence, given problem has solved.

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The electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

The electric field is a vector field that represents the force experienced by a charged particle due to an electric charge distribution. It is a measure of the electric force per unit charge at a particular point in space. The electric field is defined as the negative gradient of the electric potential, which is the energy per unit charge that a charged particle would have at that point in space. The electric field can be used to calculate the force experienced by a charged particle in the presence of other charges, and is a fundamental concept in the study of electromagnetism.

The electric field force between two point charges is given by Coulomb's law:

F = k * (q₁ * q₂) / r²

where k is the Coulomb constant (8.99 x 10⁹ N m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.

To calculate the work done by the electric field force, we need to find the force at the initial distance (0.30 m) and the final distance (1.05 m), and then subtract the work done at the initial distance from the work done at the final distance.

At a distance of 0.30 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (0.30 m)² = 4.02 x 10⁻⁸ N

The work done at this distance is:

W = F * 0.30 m = 1.21 x 10⁻⁷ J

At a distance of 1.05 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (1.05 m)² = 1.33 x 10⁻⁸ N

The work done at this distance is:

W = F * 1.05 m = 1.40 x 10⁻⁷ J

Finally, to find the total work done, we subtract the work done at the initial distance from the work done at the final distance:

W total = W final - W initial = 1.40 x 10⁻⁷ J - 1.21 x 10⁻⁷ J = 1.90 x 10⁻⁸ J.

Therefore, the electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

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Answer:

\(-5\dfrac{31}{40}\)

Step-by-step explanation:

Convert to improper fractions:

\(1\dfrac{1}{10}-6\dfrac78=\dfrac{1 \times10+1}{10}-\dfrac{6 \times8+7}{8}=\dfrac{11}{10}-\dfrac{55}{8}\)

Make denominators the same:

\(\dfrac{11}{10}-\dfrac{55}{8}=\dfrac{11\times8}{10\times8}-\dfrac{55\times10}{8\times10}=\dfrac{88}{80}-\dfrac{550}{80}\)

Therefore,

\(\dfrac{88}{80}-\dfrac{550}{80}=\dfrac{88-550}{80}=-\dfrac{462}{80}=-\dfrac{231}{40}\)

Convert to mixed number:

\(-\dfrac{231}{40}=-5\dfrac{31}{40}\)

Answer: The image is (6,-3)

Step-by-step explanation:

The coordinates of R is  ( 4,-2)  and to find the image using the scale factor 1.5 you will multiply the x coordinates by 1.5 and the y coordinate also by 1.5 to have the new image of R.

4 * 1.5 = 6

-2 * 1.5 = -3

The new coordinates care (6, -3)

By using conventional units of measurement, calculations are made consistently and without confusion.

Distance in mathematics refers to the numerical measurement of the actual distance between two locations. It is a measurement of the distance between two things or places, typically expressed in terms of meters, kilometers, feet, miles, etc. The Pythagorean theorem can be used to determine the separation between two points in a plane in Euclidean mathematics. The following equation can be used to determine how far two locations (x1, y1) and (x2, y2) are from one another in a two-dimensional space:

distance is equal to (((x2 - x1)2 Plus ((y2 - y1)2)

The following formula can be used to determine how far two locations are from one another in three dimensions: (((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2) is the formula for distance. In many areas of mathematics, including geometry, algebra, and calculus, distance is a crucial notion.

given

To preserve the use of standard units of measurement, the measurement of 7 feet 2 inches rather than 6 feet 14 inches is preferred.

One foot is equal to 12 inches in this method. In cases where the total number of inches is less than 12, 6 feet and 14 inches should be changed to feet and inches.

The following formula can be used to change 6 feet, 14 inches to 7 feet, 2 inches:

It is possible to divide 14 inches into 12 inches and 2 inches, or 1 foot and 2 inches.

To get 7 feet, multiply 1 foot by 6 feet.

Therefore, the post office has a total height and width of 7 feet 2 inches.

By using conventional units of measurement, calculations are made consistently and without confusion.

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Answer:

(5/2, 6)

Step-by-step explanation:

(x, y)=[(5+0)/2, (9+3)/2]

(x, y)=[5/2, 12/2]

(x, y)=(5/2, 6)

The Midpoint of the Line Segment that has the endpoints (5,9) and (0,3) is (5/2,6).

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now it is given that,

The endpoints of line segment is (5,9) and (0,3)

So, x₁ = 5

y₁ = 9

x₂ = 0

y₂ = 3

Let (x,y) be the midpoint of segment .

∴To find the midpoint of segment we have,

(x,y) =  {[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}

Put the values, we get

(x,y) = (5+0)/2 , (9+3)/2

solving them,

(x,y) = {(5/2) ,(12/2)}

or,

(x,y) = (5/2,6)

which is the required midpoint of the line segment.

Hence,the Midpoint of the Line Segment that has the endpoints (5,9) and (0,3) is (5/2,6).

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Answer:

w = 6    x = 5.6

Step-by-step explanation:

w/8 = 7.5/10

10w = 8 (7.5)

10w = 60

w = 6

x/7.5 = 4.5/6

6x = 7.5 (4.5)

6x = 33.75

x = 5.625

$36.40

1) Let's find out how much in dollars, Austin spent

Regular price: $91

60% off

60% = 0.6

2) To find that out let's multiply 91

91 ( 1-0.6) Subtract

91 (0.4) Distribute

36.4

3) So Austin bought that item for $36.40 (taxes not included)

Answer:

32 ft tall

Step-by-step explanation:

24 divided by 4.5 is 5.3 repeating. 6 times 5.3 is around 32

Answer:

40% chance

I hope I'm right srry if its wrong

Explanation:

The drawings you made are constructions of the perpendicular bisector. The "perpendicular" refers to the fact the second line meets the first line at a right angle (aka 90 degree angle). The "bisector" portion indicates the segment has been bisected, which is mathematical way of saying "cut in half".

The key here is the "bisector" portion. Because we've cut a segment like AB in half, this means segment AC and CB are the same length. The point C is the midpoint of AB. Point C is formed by intersecting the perpendicular bisector and the original segment. I'm referring to drawing (a), but the same idea applies to drawing (b) as well. I recommend using another letter than C for the second drawing.

For the given figure, the lines w, x, y, z are parallel to each other and lines a, b, c, d are parallel to each other.

Lines that never converge and are consistently spaced at equal intervals are said to be parallel. || is the symbol used to represent parallel lines. For instance, AB||CD indicates that line AB and line CD are parallel.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

We must compare the slopes of two lines to determine whether or not they are parallel. Only if the slopes of two lines are equal can they be said to be parallel.

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Answer:

\(y=-\dfrac{1}{2}x+2\)

Step-by-step explanation:

Define two points on the line:

  \(\textsf{let}\:(x_1,y_1)=(0,2)\)

  \(\textsf{let}\:(x_2,y_2)=(4,0)\)

Use the slope formula and the defined points to find the slope:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-2}{4-0}=-\dfrac{1}{2}\)

Substitute the found slope and one of the points into the point-slope form of a linear equation:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-2=-\dfrac{1}{2}(x-0)\)

Simplify:

\(\implies y-2=-\dfrac{1}{2}x\)

\(\implies y=-\dfrac{1}{2}x+2\)

The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

80

Step-by-step explanation:

8 pints in a gallon so then you multiply 8 x 10 and get 80

Answer:

24,500, 6 rounds up

Answer:

61

Step-by-step explanation:

using the rule to find the fifth term from the fourth term 29

5th term = 2 × 29 + 3 = 58 + 3 = 61

Answer:

17>16

Step-by-step explanation:

Answer:

17 is greater than or (>) than any number lower than 17 :)

Step-by-step explanation:

For example, 17>16.. 17> 15, or 17> 14...ect.

Hope this helps! :)

Have a nice day <3

The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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As a result, the probability that a randomly selected student in Gianna's probability maths class has read or seen the movie adaptation of her favourite book is 44%.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

solve this problem,

P(A or B) = P(A) + P(B) - P(A and B)

P(A) = 28%

P(B) = 36%

P(A and B) = 20%

Using the formula, we can find:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 28% + 36% - 20%

P(A or B) = 44%

As a result, the probability that a randomly selected student in Gianna's maths class has read or seen the movie adaptation of her favourite book is 44%.

As a result, the right answer is (a) 44%.

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Answer:

Volume V ≈ 1481.3269 cubic inches

Step-by-step explanation:

Volume V of a cylinder is given by the formula

V = πr²h  where r = radius of the base of the cylinder and h the height

Here we are given the diameter, d = 5.9375 inches

Radius r = d/2 = 5.9375/2 = 2.96875 in

Height h = 53.5 in

V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches

Answer V ≈ 1481.3269 cubic inches

Answer: \(c=\frac{1}{2}\)

Step-by-step explanation:

To find the solution, we have to solve for c by using inverse properties.

\(17c+3(4-2c)=5(7c)\)         [multiply]

\(17c+12-6c=35c\)               [combine like terms]

\(11c+12=35c\)                      [subtract both sides by 11c]

\(12=24c\)                                [divide both sides by 24]

\(c=\frac{12}{24}\)                                   [simplify]

\(c=\frac{1}{2}\)

So the solution is \(c=\frac{1}{2}\).

Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Answer:144

Step-by-step explanation: I explained what to do in the comments.

Answer:

slope:-2/3

y-intercept= 2

equation y= -2/3x+2

Step-by-step explanation:

pick two points from graph then plug to the formula to find the equation

Answer:

36 servings

Step-by-step explanation:

36 different servings

Simply,

3 x 12 = 36