how does a form differ from shape? form is defined by its allegiance to mathematical construction. form has more than three sides. form has the third dimension of depth. shape has more volume than form. save

The solution to the logarithmic equation [tex]2log12(-8x) = 6[/tex] is [tex]x = -9/32[/tex] .

What are logarithmic properties ?

Logarithmic properties are the rules that govern the behavior of logarithmic functions. These properties are important in simplifying logarithmic expressions and solving logarithmic equations. Some of the commonly used logarithmic properties include:

Product property: [tex]logb(xy) = logb(x) + logb(y)[/tex]

This property allows us to simplify the logarithm of a product of two numbers into the sum of logarithms of the individual numbers.

Quotient property: [tex]logb(x/y) = logb(x) - logb(y)[/tex]

This property allows us to simplify the logarithm of a quotient of two numbers into the difference of logarithms of the individual numbers.

Power property:[tex]logb(x^y) = ylogb(x)[/tex]

This property allows us to simplify the logarithm of a power of a number by bringing the exponent outside of the logarithm and multiplying it with the logarithm of the base.

Change of base formula: [tex]logb(x) = logc(x) / logc(b)[/tex]

This property allows us to change the base of a logarithm by dividing the logarithm of the number by the logarithm of the base in a different base.

Solving the given logarithmic equation :

The equation can be solved by using logarithmic properties and basic algebraic manipulation.

We can begin by using the property that states [tex]loga(b^n) = nloga(b)[/tex] for any base a and any positive real number b. Applying this property, we can rewrite the left side of the equation as:

[tex]log12((-8x)^2) = log12(64x^2)[/tex]

Next, we can use the property that states [tex]loga(b) = c[/tex] is equivalent to [tex]a^c = b[/tex]. Applying this property, we can rewrite the equation as:

[tex]12^{2log12(64x^2)} = 12^6[/tex]

Simplifying the left side, we get:

[tex]64x^2 = 12^6 / 12^2[/tex]

[tex]64x^2 = 144[/tex]

Dividing both sides by 64, we get:

[tex]x^2 = 144/64[/tex]

[tex]x^2 = 9/4[/tex]

Taking the square root of both sides, we get:

[tex]x=\pm 3/2[/tex]

However, we need to check the solutions for extraneous roots since the original equation has a logarithm with a negative argument. We can see that the solution x = 3/2 is extraneous since it results in a negative argument for the logarithm. Therefore, the only valid solution is x = -9/32.

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The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.

The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.

A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.

Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.

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Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.

Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,

therefore, we can say that 215 - 100 = 115

therefore, Mark now needs only 115 for him to buy sneakers and  now we need to find how many full hours do Mark need to work to buy sneakers:

therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:

115/16 = 7.2

we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:

8 hours.

Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.

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Answer:

25 computers per hour

Step-by-step explanation:

look ate the point 2 hours corresponding to 50 computers

50/2 = 25/1 or 25 computers per hour

The length of a side of the square is 8 cm.

What do you mean by perimeter of a rectangle and square?

When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.

The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.

Calculating the length of a side of the square:

The length of the rectangle is 11 cm and the width is 5 cm.

Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.

Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.

Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:

[tex]32 = 4s[/tex]

[tex]s = 32/4[/tex]

[tex]s = 8[/tex]

Therefore, the length of a side of the square is 8 cm.

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Answer:

To indicate that we want both the positive and the negative square root of a radicand

Answer:

Because a negative number times a negative number has a positive answer

Step-by-step explanation:

The volume of lemon juice in the glass is 0.38 cubic inches.

Explanation:

Given,

Let the volume of the lemonade in the glass be V cubic inches

Therefore, the volume of lemon juice in the lemonade is [tex]$\frac{1}{12}$[/tex] V cubic inches

Volume of water in the lemonade is [tex]$\frac{11}{12}$[/tex] V cubic inches

The volume of the cylindrical glass is given by:

[tex]$V_{\text{cylindrical glass}} = \pi r^2h$[/tex]

Here,

Radius r = 1 inch

Height h = 6 inches

[tex]$V_{\text{cylindrical glass}} = \pi r^2h = \pi (1)^2(6) = 6 \pi$[/tex]

Since the glass is half full of lemonade, the volume of lemonade in the glass is:

[tex]$V_{\text{lemonade}} = \frac{1}{2}V_{\text{cylindrical glass}} = \frac{1}{2} 6 \pi = 3\pi$[/tex]

The volume of lemon juice in the lemonade is given by:

[tex]$V_{\text{lemon juice}} = \frac{1}{12}V$[/tex]

Therefore

[tex]$V_{\text{lemon juice}} = \frac{1}{12}3\pi = \frac{1}{4}\pi = 0.7854$[/tex] cubic inches

Hence, the volume of lemon juice in the glass is 0.38 cubic inches (rounded to the nearest hundredth).

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Answer:

D. The electrician charges $23 per hour.

Step-by-step explanation:

C(h)= 23h+30 is in the form y=mx +b

$30 is the initial fee (b)

$23 is the amount charged per hour (h)

The function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)

A function, which produces one output from a single input, is an illustration of a rule. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this.

a) We can see that the function is increasing from approximately x = -3 to x = -1 and from approximately x = 1 to x = 2.5. So, the increasing intervals are (-3,-1) and (1, 2.5)

(b) We can see that the function is decreasing from approximately x = -2 to x = -0.5 and from approximately x = 3 to x = 4. So, the decreasing intervals are (-2, -0.5) and (3, 4)

(c) We can see that the function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)

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The value of sec A as required to be determined in the task content is; -√13 / 2.

As evident from the task content; it follows that the terminal ray of angle A, drawn in standard position, passes through the point (-4, -6).

Therefore, the length that the line from the origin to A has length;

L = √((-4)² + (-6)²)

L = √52.

On this note, it follows that the value of sec A which is represented by; hypothenuse/ adjacent is;

sec (A) = -√52 / 4

sec (A) = -√13 / 2.

Ultimately, the value of sec (A) as required is; -√13 / 2.

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Answer: 61

Step-by-step explanation:

explination in image

At Station Y, 15 litres of gasoline would cost £18.

Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.

Ellie must have visited Station Y because she paid $24 for 20 litres of gasoline, proving that she did.

b) We can observe from the graph that 20 litres of gasoline at Station Y costs £24. With the help of this data, we can calculate how much a litre of gasoline costs:

Cost of 1 litre of petrol = Cost of 20 litres of petrol / 20

Cost of 1 litre of petrol = £24 / 20

Cost of 1 litre of petrol = £1.20

Therefore, 15 litres of petrol at Station Y would cost:

Cost of 15 litres of petrol = Cost of 1 litre of petrol x 15

Cost of 15 litres of petrol = £1.20 x 15

Cost of 15 litres of petrol = £18

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Answer: I couldn't honestly help with that I would if I could

Step-by-step explanation:

Answer:

2.31 Years

Step-by-step explanation:

To calculate the time it will take for ₹5000 to grow to ₹5618 with a 6% annual interest rate when compounded annually, we can use the following formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (₹5618)

P = the principal amount (₹5000)

r = the annual interest rate (6% or 0.06)

n = the number of times the interest is compounded per year (1, since it's compounded annually)

t = the time period in years

Plugging in the values, we get:

5618 = 5000(1 + 0.06/1)^(1t)

Simplifying:

1.1236 = 1.06^t

Taking the natural logarithm of both sides:

ln(1.1236) = ln(1.06^t)

Using the power rule of logarithms:

ln(1.1236) = t ln(1.06)

Solving for t:

t = ln(1.1236) / ln(1.06)

t ≈ 2.31 years

Therefore, it will take approximately 2.31 years for ₹5000 to grow to ₹5618 at a 6% annual interest rate when compounded annually.

Answer: 61 kg

Step-by-step explanation:

To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:

   Find the total mass of all six people:

   To find the total mass of all six people, we can multiply the average mass by 6:

Total mass of all six people = 58 kg/person x 6 people = 348 kg

   Subtract the mass of the lightest person:

   We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:

Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person

Total mass of the other 5 people = 348 kg - 43 kg = 305 kg

   Find the average mass of the other 5 people:

   Finally, we divide the total mass of the other 5 people by 5 to find the average mass:

Average mass of the other 5 people = Total mass of the other 5 people / 5

Average mass of the other 5 people = 305 kg / 5 = 61 kg

Therefore, the average mass of the other 5 people is 61 kg.

A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).

A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is

f(x) = ax² + bx + c ----(1)

is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),

=> 0 = a(-8)² + b(-8) + c

=> 64a - 8b + c = 0 --(2)

Similarly, for second point ( -5,-3) , f(x) = -3, x = -5

=> - 3 = a(-5)² + (-5)b + c

=> 25a - 5b + c = -3 --(3)

Continue for third point (-2,0)

=> 0 = a(-2)² + b(-2) + c

=> 4a -2b + c = 0 --(4)

So, we have three equations and three values to determine.

Subtract equation (4) from (2)

=> 64 a - 8b + c - 4a + 2b -c = 0

=> 60a - 6b = 0

=> 10a - b = 0 --(5)

subtract equation (4) from (3)

=> 21a - 3b = -3 --(6)

from equation (4) and (5),

=> 3( 10a - b) - 21a + 3b = -(- 3)

=> 30a - 3b - 21a + 3b = 3

=> 9a = 3

=> a = 1/3

from (5) , b = 10a = 10/3

from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3

So, f(x)= (1/3)( x² + 10x + 16)

Hence, required values are 1/3, 10/3, and 16/3.

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Answer: b

Step-by-step explanation: just took it on edge.

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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Answer:

C is your answer

Step-by-step explanation:

in my opinion, i think it would be the mode.

If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).

The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).

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The scale factor of the following pair of similar polygons after the dilation is 0.7

Given

The pair of similar polygons

From the pair of similar polygons, we have the following corresponding side lengths

Pre-image of the polygon = 30

Image of the polygon = 21

The scale factor of the similar polygons is then calculated as

Scale factor = 21/30

Evaluate the quotient

Scale factor = 0.7

Hence, the scale factor is 0.7

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Answer: It should be 470 cm^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

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Answer:

s= 6

Step-by-step explanation:

The speed s (in miles per hour) of a car can be given by s = √(30fg), where fis the

coefficient of friction and d is the stopping distance (in feet). The table shows the

coefficient of friction for different surfaces. You are driving 35 miles per hour on an

icy road when a deer jumps in front of your car. How far away must you begin to

brake to avoid hitting the deer? Round your answer to the nearest whole integer. NO

UNITS NEEDED

Answer:

Step-by-step explanation:

Given f(x) = 2x³ +x² +ax +b has a factor (x -2) and a remainder of 18 when divided by (x -1), you want to know a, b, and the factored form of f(x).

If (x -2) is a factor, then the value of f(2) is zero:

  f(2) = 2·2³ +2² +2a +b = 0

  2a +b = -20 . . . . . . . subtract 20

If the remainder from division by (x +1) is 18, then f(-1) is 18:

  f(-1) = 2·(-1)³ +(-1)² +a·(-1) +b = 18

  -a +b = 19 . . . . . . . . . . add 1

Subtracting the second equation from the first gives ...

  (2a +b) -(-a +b) = (-20) -(19)

  3a = -39

  a = -13

  b = 19 +a = 6

The values of 'a' and 'b' are -13 and 6, respectively.

We can find the quadratic factor using synthetic division, given one root is x=2. The tableau for that is ...

  [tex]\begin{array}{c|cccc}2&2&1&-13&6\\&&4&10&-6\\\cline{1-5}&2&5&-3&0\end{array}[/tex]

The remainder is 0, as expected, and the quadratic factor of f(x) is 2x² +5x -3. Now, we know f(x) = (x -2)(2x² +5x -3).

To factor the quadratic, we need to find factors of (2)(-3) = -6 that have a sum of 5. Those would be 6 and -1. This lets us factor the quadratic as ...

  2x² +5x -3 = (2x +6)(2x -1)/2 = (x +3)(2x -1)

The factored form of f(x) is ...

  f(x) = (2x -1)(x -2)(x +3)

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.

given

To get the mean and variance of y, we can apply the characteristics of expected value and variance:

We can start by determining the expected value of y:

E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]

By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.

Next, we may determine y's variance:

Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4

Var(x1)

Var(x2) + 9

Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

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In Δ ABC and Δ PQR, if AB = PR, BC = RQ and AC = PQ, then Δ ABC is congruent to Δ PRQ, which means option D is the right answer.

The congruency theorem is used to determine the relation between two similar looking figures in two dimensional space. The word congruent itself means being in harmony. There are different rules which are used to determine the congruency between the triangles.

These rules are given as follows:

In the given question, it is given that sides AB = PR, BC = RQ and AC = PQ, this implies that the congruency can be setup using SSS rule, which if followed will suggest that Δ ABC will be congruent to Δ PRQ.

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We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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Answer:

x=1

Step-by-step explanation:

2.5+x=3.5

3.5-2.5=x

1=x

x=1

The solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6. This was achieved by simplifying the left side of the equation and isolating x on one side.

To solve the equation √(1 + 25/144) = 1 + x/12, we start by simplifying the left side of the equation. The expression inside the square root can be simplified to (144 + 25)/144 = 169/144. Taking the square root of this fraction gives us √(169/144) = (13/12).

Next, we subtract 1 from both sides of the equation to isolate x on one side: (13/12) - 1 = x/12. This simplifies to 1/12 = x/12.

Finally, we multiply both sides by 12 to solve for x: x = (1/12)*12 = 5/6.

So the solution to the equation √(1 + 25/144) = 1 + x/12 is x = 5/6.

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10/73 is the value of x in inequality.

What does the word "inequality" mean?

In mathematics, inequalities describe the connection between two values that are not equal. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal.

                    However different inequalities are used to compare the values to determine if they are less than or higher than. The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

the inequality  12≥ 73x + 2

                    = 12 - 2  ≥  73x

                     = 10 ≥ 73x

                   = 10/73 ≥ x

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