function rule to find f(10)

The value of the given logarithmic expression is -142.20.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given the logarithmic values as,

log₃ (t) = 5.44

log₃ (y) = 11.03

log₃ (z) = 7.74

Now, the value of the expression can be written as,

12 log₃ (z⁷ / y⁵t²)

= 12 { log₃ (z⁷) - [ log₃ (y⁵) + log₃ (t²) ] }

= 12 { 7log₃ (z) - [ 5log₃ (y) + 2log₃ (t) ] }

= 12 [7×7.74 - (5×11.03 + 2×5.44)]

= 12 [ 54.18 - (55.15 + 10.88)]

= 12(54.18-66.03)

= 12 × (-11.85)

= -142.20

Hence, the value of the given expression is -142.20.

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The solution of the logarithmic expression is 2x² - x - 6 = 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is log(x) + log3(2x - 1) = log3 (6). The expression will be solved as below,

log(x) + log3(2x - 1) = log3 (6)

log ( 3x (2x-1) = log18

3x ( 2x - 1 ) = 18

x ( 2x - 1 ) = 6

2x² - x = 6

2x² - x - 6 = 0

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The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. For instance, the polynomial 2x+5 has an exponent of 1. The zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most common types of polynomials in precalculus and algebra.

Given,

f(x)=(x-a)(x-b)

From the above graph, f(x) passes through points (2, 0), (-1, 0), (0, -2)

Let us take (2, 0)

(2-a)(2-b)=0

4-2b-2a+ab=0

(-1, 0)⇒(-1-a)(-1-b)=0

1+b+a+ab=0

(0, -2)⇒-2=(-a)(-b)

ab= -2

a= -2/b

4-2b-2a-2=0

-2a-2b+2=0

a+b-1=0

b²-2b+b-2=0

b(b-2)+1(b-2)=0

b= 2 or b= -1

a+2-1=0

a= -1

a-1-1=0

a=2

The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.

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Answer:

$80

Step-by-step explanation:

His buying cost for 1 pair of shoes: $49

His selling price for 1 pair of shoes: $65

His profit on selling 1 pair of shoes: $65 - $49 = $16

His profit on selling 5 pairs of shoes: 5 × $16 = $80

Based on the table and equation given:Gymnastics is less expensive when the classes is 1.Ice-skating is less expensive when the classes is 3 or 4.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.

Ice-skating is less expensive when the classes is 3 or 4.

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Answer:

The equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:

x - 3y + 15 = 0

Step-by-step explanation:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To find the equation of the line that passes through the point (-6, -7) and has a slope of 1/3, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope of the line.

Plugging in the given values, we have:

y - (-7) = (1/3)(x - (-6))

Which simplifies to:

y + 7 = (1/3)x + 2

Multiplying both sides by 3, we have:

3y + 21 = x + 6

Subtracting 21 and 6 from both sides, we have:

3y - x - 15 = 0

Therefore, the equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:

x - 3y + 15 = 0

Answer:

1. 29 2. 35

Step-by-step explanation:

check the attached file

Answer:

∠EGC

Step-by-step explanation:

Just like for the other problem, you're looking for an angle that's opposite the one you're given and is the same size as the one you're given (meaning they're congruent). If you use you hands to cover the parts of the line AD, you can see how ∠FGB and ∠EGC are opposite of each other and are congruent..

Answer:

Step-by-step explanation:

The graph of y = 8 is a horizontal line through 8, on the y-axis

The least number of point the team could have scored is the LCM of the factors given = 60.

Factor 1 = 3

Factor 2 = 4

Factor 3 = 5

therefore, LCM  

= 4 * 5 * 3   [because they don't have any factors in common]

= 60

The positive integers that can divide a number evenly are referred to as factors. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied.

Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.

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The equivalent equation is when n is equal to 4.

        axc = bxc.

Here given equation,

7n = 28

Multiply both sides of equation by 1/7

7n x 1/7 = 28 x 1/7

7n / 7 = 28 / 7

n = 28 / 7

n = 4

So the equation equivalent to 7n = 28 is n = 4.

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Answer:

The sequences below is geometric sequences. 8,16,32

Step-by-step explanation:

It is geometric as far as it goes.

Notice that the ratio between each successive pair of terms is constant:

4/2=2

8/4=2

16/8=2

That these ratios are all the same is sufficient for the given terms to form a geometric sequence with general term:

an=[tex]2^{n}[/tex]

The sequence then continues:

2

,

4

,

8

,

16

,

32

,

64

,

128

,

256

,

512

,

1024

,

2048

,

...

The question is in the "...". Any finite number of terms does not determine an infinite sequence.

For example we can match the sequence  

2

,

4

,

8

,

16

 with a cubic polynomial:

[tex]a_{n}[/tex]=1/3([tex]n^{3}[/tex] -3[tex]n^{2}[/tex] +8n)

Then we would find that the next terms would be  

30

,

52

,

84

,

.

the second 4 11 ,17 is wrong

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After dividing 451 by 51, we get a quotient of 008 and a remainder of 43.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.

It's not necessary for this number to be an integer.

For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 of them.

So, we have 451/51.

Now calculate as follows:

451/51

Quotient = 008

Remainder = 43

(Refer to the image attached below)

Therefore, after dividing 451 by 51, we get a quotient of 008 and a remainder of 43.

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To find the answer to this problem, you will need to use the Pythagorean Theorem.

What is the Pythagorean Theorem?

The Pythagorean Theorem is an equation that represents the summation of the sides of a right triangle.

a² + b² = c², where a is the shortest leg of the triangle, b is the longest leg and c is the hypothenuse.

You have been given a (12) and b (16)

First, plug your given information into the equation: 12² + 16² = c²

Next, simplify your equation by squaring both terms:

12² = 144

16² = 256

Then, add these two answers together: 144+ 256= 400

This leaves you with the equation: 400 = c²

To isolate the c as an individual term, take the square root of both sides:

          [tex]\sqrt{400} = \sqrt{c^{2} }[/tex]

The above equation leaves you with the answer 20 = c, which is the hypothenuse

Answer: -2

Step-by-step explanation:

Slope is rise/ run or y2 - y1 / x2 - x1

We see that y goes down by 6, and x go over by 3

So slope is -6/3 = -2

The ratio of heads to tails in the probability test is 2:1 or (D) 2/1.

A ratio is a relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other.

For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.

So, we know that the coin is flipped 36 times in the probability test:

Head = 24

Tails = 36 - 24 = 12

The ratio of heads to Tails:

Heads:Tails
24:12

24/12

2/1

2:1

Therefore, the ratio of heads to tails in the probability test is 2:1 or (D) 2/1.

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Complete question:
In a probability, experiment Eric flip a coin 36 times. The coin landed on the head 24 times. What is the ratio of heads to tails in this experiment?

A.3/2

B.1/2

C.2/3

D.2/1

Answer: 3(x-1)

Step-by-step explanation:

3 (x-1)

The gradient of this straight line through the points is 0.16.

The gradient of this lines simply means that it would require one (1) unit to use £0.16 worth of electricity.

Mathematically, the gradient of a straight line can be calculated by using this formula;

Gradient, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Gradient, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided through this graph, we have the following data points:

Points on x-axis = (30, 100).

Points on y-axis = (4, 15).

Substituting the given points into the formula, we have the following;

Gradient, m = (15 - 4)/(100 - 30)

Gradient, m = 11/70

Gradient, m = 0.16

This ultimately implies that, £0.16 worth of electricity would require one (1) units to be used by David.

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The total cost of the Television is $ 1201.68.

The governments collect a consumption tax known as a sales tax on purchasing goods and services. It is always expressed as a percentage of the Purchase cost of goods and services. Here

Here we have

Alexandra bought a television set for $ 1105 in Newyork  

The rate of sales tax = 8.75%

Therefore,

The total cost of Television = Cost of Television + sales tax  

As we know sales tax = 8.75%

=> tax on Television = 8.75% of 1105  

= [tex]\frac{8.75}{100} \times 1105[/tex]

= 0.0875 × 1105

= 96.68

The total cost of Television = 1105 + 96.68

= 1201.68

Therefore,

The total cost of the Television is $ 1201.68.

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Clare's mistake is at the second step and the solution to the equation is -65/11.

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Based on the information provided above, we can logically deduce that Clare's mistake is at the second step because the product of 12 and 5 is equal to 60, rather than 72. Additionally, Clare did not distribute the negative sign to all the terms of the equation.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

12(5 + 2y) = 4y - (5 - 9y)

60 + 24y = 4y - 5 + 9y

60 + 24y = 13y - 5

24y - 13y = -5 - 60

11y = -65

y = -65/11

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Answer:

[tex]\frac{3m^{2}n-2-40nm }{6m}[/tex]

Step-by-step explanation:

Answer: second and third from the top right

Step-by-step explanation: 1:2 and 1 to 2 are the same thing, and are ratios. The rest of the answers have nothing to do with ratios.

Mrs. smith told her students that anyone who scores over 90% on the test will get an extra 30 minutes of recess: Among the group contingency this is an independent group,

A particular kind of contingency known as a group contingency (GC) takes use of peer influence by using group reinforcement.

The instructor may use a group contingency to praise an entire class or a smaller subset of pupils for finishing assignments, exhibiting good classroom behavior, or engaging in other desired behavior. Multiple kids' problematic behaviors can be addressed at once using group contingencies.

Dependent, independent, and interdependent group contingencies are the three different types.

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The complete question is as follows:

Mrs. Smith implemented a procedure where she exclaimed that if any student scored over 90% on the test, they would get an extra 30 minutes of recess. Which group contingency is this?

a. Token economy

b. Dependent group contingency

c. Interdependent group contingency

d. Independent group

The difference between a formal and informal proof in arithmetics is that a formal proof uses equations, whereas an informal proof only uses text. That is option D.

A formal proof is defined as the concept used in arithmetics to show that the final answer to an expression obeys a particular rule of an equation or formula.

An informal proof is defined as the concept that shows the answer to a mathematical expression without the use of formula or derived equation.

Therefore, the difference between the formal and informal proof is that a formal proof uses equations, whereas an informal proof only uses text.

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Answer:

m∠1 = (180 - 110)° = 70°

m∠2 = (180 - 115)° = 65°

m∠3 = 115°

m∠4 = m∠2 = 65°

m∠5 = (180 - (65 + m∠1))° = 45°

m∠6 = m∠5 = 45°

m∠7 = m∠6 = 45°

Answer: m=8/7

Step-by-step explanation:

use this formula m=y2-y1/x2-x1

Answer:

For this question, you would have to subtract

1.679-1.439 = 0.24   Melvin pays 0.24 cents less. (not that much honestly lol!!)

Answer: 2(x-5)(x+3)

Step-by-step explanation:

(x+3)(2x-10)

2(x-5)(x+3)

The Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

Define Domain and Range

Given expression is,

f(x) = -1/4x³ + 4x - 3

In this x ∈ R, so

Domain = (-∞,∞) , { x|x  ∈ R }

Range =   (-∞,∞) ,{ y|y ∈ R }

Hence, the Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

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There are total amount of 108 quarters and 18 dimes in a jar.

Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

There are six times more quarters than dimes in a jar of coins.

If x represents the dimes, then the number of quarters will be 6*x if there are 28.80 in total.

A dime is worth 10 cents. In terms of money, we have 10 times as many dime.

A quarter is equal to 25 cents. We have 6 times as many quarters, which is 150 times (6 x 25).

10x +150x = 28.80

160x = 28.80

x = 0.18 that is for coins it will be 10x

10*0.18

18 dimes

similarly

6 times dimes is equal to quarters that is 6*18

108 quarters are there.

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