Rotational symmetry? O Yes O No
Angle?
Point symmetry? Yes O No
Rotational symmetry? Yes O No
Angle?
Point symmetry? O Yes O No
O

The expression becomes 3log₁₀2-3log₁₀3

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

logₐb where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logₐbc where a is the base is given as logₐb + logₐc

logₐbc where a is the base is given as logₐb-logₐc

Now it is given to us to find the logarithmic form of 8/27=(2/3)^3

Let us consider the base of the logarithm to be 10

thus log₁₀8/27=log₁₀(2/3)^3

log₁₀8/27=log₁₀(2/3)^3

We know that logₐb can be written as log₂b/log₂a

Hence

log₁₀8/27= 3(log2/3)

log₁₀8/27=3(log2-log3)

log₁₀8/27= 3log2-3log3

Hence the expression becomes 3log2-3log3

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After solving the given inequality the answer is x∈(-∞, 2/15].

So,

Then,

Therefore, after solving the given inequality the answer is x∈(-∞, 2/15].

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Answer: x² + y² = 9 is not a function

Step-by-step explanation: In order for an equation to represent a function any single value of x must have at most one corresponding value of y which satisfies the equation. and therefore the equation is not a function.

x^2+y^2=9

if for example x=0

There are two values for y(namely+3 and -3) which satisfy the equation and therefore the equation is not a function

Answer:(5x+1)(x+1)

Step-by-step explanation:

Factor 5x2+6x+1

5x2+6x+1

=(5x+1)(x+1)

hope its correct by my correction

The relation between these two variables can be represented by the linear equation:

y = 4ft + 2.5ft*x

We know that the original height of the tree was 4 ft, and it grows 2.5 feet each year.

Then if we define the variables:

y = height.

x = number of years.

The relation between these two variables can be represented by the linear equation:

y = 4ft + 2.5ft*x

This linear equation relates the height of the tree as a function of the number of years since it was planted.

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Answer:

y = 4ft + 2.5ft*x

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Triangle fits inside of a rectangle (A=15).

If the rectangle is drawn around the triangle, three other right triangles are formed outside of it. Find the area of each right triangle (4, 1.5, and 2.5), add those together, and subtract from the area of the rectangle.

(15 - 8 = 7)

Answer:

51

Step-by-step explanation:

$3 time 7 = $21

$5 time 6 =30

21+30 = $51

Answer:

^{4}+36+8x^{2}

x^{4}+8x^{2}+36

Step-by-step explanation:

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.  

i hope this helped

Answer:

Step-by-step explanation:

This is a straight line with positive gradient 4/7

There is no horizontal asymptote.

value of x in given logarithmic equation is =  2000

In, mathematics a logarithmic function is inverse of exponential function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function

           x is the expression

Mathematically, if [tex]a^x = N[/tex] is and exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

Some important formulas of logarithms :

According to given statement,

log x - log 2 =3

using formula, log a - log b = log a/b

=> log x/2 = 3

=> x / 2 = 10³

=> x = 2 . 10³ = 2000

Thus solution for this equation is x =2000.

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Answer:

22

Step-by-step explanation:

add ab and bc to get ac

Answer:

The vertex is (4,-4)

Step-by-step explanation:

Plug in x=4 in the equation

The approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The complete question is added at the end of the solution

The equation of the height function is given as

h(t) = -5t² + 10t+4

After 1,2 seconds, we have:

t = 1.2

Substitute t = 1.2 in the equation h(t) = -5t² + 10t+4

So, we have

h(t) = -5 x 1.2² + 10 x 1.2 + 4

Evaluate the exponent

So, we have

h(t) = -5 x 1.44 + 10 x 1.2 + 4

Evaluate the products

So, we have

h(t) = -7.2 + 12 + 4

Evaluate the sum

So, we have

h(t) = -7.2 + 16

Evaluate the difference

So, we have

h(t) = 8.2

Hence, the approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet

This means that the required approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet

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Complete question

The function h(t) = -5t² + 10t+4 models the height of a gymnast on a trampoline over time, where is feet above the ground level and is the number of seconds since the start of their jump.

Using the function, approximately how high is the gymnast above the ground level after 1.2 seconds?

The required domain of g ( x ) = 3 x - 1 is R ( real nos . ) .

Given : g ( x ) = 3 x - 1

To find : Domain of function

Domain : The set of all possible values of input variable  ( x in this case ) is called the domain of the function .

Calculating domain :

g ( x ) = 3 x - 1

Since , it is a polynomial function with degree 1 , therefore it's domain will be real nos .

Hence , domain of g ( x ) = 3 x - 1 is R .

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Check the picture below.

Answer:

[tex] {6}^{12} \times 36 =[/tex]

Answer:

216

Step-by-step explanation:

If x = 8 & y = -9
Put in place -3 (8)(-9)
-24 * -9 = 216

Answer: its (2,5) or (2,-5)

Step-by-step explanation:

basically it depends on the location like for example: if a dot is in the Q4 area which is (-x,-y) or Q3 is (-x,y) and Q2 is (x,-y) and Q1 is (x,y) so yeah hope it helps

Answer:

q=10, r=8

Step-by-step explanation:

You have to first cancel one of the variables.

8q-15r=-40

4q+2r=56

To do this, multiply the second equation by -2.

8q-15r=-40

-2(4q+2r)=(56)(-2)

Multiply it out.

8q-15r=-40

-8q-4r=-112

Combine like terms.

-19r = -152

Divide by -19 to get the value of r.

r=8

Substitute r back into one of the equations, it does not matter which one. I'll do both.

8q-15(8)=-40

8q-120=-40

8q=80

q=10

4q+2(8)=56

4q+16=56

4q=40

q=10

You should get the same value for q for both.

In the instance where the variables are x and y, which they usually are, you would write your answer as an ordered pair, (x, y).

(10, 8)

Answer:

q=10 and r=8

Step-by-step explanation:

8q-15r=-40 ...........equation(i)

4q+2r=56................eqn(ii)

Now,

Multiplying eqn (ii) by 2 then we get,

8q+4r=112..........eqn(iii)

Here, Subtracting eqn (i) and (iii)

8q-15r=-40

8q+4r=112

(-) (-) (-)

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

-19r=-152

r= -152/-19

r= 8

Again, Putting the value of r in eqn (ii)

4q+2r=56

4q+2×8=56

4q=56-16

q=40/4

q=10

The total percentage decrease in the number of students on the honor roll is 16.67%.

Percentage is a measure of frequency that is used to express a number as a fraction of an amount out of 100. The sign used to denote percentage is %. In order to convert a number to percentage, multiply the number by 100.

The first step is to determine the number of boys on the honor roll this year.

Number of  boys on the honor roll this year : (1 - percentage decrease) x number of boys last year

(1 - 0.12) x 150

0.88 x 150 = 132

The second step is to determine the number of girls on the honor roll this year.

Number of girls on the honor roll this year : (1 - percentage decrease) x number of girls last year

(1 -0.25) x 84

0.75 x 84 = 63

Total number of students on the honor roll last year = 150 + 84 = 234

Total number of students on the honor roll this year = 63 + 132 = 195

Percentage decrease :[ (195 /234) - 1] x 100 = 16.67%

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Answer:

Below.

Step-by-step explanation:

In Δ ABC m < B = 180 - (50+70) = 60 degrees.

in Δ DEF m < D = 180- ( 60 + 70) = 50 degrees.

BC = DE  ( both are 10 cm).

m < A = m < F  ( both 70 and directly opposite BC and DE)

m < C = m < D (corresponding angles and both = 50 degree)

Therefore, Δ's ABC and DEF are congruent by AAS.

Answer:

5.16666666,...

Step-by-step explanation:

5 + (5/3) - (3/2)

5 + 1.66666666667 - 1.5

5 + 0.16666666666

5.16666666666,...

Nhân chia trc cộng trừ sau

Answer:

31/6 ( or 5 1/6)

Step-by-step explanation:

5 + 5/3 - 3/2 =

5 + 1/6 =

31/6

From the given distribution, we have that:

a) The distribution is skewed to the left.

b) The median is of 74.

c) The mean will be smaller than the median.

Since life expectancies are clustered at the high end, the outliers are small life expectancies, meaning that the mean will be smaller than the median and the distribution is skewed to the left.

The median of a data-set is the 50th percentile, the value that separates the bottom 50% of the data-set from the upper 50%.

In this problem, we have that about half of all the countries having a life expectancy between about 74 and the maximum of 84.7, meaning that 74 is the median.

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Using division and the graph, the zeroes of the function are given as follows:

The function in this problem is defined as follows:

f(x) = -3x³ -4x² + x + 2.

From the graph, we have that x = -1 is a zero of the function, meaning that it can be written as follows:

-3x³ -4x² + x + 2 = (x + 1)(ax² + bx + c).

The other zeros will be the zeros of ax² + bx + c. To find the coefficients, we use a system of equations, hence:

(x + 1)(ax² + bx + c) = -3x³ -4x² + x + 2

ax³ + (a + b)x² + (c + b)x + c = 2.

Hence the coefficients are given by:

Thus the quadratic equation that we have to solve is:

-3x² - x + 2 = 0

3x² + x - 2 = 0.

Hence:

The zeroes of the function are given as follows:

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The value for g(f(-4)) = -4

Given:

          g(x) = 3 x+2 and  f(x)= x-2 / 3

Take,   f(x) =  x-2 / 3

substitute x = -4  into the function f(x). Then:

           f(-4)  = (-4)-2/ 3

           f( -4)  = -6/3

           f( -4)  = -2

Now, the next step is to substitute  f(-4) into the function g(x)

            g(x) = 3 x+2

         g(f( x)) = 3 x+2

         g(f(-4)) = 3(-2) +2

          g(f(-4) = -6+2

         g(f(-4) = -4

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Answer:

Step-by-step explanation:

The constant of proportionality is 70.

Answer:

x² + 5x + 8

Step-by-step explanation:

This issue is about "function composition",

(g ° f) means

g(f(x)) = g(x² + 5x +6)

= x² + 5x +6 + 2

= x² + 5x +8