pls answer both.........

The numeric value for the logarithmic expressions is given as follows:

1. [tex]\log_{6}{\left(\frac{5}{8}\right)} = -0.263[/tex]

2. [tex]\log_6{40} = 2.059[/tex]

3. [tex]\log_6{64} = 2[/tex]

4. [tex]\log_6{125} = 2.694[/tex]

a. [tex]\log_{5}{\left(\frac{11}{30}\right)} = -0.623[/tex]

b. [tex]\log_5{330} = 3.603[/tex]

c. [tex]\log_5{121} = 2.98[/tex]

For the first expression, we have that the logarithm of the quotient is the subtraction of the logarithms, hence:

[tex]\log_{6}{\left(\frac{5}{8}\right)} = \log_6{5} - \log_6{8} = 0.898 - 1.161 = -0.263[/tex]

The same rule is applied for item a, hence:

[tex]\log_{5}{\left(\frac{11}{30}\right)} = \log_5{11} - \log_5{30} = 1.49 - 2.113 = -0.623[/tex]

For the second expression, we apply the logarithm of the product, which is the sum of the logarithms, hence:

[tex]\log_6{40} = \log_6{5 \times 8} = \log_6{5} + \log_6{8} = 0.898 + 1.161 = 2.059[/tex]

For item b, we have that:

[tex]\log_5{330} = \log_5{11 \times 30} = \log_5{11} + \log_5{30} = 1.49 + 2.113 = 3.603[/tex]

For the third expression, we have that the exponent is equals to the base, hence we just take the lower term, as follows:

[tex]\log_6{64} = \log_6{2^6} = 2[/tex]

For the fourth term, we have the rule for the logarithm of an exponent, hence:

[tex]\log_6{125} = \log_6{5^3} = 3\log_6{5} = 3 \times 0.898 = 2.694[/tex]

The same rule is applied for item c, as follows:

[tex]\log_5{121} = \log_5{11^2} = 2\log_5{11} = 2 \times 1.49 = 2.98[/tex]

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The proper method of finding a value table has been mentioned and explained below.

Value tables are a part of domain definition. The value table is maintained at the domain level and thus, is also called domain-level validation. Whenever you create a domain, you can enter the required values. Whenever you use this Domain, the system will make it so that you are forced to enter only these values. This is a sort of master check.

This means that if you want to enter values into this table you have to create a development request & transport the same. The system, then, proposes the value table as a check table. The check against the value table only takes place when a foreign key is defined

.

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The total cost of the move when hiring movers for 35 hours is $1221, and the total cost of the move when hiring movers for 10 hours is $546.

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Answer:

3/4 : 1 1/2    1 2/4 : 3.  5 : 10

Step-by-step explanation:

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form. The three graphs in the image below are all parabolas.

A quadratic function's graph takes the form of a parabola. The parabola will open upward if the value of the "a" term is positive, and downward if the value is negative

A function can be raised by adding outside of it: f (x) + b raises f (x) by b units. The same principles apply for moving a function down, except instead of subtracting a positive integer, f (x) b represents f (x) moved down b units.

You can represent a vertical (up, down) shift of the graph of f(x)=x2 by adding or subtracting a constant, k.

f(x)=x2+k

By increasing or decreasing the output or the input, you can change the direction of the function's graph to the right, left, up, or down. A function's output can be increased to move the graph up. The graph is shifted downward when a function's output is subtracted from.

The output has a constant added to it, which causes the vertical shift. For a positive constant, move the graph upward; for a negative constant, move it below. A constant supplied to the input causes a horizontal shift. For a positive constant, move the graph to the left; for a negative one, move it to the right.

You can represent a horizontal (left, right) shift of the graph of f(x)=x2  by adding or subtracting a constant, h, to the variable x, before squaring.

f(x)=(x−h)2

If h>0, the graph shifts toward the right and if  h<0 , the graph shifts to the left.

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Answer:

a = -6

Step-by-step explanation:

9+a/6=8 1. -9 both sides

(6)a/6= -1(6)    2. multiply 6 on both sides

a = -6

Answer: 36

Step-by-step explanation:

80% or 200 is 16

16+20=36

a) The monthly payment for a loan of $38,000 borrowed by Fred for 5 years at 4% APR is $699.83.

b) The total payment to be made is $41,989.80.

c) The finance charge is $3,989.80.

The finance charge is the difference between the sum of the monthly payments and the loan amount.

The monthly payments, total payment, and finance charge can be computed using an online finance calculator as follows:

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $38,000

FV (Future Value) = $0

Results:

PMT (Monthly Payments) = $699.83

Sum of all periodic payments (Total Payment) = $41,989.80

Total Interest (Finance Charge) = $3,989.80

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Out of the 500 homes, 226 Type A forms were sent while 274 Type B forms were sent.

To determine the number of forms sent, we can begin by identifying how much Jeannie spent on mailing each of the questionnaires. The sum of $0.19 and $0.23 is $0.42. Now, we will find out how much of these were the total cost as follows:

Type A:

$0.19 / $0.42 ×  $106.20

= $48.

Type B:

$0.23 / $0.42 ×  $106.20

= $58.2

Next, we will determine how much of these went into the 500 homes as follows:

Type A:

$48 / 106.2 × 500

= 225. 9 ≈ 226 homes

Type B:

$58.2 / $106.2 × 500

= 274 homes

So, while Type A was sent to 226 homes, Type B was sent to 274 homes.

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AAA(Angle angle angle) Theorem can be used to prove given triangles as similar.

As we know we have to show all three angles equally.

so we have to show the similarities between T(DNM) and T(DFE) ....

(T Means Triangle.)

(A Means Angle)

As  D is a common vertex in both the triangles

by equations 1, 2, and 3 we can conclude that all three angles of T(DFE) =  T(DNM)

SO By the AAA rule, we can say that the two Triangles are similar.

Now we can say all the sides of T(DFE) will be in all propositions of T(DNM).

Like DN/DF=DM/DE=NM/FE

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The graph solution is in the attached images, for all the systems of inequalities.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

we have the following inequalities:

i)

y > 3x - 17,

y ≤ -4x +11.

ii)

4x - 4y > -40,

-5x + 5y < 10.

iii)

x + 3y ≥ 31,

4x - 2y ≥ -2,.

iv)

5x + y < 3,

5x + y > 37

Hence, the graph solution is in the attached images, for all the systems of inequalities.

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Answer: 562.50

Step-by-step explanation:

Answer: Cosine ratios are exactly the same idea of sine ratios or tangent ratios. The only difference between it and the other two trigonometric ratios is that it is the ratio of the adjacent side to the hypotenuse of a right triangle.

The compositions between functions f(x) = 3 · x - 2 and g(x) = x + 1 are f[g(x)] = 3 · x + 1 and g[f(x)] = 3 · x - 1, respectively.

Let be f(x) and g(x) functions, there is a composition of the form f[g(x)], when the independent variable of function f is substituted by function g. That is to say:

f ° g(x) = f [g(x)]

First, define functions f(x) and g(x):

f(x) = 3 · x - 2

g(x) = x + 1

Second, perform the required compositions and simplify the expressions:

f[g(x)] = 3 · (x + 1) - 2

f[g(x)] = 3 · x + 1

g[f(x)] = (3 · x - 2) + 1

g[f(x)] = 3 · x - 1

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Answer:

[tex]4^{-3}[/tex]

Step-by-step explanation:

[tex]4^{3}[/tex] = 64

Take the reciprocal of both sides.

1/64 = [tex]4^{-3[/tex]

An infinite solution has both sides equal.

What number has an unlimited number of answers?

There are infinitely many possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable.

             If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions. 2x and 2x should be combined.

Are all possible solutions parallel?

There are no answers when the lines are parallel, and occasionally the two equations will graph as the same line, in which case there are an endless number of solutions. These kinds of systems are occasionally described using specific words.

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The degree 3 polynomial equation is  1/2(4 - x)(x - 1)(x - 2).

Here given,

With zeros and a coefficient, the function is:

f(x) = a(x - 4)(x - 1)(x - 2)

Regarding the y-intercept:

f(0) = a(0 - 4)(0 - 1)(0 - 2)

4 = a(-4)(-1)(-2)

4 = -8a

a = -1/2

As a result, the function is:

f(x) = -1/2(x - 4) (x - 1)(x - 2)

= 1/2(4 - x)(x - 1)(x - 2)

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The correct option for the area of rectangle is A: 7(x + 2) sq in.

The characteristics of a rectangle were just as follows:

An area is the amount of space a rectangle takes up.By calculating the product of a rectangle's length and breadth, one can get the area of the shape.

So,

Area of a rectangle = Length × Width

Dimension are-

So,

Area of a rectangle = 7 × (x + 2) sq in..

Thus, the expression represents area of a rectangle is 7 × (x + 2) sq in.

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The complete question is-

The dimensions of a rectangle are 7 in by (x+2)in. Which expression represents its area?

A: 7(x + 2) sq in..

B: 7 + (x + 2) sq in..

Answer:

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

Given system:

We can solve it by elimination.

Multiply the first equation by 6 and add up to get:

Without solving for x we can see there is one solution.

The last answer choice is the correct one.

Answer:

The given system of equations has exactly one solution (1, ⁴/₃).

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-x+6y=7\\6x-30y=-34\end{cases}[/tex]

To solve the given system of equations, multiply all terms of the first equation by 5:

[tex]\implies -x \cdot 5+6y \cdot 5=7 \cdot 5[/tex]

[tex]\implies -5x+30y=35[/tex]

Add this to the second equation to eliminate the term in y:

[tex]\begin{array}{crcccl}&6x & - & 30y & = &-34\\\vphantom{\dfrac12}+ & (-5x & + & 30y & = & \;\;\:35)\\\cline{2-6}\vphantom{\dfrac12}&x&&&=&\;\;\;\;\:1\\\cline{2-6}\end{array}[/tex]

Therefore, x = 1.

Substitute the found value of x into the first equation and solve for y:

[tex]\implies -(1)+6y=7[/tex]

[tex]\implies 6y=8[/tex]

[tex]\implies y=\dfrac{8}{6}[/tex]

[tex]\implies y=\dfrac{4}{3}[/tex]

Therefore, the given system of equations has exactly one solution (1, ⁴/₃).

Yes, (3, 2) is an ordered pair.

The combination of the x coordinate (abscissa) and the y coordinate (ordinate) is called an ordered pair, which has two values written in a fixed order within parentheses.

It can help us to locate a point on the cartesian plane for better visual understanding. The numerical values in an ordered pair can be both integers or fractions. 

In the Cartesian plane, we can define a two-dimensional space with two perpendicular reference lines, the x-axis and the y-axis. The point where the two lines meet is the origin (O).

For example plot the point Q with the coordinates (3, 2)

According to the definition of ordered pair, the point Q will be written as:

Q = (3, 2)

The left number in the ordered pair shows the distance from the “x” axis which is 3

The right number shows the distance from the “y” axis which is 2.

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The statement which is correct about the Area of the rectangle in discuss as required is that the area decreased by; Choice C; 33.(3)%.

As evident in the task content; the length of a rectangle increases 2 times and the width decreses 3 times;

Since the initial length can be said to be; l and the initial width can be said to be; w and Area A = l × w.

However, when the length and width change as described; the area of the rectangle is;

Area = 2l × ( w / 3 )

Area = ( 2/3 ) × lw

On this note, the new Area of the rectangle is two-third the initial area.

On this note, the area of the rectangle has decreased by one-third which is equivalent to; Choice C; 33.(3)%.

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Answer: x < -4

Step-by-step explanation: This is a question of an inequality. Here, everything proceeds like a normal equation that we solve. To obtain the value of x, we will divide 32 by 8.

  -8x<32

   x<-32/8

   x<-4  (On dividing -32 by 8)

This means x can take any value less than -4 i.e. -5,-6,-7,......

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As per the given ratio, the number of roses is 45 and the number of tulips is 27

The term ratio also known as proportion is defined as an ordered pair of numbers a and b, written a / b where b does not equal 0

Here we have given that the ratio of roses to tulips is 5: 3.

Here we also know that the shop has 72 tulips on Friday morning.

And then let us consider that if the florist uses up half of each type of flower to fill an order, then the ratio of roses to tulips in the shop change is calculated as,

=> 5x + 3x = 72

=> 8x = 72

Then the value of x is calculated as,

=> x = 9

Therefore, the number of roses is

=> 5(9) = 45

And the number of tulips is written as,

=> 3(9) = 27

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The midpoint method is a numerical integration technique used to approximate the definite integral of a function over a given interval. It is a Riemann sum method.

The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them.

Here,

The midpoint method is used for a few reasons:

Simplicity: The midpoint method is relatively easy to understand and implement, compared to other numerical integration techniques.

Accuracy: The midpoint method is more accurate than some other Riemann sum methods like the left-hand rule or right-hand rule, which evaluate the function at the endpoints of each subinterval.

Efficiency: The midpoint method is more efficient than some other numerical integration techniques, especially for functions that are not smooth or have sharp changes.

Flexibility: The midpoint method can be used for both definite and indefinite integrals, and for functions that are not well-behaved.

Overall, the midpoint method is a simple, accurate, efficient and flexible numerical integration method that can be used to approximate the definite integral of a function over a given interval.

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The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.

The Pythagorean Theorem, often known as the Mathematicians, is the fundamental Euclidean geometry relation between the three sides of a right triangle. The area of a cube with the velocity vector side equals the sum of the areas of polygons with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect distance equals a sum of the squares that span its sides. It is sometimes written as the basic algebra notation a2 + b2 = c2.

given

According to Pythagoras's Theorem, which states that

c2 = a2 + b2

c2 = 3600 + 1369

c2 = 4969

c = 70.49, the water slide in Atlantis is 60 feet high and has a base that is 37 feet from the pool.

The Atlantis water slide measures 70.69 feet in length when the slide's base is 37 feet from the pool and it is 60 feet tall.

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The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 number of cups.

The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 cups. The district restaurant manager purchased four cases of disposable cups, each costing $150 and containing 3,600 cups. He needed to split the cups among six restaurants. To determine how many cups each restaurant would receive, he divided 3,600 by 6. This gave him an answer of 600 cups for each restaurant.

3,600 ÷ 6 = 600 cups

The district restaurant manager divided 3,600 cups among six restaurants, giving each restaurant 600 number of cups.

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The store that sells strawberries at a cheaper unit price is Fine Foods.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 2/1 = 6/3 = 10/5 = 14/7

Constant of proportionality (k) = 2.

Therefore, an equation for the price of strawberries at Fine Foods is y = 2x and as such, it sells strawberries at a cheaper unit price.

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Answer:

Below

Step-by-step explanation:

When it reaches the ground h = 0

h =     0 = -16t^2+676

            16t^2 = 676

             t^2 = 42.25       t = 6.5 s

Answer: Well for a family of 6 we spend around 200-300$, so a family of 4-5 if older like teens, or 6-7 for young toddlers.

Answer:235

Step-by-step explanation: its because.......