Simplify each expression.
3¹/₄+27¹/₄

The greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.

The given logarithmic expression is log(1.3 x 10⁷)

Use the product rule of the logarithm logₐ(X.Y) = logₐ(X) + logₐ(Y), to get

log(1.3 x 10⁷)

= log(1.3) + log(10⁷)

= log(1.3) + 7 log(10) (Using the power rule of the logarithm logₐ(Xⁿ) = n logₐ(X))

= log(1.3) + 7            (Since log(10) = 1)

≈ 7.113 (approximate value)

We know that, log(1) = 0 and log(10) =1. And the logarithm is an increasing function.

So, log(1.3) is very close to 0 and strictly less than 1.

Therefore, the greatest integer that is less than the value of the logarithm log(1.3 x 10⁷) is 7.

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Step-by-step explanation:

ATTACHED ARE THE SOLUTIONS !!!!

Step-by-step explanation:

a)=

y = 70 + 41 (exterior angle is equal to sum of its opposite interior angles)

so, y = 111°

Now,

y = x + 58° ((exterior angle is equal to sum of its opposite interior angles)

or. 111° - 58° = x

so, x = 53°

b)=

x = 180° - 127° (linear pair of x is corresponding to 127)

so, x = 53°

Now,

y = 83° (y is vertically opposite to angle that is corresponding to 83)

c)= x = 47° (alternate angles)

y = 47 + 32 (exterior angle is equal to sum of its opposite interior angles)

so, y = 79°

d)= other angle = 180-45-45 = 90

Using the formula:-

sinA/a = sinB/b = sinC/c

or, sin45/3 = sin45/y

or, 1/√2/3 = 1/√2/y

or, y = 3

Now,

sinC/c = sinA/a

or, sin90/x sin45/3

or, 1/x = 1/√2/3

or, 1/x = 1/3√2

so, x = 3/√2

The better way for the customer to buy a sofa is to apply the Sale Tax after the discount.

Let us assume that the marked price of a sofa is $1000.

Now we will first take the sale tax and then the discount on the marked price.

Sale = 1000 × 5/100

= 50

So the price after the sale = 1000 + 50

= 1050

As the discount is $100

Therefore total is to be paid is

1050- 100

i.e., $950

Now we will calculate discount first then the sale tax.

As marked price is $1000 and discount is $100

So price after discount = $1000- $100

= $900

Now we will apply the sale tax on the discount price which is 5%

Sale price = 900 × 5/100

=45

Total price to be paid = 900 + 45

= $945

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If the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by y = 3.50x + 6.00, then the number of games you can bowl for $34 is equal to 8.

A linear function can be described as an equation in which the highest power of the variables is not more than 1. As the linear function given is;

y = 3.50x + 6.00

Here y represents the total cost and x represents the number of games played.

We can find the number of games you can bowl for $34 as follows;

y = 3.50x + 6.00

34 = 3.50(x) + 6.00

34 - 6.00 = 3.50(x)

28 = 3.50(x)

x = 28 ÷ 3.50

x = 8

Hence, the number of games you can bowl for using the equation y = 3.50x + 6.00 is calculated to be 8.

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Answer:

B. 2(5+3)

Step-by-step explanation:

PEMDAS

2(5+3)

5+3= 8

2 × 8 = 16

10 + 6 = 16

Answer:

26

Step-by-step explanation:

[tex]2(4)^0+4! \\ \\ =2(1)+24 \\ \\ =26[/tex]

Answer:

0.2

Step-by-step explanation:

Divide 2 by 9. You’ll get 0.222222…

So, you have to round it down to 0.2

I hope this helps. Please mark me brainliest.

6t ÷ 9

I hope this helps!

Answer: 6t

Step-by-step explanation:

there are 6 t's so yea it's  the 6th work for me -_-

Yes, the claim is correct because √16 + π = 4 + π and  4 + π  is an irrational number

Rational numbers are numbers that can be expressed as the ratio of two integers while Irrational numbers cannot be expressed as the ratio of two numbers.

The sum of a rational and an irrational number is always an irrational number.

Example:

Consider a rational number: 4 and an irrational number: 2.7582...

When we add these two numbers, we get,

4 + 2.7582... = 6.7582....

Thus, it is clear that this sum is also an irrational number as the numbers after decimal are non-terminating and non-recurring.

Thus, the correct option is that the claim is correct because √16 + π = 4 + π which is an irrational number

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The amount of fuel required to drive 250 miles will be 25.14 liters.

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

Given that a car consumes 25.00 liters of fuel when driving a distance of 400.0 km. The amount of fuel required for 250 miles will be calculated as:-

1 km = 0.6213 miles

400 km = 400 x 0.6213 miles

400 km = 248.52 miles

248.52 miles = 25 litres

1 mile = 25 / 248.52 litres

250 miles = ( 250 x 25 ) / 248.52 litres

250 miles = 25.14 litres

Therefore, the amount of fuel required to drive 250 miles will be 25.14 liters.

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Equation that has the specified asymptotes for the translation of y=2/x. x=4 and y=-8  is :

y = 2 / x- 4   -  8

The graph is shifted by that many units in the positive direction if you deduct a constant from your original function's x.

The original function's graph is shifted downward by that many units if a constant is subtracted from the y value.

Your first formula was y=2/x. The vertical asymptote is discovered when the denominator's root is solved for. It is x=0 in this instance, or the y-axis.

And when x changes to ∞, y=2/∞=0. This indicates that the y-axis, or your horizontal asymptote, is at y=0.

After seeing the first graph

Now, you can see the transformation of y=2/x below. As is evident, it has shifted 2 units to the right and 8 units down with vertical asymptote at x=4 and horizontal asymptote at y=−8.

you can see the second graph here...

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The two triangles are similar triangles and the graph of the triangles are attached

The complete question is added as an attachment

The coordinates of the triangle are given as

A (0, 3), B (3, 3) and C (3, -1)

So, we enter the above coordinates in a graphing calculator

See attachment for the graph of the triangle

Multiply each coordinate by a scale factor of 3 (k=3).

Here, we have

A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)

This gives

A' (0, 9), B' (9, 9) and C' (9, -3)

Next, we enter the above coordinates in a graphing calculator

See attachment for the graph of the triangle

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The image of Quadrilateral ABCD after transformation is shown in graph with coordinates A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).

What is Transformation?

Transformation is the act or process of changing completely.

The rule of transformation is given as;

(x, y) --> (x-2, y+5)

Now, The coordinates of Quadrilateral ABCD are;

A (2, -3) , B (4, -1), C (7, -1) and D (6, -2)

Apply the rule of transformation to find the coordinates of the image of Quadrilateral ABCD as;

A' (2-2, -3+5) = (0, 2)

B' (4-2, -1+5) = (2, 4)

C' (7-2, -1+5) = (5, 4)

D' (6-2, -2+5) = (4, 3)

Hence, The coordinates of image of Quadrilateral ABCD are;

A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).

And, The image of Quadrilateral ABCD after transformation is shown in graph.

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The simplified value of the expression is [tex]-2^{2/3}[/tex].

The cube root of any given number is that number which we can multiply 3 times by itself to get the original number. It is denoted by ∛, for example- the cube root of x will be ∛x. It can also be written as (x)^1/3.

Here, we are given the expression ∛4 - 2∛4

We can also write this expression as follows-∛4 (1 - 2)= ∛4(-1)= - ∛4

Further, 4 can be written as: 2 × 2 = 2² = - (∛2)² = [tex]-2^{2/3}[/tex]

We cannot simplify this expression any further.

Thus, the value of the expression comes out to be [tex]-2^{2/3}[/tex].

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Answer:

I think the answer is 4 not sure though

Answer:

28 is the answer!

I got it right, look at the pic!!

Answer:  Robbie pay in twelve months $1080 .

$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.

Step-by-step explanation:

As given

Robbie Morse has a $47,500 insurance policy.

The annual premium is $987.53.

Robbie pays $90.00 monthly.

First find out the Robbie pay in twelve months .

Robbie pay in twelve months = 12 × 90

                                                 = $ 1080

Second find out how much more does Robbie pay .

Robbie pay extra = Robbie pay in twelve months -  annual premium

                            = $ 1080 - $987.53

                            = $92.47

Therefore the $92.47 more Robbie pay .

Third find out the what percentage does Robbie pay .

Formula

Robbies pay more = $92.47

Annual premium = $987.53

Put in the above

Percentage = 9.36 % (Approx)

9.36 %(Approx) Robbie pay.

Answer: 140

Step-by-step explanation: 25x20=500

32x20=640

640-500= 140!!

Answer:

$58.32

Step-by-step explanation:

x = 1/3(79.26 + 95.70)

x = 1/3(147.96)  Divide 147.96 by 3

x = 58.32

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.105ft2 is the area of given figure.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The given figure has rectangle and semi circle.

Area of rectangle=length * Breadth

=10*8

=80 ft2

Area of semicircle=1/2πr2 (r=4ft)

=1/2*3.14*(4)^2

=3.14*4*2=25.12ft2

Therefore area of figure is

=Area of rectangle+Area of semicircle

=80ft2+25.12ft2

=105ft2.

Therefore area of figure is 105ft2.

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The logarithmic form of 5⁻³ = 1/125 is , [tex]log_5(\frac{1}{125} ) =-3[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation 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 or equation

           x define expression

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

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to statement,

5⁻³ = 1/125

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

Here,

a= 5, x= -3, N = 1/125

therefore logarithmic form is :  [tex]log_5(\frac{1}{125} ) =-3[/tex]

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Answer:

1. y = 0.5x – 0.5 or y =  1/2x -1/2

2. y = -1.5x – 2   or  y= -3/2x- 2

3. y= -x -5

4. y=x+3

i dk how to do the last picture

A potential exponential function (y = abˣ) that has a y-intercept of (0, 3) and passes through the point (2, 48) is equal to y = 3·4ˣ

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be represented by this standard formula:

y = abˣ

Next, we would solve for the value of "a" using y-intercept (0, 3):

y = abˣ

3 = ab⁰

3 = a(1)

a = 3.

Also, we would determine the value of "b" from point (2, 48):

y = abˣ

48 = 3b²

16 = b²

b = √16

b = 4.

Substituting the parameters into the standard formula, we have;

y = 3·4ˣ

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The statement which are true for triangle LMN are :

1 ) The angle at vertex L is acute.

2) The angle at vertex N is acute.

What is obtuse angle ?

An obtuse angle is defined as an angle measuring less than 180 degrees and greater than 90 degrees. Examples of obtuse angle degrees include 165°, 135°, 110°, 179°, 91°, etc., which lie between 90° and 180°.

Here, it is given that triangle LMN has an obtuse angle at vertex M that is :

The angle formed by vertex L and N will be acute angle that is less then 90 degrees as to satisfy the triangle law of addition (all sum of all the angles of a triangle is 180 degree).

Therefore, option A and D are correct.

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Answer:  1, 2 and 5

Step-by-step explanation:

Analyzing Obtuse Triangles
see picture

The proof that is correct about vertical angles being congruent is; Joby's proof

Vertical angles are defined as the angles formed when two lines meet each other at a point. They are always equal to each other and as such they are congruent.

Now, from the given image, we see that four angles are formed which are; ∠1, ∠2, ∠3, ∠4

Now, according to vertical angle theorem, we can say that;

∠2 = ∠4 and ∠1 = ∠3

Thus, we can conclude that vertical angles are congruent by the vertical angle theorem

Thus, we conclude that Joby's proof is correct.

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x + 2 is the graph of the function g, whose graph is a horizontal reduction of the graph of f by a factor of 1/2.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The translation is a way of changing the position of an object on a xy-plane.

The function that results from shrinking a function f(x) horizontally by a factor of 1/a is given as;

g(x) =1/a f(x)

Give the function f(x) = 2x + 4, which will result in the following function if the function is shortened horizontally:

g(x) = 1/2(2x+4)

g(x) = x + 2

Hence the function g whose graph is a horizontal shrink of the graph of f by a factor of 1/2 is x + 2.

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Answer:

$690.63

Step-by-step explanation:

45 minutes = 0.75 hr, so he worked for 48.75 hrs.

This means he worked 8.75 hours of overtime, so his pay is

[tex]40(13)+(8.75)(13)(1.5) \approx \$690.63[/tex]

The value of logarithmic expression log 4 √47/5² is log (47/25)^1/4.

By considering the given  logarithmic expression

log 4 √47/5²

log  4 √47/25

log (47/25)^1/4

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:transversal

Step-by-step explanation:

x = 6 is the extraneous solution of the equation

The equation given is

[tex]\sqrt{3x + 7}[/tex] = x -1

To find the Extraneous solution we need to square on both sides of the equation

[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]

3x + 7 = [tex]x^{2}[/tex] --2x + 1

[tex]x^{2}[/tex] - 5x - 6 = 0

[tex]x^{2}[/tex] - 6x + x - 6 = 0

x(x - 6) +1(x -6) =0

(x-6)(x+1) = 0

x = -1, 6

Now we need to put the value of x in the equation

x = -1

[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1

[tex]\sqrt{4}[/tex] = -2

2≠ -2

Now put

x = 6

[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1

[tex]\sqrt{25}[/tex] = 5

5=5

Therefore we get to know that x = -1 is the extraneous solution and x = 6 is the solution of the equation

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Since Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college, the occupation that fits her will be C Private detective.

It should be noted that from the information, Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college.

A Makeup artist earns $31,820.

A Mathematician earns $86,930.

A Private detective earns $33,750

A Massage therapist earns $33,400.

Therefore, the best occupation for her since she doesn't want to go to college and earns above $33500 is the private detective.

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Answer:

C. Private detective

Step-by-step explanation: