Help me pls!! 4 math questions

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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Answer:

B. 2(5+3)

Step-by-step explanation:

PEMDAS

2(5+3)

5+3= 8

2 × 8 = 16

10 + 6 = 16

Answer: rational

explain

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 coordinates of the midpoint are:

x = (A + C) / 2

y = (B + D) / 2

Where (A, B) and (C, D) are the coordinates of the points M and J.

The midpoint is the middle point of a line segment and it is equidistant from both endpoints.

We have,

M_______X_______J

MX : XJ = 1 : 1

The formula for finding the coordinates of the midpoint is:

x = (a + c ) / 2

y = ( b + d ) / 2

(x, y) = coordinates of the midpoint.

Where (a, b) and (c, d) are the coordinates of the two endpoints.

We can consider,

M = (A, B)

J = (C, D)

X = (x, y)

Thus the coordinates of the midpoint X are:

x = (A + C) / 2

y = (B + D) / 2

Where (A, B) and (C, D) are the coordinates of the points M and J.

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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!!

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 -_-

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 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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Answer:

1:12

Step-by-step explanation:

You have to convert both value to the same measurement, so you gonna find how many minutes is in 5 hours which is (300 minutes) then you put 25/300 then cancel out

Answer:

X = 32

Step-by-step explanation:

X/4 = 8

To solve for x, multiply each side by 4

X/4*4 = 8*4

X = 32

Answer:transversal

Step-by-step explanation:

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.

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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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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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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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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Answer:

[tex]\csc ^2(\theta)[/tex]

Step-by-step explanation:

Using Pythagorean identity,

[tex]\mathrm{1+\cot ^2(x)=\csc ^2(x)}\\\mathrm{=\csc ^2(\theta)}[/tex]

Answer:

1 + cot² θ = sec² θ

Step-by-step explanation:

1 + cot²θ =

I know this identity to be true:

sin² θ + cos² θ = 1

Divide both sides by sin² θ.

sin² θ / sin² θ + cos² θ / sin² θ = 1 / sin² θ

1 + cot² θ = sec² θ

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

The value of y when we make y the subject of the formula in 5x - 5y = 40 will be B. y = -3x - 8

It should be noted that an equation is simply used to show the relationship that exists between the variables that are given.

In this situation, the equation given s

is illustrated as:

-15x - 5y = 40

Divide through by -5

-3x - y = 8

Then make y the subject of the formula

y = -3x - 8

Therefore, value of y when we make y the subject of the formula in 5x - 5y = 40 will be y = -3x - 8.

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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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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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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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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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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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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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Check the picture below.

keeping in mind that perpendicular lines have negative reciprocal slopes, and that we also know that the line is a perpendicular bisector, namely it cuts that segment into two equal halves as you can see in the picture, so it really passes through the midpoint of that segment, so let's get the slope of that green segment

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{7}}} \implies \cfrac{4}{-8}\implies -\cfrac{1}{2}[/tex]

so for the perpendicular bisector that'd be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1}\implies 2}}[/tex]

now let's check for the midpoint of the green segment

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 +7}{2}~~~ ,~~~ \cfrac{ 9 +5}{2} \right) \implies \left(\cfrac{ 6 }{2}~~~ ,~~~ \cfrac{ 14 }{2} \right)\implies (3~~,~~7)[/tex]

so we're really looking for the equation of a line whose slope is 2 and that it passes through (3 , 7)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 2}(x-\stackrel{x_1}{3}) \\\\\\ y-7=2x-6\implies {\LARGE \begin{array}{llll} y=2x+1 \end{array}}[/tex]

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