MN¯has an endpoint at M(–2, –2) and an endpoint at N(7, –5).

What is the length of MN to the nearest tenth?

After solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.

So,

Then,

Therefore, after solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.

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The given expression is equivalent to [tex]\frac{l}{m}[/tex]. The  correct option is C. None of the above

From the question, we are to determine the expression that is equivalent to the given expression

The given expression is

[tex]- \frac{l}{-m}[/tex]

This expression can be written as

[tex]\frac{-l}{-m}[/tex]

Multiplying the numerator and the denominator by -1

[tex]\frac{-l \times -1 }{-m \times -1 }[/tex]

= [tex]\frac{l}{m}[/tex]

Hence, the given expression is equivalent to [tex]\frac{l}{m}[/tex]. The  correct option is C. None of the above

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simplify answers to each algebra equation

1) 9x + 13

2) 3x - 16

3) 5x + 17

4) x + 13

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.

on solving the equation we get the solution of algebra as

9x +13

3x-16

5x+17

x+13

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The cost of each ticket for the ballet is $13.25.

The cost price or simply the cost in retail systems represents the particular value that corresponds to the unit price paid. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

There are numerous ways to calculate cost pricing, however it all relies on the kind of query we are asking. For instance,

If a selling price and profit are provided, then,

Cost price = Selling price (SP) − profit

If a selling price and loss are provided, then,

Cost price =Selling price + loss

In the given question,

The total amount that Marta paid is $53

=> amount = $53

and total number of tickets = 4

Now, the cost of each ticket = Total amount / number of tickets

                                               = $53 / 4

                                               = $ 13.25

Hence, the cost each ticket for the ballet is $13.25.

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The value of x is 5 which is option (D) .

It is given that 25/20 = x/4

On simplifying , we get

          [tex]\frac{25}{20} =\frac{x}{4} \\\\x=\frac{25\times4}{20} \\\\x=\frac{100}{20} \\\\x=5[/tex]

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The complete question is mention below :

What value of x makes this proportion true? 25/20 = x/4

A.6

B.20

C.9

D.5

Using proportions, it is found that the conservationist would expect there to be 310 trouts in the lake.

A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.

Direct relations, which are the most usual, are when both variable behave similarly(both increase or both decrease), while for inverse relations, they behave differently.

For this problem, we have that from the fact that out of the 26 trout, 13 were tagged, the proportion of tagged trouts is:

p = 13/26 = 0.5.

Hence, if 155 trouts were tagged, the expected amount is given by:

0.5n = 155

n = 155/0.5

n = 155 x 2

n = 310.

The conservationist would expect there to be 310 trouts in the lake.

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The complete table is shown in the attachment.

1. 4.8 gallons of water

2. 25 mins

3. The constant of proportionality = 1.6

An example of a proportional relationship is the relationship between time taken and the number of gallons of water that fills the tank which is at a constant rate.

Constant rate is the same as constant of proportionality. It is calculated as, k = y/x.

The equation of a proportional relationship is expressed as y = kx.

Using the pair, (0.5, 0.8), find the constant rate/constant of proportionality (k):

k = y/x = 0.8/0.5

k = 1.6 gallon/min

Substitute k = 1.6 into y = kx

y = 1.6x

Fill the table using the equation, y = 1.6x

For 1 min (x):

y = 1.6(1) = 1.6

1.6 gallon

For 3 mins (x):

y = 1.6(3) = 4.8

4.8 gallons

For 40 gallons (y):

40 = 1.6x

40/1.6 = x

x = 25

25 mins.

The complete table is shown in the attachment.

1. 4.8 gallons of water will be in the tank after 3 mins

2. It will take 25 mins to fill the tank with 40 gallons of water.

3. The constant of proportionality = 1.6

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The system of equations are:

25s + 15j = 205

s - j = 5

Where:

s = number of soda bought

j = number of juice bottles bought

In order to determine the number of bottles of soda and juice bought, two sets of equations would need to be formed based on the information provided in the question. The equations would be solved simultaneously.

Grams of sugar in the soda bottle + grams of sugar in the juice bottle = total grams of sugar

difference in the number of bottles bought

25s + 15j = 205

s - j = 5

The methods that can be used to solve the simultaneous equations :

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Answer:

An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian axes in the plane or in space. The plural of "axis" is "axes," pronounced "ax-ees."

Step-by-step explanation:

that

Answer:

y = 22.5x

Step-by-step explanation:

Using the scale 1:22.5

then the actual length is y = 22.5x

The cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

Based on the information, the appropriate equation will be:

6g + 9y = 144

9g + 7y = 151

where g = grass sod

o = ornamental grass

Multiply equation I by 9

Multiply equation ii by 6

54g + 81y = 1296

54g + 42y = 906

Subtract

39y = 390

y = 390/39

y = 10

From 9g + 7y = 151

9g + 7(10) = 151

9g = 151 - 70

9g = 81

g = 81/9

g = 9

Therefore, the cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.

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The college bookstore is 40 percent off

T-shirt are usually on sale for $34.50

The price was marked down to $20.7

The price change is = 34.5 - 20.7

= 13.8

The percent off can be calculated as follows

= 13.8/34.50 × 100

= 0.4 × 100

= 40

Hence the percent off the college bookstore is 40 percent

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Step-by-step explanation:

her ratio is therefore 25/10, which can be also written as 5/2, because ratios are just a special form of fractions.

to find how many labels she can type in 1 hour, we need to find the rehashing between 10 minutes and 1 hour.

1 hour = 60 minutes.

60 minutes = 6 × 10 minutes.

so, to find the equivalent ratio based on 1 hour, we need to multiply the denominator (bottom part) by 6.

and to keep the ratio value we need to multiply the numerator (top part) by the same number :

25/10 × 6/6 = 150/60

and since the ratio is always telling us how many labels can be typed per unit of time, we see,

she can type 150 labels in 1 hour (60 minutes)

The inverse of the function will be y = x/2 + 3/2. Yes, inverse is a function as well.

Functions that "undo" one another are known as inverse functions. In other words, f(g(x)) = g(f(x)) = x if g(x) is the inverse of f(x). We have a great approach we can use to achieve this given an equation for which we wish to get the inverse.

Not all functions have their opposite. It is simple to see that f(x) will never take on the same value again if f(x) has an inverse. We give this asset a unique name.

If each member of the range corresponds to precisely one element of the domain, a function is said to be one-to-one (f(x)).

Given,

We have a function,

y=2 x-3

Add 3 to each side.

⇒ y + 3 = 2x

Divide by 2 and then either

⇒ x = y/2 + 3/2 or y/2 + 3/2

Just change the labels now, x to y.

⇒ y = x/2 + 3/2

So, the inverse of given function is y = x/2 + 3/2

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The value of subtraction will be equal to 723,862.58.

The mathematical expression is the combination of 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 be used to denote the logical syntax's operation order and other properties.

Given that 2 is subtracted from the number 724,062.58. The value of the subtraction is calculated as:-

Subtraction = 724,062.58  -  200

If we write 2 at the hundredth place it will become 200.

Subtraction = 724,062.58  -  200 = 723,862.58

Therefore, the value of subtraction will be equal to 723,862.58.

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The cubic polynomial equation has three real roots. Simplify the expression to a linear factor and a quadratic expression. The linear factor is obtained by taking values for x and substituting in f(x) to get f(x) = 0. If a value of x gives f(p) = 0, then x-p is a linear factor. By algebraic long  division, obtain the quadratic equation and solve it to obtain the real roots.

f(x) = x³-7 x²+13 x-4

x = 4,

f(x) = 4³-7 (4)²+13 (4)-4 = 0

Thus, x-4 is a linear factor.  

x³-7 x²+13 x-4/ x-4.

(x³-7 x²+13 x-4)/ x-4 =  x²-3 x+1

x²-3 x+1  = 0

By quadratic formula: x = (-b±√(b²-4ac))/(2a)

x =  (--3±√((-3)²-4(1x1))/(2)

x = (3±√(9-4))/(2)

x  = (3±√5)/(2)  

x  = (3±2.24)/(2)  

x = (3+ 2.24)/2 = 2.62

x = (3- 2.24)/2 = 0.38

The real roots are x = 0.38, 2.62 and 4

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According to this definition given below, we identify all lines and rays as follows, EA, EB, EC, and ED are rays, and ED and BE are, Line.

A line is, it is actually difficult to give a good mathematical definition. Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.

A line can be named either using two points on the line (for example, AB←→ ) or simply by a letter, usually lowercase (for example, line m ).

A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.

                                                                                           ___

A segment is named by its two endpoints, for example, AB.

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.

A ray is named using its endpoint first, and then any other point on the ray (for example, BA−→− ).

according to this definition, EA EB EC ED are rays, and ED, and BE are Line

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Answer:

about 42%

Step-by-step explanation:

3/7 = 0.41857... =  42%

Answer:

Step-by-step explanation:

Draw a line in the middle of the compass slightly slanted like this /with an on top of the line indicating 2 congruent angles being created.

Answer: The question is not clear.

Step-by-step explanation:

Slope can be described as rise/ run, change in the dependent variables relative to the change in the independent variables and Δy / Δx.

The slope of a line is a number that describes both the direction and the steepness of the line.

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

Therefore, slopes can be described as follows:

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log₅(-25) is undefined

Since the logarithmic function y = logₐ(x)  is the inverse  of the exponential function,

As the base is positive so x must also be positive

The logarithm of the real base of negative numbers is undefined.

Hence, log₅(-25) is undefined

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It will take 10.3 years for the account to contain $3000.

The formula to be used is given as follows :

              A(t) = a ( 1 + r )^t      (1)

where,  A(t) = future value

               a = principal amount or amount initially deposited.

               r = annual interest rate

               t = time

According to the question we have been given that

            a = $2000

            r = 0.04

            A(t) = $3000

putting the required values in equation (1) we get

          3000 = 2000(1+0.04)^t

          1.5 = (1.04)^t

Taking log both sides we get

    log(1.5) = t log(1.04)

       0.176 = t *0.017

       t = 10.3 years.

Thus it takes 10.3 years for the account to contain $3000.

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Using the properties of logarithm the value of the expression is  [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]

A logarithm is the power to which a number must be raised in order to get some other number.

According to the question we have been given the expression as

                        =  [tex]log_{4} 48 - \frac{1}{2}log_{4} 9[/tex]

The properties of logarithm that we are going to use are :

         [tex]log(\frac{x}{y} ) = logx - logy[/tex]  and   [tex]log_{a} a = 1[/tex]

Also we can see that the base are same so we can use the property of logarithm in the given equation and we know that √2304 = 48. Thus replacing 48 by √2304.

Now solving this step by step using the properties of logarithm we get

                       [tex]=log_{4} \sqrt{2304} - \frac{1}{2} log_{4} 9 \\=\frac{1}{2} log_{4} 2304 - \frac{1}{2} log_{4} 9\\= \frac{1}{2} [log_{4} 2304 - log_{4} 9]\\= \frac{1}{2} [log_{4} (2304/9)]\\= \frac{1}{2} log_{4} 256\\= \frac{1}{2} log_{4} (4^{4} )\\= 2 * log_{4} 4\\= 2*1\\= 2[/tex]

Hence using the properties of logarithm the value of the expression is                        

             [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]

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No extraneous solution to the equation

The equation given is

   3[tex]\sqrt{x}[/tex] = 6

Now we have to find the value of x.

[tex]\sqrt{x}[/tex] = 2

[tex](\sqrt{x} )^{2}[/tex] = [tex]2^{2}[/tex]

x = 4

To find whether it is an extraneous solution or not put the value of x in the given equation.

3[tex]\sqrt{4}[/tex] = 6

3 × 2 = 6

6 = 6

Therefore we get to know that there is no extraneous solution.

x = 4 is the solution of the equation.

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Answer:

91678 milliliters

Step-by-step explanation:

hope this is helpful! stay safe, and have a blessed day! :)

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]y=7-3x-2x^2\implies \cfrac{dy}{dx}=-3-4x\implies \stackrel{\textit{setting the derivative to 5}}{5=-3-4x} \\\\\\ 8=-4x\implies \cfrac{8}{-4}=x\implies \boxed{-2=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{when x = -2, what's "y"?}}{y=-7-3(-2)-2(-2)^2}\implies y=-7+6-8\implies \boxed{y=-9} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-2~~,~~-9)~\hfill[/tex]

The length of the countertop on the blueprint is 5 cm.

For the given question;

The length of kitchen countertop = 8.75 feet.

The scale used in blueprint is 1 centimeter = 1.75 feet.

Thus, use the unitary method.

1.75 feet -----> 1 cm.

Divide both side by 1.75.

1 feet ------>1/1.75 cm

Multiply both side by 8.75.

8.75 feet ---> 8.75/1.75 cm

8.75 feet ------> 5 cm.

Therefore, the the length of a countertop for the blueprint is found as 5 cm.

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The factors of equation are 5 and 3.

Rewriting the equation -

x² - 8x + 15 = 0

ax² + bx + c = 0

Factorizing the equation such that -

The suitable factors that can be used for solving the expression are 5 and 3.

x² - 5x - 3x + 15 = 0

x(x - 5) -3 (x - 5) = 0

(x - 5) (x - 3) = 0

(x - 5)= 0

x = 5

(x - 3) = 0

x  = 3

Hence, the two factors of expression are 5 and 3.

To check the factors, we will keep each value of x to see if Left Hand Side is equal to Right Hand Side or not

When x = 5

x² - 8x + 15 = 0

5² - 8×5 + 15 = 0

25 - 40 + 15 = 0

-15 + 15 = 0

0 = 0

When x = 3

x² - 8x + 15 = 0

3² - 8×3 + 15 = 0

9 - 24 + 15 = 0

- 15 + 15 = 0

0 = 0

Since for both factors Left Hand Side is equal to Right Hand Side, thus, 5 and 3 are correct factors of the equation.

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