Solve. Check for extraneous solutions. 3 √2x -3=9

Answer:

[tex] \large \bf \implies{(6,10)}[/tex]

Step 1) : Solve the inequality

[tex] \bf \longrightarrow{8 \leqslant 2m - 4 < 16}[/tex]

Separate compound inequalities into system of inequalities

[tex] \begin{cases}2m - 4 \geqslant 8 \\2m - 4 < 16\end{cases}[/tex]

[tex]1) \: \: \: \: \: \large\boxed{ \tt2m - 4 \geqslant 8}[/tex]

[tex] \bf \longrightarrow2m \geqslant 8 + 4[/tex]

[tex] \bf \longrightarrow2m \geqslant 12[/tex]

[tex]\bf \longrightarrow \: m \geqslant \frac{12}{2} [/tex]

[tex]\bf \longrightarrow \: m \geqslant 6[/tex]

[tex]2) \: \: \: \: \: \large \boxed{ \sf2m - 4 < 16}[/tex]

[tex]\bf \longrightarrow2m < 16 + 4[/tex]

[tex]\bf \longrightarrow2m < 20[/tex]

[tex]\bf \longrightarrow \: m < \frac{20}{2} [/tex]

[tex]\bf \longrightarrow \: m < 10[/tex]

[tex] \pink{ \rule{7cm}{0cm}}[/tex]

[tex]\bf \longrightarrow \: m \geqslant 6 \: and \: m < 10[/tex]

[tex]\bf \longrightarrow \boxed{ \sf6 \leqslant m < 10}[/tex]

Step 2) : Graph on a number line attached above

Step 3) : Express solution set in interval notation

[tex]\bf \longrightarrow {\boxed {\underline {\underline{{( \bold{6,10)}}}}}}[/tex]

Based on the number of cups of flour and the number of teaspoons of cooking oil, if 1 cup of flour is used, the number of teaspoons of cooking oil needed is 2 / 5 teaspoons of cooking oil

When 5 cups of flour are used, then 2 teaspoons of cooking oil are needed by the recipe.

If there is only 1 cup of flour being used therefore, the number of teaspoons of cooking oil needed will be:

= Number of teaspoons needed for 5 cups / Number of cups of flour needed
= 2 / 5 teaspoons of cooking oil

First part of question is:
A recipe calls for 5 cups of four and 2 teaspoons of cooking oil.

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The two segments which have the same length are: D. segments YZ and VW.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

Next, we would determine the length of each segment as follows:

Length of segment WX is given by:

W (-2) and X (3)

WX = 3 - (-2)

WX = 3 + 2

WX = 5

Length of segment YZ is given by:

Y (10) and Z (18)

YZ = 18 - 10

YZ = 8

Length of segment XY is given by:

X (3) and Y (10)

XY = 10 - 3

XY = 7

Length of segment VW is given by:

V (-10) and W (-2)

VW = -2 - (-10)

VW = -2 + 10

VW = 8.

Therefore, segments YZ and VW are equal and have the same length.

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Complete Question:

Which two segments have the same length?  

A. segments WX and YZ

B. segments XY and YZ

C. segments VW and XY

D. segments YZ and VW

Answer:

BD = [tex]\sqrt{82}[/tex]

Step-by-step explanation:

calculate BD using the distance formula

BD = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = B (- 4, 6 ) and (x₂, y₂ ) = D (- 3, - 3 )

BD = [tex]\sqrt{(-3-(-4))^2+(-3-6)^2}[/tex]

     = [tex]\sqrt{(-3+4)^2+(-9)^2}[/tex]

     = [tex]\sqrt{1^2+81}[/tex]

     = [tex]\sqrt{1+81}[/tex]

     = [tex]\sqrt{82}[/tex]

     ≈ 9.1 ( to 1 dec. place )

Answer:

9.055385 rounded to 6 decimal places

Step-by-step explanation:

The distance between 2 points in a 2_D Cartesian coordinate can be determined by the distance formula

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

where [tex](x_1, y_1) \mathrm{\;and\:} (x_2, y_2)[/tex] are the coordinates of the two points

This is also called Euclidean distance between the two points

Here coordinates of B are (-4, 6)  and those of D are (-3, -3)

So distance between them

[tex]d = \sqrt {(-3 - (-4))^2 + (-3 - 6)^2}[/tex]

[tex]= \sqrt {(1)^2 + (-9)^2}[/tex]

[tex]= \sqrt {{1} + {81}}[/tex]

[tex]= \sqrt {82}[/tex]

[tex]= 9.055385[/tex]  rounded to 6 decimal places

0.1678 is the probability that all the light bulbs work

Define probability?

Probability is a branch of mathematics and can be defined as the one which deals with the explanation of the possibility of an event to occur or take place. Probability has a range between 0 to 1. In probability, 0 indicates the impossibility of an event to occur and 1 indicates the certainty of that event to occur or take place.

As the light bulbs are not dependent on each other and work independently, the probability that all eight of the light bulbs will work can be calculated by multiplying the probability of each of the eight light bulbs.

As the probability of each of the eight light bulbs to work = 0.8

probability all the eight light bulbs work = 0.8^8

probability all the eight light bulbs work = 0.1678

Hence, 0.1678 is the probability that all the light bulbs work.

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Answer:

$948 will be the price per year lessons

Step-by-step explanation:

Hope it helps you

Answer:

Step-by-step explanation:

$1352 per year

After evaluating the expression we get 2.

Given, x² ₋  x

Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.

A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.

substitute the value of x =2

2² ₋ 2

= 4 ₋ 2

= 2

hence we get the answer as 12.

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Answer:

X=-5 :)

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

14+5=19, so -14+ -5= -19

Is there an attachment? I don't get the worksheet!

The maximum occupancy of the commuter train is 568 passengers

The given parameters can be represented using the following table of values

                         1              2

Passenger       56            40

Cars                  8              3

The maximum occupancy of the commuter train is then calculated as

Maximum occupancy = Sum of (Passengers * Cars)

So, we have

Maximum occupancy = 56 * 8 + 40 * 3

Evaluate the products in the above equation

So, we have

Maximum occupancy = 448 + 120

Evaluate the sum in the above equation

So, we have

Maximum occupancy = 568

Hence, the maximum occupancy of the commuter train is 568 passengers

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'x' in each expression is as follows:

So, the value of 'x' in each expression:

Therefore, 'x' in each expression is as follows:

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The volume of the sports drink that they have with them, in whole liters is: d. 30 liters

The volume of a rectangular shape, just like the rectangular block in the given problem, can be calculated using the formula:

Volume = (length)(width)(height).

From the information given, the rectangular block's dimensions are:]

Volume of one rectangular block = (6.0)(4.0)(10.5)

Volume of one rectangular block = 252 cm³

Convert 252 cm³ to liters:

1,000 cm³ = 1 liters

252 cm³ = 252/1,000 = 0.252 liters

120 packs of 0.252 liters = 120 × 0.252

= 30.24 ≈ 30 liters

Therefore, the volume of the sports drink that they have with them, in whole liters is: d. 30 liters

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For continuous compounding, the effective annual interest rate is e^r - 1.

The following is the continuous compounding formula:

So,

Given: A(t) = a(1+r)^t and A(t) = a.e^rt.

Let the effective rate be R.

Then,  

Therefore, for continuous compounding, the effective annual interest rate is e^r - 1.

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Based on the given task content; the value of v from the points (5,6) and (6,v) which has a slope of –9 is -3

Slope refers the change in y over the change in x.

Slope = Change in y / Change in x

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Slope m = -9

Point 1( 5, 6 )

x₁ = 5

y₁ = 6

Point 2( 6,v )

x₂ = 6

y₂ = v

Substitute the given values into the formula and solve for v.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )-9

= ( v - 6 ) / ( 6 - 5 )-9

= ( v - 6 ) / ( 1 )

-9( 1 ) = ( v - 6 )

-9 = v - 6

v = -9 + 6

v = -3

Therefore, the value of v from the points (5,6) and (6,v) which has a slope of –9 is -3

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The numerical value of v in the coordinates of a line that passes through (5,6) and (6,v) with a slope of –9 is -3

Slope is simply the change in y over the change in x.

Slope = Change in y / Change in x

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Slope m = -9

Point 1( 5, 6 )

Point 2( 6,v )

Plug the given values into the slope formula and solve for v.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

-9 = ( v - 6 ) / ( 6 - 5 )

-9 = ( v - 6 ) / ( 1 )

Cross multiply

-9( 1 ) = ( v - 6 )

-9 = v - 6

v = -9 + 6

v = -3

Given the slope and coordinates of the two points of the line, the numerical value of v is -3.

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The  equation in logarithmic form is log₁₀(0.01)=−2.

Given the equation is:

10⁻²=0.01

The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function ay = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).

Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).

A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form

Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.

log₁₀(0.01)=−2

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Domain: -4 is less than x which is less than or equal to 4

Range: -2 is less than or equal to y which is less than 5

What is domain and range ?

The bis the set of possible input values, and the range is the set of all possible output values of the graph

The completed inequality representing the set of the domain and range are presented as follows;

Given:

Question The graph of the question appear missing and the required graph to complete the question is attached here

Solution:

From the attached graph, we have that there is an open circle at the point (-4, 5), which represents that there is no value at the point

However, at the other end of the graph, which is the point (4, -2), we have a closed circle, which represents that the graph has a value at the point (4, -2)

Part A

The domain of a graph are the possible input (x-values) of the graph, in inequality format, the domain of the attached graph is -4 < x ≤ 4

Therefore;

To complete the inequality for the domain, gives;

Domain: -4 is less than x which is less than or equal to 4

Part B

The range of a graph are the possible output (y-values) of the graph, in inequality format, the domain of the attached graph is -2 ≤ y < 5

To complete the inequality for the domain gives;

Range: -2 is less than or equal to y which is less than 5

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Answer:

170 ft²

Step-by-step explanation:

4ft = 48 in

You then multiply 48 by each given side.

48 in · 4.25in = 204 in

Divide by 12 to get answer in feet.

204 in ÷ 12 = 17

So the actual length of the side labeled 4.25 in is 17 ft.

48 · 2.5 = 120

Divide by 12 to get the answer in feet.

120 ÷ 12 = 10

The actual length of the side labeled 2.5in is 10 ft.

Area= L x W

Area= 17ft · 10ft = 170 ft²

After five months, the percentage decrease in the daylight is 51.815%

As per the question, On the first day of June, there was 16.81 hours of daylight in a city and five months later, there was 8.10 hours of daylight. We are supposed to find the percent decrease in the daylight.

Percentage increases or decreases are calculated by setting the problem up proportionally.

We are trying to calculate at what percentage of 16.81 is 8.10 first

Let "x" be the percentage required percentage

therefore [tex]\frac{x}{100} =\frac{8.10}{16.81}[/tex]

[tex]x = \frac{8.10*100}{16.81} \\x=\frac{810}{16.81} \\x=48.185%[/tex]

8.10 is approximately 48.185% of 16.81.

So the percentage decrease is [tex]100 - 48.185=51.815[/tex]%

Hence the percentage decrease is 51.815%

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Answer:

Two and three

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

36÷12=3

36÷18=2

Answer: 16

Step-by-step explanation:

12 divided by 3/4. You write 12 and change to multiplication and flip 3/4 to 4/3 and the answer will be 48/3 which equals 16.

The length of the rectangular pool is 50 meters

The formula for perimeter of a rectangle is expressed as;

Perimeter = 2 ( l + w)

Where:

From the information given, we have;

Perimeter = 160 meters

Length = 20 + w

Substitute into the formula

160 = 2( 20 + w+ w)

expand the bracket

160 = 2(20 + 2w )

160 = 40 + 4w

collect like terms

160 - 40 = 4w

4w = 120

w = 120/ 4

w = 30 meters

But length = 20 + w = 20 + 30 = 50 meters

Thus, the length of the rectangular pool is 50 meters

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Answer:

p + 3.6 > −5.8?​

Step-by-step explanation:

If you bought and then sold 300 shares at these prices, then the loss

would be $4,806.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given:

General Motors' stock fell from $41 per share in 2013 to $24.98 per share in 2016.

You bought and then sold 300 shares at these prices.

The price of 300 shares of General Motors stock in 2013 was:

300 x $41 = $12,300

The selling price of 300 shares of General Motors stock in 2016 was:

300 x $24.98 = $7,494

Therefore, the loss would be the difference between the purchase price and the selling price:

$12,300 - $7,494 = $4,806.

Therefore, the loss would be $4,806.

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The complete question;

General Motors' stock fell from $41 per share in 2013 to$24.98 per share in 2016. If you bought and then sold 300 shares at these prices, what was your loss?

The appropriate choice of ratio  will be given by

Polly got £30, Andy got £60, Phoebe got £180

What is ratio?

Ratio determines the comparision among many quantities with the same unit.

Here,

Let Polly got £x

So Andy got £2x and Phoebe got £3(2x) = £6x

Total Amount = £(x + 2x + 6x)

                       = £9x

By the problem,

                         9x = 270

                           x = [tex]\frac{270}{9}[/tex]

                           x = 30

So Polly got £30,

Andy got £(2 * 30) = £60

Phoebe got £(6 * 30) = £180

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There are 256 ways to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among $4$ people

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

We are given that for bracelet Yellow, green,black  and red

We need to find the number of ways in which

Each person receive any number of bracelet.

Number of peoples=4

If each person receive exactly one bracelet then , the number of ways= 4 x 3 x 2 x 1 = 24

If all bracelet received by one person and other have no bracelet 4 ways

If one person receive 2 bracelet and other two received by any other=

144 way.

If two person gets  two bracelet each and other two have no bracelet= 36 ways

Same, one person received three bracelet and one received by any of them =48 ways

So Total number of ways=24+4+144+48+36=256 ways

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Answer:

See below

Step-by-step explanation:

Lindsey height = 190 + 130 m       ( m = minutes)

Eduardo height = 240 m

Equate them

190 + 130 m  = 240 m

190 = 110 m

190/ 110 =  1  8/11 minutes  after Eduardo starts