Justify Solution Paths of Linear Equations
3(x−2)+5x=26 (What property is this?)
3x−6+5x=26 (What property is this?)
8x−6=26 (What property is this?)
8x=32 (What property is this?)
x=4 (What property is this?)


Here are a list of the properties-

Subtraction Property of Equality
Addition Property of Equality
Multiplication Property of Equality
Division Property of Equality
Combine Like Terms
Distributive Property
Given Equation

Answer:

last one 12/8 = 9/X

Step-by-step explanation:

according to the rule of similarity in triangles

The equation that can be used to find the length of CD is 9/x = 12/8.

Where x is CD.

Option D is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

ΔABC ≅ ΔEDC

We can write:

BC/BA = CD/DE

9/12 = x/8

9/x = 12/8

Thus,

The equation 9/x = 12/8 can be used to find x.

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Answer:

Divide the numerator and denominator of the given rate by the denominator of the given rate.

Step-by-step explanation:

Answer:

your answer is 463

Step-by-step explanation:

Hope this help you

have a great thanksgiving

Answer:

✅[tex] R = 4c [/tex]

Step-by-step explanation:

The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as [tex] y = mx + b [/tex].

Where,

y = R (amount of cake sold in dollars)

x = c (cakes sold)

m = slope

b = y-intercept.

The equation would look like:

[tex] R = mc + b [/tex]

We need to find the value of m and b, to get an equation to represent the situation.

The first point we have from the information given is (15, 60) => 15 cakes sold for $60.

The second point is (22, 88) => 22 cakes sold for $88.

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{88 - 60}{22 - 15} = \frac{28}{7} = 4 [/tex]

To find b, substitute c = 15, R = 60 and m = 4, into [tex] R = mc + b [/tex].

[tex] 60 = 4(15) + b [/tex]

[tex] 60 = 60 + b [/tex]

[tex] 0 = b [/tex]

Since b = 0, this means there is a proportional relationship between R and c.

Substitute m = 4 and b = 0 into [tex] R = mc + b [/tex] to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.

[tex] R = 4c + 0 [/tex]

✅[tex] R = 4c [/tex]

a. If sea level is represented by 0, then something below sea level would be a value of something less than zero, a negative number. Because the Challenger Deep is 35,814 feet below sea level, it will be represented by -35,814.

b. Trieste is trying to reach the bottom of the challenger deep, which is y, and descending the ocean at -3 feet per second. So the equation would be like this

-35,814 = -3x

We are just looking for x. Notice how both number values are negative so the time it would take Trieste to reach the bottom would be a positive value.

-35,814 divided by -3 = 11938, so it would take 11938 seconds to reach the bottom.

c. y and x would be used in the same context as it would just now. Except that Trieste is coming up to the surface, so the depth of the Challenger Deep is positive.

35814 = k * 11938

k = 3, the amount of time it took to reach the surface in hours.

Hope this helps!

Answer:

x+6<20

x<14

Step-by-step explanation:

Answer:

20-6+x

Step-by-step explanation:

you would add six and x and then subtract it from twenty becouse less than means to subract

Answer:

A, B, and C.

Step-by-step explanation:

We have the equation:

[tex]4(x-3)=4x-12[/tex]

Let’s distribute the left. This yields:

[tex]4x-12=4x-12[/tex]

Let’s add 12 to both sides:

[tex]4x=4x[/tex]

And subtract 4x from both sides:

[tex]0=0[/tex]

We get the true statement 0=0.

Hence, A is correct.

Because it is a true statement, any input will yield an equivalent output.

Hence, B is also correct.

We also have the form a=a, where a is 0.

Hence, C is also correct.

Therefore, our correct answers are A, B, and C.

Answer:

It is a true statement.

Any input will result in an equivalent equation.

It is equivalent to an equation of the form a = a.

Answer:45 mins.

Step-by-step explanation: half of 30 is 15 (one box = 15) and 15 times 3 is 45

The area of a rectangle is the product of length and width thus the area will be 1358 square meters.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

The perimeter of the rectangle = 2( length + width).

It is known that,

Area of rectangle = length × width.

Area = 97 x 14 = 1358 sqare meters

Hence "The area of a rectangle is the product of length and width thus the area will be 1358 square meters".

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Answer:

$50.23

Step-by-step explanation:

f(t)=1.35(t)+9.73

First I found out how many years are after 1985 so you would do 2020-1985 which equals 30.

I plug it in for t.

f(t)=1.35(30)+9.73

Then you multiply 1.35 and 30 which would leave us with.

f(t)=40.5+9.73

Add them and you get $50.23

Answer:

x=NaN your welcome hehe

Answer:

Part A 40

Part B 90

part C show your work

please mark brainliest i need it

Hope helps

Answer:

0.55199

Step-by-step explanation:

When we have a random number of samples, We solve using z score formula

z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation

n is random number of samples

z = 0.83/77/√147

z = 0.13069

Probabilty value from Z-Table:

P(x<48.83) = 0.55199

The probability that the mean of the sample would differ from the population mean by less than 0.83 months is 0.55199

Answer:

y-18,000=2,750(x-0) --> point-slope

y=2,750x+18,000   --> slope-intercept

-2,750x + y = 18,000  --> standard

Step-by-step explanation:

Linear Modeling

Some situations can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The pool being drained contained initially 18,000 gallons of water. If we set the variable x as the time in hours and y as the remaining gallons of water in the pool, this first point is (0;18,000).

We are also aware that after 2 hours 12,500 gallons of water remain. This gives us the second point as (2;12,500).

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Let's find the equation of the line with the 2 points:

[tex]\displaystyle y-18,000=\frac{18,000-12,500}{2-0}(x-0)[/tex]

Calculating:

[tex]\displaystyle y-18,000=\frac{5,500}{2}(x-0)[/tex]

[tex]y-18,000=2,750(x-0)[/tex]

The equation above is the point-slope form of the line

Simplifying and adding 18,000:

[tex]y=2,750x+18,000[/tex]

The equation above is the slope-intercept form of the line

Moving all the variables to the left side:

[tex]-2,750x + y = 18,000[/tex]

The equation above is the standard form of the line

Answer:

y-18,000=2,750(x-0) --> point-slope

y=2,750x+18,000   --> slope-intercept

-2,750x + y = 18,000  --> standard

Answer:

65,000 grams

Step-by-step explanation:

1 kilogram = 1,000 grams

The giraffe weighs 65,000 grams.

The product of 2.3 × 1.5 from the area model is 3.45

The product of two numbers implies the multiplication of the two numbers. Here, the two numbers to be multiplied together are decimal numbers.

Using the long multiplication method.

     2.3

×     1.5    

   1 1 5

+ 2 3      

  3 . 4 5  

So, what we did basically is to first multiply the two numbers normally and then, decide how many decimal places are the two numbers which two.

Therefore, the product of 2.3 × 1.5 from the area model is 3.45

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Answer:

Step-by-step explanation:

im traade =23423423423

Answer:

10 4/10

Step-by-step explanation:

multiply it together

Answer:

2 gallons converted to liters is 7.57 or 8 liters rounded

Answer:

-0.5. -0.5 is to the right of -1.5

Answer:

Trig ratios on coordinates can be negative or positive in value

But

Trig ratios on triangles can only be positive

Step-by-step explanation:

The difference is that, the length of sides used in trig on the coordinates is not absolute

What this mean is that it is dependent on the axes that we are and thus might take up a negative or positive value for trig on coordinates

What we are saying is that while trig on triangle can be positive only, trigonometric ratios on coordinates can be negative or positive

Answer:   5/9

This is assuming the equation is y = (5/9)x

Note it is in the form y = kx with k = 5/9 as the constant of proportionality.

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval of mean pulse rate for adult female is [tex]71.98 <  \mu <  79.88 [/tex]

The 95% confidence interval of mean pulse rate for adult male is  [tex]62.89 <  \mu <  70.57 [/tex]

The correct option is  C

Step-by-step explanation:

  Generally the sample mean for Male pulse rate is mathematically represented as

       [tex]\= x_1 = \frac{\sum x_i }{n}[/tex]

= >    [tex]\= x_1 = \frac{81 + 74 + \cdots + 59 }{40 }[/tex]

= >    [tex]\= x_1 = 66.73[/tex]

Generally the standard deviation for male pulse rate is mathematically represented as

      [tex]\sigma_1 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]

=>   [tex]\sigma_1 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (74 - 66.73 )^2+ \cdot + (59 - 66.73 )^2 }{40-1 } }[/tex]

=>   [tex]\sigma_1 = 12.24[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma_1 }{\sqrt{n} }[/tex]

=>    [tex]E = 1.96 *  \frac{12.4 }{\sqrt{40} }[/tex]

=>    [tex]E =3.84 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x_1 -E <  \mu <  \=x_1  +E[/tex]

=>    [tex]66.73 -3.84 <  \mu < 66.73 +3.84 [/tex]

=>    [tex]62.89 <  \mu <  70.57 [/tex]

  Generally the sample mean for Female pulse rate is mathematically represented as

       [tex]\= x_2 = \frac{\sum x_i }{n}[/tex]

= >    [tex]\= x_2 = \frac{81 + 94 + \cdots + 73 }{40 }[/tex]

= >    [tex]\= x_2 = 75.93[/tex]

Generally the standard deviation for Female  pulse rate is mathematically represented as

      [tex]\sigma_2 = \sqrt{\frac{\sum (x - \= x)^2 }{n-1 } }[/tex]

=>   [tex]\sigma_2 = \sqrt{\frac{\sum (81 - 66.73 )^2 + (94 - 66.73 )^2+ \cdot + (73 - 66.73 )^2 }{40 } }[/tex]

=>   [tex]\sigma_2 = 12.73[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma_2 }{\sqrt{n} }[/tex]

=>    [tex]E = 1.96 *  \frac{12.73 }{\sqrt{40} }[/tex]

=>    [tex]E =3.95 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x_2 -E <  \mu <  \=x_2  +E[/tex]

=>    [tex]75.93 -3.95 <  \mu < 75.93 + 3.95 [/tex]

=>    [tex]71.98 <  \mu <  79.88 [/tex]

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[tex]2 \times \frac{1}{2} hour = 1hour \\ [/tex]

Thus ;

[tex]2 \times \frac{5}{12} \: \: miles = \frac{10}{12} \: \: miles = \frac{5}{6} \: \: miles \\ [/tex]

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I think the answer is 5/6

Answer:

(-1, -3)

Step-by-step explanation:

Answer:no

Step-by-step explanation:

Answer:

17 [tex]\frac{1}{4}[/tex]

Answer:

The type of coins =pennies  has = 100 pennies.

servant has a total number of 100 coins

The sum of the percentage and pennies = $100

Let us represent the number of nickels as which is _% = 55.4

The number of pennies as y

Step-by-step explanation: