Find the slope and y-intercept of the graph of the linear equation. Write your answers in simplest form.
y=9.5
Slope: ?
y-intercept: ?

The unit rate or miles per gallon for Blue car is 35.6 miles and for Red car is 36 miles. Red car could travel the greater distance on 1 gallon of gasoline.

44 1/2 = 44 + 1/2

         = (88+1)/2

         = 89/2

1 1/4 = 1 + 1/4

       = (4+1)/5

       = 5/4

28 4/5 = 28 + 4/5

           = (140+4)/5

           = 144/5

Distance blue car covers in 5/4 gallons of fuel = 89/2

     Distance blue car covers in 1 gallon of fuel = (89/2) / (5/4)

                                                                             = (89*4)/(2*5)

                                                                             = 178/5  

                                                                             = 35.6

Distance red car covers in 4/5 gallons of fuel = 144/5

     Distance red car covers in 1 gallon of fuel = (144/5) / (4/5)

                                                                             = (144*5)/(4*5)

                                                                             = 144/5  

                                                                             = 36

Hence, Red car could travel the greater distance on 1 gallon of gasoline by 0.4 miles.

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By using the formula for the gradient, we can solve a simple equation to find that the value of x is 9.

For a segment whose endpoints are:

P = (x₁, y₁) and Q = (x₂, y₂)

The gradient of the line PQ is:

G = (y₂ - y₁)/(x₂ - x₁)

So it is like the slope of a linear equation.

In this case, the endpoints are:

P = (5, 7)

Q = (x, 15)

And the gradient is equal to 2, so we have G = 2, then we can write the equation:

2 = (15 - 7)/(x - 5)

We can solve this to get:

2*(x - 5) = (15 - 7)

2x - 10 = 8

2x = 10 + 8

2x = 18

x = 18/2 = 9

The value of x is 9.

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The domain choice that is a possibility is A. A. Real numbers greater than 0.

A continuous function in mathematics is one in which a continuous variation of the argument causes a continuous variation of the function's value. This means that there are no abrupt changes in value, which are referred to as discontinuities.

Option A: Real numbers greater than zero:

Because real numbers are continuous functions, the greater than zero part of them can be used to represent the balance sheet.

Option B: Use only whole numbers: It is not possible.

Whole numbers are discrete, not continuous, and thus cannot represent decimal points.

Option C: Integers: Invalid

Because integers are discrete rather than continuous, they cannot represent decimal points.

Natural numbers are not an option.

Natural numbers, like whole numbers, are discrete rather than continuous and cannot represent decimal points.

In conclusion, the correct option is A.

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According to the given triangle, ΔBCE ≅ ΔCBD is proved.

Triangle:

The three-sided polygon that consists of three edges and three vertices is know  as triangle.

Given,

Here we have the triangle and we need to prove the ΔBCE ≅ ΔCBD.

Let us consider ABC be the triangle with sides BC, AC, AB add the opposite angles A, B, C being in length equal to a, b, c respectively.

Here they draw a perpendiculars AD, BE and CF from A, B, C to opposite sides meeting sides BC, AC and AB at D, E, F respectively.

So, here we take the ΔCBD and ΔBCE,

Then the

∠D = ∠E = 90°

So, the Side BC = Side BC and the Side BD = Side CE.

From this relation, and based one the concept of RHS Congruence Criterion

We have identify that, the Corresponding Angle Congruence Test

∠DCB = ∠EBC

Therefore, the  ΔBCE ≅ ΔCBD is proved

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135.53 centimeters the height of a patient in cm if he weighs 68kg and has a BSA of 1.6m².

Given that,

Some medical professionals determine a patient's medicine dosage based on the patient's body surface area (BSA). The BSA calculation method that is most frequently employed is BSA = [tex]\sqrt{\frac{wh}{3600} }[/tex].

where BSA is expressed in square meters, w is the patient's weight (in kg), h is their height (in cm),

We have to determine the height of a patient in centimeter if he weighs 68kg and has a BSA of 1.6m².

1.6= [tex]\sqrt{\frac{wh}{3600} }[/tex]

1.6= [tex]\sqrt{\frac{68h}{3600} }[/tex]

Squaring on both sides.

1.6²= 68h/3600

2.56 × 3600 =68h

9216 = 68h

h= 9216/68

h = 135.53.

Therefore, 135.53 meters the height of a patient in cm if he weighs 68kg and has a BSA of 1.6m².

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Answer:

  150 miles

Step-by-step explanation:

Jina wants to know the number of miles driven that would make the cost of two rental plans the same. One costs $0.15 per mile plus $49.98; the other costs $0.19 per mile plus $43.98.

The difference in cost between the to plans for m miles driven is zero when ...

  (0.15m +49.98) -(0.19m +43.98) = 0

  -0.04m +6.00 = 0 . . . . . . . . simplify

  m -150 = 0 . . . . . . . . . . . . divide by -0.04

  m = 150 . . . . . . . . . . . . . add 150

Jina would need to drive 150 miles for the two plans to cost the same.

14.375 grams of the radioactive isotope will be left after 3 half-lives.

The initial mass of the isotope = 115 gm

after each half-life, the amount of the isotope is reduced to half

therefore,

after the first half-life, the mass of the isotope will become = 115/2

                                                                                          = 57.5 gram

now after the second half live, the mass will again be reduced to half of the previous mass = 57.5/2

                              = 28.75 gram

similarly, after the third half-life, the mass will be half of the previous mass  = 28.75/ 2

           = 14.375 gram

OR

simply we can write that

weight after 3 half-lives will be = 115/ 2³        

                                                = 115 / 8

                                                = 14.375 grams.

So the mass after 3 half-lives is 14.375 grams.

A risky form of a chemical element that releases radiation as it breaks down and will become extra stable. Radioisotopes may additionally arise in nature or be made in a laboratory. In medication, they may be used in imaging exams and in treatment. additionally known as a radionuclide.

Atoms of equal detail with extraordinary numbers of neutrons are known as isotopes. Many elements have one or extra isotopes which might be radioactive. Their nuclei are risky, so they destroy down, decay, and emit radiation.

whilst utilized in cautiously controlled clinical programs, radioactive isotopes are safe and no longer almost as frightening as we first imagined. The radiation from those isotopes has a quick half of lifestyles and handiest give off low stages of radiation. Radioactive isotopes are not constantly risky, though. a few most effective ones supply tiny amounts of radiation. There are radioactive isotopes in nature all around us. maximum of them cause us very little damage.

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The time that it take to knit the scarf from start to finish is 10 hours.

From the information, the volunteer knits a 5-foot long scarf at a constant rate and after 4 hours, the volunteer still has to knit 3 feet of the scarf.

Therefore, the volunteer used 4 hours to knit 2 scarf. The time used per scarf is 4/2 = 2 hours.

In this case, the time taken to finish the scarf will be:

= Time per feet × Total feet

= 2 × 5

= 10 hours.

It'll take 10 hours.

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Answer:

  x = 9

Step-by-step explanation:

Apparently, you want the solution to (10x -27) = 7x.

Subtract 7x from both sides to get ...

  3x -27 = 0

Divide by 3, and you have ...

  x -9 = 0

Add 9 to show the value of x:

  x = 9

The solution to the given equation is x=9.

__

Additional comment

There is no information here that relates the given equation to b, so we cannot help you find b.

Answer:

$124.80

Step-by-step explanation:

$58.23 + $66.57 = $124.80

Answer:

60

Step-by-step explanation:

5 x8 = 40 40 + 20 = 60

Answer:

-14

Step-by-step explanation:

Hello!

You can evaluate the value of z + 3x by substituting the given values of z and x into the equation.

The evaluated value is -14.

Answer:

-14

Step-by-step explanation:

4+3(-6)

4-18

-14

If they have 50 plants growing in the garden. The number of vegetable plants they have is :20.

Using this formula to find the number of vegetable plants

Number of vegetable plants = Percentage of vegetable plants  × Number of plants in the garden

Let plug in the formula

Number of vegetable plants = 40% × 50

Number of vegetable plants = 20

Therefore the number of vegetable plants is 20.

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Answer:

[tex]y=\frac{3}{2}x-6[/tex]

Step-by-step explanation:

y=Mx+b is slope intercept form

M- slope

b- y intercept

We know b because when x is zero y is -6 so that is the y intercept

b=-6

Now to fin the slope we use y2-y1/x2-x1

0-(-3)/4-2

3/2

m=3/2

So we just put it all into the equation to get

y=3/2x-6

Hopes this helps

Answer:  i'm writeing this so you can mark the other person brainliest

Step-by-step explanation:

No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent .

What is Probability ?

Probability is the study of likeliness of an event to happen. The range of probability is 0 to 1.

Now, According to the question:

It is given that

In a certain city, 60% of the heads of household own the house in which they reside,

and 80% of the heads of the household have full-time employment.

percentage of heads of household both own their home and have a full-time job =?

As the probability of a person having both their own home and having

full time employment are not independent.

Hence, No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent.

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Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

Answer:

$2,700

Step-by-step explanation:

15% of $18,000 = 0.15 × $18,000 = $2,700

Answer: He should shade 3 and leave 4 unshaded.

Step-by-step explanation:

The results of the division between the two functions are listed below:

a) (h / g) (- 1) = - 1 / 15

b) x = 7 / 8 is not in the domain of (h / g) (x).

Herein we have two functions h(x) and g(x), the former is a quadratic equation and the latter is a linear equation and the division between the two functions is described below:

(h / g) (x) = h(x) / g(x), for all x such that g(x) ≠ 0

If we know that h(x) = 2 · x² - 3 and g(x) = - 8 · x + 7, then the division between the two functions is:

(h / g) (x) = (2 · x² - 3) / (- 8 · x + 7)

Now we evaluate the function at x = - 1:

(h / g) (- 1) = [2 · (- 1)² - 3] / [- 8 · (- 1) + 7]

(h / g) (- 1) = (- 1) / 15

(h / g) (- 1) = - 1 / 15

To determine the value of x such that does not belong to g(x), we need to solve the following expression:

g(x) = 0

- 8 · x + 7 = 0

8 · x = 7

x = 7 / 8

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At a profit of $30 per bike and $1950 operating cost per month the store needs to sell 65 bikes to break even.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The store pays an average of ​$60 per bike. The average selling price of each bicycle is ​$90.

∴ The profit per bike the bicycle store make is $(90 - 60) = $30.

Also, the bicycle store costs ​$1950 per month to operate,

Assuming no. of bikes the store needs to sell to break even is x.

∴ 30x = 1950.

x = 195/3.

x = 65.

The store needs to sell 65 bikes to break even the cost.

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To find the constant of proportionality of a given relationship, divide the given ratios:

8​ grams of yeast for every 500​ grams of flour

⇒ 8/500

⇒ 0.016

We can find the constant that is greater than 1 by reversing the values:

500​ grams of flour for every 8​ grams of yeast

⇒ 500/8

⇒ 62.5

Greater than 1: 62.5

Less than 1: 0.016

Answer: Y+5= 2/9(X+2)

Answer: (x + 2) = 2/9 (y + 5)

Step-by-step explanation:

y – y₁ = m(x – x₁)

The system of inequalities has been solved graphically and one possible solution is buying 4 apples and 12 peaches.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of apples purchased and number of peaches purchased by Alang and his children, and then translate the word problem into algebraic equation as follows:

Since apples for $2 each and peaches for $0.50 each, the cost of fruits is given by:

2x + 0.5y ≤ 20

Also, they must buy a minimum of 16 apples and peaches altogether:

x + y ≥ 16

Therefore, a possible solution when x = 4 is given by:

x + y ≥ 16

4 + y ≥ 16

y ≥ 16 - 4

y ≥ 12

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The value of Indices 10x^2y÷ 5xy is 2x^(2y-1)×y^-1

An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 4^3. 4 is the base and 3 is the index.

10x^2y = 10x^2(y)

dividing 5xy with 10x^2y

the coefficient 5 will divide 10 to give 2

therefore the value is

2x^2y÷ xy

using law of INDICIES

the value will be 2x^(2y-1)×y^-1

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The answer is [tex]a^{-3}=\frac{1}{x^{3} }[/tex]

Exponent

An exponent is a number that has a power. In numbers with exponents, there are several rules. This rule is used to calculate the exponents operation.

The rules are, including:

[tex]a^{m}a^{n}=a^{m+n} \\\frac{a^{m} }{a^{n} }=a^{m-n}\\( a^{m}) ^{n}=a^{mn}\\ (ab)^{m}= a^{m}b^{m} \\\frac{a}{b} ^{m}=\frac{a^{m} }{b^{m} } \\a^{-m}=\frac{1}{a^{m} }\\ \sqrt[n]{a^{m} } =a^{\frac{m}{n} }[/tex]

From the properties rules, the rules that can be used in the problem are

[tex]a^{-m}=\frac{1}{a^{m} }[/tex]

From the properties above, it can be concluded that negative exponents mean one per number to that power. Do not reverse with the cube root, where the cube root the one per is the power, not the base number.

If the question is asked [tex]a^{-3}[/tex]

then it can be directly substituted in the rule above.

With that rule, let's find the number that equivalent with [tex]4^{-3}[/tex].

[tex]a^{-3}=\frac{1}{x^{3} }[/tex]

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Answer:

below

Step-by-step explanation:

x = (3+x) / y      divide both sides by x and multiply by y

y = (3+x) / x

y = 3/x  + 1        

y - 1 = 3/x

x = 3 / ( y-1)

The equivalent expression for the expression given; (( 5/7 )² × (1/3)-³)-¹ is; (7/5)² • (1/3)³.

It follows from the task content that the expression which is equivalent to that which is given is to be determined.

Hence, since the given expression is; (( 5/7 )² × (1/3)-³)-¹;

It follows from the power of powers law of indices that we have;

( 5/7 )-² • (1/3)³

Also, according to the negative exponent law of indices; we have;

(7/5)² • (1/3)³.

On this note, the required equivalent expression is; (7/5)² • (1/3)³.

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Answer:

18

Step-by-step explanation:

to make the 11 denominator turn into 22 they had to multiply by 2

So we multiply the numerator by 2 too

9x2=18

Hopes this helps please mark brainliest

Answer:

If you would like to solve the equation 9/11 = x/22, you can calculate this using the following steps:

Steps to find ?

9/11 = x/22    /*22

x = 9/11 * 22

x = 18

The correct answer should be 18 through my calculations

You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.

What does a biconditional mean?

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You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.

When both sides of a biconditional statement have the same truth value, the statement is said to be true. A double-headed arrow indicates the biconditional operator. If both the initial conditional assertion and the opposite statement are true, a statement is said to be biconditional.

"An A is guaranteed if you receive a perfect score on the final." ... Last but not least, it is a widely recognized principle that the conditional and biconditional operators have. A statement is logically true if it cannot logically be wrong. If a sentence can be expressed in the form "P if and only if Q," it is a biconditional assertion.    

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The mean height of the team  rounded  to 1 decimal place is 200.0.

The height of this new player is 206.

What is mean Average?

The mean average, of a data set is the sum of all  the numbers divided by the total number of values.

Formular for calculating mean Average:

Mean Average = {Sum of all the values} ÷ {Total numbers of values}

From the question the height of the  players are as follows:

(height) 198,199,200,201,202)

a) Mean Average =(198 +199 +200 +201 +202)

                                             5

                          =1000

                                5

                           =200.0

b) The new player joins the  team to make the Mean Average 201. hence the height of the new player will be calculated using:

Mean Average = {Sum of all the values} ÷ {Total numbers of values}

201 =(198 +199 +200 +201 +202 + x )

                                             6

201  = 1000+ x

               6

crossmultiply to solve for X:

201 *6 =1000+ x

1,206 = 1000+ x

making x subject of the formular we have:

x = 1,206 - 1000

x = 206

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