A rectangle has a length of 3x-5 and a width of 2x+9.

a. Write an expression for the perimeter of the rectangle.

b. Write an expression for the area of the rectangle.

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =143 \end{cases}\implies s=\cfrac{(143)\pi (3)}{180}\implies s=\cfrac{143\pi }{60}\implies s\approx 7.5[/tex]

Answer:

about 15.8 inches

Step-by-step explanation:

Use the equation [tex]a^{2} + b^{2} = c^{2}[/tex]

Where "a" and "b" are the leg lengths and "c" is the hypotenuse.

The solution is, 15.8 inches is the approximate length of the hypotenuse.

here, we have,

given that,

A right triangle has legs that are 10.1 inches and 12.2 inches long.

We only need to apply Pythagoras theorem to solve this problem.

Pythagoras theorem state that in a right-angle triangle,

opposite² + adjacent²  = hypotenuse²

From the question, the length of the leg = 10.1 inches

one of the leg, lets say adjacent = 12.2 inches

Let x be the hypotenuse of the other leg.

We can now proceed to insert our values into the formula;

opposite² + adjacent²  = hypotenuse²

        10.1²    +      12.2²           = x²

so, we get,

x²  = 10.1² + 12.2²  

x²  = 102.01 + 148.84

x²   =  250.85

Take the square root of both-side to get the value of x

√x²   =  √250.85

x = 15.83

x≈15.8

Therefore the approximate length of the other leg is 15.8 inches.

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Answer:

c(5,3)

5×4×3=60

60÷3!=10

the selection can be made in 10 ways

Answer:

x =5.5

Step-by-step explanation:

The directions say to use x for the number.

"take 10 away from"

x - 10

"then square the result"

(x - 10)^2

"I get the same answer" means the two expressions will be equal to each other.

"if I square my number"

x^2

"then subtract 10 from the result"

x^2 - 10

SET EQUAL TO EACH OTHER.

(x - 10)^2 = x^2 -10

Multiply on the left side.

x^2-20x+100 =x^2-10

subtract x^2 from both sides.

-20x + 100 = -10

subtract 100.

-20x = -110

divide by -20

x = 11/2 or 5.5

CHECK:

(5.5-10)^2=20.25

5.5^2 - 10=20.25

The number would be equal to x =5.5

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The directions say to use x for the number means x - 10

"then square the result" means (x - 10)^2

"I get the same answer" means the two expressions will be equal to each other.

"if I square my number" means x^2

"then subtract 10 from the result" means x^2 - 10

therefore,

(x - 10)^2 = x^2 -10

Now Multiply on the left side.

x^2-20x+100 =x^2-10

Then subtract x^2 from both sides.

-20x + 100 = -10

-20x = -110

x = 11/2 or 5.5

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Answer:

3x^4+297

Step-by-step explanation:

First, simplify 6³ and 9².

6³ = 6•6•6 = 36•6 = 216

9² = 9•9 = 81

Add.

3x^4+216+81

3x^4+297

Note:

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Answer:

4<sqrt24<5

Step-by-step explanation:

sqrt 16=4

sqrt 25= 5

16<24<25

sqrt 16< sqrt 24 < sqrt 25

Therefore 4< sqrt24 < 5

Answer:

x = 8

Step-by-step explanation:

Part a: <1 and <2 are alternate exterior angles because line horizontal lines are parallel

Part b: the value of x can be calculated with the following equation

7x + 15 = 10x - 9 because alternate angles has same measure

15 + 9 = 10x - 7x

24 = 3x divide both sides by 3

8 = x

Answer:

The next term in the sequence can be found by adding 15 to the previous term in the sequence.

Therefore, the next term = 45 + 15 = 60

This is a arithmetic sequence having common difference d=15

If you want next term add 15to the previous one

Like

Next term is

Answer:

17.4 grams butane, C4H10

Step-by-step explanation:

I'll assume the water, H2O, is produced from the butane, C4H10, by a combustion process using oxygen, O2.  We need a balanced equation to start the calculation.

The basic combustion reaction is:

C4H10 + O2 =  CO2 + H2O

The basic equation needs to be balanced.  The same numbers and types of atoms must be equal on both sides.  We can see that one atom of C4H10 contains 4 carbons and 10 hydrogens.  

Carbon:  The carbons wind up in the CO2 molecule.  But each CO2 only has 1 carbon, so we need at least 4 CO2 molecules:

C4H10 + O2 =  4CO2 + H2O

Hydrogen:  Hydrogen atoms are used to form the water.  10 hydrogens from 1 C4H10 will be used to produce 5 H2O molecules, since each requires 2 hydrogens.

The leads to:

C4H10 + O2 =  4CO2 + 5H2O

Now all the carbons and hydrogens are accounted for.  But the oxygens are still not balanced.  As written, we have 1 molecule of O2, for 2 oxygen atoms.  But from the last step in our balancing work, we need 8 from the 4CO2) and 5 for the H2O, for a total of 13 oxygen atoms.  Normally, this would be easy to add more oxygen molecules, but since they comes in pairs (O2), we can only add two at a time, so there will never be an odd number of O atoms from the reactant side.

To solve this, try adding a coefficient of 2 to the C4H10 and rebalancing the H2O and CO2:

2C4H10 + O2 =  4CO2 + 5H2O

We need to adjust both the CO2 and H2O to accommodate the added C and H atoms (a total of 8C's and 20 H's):

2C4H10 + O2 =  8CO2 + 10H2O

Now we see we need more O2, since there is a total of 16 plus 10, or 26 O atoms in the 8CO2 and 10H2O molecules.  To provide 26 O atoms, we need a coefficient of 13 in front of the O2 on the reactant side:

2C4H10 + 13O2 =  8CO2 + 10H2O

Now the equation is balanced.  It tells us we'll need 2 moles of C4H10 to produce 10 moles of H2O.  That's a molar ratio of 5 moles water/1 mole butane.  Or, (0.2 moles butane)/(mole water).

Now convert 27 grams water into moles water:

The molar mass of water is 18 grams/mole.  27 grams of H2O is therefore:

(27 grams)(18 grams/mole) = 1.5 moles H2O

We discovered earlier that we need (1/5) that number of moles of butane.  Therefore, we need:

(1.5 moles H2O)*((0.2 moles butane)/(mole water)) = 0.3 moles butane to produce 1.5 moles (or 27 grams) of water.

Now convert 0.3 moles butane into grams butane by multiplying by  butane's molar mass of 58.0 g/mole:

(0.3 moles)(58.0 g/mole) = 17.4 grams butane to produce 27 grams of water.

=====

Wheh!  That's a lot of work for 27 grams of water.  But the heat released will be fun.

Answer:

3.5 hours

Step-by-step explanation:

First, subtract the consultation fee from $262.50 as it is a one off charge and is not applied hourly

$262.50 - 35 = $227.50

Then find how many times $65 fits into $227.50, in this case it is 3.5 times

To find this on a calculator:

$227.50 / $65 = 3.5

Hope this helps :)

Answer: Choice D

Step-by-step explanation:

cos(32) = 0.8480480962

cos(58) = 0.5299192642

cos(68) = 0.3746065934

sin(32) = 0.5299192642

sin(58) = 0.8480480962

Cos(58) = sin(32)

Cos(32) = sin(58)

The sample who prefer a finished basement is 126 homeowners

Given the following parameters

The total number of people surveyed = 300 homeowners

If a realtor has been told that​ 43% of homeowners in a city prefer to have a finished basement, the sample of owners that prefer a finished basement is expressed as:

Sample of owners = 43% of 300

Sample of owners = 0.43 * 300
Sample of owners = 126

Hence the sample who prefer a finished basement is 126 homeowners

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Answer:

x=26

Step-by-step explanation:

(0.5x-3)(x-14)=120

foil then solve for x

Answer:

c = 177.8

Step-by-step explanation:

121² + 134² = c²

13641 + 17956 = c²

31597 = c²

[tex] c \: = \sqrt{31579} [/tex]

Answer:

The equation on the graph is: y = -(x+1)(x-6)

Answer:

-5<x<3

Step-by-step explanation:

Answer:

18+x

Step-by-step explanation:

since the plus is between the 8 and the perinthesis, you can basically just get rid of them and the expression is then

8+10+x

which is equal to 18+x

Answer:

18 + x

Step-by-step explanation:

combine 10 and 8 to make 18, then add x.

Answer:

x = 4

Step-by-step explanation:

To see when g(x) = f(2)

First, find f(2)

f(2) = 3(2) - 1 = 5

Now g(x) = 2x-3  = f(2) = 5

2x - 3 = 5

Adding 3 to both sides

2x = 8

Dividing 2 on both sides

x = 4

The total of T-shirts is proportional to the total of players, which means 15 players = 15 t-shirts.

A proportion describes the number of elements from one category compared to the number of elements in another. For example, if there are 15 boys and 15 girls in a classroom the number of girls and boys is proportional.

These have a proportional relationship because for every player it is expected there is a determined t-shirts number and this number can only increase if the players increase.

1 t-shirt per player:

36 players = 36 t-shirts

2 t-shirts per player:

36 players = 72 t-shirts

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The player that should be backed is specified by: Option B:  E(Jeter) = 0. 39 and E(Pujols) = 0. 51, so back Pujols.

Supposing that the considered random variable is discrete, we get:

[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i[/tex]

where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values

and [tex]f(x_i)[/tex] is the probability of   [tex]X = x_i[/tex]

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For the considered case, the scores of Pujols and Jeter are specified as:

                Bats      Hits      Home runs

Jetter         488      156           9

Pujols        448       125           26

The points that will be earned are:

On each hit : 1 point

On each home run: 4 points

From the statistics specified , the probability of Jetter scoring hits is estimated as:

[tex]P(\text{Jetter scoring hits})=\dfrac{\text{n(hits by Jetter)}}{\text{n(total bats for Jetter)}} = \dfrac{156}{488}\\\\[/tex]

The probability of Jetter scoring home run is estimated as:

[tex]P(\text{Jetter scoring home runs})=\dfrac{\text{n(home runs by Jetter)}}{\text{n(total bats for Jetter)}} = \dfrac{9}{488}\\\\[/tex]

Therefore, we get:

E(Jetter's score) = Score for hits × hits probability by Jetter + Score for home runs × home run's probability by Jetter

E(Jetter's score) = [tex]1 \times \dfrac{156}{488} + 4 \times\dfrac{9}{488} = \dfrac{192}{488} \approx 0.39[/tex]

Similarly, from the statistics specified , the probability of Pujol scoring hits is estimated as:

[tex]P(\text{Pujols scoring hits})=\dfrac{\text{n(hits by Pujols)}}{\text{n(total bats for Pujols)}} = \dfrac{125}{448}\\\\[/tex]

The probability of Pujol scoring home run is estimated as:

[tex]P(\text{Pujols scoring home runs})=\dfrac{\text{n(home runs by Pujols)}}{\text{n(total bats for Pujols)}} = \dfrac{26}{448}\\\\[/tex]

E(Pujol's score) = Score for hits × hit's probability by Pujol + Score for home runs × home run's probability by Pujol

E(Pujol's score) = [tex]1 \times \dfrac{125}{448} + 4 \times\dfrac{26}{448} = \dfrac{229}{448} \approx 0.51[/tex]

Thus, the player that should be backed is specified by: Option B:  E(Jeter) = 0. 39 and E(Pujols) = 0. 51, so back Pujols.

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Answer:

a

Step-by-step explanation:

on edge 22

Answer:

 y = 4/3x +2

Step-by-step explanation:

The graph crosses the y-axis at y=2, so that is the y-intercept.

The points have a rise of 4 units for each horizontal run of 3 units, so the slope is ...

 m = rise/run = 4/3

The slope-intercept equation for the line is ...

 y = mx +b . . . . . . line with slope m and y-intercept b

 y = 4/3x +2

Still stuck? Get 1-on-1 help from an expert tutor now.

Step-by-step explanation:

Substitute the given values into the expression;

[tex]12(3) - 3( \frac{1}{3} ) \div 4(3) - 5[/tex]

Multiply;

[tex]36 - 1 \div 12 - 5[/tex]

Solve Using PEMDAS;

[tex]36 - \frac{1}{12} - 5[/tex]

[tex]35 \frac{11}{12} - 5[/tex]

[tex]\boxed{30 \frac{11}{12} } [/tex]

Answer:

Step-by-step explanation:

PS: if this is correct pls mark me brainly thanks :)

The area of triangle ABC is the amount of space on the triangle

The area of the triangle is 54.84 square units

Start by drawing the triangle (see attachment)

Next, calculate the measure of angle B using the following tangent ratio

[tex]\tan(B/2) = \frac 34[/tex]

This gives

[tex]\tan(B/2) = 0.75[/tex]

Take the arc tan of both sides

[tex]B/2 = 36.87[/tex]

Multiply by 2

[tex]B = 73.74[/tex]

Next, calculate the length of side AD using the following equation

[tex]AD = \tan(B) * BD[/tex]

This gives

[tex]AD = \tan(73.74) * 4[/tex]

[tex]AD =13.71[/tex]

The area of the triangle is then calculated as:

[tex]Area = AD * BD[/tex]

This gives

[tex]Area = 13.71 * 4[/tex]

[tex]Area = 54.84[/tex]

Hence, the area of the triangle is 54.84 square units

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Answer:

The first coordinate plane has a constant additive rate of change of -1/4

Step-by-step explanation:

Additive rate of change is determined using the slope formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

It must be applied to all of the coordinates given, as sometimes, answer options will have the right slope for the first few options but then change it later in the list. Remember that this is a constant rate of change; it must be the same throughout all of the coordinates.

The first coordinate plane with (-2, 2) and (2, 1) is

[tex]m=\frac{1-2}{2-(-2)} =-0.25[/tex]

so this is the answer. I encourage you to look below to see why the others are not the answer, as there are some tips throughout the rest of my response.

The second plane is a curved line, and this means that it is a function with some kind of exponent or log (judging by the shape, it is probably a quadratic function). Regardless, it will not have a constant change from point to point because of the curve. This is not the answer for those reasons.

The first table is linear (with a constant slope), so that meets the first requirement. The slope, however, is -1/2, so it is not what we are looking for. This is also not the solution.

The last table has a positive slope of 3.3, so this does not fit what we want from an answer.

Hope this helps :)

Answer:

A coordinate plane with a straight line with a negative slope. The line passes through (negative 2, 2) and (2, 1).

Answer:

  8.  35

Step-by-step explanation:

An expression is evaluated for a particular value of a variable by replacing the variable in the expression with its value. Then the numerical expression is evaluated according to the Order of Operations. Here, that means the multiplication is carried out first, then the addition.

__

Put 5 where x is:

  15 +4x

  = 15 +4·5

Do the multiplication:

  = 15 +20

Do the addition:

  = 35

Answer:

40 students

Step-by-step explanation:

you have to minus 9 because of the cars then you have 320 divide 8 and you get 40.

The expression that is not a variation of the Pythagorean identity is the third option.

The Pythagorean identity can be written as:

[tex]sin^2(x) + cos^2(x) = 1[/tex]

For example, if we subtract cos^2(x) on both sides we get the second option:

[tex]sin^2(x) = 1 - cos^2(x)[/tex]

Which is a variation.

Now, let's divide both sides by cos^2(x).

[tex]sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1[/tex]

Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.

Concluding, the correct option is the third one.

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Answer:

I would say C not to sure tho