The sum of three consecutive even integers is 168. Define an appropriate variable and write an equation that represents the statement. Solve to find the integers. Show all work and write a conclusion.

The 4 steps in solving simple problems in mathematics is explained below.

According to the author called Polya created his famous four-step process for problem solving that one is used all over to aid people in problem solving

The first and foremost Step is to understand the problem which includes identification of  the unknowns and figure out what the problem tells you is important and then we have to identify any information that is irrelevant to the problem.

Then the nest step is to Devise a plan which means that Look for a pattern and then by using it we have to make a table, diagram or chart and then write an equation.

Then we have to move onto the next steps that is to carry out the plan which means the process of solving the question.

Then the final step is to Look back problem that is none other than check and interpret its reliability of the solution

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Answer:

initial amount is 130

decaying at 55%

Step-by-step explanation:

Answer:

y + 2 = (4/5)(x - 2)

Step-by-step explanation:

Two dots on the line are shown:  (-3, -6) and (2, -2).

As we move from the first to the second, x (the 'run') increases by 5 and y (the rise) increases by 4.  Thus, the slope of this line is m = rise / run = 4/5.

Using the point-slope formula y - k = m(x - h), we get:

y + 2 = (4/5)(x - 2)

Answer:

a- 10x^2 - 4x + 12

b- no, the first equation is −1/4⋅(5x^2+6x−24) and the second is -1/4⋅(10x^2+7x-24)

Step-by-step explanation:

m6th w6y

BRAINLIEST??

Step-by-step explanation:

13x-3= 3x+2 +55 (exterior angle is equal to the sum of 2 opposite interior angles)

or, 13x-3x=57+3

or,10x=60

x=60/10

x=6

FAB =13x-3

=13*6-3

=75

un millon cincuenta y tres mil quinientos siete

he is going to pay $3 for the small one

for the large one we have that it is 5 times ithe price of the small one so w gotta multiply 3 by 5 which gives us 15 dollars we add them 15+3=18 so he gotta pay $18 for both the small one and the large one

Answer:

The union of the intervals is (0,8]

The intersection of the intervals is [1,5]

Hope this helped!

The X-intercept is the point where the line crosses the x-axis. This happens where the Y is equals to zero.

The point slope form of a line is an equation of the line that takes on the form y - y1 = m(x - x1). In this equation, m is the slope of the line, and (x1, y1) is a point on the line. The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. This always happens at the point where y is equal to 0. Therefore, we find the x-intercept of a line in point-slope form by plugging y = 0 into the equation and then solving for x. The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. It is said to be as the x-coordinate of a point where a line, curve, or surface intersects the x-axis.

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Answer:

B

Step-by-step explanation:

Remark

This is a monster when you first come across it, but later on you will not be fooled.

Construction

Solution

Find the value of Arc EF

The value of Arc EF = 360 - 244 = 116

The value of <FOE also = 116. (The arc and the central angle are equal.)

ΔFOE = 116 degrees                See above statement

ΔFOE is isosceles                   Two of it's sides are radii.

The two base angles can be solved. Call each one x

2x + 116 = 180                           All triangles have 180 degrees

     -116    -116                            Subtract 116 from both sides

2x = 64                                     Divide by 2

x = 32                                        <EFO = 32

<EFO = 90                               Where the tangent meets the radius forms a 90o angle.

<EFO + GFE = 90

32 + GFE =90

GFE = 90 - 32

GFE = 58

Answer: B

Answer:

b

Step-by-step explanation:

360-244/2= 116/2=58 or b

Answer:

m = 8

Step-by-step explanation:

Expand the left side

Each term in the second factor is multiplied by each term in the first factor

7a²(4a² - 1) + 2a(4a² - 1) - 3(4a² - 1) ← distribute parenthesis

= 28[tex]a^{4}[/tex] - 7a² + 8a³ - 2a - 12a² + 3 ← collect like terms

= 28[tex]a^{4}[/tex] + 8a³ - 19a² - 2a + 3

Comparing the coefficients of like terms with those on the right , then

m = 8

Answer: Since y varies directly as x and inversely as the square root of z, we can write the following equation:

y = kx/(sqrt(z)), where k is a constant.

We can find the value of k by substituting the known values into the equation. We get:

1/6 = k*20/sqrt(6)

k = 1/240

Substituting this value of k into the original equation, we get:

y = (1/240)x/(sqrt(z))

Substituting the values x = 14 and z = 5 into this equation, we get:

y = (1/240)(14)/(sqrt(5)) = 7/120 sqrt(5) ≈ 0.22

Step-by-step explanation:

Answer:

140 doses

Step-by-step explanation:

1 gram = 1000 milligrams

1 gram = 10 doses

10*14 = 140

Answer:

A

Step-by-step explanation:

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

In a right triangle, the hypotenuse is the longest side, the "opposite" side is the one that faces a particular angle, and the "adjacent" side is the one that faces that angle.

Step 1: Simplify both sides of the equation.

[tex]$$4 g-6=8$$\\Step 2: Add 6 to both sides.$$\begin{aligned}& 4 g-6+6=8+6 \\& 4 g=14\end{aligned}$\\$Step 3: Divide both sides by 4 .$$\begin{aligned}& \frac{4 g}{4}=\frac{14}{4} \\& g=\frac{7}{2}\end{aligned}$$[/tex]

[tex]$g=3 \frac{1}{2}$[/tex]

Therefore, the correct answer is option a)[tex]$g=\frac{7}{2}$[/tex].

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Using doubles plus one fact the sum of 7 + 7 is equal to 15 it is done by simply adding 1 to the given number.

When we add two of the same number, we add using the “doubles fact”. For example, 1 + 1 and 2 + 2 are both doubles facts. Look at the example below: 4 + 4 = 8 is a doubles fact. Doubles fact can help us know other additional strategies like doubles plus one

A double is a number or an amount that is twice as large as the given number or amount. So, if we multiply a number by 2 or if we add a number to itself we say that the number is doubled

The sum of 7 + 7 can be determined by using doubles plus one fact as:

Simply add 1 in 7 + 7 to get the result required.

Therefore by using doubles plus one fact the sum of 7 + 7 is equal to 15.

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Based on the description above, the individuals in this setting is option A: homes.

The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.

In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.

Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.

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The correct answer is option c as DE/AE=BC/AC

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line. So, tan θ to be the slope of a line.

Given here ΔADE ≈ΔABC and thus  DE/AE=BC/AC

but tanθ = DE/AE=BC/AC where tan θ is the slope of the line thus both the lines have identical slopes.

Hence, The correct answer is option c)  ΔADE ≈ΔABC thus DE/AE=BC/AC Therefore the slope of AD is the same as the slope of AB

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Probability measures how probable something is to occur.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

Probability is a measure of how likely something is to happen.

18 Marines, 10 Navy personnel, and 3 Coast Guard troops received their wings at a recent naval aviation school graduation.

Total: 18 + 10 + 3 = 31

a. 1 of each.  P = C 18 * C 10 * C 3  / C 3 31  

= (18 * 10 * 3) / 4495 = 0.120

b: 0 members of the navy = (C_{21} ^ 3)/(C_{21} ^ 3) = 1330/4495 = 0.296

c: 3 Marines.

p = (G ^ 3)/(C_{31} ^ 3) = (8 + 6)/4495 = 0.182

The complete question is

At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be

a.1 of each 0.120  b.  members of the Navy 0.296 c.  Marines 0.182.

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Answer:

a=10.8; c=4.3

Step-by-step explanation:

The sum of all the angles in a triangle is 180 degrees.

Two of the angles are given as 40 deg and 120 deg.

Subtract the measures of both from the sum to get the last angle:

180-40-120=20; ∠C=20°

Using Law of Sines: [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

[tex]\frac{a}{sin120}=\frac{8}{sin40}; a=\frac{8*sin120}{sin40}; a=10.77837084[/tex]

[tex]\frac{c}{sin20}=\frac{8}{sin40}; a=\frac{8*sin20}{sin40}; c=4.25671109[/tex]

Answer:

c=20 a=10.8 c=4.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s A

The measure of the arc ADC is 252°

The arc of a circle is defined as the part or segment of the circumference of a circle.

Given that, a circle O, with tangents AB and BC, the measure of arc AC is 108°, the measure of angle ABC is 72°, we need to find the measure of arc ADC,

According to the definition of circle,

We have,

m ∠ABC = (m arc ADC + m arc ADC) / 2

72° = (m arc ADC - 108°) / 2

144° = m arc ADC - 108°

m arc ADC = 144° + 108°

m arc ADC = 252°

Hence the measure of the arc ADC is 252°

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Answer:

424x - 136

Step-by-step explanation:

16x + 34 ( 12x - 4 )

= 16x + 408x - 136

= 424x - 136

V = & x w x h

V = 6 1/2 x 9 x 3 1/2

V = 204 3/4

So answer is 204 3

                             4

To find the unknown part of a right triangle, you can use the Pythagorean theorem or the trigonometric ratios.

A right triangle is a triangle that has one angle measuring exactly 90 degrees, this angle is called the right angle.

To find the unknown part of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (the hypotenuse). The formula is:

a² + b² = c²

Where c is the length of the hypotenuse and a and b are the lengths of the legs.

You can use this theorem to find the length of a missing side, if you know the length of the other two sides. For example, if you know the lengths of the two legs (a and b) and you need to find the length of the hypotenuse (c), you can use the formula:

c = √(a² + b²)

Alternatively, if you know the length of the hypotenuse (c) and one leg (a), you can use the formula to find the length of the other leg (b):

b = √(c² - a²)

Another way to find the unknown part of a right triangle is the use of trigonometric ratios. As you know, in a right triangle, there are three main ratios: sine, cosine, and tangent. These ratios are defined as follows:

Sin(A) = a/c

Cos(A) = b/c

Tan(A) = a/b

Where A is one of the acute angles of the triangle, and a,b,c are the sides of the triangle. By using the known side and the known angle you could find the unknown side.

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Two slopes can be compared on a graph by analyzing the steepness of the lines and their direction (positive or negative).

The steepness of a line on a graph is determined by its slope, which is the ratio of the change in y to the change in x (rise over run). A steep line has a large slope, meaning that for a small change in x, there is a large change in y. A shallow line has a small slope, meaning that for a small change in x, there is a small change in y. To compare two slopes, one can compare the steepness of the lines by comparing the absolute value of the slopes.

If one line has a larger absolute value than the other, it is steeper. Additionally, one can also compare the direction of the slope, which is determined by the sign of the slope. A positive slope indicates that the line is increasing and a negative slope indicates that the line is decreasing. By comparing the steepness and direction of the slopes, one can determine whether the two lines are parallel or not, and whether they are going in the same direction or not.

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Answer:

31.4cm

Step-by-step explanation:

Formula for circumference of a circle:

[tex]C = 2\pi r[/tex]

The radius of a circle is half of the diameter:

10/2 = 5

Plug in the values using 3.14 for pi:

C = 2(3.14)(5)

C = 31.4cm

Answer:

D. 70.39

Step-by-step explanation:

This is not a good question, but I will show you how to get the answer I chose.

Area = (pi)(r)^2

394.38 = (3.14)(r)^2

divide both sides by 3.14

125.598726 = r^2

take the square root of both sides

r = 11.207083...

rounded is 11.21

---------------------------

Circumference = (2)(pi)(r)

C = (2)(3.14)(11.207083)

C = 70.38

----------------------------------------

Here's why it's a bad question:

If the diameter is 10, the radius is half of that, = 5

Area = (pi)(r)^2

Area = (3.14)(5)^2

A = (3.14)(25)

A = 78.5

So the question says the diameter is 10, but if that's true, the area cannot be 394.38

Also, the circumference can be calculated as (pi)(diameter), so 3.14 x 10 = 31.40, which is not an answer option.

Answer:

26 - 11√5

Step-by-step explanation:

(4√5-3)(√5-2)

= 4√5 (√5-2) -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3 (√5-2)

= 4√5 √5 + 4√5 ⋅ -2 -3√5 -3 ⋅ -2

= 26 - 11√5

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