what is the opportunity cost of one gun in this nation

Answer:

Step-by-step explanation:

3x - 70 = x

2x = 70

x = 35

3(35) - 70

105 - 70 = 35

m<ABC = 35

answer is C

The value of the angle ∠ABC = 35°

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the angle be ∠ABC = ( 3x - 70 )°

Now , from the figure ,

The value of angle ∠A = x°

The value of x° is equal to ( 3x - 70 )° because they are corresponding angles

Now , from the theorem of angles cut by transversal , we get

The pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are called corresponding angles and are equal in size

Each pair of corresponding angles on the same side of the intersecting transversal are equal to each other

So ,

Substituting the values in the equation , we get

x° is equal to ( 3x - 70 )°

x° = ( 3x - 70 )°

x = 3x - 70

Adding 70 on both sides of the equation , we get

3x = x + 70

Subtracting x on both sides of the equation , we get

2x = 70

Divide by 2 on both sides of the equation , we get

x = 35°

So , the value of ∠ABC = ( 3x - 70 )°

∠ABC = ( 3x - 70 )°

∠ABC = ( 135 - 70 )°

∠ABC = 35°

Hence , The value of the angle ∠ABC = 35°

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Given :

A number [tex]12\dfrac{1}{4}=\dfrac{49}{4}[/tex] .

To Find :

What is the sum of 12 1/4 and it’s additive inverse .

Solution :

Fist we should know what is additive inverse .

Additive inverse of a number is that number , when added to it yield zero ,

Basically , for a real number , it reverses its sign :

The opposite to a positive is negative .

The opposite to a negative is positive .

Therefore , the sum of [tex]12\dfrac{1}{4}[/tex] and it's additive inverse is 0 .

Hence , this is the required solution .

Answer:

(x - 12)(x - 4)

Step-by-step explanation:

Given

x² - 16x + 48

Consider the factors of the constant term (+ 48) which sum to give the coefficient of the x- term (- 16)

The factors are - 12 and - 4, since

- 12 × - 4 = + 48 and - 12 - 4 = - 16 , thus

x² - 16x + 48 = (x - 12)(x - 4) ← in factored form

Answer:

a(t)=10000+1.08t

Step-by-step explanation:

t

1

2

3

Alt)

10,800.00

11,664.00

12,597.12

Answer:x=-4

Step-by-step explanation:

move 5x to the other side by cancelling it out with -5x

that causes it to be 6-6x=30

move 6 to other side by cancelling out with -6

causes it to be -6x=24

divide by -6 to get x alone

x=24/-6

answer is -4 when reduced

The solution to the equation 6 - x = 5x + 30 is x = -4.

To solve the equation 6 - x = 5x + 30,  follow these steps:

Start by combining like terms on each side of the equation:

6 - x = 5x + 30

Rearranging the equation:

6 - 30 = 5x + x

-24 = 6x

Divide both sides of the equation by 6 to isolate the variable x:

-24/6 = 6x/6

-4 = x

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Answer:

I got 2.3

Step-by-step explanation:

line them up in order and count from the outside

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{2.3}}}}}[/tex]

Step-by-step explanation:

[tex] \star{ \tt{ \: Given \: data}}[/tex] :

[tex] \sf{2.5 \: , \: 2.3 \: , \: 2.3 \: , \: 1.8 \: , \: 2.3 \: , \: 1.5}[/tex]

[tex] \star{ \sf{ \: Arranging \: the \: given \: data \: in \: ascending \: order}}[/tex] :

[tex] \sf{1.5 \: , \: 1.8 \: , \: 2.3 \: , \: 2.3 \: , \: 2.3 \: , \: 2.5}[/tex]

[tex] \star{ \sf{ \: n \: ( \: Total \: number \: of \: observation \: ) \: = \: 6}}[/tex]

Finding the position of median

[tex] \bold{ \boxed{ \sf{ \: Position \: of \: median = ( \frac{n + 1}{2} ) ^{th} item}}}[/tex]

[tex] \longmapsto{ \sf{position \: of \: median = ( \frac{6 + 1}{2} ) ^{th} item}}[/tex]

[tex] \longmapsto{ \sf{position \: of \: median \: = \: ( \frac{7}{2} ) ^{th} item}}[/tex]

[tex] \longmapsto {\sf{position \: of \: median = {3.5}^{th} item}}[/tex]

[tex] \sf{ {3.5}^{th} }[/tex] item is the average of 3rd and 4th items.

[tex] \sf{∴Median = \frac{ {3}^{rd} item + {4}^{th} item}{2} }[/tex]

[tex] \longmapsto{ \sf{median = \frac{2.3 + 2.3}{2}}} [/tex]

[tex] \longmapsto{ \sf{median = \frac{4.6}{2} }}[/tex]

[tex] \longmapsto{ \sf{median = 2.3}}[/tex]

∴ Median = 2.3

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

[tex] \star \: \underline{ \tt{Remember ! }}[/tex]

▪️If n is odd , the median is the value of the [tex] \sf{( \frac{n + 1}{2} ) ^{th} }[/tex] observation.

▪️If n is even, the median is the average of [tex] \sf{( \frac{n}{2} ) ^{th}} [/tex] and [tex] \sf{( \frac{n}{2} + 1) ^{th} }[/tex] observation.

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer:

2x²

Step-by-step explanation:

Answer:

11y-5

Step by step:

X^2-8x^2+7x^2=0

x+x-2x=0

3-8=-5

2y+9y=11y

Answer:

9000/6=1500

and

6/9000=0.00067

Answer:

Step-by-step explanation:

E=9x-38

F=2x+40

9x+2x+2=90

11x=90-2

11x=88

x=88/11=8

F=2*8+40

16+40

=56

Answer:

b

Step-by-step explanation:

lamaoamapa9meudvudjege

Answer:

x < 0

Step-by-step explanation:

Answer:

TU = 5

Step-by-step explanation:

Since, U is the midpoint of TV.

[tex]\therefore TV = 2 \times TU \\ 3x - 23 = 2(x - 6) \\ 3x - 23 = 2x - 12 \\ 3x - 2x = 23 - 12 \\ x = 11 \\ \\ TU = x - 6 \\ TU = 11 - 6 \\ \huge \red { \boxed{TU = 5}}[/tex]

Answer:

Number of donuts each student get = 144 / x

Step-by-step explanation:

Given:

Number of donuts = 12 dozen

Number of students = x

Find:

How many donuts each student get

Computation:

Total number of donuts = 12 × 12 = 144

Number of donuts each student get = Total number of donuts / Number of students

Number of donuts each student get = 144 / x

C.D.And E..

I'm sure..

Answer:

Tienes 3 números, "x", "y", "z"

=> El primero es 20 unidades menor que el segundo:

El primero es "x", y el segundo es "y", entonces:

x = y - 20

=> El tercero es igual a la suma de los dos primeros:

El tercero es "z", entonces:

z = x + y

z = (y - 20) + y

z =  2y - 20

=> Entre los tres suman 120

x + y + z = 120

y - 20 + y + 2y - 20 = 120

4y - 40 = 120

4y = 160

y = 40

Si y = 40, entonces:

x = y - 20

x = 20

Además, z = 2y - 20

z= 60

RPTA:

x=20

y=40

z=60

Step-by-step explanation:

Answer:

A. 2x+8

Step-by-step explanation:

you take the two and multiply it to the X and the eight and that would give you 2X2 + 64

Answer:

2 1/4

Step-by-step explanation:

Because I got it wrong and it showed me the answer. YOUR WELCOME

Answer:

2 1/4

Step-by-step explanation:

got it corrrect

Answer:

81 2/3 words per minute

Step-by-step explanation:

245/3= 81 2/3

Answer:

Suki's typing rate is 82wpm

Step-by-step explanation:

Words per minute is a typing rate calculated by the minutes that the person has typed for and the amount of words that they typed. In this case I did 245 / 3 which is 81.6666666667 , but words per minute has to be round up to the nearest number, so if it were 81 to 81.49 it would go to 81, if it were 81.5 to 81.99 it would go to 82. So since it is 81.6 it goes up to 82wpm.

Answer:

all of the expressions are probably random so I have no idea

Answer:

a = 29

b = 64

c = 87

Step-by-step explanation:

Let the angles be a (smallest), b, and c (largest).

We know that a triangle's angles must add up to 180 degrees, so we can construct the following equations.

a + b + c = 180

c = 3a

b = a +35

With some solving and substitution...

a + (a + 35) + c = 180

2a + c = 145

2a + (3a) = 145

5a = 145

a = 29

and therefore,

b = 29 + 35 = 64

c = 3(29) = 87

Answer:

Let smallest angle be :x

So, the largest angle will be:3x

And the other angle will be :x+35

According to angle sum property of triangle,

x+3x+x+35=180

5x+35=180

5x=180-35

5x=145

x=(145/5)

Therefore, x=29

So, the smallest angle =x=29

The largest angle=3x=87

And the other angle=x+35=64

Answer:

Step-by-step explanation:

3x + 6y = 3

x - y = -7

3x + 6y = 3

-3x - 3y = 21

3y = 24

y = 8

x - 8 = -7

x = 1

(1, 8)

answer is one solution

Answer:

  53°

Step-by-step explanation:

If you translate the 4 N force to the right so its tail is at the tip of the 3 N force, you see these are the legs of a 3-4-5 right triangle. The 4 N force is opposite the angle of interest, and the 3 N force is adjacent. Then the angle of interest, α, has the relation ...

  Tan = Opposite/Adjacent

  tan(α) = 4/3

  α = arctan(4/3) ≈ 53°

The direction of the resultant is 53° clockwise from the horizontal axis.

Answer:

9.5

Step-by-step explanation:

The correct answer is 9.5 because 9.49 is closer to 9.5 than 9.4

Answer:

9.5

Step-by-step explanation:

9.492 to the nearest tenth

First you would round 0.092, which would just be 0.09 because 2 is less than 5. You would then have 9.49. You would then round the 0.49, and since 9 is greater than 5, it would be 9.5 because 9 would round to 10.

Answer:

[tex] \boxed{\sf 3x + 10} [/tex]

Step-by-step explanation:

Simplify the following:

⇒-9 x + 12 x + 10

Grouping like terms:

⇒(12 x - 9 x) + 10

12 x - 9 x = 3 x:

⇒3 x + 10

Answer:

(i). [tex]y = 2\, x^2 - 4\, x + 1 = 2\, (x - 1)^2 - 1[/tex]. Point [tex]A[/tex] is at [tex](1, \, -1)[/tex].

(ii). Point [tex]Q[/tex] is at [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex].

(iii). [tex]\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}[/tex] (slope-intercept form) or equivalently [tex]x + 5\, y - 17 = 0[/tex] (standard form.)

Step-by-step explanation:

Note, that when [tex]a(x + b)^2 + c[/tex] is expanded, the expression would become [tex]a\, x^2 + 2\, a\, b\, x + a\, b^2 + c[/tex].

Compare this expression to the original [tex]2\, x^2 - 4\, x + 1[/tex]. In particular, try to match the coefficients of the [tex]x^2[/tex] terms and the [tex]x[/tex] terms, as well as the constant terms.

Hence, the original expression for the parabola is equivalent to [tex]y = 2\, (x - 1)^2 - 1[/tex].

For a parabola in the vertex form [tex]y = a\, (x + b)^2 + c[/tex], the vertex (which, depending on [tex]a[/tex], can either be a minimum or a maximum,) would be [tex](-b,\, c)[/tex]. For this parabola, that point would be [tex](1,\, -1)[/tex].

Assume [tex](m,\, n)[/tex] is an intersection of the graphs of the two functions [tex]y = 2\, x^2- 4\, x + 1[/tex] and [tex]x -y + 4 = 0[/tex]. Setting [tex]x[/tex] to [tex]m[/tex], and [tex]y[/tex] to [tex]n[/tex] should make sure that both equations still hold. That is:

[tex]\displaystyle \left\lbrace \begin{aligned}& n = 2\, m^2 - 4\, m + 1 \\ & m - n + 4 = 0\end{aligned}\right.[/tex].

Take the sum of these two equations to eliminate the variable [tex]n[/tex]:

[tex]n + (m - n + 4) = 2\, m^2 - 4\, m + 1[/tex].

Simplify and solve for [tex]m[/tex]:

[tex]2\, m^2 - 5\, m -3 = 0[/tex].

[tex](2\, m + 1)\, (m - 3) = 0[/tex].

There are two possible solutions: [tex]m = -1/2[/tex] and [tex]m = 3[/tex]. For each possible [tex]m[/tex], substitute back to either of the two equations to find the value of [tex]n[/tex].

Hence, the two intersections are at [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex] and [tex](3,\, 7)[/tex], respectively.

The coordinates of point [tex]A[/tex] and point [tex]P[/tex] each have two components.

Let [tex]M[/tex] denote the midpoint of segment [tex]AP[/tex]. The [tex]x[/tex]-component of point [tex]M[/tex] would be [tex](1 + 3) / 2 = 2[/tex], the average of the [tex]x[/tex]-components of point [tex]A[/tex] and point [tex]P[/tex].

Similarly, the [tex]y[/tex]-component of point [tex]M[/tex] would be [tex]((-1) + 7) / 2 = 3[/tex], the average of the [tex]y\![/tex]-components of point [tex]A[/tex] and point [tex]P[/tex].

Hence, the midpoint of segment [tex]AP[/tex] would be at [tex](2,\, 3)[/tex].

The slope of the line joining [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex] (the coordinates of point [tex]Q[/tex]) and [tex](2,\, 3)[/tex] (the midpoint of segment [tex]AP[/tex]) would be:

[tex]\displaystyle \frac{\text{Change in $y$}}{\text{Change in $x$}} = \frac{3 - (7/2)}{2 - (-1/2)} = \frac{1}{5}[/tex].

Point [tex](2,\, 3)[/tex] (the midpoint of segment [tex]AP[/tex]) is a point on that line. The point-slope form of this line would be:

[tex]\displaystyle \left( y - \frac{7}{2}\right) = \frac{1}{5}\, \left(x - \frac{1}{2} \right)[/tex].

Rearrange to obtain the slope-intercept form, as well as the standard form of this line:

[tex]\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}[/tex].

[tex]x + 5\, y - 17 = 0[/tex].

Answer:

I think the answer is O