2(v-1) + 8 = 6(2v -4)
Choose statement that solves the solution

Answer:

1 and 4 are alternate interior angles.

m5 + m1 = 180

m5 = m3 + m2

Question:

The complete version of your question as found in other site is stated below:

In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.

1 and 4 are alternate interior angles.

m4 + m5 + m6 = 180.

m5 + m1 = 180.

m5 = m3 + m2

Step-by-step explanation:

Given: line l is parallel to line m

We need prove that the interior angles of a triangle have a sum of 180°. In order to do that, the angles in the triangle = 180°

∠1 + ∠2  + ∠3  = 180°

Alternate angles:

∠1 = ∠4

∠6 = ∠2

∠5 = ∠3 + ∠6

Checking the options and inserting the values above in them:

a) 1 and 4 are alternate interior angles

∠1 = ∠4

This gives one of the side of the interior angles. The alternate angles enables us to find the sum of the interior angles. It is correct

b) m4 + m5 + m6 = 180

∠4 + ∠5 + ∠6 = 180°

∠1 + (∠3 + ∠6) + ∠2 = 180°

The above option wont give ∠1 + ∠2  + ∠3  = 180°. Hence it is wrong.

c) m5 + m1 = 180

(∠3 + ∠6) + ∠1 = 180°

∠5 = (∠3 + ∠6) = ∠3 + ∠2

∠3 + ∠2 + ∠1 = 180°

This option is correct

d) m5 = m3 + m2

∠5 = ∠3 + ∠2

From the diagram, ∠5 + ∠1 = 180° (angles on a straight line)

∠5 = ∠3 + ∠2

This option can be used to get sum of interior angles.

Answer:

8

Step-by-step explanation:

(290-25)/30

265/30

8 and 5/6

so how many full 30 cm lengths?

8

Answer:

7

Step-by-step explanation:

3 × 25 = 75cm

He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm

→ He then cuts the rest of the wire into as many 30 cm lengths as possible.

215 ÷ 30 = 7.17

Answer:

13 2/3 cm

Step-by-step explanation:

To find the perimeter, add up all the sides

2 1/2 + 3 1/3+ 4 1/2 + 3 1/3

Add up the whole numbers

2+3+4+3 = 12

Add up the fractions

1/2+1/3+1/2+1/3

2/2 + 2/3

1 +2/3

Put them together

12+1+2/3

13 2/3

Answer: 13 2/3 cm

Step-by-step explanation:

1. Turn mixed fractions into improper fractions:

2 1/2 = 5/2

3 1/3 = 10/3

3 1/3 = 10/3

4 1/2 = 9/2

2. Formula for perimeter: left side + right side + upper base + lower base

3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2

4. Solve: 41/3

5. Simplify into mixed fraction: 41/3 = 13 2/3

6. Don't forget to add the unit!

Answer:

56 out of 224 times

Step-by-step explanation:

8 out of 32 = 1 out of 4

56 out of 224 = 1/4

Answer:56

Step-by-step explanation:

Answer:

A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]

Step-by-step explanation:

The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.

Answer:

€60

Step-by-step explanation:

€45 = 75%

100% (original) = (100/75)

[tex](100 \div 75) \times 45 = 60[/tex]

Answer:

Step-by-step explanation:

remove parentheses by multiplying factors.

use exponent rules to remove parentheses in terms with exponents.

combine like terms by adding coefficients.

combine the constants.

Answer: answer is D

Step-by-step explanation:

Answer: The correct answer is 6,4,2

Step-by-step explanation: Doing a 100 point giveaway stay tuned!

Answer:

Step-by-step explanation:

48 cups of trail mix

Answer:

9.600

9.6

Step-by-step explanation:

These two decimals above are equivalent to 9.60 because no matter the amount of zeroes there are, as long as the numbers before the zeroes maintain the same location (in this case, ones and tens place) the decimals will be equivalent. For example, 9.60 is also equivalent to 9.600000000000000000000000...

Answer:

65

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

130 = y+y

130 = 2y

Divide by 2

130/2= 2y/2

65=y

Answer:

D. 65

Step-by-step explanation:

I agree with the above reasoning

Answer:

Step-by-step explanation:

We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.

  (x^2 +4x) +(y^2 -10y) = 7

  (x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25

  (x +2)^2 +(y -5)^2 = 6^2

Compare to ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle

We see that the center is ...

  (h, k) = (-2, 5)

and the radius is ...

  r = 6

Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]

Answer:

  both functions have the same graph

Step-by-step explanation:

The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...

  y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)

  y = -7/9x +3

__

The second function is written in point-slope form:

  y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)

  y +11 = -7/9(x -18)

If we rearrange the second equation to the form of the first, we get ...

  y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11

  y = -7/9x +3 . . . . . . . matches the equation of the first function

__

Both functions describe the same relation.

Answer:

54

Step-by-step explanation:15+15+9+9+3+3=54

Answer:

d=2

Step-by-step explanation:

Shape: Circle

Solved for diameter

Radius: 1

Formula: d=2r

Formula: Radius

Answer: 2

Hope this helps.

Answer:

20

Step-by-step explanation:

The rectangle is 2 x 8.

2 + 2 + 8 + 8 = 20

Perimeter=8+8+2+2

=20

Answer:

[tex] \frac{11}{24} [/tex]

Answer:

D. 11/24

Step-by-step explanation:

Total students' reading preferences = 240

Using electronic device = 110

Probability of having electronic device = 110/240

= 11/24

Answer:

Error interval is [tex]35\leq x< 45[/tex]

Step-by-step explanation:

Given: A number x becomes 40 if it is rounded to 1 significant figure

To find: error interval for x

Solution:

In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.

As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].

A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.

Answer:

[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]

Step-by-step explanation:

Solution:-

- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.

- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:

                                [tex]f ( t ) = A*sin ( w*t ) + c[/tex]

Where,

                  A: The amplitude of the hours of daylight

                  w: The angular frequency of occurring event

                  c: The mean hours of daylight

                  t: The time taken from reference ( days )

- We are given that the longest day [ [tex]f ( t_m_a_x )[/tex] ] occurred on June 21st and the shortest day [ [tex]f ( t_m_i_n )[/tex] ] on December 21st.

- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:

                              [tex]c = \frac{f(t_m_a_x ) +f(t_m_i_n ) }{2} \\\\c = \frac{15.7 + 8.3}{2} = \frac{24}{2} \\\\c = 12[/tex]

- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):

                              [tex]A = f ( t_m_a_x ) - c\\\\A = 15.7 - 12\\\\A = 3.7[/tex]

- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.

- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):

                              [tex]0.5*T = 7 + 31 + 31 + 30 +31 +30 +21\\\\T = 2* [ 181 ] \\\\T = 362 days[/tex]

- The angular frequency ( w ) is then defined as:

                              [tex]w = \frac{2\pi }{T} = \frac{2\pi }{362} \\\\w = 0.01736[/tex]

- We will now express the model for the duration of daylight each day as function of each day:

                              [tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]

Answer:

raising a number to the 34th power

Step-by-step explanation:

Answer:

2500

Step-by-step explanation:

Monthly total cost, C(x) = 400 + 200x dollars

Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars

Profit = Revenue - Cost

[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]

To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.

[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]

Next, we check if the point x=7500 is a maxima or a minima.

To do this, we find the second derivative of P(x).

[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]

Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.

Therefore, the company needs to produce 2500 units to maximize profit.

Answer:

(5,2)

Step-by-step explanation:

From the graph attached below:

Since the temperature at 5 p.m. is halfway between the temperature at 2 p.m. and 8 p.m. , the coordinate of the temperature at 5 p.m. is the midpoint of (2,7)  and (8,-3).

For two coordinate points [tex]A(x_1,y_1)$ and B(x_2,y_2)[/tex]

[tex]\text{Midpoint of AB }=\dfrac{1}{2} \left( x_1+x_2,y_1+y_2 \right)[/tex]

Therefore, the coordinates for 5p.m.

[tex]=\dfrac{1}{2} \left( 2+8,7+(-3) \right) \\=\dfrac{1}{2} \left( 10,4 \right)\\\\=(5,2)[/tex]

Answer:

number of box of pen = 16

number of box of ribbon bands = 8

Step-by-step explanation:

Let

number of boxes of pen = p

number of boxes of rubber bands = r

He ordered 24 boxes of both items. Therefore,

p + r = 24...............(i)

The total cost of what he ordered is $200 . Therefore,

10p + 5r = 200.......(ii)

combine the equations

p + r = 24...............(i)

10p + 5r = 200.......(ii)

from equation (i)

p = 24 - r

insert the value of p in equation (ii)

10(24 - r) + 5r = 200

240 - 10r + 5r = 200

240 - 200 = 5r

40 = 5r

divide both sides by 5

r = 40/5

r = 8

insert the value of r in equation(i)

p + 8 = 24

p = 24 - 8

p = 16

number of box of pen = 16

number of box of ribbon bands = 8

Answer:

Step-by-step explanation:

Here,

H_o: The way of reservation is independent of gender.

H_a: The way of reservation is not independent of gender.

We use a chi square test because we can calculate the expected frequencies for this chart.

Doing an Expected Value Chart,          

33.7625   9.7125   30.525  

39.2375   11.2875   35.475

Using chi^2 = Sum[(O - E)^2/E],          

chi^2 =    4.482385929

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,

a =    3      

b =    2

df =    2

Thus, the critical value is

significance level =    0.05

chi^2(critical) =    5.991464547

Also, the p value is

P =    0.106331579

Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]

Answer:

(a) There are 32,760 different ways to appoint the officers.

(b) 3003 different ways can the committee be​ appointed.

(c) ​Probability of getting the five youngest of the qualified ​candidates is 0.00033.

Step-by-step explanation:

We are given that a corporation must appoint a​ president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO). It must also appoint a planning committee with five different members.

There are 15 qualified​ candidates, and officers can also serve on the committee.

(a) The number of officers are 4, i.e; A president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO).

There are 15 qualified candidates.

To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.

So, the number of ways to appoint the officers = [tex]^{15}\text{P}_4[/tex]

            =  [tex]\frac{15!}{(15-4)!}[/tex]              {[tex]\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}[/tex] }

            =  [tex]\frac{15!}{11!}[/tex]  =  32,760 ways

(b) The number of committee numbers to appoint include five members.

There are 15 qualified candidates.

To find the number of ways in which the committee can be​ appointed, we will use combination because here the order of selecting the members doesn't matter.

So, the number of ways to appoint the committee = [tex]^{15}\text{C}_5[/tex]

            =  [tex]\frac{15!}{5! \times (15-5)!}[/tex]              {[tex]\because ^{n}\text{C}_r = \frac{n!}{r! \times (n-r)!}[/tex] }

            =  [tex]\frac{15!}{5! \times 10!}[/tex]  =  3003 ways

(c) The probability of randomly selecting the committee members and getting the five youngest of the qualified​ candidates is given by;

Number of ways of selecting the committee = 3003

Selecting the five youngest of the qualified​ candidates = 1

So, the required probability =  [tex]\frac{1}{3003}[/tex]

                                              =  0.00033

Answer:

The house will be worth $184,699.6847 in 6 months.

Step-by-step explanation:

Since the cost of the houses is dropping by 2.5 % per month, then it is decreasing exponentially and can be modeled by the following formula:

[tex]cost(x) = 215000*(1 - \frac{2.5}{100})^t\\cost(x) = 215000*(1 - 0.025)^t\\cost(x) = 215000*(0.975)^t\\[/tex]

After 6 months:

[tex]cost(6) = 215000*(0.975)^6\\cost(6) = 184699.6847[/tex]

The house will be worth $184,699.6847 in 6 months.

Answer:

Step-by-step explanation:

Answer:

  3)  -4 and 6

Step-by-step explanation:

I find it easiest to solve these by factoring. Here, you're looking for factors of the constant (-24) that have a sum equal to the coefficient of the linear term (-2). You know the divisors of 24 are ...

  -24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)

The sums of these factors are, respectively, -23, -10, -5, -2. So, the last pair of factors are the ones we're looking for. These are the constants that go into the binomial factors of the function:

  p(x) = x^2 -2x -24

  p(x) = (x +4)(x -6)

Then the zeros are the values of x that make these factors zero:

  x +4 = 0   ⇒   x = -4

  x -6 = 0   ⇒   x = 6

The zeros of the function are -4 and 6.

____

The graph of the function confirms these values.