The 3 question please with explained

Answer:

The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel

Step-by-step explanation:

To prove that DE is parallel to BC, we have;

The slope, m of the lines DE and BC are found from the following equation;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where;

(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;

[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]

Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;

[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]

Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.

Answer:

slope of DE = 0

slope Bc = 0

slopes are =

Step-by-step explanation:

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle [tex]\triangle PQR[/tex] where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And [tex]\angle Q \neq 90^\circ[/tex]

Given that:

PQ = 44 ft

PR = 51 ft

[tex]\angle R = 58^\circ[/tex]

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

[tex]\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ[/tex]

Now,

[tex]\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ[/tex]

Let us use the Sine rule again:

[tex]\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft[/tex]

So, the answer is 35.11 ft.

Answer:

5 -3 = 2

3-5 = -2

Step-by-step explanation:

In this question, we want to examine the validity of the statement by the use of an example.

Firstly, we need to understand the meaning of the fact that they are ‘closed’

By saying these numbers are closed under this arithmetic operation i.e subtraction, we directly mean that they obey the closure property.

Now, to obey the closure property means that if we move either way i.e by switching the numbers and performing the same arithmetic operation of subtraction, we are supposed to get same answer.

What this means in terms of examples is as follows;

Consider two positive numbers, 5 and 3

Now we know that 5-3 = 2

To check if the closure property is obeyed, switch the place of the numbers.

This means we would have;

3-5 = -2

We can see that both results are not the same. We can then conclude that the arithmetic operation of subtraction is not closed or does not obey the closure property for positive numbers.

Answer:

3,781

Step-by-step explanation:

To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.

First, recognize the formula for the area of a circle:

A = 3.14[tex]r^{2}[/tex]

In this scenario, the radius (r) is 85 feet:

A = 3.14(85[tex])^{2}[/tex]

A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:

A = [tex]\frac{3.14(85)^{2} }{6}[/tex]

Finally, we will simplify and round:

A = 3,781

Answer:

dependent

Step-by-step explanation:

This is a dependent event.  There is one less marble in the bag to choose from

Say there was 1 red marble and 4 blue marble.  You drew the red marble on the first pick, now you cannot get a red marble on your second pick.

If you drew a blue marble on the first pick you could get a red marble on the second pick.

So what happens on the first pick affects the second pick

Answer:

D

Step-by-step explanation:

To solve for T in this, you need to to divide r from both sides of the equation.

d=rt

divide r

d/r=t

The correct equation is t= d/r.

The answer is option D.

Rearrange the equation in order that the unknown variable is by itself on one aspect of the equals sign (=) and all the different variables are on the opposite side. Rule 1: you could add, subtract, multiply and divide by means of something, so long as you do the identical aspect to both aspects of the equals sign.

We can express an equation in phrases of the opposite variable. For example, to arrange the equation in order that it's far written as taking each time period and circulate to the opposite side of the equal sign the usage of the opposite operation till you most effective have.

Learn more about the equation here: https://brainly.com/question/1214333

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Answer:

1/6

Step-by-step explanation:

People who answered less than 1/2 were:  2 +  1 + 3 = 6 people.

There are a total of 36 people.

People who answered their calls before the second ring were only 6/36.

When we simplify the fraction, we get 1/6.

So, the answer is 1/6

Answer:

565.80

Step-by-step explanation:

600.79-40.0032+5.01 =  565.7968

565.7968 to the nearest Hundredths​ =

565.80

Answer:

565.80

Step-by-step explanation:

600.79 - 40.0032 + 5.01

600.79 - 40.0032 = 560.7868

560.7868 + 5.01 = 565.7968

565.7968 to the nearest hundredth = 565.80

Everything you answered so far looks good. Nice work.

For question 10, we need to find two numbers that multiply to 3(-1) = -3 and also add to 2. The 3 and -1 are the first coefficient and last term. The 2 is the middle coefficient.

Through trial and error, the two numbers we're after are 3 and -1

3 times -1 = -3

3 plus -1 = 2

We break up the 2x into 3x - 1x and factor like so...

3x^2 + 2x - 1

3x^2 + 3x - 1x - 1 ... replace 2x with 3x-1x

(3x^2+3x) + (-1x-1) ... pair up terms

3x(x+1) - 1(x+1) .... factor each parenthesis group

(3x-1)(x+1) ... pull out the gcf (x+1)

You can use FOIL, the box method, or distribution to go from (3x-1)(x+1) back to 3x^2+2x-1 again.

Answer:

Step-by-step explanation:

Answer:

PY = 14.5

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other, thus

XZ = WY , that is

4x - 1 = x + 7 + x + 7

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = 7.5

Thus

PY = x + t = 7.5 + 7 = 14.5

Step-by-step explanation:

x+7+x+7= 4x-1

2x+14=4x-1

14= 2x-1

15= 2x (divide)

x = 7.5

wp= 7.5cm

not really sure

Answer:

Option (D)

Step-by-step explanation:

Option (A).

3x⁵ - 2x³

There are two terms with the variable 'x' in the given expression. therefore, it's a binomial with no constant term.

Option (B).

x⁵ - 3x² + 5x

This expression has three terms with variable 'x'.

Therefore, it's a trinomial without no constant term.

Option (C).

7x⁶ + 2x⁴ - x³ + 7

It's a quadrinomial having 4 terms. '7' is the constant term in the given expression.

Option (D).

4x² + x³ - 3 ≈ x³ + 4x² - 3

It's a trinomial with a constant term 3.

Therefore, Option (D) is the answer.

Answer:

Step-by-step explanation:

6):

Take the small right triangle with the sides 25 and 7.

☆ The Pythagorian theorem ☆

Let x be the third side.

● 25^2 = x^2 + 7^2

Substract 7^2 from both sides

● 25^2 -7^2 = x^2 +7^2 -7^2

● x^2 = 25^2 -7^2

● x^2 = 576

● x = 24 inches

The third that we find is the half of the side of the square.

Multiply it by 2 and get the side of the square.

● 24 × 2 = 48 inches

The perimeter of the square is the side times 4.

● P = 48 × 4

● P = 192 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

7):

Both triangles are righr and they have a khown angle.

Start with the small one and calculte the third angle.

The sum of a triangle angles is 180°

Let B be the third angle.

● B = 180-(90+51) = 39°

That's equal to the second angle of the second's triangle.

So it's an AA similarity.

So:

● x/24 = 7/15

● x = (7/15)×24

● x = 11.2

Answer:

  [tex]\dfrac{3}{14}[/tex]

Step-by-step explanation:

The even number of minus signs means the product will be positive. A factor of 3 can be removed to simplify the product. As usual, the numerator of the product is the product of numerators, and the denominator of the product is the product of denominators.

  [tex]-\dfrac{1}{6} \times \left(-\dfrac{9}{7}\right)=\dfrac{1\cdot 9}{6\cdot 7}=\dfrac{3\cdot 3}{3\cdot 14}=\boxed{\dfrac{3}{14}}[/tex]

Answer:

→ 3/4 ←

-1/6 × (-9/7)= 1·9/6·7  3·3/3·14 = 3/4

Answer:

(1) Variance = 4.5 and Standard deviation = 2.121.

(2) Variance = 4.5 and Standard deviation = 2.121.

(3) The effect on the measure of dispersion if each value is changed uniformly ​is that it remains unchanged.

Step-by-step explanation:

We are given with the following set of data below;

              X                     [tex]X-\bar X[/tex]                   [tex](X-\bar X)^{2}[/tex]

              5                   5 - 8 = -3                     9

              5                   5 - 8 = -3                     9

              8                   8 - 8 = 0                      0

             10                  10 - 8 = 2                     4

             10                  10 - 8 = 2                     4

             10                  10 - 8 = 2                     4

              9                   9 - 8 = 1                       1

              9                   9 - 8 = 1                       1

              6                  6 - 8 = -2                    4                

Total    72                                                   36      

Firstly, the mean of the above data is given by;

              Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                              =  [tex]\frac{72}{9}[/tex]  = 8

(1)Now, the variance of the given data is;

            Variance  =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]

                                  =  [tex]\frac{36}{9-1}[/tex]  = 4.5

So, the standard deviation, (S.D.)  =  [tex]\sqrt{\text{Variance}}[/tex]

                                                        =  [tex]\sqrt{4.5}[/tex] = 2.12

(2) Now, each value is added by 2; so the new data set is given by;

              X                     [tex]X-\bar X[/tex]                   [tex](X-\bar X)^{2}[/tex]

              7                   7 - 10 = -3                     9

              7                   7 - 10 = -3                     9

             10                  10 - 10 = 0                     0

             12                  12 - 10 = 2                     4

             12                  12 - 10 = 2                     4

             12                  12 - 10 = 2                     4

              11                  11 - 10 = 1                       1

              11                  11 - 10 = 1                       1

              8                  8 - 10 = -2                    4                

Total    90                                                   36      

Firstly, the mean of the above data is given by;

              Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                              =  [tex]\frac{90}{9}[/tex]  = 10

(1)Now, the variance of the given data is;

            Variance  =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]

                                  =  [tex]\frac{36}{9-1}[/tex]  = 4.5

So, the new standard deviation, (S.D.)  =  [tex]\sqrt{\text{Variance}}[/tex]

                                                                =  [tex]\sqrt{4.5}[/tex] = 2.12

(3) The effect on the measure of dispersion if each value is changed uniformly ​is that it remains unchanged as we see in the case of variance or standard deviation.

Answer:

x³ + 5x

Step-by-step explanation:

2x+5x3+3x−4x3

=2x+5x3+3x+−4x3

Combine Like Terms:

=2x+5x3+3x+−4x3

=(5x3+−4x3)+(2x+3x)

=x3+5x

Answer:

[tex]\large \boxed{x^3+5x}[/tex]

Step-by-step explanation:

[tex]2x + 5x^3 + 3x - 4x^3[/tex]

[tex]\sf Group \ like \ terms.[/tex]

[tex]5x^3 - 4x^3+2x+3x[/tex]

[tex]\sf Combine \ like \ terms.[/tex]

[tex]x^3+5x[/tex]

Answer:

see explanation

Step-by-step explanation:

If (2x + 1) is a factor then x = - [tex]\frac{1}{2}[/tex] is a root and P(- [tex]\frac{1}{2}[/tex] ) = 0 ← Factor theorem

P(- [tex]\frac{1}{2}[/tex] )

= 2(- [tex]\frac{1}{2}[/tex] )³ - 11(- [tex]\frac{1}{2}[/tex] )² - 4(- [tex]\frac{1}{2}[/tex] ) + 1

= - [tex]\frac{1}{4}[/tex] - [tex]\frac{11}{4}[/tex] + 2 + 1

= - [tex]\frac{12}{4}[/tex] + 3

= - 3 + 3

= 0

Since P(- [tex]\frac{1}{2}[/tex] ) = 0 then g(x) is a factor of P(x)

Answer: a=5

Step-by-step explanation:

1/12a=10/24

24a=120

a= 5

Answer:

sorry i am late but the answer is The name of the shape on the right is M prime N prime O prime P prime Q prime R prime S prime because it is the image of the shape on the left. and if you dont  want to read that  its D

hope it helped anyone :)

The name of the shape on the right is M’N’O’P’Q’R’S' because it is the pre-image of the shape on the left

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Translation is the movement of a point up, down, left or right.

The name of the shape on the right is M’N’O’P’Q’R’S' because it is the pre-image of the shape on the left

find out more on Transformation at: https://brainly.com/question/1462871

Answer:

  d) m - 2 l = - 6; m - l = 5

Step-by-step explanation:

Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...

  m = 2l -6

Subtracting 2l from both sides gives the equation ...

  m -2l = -6 . . . . . matches choice D

Answer:

44 degrees.

Step-by-step explanation:

The 3 small triangles are isosceles  so m < a = m < b , therefore

m < a = (180 - 92) / 2 = 44 degrees.

m < f = m < a ( they are both subtended on the circle by the same chord (cd)),

So m < f = 44.

Answer:

No! They are not proportional!

Step-by-step explanation:

Proportional prices to the length means that

(price 1/length 1)=(price 2/length 2)=(price 3/length 3)

Even by plugging in the numbers yourself to double check my numbers, and getting and answer for each ratio, it is clear that they are not proportional.

Answer:

The ratio of screen length to price in the first row is 16/160, which simplifies to 1/10.

The ratio of screen length to price in the second row is 20/180, which simplifies to 1/9.

The ratio of screen length to price in the third row is 24/200, which simplifies to 3/25.

Because 16/160 doesn't = 20/180 doesn't = 24/200, the ratios are not equivalent. This is not a proportional relationship.

Answer:

0.46 feet

Step-by-step explanation:

Length = 5/6 feet (or 0.254 m)

Width = 3/8 feet (or 0.114 m)

(5/6 - 3/8) feet = 11/24 feet or 0.46 feet (0.140 m)

Answer:

32

Step-by-step explanation:

the country would need 30 to 33 trees

Answer:

f = - [tex]\frac{19}{7}[/tex]

Step-by-step explanation:

Given f varies directly with m then the equation relating them is

f = km ← k is the constant of variation

To find k use the condition f = - 19 when m = 14, thus

- 19 = 14k ( divide both sides by 14 )

- [tex]\frac{19}{14}[/tex] = k

f = - [tex]\frac{19}{14}[/tex] m ← equation of variation

When m = 2, then

f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]

Answer:

mean would decrease

Step-by-step explanation:

Answer:

12,157,665,459,057,000,000

Step-by-step explanation:

It seems like it would have to involve exponents.  3 to the 40th power would be 12,157,665,459,057,000,000.  

Answer:

(4x + 1)(2x² - 5)

Step-by-step explanation:

Given

8x³ + 2x² - 20x - 5 ( factor the first/second and third/fourth terms )

= 2x²(4x + 1) - 5(4x + 1) ← factor out (4x + 1) from each term

= (4x + 1)(2x² - 5)

Answer:

blank 1 is -20-5

blank 2 is 4x+1

blank 3 is -5

blank 4 is 2x^2-5

Step-by-step explanation:

See the diagram, and tell me if it's clear