Assignment - 3. Deductive Reasoning

State a true conclusion.
1) If two planes intersect, their intersection is a line.
2) Plane Rand plane S intersect.
Conclusion:
WRITER

Answer:

Step-by-step explanation:

let the speed of Landon=x

speed of Eduardo=x+9

5x+5(x+9)=135

divide by 5

x+x+9=135/5=27

2x+9=27

2x=27-9

2x=18

x=18/2=9

speed of Landon=9 mph

speed of Eduardo=9+9=18 mph

Answer:

98 m³

Step-by-step explanation:

For similar shapes

The ratio of the cube of the corresponding length of similar shapes is equal to the ratio of their volume.

Applying,

L³/L'³ = V/V'............... Equation 1

Where, L = Length of the smaller prism, L' = Length of the larger prism, V = Volume of the smaller prism, V' = Volume of the larger prism

From the question,

Given: L = 5 m, L' = 7 m, V = 50 m³

Substitute these values into equation 1

5²/7² = 50/V'

25/49 = 50/V'

V' = (50×49)/25

V' = 98 m³

Answer: 137.2

Step-by-step explanation:

I'm just making the correct answer an actual answer instead of a comment so it's easier to see

Answer:

x = 15 , x = 2

Step-by-step explanation:

[tex]x^2 -17x + 30 =0\\\\x^2 -2x-15x +30=0\\\\x(x-2)-15x(x-2) =0\\\\(x-15)(x-2)=0\\\\[/tex]

x = 15 , x = 2

The graph of the function f ( x ) = x² - 2x + 3 is plotted

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as A

Now , the value of A = f ( x )

f ( x ) = x² - 2x + 3   be equation (1)

Now , the function is a parabolic equation with the vertices at ( 1 , 2 )

Therefore , the function is f ( x ) = x² - 2x + 3  and the graph is plotted

Hence , the parabolic function is f ( x ) = x² - 2x + 3

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Answer:

50 minutes

Step-by-step explanation:

First you need to find out how many times 100 will fit into 10

1000/100 = 10

then you need to multiply it by 5, because each 100 negatives takes 5 minutes.

10 * 5 = 50

your answer is 50.

Answer:

C

Step-by-step explanation:

[tex] \frac{4x}{2y} = 4[/tex]

Simplify fraction:

[tex] \frac{2x}{y} = 4[/tex]

Divide both sides by 2:

[tex] \frac{x}{y} = 2[/tex]

[tex] \frac{x}{y} = \frac{2}{1} [/tex]

[tex] \frac{y}{x} = \frac{1}{2} [/tex]

[tex] \frac{3y}{x} [/tex]

[tex] = 3( \frac{y}{x} )[/tex]

[tex] = 3( \frac{1}{2} )[/tex]

[tex] = \frac{3}{2} [/tex]

Step-by-step explanation:

everything can be found in the picture

Answer:

the answer would be -1339/24

Answer:

D

Step-by-step explanation:

notice how everything goes up by 3? that's a sequence.

Answer:

72.4 m

Step-by-step explanation:

The area of a triangle is

A = l*w

161.2 = 5.2 *w

Divide each side by 5.2

161.2/5.2 = w

31 =w

Now find the perimeter

P =2 (l+w)

P =2 ( 5.2+31)

P =2( 36.2)

P =72.4

Answer:

shshghhhsjsjjsjsjs

Step-by-step explanation:

snnsbzhhhshs

Answer:

(2,1)

Step-by-step explanation:

one half of (4,2) would be (2,1)

easy math, just a little tricky logic

3/5×(-3)/10 + 1/15 - 3/5×1/5 =  -7/30 ≅  -0.2333333

I hope this helps!

Step-by-step explanation:

B) opposite sides are congruent !!!!!!

Answer:

option c is the correct answer

Answer:

c=13 and a=20

Step-by-step explanation:

Here you need to use the Pythagoras theorem :

c²=a² + b²

c = √a² + b²

c = √(12)²+(5)²

c= √144+25

c = √169

c = 13

2) c²=a²+b²

    b= √c²-b²

    b= √(29)²-(21)²

    b = √400

    b = 20

In 2 you change your formula just so that it can be easier and just calculate your length straight forward but you can also just do it in the original equation

Answer:

1:1 because they ate the same amount both weeks

Answer:

A dozen is 12.

12*5 = 60 eggs

5 dozen eggs are equal to 60 eggs.

A dozen is a unit of measurement equal to 12 items. So, 5 dozen is equivalent to 5 times 12, which gives us a total of 60 items.

When referring to eggs, the term "dozen" is commonly used to represent a quantity of eggs. In this case, if we have 5 dozen eggs, it means we have 5 sets of 12 eggs each.

To calculate the total number of eggs, we multiply the number of dozens (5) by the number of eggs in a dozen (12):

5 dozen x 12 eggs/dozen = 60 eggs

Therefore, 5 dozen eggs are equal to 60 eggs. This means that if you have 5 sets of 12 eggs, you would have a total of 60 eggs.

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]a-3b+4[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying the Equation...}}\\\\\frac{1}{2}(2a-6b+8)\\----------------\\\rightarrow\frac{1}{2}* 2a = a\\\\ \rightarrow\frac{1}{2}*-6b = -3b\\\\\rightarrow\frac{1}{2}*8 = 4\\\\\text{\underline{Therefore:}}\\\\\frac{1}{2}(2a-6b+8)\rightarrow \boxed{a-3b+4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: a-3b+4

Step-by-step explanation:

Credits to guy up there

Answers:

========================================================

Explanations:

8) Positive r values always go with positive regression slopes. The r value will likely not equal the slope, but they share the same sign.

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

9) The data set isn't given so I'm not sure. But it seems like your teacher just wants to know a hypothetical situation in which r value will produce the best fit. That would be r = -0.95 since we're the furthest from zero. The closer you are to r = 1 or r = -1, the better the fit.

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

10) The blue regression line, aka line of best fit, is fairly close to all of the data points. Also, the blue line has a positive slope. This means r is fairly close to 1. So that's why we go with r = 0.9

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

11) The general equation is y = mx+b. We simply replace x,y with x1,y1.

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

12) When considering y = mx+b, the m is the slope. I'm not entirely sure where the m comes from, but I've read some sources that say 'm' somehow represents 'mountain' which involves slopes. This could have simply been a memorization tool and not the actual reason why m was chosen to be the slope.

As an example, y = 2x+5 has slope 2.

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

13) The b in y = mx+b is the y intercept. It's the initial value.

It always occurs when x = 0 since

y = mx+b

y = m*0+b

y = b

Meaning the point (0,b) is the location of the y intercept.

For example, y = 2x+5 has y intercept 5 located at the point (0,5).

Answer:

6cm

Step-by-step explanation:

Area of the trapezoid = Area of the square + Area of the triangle

Area of the square= Area of the trapezoid - Area of the triangle

Area of the square= 60 - 24

Area of the square= = 36 square metres

Since Area of the square= L²

L is the length of the side of the square

L² = 36

L = √36

L = 6cm

Hence the required length is 6cm

Answer:

C

Step-by-step explanation:

For any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

[tex]\sqrt{x^2+(y-5)^2}[/tex] = | y + 5 | ← square both sides

x² + (y - 5)² = (y + 5)² ← expand parenthesis on both sides

x² + y² - 10y + 25 = y² + 10y + 25 ( subtract y² - 10y + 25 from both sides )

x² = 20y

Answer:

i think 88

Step-by-step explanation:

(it's been a while since I've done this so I'm not too sure it's correct)

The formula we need to use is

2πr(angle/360)

we need the radius (r)

To get r we need angle AES

180-80= 100

using the equation from before

88=2πr*(100/360)

raidus: 50.42

Then to get the length CD we need angle DEC

180-80=100

2π*50.42*(100/360)=88

there probably was some kind of shortcut we could've used to figure this out faster but whatever

Answer:

C. 8

Step-by-step explanation:

Options

A. 5

B. 6

C. 8

D. Can't say without knowing the number of participants

Number of sweet distributed = Total number of sweets - left over sweets

= 1025 sweets - 1 left over sweet

= 1024 sweets

Number of participants = Number of sweets distributed / number of sweets given to each participant

A. 5

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024 /5 Sweets

= 204.8 participant

B. 6

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024/6

= 170.67 participant

C. 8

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1,024/8

= 128 participant

D. Can't say without knowing the number of participants

From the options given, the number of sweets given away to each participant could be 8

Number of sweets given to each participants is 32.

Since, A sports teacher had 1025 sweets and he had one sweet left after distributing.

So, number of sweets he distributing is, [tex]1025-1=1024[/tex]

Since, distributing these equally amongst all the participants

Therefore, number of sweets given to each participants is, [tex]=\sqrt{1024}=32[/tex]

So, total number of participants is 32 and number of sweets given to each participants is 32.

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Answer:

y = 6x - 19

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 4 ← is in slope- intercept form

with slope m = 6

Parallel lines have equal slopes , then

y = 6x + c ← is the partial equation

To find c substitute (3, - 1) into the partial equation

- 1 = 18 + c ⇒ c = - 1 - 18 = - 19

y = 6x - 19 ← equation of parallel line

Answer:

True

Step-by-step explanation:

The formula to convert Fahrenheit degrees to Celcius degrees is [tex]C=5/9*(F-32)[/tex]

Answer:

3 : 7 =>

Anna = $180

Raman = $420

1 : 4 =>

Anna = $120

Raman = $480

Step-by-step explanation:

Shares when ratio is 3 : 7

Anna : Raman = 3 : 7

Sum of ratio 10

Anna's share=

                   [tex]\frac{3}{10} \times 600 = \$ 180[/tex]

Raman 's share=

                  [tex]\frac{7}{10} \times 600 = \$ 420[/tex]

Shares when ratio is 1 : 4

Anna : Raman = 1 : 4

Sum of ratio = 5

Anna 's share =

                   [tex]\frac{1}{5} \times 600 = \$ 120[/tex]

Raman's share =

                  [tex]\frac{4}{5} \times 600 = \$ 480[/tex]

Answer:

x+8

Step-by-step explanation:

Simplify the numerator

list the factors of 16

16: 1, 2, 4, 8, 16

look for two factors that add up to the b value

in this case it is 18

by looking at the factors 2 and 8 add up 10

so you can rewrite the numerator as [tex]x^{2}+2x+8x+16[/tex]

Split the trinomial into two separate binomials each having one of the factors that add up to 10

So it should be [tex]x^{2} +2x and 8x+16[/tex]

Factor both binomials

you can factor an x from the first one

Then it is x(x+2)

Factor an 8 from the second one

8(x+2)

So it should be [tex]x(x+2) 8(x+2)[/tex]

This can rewritten as (x+8)(x+2)

So now you have [tex]\frac{(x+2)(x+8)}{x+2)}[/tex]

simplify it by canceling out the two (x+2)'s

this is because (x+2)/(x+2) is 1

Finally you get x+8

Answer:

Multiply the numerator by the numerator and the denominator by the demoninator.

Step-by-step explanation:

Answer:

Nope, to multiply two fractions = numerator × numerator / denominator × denominator

Step-by-step explanation:

For Example:

[tex]\frac{5}{3}[/tex] × [tex]\frac{8}{2}[/tex]

Multiply 5 by 8

40

Multiply 3 by 2

6

Result: [tex]\frac{40}{6}[/tex]

Finally Simplify

[tex]\frac{40}{6} =[/tex] [tex]40[/tex] ÷ 6 = [tex]6\frac{4}{6}[/tex] or 6.6 as a decimal