Algebraic Proof
Match the justification to each step of the deductive reasoning about this picture. Please Help!
The following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
3. 3x + 15 = 6x (Combining like terms)
4. 15 = 3x (Subtraction Property of Equality)
5. x = 5 (Division Property of Equality)
6. CE = 6(5) (Substitution)
Recall:
The Segment Addition Postulate states that when a point lies between two endpoints on a line segment, the length of the larger segment equals the sum of the lengths of the two smaller segments formed.Thus, the following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
Rationale: Plug in the values of CD, DE and CE3. 3x + 15 = 6x (Combining like terms)
Rationale: Add 8 and 7 together4. 15 = 3x (Subtraction Property of Equality)
Rationale: Subtract 3x from each side of the equation.5. x = 5 (Division Property of Equality)
Rationale: Divide each side of the equation by 3).6. CE = 6(5) (Substitution)
Rationale: Plugging in the value of x into "6x"Learn more about Segment Addition Postulate on:
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Factorise:
a) 22y -33z b) ax + bx –ay – by
If Jada runs 5 laps around the track in 6 minutes how many minutes per lap is that
Answer:
1.2 minutes
Step-by-step explanation:
5 laps >> 360 ( 6×60)
1 lap >> x
cross multiplication
5x = 360
x = 360/5
x= 72 second
x = 72/60 = 1.2 minute
A city has 3 new houses for every 7 old houses. If there are 21 new houses in the city, how many old houses are there
A. 49
B. 47
C. 52
D. 51
Answer:
A. 49
Step-by-step explanation:
ratio of houses is 3 new to 7 old
21 new is 7 times more than 3, so 7 will also be 7 times more
so, 21 to 49
I hope that made sense
A mailman earned $832 a week last year. What was his yearly salary?
Answer:
$43,264
Step-by-step explanation:
theres 52 weeks in a year so you just do $832 x 52
A watt is the basic unit measurement of electrical power. Suppose you are running the air conditioner, the washing machine, the clothing dryer, two computers, four light bulbs, the refrigerator, and two televisions Use the chart at the right and calculate how much wattage you might need in this situation. Show your k = write an inequality that shows what the available wattage must be greater than
Considerations based on the wattage of the available appliances are required when designing for the electricity.
The required wattage inequality is; Available wattage > 10,460 WattsReasons:
The items used and the possible power consumption obtained from a similar are as follows;
Appliance [tex]{}[/tex] Average power (Watts)
One air conditioner; [tex]{}[/tex] 3,500
Washing machine; [tex]{}[/tex] 500
Clothing dryer; [tex]{}[/tex] 5,000
Computers × 2; [tex]{}[/tex] 70 × 2 = 140
Light bulbs × 4; [tex]{}[/tex] 60 × 4 = 240
Refrigerator; [tex]{}[/tex] 600
Television × 2; [tex]{}[/tex] 240 × 2 = 480
The power, P, in watts that might be needed is found as follows;
Power, P = 3,500 + 500 + 5,000 + 140 + 240 + 600 + 480 = 10,460
The electric power in watts that might be needed, P = 10,460 Watts
Therefore;
The available wattage must be greater than 10,460 Watts
The inequality is; Available wattage > 10,460 Watts
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Plz help fast I will mark brainliest
I NEED HELP WITH MATH QUESTION PLEASE HELP ME NO LINKS !!!
Answer:
21.8
Step-by-step explanation:
1.9 + 9 = 10.9
10.9 x 2 = 21.8
Answer:
21.8
Step-by-step explanation:
2×1.9=3.8
2×9=18
total=21.8
Increase 80 by 12.5%
Answer:
90
Step-by-step explanation:
Answer:
[tex]80 \times \frac{12.5}{100} \\ = 10 [/tex]
then 80+10 =90
Pls help ::::………..
——-////
Answer:
you will have $133920 intrest monthly and $151920 in the bank
Step-by-step explanation:
Suppose you give $100 to a bank which pays you 5% simple interest at the end of every year. After one year you will have $105, and after two years you will have $110. This means that you will not earn an interest on your interest. Your interest payments will be $5 per year no matter how many years the initial sum of money stays in a bank account.
plsss helppp
can you pls do this?
Work out the mean for the data set below:
3.4, 5.2, 4.7, 3.5, 0.5
Give your answer as a decimal.
Answer:
3.4 + 5.2 + 4.7 + 3.5 + 0.5
= 17.3
There are a total of 5 numbers
17.3 / 5
= 3.46
Mindy can a drive a total of 375 miles on a full tank of gas, which is 25 gallons. Based on this information, what is the constant of proportionality?
25
15
375
10
Answer:
15
Step-by-step explanation:
[tex]\frac{25}{375} = \frac{1}{x}[/tex]
Cross multiply to get 25x = 375
Divide each side by 25 to get x = 15
4x+8=3
help asap
step by step please
[tex]4x +8 =3\\\\\implies 4x = - 5 \\\\\implies x = - \dfrac 54[/tex]
Answer:
x= -5/4
Step-by-step explanation:
4x+8=3
4x=3-8
4x=-5
x= -5/4
deffenition of polynomial function
Answer:
A polynomial function is a function such as a quadratic, a cubic,a quadratic, and so on, but to sum it up for you the answer is involving only non negative integer power of x.
I dont know what this is no links please
Answer:
Hamm i think si r or q mm sorry if it's wrong
Step-by-step explanation:
I think the answer would be q
If one angle of a triangle is 30° more than twice another angle, and the third angle is equal to the sum of the first two angles, find the measure of each angle.
Answer:
Answer:first angle = 25 degrees
Second angle = 35 degrees
Third side = 120/degrees
Step-by-step explanation:
Please help mee …………..
Answer: i think its A
Step-by-step explanation:
Let's say that a is 8, b is 17, and c is x,
Maximum:
a + b > c
8 + 17 >c
c < 25
Minimum:
b + c > a
17 + c > 8
c > -9
(As it cannot be negative, we will call this 9.)
So, our answer is D as c, x, must be less than 25 and greater than 9.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Simplify the following expression. (0.5x – 3)(0.5x + 3)
Answer:
0.25x^2-9
Step-by-step explanation:
Difference of squares converse:
0.25x^2-9
Answer:
0.25x^2-9
Step-by-step explanation:
multiply 0.5x with 0.5x which is 0.25x^2. then multiply 0.5x with 3 which is 1.5x. then multiply -3 with 0.5x which is -1.5x. then multiply -3 with 3 which is 9. so you will have 0.25x^2+1.5x-1.5x-9.
1.5x and -1.5x is 0. so you are left with 0.25x^2-9
Ada is making fresh orange juice for her family. She discovers that for every 3 oranges she squeezes, she gets 5 ounces of juice. Select all the ratios that have the same constant of proportionality as Ada's observation.
The ratios that have the same constant of proportionality as Ada's observation 15/9, 30/18
According to the question:
We are required to select all the ratios that have the same constant of proportionality as Ada's observation.let y and x represent amount of juice and oranges respectively;
y = juices squeezed outx = Oranges squeezed iny = k × x5 = k × 35 = 3kk = 5/3
The ratios equivalent to the constant of proportionality is 15/9, 30/18
Read more:
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Answer:
Step-by-step explanation:
9:15 15:25 6:10
Given the complementary angle of y is 43º. Find the supplementary angle of y
Step-by-step explanation:
complementary = adds up to 90 degrees.
supplementary = adds up to 180 degrees.
the complementary angle of y is 43 degrees.
so, y = 90 - 43 = 47 degrees.
the supplementary angle of y = 47 is
180 - 47 = 133 degrees
Hello!
Given the complementary angle of y is 43º.
90 - 43 => 47°
Find the supplementary angle of y
180-43 => 137°
please help and show work
Answer:
Just do scan and solve by brainly really helpful ngl
Step-by-step explanation:
What is the area of this tile?
Answer:
Area: 9 in.²
Step-by-step explanation:
Area of square: side²
=> Area of Square tile: 3²
=> 9 in.²
Hoped this helped.
Answer:
9
Step-by-step explanation:
To find the area of a square, multiply both sides.
3*3=9
ne ajudemmmm pfvvv ...
Answer:
NEED TRANSLATOR
Step-by-step explanation:
ENGLISH PLEASE
Please I really do need ur help. 4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.
What is the number?
Enter your answer as a mixed number in the simplest form in the box.
Answer: X = 2 2/3
Step-by-step explanation:
4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.
Let X be the "number." Translate the sentence:
(4 5/9) = ((2 1/3) + (5/6))*X
"4 5/9 is the same": (4 5/9) =
"as the sum of 2 1/3 and 5/6": ((2 1/3) + (5/6))
"times a number": *X
Put them all together:
(4 5/9) = ((2 1/3) + (5/6))*X
(41/9)-(7/3) = (5/6)X
(41/9)-(21/9) = (5/6)X
(20/9) = (5/6)X
X = (20/9)*(6/5)
X = 120/45
X = 2 30/45 or 2 2/3
Jake sold 39 tickets to the school fair and jeanna sold 12 tickets. What is the ratio in simplest form of the number of tickets jeanna sold to the number of tickets jake sold?
Step-by-step explanation:
12 to 39 divide each by 3
4 to 13 is the simpliest ratio
Which answer is an equation in point-slope form for the given point and slope? point: (7, 4); slope: 6.
Answer: the answer is
y-4=6*(x-7)
Step-by-step explanation:
What number does this Roman numeral represent?
XXXII
Answer: 32
Step-by-step explanation:
The roman numeral XXXII is 32 and XXIII is 23.
The number for this Roman numeral XXXII is, 32
Given that,
We have to write the number for this Roman numeral XXXII.
Since, We know that,
X represent in number = 10
I represent in number = 1
Hence, The number for this Roman numeral XXXII is,
⇒ XXXII
⇒ (10 + 10 + 10 + 1 + 1)
⇒ 32
Therefore, the number for this Roman numeral XXXII is, 32
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which expression means the same as subtract from 7 and then multipy by 4
Answer:7-3x4 subtract 3 from 7 means you need to take 3 out of 7 (7-3) then you need to multiply that by 4! Hope this helped!
Step-by-step explanation:
Answer:
[7-3]4 or [7-3]x4 your welcome hope it helps!
Step-by-step explanation:
2x-4>-14 or 2x-4\leq10
Answer:
x>0
Step-by-step explanation:
2x−4>−142x−4
Multiplica −14 y 2 para obtener −28.
2x−4>−28x−4
Agrega 28x a ambos lados.
2x−4+28x>−4
Combina 2x y 28x para obtener 30x.
30x−4>−4
Agrega 4 a ambos lados.
30x>−4+4
Suma −4 y 4 para obtener 0.
30x>0
El producto de dos números es >0 si ambos son >0 o <0. Puesto que 30>0, x debe ser >0.
x>0