Learning Task 3
A. Write each sentence as:
(a) Conditional Statement
(c) Inverse Statement
(b) Converse Statement
(d) Contrapositive Statement
1. Vegetables are good for your health.
2. 3x + 8 = 14, x = 2
3. A right triangle has a 90° angle.
4. An eagle is a bird.
5. A whale is a mammal.
6. Two circle with equal diameters are congruent.
7. An angle that measures between 90 and 180 degrees is obtuse
angle.
8. Two planes with no common point are parallel.
9. Carrot is rich in Vitamin A.
10. All reptiles have scales.
B. Determine which statements in A both the conditional and converse
statements are true. Write it in biconditional statement.
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Answers
Answer:
A)
1.
Statement is - Vegetables are good for your health.
Let P - There are Vegetables , Q - they are good for health
Conditional statement is -If there are Vegetables , then they are good for the health.
Inverse Statement is - If there are no Vegetables, then they are not good for health.
Converse statement - If they are good for health , then they are vegetables.
Contra-positive statement - If they are not good for health , then they are not vegetables.
2.
Statement is - 3x + 8 = 14, x = 2
Let P - 3x + 8 = 14 , Q - x = 2
Conditional statement is -If 3x + 8 = 14 , then x = 2.
Inverse Statement is - If 3x + 8 ≠ 14 , then x ≠ 2.
Converse statement - If x = 2 , then 3x + 8 = 14
Contra-positive statement - If x ≠ 2 , then 3x + 8 ≠ 14
3.
Statement is - A right triangle has a 90° angle.
Let P - Triangle has a 90° angle , Q - It is right triangle .
Conditional statement is -If Triangle has a 90° angle , then It is right triangle.
Inverse Statement is - If Triangle has not a 90° angle , then It is not right triangle.
Converse statement - If It is right triangle , then Triangle has a 90° angle.
Contra-positive statement - If It is not a right triangle , then Triangle has not a 90° angle.
4.
Statement is - An eagle is a bird .
Let P - It is an eagle , Q - It is a bird
Conditional Statement - If it is an eagle , then it is a bird.
Inverse statement - If it is not eagle , then it is not bird.
Converse statement - If it is a bird , then it is an eagle.
Contra-positive statement - If it is not a bird , then it is not an eagle.
5.
Statement is - A whale is a mammal
Let P - It is a whale , Q - It is a mammal
Conditional Statement - If it is a whale , then it is a mammal.
Inverse statement - If it is not whale , then it is not mammal.
Converse statement - If it is a mammal , then it is a whale.
Contra-positive statement - If it is not a mammal , then it is not a whale.
6.
Statement is - Two circle with equal diameters are congruent
Let P - Two circles have equal diameters , Q - They are congruent
Conditional Statement - If Two circles have equal diameters , then they are congruent.
Inverse statement - If two circles have not equal diameters , then they are not congruent.
Converse statement - If two circles are congruent , then they have equal diameters.
Contra-positive statement - If two circles are not congruent , then they have not equal diameters.
7.
Statement is - An angle that measures between 90 and 180 degrees is obtuse angle
Let P - An angle that measures between 90 and 180 degrees , Q - They are obtuse angle.
Conditional Statement - If An angle that measures between 90 and 180 degrees , then they are obtuse angle.
Inverse statement - If An angle that does not measures between 90 and 180 degrees , then they are not obtuse angle.
Converse statement - If an angle is obtuse angle , then that angle measures between 90 and 180 degrees.
Contra-positive statement - If an angle is not an obtuse angle , then that angle does not measures between 90 and 180 degrees.
8.
Statement is - Two planes with no common point are parallel.
Let P - Two planes have no common point , Q - they are parallel.
Conditional Statement - If Two planes have no common point , then they are parallel.
Inverse statement - If two planes have common point , then they are not parallel.
Converse statement - If two planes are parallel, then they have no common point.
Contra-positive statement - If two planes are not parallel, then they have common point.
9.
Statement is - Carrot is rich in Vitamin A.
Let P - There are carrots , Q - they are rich in Vitamin A
Conditional statement is -If There are carrots , then they are rich in Vitamin A.
Inverse Statement is - If there are no carrots , then they are not rich in Vitamin A.
Converse statement - If they are rich in Vitamin A , then they are carrots
Contra-positive statement - If they are not rich in Vitamin A , then they are not carrots.
10.
Statement is - All reptiles have scales.
Let P - All are reptiles , Q - they all have scales.
Conditional statement - If all are reptiles , then they all have scales.
Inverse statement - If all are not reptiles , they have no scales.
Converse statement - If all have scales , then all are reptiles.
Contra-positive statement - If all have no scales , then they all are not reptiles.
B)
1. Both the conditional and converse statements are true.
Bi-conditional statement - There are vegetables if and only if they are good in health.
3. Both the conditional and converse statements are true.
Bi-conditional statement - A triangle has a 90° angle if and only if it is a right triangle.
6. Both the conditional and converse statements are true.
Bi-conditional statement - Two circle are equal diameter if and only if they are congruent.
7. Both the conditional and converse statements are true.
Bi-conditional statement - An angle that measures between 90 and 180 degrees if and only if it is an obtuse angle.
8. Both the conditional and converse statements are true.
Bi-conditional statement - Two planes has no common point if and only if they are parallel.
Related Questions
If a Canada savings Bond is worth $6225 after 7 years, and was originally bought for $5000, what was the annual simple interest rate? Answer as a percentage.
[Formulas are,
[I = P, R, T]
[A = P + I]
[A = P(1 + R times T)
Answers
Answer:
3.5%
Step-by-step explanation:
Given data
A=$6225
P=$5000
T= 7years
R=???
Simple interest
A=P(1+rt)
substitute
6225=5000(1+7r)
6225=5000+35000r
collect like terms
6225-5000=35000r
1225=35000r
r= 1225/35000
r=0.035
Hence the rate is 0.035*100= 3.5%
A 34-foot pole is casting a shadow that is 17 feet long. How far is the top of the flag pole from the end of the shadow?
Answers
Answer:
108
Step-by-step explanation:
Find the length of the
missing side of the triangle
to the nearest tenth.
Answers
You’re looking for one of the legs here, so after inputting the values your equations should look like this: 6^2 + b^2 = 10^2.
Next, find what the numbers squared are: 36 + b^2 = 100.
Then, isolate the variable: b^2 = 64.
Lastly, square root both sides: √b^2 = √64.
You should find the answer is 8.
if a circle has an area of 100 cm squared, what would be the area of a section of 45 degrees?
Answers
Answer:
45 degrees/360 degrees=1/8
So the area would be 1/8 *100=100/8=25/2
Step-by-step explanation:
what is $78 discounted 12%
Answers
Answer:
$78 discount off 12% you would get $68.64. That is $9.36 off
Find the side indicated by the variable. Round to the nearest tenth.
Answers
Answer:
b ≈ 25.6
Step-by-step explanation:
From the figure attached,
By applying tangent rule in the given triangle,
tan(32°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(32°) = [tex]\frac{16}{b}[/tex]
b = [tex]\frac{16}{\text{tan}(32)}[/tex]
b = [tex]\frac{16}{0.62487}[/tex]
b = 25.605
b ≈ 25.6
HELP ASAP ASAP ASAP PLS PLS JUST PLS
Answers
i hope my answer help you
1st=5x-100
2nd=1/3x-7
3rd=x²×4
please, I need your help!! I will mark correct answer as brainliest.
Answers
Answer:
3, -3, 0
Step-by-step explanation:
The exlcusions of x are where the denominator =0
So we can write the following equations
x²-9=0
and
5x=0
Let's solve the first one
x²-9=0
x²=9
x= ±3
and
5x=0
x=0
Therefore x cannot equal 3, -3, 0
Answer: 3, -3, 0
So, yea. The answer ontop is also correct
F(x) = 24/x^2. When x=8
Answers
Answer:
3/8
Step-by-step explanation:
F(8)=24/8^2=24/(8*8)=24/64=3/8
Please teach me how to do this thank youuu.
Answers
Answer:
-10.2
Step-by-step explanation:
To find the equation you have to pick to random points, find the slope, and the y-intercept.
(1,-2) (2,2)
Slope = 2 - - 2 / 2 - 1
Slope = 4 / 1
Slope = 4
an estimate of the y-intercept is -2.2 meaning the function is f(x) = 4x - 2.2
when x is replaced by -2 like the question is requesting f(-2) = 4(-2) - 2.2
f(-2) = -10.2
* i really hope this made sense
What is the slope (-5,5) and (5,1)
Answers
Answer:
m= - 2/5
Step-by-step explanation:
Fill in the blank with a number to make the expression a perfect square.
Answers
Answer:
25
Step-by-step explanation:
if the expression is [tex]x^{2}[/tex] + 10x + 25, then the binomial factors will be the same which is (x+5)(x+5).
A perfect square is 25.
What is a perfect square?In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 3² and can be written as 3 × 3
Given
if the expression is x²+ 10x + 25, then the binomial factors will be the same which is (x+5)(x+5).
To know more about perfect square refer to :
https://brainly.com/question/17744523
#SPJ2
Which graph represents the inequality you found in part i.?
Answers
Answer:
Graph A represents the inequality x > 6.
A
Hope this helps have a great day
Trey is currently in debt and the balance of his account is -$24. If his
sister Catherine is in three times as much debt as he is, what is the balance
of Catherine's account?
Answers
GEOMETRY STUFF PLEASE ANDWER DUE IN 20 MINUTES
Answers
Answer:
Statement 2: m∠ ELD = (2x)°
Reason 4: Sum of angles on a straight line is equal to 180°
Statement 6: 2x = 56
Step-by-step explanation:
Since the first step talks about we being given m∠ ELG = 124°, the next thing we are given in the question is that; m∠ ELD = (2x)°
In statement 4,it is written that;
m∠ ELD + m∠ ELG = 180°
The reason behind this is that;
Sum of angles on a straight line is equal to 180°.
For reason 6, we are told it is a subtraction property.
Now the preceding statement gave us;
2x + 124 = 180
Which means that for subtraction property here, we will have;
2x = 180 - 124
2x = 56
what is the value of x
10= 3x - 6
X=
Answers
Answer:
[tex]x= \frac{16}{3}[/tex]
Step-by-step explanation: Can i get brain plz!
simply/ 16=3x
divide both sides by 3
x = 16/3
help with rounding off please !:(
Answers
The answers are given are below:
Answer:
(a) 3800
(b) 7000
(c) Does unit mean ones place? 31
(d) 82.8
(e) 1000
(f) 0.48
Step-by-step explanation:
What is 9867 rounded to the nearest 1000
Answers
Answer:
10,000Hope it helps
Have a good day
Hole this helps
simplify the expression
3x +4 +yxy +7y -10x + 6
Answers
Answer:
- 7x + 10 + y² + 7 y
Step-by-step explanation:
Hope this will help
The angles shown are supplementary. (3x + 15)° 60° What is the value of x?
Answers
Answer:
x = 35
Step-by-step explanation:
Supplementary angles add up to 180°.
if (3x + 15)° and 60° are supplementary, then
3x + 15 + 60 = 180
now, you just have to solve the equation.
3x + 75 = 180
3x = 105
x = 35
Check
3*35 + 15 + 60 = 180
105 + 15 + 60 = 180
180 = 180
I need help with this question
Answers
Answer:
a) 2.5 x 10^5
b) 8.1 x 10^4
c) 9.06 x 10^8
d) 1.034 x 10^10
-2/9 +1/5 help me please
Answers
Answer:
-1/45
Step-by-step explanation:
I did the equation okay hope this help!! <3
Answer:
1/40
Step-by-step explanation:
-2/9+ 1/5=0.2r
0.2r convert to fraction=1/40
hope that helps
plz mark as brainliest
4x³ + 9 + 16x² +4 + 12x³ + 17
combine like terms and order
Answers
Answer:
16x^3+16x^2+30
Step-by-step explanation:
Sports team is building a new stadium on a rectangular lot of land. It's a lot measures 10 X by five eggs and the sports field will be 6X by 2X, how much of the lot will be left over to build bleachers on
Answers
Answer:
4 X 2
8 unit²
Step-by-step explanation:
Given that:
Lot size = 10 X 5
Sport field = 6 X 2
Dimension of lot left :
(10 - 6) X (5 - 2)
4 X 2
Area left :
Length x width
4 * 2
= 8 units²
Six added to the quotient of 84 and seven
Answers
Answer:
84 divided by 7 is 12 + 6 = 18
what is the slope of a line that passes through the points (2,7) and (4,11)?
Answers
slope = y2-y1/x2-x1
slope = 11-7/4-2
slope = 4/2
slope = 2
A right triangle has side lengths 5, 12, and 13 as shown below.
Use these lengths to find cos B, tan B, and sin B.
COS
B
13
5
5
tan
A
12
с
Sin
Answers
Answer:
c
Step-by-step explanation:
a. 3in, 4in, 5 in
5^2 ? 3^2 + 4^
25 ? 9 + 16
25 = 25
Because the two sides are equal, this is a right triangle.
b. 5in, 6in, 7in
7^2 ? 5^2 + 6^2
49 ? 25 + 36
49 < 61
Because 49 < 61, this is an acute triangle.
c. 8in, 9in, 12in
12^2 ? 8^2 + 9^2
144 ? 64 + 81
144 < 145
Because 144< 145, this is an acute triangle.
Tan b) 12/5 or 2 1/6 or 2 2/12
Sin b) 12/13
Evaluate the function
F (-2) = x² - 5x + 2
Answers
Answer:
Step-by-step explanation:
Can you help me solve this please.
Answers
Answer:
down five units, and left three units.
Step-by-step explanation:
The bottom corner moved down five units.
Then that point moved three units to the left.
It's the same for the other points too.
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Answers
Answer:
c
Step-by-step explanation:
Answer:
HMMMMMM
Step-by-step explanation:
i think its b or c