What is the contrapositive of the statement? All squares are rectangles. A.If a figure is a square, then it is a rectangle.
B.If a figure is a rectangle, then it is a square.
C.If a figure is not a square, then it is not a rectangle.
D.If a figure is not a rectangle, then it is not a square.

Answers

Answer 1

Answer: D.) If a figure is not a rectangle, then it is not a square
Contrapositive is when it switches the two sides up and makes it negative as well.

Answer 2

Answer:

Answer:

Step-by-step explanation:

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A 13 foot board is cut into two pieces. If one piece is x feet long express the other length in terms of x

Answers

Since the foot board is 13 feet long, it can be said that the sum of the two pieces is 13. If one piece is x, the other piece can be expressed as the difference of 13, the total length of the foot board, and x, the length of the first piece. Hence, the other piece, in mathematical terms, is expressed as 13-x.

There are chickens and pigs in a farm yard? There are 68 feet and 23 tails in the farm yard. How many chickens and how many pigs does grandma have?

Answers

You have animals with 4 legs, and animals with 2 legs. Both animals only have one tail. So, given that they only have one tail, there are only 23 animals in the farmyard.
Now, the equation would be,
$(68)/(x) =23$
$68=23x$
$(68)/(23) =x$

Answer:

12 chickens and 11 pigs

Step-by-step explanation:

We know that...

Chickens have 2 feet and 1 tail.

Pigs have 4 feet and 1 tail.

Let c represent chickens.

Let p represent pigs.

We need to create two equations. One for feet, and one for tails.

Tails:

Because each animal has 1 tail, we can say that the number of pigs, (p) plus the number of chickens, (c) must equal 23. So...

c + p = 23

Feet:

Because each chicken has two feet, and each pig has 4 feet, we can say that 2 times the number of chickens, (c) plus 4 times the number of pigs, (p) needs to equal 68. So...

2c + 4p = 68

Now we have two equations.

2c + 4p = 68

and

c + p = 23

We can use the substitution method to find c and p. The substitution method involves solving for one of the variables with one of the equations, then placing it into the other equation, so that you only have one variable to solve for, which you can do with simple algebra.

Solve for c

c + p = 23

c = 23 - p

Add that to the other equation.

2c + 4p = 68

2(23 - p) + 4p = 68

Solve for p

46 - 2p + 4p = 68

46 + 2p = 68

2p = 22

p = 11

Now that we know p, we can plug that into one of the equations to find c.

c + p = 23

c + (11) = 23

c = 12

Now we have c and p.

There are 12 chickens and 11 pigs on the farm.

One of two complementary angles is 4 degrees more than the other. Find the angles. (Recall that complementary angles are angles whose sum is 90 degrees.)Which of the following equations can not be used to solve the problem if x represents one of the angles?

Answers

$\displaystyle \n \alpha + \beta = 90^o \n \alpha - \beta = 4^o \n \texttt{----------- } + \n 2\alpha ~~/~= 94^o \n \n \alpha = (94)/(2) = \boxed{47^o}\n \n \beta = 90 -\alpha = 90 - 47 = \boxed{43^o}$

Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?

Answers

assuming that the river doesn not move
if they kept a constand speed then they passes
the problem doesn't say how fast they were moving, but we can see that 1 boat is faster so

first pass
1400 meters from 1 bank
if they turn around they are 600 meters from the other bank
since they kept constant speed, they passed in the same place so
distance from bank1 to markx=1400
distance from bank2 to markx=600
distance from bank1 to bank2=600+1400
1400+600=total distance=2000 m

A total of 234 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?

Answers

234 = a + s s = students a = adults
2a = s
after you get the equations you solve. plug 2a into the above equation.
so u get
234 = a + 2a
234=3a then divide 3 from each side
78 = a
so 78 adult tickets were sold

60% of what number is 150?

Answers

Answer:

Step-by-step explanation:

To solve this you must make a proportion of x/150 60/100. Then you need to find the relation between 100 and 150 which is x 1.5. Then apply the same thing to 60 which results in 90.

Answer: 250

You must set this up as a proportion

Remember the percent is always over 100

150/x=60/100

Then solve the proportion

60x=15000

Get the x by its self

15000/60 is 250

x=250

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