Express each of these statements using quantifiers. then form the negation of the statement so that no negation is to the left of a quantifier. next, express the negation in simple english.
(do not simply use the phrase "it is not the case that.")
a) all dogs have fleas.
b) there is a horse that can add.
c) every koala can climb.
d) no monkey can speak french.
e) there exists a pig that can swim and catch fish.

Ok, so you want to negate the whole statement, first you if you want to negate the all dogs have fleas you need to find at least one dog that doesn't have fleas.

all the answers follow the same way of thinking.

a) All dogs have fleas. At least one dog doesn't have fleas.

b) There is a horse that can add. all horses can't add.

c) Every koala can climb. at least one coala cant climb

d) No monkey can speak French. at least one monkey can speak french

e) There exists a pig that can swim and catch fish. --- all pigs can't swim and catch a fish

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

$450 i think. hope this ☺