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katen-ka-za [31]

2 years ago

14

Translate these statements into English, where R(x) is "x is a rabbit "and H(x) is "x hops" and the domain consists of all anima

ls. a) ∀x(R(x) → H(x)) b) ∀x(R(x) ∧ H(x)) c) ∃x(R(x) → H(x)) d) ∃x(R(x) ∧ H(x))

2 answers:

Hatshy [7]2 years ago

8 0

Answer:

A- for every animal, if the animal is a rabbit, the animal hops.

B- every animal is a rabbit and it hops.

C-there are animals that, if they are rabbits, they hop.

D-there are animals that are rabbits and they hop

muminat2 years ago

8 0

Answer:

a) For every animal, if the animal is a rabbit, then the animal hops

b) For every animal, the animal is a rabbit and the animal hops

c) there are animals such that if they are rabbits then they hop

d) there are animals such that they are rabbits and they hop

Step-by-step explanation:

∀ For every

a⇒b a then b

a∧b a and b

∃ there are

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Elaine bought $4 worth of apples and $3 worth of lemons did her grocery bag weigh more than 5 1/4

inysia [295]

1/4 will be your answer

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1 year ago

Mr. mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a

Dimas [21]

Answer:

$f(t)=-\frac{3}{2}t-7$

Step-by-step explanation:

We know that:

The initial conditions are -7 meters at 0 minutes.
Then, after 6 minutes, he was 16 meters below the ground.

According to these two simple facts we can found the linear function that describes this problem. First, the problem says that Mr. Mole is descending at a constant rate, which is the slope of the function. Now, to calculate the slope we need to points, which are $(0;-7)$ and $(6;-16)$ , where <em>t-values </em>are minutes, and <em>y-values </em>are meters. You can see, that the first point is the initial condition and the second point is 6 minutes later.

So, we calculate the slope:

$m=\frac{y_{2}-y_{1}}{t_{2}-t_{1}} \\m=\frac{-16-(-7)}{6-0}=\frac{-16+7}{6}=\frac{-9}{6}=\frac{-3}{2}$

From the slope we can see that Mr. Mole is descending, because it has a negative sign. Also, the point $(0;-7)$ is on the <em>y-axis</em>, because <em>t</em> is null, so -7 is part of the function. Therefore the function that describes this problem is:

$f(t)=-\frac{3}{2}t-7$

7 0

2 years ago

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When they are both racing on hoverboards, Victoria is 3 times as fast as her brother Max. When she is on foot, she is 3 times sl

kakasveta [241]

Answer:

The time taken from start to finish is 48 minutes.

Step-by-step explanation:

Given : When they are both racing on hoverboards, Victoria is 3 times as fast as her brother Max. When she is on foot, she is 3 times slower than Max on his hoverboard. They took off on hoverboards at the same time, but after 12 minutes, Victoria’s hoverboard broke and she immediately started to run.

To find : How long, in minutes, did it last from start to finish?

Solution :

Distance = Speed × Time

Let the speed of Max = s

Time taken = t

At 12 minutes,

Distance covered by Max = $s\times12=12s$

Victoria is 3 times as fast as her brother Max.

Distance covered by Victoria = $3\times s\times12=36s$

After 12 minutes,

Victoria’s hoverboard broke and she immediately started to run.

When Victoria is on foot, she is 3 times slower than Max on his hoverboard.

Distance covered by Max = $s\times(t-12)=(t-12)s$

Distance covered by Victoria = $\frac{s}{3}\times(t-12)=\frac{(t-12)s}{3}$

Since the race was a tie, then

Total distance of Max = Total distance of Victoria

$12s+(t-12)s=36s+\frac{(t-12)s}{3}$

$s(12+(t-12))=\frac{s(96+t)}{3}$

$t=\frac{96+t}{3}$

$3t=96+t$

$2t=96$

$t=48$

The time taken from start to finish is 48 minutes.

7 0

2 years ago

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Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

Sati [7]

Answer: The answer is f(x) = (x-3)²-h = (x-3-√h)(x-3+√h).

Step-by-step explanation: We are given to write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.

A quadratic function with vertex having x-coordinate k takes the form of a parabola as follows:

$f(x)+h=(x-k)^2.$

Here, 'k' and 'h' are both real.

Since we the the x-coordinate of the vertex as 3, so k = 3.

Therefore, the quadratic function becomes

$f(x)+h=(x-k)^2\\\\\Rightarrow f(x)=(x-k)^2-h\\\\\Rightarrow f(x)=(x-3-\sqrt h)(x-3+\sqrt h).$

This is the required factored form of the quadratic function.

See the attached graph, where the x-coordinate of the vertex is 3 and h is taken to be 2 units.

3 0

1 year ago

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Which expression is equivalent to Negative 2 and one-fourth divided by negative two-thirds? StartFraction 9 over 4 EndFraction d

Tanzania [10]

Answer:

The correct answer is:

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

i.e.

$-\dfrac{9}{4} \div \dfrac{2}{3}$

Step-by-step explanation:

We have to find equivalent expression to :

Negative 2 and one-fourth divided by negative two-thirds

i.e.

$-2\dfrac{1}{4} \div \dfrac{2}{3} = ?$

We have to convert the the mixed fraction form $-2\frac{1}{4}$ to simpler $\frac{p}{q}$ fraction form.

Let us learn the concept first.

Mixed fraction is combination of a whole number and a fraction.

Expression of the form $a\frac{b}{c}$ have the following understanding:

c is the divider

b is the remainder and

a is the quotient.

To convert mixed fraction to fraction we can use the following:

$a\dfrac{b}{c} = \dfrac{a \times c+b}{c}$

$\therefore -2\dfrac{1}{4} = -\dfrac{(2 \times 4+1)}{4} = -\dfrac{9}{4}$

Hence

$-2\dfrac{1}{4} \div \dfrac{2}{3} = -\dfrac{9}{4} \div \dfrac{2}{3}$

i.e. the given expression is equivalent to :

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

8 0

2 years ago

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