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KonstantinChe [14]

2 years ago

12

A boat went downstream and traveled a distance in 3 hours. the return took 3 hours and 40 min. find the speed of the water curre

nt of the speed of the boat in still water is 18

1 answer:

Katen [24]2 years ago

7 0

Answer:

Step-by-step explanation

:

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How do you solve X+10y=-9 X=5y+21

oee [108]

Answer:

Step-by-step explanation:

4 0

3 years ago

Translate "Three is less than thirty-seven" into a mathematical expression.

scoray [572]

$3 < 37$
Hope it will help you

5 0

3 years ago

Read 2 more answers

Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How

mylen [45]

Answer:

5.5 years old.

Step-by-step explanation:

Let D represent present age of Robert's dog and C represent present age of Karen's cat.

We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:

$D=C+4...(1)$

We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be $D+3$ and $C+3$ respectively.

We can represent this information in an equation as:

$D+3+C+3=13...(2)$

From equation (1), we will get:

$C=D-4$

Upon substituting this value in equation (2), we will get:

$D+3+D-4+3=13$

Combine like terms:

$2D+2=13$

$2D+2-2=13-2$

$2D=11$

$\frac{2D}{2}=\frac{11}{2}$

$D=5.5$

Therefore, Robert's dog is 5.5 years old right now.

3 0

3 years ago

Translate the following statement to an inequality.

Irina-Kira [14]

Answer:

Step-by-step explanation:

a number no less then 15

let the number be x

no less then 15....means it has to be 15 or more

x > = 15 (thats greater then or equal to)

3 0

3 years ago

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating <em>11 units to the left:</em>

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating<em> 5 units down:</em>

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>

SECOND.

Translating <em>8 units to the right:</em>

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating<em> 1 unit down:</em>

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

7 0

3 years ago