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2 years ago

Rita runs 6 miles in 44 minutes. At the same rate, how many minutes would she take to run 9 miles?

1 answer:

5 0

You run 0.5 miles every 3 minutes => 1 mile every 6 minutes. Your friend runs 2 miles every 14 minutes => 1 mile every 7 minutes. You run a whole number of miles every number of minutes that is a multiple of 6. Your freind runs a whole number of miles every number of minutes that is a multiple of 7 Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes. This is 7 * 6 = 42 minutes. You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles

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HELP PLEASE ITS DUE IN 10 MIN Use algebraic strategies to solve for x.

mr Goodwill [35]

Answer:

x = 4, x ≠ -1

Step-by-step explanation:

√3x + 4 = x

(√3x + 4)² = x² (Square both sides to get rid of the radical.)

3x + 4 = x²

0 = x² - 3x - 4 (Set everything to 0 by moving everything to one side.)

0 = (x - 4)(x + 1) (Factor.)

x = 4 x = -1

Now we need to check for extraneous solutions:

√3(4) + 4 = 4

√12 + 4 = 4

√16 = 4

4 = 4

√3(-1) + 4 = -1

√-3 +4 = -1

√1 = -1

1 ≠ -1

-1 is an extraneous solution.

8 0

2 years ago

Translate triangle HIK 4 units to the right and 1 unit up.

Fiesta28 [93]

C because K is 1,-8 so if you go up 1, -7, and right 4,5. So you get k(5,-7)

4 0

2 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 11 units to the left:

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

Then translating 5 units down:

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

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

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

SECOND.

Translating 8 units to the right:

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

Then translating 1 unit down:

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

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

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

7 0

3 years ago

Help please! anything will help thanks ya'll.!

zzz [600]

The cosine of A is (adjacent side)/(hypotenuse) = 55/73. Do the division, then find the angle whose cosine is that number. The whole thing takes maybe 6 or 7 seconds with your calculator. It's choice-B.

6 0

2 years ago

D-13=6 F-26=12 M+18=109 56+k=231 How do you solve these with steps

lapo4ka [179]

Answer:

D=6+13=19

Step-by-step explanation:

F=26+12=38

M=109-18=91

k=231-56=175

8 0

3 years ago