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Romashka-Z-Leto [24]
2 years ago
13

The function g(x) = –3x2 – 36x – 60 written in vertex form is g(x) = –3(x + 6)2 + 48. Which is one of the transformations applie

d to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60? The graph of f(x) = x2 is made narrower. The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.
Mathematics
1 answer:
navik [9.2K]2 years ago
3 0
The vertex form of the function gives the vertex as (-6,48). The vertex of f(x)=x^2 is (0,0) so from this information, the vertex is moved LEFT 6 and UP 48. This cancels out two options. The coefficient -3 tells us that the graph is flipped or reflected over the x-axis (negative sign flips graph) and that all y-values will be 3 times as large. Larger y-values for the same x inputs makes the graph narrower.
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Jeff earned his pilot's license and flew to visit his brother 200 miles away. A headwind of 20 mph slowed down the plane's speed
lora16 [44]
<h2>Plane's speed without wind i s 117.68 mph</h2>

Step-by-step explanation:

We have speed of plane without wind is x.

Distance to brothers place = 200 miles.

A headwind of 20 mph slowed down the plane's speed on the first leg of the trip

Speed to brothers place = x - 20

We have

         Distance = Speed x Time

         200=(x-20)\times t_1\\\\t_1=\frac{200}{x-20}

A tailwind of 20 mph sped up the plane on the return trip

Speed of return trip = x + 20

We have

         Distance = Speed x Time

         200=(x+20)\times t_2\\\\t_2=\frac{200}{x+20}

The entire trip took 3.5 hours.

That is

            t_1+t_2=3.5\\\\\frac{200}{x-20}+\frac{200}{x+20}=3.5\\\\200x+4000+2000x-4000=3.5(x-20)(x+20)\\\\400x=3.5x^2-1400\\\\7x^2-800x-2800=0\\\\\texttt{x = 117.68mph or x =-3.40mph}

Plane's speed without wind i s 117.68 mph

7 0
2 years ago
Which statement identifies how to show that j(x) = 11.6ex and k(x) = In (StartFraction x Over 11.6 EndFraction) are inverse func
Vadim26 [7]

Answer:

<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>

Step-by-step explanation:

Given the function  j(x) = 11.6e^x and k(x) = ln \dfrac{x}{11.6}, to show that both equality functions are true, all we need to show is that both  j(k(x)) and k(j(x)) equal x,

For j(k(x));

j(k(x)) = j[(ln x/11.6)]

j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}

j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)

j[(ln x/11.6)] = 11.6 * x/11.6

j[(ln x/11.6)] = x

Hence j[k(x)] = x

Similarly for k[j(x)];

k[j(x)] = k[11.6e^x]

k[11.6e^x] = ln (11.6e^x/11.6)

k[11.6e^x]  = ln(e^x)

exponential function will cancel out the natural logarithm leaving x

k[11.6e^x]  = x

Hence k[j(x)] = x

From the calculations above, it can be seen that j[k(x)] =  k[j(x)]  = x, this shows that the functions j(x) = 11.6e^x and k(x) = ln \dfrac{x}{11.6} are inverse functions.

4 0
2 years ago
A church steeple is 30 feet tall with square cross sections. The square at the base has side 3 feet, the square at the top has s
JulijaS [17]

Answer:

Volume= 540 ft^3

Step-by-step explanation:

Since volume= length times Width times height, you do 3 times 6 times 30= 540 ft^cubed.

3 0
2 years ago
There are 365 days in a year and 24 hours in a day. An airport camera records for 18 hours and then automatically resets itself
likoan [24]

The answer is 486.6

There are 8,760 hours in a year, so 18 divided by 8,760 would = 486.6

5 0
2 years ago
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A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new subs
Nitella [24]

Answer How many liters of a 20% acid solution should be mixed with 30 liters of 50% acid solution in order to obtain a 40% solution. ... x=15 liters 15*(.20 pure acid)=3 liters 30*(.50 pure acid)=15 liters That is 18 liters pure acid That is 45 liters solution *0.45 pure acid=18 liters.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
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