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2 years ago

Find the vertex of this function. Is it a maximum or a minimum? y=-3(x + 4)2 + 2

Mathematics

1 answer:

Vika [28.1K]2 years ago

8 0

Step-by-step explanation:

The equation given is of the form

$y = a(x - h)^2 + k$

where (h, k) are the coordinates of the vertex. So in this case, the vertex is located at (4, 2). Since a is a negative number (a = -3), this means that the vertex is a maximum because the parabola opens downward.

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD=√2 cm.

Zielflug [23.3K]

Given that triangle ABC is right angle triangle. CD is altitude such that AD=BC

ABC is a right angle triangle so apply Pythogorean theorem

$AC^{2} + BC^{2} = AB^{2}$

$AC^{2} + AD^{2} = AB^{2}$ (Given that AD = BC)

$AC^{2} + AD^{2} = 3^{2}$ (Given that AB=3)

$AC^{2} + AD^{2} = 9$ ...(i)

ADC is a right angle triangle so apply Pythogorean theorem

$AD^{2} + CD^{2} = AC^{2}$

$AD^{2}+(\sqrt{2})^2= AC^{2}$

$AD^{2}+2= AC^{2}$

$AD^{2}=AC^{2} -2$ ...(ii)

Plug value (ii) into (i)

$AC^{2} + AC^{2}-2 = 9$

$2AC^{2} -2=9$

$2AC^{2} =11$

$AC^{2} =\frac{11}{2}$

$AC=\sqrt{\frac{11}{2} }$

Hence final answer is $AC=\sqrt{\frac{11}{2} }$

8 0

3 years ago

Read 2 more answers

Measuring the speed of sound in the ocean is an important part of marine research. One application is the study of climate chang

dalvyx [7]

Answer:

A linear formula for S as a function of D is S=17D+1534

Step-by-step explanation:

We are supposed to find a linear formula for S as a function of D.

Equation of line : y = mx+c

We are given that At the surface, the speed of sound is 1534 meters per second.

c = 1534

We are given that for each increase in depth by 1 km, the speed increases by 17 m/s

So, Slope = m = 17

Substitute the values in equation

y=17x+1534

x denotes depth

y denotes speed

We are given that Use D for depth and S for the speed of sound

So, S=17D+1534

Hence a linear formula for S as a function of D is S=17D+1534

7 0

3 years ago

Please Help Me

Ymorist [56]

Answer:

81 m/s

Step-by-step explanation:

If the box is sliding at 27 m per second, and it's been sliding for 3 seconds, then you should multiply 3 × 27 and your answer would be 81 m/s

4 0

2 years ago

Please help!!! 43+29= ? +60

NemiM [27]

Answer:

Step-by-step explanation:

43 + 29 = 72

? = 72 - 60 = 12

therefore, 43 + 29 = 12 + 60

8 0

2 years ago

Hurry show your work

Nikolay [14]

Answer: $\huge\boxed{\boxed{15}}$

Step-by-step explanation:

Given expression

$\large\boxed{\frac{12[30 - (9+4^2)]}{|10|-|-6| } }$

Simplify the exponents

$\large\boxed{=\frac{12[30 - (9+16)]}{|10|-|-6| } }$

Simplify values in the parenthesis

$\large\boxed{=\frac{12[30 - 25]}{|10|-|-6| } }$

$\large\boxed{=\frac{12[5]}{|10|-|-6| } }$

Simplify absolute values (all positive)

$\large\boxed{=\frac{12[5]}{10-6 } }$

$\large\boxed{=\frac{12[5]}{4 } }$

Simplify by division

$\large\boxed{=3~[5]}$

Simplify by multiplication

$\huge\boxed{\boxed{=15}}$

Hope this helps!! :)

Please let me know if you have any questions

7 0

1 year ago