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2 years ago

Let x be a real number. Find the lowest possible value of |5x^2 - 16| + |10x - 2|.

1 answer:

4 0

Since the equations are for absolute value this means any negative number used the answer would become positive, so to get the lowest value possible x would need to equal 0, which would eliminate the x variable from the equations.

Replace x with 0 and solve:

|5(0)^2 - 16| + |10(0) - 2|

Simplify:

|0 - 16| + |0 - 2|

|-16| + |-2|

Combine:

|-18|

Absolute Value = 18

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The point 3,4 lies on the graph of f(x)= sqrt(2x+a). Which ordered pair below lies on the graph of g(x)=1/2sqrt(2x+a)?

Rina8888 [55]

$(3;\ 4);\ f(x)=\sqrt{2x+a}\\\\\sqrt{2\cdot6+a}=4\\\sqrt{12+a}=4\ \ \ /^2\\12+a=16\\a=16-12\\a=4\\\\f(x)=\sqrt{2x+4}$

$g(x)=\frac{1}{2}\sqrt{2x+4}\\\\a)\ \left(\frac{3}{2};\ 2\right)\\R=\frac{1}{2}\sqrt{2\cdot\frac{3}{2}+4}=\frac{1}{2}\sqrt{3+4}=\frac{1}{2}\sqrt7;\ L=2;\ L\neq R\\\\b)\ \left(\frac{5}{2};\ \frac{3}{2}\right)\\R=\frac{1}{2}\sqrt{2\cdot\frac{5}{2}+4}=\frac{1}{2}\sqrt{5+4}=\frac{1}{2}\sqrt9=\frac{1}{2}\cdot3=\frac{3}{2};\ L=\frac{3}{2};\ L=R$

$c)\ (3;\ 2)\\R=\frac{1}{2}\sqrt{2\cdot3+4}=\frac{1}{2}\sqrt{6+4}=\frac{1}{2}\sqrt{10};\ L=2;\ L\neq R\\\\d)\ (27;\ 8)\\R=\frac{1}{2}\sqrt{2\cdot27+4}=\frac{1}{2}\sqrt{54+4}=\frac{1}{2}\sqrt{58};\ L=8;\ L\neq R\\\\Answer:B$

5 0

2 years ago

Determine the volume and the total surface area of the square pyramid.if its perpendicular height is 12cm and square length is 5

Vika [28.1K]

Answer:

Volume = 100 cm³

Surface area of the square pyramid = 145 cm²

Step-by-step explanation:

Given:

Perpendicular height = 12cm

Square length = 5cm

Find:

Volume

Surface area of the square pyramid

Computation:

Area of base = side²

Area of base = 5²

Area of base = 25 cm²

Volume = (1/3)(A)(h)

Volume = (1/3)(25)(12)

Volume = 100 cm³

Surface area of the square pyramid = A + 1/2(P)(h)

Perimeter square pyramid = 4(s)

Perimeter square pyramid = 4(5)

Perimeter square pyramid = 20 cm

Surface area of the square pyramid = 25 + 1/2(20)(12)

Surface area of the square pyramid = 145 cm²

3 0

2 years ago

A teacher gave a test with 50 questions, each worth the a a teacher gave a test with 50 questions, each the same number of point

igomit [66]

Answer:

Marci answered 40 out of 50

Marci answered 2 more questions correctly.

Step-by-step explanation:

Donovan got 38 out of 50

Marci got 80% which means 40 out of 50

40-38 = 2

6 0

2 years ago

During quarantine your goal was to do a total of 36 pull-ups and push ups in a minute. You end up doin 8 times as many push-ups

Semmy [17]

Answer:

36 times 8 = 288

5 0

3 years ago

Read 2 more answers

Basher collected 4 1/3 basket of peaches and Orchard if each basket holds 21

miv72 [106K]

To do this you times 3 by 4 and add it on to the numerator of the fraction, to turn it into a top heavy fraction:
3*4 = 12
1+12/3 = 13/3

Then you multiply the numerator by 21 to work out what 21 times the fraction is:
13*21/3 = 273/3

Then you can divide 273 by 3 to get the final answer:
273/3 = 91

He will have 91 peaches overall.
Hope this helps! :)

6 0

3 years ago