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3 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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Solve the system of linear equations by substituting. Check your solution

Ghella [55]

QUESTION 4

The given system of linear equations are,

$y = 5x - 7...(1)$

and

$- 3x - 2y = - 12...(2)$

We put equation (1) into equation (2) to obtain,

$- 3x - 2(5x - 7) = - 12$

We expand to get,

$- 3x - 10x + 14 = - 12$

Group like terms to get,

$- 3x - 10x = - 12 - 14$

Simplify to get,

$- 13x = - 26$

Divide both sides by -13 to get,

$x = 2$

Put the value of x into equation (1) to get,

$y = 5(2) - 7$

$y = 10 - 7 = 3$

The solution is

$x = 2 \: \: and \: \: = 3$

QUESTION 5

The given system of linear equations are

$-4x+y=6....(1)$
and

$-5x-y=21...(2)$

We make y the subject in equation (1) to get,

$y = 4x + 6....(3)$

Put equation (3) into equation (2) to get,

$- 5x - (4x + 6) = 21$

We expand to get,

$- 5x - 4x - 6 =21$

We group like terms to get,

$- 5x - 4x = 21 + 6$

This implies that,

$- 9x = 27$

We divide both sides by -9 to get,

$x = - 3$

Put the value of x in to equation 3 to get,

$y = 4( - 3) + 6$

$y = - 12 + 6 = - 6$

Therefore the solution is

$x = - 3 \: and \: y = - 6$

QUESTION 6

The given equations are,

$-7x-2y=-13...(1)$

and

$x-2y=-13...(2)$

Make x the subject in equation (2) to get,

$x = 2y - 13...(3)$

Put equation (3) into equation (1) to get,
$- 7(2y - 13) - 2y = - 13$

We expand to get,

$- 14y + 91 - 2y = - 13$

We group like terms to obtain,

$- 14y - 2y = - 13 - 91$

.Simplify to get,

$- 16y = - 104$

Divide through by -16 to get,

$y = \frac{13}{2}$

Put the value of y into equation (3) to get,

$x = 2( \frac{13}{2} ) - 13$

$x = 13 - 13 = 0$

Therefore

$x = 0 \: and \: y = \frac{13}{2}$

8 0

3 years ago

Mr. Mills is 5 feet and 11 inches tall. How many inches tall is he?

MrRa [10]

Answer:

Step-by-step explanation:

There are 12 inches in a foot:

12 inches x 5 feet = 60

60 + 11 inches = 71 inches total

3 0

3 years ago

Read 2 more answers

Find all of the zeros of f(x) = 5x^2 +40x-100

Umnica [9.8K]

Answer:the answer is B

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A 4 metre ladder is placed against a vertical wall.

Black_prince [1.1K]

Answer:

Original position: base is 1.5 meters away from the wall and the vertical distance from the top end to the ground let it be y and length of the ladder be L.

Step-by-step explanation:

By pythagorean theorem, L^2=y^2+(1.5)^2=y^2+2.25 Eq1.

Final position: base is 2 meters away, and the vertical distance from top end to the ground is y - 0.25 because it falls down the wall 0.25 meters and length of the ladder is also L.

By pythagorean theorem, L^2=(y -0.25)^2+(2)^2=y^2–0.5y+ 0.0625+4=y^2–0.5y+4.0625 Eq 2.

Equating both Eq 1 and Eq 2: y^2+2.25=y^2–0.5y+4.0625

y^2-y^2+0.5y+2.25–4.0625=0

0.5y- 1.8125=0

0.5y=1.8125

y=1.8125/0.5= 3.625

Using Eq 1: L^2=(3.625)^2+2.25=15.390625, L=(15.390625)^1/2= 3.92 meters length of ladder

Using Eq 2: L^2=(3.625)^2–0.5(3.625)+4.0625

L^2=13.140625–0.90625+4.0615=15.390625

L= (15.390625)^1/2= 3.92 meters length of ladder

<em>hope it helps...</em>

<em>correct me if I'm wrong...</em>

4 0

3 years ago

find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square unit

viva [34]

Pls. see attachment.

We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.

Given:

51 degrees.

Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.

180 – 51 – 90 = 39 degrees

39 degrees * 2 = 78 degrees.

Angle Q is 78 degrees.

In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.

We will use the formula:

Sine theta = opposite / hypotenuse

Sin(78 deg) = opposite / 4.3

Sin(78 deg) * 4.3 = opposite

4.21 = opposite. This is also the height of the triangle.

Area of a triangle = ½ * base * height

A = ½ * 3units * 4.21units

A = 6.315 square units.

7 0

3 years ago