All categories

3 years ago

Which graph represents the function f(x)=-|x|-2?

Mathematics

1 answer:

skad [1K]3 years ago

5 0

Answer:

ind the absolute value vertex. In this case, the vertex for y=−|x|−2 is (0,−2).

(0,−2)

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(−∞,∞)

Set-Builder Notation: {x|x ∈ R}

For each x value, there is one y value. Select few x values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.

x y

−2 −4

−1 −3

0 −2

1 −3

2 −4

Step-by-step explanation:

You might be interested in

Please help me big finals test!!!!

REY [17]

Answer:

c= 67 cm

x = 29 degrees

z = 29 degrees

by the rule CPCTC

4 0

2 years ago

Amy has $8 less than Maria.Together they have $30

gtnhenbr [62]

a + m = 30
a = m - 8

(m - 8) + m = 30
2m - 8 = 30
2m = 30 + 8
2m = 38
m = 38/2
m = 19

a = m - 8
a = 19 - 8
a = 11

so Amy has $11 and Maria has $ 19

8 0

2 years ago

X/2 = y/3 find value of x, y if x+y =30

Llana [10]

Answer:

x=12, y=18

Step-by-step explanation:

4 0

1 year ago

Propane is stored in a cylindrical tank with a diameter of 15 inches and a height of 48 inches. Which equation could be used to

Virty [35]

Step-by-step explanation:

remember. the radius is always half the diameter.

volume of a cylinder

pi × r² × height

pi×7.5²×48 = pi×56.25×48 = 8,482.300165... in³

volume of a sphere

4/3 × pi × r³

and that volume should be the same as the cylinder. so,

4/3 × pi × r³ = pi×56.25×48

4/3 × r³ = 56.25 × 48

1/3 × r³ = 56.25 × 12

r³ = 56.25 × 36 = 7.5² × 6² = (7.5×6)² = 45² = 2025

$r = \sqrt[3]{2025}$

which would be 12.65148998... in.

8 0

1 year ago

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ (Approximated)

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ (Approximated)

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago