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3 years ago

Solve the following quadratic function by utilizing the square root method. y = 16 – x2

Mathematics

1 answer:

xxMikexx [17]3 years ago

3 0

Answer:

The solutions are x = -4 and x = 4.

Step-by-step explanation:

Solving a quadratic equation:

We have to find x for which $y = 0$ .

In this question:

$y = 16 - x^2$

$16 - x^2 = 0$

$x^2 = 16$

$x = \pm \sqrt{16}$

$x = \pm 4$

The solutions are x = -4 and x = 4.

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Find the value of x in each case: Given: Iso. ΔABC, HM ∥DG Find: x, m∠CAB, m∠CBA

AleksAgata [21]

1. Start with ΔCIJ.

∠HIC and ∠CIJ are supplementary, then m∠CIJ=180°-7x;
the sum of the measures of all interior angles in ΔCIJ is 180°, then m∠CJI=180°-m∠JCI-m∠CIJ=180°-25°-(180°-7x)=7x-25°;
∠CJI and ∠KJA are congruent as vertical angles, then m∠KJA =m∠CJI=7x-25°.

2. Lines HM and DG are parallel, then ∠KJA and ∠JAB are consecutive interior angles, then m∠KJA+m∠JAB=180°. So

m∠JAB=180°-m∠KJA=180°-(7x-25°)=205°-7x.

3. Consider ΔCKL.

∠LFG and ∠CLM are corresponding angles, then m∠LFG=m∠CLM=8x;
∠CLM and ∠CLK are supplementary, then m∠CLM+m∠CLK=180°, m∠CLK=180°-8x;
the sum of the measures of all interior angles in ΔCLK is 180°, then m∠CKL=180°-m∠CLK-m∠LCK=180°-(180°-8x)-42°=8x-42°;
∠CKL and ∠JKB are congruent as vertical angles, then m∠JKB =m∠CKL=8x-42°.

4. Lines HM and DG are parallel, then ∠JKB and ∠KBA are consecutive interior angles, then m∠JKB+m∠KBA=180°. So

m∠KBA=180°-m∠JKB=180°-(8x-42°)=222°-8x.

5. ΔABC is isosceles, then angles adjacent to the base are congruent:

m∠KBA=m∠JAB → 222°-8x=205°-7x,

7x-8x=205°-222°,

-x=-17°,

x=17°.

Then m∠CAB=m∠CBA=205°-7x=86°.

Answer: 86°.

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Step-by-step explanation:

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Given f (x )equals 2 x minus 5 and g (x )equals 5 x squared, first find f plus g, f minus g, fg, and StartFraction f Over g

baherus [9]

Answer:

(f + g)(x) = 5x² + 2x - 5

Domain: All real numbers

(f - g)(x) = -5x² + 2x - 5

Domain: All real numbers

(fg)(x) = 10x³ - 25x²

Domain: All real numbers

(f/g)(x) = $\frac{2x-5}{5x^2}$

Domain: (negative infinity, 0)U(0, positive infinity)

Step-by-step explanation:

For f + g, we are simply adding the 2 together

Domain: All values of x work, as any value x outputs any value y

For f - g, we are simply subtracting the 2 together

Domain: All values of x work, as any value x outputs any value y

For f times g, we are simply multiplying (distributing) the 2 together

Domain: All values of x work, as any value x outputs any value y

For f divided by g, we are simply dividing (fraction) the 2 together

Domain: All values except for 0 work (undefined error), so asymptote at x = 0

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