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1 year ago

How many solutions does the equation have? |h| − 8 = 4 no solution, one solution, two solutions

Mathematics

1 answer:

Gennadij [26K]1 year ago

5 0

Since the solution to the system of equation is 12 and -12, hence the equation has 2 solutions

<h3>Modulus functions</h3>

Modulus functions are functions that can either be positive or negative. Given the modulus function below;

|h| − 8 = 4

The modulus of h can both be negative and positive

If the modulus of h is positive then;

h - 8 = 4

Add 8 to both sides

h-8 + 8 = 4 + 8

h = 4 + 8

h = 12

If the value of h is negative

-h - 8 = 4

-h = 4 + 8

h =-12

Since the solution to the system of equation is 12 and -12, hence the equation has 2 solutions

Learn more on modulus function here: brainly.com/question/23450491

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Dustin has a collenction of quarters and pennies. The total value is $4.65. Th

Hitman42 [59]

Answer:

Dustin has 18 quarters and 15 pennies.

Step By Step Solution:

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6 0

3 years ago

6) Two coastguard stations P and Q are 17km apart, with due East of P. A ship S is observed in distress on a bearing 048° fromP

adelina 88 [10]

Answer:

The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Step-by-step explanation:

Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.

But,

<P = 048°

<Q = $360^{o}$ - $324^{o}$

= 0 $36^{o}$

Sum of angles in a triangle = $180^{o}$

<P + <Q + <S = $180^{o}$

048° + 0 $36^{o}$ + <S = $180^{o}$

$84^{o}$ + <S = $180^{o}$

<S = $180^{o}$ - $84^{o}$

= $96^{o}$

<S = $96^{o}$

Applying the Sine rule,

$\frac{y}{Sin P}$ = $\frac{x}{Sin Q}$ = $\frac{z}{Sin S}$

$\frac{y}{Sin P}$ = $\frac{z}{Sin S}$

$\frac{y}{Sin 48^{o} }$ = $\frac{17}{Sin 96^{o} }$

$\frac{y}{0.74314}$ = $\frac{17}{0.99452}$

⇒ y = $\frac{12.63338}{0.99452}$

= 12.703

y = 12.70 km

$\frac{x}{Sin Q}$ = $\frac{z}{Sin S}$

$\frac{x}{Sin 36^{o} }$ = $\frac{17}{Sin 96^{o} }$

$\frac{x}{0.58779}$ = $\frac{17}{0.99452}$

⇒ x = $\frac{9.992430}{0.99452}$

= 10.0475

x = 10.05 km

Thus,

the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.

6 0

3 years ago

In<br> X = 4<br><br> Answer options; <br> A: x=e^4<br> B: x=(4/e)<br> C: x=4e<br> D: x=4^e

marshall27 [118]

Answer:

the answer is x=e⁴........

7 0

3 years ago

Y = -1.33 * X - 3 Show your work

Aleksandr [31]

Y = -1.33 * x - 3
y = -1.33 -3 *x
y = -4.33 *x

8 0

3 years ago

Read 2 more answers

a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the

nlexa [21]

Answer:

The standard equation of the parabola is:

$y=-\frac{3}{2}x^2+12x-18$

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

$y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2$

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

$y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}$

Then the equation of the parabola becomes:

$y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18$

7 0

3 years ago