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3 years ago

I'll give brainliest to whoever answers first and is correct!!

Mathematics

1 answer:

Nina [5.8K]3 years ago

6 0

Answer:

(a) $y=8x+5$

(b) 7 hours.

Step-by-step explanation:

(a) Let x be the number of hours and y is the total cost.

We have been given that Beatrice and her friends charge $8 per hour of babysitting, so the charges for x hours of babysitting will be 8x.

As they also charge a mandatory $5 per day fee for each child for snacks, so the total charges for babysit each day will be charges for x hours of babysitting plus mandatory charge.

We can represent this information in an equation as:

$y=8x+5$

Therefore, the equation $y=8x+5$ represents the total cost of using Beatrice’s babysitting service each day.

(b) To find the number of hours Beatrice babysit the daughter, we will substitute y = 61 in our equation and solve for x.

$61=8x+5$

Let us subtract 5 from both sides of our equation.

$61-5=8x+5-5$

$56=8x$

Let us divide both sides of our equation by 8.

$\frac{56}{8}=\frac{8x}{8}$

$7=x$

Therefore, Beatrice babysit 7 hours the daughter.

Expression for part c is missing.

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4 years ago

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Paraphin [41]

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Other than that, the graph shows y=x^2 so it wasn't compressed or stretched

The 2nd graph has vertex in (0, 0) which mean there is no vertical and horizontal shift. But the graph is facing down and it was slimmer than y=x^2 graph. When x=1, the result is y=3 which was 3 times more than it supposed to be.
The graph must be:
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The 3rd graph has vertex in (3, -3) which can be translated into
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3 years ago

2 3/5 - 5/6 as a mixed number

Vaselesa [24]

Answer:

1 23/30

Step-by-step explanation:

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3 years ago

Consider f and c below. f(x, y, z) = yzexzi + exzj + xyexzk,

Jet001 [13]

Answer:

$f(x,y,z)=ye^{xz}+C$

Step-by-step explanation:

We can write the given expression as :

$\vec f(x,y,z)=yze^{xz}\,\vec\imath+e^{xz}\,\vec\jmath+xye^{xz}\,\vec k$

As given, f = ∇f.

∇f = $\dfrac{\partial f}{\partial x}i$ + $\dfrac{\partial f}{\partial y}j$ + $\dfrac{\partial f}{\partial z}k$

We can write the partial derivative with respect to x, y and z.

$\dfrac{\partial f}{\partial x}=yze^{xz}$ ___(Equation 1)

$\dfrac{\partial f}{\partial y}=e^{xz}$ ______(Equation 2)

$\dfrac{\partial f}{\partial z}=xye^{xz}$ ______(Equation 3)

Take equation 2 and integrate with respect to y,

$\dfrac{\partial f}{\partial y}=e^{xz}$

$f(x,y,z)=ye^{xz}+a(x,z)$ ----------Equation 4

Derivate both sides w.r.t x , we get :

$\frac{d}{dx}(yze^{xz})=yze^{xz}+\dfrac{\partial a}{\partial x}$

$\dfrac{\partial a}{\partial x}=0$

integrate

a(x,z)=b(z)

put in equation 4 ,

we get :

$f(x,y,z)=ye^{xz}+b(z)$

take derivative wrt z

$\frac{d}{dz} (ye^{xz}+b(z))\impliesxye^{xz}=xye^{xz}+\frac{db}{dz}$

we can take here:

$\frac{db}{dz} = 0$

integrate:

$\int\ {\frac{db}{dz} } \, =\int0$

b(z) = C

The function can be written as :

from equation 4 :

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Where C is a constant.

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3 years ago

(25 points!!!!) draw the graph of the area bounded by these inequalities

Stels [109]

Step-by-step explanation:

To draw the graph, follow these steps:

Graph the lines using points from the equations. (the blue line shown should be dotted, unfortunately I cannot do that in the program I used)
Determine which direction the inequalities are correct.
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The three inequalities given form a triangle.

The first equation, y ≤ 2x + 5, has a y-intercept at (0, 5) and a point at (-2, 1).

The second equation, y < -3x + 10, has points at (3, 1) and (2, 4).

Use two points to draw the lines.

After the lines are drawn, determine which side of the line the inequality works on. You can do this by testing points that are not on the line.

I will test each inequality using (0, 1):

y ≤ 2x + 5

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This is correct, so the inequality for y ≤ 2x + 5 will be shaded towards (0, 1).

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0 < -3 + 10

This is correct, so the inequality for y < -3x + 10 will be shaded towards (0, 1).

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This is correct, so the inequality for 0 ≤ y will be shaded upwards towards (0, 1).

The end result of this graph is all three inequalities being shaded (inwards).

The solution is a triangle with points at (1, 7), (3.33333, 0), and (-2.5, 0).

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3 years ago