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3 years ago

Solve (x + 3)2 – 5 = 0 using the quadratic formula.

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

4 0

Answer:

Step-by-step explanation:

(x+3)² -5 =0 , use the formula (a+b) ² = a²+b²+2ab

x²+9 +6x -5 =0 , combine like terms

x²+6x +4 =0, use the quadratic formula x = (-b±√b²-4ac)/2a

x= (-6 ±√6²-4*1*4)/2*1

x= (-6 ± √36-16) /2

x= (-6±√20)/2

x=(-6 +2√5)/2 and x=( -6-2√5) /2, factor 2 in the numerator and simplify

x= -3 +√5 and x= -3 -√5

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Law Incorporation [45]

Answer:

Step-by-step explanation:

To solve this problem, we will use the following two theorems/definitions:

- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by $\nabla \cdot F = \frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}}+\frac{\partial W}{\partial z}$

- (Gauss' theorem)Given a closed surface S, the following applies

$\int_{S} F\cdot \vec{n} dS = \int_{V} \nabla \cdot F dV$

where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.

Let us, in our case, calculate the divergence of the given field. We have that

$\nabla \cdot F = \frac{\partial}{\partial x}(x)+\frac{\partial}{\partial y}(2y)+ \frac{\partial}{\partial z}(5z) = 1+2+5 = 8$

Hence, by the Gauss theorem we have that

$\int_{S} F\cdot \vec{n} dS = \int_{V} 8 dV = 8\cdot\text{Volume of V}$

So, we must calculate the volume V bounded by the cube S.

We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.

Take the vertices (1,1,1) and (1,1-1). The distance between them is given by

$\sqrt[]{(1-1)^2+(1-1)^2+(1-(-1)^2} = \sqrt[]{4} = 2$ .

Hence, the volume of V is $2\cdot 2 \cdot 2 = 8$ . Then, the final answer is

$\int_{S} F\cdot \vec{n} dS =8\cdot 8 = 64$

5 0

3 years ago

Carol used 114 cups of flour in 2 muffins. How many cups of flour are needed to make 12 similar muffins?

son4ous [18]

Answer:

7 1/2 cups

Step-by-step explanation:

If Carol uses 1 1/4 cups of flour for 2 muffins, then she will need to repeat this conversion 6 times since she wants to make identical 12 muffins in all.

So, 1 1/4 * 6 = 7 1/2

Therefore, she needs 7 1/2 cups of flour

Hope that helps! :)

7 0

3 years ago

Please help me!!!!! Show your work 45-45-90 method <3

aivan3 [116]

Answer:

hope it helps and u understand

check the steps in picture attached

7 0

2 years ago

Read 2 more answers

I need help i dont know what to do

vladimir1956 [14]

9514 1404 393

Answer:

∠CAB = 28°

∠DAC = 64°

Step-by-step explanation:

What you do in each case is make use of the relationships you know about angles in a triangle and around parallel lines. You can also use the relationships you know about diagonals in a rectangle, and the triangles they create.

Take advantage of the fact that ∆AEB is isosceles, so the angles at A and B in that triangle are the same. If we call that angle measure x, then we have the sum of angles in that triangle is ...

x + x + ∠AEB = 180°

2x = 180° -124° = 56°

x = 28°

The measure of angle CAB is 28°.

<u>Right</u>

Sides AD and BC are parallel, so diagonal AC can be considered a transversal. The two angles we're concerned with are alternate interior angles, so are congruent.

∠BCA = ∠DAC = 64°

The measure of angle DAC is 64°.

(Another way to look at this is that triangles BCE and DAE are congruent isosceles triangles, so corresponding angles are congruent.)

8 0

3 years ago

A clothing store used the sign show below to advertise a discount on shirts:

Murljashka [212]

Tax= Tax %(Price of 2 Shirts + 50% of 3rd Shirt)
Tax= 7.1%[49.96+49.96+1/2(49.96)]
Tax= 0.071(49.96+49.96+24.98)
Tax= 0.071(124.90)
Tax= $8.8679

Total= Tax + Price of Shirts
Total= $8.8679 + $124.90
Total= $133.7689 or rounded $133.77

Mean Price= Total ÷ 3
Mean= $44.5893 or rounded $44.59

Answer: C) $44.59

Hope this helps! :)

7 0

3 years ago

Read 2 more answers