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4 years ago

How do you complete the square of h(x)= x^2 + 6x + 7

Mathematics

1 answer:

evablogger [386]4 years ago

4 0

Answer:

$(x + 3)^{2} - 2$

Step-by-step explanation:

$h(x)= x^2 + 6x + 7 \\ = x^2 + 2.3.x + {3}^{2} - {3}^{2} + 7 \\ = (x + 3)^{2} - 9 + 7 \\ \purple { \bold{h(x)= (x + 3)^{2} - 2 }}$

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A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each

iogann1982 [59]

Answer:

The artist will make a profit if she sells 15 necklaces. This is known because 15 is greater than 11.625 (i.e. 15 > 11.625).

Step-by-step explanation:

Note: The question contains some error. The question is therefore rewritten before is answered as follows:

A jewelry artist is selling necklace at an art fair. It costs $135 to rent a booth at the fair. The cost of material for each necklace is $4.50. The artist is selling the necklace at $12 each. The inequality 12n>135+4.50 represents the situation in which the art is making the profit. Will the artist make a profit if she sells 15 necklaces? Show how you know. Be sure to indicate what the variable n represents.

The explanation of the answer is therefore given as follows:

Given;

12n > 135 + 4.50 .................... (1)

Where n represents the number of necklace that must be sold by the artist to make a profit.

Solving for n from equation, we have:

12n > 139.50

n > 139.50 / 12

n > 11.625 ..................... (2)

Equation (2) implies that more than 11.625 necklaces must be sold by the artist to make a profit.

When the artist sells 15 necklaces, it implies that n = 15.

Since more than 11.625 necklaces must be sold by the artist to make a profit, it therefore implies that the artist will make a profit if she sells 15 necklaces. This is known because 15 is greater than 11.625 (i.e. 15 > 11.625).

6 0

3 years ago

unit vector lies in the xy plane, at an angle of 145 degrees from the +x axis, with a positive y component. What is the unit vec

Fittoniya [83]

Answer:

$-0.82i+0.57j$

Step-by-step explanation:

We are given that a unit vector A which lies in the xy-plane.

Unit vector:It is that vector whose magnitude is equal to 1.

$\mid A\mid=1$

$\theta=145^{\circ}$

We have to find the unit vector.

x-component of unit vector= $A_x=\mid A\mid cos\theta$

x-component of unit vector= $A_x=1cos145^{\circ}=-0.82$

y-component of unit vector= $A_y=\mid A\mid sin\theta=1\times sin145=0.57$

Unit vector ,A= $A_xi+A_yj=-0.82i+0.57j$

Hence, the unit vector = $A=-0.82i+0.57j$

5 0

4 years ago

A cylindrical paint can has a 6.5 inch inside diameter and is 7.75 inches high. It is being filled with paint at a rate of 120in

Zina [86]

Answer:

The rate of coating of surface is = 74 inch²/min

Step-by-step explanation:

diameter = 6.5-inch, height = 7.75-inch, rate of filling or dv/dt = 120 inch/min

Since the differential of an equation is basically its rate of change with respect to another variable.

Radius = d/2 = 6.5/2 = 3.25 inch, ds/dt = ? can also be understood as the rate at which the surface area of the cylindrical paint can is coated.

We know that the surface area of a cylinder = 2πrh + 2πr², this is equation 1

The volume for the cylinder = V = πr²h

dv/dt = πr² x dh/dt, where r is constant

120 = π x (3.25)² x dh/dt

Dh/dt = 120/π x (3.25)²

Now differentiate the surface area equation 1

ds/dt = 2 x π x r dh/dt + 0 , where r is constant

replace the value of dh/dt in the above equation of ds/dt

ds/ dt = 2 x π x 3.25 x (120/π x (3.25)²

ds/dt = 73.846 ≅ 74inch²/min

3 0

3 years ago

Simplify -1-2(8-6×2÷3)² is what

Mademuasel [1]

Hope this will help u..✌

3 0

4 years ago

Read 2 more answers

community group is planning the expansion of a square flower garden in the city park if each side of the original Garden is incr

JulijaS [17]

4mm
The sides of the new garden can be represented by x+9. x is the original size and 9 is the added 9mm. Multiply the sides to get (x+9)(x+9) or $(x+9)^2$
this will equal the area. Create an equation to solve for the unknown original length.
$169=(x+9)^2$
Take the square root of both sides
13=x+9
Subtract both sides by 9
4=x The original side was 4mm long

8 0

3 years ago