Need help with Math (Quadratic)

12a - 8 -5a + 12

arranging like terms

12a - 5a - 8 + 12

a ( 12-5) - 8 - 12

a(7) - 4(2 - 3)

a(7) -4(-1)

a(7) + 4

7a + 4

simplifing the expressions

Answer:

12a-5a-8+12

=(12-5)a+4

=7a+4

Answer:

1/5764801

Step-by-step explanation:

7^-1 × 7^-7

= 1/7(7^-7)

= 1/7(1/823543)

= 1/5764801

The minimized value is 50 and the maximized value is 130

The objective function is:

P = 10x + 5y

Subject to

2x+3y ≤30

2x+y ≤ 26

-2x+3y ≤ 30

x, y >0

Next, we plot the graph of the constraints (see attachment)

From the graph, the vertices of the feasible regions are:

(0, 10),(12, 2) and (6,14)

Substitute these values in P = 10x + 5y

P = 10(0) + 5(10) = 50

P = 10(12) + 5(2) = 130

P = 10(6) + 5(14) = 130

Hence, the minimized value is 50 and the maximized value is 130

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Based on the par value of the bond and the percentage it was issued at, the cost of the bond is $852.50.

The current cost of the bond is the present value of the bond's cashflows and its par value.

This is taken into account when the bond is issued at a certain percentage which in this case is 85 ¹/₄%.

The cost of the bond is:

= 1,000 x 85 ¹/₄%

= $852.50

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Answer:

27 boxses

Step-by-step explanation:

calculations is shown in the picture

Step-by-step explanation:

Part A:

So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)

v = x(4-2x)(8-2x)

Part B:

The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation

so for the x in front it must be greater than 0 to make sense

for the (4-2x), the x must be less than 2 or else the width is  negative.

for the (8-2x) the x must be less than 4 or else the length is negative

so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0

By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317  

Answer:

216

Step-by-step explanation:

4x+8yz+3y

Let x=3 y=4 z=6

Substitute the values into the expression

4(3)+8(4)(6)+3(4)

Multiply first

12+192+12

Then add

216

Using it's formula, it is found that the estimate monthly payment is of $480.42.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

The parameters are given as follows:

P = 25000, n = 60, r = 0.0575.

Hence:

r/12 = 0.0575/12 = 0.00479167.

Hence the payment will be of:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 25000(0.00479167)\frac{(1+0.00479167)^{60}}{(1+0.00479167)^{60}-1}[/tex]

A = 480.42.

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If the Worker is retrenched, the probability that he is a plumber or a plasterer will be  0.0152.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

The probability that the employee is a plumber;

[tex]\rm P(plumber)= \frac{No \ of \ plumber}{Total \ number \ of \ employ} \\\\ P(plumber)=\frac{12}{108} \\\\\ P(plumber)= 0.11[/tex]

The probability that the employee is a plasterer;

[tex]\rm P(plasterers )= \frac{No \ of \ plasterers }{Total \ number \ of \ employ} \\\\ P(plasterers )=\frac{15}{108} \\\\\ P(plasterers )= 0.13[/tex]

The probability that he is a plumber or a plasterer:

P = 0.13 × 0.11

P= 0.0152

Hence, if the worker is retrenched, the probability that he is a plumber or a plasterer will be  0.0152.

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Answer:

Step-by-step explanation:

Answer:

x² + 3 and x² + 4x + 5

Step-by-step explanation:

(a)

to find f(g(x)) substitute x = g(x) into f(x)

f(g(x))

= f(x² + 1)

= x² + 1 + 2

= x² + 3

(b)

to find g(f(x)) substitute x = f(x) into g(x)

g(f(x))

= g(x + 2)

= (x + 2)² + 1 ← expand factor using FOIL

= x² + 4x + 4 + 1

= x² + 4x + 5

The equation in terms of t that models the situation is given by

[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex].

We know that the interest on a loan or deposit that is accrued on both the initial principal and the total interest from prior periods is known as compound interest and it can be calculated as

[tex]A = P(1+\frac{r}{n})^{nt}[/tex],

where P is the initial principal, r is the rate of interest, n is the number of times interest was charged for each time period, t is the amount of time that has passed and A is the final amount.

Here, P = 8192, r = 10% = 10/100 = 0.01, n = 12 and A = 25,710

So, we can write

[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]

Therefore the required equation is

[tex]8192(1+\frac{0.01}{12} )^{12t} = 25710[/tex]

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Answer:

x² - 10x + 9 = (x-9)(x-1)

the factored expression would be (x-9)(x-1)

Answer:

16 or -2

Step-by-step explanation:

Let the number be x.

Difference between the number and 7

= x -7 or 7-x

The square of the difference between x and 7

= (x -7)²

(x -7)²= 81

Square root both sides:

[tex]x - 7= \pm \sqrt{81} [/tex]

[tex]x - 7 = \pm9[/tex]

Add 7 to both sides:

[tex]x = 7\pm9[/tex]

x= 16 or x= -2

Thus, the number could either be 16 or -2.

Answer: The vertex of the graph of [tex]y=x^2[/tex] is shifted to the right 4 units and up 3 units.

The answer to this question is choice B

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keep learning

Answer:

x² + 6x + 9

Explanation:

[tex]\sf = \left(x+3\right)^2[/tex]

Use perfect square formula: (a + b)² = a² + 2ab + b²

[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]

simplify the following

[tex]= \sf x^2 + 6x +9[/tex]

Hence Maria is not correct. The correct answer is x² + 6x + 9.

Answer:

28 cm

Step-by-step explanation:

The corner to corner cut is a hypotenuse. We know one leg, 45cm. So use Pythagorean theorem to solve for the other leg. See image.

Answer:

[tex]x+4\geq 12[/tex]

Step-by-step explanation:

x - a number

x+4 - a number plus 4

x+4[tex]\geq[/tex] - a number plus 4 is greater than or equal to

x+4[tex]\geq[/tex]12 - a number plus 4 is greater than or equal to twelve

Answer:

Inequality:  x + 4 ≥ 12

Solution:  x ≥ 8

Step-by-step explanation:

Plus:  "+" →  to add something to something else

Greater than or equal to:  "≥" → the expression on the left side of the inequality sign is greater than the expression on the right side of the sign.

Let x be the unknown number.

A number plus four is greater than or equal to twelve:

x + 4 ≥ 12

To solve the found inequality, subtract 4 from both sides:

⇒ x + 4 - 4 ≥ 12 - 4

⇒ x ≥ 8

Therefore, the solution to the inequality is x ≥ 8.  The unknown number x can be any real number equal to or greater than 8.

The new coordinate will be T'(3.2 , -1.6) .

Dilation is the transformation that changes the size of the object without changing its shape .

If a coordinate point is (x,y) and a dilation of scale factor f is applied then the new coordinates will be (fx ,fy)

The coordinate given in the question is T(8, -4)

The scale factor is 0.4

The new coordinate is

T'( 0.4 * 8 , 0.4 * (-4))

T'(3.2 , -1.6)

Therefore the new coordinate will be T'(3.2 , -1.6)

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answer: A: 16

B: 16

C: 12.57

D: 12.57

E: 3.43 (do area of square-area of circle 16-12.57

Answer:

Z = sin(xy)

[tex]\frac{1}{y} \times \frac{\partial Z}{\partial x} =\cos \left( xy\right) =\frac{1}{x} \times \frac{\partial Z}{\partial y}[/tex]

Answer:

x= 14, –12

Step-by-step explanation:

The given question might make you believe that it's difficult due to it's frightening digit (168) but in fact in you use the following methods, it's going to be a pieces of cake.

the delta formula:

Δ=b²–4ac===> (–2)²–4(1)(–168)=676

[tex]x 1 = \frac{ - ( - 2) + \sqrt{676} }{2} = 14 [/tex]

[tex]x2 = \frac{ - ( - 2) - \sqrt{676} }{2} = - 12[/tex]

well this can be on of the methods and the other one is

The full square formula:

[tex]x ^{2} - 2x - 168 = 0 \\ {x}^{2} - 2x = 168[/tex]

[/tex]

now what you need to do is to put this on both side of the equation (½b)²=1

[tex] {x}^{2} - 2x + 1 = 168 + 1 \\ {(x - 1)}^{2} = 169 \\ x - 1 = 13 = = > x = 14 \\ x - 1 = - 13 = = = > x = - 12[/tex]

Answer:

Angles are 45, 45 and 90 degrees because

AB and BC are congruent so that means the angles eating the sides are also congruent.

So to find the congruent angles:

180-90=90/2=45 degrees

To find AC:

a²+b²=c²

x²+x²=h²

√18=√c²

3√2=c

(I don't know why it says 3√3, but I think the q is wrong)

Hope it helps!

Answer:

45 degrees

Step-by-step explanation:

This is a special right triangle with these lengths. Which leads us to find the angles of 45, 45, 90 and B is 90 so A and C are 45 degrees.

The value of x in the right angle triangle is 45 / 4 units

AB² = 20² - 15²

AB = √400 - 225

AB = √175

AB = √175 units

Hence, using similarity ratio,

x / 15 = 15 / 20

cross multiply

20x = 225

x = 225 / 20

x = 45 / 4

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Answer:

second answer is 120

firsr answer is 25

Answer:

A,E

Step-by-step explanation:

Answer:

x = 3
x = -8

Step-by-step explanation:

The parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The equation of the parabola will be

y = -x²

The given parabola is a downward parabola which is passing through origin and leading coefficient of the negative 2.

The graph of the function is given below.

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