please help , show your steps , thanks

The given Quadratic equation is

[tex]4x^2- 8x - 13 = 0\\\\4(x^2-  2 x - \frac{13}{4}) = 0\\\\ (x-1)^2-1^2- \frac{13}{4}=0\\\\ (x-1)^2=\frac{\sqrt{17}}{4}\\\\ x-1=\pm\frac{\sqrt{17}}{4}\\\\ x=1 +\frac{\sqrt{17}}{4} \text{or}     x=1-\frac{\sqrt{17}}{4}[/tex]

These are the steps to determine the roots as well as solve the quadratic equation.

You can find the mistake by looking at the procedure of solving the quadratic equation by completing the square solved above.

Answer:

step 3

Step-by-step explanation:

Answer:

option C is correct

[tex]8x^5+24x^3+48x^2[/tex]

Step-by-step explanation:

As per the statement:

The length(l), width(w) and height(h) of the rectangular prism are:

l = 4x

w = 2x

[tex]h = x^3+3x+6[/tex]

We have to find volume.

Use the formula:

[tex]V = lwh[/tex]

Substitute the given values we have;

[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]

⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

then;

[tex]V = 8x^5+24x^3+48x^2[/tex]

Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]

To find the perimeter of the regular octagon, set the expressions for the sides equal to each other to find the value of x, substitute this value into either of the expressions for the sides to find the side length, and finally multiply the side length by 8.

In mathematics, a regular polygon is a polygon that is equilateral and equiangular. In this case, you have an octagon, which means it has 8 equal sides. If one side is defined as 4/3x - 1/3 and another side is defined as x+7, since it's a regular octagon, all sides must be equal. Therefore, to find the perimeter of the octagon, you need to set the two expressions for the sides equal to each other to find the value of x, and then substitute the value of x into either of the expressions for the sides. Multiply this side length by 8 to get the perimeter.

Here are the steps:

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In a regular polygon, all sides and angles are equal. Given a regular octagon with two sides expressed as 4/3x - 1/3 and x+7, the expressions should be equal since all sides are equal in a regular polygon. Having found x, you can multiply by 8 to find the perimeter of the octagon.

Thus, If a polygon is regular, this means all of its sides have the same length. If we're given that one side of the regular octagon is 4/3x - 1/3 and another side is x+7, these two expressions should be equal to each other since it's a regular polygon. This gives us an equation:

4/3x - 1/3 = x + 7

Solving for 'x' will give us the length of one side of the regular polygon. Once you have the length of each side, you can find the perimeter of the regular octagon by multiplying this length by 8 (since an octagon has 8 sides).

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Answer: C.

[tex]Mx+Ny=P\\(2M-R)x+(2N-S)y=P-2[/tex]

Step-by-step explanation:

Given: The system [tex]Mx+Ny=P\\ Rx+Sy=T[/tex] has the solution (1,3), where M,N,P,R,S and T are non zero real numbers.

A.

[tex]Mx+Ny=P\\ 7Rx+7Sy=7T[/tex]

Divide 7 on both sides on the second equation , we will get

[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]

Thus, this system has solution (1,3)

B.

[tex](M+R)x+(N+S)y=P+T.......(1)\\\\ 7Rx+7Sy=7T................(2)[/tex]

Subtract equation (2) from equation (1), we get

[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]

Thus, this system has solution (1,3)

C.

[tex]Mx+Ny=P...........(1)\\\\(2M-R)x+(2N-S)y=P-2T............(2)[/tex]

We can rewrite the equation (2) as

[tex]2Mx-Rx+2Ny-Sy=P-2T............(3)[/tex]

Multiply 2 on both sides of equation (1), we get

[tex]2Mx+2Ny=2P.........(4)[/tex]

Subtract equation (3) from (4), we get

[tex]Rx+Sy=P+2T[/tex]

But [tex]Rx+Sy=T[/tex]

Thus, this system does not have solution as (1,3).

D.

[tex]\frac{M}{2}+\frac{N}{2}=\frac{P}{2}\\\\Rx+Sy=T[/tex]

Multiply 2 on both sides on the first equation , we will get

[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]

Thus, this system has solution (1,3)

Answer:

.13 or 13%

Step-by-step explanation:

P = area of shaded region/area of entire board

Entire area:    3.14 * (11 * 11) = 379.94

shaded area: 3.14 * (4 *4) = 50.24

p = 50.24/379.94 = .13 or 13%

Answer:

Volume of pyramid B is three times bigger than the volume of pyramid A

Step-by-step explanation:

We are given that:

The volume for 3-D pyramid A is 300 cm³ .

and the volume for 3-D pyramid B is 900 cm³.

We have to tell how many times bigger is volume of pyramid B than volume of pyramid A.

volume of 3-D pyramid B= 900 cm³

                                        = 3×300 cm³

                                       = 3×volume of 3-D pyramid A

Hence, Volume of pyramid B is three times bigger than the volume of pyramid A

Answer:

Step-by-step explanation: 3%

Answer with explanation:

The exponential function is

 [tex]3^y=7\\\\ \text{taking log on both sides}\\\\y\log3=\log7\\\\y=\frac{\log7}{\log3}\\\\y=\log_{3}7\\\\y=\frac{0.8450}{0.477}\\\\y=1.77[/tex]

It is equation of a line, parallel to X  axis.

Drawn the graph of the function , which cuts the y axis at ,(1.77,0).

None of the curve matches with the given Options.

To complete the square for the expression x^2 - 18x, add 81 to become a perfect square trinomial in the form (x - 9)^2.

To complete the square for the expression x^2 - 18x, we need to add a constant term to the expression in such a way that it can be factored as a perfect square trinomial. First, we take half of the coefficient of the linear term and square it:

Half of -18 is -9, and when we square it we get 81. Therefore, adding 81 to the expression gives us x^2 - 18x + 81. This can be factored as (x - 9)^2. So the value that completes the square is 81.

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The total amount for the investment is approximately $4062.65.

To calculate the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously, we can use the formula A = P * e^(rt), where A is the total amount, P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate, and t is the number of years. Plugging in the values, we have A = 1250 * e^(0.096 * 12). Using a calculator, we find that A is approximately $4062.65.

You are given the graph of four straight lines, P, Q, R, and S. You are asked to find which line corresponds to the function of f(x) = 4x - 3. The easiest way to answer this is to plug in the values of the coordiante points used for each graph.

f(x) = 4x - 3 = y

y = 4x - 3

for graph of line S we have the coordinates (0, -3) and (2, 5)

(0, -3)

-3 = 4(0) - 3

-3 = -3

(2,5)

5 = 4(2) - 3

5 = 8 - 3

5 = 5

So the answer is the graph of line S.

Variable 1: X= number of craft activities

Variable 2: Y= number of sports activities

Equation: X + Y=15

A. The figure given in A is a square pyramid and the formula for the surface area of this figure is:

A = l w + l sqrt [(w/2)^2 + h^2] + w sqrt [(l/2)^2 + h^2]

where l and w are the lengths of the base and h is the height of the pyramid. Since the base is square, so:

l = w = 16 in

h = 15 in

Substituting:

A = 16 * 16 + 16 sqrt [(16/2)^2 +15^2] + 16 sqrt [(16/2)^2 + 15^2]

A = 256 + 272 + 272

A = 800 in^2

B. We are given a cone, the formula for surface area is:

A = πr (r + h^2 + r^2)

where h is the height = 8 in and r is the radius = 3 in

Substituting:

A = π * 3 (3 + sqrt (8^2 + 3^2))

A = 34.63π in^2 = 108.80 in^2 

Answer:

C: Put a point 5 units to the left of zero.

Step-by-step explanation:

Final answer:

Square trinomials and difference of squares binomials can be rewritten into separate factors using methods such as completing the square, the difference of squares method, and factoring by grouping.

Explanation:

Completing the square method: Rewrite square trinomials by completing the square to factor them into separate factors. For example, [tex]x^2 + 6x + 9[/tex] can be written as (x + 3)(x + 3).

Difference of squares method: Rewrite binomials with a difference of squares by factoring them into separate factors. For instance, [tex]x^2 - 4[/tex] can be expressed as (x + 2)(x - 2).

Factoring by grouping: For more complex trinomials, you can use the method of factoring by grouping to rewrite them as separate factors.

The polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² has one possible positive real zero according to Descartes' Rule of Signs. We observe one change of sign in the coefficients. Thus, there is a maximum of one positive real root.

Determining the Number of Possible Positive Real Zeros:

To determine the number of possible positive real zeros of the polynomial  [tex]2x^{4}[/tex] + 14x³ - 35x², we can use Descartes' Rule of Signs. This rule helps us to count the number of sign changes in the polynomial and thus infer the number of positive real roots.

First, let's observe the original polynomial:

[tex]2x^{4}[/tex] + 14x³ - 35x²

We examine the coefficients: 2, 14, and -35. By running our eye across these coefficients:

The polynomial has one sign change. According to Descartes' Rule of Signs, there is a maximum of one positive real root.

Therefore, the number of possible positive real zeros of the polynomial  [tex]2x^{4}[/tex] + 14x³ - 35x² is one.