Viete's Formulas - what are they used for?
If we have a quadratic equation 2X^2 + 4X -6 = 0, whose roots are x1=1 and x2=-3 and where a = 2 b=4 and c=-6 then according to Viete's formulas (x1 + x2) = (-b/a) and (x1 • x2) = (c/a).
I suppose these formulas could be used as a double check for calculating the roots but do they serve any other purpose? (I also know there are other Viete's formulas for cubic, quartic, etc. equations).

Answer:

no solution

Step-by-step explanation:

To put the first equation into standard form, with the coefficients mutually prime, divide it by 5:

... x - y = 4

To put the second equation into standard form, with the coefficients mutually prime and the leading coefficient positive, divide by -2:

... x - y = 2

These are inconsistent equations, hence have no solution.

Answer:

a

Step-by-step explanation:

d = 46t

           d = 46(7)

           d = 322 miles                          (7, 322)

            d = 46(12)

            d =   552 miles                      (12, 552)

            d = 46(18)

           d = 828 miles                          (18, 828)    

The answer is 70494.

the perimeter is the sum of the 3 sides of the triangle, hence

x + 1 + x + 2 + x + 2 = 32

3x + 5 = 32 ( subtract 5 from both sides )

3x = 27 ( divide both sides by 3 )

x = 9

EF = x + 1 = 9 + 1 = 10

FG = x + 2 = 9 + 2 = 11

EG = x + 2 = 9 + 2 = 11

check : 10 + 11 + 11 = 32 ← perimeter

Answer: No, it is not enough to make 2 batches of Mac and cheese and 3 pizzas.

Step-by-step explanation:

Since we have given that

She needed 6 ounces of cheese and 2 tablespoons of basil for each batch of her Mac and cheese.

Now,

For every two pizzas she needed 16 ounces of cheese and 5 tablespoons of basil.

So, for 2 batches of Mac and cheese she needed = 12 ounces of cheese

and if for 2 pizzas she needed = 16 ounces of cheese

For 1 pizza she needed = 8 ounces of cheese

For 3 pizza she needed = 8× 3=24 ounces of cheese

Total requirement of cheese = 24+ 12=36 ounces

But she only buys 32 ounces package of cheese .

So, it is not enough to make 2 batches of Mac and cheese and 3 pizzas and 4 ounces is still needed i.e.

36-32 =4 ounces .

Lena bought a 32 oz package of cheese, and since 60 ounces is greater than 32 ounces, she does not have enough cheese to make 2 batches of Mac and cheese and 3 pizzas with her current supply.

If Lena has enough cheese to make 2 batches of Mac and cheese and 3 pizzas.

Each batch of Mac and cheese requires 6 ounces of cheese, and she wants to make 2 batches,

so that's 6 ounces * 2

= 12

Each pizza requires 16 ounces of cheese, and she wants to make 3 pizzas,

so that's 16 ounces * 3

= 48

In total, for the Mac and cheese and the pizzas,

Lena needs 12 ounces + 48 ounces

= 60 ounces of cheese.

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The appropriate choice is ...

.... A. The student failed to keep both sides of the equation balanced

_____

The one rule I learned in my study of Algebra that makes it all make sense is "keep the equal sign sacred." That is, whatever you do to one side of the equation must also be done to the other side of the equation. (Various teachers show various shortcuts that make it look like you're doing different things to the different sides of the equation. Don't be confused. If the operation can't be put in terms of doing the same thing to both sides, it doesn't work.)

Of course, you can always add 0 or multiply by 1 whenever and wherever you want.

_____

For the above equation, the appropriate solution is

... a + 3 = 9

... a + 3 - 3 = 9 - 3 . . . . . . addition property of equality

... a + 0 = 6 . . . . . . . . . . . .rules of arithmetic

... a = 6 . . . . . . . . . . . . . . . additive identity property of 0

Answer:

12.1

Step-by-step explanation:

We use the formula for the distance between two arbitrary points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the xy-coordinate plane, that is:

[tex]d=\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}[/tex]

So, replacing the points [tex]M=(2,16)[/tex] and [tex]M_2=(-3,5)[/tex], we obtain:

[tex]d=\sqrt{(2-(-3))^2 + (16-5)^2}\\d=\sqrt{(2+3)^2 + (16-5)^2}\\d=\sqrt{5^2 + 11^2}\\d=\sqrt{146 }=12.083045... \simeq 12.1[/tex]

that is the answer.

note: observe that we only use the coordinates between the two midpoints and not the point J.

The answer is c since it has a slope of 1/5 and a y-intercept of 1

Remark

So far what you have is the y intercept which according the graph, is (0,1)

The general equation is y = mx + b

If you put the following point (0,1) into the general line formula, you will get b

Givens

y = 1

x = 0

Solve

Substitute the givens into the general line

1 = m*0 + b            The m is no longer there.

b = 1                       The y intercept is 1

So far what you have is

y = mx + 1

The problem tells you that the slope (m) = 1/5

The equation is y = (1/5)x + 1

None of the answers are correct. There is no x anywhere that is right. If x was present, the answer would be C.

f^-1 is found by reading the table from right to left, so find the f(x) number in the right hand column and f^-1 would be the number in the left hand column.

When f(x) = 3, x = 2

f^-1(3) would be 2

When f(x) = 8, x = 7

f^-1(8) = 7

As per the given value of the function , value of [tex]f^{-1}(3) = 2[/tex] and [tex]f^{-1}(8) = 7[/tex].

" Function is defined as the for each input value there is one and only one output."

According to the question,

From the given table value of function [tex]f(x)[/tex]defined for [tex]x[/tex]

Consider,

[tex]f(x) = y\\\\\implies x = f^{-1}(y)[/tex]

Value of required function we get,

[tex]y= 3\\\\\implies f^{-1}(3)= 2[/tex]

[tex]y= 8\\\\\implies f^{-1}(8)= 7[/tex]

Hence, as per the given value of the function , value of [tex]f^{-1}(3) = 2[/tex] and [tex]f^{-1}(8) = 7[/tex].

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Answer:

bc

Step-by-step explanation:

The multiplication property of equality tells you that you can multiply both sides of the equation by the same amount. Choose that amount to be bd, the product of the denominators.

[tex]\dfrac{a}{b}=\dfrac{c}{d}\\\\\dfrac{a\cdot bd}{b}=\dfrac{c\cdot bd}{d}\\\\ad\dfrac{b}{b}=bc\dfrac{d}{d}\\\\ad=bc[/tex]

64%. You would divide 16 from 25 because you're trying to find the amount of garbage that was plastic.

Hope this helped! :)

Answer: 16x^4

Step-by-step explanation:

Given:  sin theta = 2/5.  This tells us that the lengths of the opp side and the hyp are 2 and 5 respectively.  The adj side is found using the Pyth. Thm.:  5^2-2^2= 25-4 = 21, so that the adj side is sqrt(21).

The double angle formula for the sine is sin 2theta = 2 sin theta *cos theta.

In this particular problem, the sine of 2theta is 2*(2/5)*[sqrt(21) / 5], or:

                                                                              (4/25)*sqrt(21).

Answer:

The value of [tex]\sin^2 \theta=\frac{4}{25}[/tex]                                                                            

Step-by-step explanation:

Given : [tex]\sin \thet=\frac{2}{5}[/tex] and  [tex]0<\theta<90[/tex]

To find : The value of [tex]\sin^2\theta[/tex] ?

Solution :

We have given the value of [tex]\sin \thet=\frac{2}{5}[/tex] and  [tex]0<\theta<90[/tex]

To find [tex]\sin^2\theta[/tex] we just have to square [tex]\sin\theta[/tex]

[tex]\sin \theta=\frac{2}{5}[/tex]

Squaring both sides,

[tex](\sin \theta)^2=(\frac{2}{5})^2[/tex]

[tex]\sin^2 \theta=\frac{4}{25}[/tex]

Therefore, The value of [tex]\sin^2 \theta=\frac{4}{25}[/tex]

Answer:

Step-by-step explanation:

Given that the plane passes through (1,3,3)

Also the plane contains the line x(t)=3t,y(t)=2t,z(t)=4+3t.

This means all points lying in this line will also lie in the plane.

Find out two points on this line.

First point: Let t =0.  Point is (0,0,4)

Next point : Let t = 1: Point is (3,2,7)

Now we have 3 non collinear points (0,0,4) (3,2,7) and (1,3,3) lying on the plane.

Equation of the plane is

[tex]\left[\begin{array}{ccc}x-0&y-0&z-4\\3&2&3\\1&3&-1\end{array}\right] =0[/tex]

Simplify to get

x(-2-9)-y(-3-3)+(z-4)(9-2)=0

i.e -11x+6y+7z-28 =0

11x-6y-7z+28 =0 is the equation of the plane.

Answer: 33 and 11

Step-by-step explanation: Both 11 and 33 would be the answr because 11 by the 2wice would be 33, and also 11 it's self would be the answer.

The numbers are x = 33 and y = 11 respectively.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is that one number is 11 more than twice another number and the sum of the numbers is twice their difference

Assume that the numbers are (x) and (y). Then, we can the model the equation as follows -

x = 2y + 11

x + y = 2(x - y)

Simplifying the equations, we can write -

x + y = 2(x - y)

x + y = 2x - 2y

2x - x - 2y - y = 0

x - 3y = 0

y = x/3

Put y = x/3 in x = 2y + 11, we get -

x = 2x/3 + 11

x - 2x/3 = 11

x/3 = 11

x = 33

then y = 33/3 = 11

Therefore, the numbers are x = 33 and y = 11 respectively.

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When you write expressions like this, you need to pay attention to the Order of Operations. As this is written, the only factor in the denominator is the one immediately after the division symbol: 7. This simplifies to

... (35/7)·x^(3+2)·y^(5+4) = 5x^5y^9

_____

We suspect you might intend ...

... (35x^3y^5)/(7x^2y^4) = (35/7)x^(3-2)y^(5-4) = 5xy

9x^2 + 27x + 18 . hope i helped

The factors of the quadratic equation are (-3 - √11i) and (-3 + √11i).

A quadratic equation is an algebraic equation of degree 2.

Given a quadratic equation 9x² + 27x + 45 = 0.

We know simplifying a quadratic equation doesn't change the roots of the equation.

∴ We can divide each of the terms by 9 which makes the quadratic equation x² + 3x + 5 = 0.

Now two numbers which multiplied to 5 and add to 3 are not possible for  real numbers, therefore, the roots must be imaginary.

We know Sridhar Acharya's formula which is [tex]\frac{ - b \pm\sqrt{b^2 - 4ac}}{2a}[/tex].

[tex]= \frac{ - 3 \pm\sqrt{3^2 - 4.1.5}}{2.1}[/tex].

[tex]= \frac{ - 3 \pm\sqrt{9 - 20}}{2}[/tex].

[tex]= \frac{ - 3 \pm\sqrt{-11}}{2}[/tex].

[tex]= \frac{ - 3 \pm\sqrt{11}i}{2}[/tex].

Therefore the factors of the quadratic equation are

(-3 - √11i) and (-3 + √11i).

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If you assume the rental cost changes in a linear fashion, the change over 6 years was $44. The "unit rate of change" is then $44/(6 years) ≈ $7.33/year.

Answer:

Make use of your knowledge of the maximum and minimum of the cosine function. Then scale and translate according to the way that function is scaled and translated to make f(x).

Step-by-step explanation:

f(x) is the cosine function, multplied by 4 and with 9 added to the result.

The minimum of the cosine function is -1. Multiplying that by 4 gives -4, and adding 9 gives 5.

The maximum of the cosine function is +1. Multiplying that by 4 gives +4, and adding 9 gives 13.

The minimum and maximum of f(x) are 5 and 13, respectively.

Max and Min:

Max = 13

Min = 5

COS Standard Period

[tex]2\pi[/tex]

COS Period with a multiplier of 2 on x

[tex]\pi[/tex]

COS Period with a multiplier of 2 on x and a Phase Shift

Answer to period

[tex]\frac{5}{4}\pi[/tex]

Step-By-Step Explanation:

Please view the image I have provided.

You must get two equation to find point of intersections

Answer:

x = (2,0)

y = (0,4)

Step-by-step explanation:

Solve For x:

Lets take y as 0 so the equation is 0 = -2x + 4, and if we simplify the expression we get x = 4/2 which s x = 2 so the answer for x is (2,0)

Solve for y:

Lets take x as 0 so the equation is y = -2 · 0 + 4 which simplyfied to y = 4, so the answer for y is (0,4)

To answer this, divide 1000 cm by 16:

1000 cm

------------------ = 66 2/3 cm per piece

  16 pieces

Answer:

The correct options are a and b.

Step-by-step explanation:

It is given that triangle ABC with segment AD drawn from vertex A and intersecting side BC.

Two triangle are called similar triangle if their corresponding sides are proportional or the corresponding interior angle are same.

To prove ΔABC and ΔDBA are similar, we have to prove that corresponding interior angles of both triangle as same.

If segment AD is an altitude of ΔABC, then angle ADB is a right angle.

[tex]\angle BDA=90^{\circ}[/tex]

The opposite angle of hypotenuse is right angle. If segment CB is a hypotenuse, then angle ABC is a right angle.

[tex]\angle BAC=90^{\circ}[/tex]

In triangle ΔABC and ΔDBA

[tex]\angle ABC\cong \angle DBA[/tex]              (Reflexive property)

[tex]\angle BAC\cong \angle BDA[/tex]              (Right angles)

By AA rule of similarity ΔABC and ΔDBA are similar.

Therefore correct options are a and b.

The slope we can get from using this y1-y2/x1-x2

so

10-3/-5-1=7/-6=-1 1/6

There's your slope

1. You can make use of the Pythagorean theorem considering "a" to be the longer leg of the largest right triangle. Then the value of "a" can be calculated from

(16+9)² = 15² +a²

625 -225 = a²

√400 = a = 20

2. You can find the altitude of the largest triangle (the length of the unmarked vertical line), then find "a" as the hypotenuse of the medium-sized right triangle.

That altitude is ...

√(15² -9²) = √144 = 12

so the length "a" is ...

a² = 12² +16² = 144 +256 = 400

a = √400 = 20

3. Based on the 15 and 9 dimensions of the smallest right triangle, you can realize that these triangles are multiples of the 3-4-5 right triangle. Then you can use relevant ratios of the side lengths of any of the triangles of which "a" is a part.

a = 4/3×15 = 4/5×(9+16) = 5/4×16 = 20

Hey there!!

Given equation :

... [tex]\frac{x}{2} + 3 = -5[/tex]

Subtracting 3 on both sides :

... [tex]\frac{x}{2} = -8[/tex]

Multiplying 2 on both sides :

... [tex]x = -16[/tex]

Hope my answer helps!!

the answer for x would be -16

Answer: Fourth option. 55 mistakes

Solution:

Please, see the attached graph.

Thanks.