In △ABC, m∠A=16°, m∠B=49°, and a=4. Find c to the nearest tenth.

Answer:

50

Step-by-step explanation:

This is an isosceles triangle which means opposite sides are congruent implies the base opposite angles at the base congruent.

So both of bottom angles are 65 each.

We know the sum of the interior angles of a triangle are 180 degrees.

So we have 65+65+x=180.

Combine like terms:

130+x=180

Subtract 130 on both sides:

x=180-130

x=50

Answer:

$835.20

Step-by-step explanation:

First you need to find out how many profit you had at first by multiplying 145 and $44.17.

So, 145*$44.17 = 6404.65

Then find out how much profit you had after it decreased by multiplying 145 and $38.41.

So, 145*$38.41 = 5569.45

Now to find how much profit you lost, you have to subtract $6,404.65 and $5,569.45.

$6,404.65 - $5,569.45 = $835.20

Answer:

The required absolute inequality is |x - 78| ≤ 20.

Step-by-step explanation:

Consider the provided information.

Let $x is monthly charge.

The monthly charges for a basic cable plan = $78

it is given that it could differ by as much as $20

So, the maximum charges can be $78 + $20,

And, the minimum charges can be $78 - $20,

The value of x is lies from $78 - $20 to $78 + $20

Which can be written as:

78 - 20 ≤ x and x ≤ 78 + 20

-20 ≤ x - 78 and x - 78 ≤ 20

Change the sign of inequality if multiplying both side by minus.

20 ≥ -(x - 78) and x - 78 ≤ 20

⇒ |x - 78| ≤ 20

Thus, the required absolute inequality is |x - 78| ≤ 20.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x+x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (-3, -3) and (0, 3).

Calculate the slope:

[tex]m=\dfrac{3-(-3)}{0-(-3)}=\dfrac{6}{3}=2[/tex]

Put the value of the slope and the coordinates of the point (-3, -3) to the equation of a line:

[tex]y-(-3)=2(x-(-3))\\\\y+3=2(x+3)[/tex]

[tex]y=2x+3[/tex]

You are correct in selecting choice A as the answer.

You need the middle angles between the two pairs of given congruent sides, so that you can prove the triangles to be congruent through SAS. The vertical angle theorem is used in this case. Alternate interior angles only come from parallel lines, but we dont know if any of the lines are parallel. Even if we did know the lines were paralle, we still wouldn't use the alternate interior angle theorem.

The part that is necessary in Valerie's proof using SAS to prove ΔVWX ≅ ΔYZX  is prove that ∠VWX ≅ ∠YXZ by vertical angles.

The SAS(side angle side) theorem for congruent triangle states that If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

The side WX and XZ are congruent and VX and XZ are congruent . Then the included angles ∠VWX should be congruent to ∠YXZ. The both angles are vertically opposite angles. This can be represented with mathematical symbols below

WX≅XZ

VX ≅XZ

Therefore,

∠VWX ≅ ∠YXZ(vertically opposite angles)

Therefore, the necessary step in Valerie proof is Prove that ∠VWX ≅ ∠YXZ by vertical angles.

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[tex]\tan x=0[/tex] for [tex]x=n\pi[/tex], where [tex]n[/tex] is any integer. The inverse tangent function returns numbers between [tex]-\dfrac\pi2[/tex] and [tex]\dfrac\pi2[/tex]. The only multiple of [tex]\pi[/tex] in this range is 0, so [tex]\tan^{-1}0=0[/tex].

Then

[tex]\sin\left(\tan^{-1}0\right)=\sin0=\boxed0[/tex]

To evaluate sin(Tan^-10), we find that the angle whose tangent is 0 also has a sine of 0, thus the answer is 0.

The question asks to evaluate sin(Tan-10), which is essentially asking for the sine of the angle whose tangent is 0. We know that tangent is the ratio of sine to cosine, and when the tangent is 0, it means that the sine must be 0 as long as the cosine is not 0. Given that the cosine of 0 degrees (or 0 radians) is 1, and the sine of 0 degrees is 0, we can conclude that sin(Tan-10) is 0.

Answer:

[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Step-by-step explanation:

I'm going to write 105 as a sum of numbers on the unit circle.

If I do that, I must use the sum identity for sine.

[tex]\sin(105)=\sin(60+45)[/tex]

[tex]\sin(60)\cos(45)+\sin(45)\cos(60)[/tex]

Plug in the values for sin(60),cos(45), sin(45),cos(60)

[tex]\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\frac{1}{2}[/tex]

[tex]\frac{\sqrt{3}\sqrt{2}+\sqrt{2}}{4}[/tex]

[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Sin 105 degrees is equivalent to (√6 - √2) / 4.

The exact value of sin 105 degrees can be determined using trigonometric identities. Knowing that sin (90 + θ) = cos θ, we can rewrite sin 105 degrees as sin (90 + 15) degrees.

Applying the identity, sin (90 + 15) degrees equals cos 15 degrees.

Utilizing the trigonometric values of common angles, cos 15 degrees can be expressed as (√6 - √2) / 4.

This value is derived from trigonometric relationships, providing an exact representation of sin 105 degrees without resorting to decimal approximations.

Answer:

[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]

Step-by-step explanation:

[tex]\frac{(x-h)^2}{a^2}+\frac[(y-k)^2}{b^2}=1[/tex]

her center [tex](h,k)[/tex], and [tex]a[/tex] is the horizontal radius, and [tex]b[/tex] is the vertical radius.

So the center is [tex](h,k)=(0,0)[/tex].

[tex]a=5[/tex] because (5,0) has a distance of 5 from (0,0).

[tex]b=3[/tex] because (0,-3) has a distance of 3 from (0,0).

So the equation is:

[tex]\frac{(x-0)^2}{5^2}+\frac{(y-0)^2}{3^2}=1[/tex]

Simplifying a bit:

[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]

Final answer:

The equation of the ellipse with a vertex at (5,0) and a co-vertex at (0, -3) with the center at the origin is [tex]\(\frac{x^2}{25} + \frac{y^2}{9} = 1\).[/tex]

Explanation:

The equation of an ellipse in standard form with a center at the origin can be derived from its vertices and co-vertices. For an ellipse centered at the origin, the standard form of the equation is [tex]\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Given that one vertex is at (5,0), we can deduce that the semi-major axis a is 5. Since a co-vertex is at (0, -3), the semi-minor axis b is 3. Thus, the equation of the ellipse in standard form is [tex]\(\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1\), or \(\frac{x^2}{25} + \frac{y^2}{9} = 1\).[/tex]

The quadratic equation 12t^2 + 4t - 9 = 0 has a discriminant value of 448, which is greater than zero indicating two real solutions. These solutions are irrational given that the square root of the discriminant (448) is not a clean number, hence answer A. 2; irrational, is correct.

The quadratic equation in question is 12t² + 4t - 9 = 0. The discriminant (D) of a quadratic equation in the form at² + bt + c = 0 is defined as D = b² - 4ac. Use the values from your equation: a = 12, b = 4, and c = -9. Plugging these values into the formula gives D = 4² - 4*(12)*(-9) = 16 + 432 = 448.

The value of the discriminant determines the solutions of the quadratic equation. If D > 0, then there are two real solutions. If D = 0, then there's one real solution. If D < 0, then there are no real solutions. Here, we have that D = 448 which is greater than 0, hence, the quadratic equation has two real solutions.

The type of solutions depends on whether the square root of D is a rational or irrational number. The square root of 448 is not a clean number, meaning it's an irrational number. Therefore, the solutions are of an irrational type.

So, this quadratic equation has 2 solutions that are irrational meaning the correct answer is A. 2; irrational.

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The equation 12t^2+4t-9=0 has a. two irrational solutions.

To determine the number and type of solutions for the equation 12t^2+4t-9=0, we can use the discriminant formula.

The discriminant is found by calculating b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 12, b = 4, and c = -9. Substituting these values into the discriminant formula, we get b^2 - 4ac = (4)^2 - 4(12)(-9) = 16 + 432 = 448.

Since the discriminant (448) is positive, this means that the quadratic equation has two real solutions. The nature of these solutions can be determined by the discriminant as well. If the discriminant is a perfect square, the solutions are rational. If the discriminant is not a perfect square, the solutions are irrational.

In our case, the discriminant (448) is not a perfect square, so the solutions to the equation 12t^2+4t-9=0 are two irrational solutions. Therefore, the correct answer is a. 2; irrational.

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Use the substitution method

f(x)= 6x-4

f(8)= 6(8)-4

f(8)= 48-4

f(8)= 44

Answer is f(8)= 44

Answer:

Step-by-step explanation:

[tex]f(x)=6x-4\\\\\text{Put x = 8 to the equation:}\\\\f(8)=6(8)-4=48-4=44[/tex]

Answer:

=64 ft

Step-by-step explanation:

The wire, the pole and the flat surface form a right triangle with a base angle of 40°. The pole is the height of the triangle and is opposite the angle 40°.

Therefore we can use the trigonometric ratio -sine of the angle 40° -to find the height.

Sin∅ =opposite/hypotenuse

opposite=hypotenuse × sin∅

=100ft × Sin 40°

=64.28ft

≅64 ft

Answer:

the answer is D. all real numbers greater than or equal to 2.

Step-by-step explanation:

looking at the graph, half of a parabola is curved upwards, and will never stop going up. looking at (1, 2), the dot (instead of circle) indicates the range is greater than or equal to itself, which is 2.

Option: d is the correct answer.

  d.   all real numbers greater than or equal to 2

Domain of a function--

The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--

The range of  a function is the set of all the values which are attained by a function in it's defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2) )

            Hence, the range is: [2,∞)

Answer:

M=T = angle A

try it

then. find angle a the sum of palleogram is .... then 12+A=....

angle A=........

Answer:

If want just the approximated solutions in the interval from 0 to 360:

199.47

340.53

90

270

If you want all the approximated solutions:

199.47+360k

340.53+360k

90+360k

270+360k

Step-by-step explanation:

2 cos(x)+3 sin(2x)=0

First step: Use double angle identity for sin(2x). That is, use, sin(2x)=2sin(x)cos(x).

2 cos(x)+3*2sin(x)cos(x)=0

2 cos(x)+ 6sin(x)cos(x)=0

Factor the 2cos(x) out, like so:

2cos(x)[ 1  + 3 sin(x)]=0

In order for this product to be zero, we must find when both factors are 0.

2cos(x)=0         or     1+3sin(x)=0

Let's do 2cos(x)=0 first.

2cos(x)=0

Divide both sides by 2:

 cos(x)=0

So the x-coordinate is 0 on the unit at x=90 deg  and x=270 deg (in the first rotation).

Let's do 1+3sin(x)=0.

1+3sin(x)=0

Subtract 1 on both sides:

  3sin(x)=-1

Divide both sides by 3:

   sin(x)=-1/3

Unfortunately this is not on the unit circle so I'm just going to take sin^-1 or arsin on both sides (this is the same thing sin^-1 or arsin).

   x=arcsin(-1/3)=-19.47 degrees

So that means -(-19.47)+180 is also a solution so 19.47+180=199.47 .

And that 360+-19.47 is another so 360+-19.47=340.53 .

So the solutions for [0,360] are

199.47

340.53

90

270

If you want all the solutions just add +360*k to each line where k is an integer.

Answer:

95 degrees

Step-by-step explanation:

The sum of the two angles 10 and 7 must be 180 degrees, so 180-85 = 95 degrees.

Answer:

m∠7 = 95°

Step-by-step explanation:

From the figure attached,

Rails N and P are parallel and vertical post L works as transverse.

Therefore, by the property of parallel lines, sum of interior angles formed by the transverse are supplementary.

In other words, ∠7 and ∠10 are interior angles and both are supplementary angles.

m∠7 + m∠10 = 180°

Since m∠10 = 85°

m∠7 + 85 = 180

m∠7 = 180 - 85

m∠7 = 95°

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

(x - 4)(x + 3) = (x)(x) + (x)(3) + (-4)(x) + (-4)(3)

= x² + 3x - 4x - 12          combine like terms

= x² + (3x - 4x) - 12

= x² - x - 12

Answer:

Step-by-step explanation:

You have a dangling bracket. I'm not sure what to make of it. I will solve it as

(x - 4)(x + 3) if this is not correct, could you leave me a note.

x^2 + 3x - 4x - 12

x^2 - x - 12

If you meant

(x - 4(x + 3)) then it would be solved as

x - 4x - 12     combine the xs

-3x - 12

dangling brackets are to math what dangling modifiers are to English.

Running up a tree, I saw a squirrel.

If you mean anything but that you were running up a tree, the sentence is incorrect.

Answer:

x = 6, y = 9

Step-by-step explanation:

One of the properties of a parallelogram is

The diagonals bisect each other, hence

2x = y + 3 → (1)

2y = 3x → (2)

Rearrange (1) in terms of y by subtracting 3 from both sides

y = 2x - 3 → (3)

Substitute y = 2x - 3 into (2)

2(2x - 3) = 3x ← distribute left side

4x - 6 = 3x ( add 6 to both sides )

4x = 3x + 6 ( subtract 3x from both sides )

x = 6

Substitute x = 6 into (3) for value of y

y = (2 × 6) - 3 = 12 - 3 = 9

Hence x = 6 and y = 9

Answer:

[tex]35+50x\le 1325[/tex]

Step-by-step explanation:

So y=mx+b tells us the initial amount is b (also known as the y-intercept).

Anyways you have to pay a one time fee of 35 dollars and then it is 50 dollars per month.

Let x represent the number of months she goes to yoga.

If she goes 1 month it costs her 35+50.

If she goes 2 months it costs her 35+50+50 or just 35+50(2).

If she goes 3 months it costs her 35+50+50+50 or just 35+50(3).

If she goes x months it costs her 35+50x.

Now she only has 1325.

So we want the cost of her x months to be less than or equal to 1325 because she doesn't have more than that.

So we want [tex]35+50x\le 1325[/tex]

Answer:

C

Step-by-step explanation:

Since she want to use her savings of $1325 it means that that is all the money Abbey is going to use so it means that the $1325 is greater or equal to the money she can or is going to spend. There is a one time fee of $35 which is going to be added to it and a monthly fee of $50. Since you don't know how many months, it'll be replaced with an x. so the equation will be 35+50x≤$1325

Answer:

x² - 16 ⇒ (x + 4)(x - 4)

(2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1

(2x + 3y)² ⇒ 4x² + 12xy + 9y²

x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)

Step-by-step explanation:

* Lets explain how to solve the problem

# x² - 16

∵ x² - 16 is a difference of two squares

- Its factorization is two brackets with same terms and different

 middle signs

- To factorize it find the square root of each term

∵ √x² = x and √16 = 4

∴ The terms of each brackets are x and 4 and the bracket have

   different middle signs

∴ x² - 16 = (x + 4)(x - 4)

* x² - 16 ⇒ (x + 4)(x - 4)

# (2x + 1)³

- To solve the bracket we will separate (2x + 1)³ to (2x + 1)(2x + 1)²

∵ (2x + 1)² = (2x)(2x) + 2(2x)(1) + (1)(1) = 4x² + 4x + 1

∴ (2x + 1)³ = (2x + 1)(4x² + 4x + 1)

∵ (2x + 1)(4x² + 4x + 1) = (2x)(4x²) + (2x)(4x) + (2x)(1) + (1)(4x²) + (1)(4x) + (1)(1)

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 8x² + 2x + 4x² + 4x + 1 ⇒ add like terms

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + (8x² + 4x²) + (2x + 4x) + 1

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 12x² + 6x + 1

∴ (2x + 1)³ = 8x³ + 12x² + 6x + 1

* (2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1

# (2x + 3y)²

∵ (2x + 3y)² = (2x)(2x) + 2(2x)(3y) + (3y)(3y)

∴ (2x + 3y)² = 4x² + 12xy + 9y²

* (2x + 3y)² ⇒ 4x² + 12xy + 9y²

# x³ + 8y³

∵ x³ + 8y³ is the sum of two cubes

- Its factorization is binomial and trinomial

- The binomial is cub root the two terms

∵ ∛x³ = x and ∛8y³ = 2y

∴ The binomial is (x + 2y)

- We will make the trinomial from the binomial

- The first term is (x)² = x²

- The second term is (x)(2y) = 2xy with opposite sign of the middle

  sign in the binomial

- The third term is (2y)² = 4y²

∴ x³ + 8y³ = (x + 2y)(x² - 2xy + 4y²)

* x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)

Answer:

P(factor of 56)=5/8

P(multiple of 3)=1/4

Step-by-step explanation:

The positive factors of 56 are 1,2,4,7,8,14,28,56.

The factors of 56 on the spinner are 1,2,4,7, and 8.  There are 5 numbers there that are factors of 56.

There are 8 numbers to land on in all.

So the P(factor of 56)=5/8.

Multiples of 3 are 3,6,9,...

The multiples of 3 on the spinner on the board are 3 and 6.  There are 2 numbers there that are multiples of 3.

There are 8 numbers to land on in all.

So the P(multiple of 3)=2/8 which reduced to 1/4.  I divided top and bottom by 2.

Answer:

Answer:

Option B is correct.

Step-by-step explanation:

We will compare the interest earned by both.

Tasha: p = $5000

r = 6% or 0.06

n = 1

So, Amount after a year will be = = $5300

And amount the next year with p = 5300: 5300*1.06= $5618

Additional $5000 at 8%

Here the amount will be = =5400

Next year amount with p = 5400 : 5400*1.08 = $ 5832

Amount in total Tasha will have in 2 years = 5618+5832 = 11450

Thomas:

p = 10000

r = 7% or 0.07

n = 1

After a year the amount will be = =$10700

Amount Next year with p = 10700 : 10700*1.07 = $11449

*****Just after 1 year we can see that Tasha's total amount is high than Thomas. This means at the same consistent rate, each year Tasha's amount will always be higher than Thomas.

So, option B is correct. Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Answer:

B) Tasha’s investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Step-by-step explanation:

I just took the test on edge

Answer:

Step-by-step explanation:

Note. You should put the item you are trying to solve for in the numerator when using the sine law.

sin(x) / 15 = Sin 27 / 11

sin(x) = 15 * sin(27 / 11

sin(x) = 0.4539

sin(x) = 15 * 0.4539/11

sin(x)  = 6.809 / 11

sin(x) = 0.6191

x = sin-1(0.6191)

x = 38.3

Answer: its 38.2 :)

Step-by-step explanation:

Answer:

x-intercept equals 3

y-intercept equals 9

Step-by-step explanation:

we have

[tex]3x+y=9[/tex]

step 1

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation and solve for y

[tex]3(0)+y=9[/tex]

[tex]y=9[/tex]

The y-intercept is the point (0,9)

step 2

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

substitute in the equation and solve for x

[tex]3x+0=9[/tex]

[tex]x=3[/tex]

The x-intercept is the point (3,0)

therefore

x-intercept equals 3

y-intercept equals 9

Answer:

7, 3 and 0

Step-by-step explanation:

10, 3, 5, 7

Because the numbers are differ by prime numbers less than 10, i.e, the difference between the numbers are 7,5 and next will be 3.

8, 5, 4, 3.

The difference between the numbers are 3, 4 and similarly it will be differ by 5 which means next will be no. 3.

12, 6, 3, 0.

The numbers are differ by 6, 9 and next will be differ by 12 resulting the next no. 0.

Answer:

2/5, 8/20, 4/10,16/40

Step-by-step explanation:

40%

Percent means out of 100

40/100 = 4/10 = 2/5

Lets look at the choices

8/100 =4/50 =2/25  not equal

2/5  equal

8/20 = 4/10 =2/5 = equal

4/10 = 2/5 = equal

16/40 = 4/10 = 2/5 equal

Answer:

Second option.

Third option.

Fourth option.

Fifth option.

Step-by-step explanation:

In order to find equivalent fractions to 40%, you can:

- Write 40 as the numerator and 100 as the denominator and then reduce the fraction:

[tex]\frac{40}{100}=\frac{4}{10}=\frac{2}{5}[/tex]

- Multiply the numerator and the denominator of the fraction [tex]\frac{4}{10}[/tex] by 2:

[tex]\frac{4*2}{10*2}=\frac{8}{20}[/tex]

- Multiply  the numerator and the denominator of the fraction [tex]\frac{4}{10}[/tex] by 4:

[tex]\frac{4*4}{10*4}=\frac{16}{40}[/tex]

Answer:

C

Step-by-step explanation:

Given the roots of the polynomial are x = - 6, x = 1 and x = 4 the the factors are

(x + 6), (x - 1) and (x - 4)

The polynomial is the product of the factors, that is

f(x) = a(x - 1)(x - 4)(x + 6) ← a is a multiplier

let a = 1 and expand the first pair of factors

f(x) = (x² - 5x + 4)(x + 6)

     = x(x² - 5x + 4) + 6(x² - 5x + 4) ← distribute both parenthesis

     = x³ - 5x² + 4x + 6x² - 30x + 24 ← collect like terms

f(x) = x³ + x² - 26x + 24 → C

Answer:

x^3 + x^2 - 26x + 24.

Step-by-step explanation:

Knowing the roots we can immediately write it in factor form as follows:

f(x) = (x + 6)(x - 1)(x - 4).

Note that when  f(x) = 0 each of the factors can be zero and , for example, when  x + 6 = 0 then x = -6.

We now expand the  expression:

(x + 6)(x - 1)(x - 4)

= (x + 6)(x^2 - 4x - 1x + 4)

= (x + 6)(x^2 - 5x + 4)

= x(x^2 - 5x + 4) + 6(x^2 - 5x + 4)

= x^3 - 5x^2 + 4x + 6x^2 - 30x + 24    Adding like terms:

= x^3 + x^2 - 26x + 24.  (Answer).

Answer:

(x+16)^2=20^2+x^2

Step-by-step explanation:

Given there was no bending of the tree, the Pitagorean Theory would help finding the value of the trees hight.

x^2+32x+16^2=400+x^2

32x=(20-16)×(20+16)

x=144/32

x=4m and 50cm

Answer:

Step-by-step explanation:

Answer:

The correct answer is third option

1/√3

Step-by-step explanation:

From the figure we can see a right angled triangle ABC.

Right angled at C.

AB = 10

AC = 5

BC = 5√3

Points to remember

Tan θ = Opposite side/Adjacent side

To find the value of tan(B)

Tan B =  Opposite side/Adjacent side

 = AC/BC

 = 5/5√3

 = 1/√3

Therefore the value of tan(B) =  1/√3

Answer:

Option C is correct.

Step-by-step explanation:

tan (B) = Perpendicular / Base

For angle B:

Perpendicular = 5

Base = 5√3

tan (B) = Perpendicular / Base

tan (B) = 5/5√3

tan (B) = 1/√3

So, Option C is correct.

Answer:

[tex]3x^2 + 2x - 1 = 3(x-\frac{1}{3})(x+1)[/tex]

Step-by-step explanation:

Answer:

(3x-1)(x+1)

Step-by-step explanation:

I like to factor by grouping.

a=3

b=2

c=-1

To get those values I compared 3x^2+2x-1 to ax^2+bx+c.

Now our objective to help us factor this is:  Find two integers that multiply to be a*c and add up to be b.

a*c=3(-1)

b=2

Guess what? Our numbers are already visible to us; that doesn't always happen. However, a*c=3(-1) and b=2=3+(-1).

So we are going to replace our 2x with 3x+-1x or -1x+3x. Either one is fine; they are the same thing.

3x^2+2x-1

Replacing 2x with -1x+3x.

3x^2-1x+3x-1

Grouping first 2 terms together and grouping 2nd 2 terms together.

(3x^2-1x)+(3x-1)

Now we are going to factor each grouping.

x(3x-1)+1(3x-1)

Now notice we have two terms here x(3x-1) and 1(3x-1).  Both of these terms have a common factor of (3x-1).  We are going to now factor out (3x-1).

(3x-1)(x+1)