Find b and then solve the equation: d (b−5)x2−(b−2)x+b=0, if one of its roots is 1/2

Answer:

A. quadrilateral, parallelogram, rhombus

Step-by-step explanation:

Parallel sides are equal

Answer:1/3

Step-by-step explanation:

2/3*1/2=1/3

The area of a parking lot measuring 2/3 km long and 1/2 km wide is 1/3 km². This is found by multiplying the length by the width.

The question is asking for the area of a rectangular parking lot that measures 2/3 km long and 1/2 km wide. The formula for the area of a rectangle is length times width. Applying this formula, we multiply 2/3 km by 1/2 km.

It's important to remember that when multiplying fractions, you just multiply the numerators (top numbers) and the denominators (bottom numbers) separately. So, (2/3) x (1/2) = 2/6 km², which simplifies to 1/3 km².

So, the area of the parking lot is 1/3 km².

https://brainly.com/question/15218510

#SPJ3

x3 + 4x2 - 9x - 36

x2 (x + 4) - 9(x + 4)

(x2 - 9) (x + 4)

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

To determine when Tyron's savings will surpass Linda's, we can set up an inequality using their daily saving rates and the fact that Linda started 3 days earlier. Solving for the number of days Tyron needs to save, we find that Tyron will surpass Linda's savings after saving for 2 full days.

Linda and Tyron are saving money on a daily basis, but Linda started saving 3 days earlier than Tyron. To find out on which day Tyron's savings will be more than Linda's, we need to set up an equation.

Let's define x as the number of days after which Tyron starts saving. Since Linda starts 3 days earlier, she has been saving for x + 3 days by the time Tyron starts saving.

Linda's daily savings: $1.55
Tyron's daily savings: $3.90

 Linda's total savings after x + 3 days: $1.55(x + 3)
Tyron's total savings after x days: $3.90x

We want to find the value of x at which Tyron's total savings exceed Linda's, so we set up the inequality:
$3.90x > $1.55(x + 3)

Now, solve for x:

$3.90x > $1.55x + $4.65
$3.90x - $1.55x > $4.65
$2.35x > $4.65
x > $4.65 / $2.35
x > 1.978

Since x represents the number of days and we cannot have a fraction of a day in this context, x must be at least 2 days. Therefore, Tyron's savings will be more than Linda's after he has saved for 2 days.

For the last part, you have to find where [tex]f'(t)[/tex] attains its maximum over [tex]0\le t\le8[/tex]. We have

[tex]f'(t)=-6\sin3t+6\cos2t[/tex]

so that

[tex]f''(t)=-18\cos3t-12\sin2t[/tex]

with critical points at [tex]t[/tex] such that

[tex]-18\cos3t-12\sin2t=0[/tex]

[tex]3\cos3t+2\sin2t=0[/tex]

[tex]3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0[/tex]

[tex]\cos t(3\cos^2t-9\sin^2t+4\sin t)=0[/tex]

[tex]\cos t(12\sin^2t-4\sin t-3)=0[/tex]

So either

[tex]\cos t=0\implies t=\dfrac{(2n+1)\pi}2[/tex]

or

[tex]12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi[/tex]

where [tex]n[/tex] is any integer. We get 8 solutions over the given interval with [tex]n=0,1,2[/tex] from the first set of solutions, [tex]n=0,1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1+\sqrt{10}}6[/tex], and [tex]n=1[/tex] from the set of solutions where [tex]\sin t=\dfrac{1-\sqrt{10}}6[/tex]. They are approximately

[tex]\dfrac\pi2\approx2[/tex]

[tex]\dfrac{3\pi}2\approx5[/tex]

[tex]\dfrac{5\pi}2\approx8[/tex]

[tex]\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1[/tex]

[tex]2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7[/tex]

[tex]2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6[/tex]

The correct answer for part (d) is: The particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]5[/tex] units per time period.

To find when the particle is moving the fastest, we need to determine the time at which the velocity of the particle is maximized. The velocity of the particle is given by the derivative of the position function with respect to time. The position function is [tex]\( f(t) = 2 \cos(3t) + 3 \sin(2t) \)[/tex]. Differentiating this with respect to [tex]\( t \)[/tex] gives the velocity function:

[tex]\[ v(t) = \frac{d}{dt}(2 \cos(3t) + 3 \sin(2t)) = -6 \sin(3t) + 6 \cos(2t) \][/tex]

To find the maximum velocity, we need to find the critical points of the velocity function by setting its derivative equal to zero:

[tex]\[ \frac{d}{dt}(-6 \sin(3t) + 6 \cos(2t)) = -18 \cos(3t) - 12 \sin(2t) = 0 \][/tex]

Solving for [tex]\( t \)[/tex] in the interval [tex]\( 0 \leq t \leq 8 \)[/tex] will give us the times at which the velocity is maximized or minimized. Let's solve for [tex]\( t \)[/tex]:

[tex]\[ -18 \cos(3t) = 12 \sin(2t) \][/tex]

This is a transcendental equation and cannot be solved algebraically. We would typically use numerical methods or graphing to find the solutions. However, since we are given that the time when the particle is moving the fastest is [tex]\( t = 4.7 \)[/tex], we can assume that this is the time at which the velocity function reaches its maximum value.

Now, to find the speed at which the particle is moving the fastest, we evaluate the velocity function at [tex]\( t = 4.7 \)[/tex]:

[tex]\[ v(4.7) = -6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7) \][/tex]

Calculating the sine and cosine values and then substituting them into the equation will give us the maximum velocity. Since we are looking for the speed, which is the absolute value of the velocity, we take the absolute value of the result.

The speed is given by the magnitude of the velocity vector, so we have:

[tex]\[ |v(4.7)| = |-6 \sin(3 \cdot 4.7) + 6 \cos(2 \cdot 4.7)| \][/tex]

Evaluating this expression will give us the speed at which the particle is moving the fastest. The correct answer, rounded to the nearest integer, is [tex]\( 5 \)[/tex] units per time period, not [tex]\( -5 \).[/tex] The negative sign in the velocity does not affect the speed, as speed is a scalar quantity and is always positive.

Therefore, the particle is moving the fastest at [tex]\( t = 4.7 \)[/tex] with a speed of [tex]\( 5 \)[/tex] units per time period.

Answer:

1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) [tex]\pi=\frac{c}{d}[/tex], where c is the circumference of a circle and d is its diameter

(2) [tex]A=\pi r^2[/tex], where A is the area of a circle with radius r. To put it in terms of d, remember that a circle's diameter is simply twice its radius, or mathematically, (3) [tex]d=2r \rightarrow r=\frac{d}{2}[/tex].

We can rearrange equation (1) to put d in terms of π and c, giving us (4) [tex]d = \frac{c}{\pi}[/tex], and we can make a few substitutions in (2) using (3) and (4) to get use the area in terms of the circumference and π:

[tex]A=\pi r^2\\=\pi\left(\frac{d}{2}\right)^2\\=\pi\left(\frac{d^2}{4}\right)\\=\pi\left(\frac{(c/\pi)^2}{4}\right)\\=\pi\left(\frac{c^2/\pi^2}{4}\right)\\=\pi\left(\frac{c^2}{4\pi^2}\right)\\\\=\frac{\pi c^2}{4\pi^2}\\ =\frac{c^2}{4\pi}[/tex]

We can now substitute c for our circumference, 65, to get our answer in terms of π:

[tex]A=\dfrac{65^2}{4\pi}=\dfrac{4225}{4\pi}=1056.25\pi[/tex]

Answer:

Area = 2112.5 / pi

Step-by-step explanation:

They are asking you not to use 3.14 for pi. Just leave it as a symbol.

C = 2*pi*r

C = 65

65 = 2*pi*r

65/(2*pi) = r

The area of a circle is 2*pi * r^2

Area = 2 * pi * (65/2pi)^2

Area = 2 * pi * 65^2/(4*pi^2)           Cancel out one of the pi-s in the denominator

Area = 2 * 65^2 / (4 * Pi)                  Expand the numerator

Area = 8450/(4*pi)                           Divide by 4

Area = 2112.5 / pi

a. The series is

[tex]\displaystyle\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-4-\frac43-\frac4{3^2}-\frac4{3^3}-\cdots[/tex]

(first four terms are listed)

b. The series converges because this is a geometric series with [tex]r=\dfrac13<1[/tex].

c. Let [tex]S_N[/tex] be the [tex]N[/tex]-th partial sum of the series:

[tex]S_N=\displaystyle\sum_{n=1}^N-4\left(\frac13\right)^{n-1}[/tex]

[tex]S_N=-4-\dfrac43-\dfrac4{3^2}-\cdots-\dfrac4{3^{N-1}}[/tex]

Multiplying both sides by [tex]\dfrac13[/tex] gives

[tex]\dfrac13S_N=-\dfrac43-\dfrac4{3^2}-\dfrac4{3^3}-\cdots-\dfrac4{3^N}[/tex]

Subtracting this from [tex]S_N[/tex] gives

[tex]S_N-\dfrac13S_N=\dfrac23S_N=-4+\dfrac4{3^N}[/tex]

[tex]\implies S_N=-6+\dfrac6{3^N}[/tex]

As [tex]N[/tex] gets larger and larger [tex](N\to\infty)[/tex] the rational term converges to 0 and we're left with

[tex]\displaystyle\lim_{N\to\infty}S_N=\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-6[/tex]

Answer:

b.  (√15)/4

Step-by-step explanation:

Since Sin Ф = (opposite side)/Hypotenuse, we have 2 sides of a right triangle.  

Use Pythagorean theorem to solve for the missing leg (the adjacent side)

 1² + b² = 4²

    1 + b² = 16

            b² = 15

                 b = √15

So the adjacent side is √15, so Cos Ф = (√15)/4

Answer:

b. [tex]\frac{\sqrt{15}}{4}[/tex]

Step-by-step explanation:

Given that [tex]\sin(\theta)=\frac{1}{4}[/tex] where [tex]0\:<\: \theta \:<\:\frac{\pi}{2}[/tex].

Recall and use the Pythagorean Identity;

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

This implies that;

[tex](\frac{1}{4})^2+\cos^2(\theta)=1[/tex]

[tex]\frac{1}{16}+\cos^2(\theta)=1[/tex]

[tex]\cos^2(\theta)=1-\frac{1}{16}[/tex]

[tex]\cos^2(\theta)=\frac{15}{16}[/tex]

Take the square root of both sides;

[tex]\cos(\theta)=\pm \sqrt{\frac{15}{16}}[/tex]

[tex]\cos(\theta)=\pm \frac{\sqrt{15}}{4}[/tex]

Since we are in the first quadrant;

[tex]\cos(\theta)=\frac{\sqrt{15}}{4}[/tex]

The lateral area is the area not including the base.

You have 2 sides that are 6 x 8 = 48 x 2 = 96 square feet.

One side of 4 x 8 = 32 square feet

And the top triangle = 1/2 x 4 x 6 = 12 square feet.

For lateral area you would not include the triangle at the bottom ( base).

Total Lateral area = 96 + 32 + 12 = 140 square feet.

Parallel lines are lines that do not intersect each other at any point.

The correct definition of parallel lines is option A: 'Parallel lines are lines that do not intersect.' Parallel lines are two lines in a plane that do not intersect each other at any point, no matter how far they are extended.

https://brainly.com/question/7966281

#SPJ12

i think its 5x-15 OR -1x-15

You're answer to the following question: "Which Point Must be the Centre of the Circle?" Is C

Answer:

A

Step-by-step explanation:

To find the best equation, we simply substitute the values of a, b, and c into the given equations.

a = 21

b = 5

c = 36

[tex]a=\dfrac{7}{10}b\sqrt{c}[/tex]

[tex]21=\dfrac{7}{10}5\sqrt{36}[/tex]

[tex]21=\dfrac{7}{10}5(6)[/tex]

[tex]21=\dfrac{7}{10}30[/tex]

[tex]21=(0.7)30[/tex]

[tex]21=21[/tex]

Answer:

[tex]\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)[/tex]

Step-by-step explanation:

The given logarithmic expression is

[tex]log_{3}(x^4y)[/tex]

Recall and use the product property of logarithm: [tex]\log_a(MN)=\log_a(M)+\log_a(N)[/tex];

This implies that;

[tex]\log_{3}(x^4y)=\log_{3}(x^4)+\log_{3}(y)[/tex]

Recall again that; [tex]\log_a(M^n)=n\log_a(M)[/tex];

We apply this property to get;

[tex]\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)[/tex]

Answer:

The measure of angle R is [tex]22.62\°[/tex]

Step-by-step explanation:

we know that

In the right triangle PQR

The cosine of angle R is equal to divide the adjacent side angle R by the hypotenuse

so

[tex]cos(R)=\frac{QR}{PR}[/tex]

substitute the values

[tex]cos(R)=\frac{12}{13}[/tex]

[tex]<R=arccos(\frac{12}{13})=22.62\°[/tex]

see the attached figure to better understand the problem

Answer:

a:  That the mean weight of the trials is 10 kg

b:  See attached photo for work

Step-by-step explanation:

We want to see if the scale is weighing properly and are using a 10 kg weight to calibrate it.  That means our hypothesis test is that the mean weight of the trails (in this case 25) is 10 kg.

The hypothesis we will use are

H0:  µ = 10

Ha:  µ ≠ 10

The alternate hypothesis has a not equals to sign because if the scale weighs too much or to little, then it needs to be better calibrated, so it's a two tailed test.

The calibration of the scale follows a normal distribution.

The given parameters are:

[tex]\mathbf{\sigma = 0.200}[/tex]

[tex]\mathbf{\mu = 10}[/tex]

[tex]\mathbf{n = 25}[/tex]

[tex]\mathbf{\bar x = 9.85}[/tex]

(a) The null and the alternate hypotheses

The true average weight is to be tested.

So, the null and the alternate hypotheses are:

[tex]\mathbf{H_o: \mu = 10}[/tex]

[tex]\mathbf{H_a: \mu \ne 10}[/tex]

(b) The p-value when [tex]\mathbf{\bar x = 9.85}[/tex]

First, we calculate the test statistic

[tex]\mathbf{t = \frac{\bar x - \mu}{\sigma/\sqrt n}}[/tex]

So, we have:

[tex]\mathbf{t = \frac{9.85 - 10}{0.2/\sqrt{25}}}[/tex]

[tex]\mathbf{t = \frac{9.85 - 10}{0.2/5}}[/tex]

[tex]\mathbf{t = \frac{-0.15}{0.04}}[/tex]

[tex]\mathbf{t = -3.75}[/tex]

Using p-value calculator, we have:

[tex]\mathbf{p=0.000494}[/tex]

The critical regions of [tex]\mathbf{t = -3.75}[/tex] are t >2.797 and t < -2.797

Because -3.75 < -2.797, we reject the null hypothesis.

This means that, the scale needs to be calibrated

(c) Probability that recalibration is judged when [tex]\mathbf{\mu = 10.2}[/tex]

First, we calculate the test statistic

[tex]\mathbf{t = \frac{\bar x - \mu}{\sigma/\sqrt n}}[/tex]

So, we have:

[tex]\mathbf{t = \frac{9.85 - 10.2}{0.2/\sqrt{25}}}[/tex]

[tex]\mathbf{t = \frac{-0.35}{0.04}}[/tex]

[tex]\mathbf{t = -8.75}[/tex]

Using p-value calculator, we have:

[tex]\mathbf{p<0.00001}[/tex]

The probability that  recalibration is judged unnecessary is less than 0.00001

Read more about probabilities using test statistics at:

https://brainly.com/question/22783864

Answer:

158 square feet

Step-by-step explanation:

The surface area of a prism is found using the following formula: SA = 2(lh+lb+bh). This formula takes the area of each face (6 in total( and adds them together to find a total sum. Substitute l = 8, b = 3 and h = 5 to solve for the surface area.

SA = 2(lh+lb+bh)

SA = 2(8*5+8*3+3*5)

SA = 2(40 + 24 + 15)

SA = 2(79)

SA = 158

Answer: [tex]x=\frac{41}{10}[/tex]

Step-by-step explanation:

Descompose the denominators into their prime factors to calculate the Least Common Denominator (LCD):

[tex]5x=5*x[/tex]

[tex]2=2*x[/tex]

Choose the common and non-common numbers and varibles with the largest exponents and multiply them:

[tex]LCD=5*2*x=10x[/tex]

Divide eac originl denominator by the LCD and multiply the resul by each numerator. Then, make the addition and solve for x:

[tex]\frac{3(2)+7(5)}{10x}=1\\\\\frac{6+35}{10x}=1\\\\\frac{41}{10x}=1\\\\41=10x\\x=\frac{41}{10}[/tex]

Answer:

[tex]x=4.1[/tex]

Step-by-step explanation:

The given equation is;

[tex]\frac{3}{5x}+\frac{7}{2x}=1[/tex]

Multiply through by the Least Common Denominator which is [tex]-10x[/tex]

[tex]10x(\frac{3}{5x})+10x(\frac{7}{2x})=10x[/tex]

Cancel the common factors to obtain;

[tex]2(3)+5(7)=10x[/tex]

[tex]6+35=10x[/tex]

[tex]41=10x[/tex]

Divide by 10

[tex]x=\frac{41}{10}[/tex]

[tex]x=4.1[/tex]

Answer:

  an = 2(−4)^(n − 1); all integers where n ≥ 1

Step-by-step explanation:

The equation has the form ...

  an = a1(r)^(n-1) . . . . . where a1 is the first term and r is the common ratio.

The first term is given as 2, and the ratio will be the ratio of the first two terms:

  r = (-8)/(2) = -4

Terms are numbered starting with n=1, so the formula is ...

  an = 2(-4)^(n-1) for n≥1

Carol's total earnings can be calculated by adding up her net salary plus her taxes paid.                                              

So, Total earnings of Carol = 642.20 + 115.34 + 62.75 = $820.29

So, her hourly wage = [tex]\frac{820.29}{37} =22.17[/tex]

Hence, Carol's hourly wage is = $22.17                                                        

See the attached picture for the solution:

Answer:

Step-by-step explanation:

1/(1+sinθ) + 1/(1-sinθ)

= (1-sinθ)/[(1+sinθ)(1-sinθ)] + (1+sinθ)/[(1-sinθ)(1+sinθ)]

= [(1-sinθ) + (1+sinθ)] / [(1-sinθ)(1+sinθ)]

= [1 - sinθ + 1 + sinθ] / [1 - sin^2sθ]

= 2 / cos^2θ

Answer:

D) 59.8

Step-by-step explanation:

m<B = 120 deg

Since we know the measure of an angle and the length of the opposite side, we can establish the ratio of the law of sines, so we use the law of sines to find the length of side BA.

[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} [/tex]

[tex] \dfrac{\sin A}{BC} = \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB} [/tex]

[tex] \dfrac{\sin B}{AC} = \dfrac{\sin C}{AB} [/tex]

[tex] \dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB} [/tex]

[tex] \dfrac{\sin 120^\circ}{200} = \dfrac{\sin 15^\circ}{AB} [/tex]

[tex] (AB)\sin 120^\circ = 200 \sin 15^\circ [/tex]

[tex] AB = \dfrac{200 \sin 15^\circ}{\sin 120^\circ} [/tex]

[tex] AB = 59.8 [/tex]

In a system of equations, if the variable x is found to be equal to 2 and y is found to be equal to 4, the value of x - y is -2.

To solve for the values of x and y in this pair of linear equations, we can use a method known as substitution or elimination. However, the question asks for the value of x-y, not for the individual values of x and y.

First, let's multiply the first equation by 2 and the second equation by 3:

4x - 6y = -28 (equation 1)

9x - 6y = -18  (equation 2)

If we subtract Equation 2 from Equation 1, we get -5x = -10. Solving for x, we find that x = 2.

Substituting the value of x into the first equation, we get:

2(2) - 3y = -14

Solving for y, we find that y = 4.

Therefore, x - y = 2 - 4 = -2.

https://brainly.com/question/21620502

#SPJ6

Answer:

B. (0, 3)

Step-by-step explanation:

Trying the offered solutions in the given equations gets you there pretty quickly.

7·(-6) -2(3) ≠ -6 . . . eliminates choice A

__

7·0 -2·3 = -6

8·0 +3 = 3 . . . . . . . choice B is the solution

Answer:

(0,3)

B is correct

Step-by-step explanation:

Given: The system of equation.

[tex]7x-2y=-6[/tex]

[tex]8x+y=3[/tex]

Now, we solve for x and y using elimination method.

Elimination method: In this method to make the coefficient of one variable same and then cancel out by addition of both equation.

Multiply 2nd equation by 2 and we get

[tex]16x+2y=6[/tex]

[tex]7x-2y=-6[/tex]

Add both equation and eliminate y

[tex]23x=0[/tex]

[tex]x=0[/tex]

Put x=0 into 1st equation, 7x-2y=-6

7(0) - 2y = -6

           y = 3

Solution: x = 0 and y = 3

Hence, The solution of the equation would be (0,3)

➷ There is only one '3' on the cube

Therefore, it would be B. 1/6

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Factor out the common term 6

6(x^2 - 11x + 24) = 0

Factor x^2 - 11x + 24

6(x - 8)(x - 3) = 0

Solve for x;

x = 8,3

Answer:

6

Step-by-step explanation:

***If choosing one of each, this is the answer*** This wasn't clearly asked for in the question though

When counting the number of arrangements of multiple choices, multiply the number of choices of each item together.

(3)(2)(1) = 6

Here is them listed..

Green ball 1, red ball 1, white ball

Green ball 1, red ball 2, white ball

Green ball 2, red ball 1, white ball

Green ball 2, red ball 2, white ball

Green ball 3, red ball 1, white ball

Green ball 3, red ball 2, white ball

Answer:

The statement is false.

Step-by-step explanation:

When you are looking at used cars, you should only look at local lots and newspapers - This statement is false.

When you are buying a used car, you should look not only in the local lots and newspapers but also online ans various used cars websites.

You can also personally visit the used car market to get wide range of cars and various comparative prices.

Answer:

the the third graph

Step-by-step explanation:

this is because the third graph shows a correlation of the time and when the rainfall in a proporational relesho=inshop

Answer:

the third graph :)

Step-by-step explanation:

each hour the rain is increasing by 2 drops.

Answer:

Part B. see the procedure

Part C. see the procedure

Step-by-step explanation:

we have

[tex]f(x)=x^{2}+2x+1[/tex] -----> equation A

[tex]g(x)=3-x-x^{2}[/tex] -----> equation B  

Part B. Solve the system algebraically

equate the equation A and the equation B

[tex]x^{2}+2x+1=3-x-x^{2}[/tex]

[tex]2x^{2}+3x-2=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}+3x-2=0[/tex]

so

[tex]a=2\\b=3\\c=-2[/tex]

substitute in the formula

[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4a(2)(-2)}} {2(2)}[/tex]

[tex]x=\frac{-3(+/-)\sqrt{25}} {4}[/tex]

[tex]x=\frac{-3(+/-)5} {4}[/tex]

[tex]x1=\frac{-3(+)5} {4}=0.5[/tex]

[tex]x2=\frac{-3(-)5} {4}=-2[/tex]

Find the values of y

For x=0.5

[tex]f(0.5)=0.5^{2}+2(0.5)+1=2.25[/tex]

For x=-2

[tex]f(-2)=(-2)^{2}+2(-2)+1=1[/tex]

the solutions are the points

(0.5,2.25) and (-2,1)

Part C. Solve the system by graph

using a graphing tool

we know that

The solution of the non linear system is the intersection point both graphs

The intersection points are (0.5,2.25) and (-2,1)

therefore

The solutions are the points (0.5,2.25) and (-2,1)

see the attached figure