At which points are the equations y = x2 3x 2 and y = 2x 3 approximately equal?

Answers

Answer 1

The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. 

 we have

 y = x² + 3x + 2   .............(a)

 y = 2x + 3    ...................(b)

To solve the system of equations equate equation A to equation B

  x² + 3x + 2 = 2x + 3

 Group terms that contain the same variable

   x² + 3x + 2 - 2x - 3 = 0

  x² + x - 1 = 0

The formula to solve a quadratic equation of the form ax² + bx+ c  is equal to

     in this problem we have

       x² + x - 1 =0

 so,   a= 1

        b = 1

        c = -1

substitute in the formula

  x = -1 ± √1² - 4(1)(-1)/2(1)

  x = -1 ±√5/2

  x = -1+√5/2 = 0.618

   x = -1 - √5/2  =  - 1.618

  Find the values of y

 for  x = 0.618

    y = 2(0.618) + 3 = 4.236

  for  x = - 1.618

   y = 2(-1.618) + 3  = -0.236

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The complete question is -

At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?


Related Questions

Willow has a board that is 10 feet long. She needs to cut the board into equal pieces that are 1/3 feet long.

How many pieces can she cut?

Answers

Answer:

12

Step-by-step explanation:

6^7/6^5 in index form

Answers

Answer:

[tex]6^{2}[/tex]

Step-by-step explanation:

When dividing numbers with same bases with indices this is the rule:

[tex]\frac{x^{y}}{x^{z} } =x^{y-z}[/tex]

So the answer is:

[tex]6^{7-5} = 6^{2}[/tex]

10) En un triángulo rectángulo ABC, B es un ángulo
recto y m < A = 23° (medida del ángulo A). Si el
lado opuesto al ángulo A mide 17cm ¿Cuánto
mide la hipotenusa?

Answers

Answer:

140

Step-by-step explanation:

Primera tienes que sumar 23 y 17 despues tienes que buscar la differencia de 180 y 40.

The average weekly salary of two employees is $5350. One makes $250 more than the other. Find their salaries.
One employee makes $
and the other makes $?

Answers

Answer:

g

Step-by-step explanation:

g


Complete the table with values for x or y that make this equation true : 3x+y=15.

Answers

Answer:

Step-by-step explanation:

So first, with the given table you need to "plug-in" the numbers that are there for x and y.

Ok, for example 2 is listed in the "x" row. So plug it 2 for "x":

3x+y=15

3(2)+y=15

6+y=15

-6      -6

y=9

So do this for all of them...the same goes with all of the values...just plug in one, complete the steps then you'll get the answer for the other variable.

Hope this helps!

Answer is in the attachment. A graph and a filled in table.

Step by step

I graphed the line and found the matching x and y points. Example, given x=2 on the table, find x =2 and find where y crosses, that’s your y value of 9. Next is a y=3, find that point on the graph, where does the line cross for x? At x=4. Continue with the remainder numbers on the table. Graph all the points.


Table as follows

2 4 6 0 3 5 2.3333
_________________________
9 3 -3 15 6 0 8

To indirectly measure the distance across a river, Houa stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Houa draws the diagram below to show the lengths and angles that she measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

Answers

According to the Houa's drawing the distance across the river PR is

198.95 feet

How to measure the distance PR

The length of line PR is calculated using the knowledge of similar triangles

While similar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent.

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shown, the pair of equivalent sides are

PO and OC, PR and RE,

The solution is worked out using sides PO and OC, PR and RE,

PO / OC = PR / RE

let PR be equal to y such that PO = 140 + y

(140 + y) / 230 = y / 135

cross multiplying

135(140 + y) = 230y

Expanding

18900 + 135y = 230y

collecting like terms

18900 = 230y - 135y

95y = 18900

y = 198.95 feet

Hence PR = 198.95 feet

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Solve the proportion.
8 / 3 = g / 3
a. 1 / 8
b. 9 / 8
c. 8
d. 8 / 9

Answers

g equals 8 the bottom 3’s cancel out so your left with g=8

What additional information would be necessary to determine sin A?

Answers

We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.

We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.

Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent

We must now locate a side opposing the angle A or the hypotenuse.

As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.

Finally, the length of BC is required because it is the side opposite A.

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The complete question should be like:

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.

In altitude BH and angle bisector AL intersect at point M. Given m∠HML = 100° and m∠MLC = 110°. Find angles of △ABC

Answers

The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.

Given that:

[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]

Since, BH is the altitude [tex]\angle MHC= 90[/tex].

The total angle of a quadrilateral is 360, hence:

100 + 110 + 90 + C = 360

C = 60 degrees.

Now consider triangle BHC:

The sum of angle of a triangle is 180, hence:

90 + 60 + B = 180

B = 30

Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].

Consider triangle ABC:

Using sum of triangles, we have:

[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]

Hence the measure of angles of triangle ABC is 60 degrees.

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Find the greatest common factor of $144$ and $405$.

Answers

Answer:The answer to your question is 9

Evaluate the expression: 15(6 – 4)


WILL MARK BRAINLIEST

Answers

Answer:

30

Step-by-step explanation:

15(6 – 4)

=15(2)

=30

Answer:

larespuesta a conseguir sería 86

what is the correct value of 3x + 2 for x = 5?

Answers

Answer:

17

Step-by-step explanation:

3x + 2

x = 5

3x + 2

3(5) + 2

15 + 2

17

[tex]\boxed{The\:value\:of\:3x\:+\:2\:for\:"x\:=\:5"\:is\:17.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]3x + 2 \\ = 3(5) + 2 \\ = 3 \times 5 + 2 \\ = 15 + 2 \\ = 17[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

I need help for number 2

Answers

The measure of the exterior angle for Object 1 - a decagon is 36°, while th measure of the exterior angle for Object 2  - a dodecagon is 30°.

What is a Decagon and a Dodecagon?

n object with 12 sides is called a dodecagon while an object with 10 sides is called a decagon.

Note that the exterior angles of all shapes, regular or irregular is 360°. In this case, the shapes are regular, which means that the sides are equal, hence their angles will be equal.

To derive the exterior angle of a regular geometric shape, the formula is given as:

Exterior angle measure = 360 / number of sides

Hence for A (the decagon), we have:

EAM = 360/10

= 36°

For B (the dodecagon) we have:

EAM = 360/12

= 30°

Thus the exterior angle for both shapes are 36° and 30° respectively.

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Quadrilateral ABCD is similar to quadrilateral A'B'C'D'. Write 2 equations that could be used to solve for missing lengths?

Answers

2 equations that could be used to solve for missing lengths are:

[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]

Now, According to the question:

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

Quadrilateral ABCD is similar to quadrilateral A'B'C'D'.

ABCD ~ A'B'C'D'

So,

[tex]\frac{AB}{A'B'} = \frac{BC}{B'C'}\\ \\ \frac{CD}{C'D'} = \frac{AD}{A'D'}[/tex]

Hence,  2 equations that could be used to solve for missing lengths are:

[tex]\frac{AD}{A'D'} = \frac{BC}{B'C'}[/tex]

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What is 200/51 equal to

Answers

Answer:

Approx 3.92

Step-by-step explanation:

Simplify the polynomial.
3x2 – 2x + 4x2 – X+X

Answers

Answer:

[tex]7x^{2} - 2x[/tex]

Step-by-step explanation:

combine like terms. not trying to be mean, but that all you have to do.

Answer:

14-2x

Step-by-step explanation:

collect like terms

3×2+4×2-2x-x-x

6+8-2x

=14-2x

8⁶ ÷ 8?
can yall help me my brains gone dead ​

Answers

Answer:

32768

Step-by-step explanation:

8^6 is 262144, divide by 8. Your answer is 32768

Answer:

32768

Step-by-step explanation:

8 to the power of 6 is 262144

262144 divided by 8=32768

also invite me to ur brains funeral

i need help PLEASE DONT GIVE ME THE BITLY LINKS

Answers

Answer:

610

Step-by-step explanation:

area of triangle is A=0.5*h*b

a=0.5*20*(8+8+15)

a=310

area of square=lh

a=15*20

a=300

300+310=610

If you have 10 friends and make two equal teams, what fraction do you use?

Answers

10/2 is the correct answer

Pls solve this 15 points

Answers

Answer:

128

Step-by-step explanation:

1/3base area×height

PLEASE ASAP ILL GIVE BRAINLIEST.

Answers

Answer:

The first law of motion

Step-by-step explanation:

y 65° 25
can someone solve this ? ​

Answers

Answer: a=25

Explanation: I am assuming you are looking for “a” so if you heard the method of 45, 45, 90 it helps you solve it. So by the 45 being across from 25 makes the 45 across a 25 as well, hope this was what you were looking for…

A store that specializes in shipping packages reports that the distribution of packages shipped during the winter holidays is normally distributed with a mean of 4. 5 pounds with a standard deviation of 1. 8 pounds


What is the probability that two randomly selected packages are both more than 4. 5 pounds? (assume the packages are independent of each other)

a. ) 0. 5

b. ) 1

c. ) 0

d. ) 0. 25

Answers

The correct option is option (d).

To solve this problem, we need to find the probability that two randomly selected packages are both more than 4.5 pounds. Since the distribution is normal, we can use the standard normal distribution table to find the probability.

The first step is to standardize the weight of the packages by subtracting the mean from the weight and dividing it by the standard deviation. The weight of 4.5 pounds is the mean, so the standardized weight is (4.5 - 4.5) / 1.8 = 0.

The probability that a package weighs more than 4.5 pounds is the same as the probability that a standardized package weighs more than 0. This probability is equal to 1 - P(Z < 0) , where Z is the standardized weight.

Using a standard normal distribution table, we find that P(Z < 0) = 0.5. Therefore, the probability that a package weighs more than 4.5 pounds is 1 - 0.5 = 0.5.

Since the two packages are independent, we can find the probability that both packages are more than 4.5 pounds by multiplying the probability of one package being more than 4.5 pounds by itself. So, the probability that two randomly selected packages are both more than 4.5 pounds is 0.5 * 0.5 = 0.25.

In conclusion, the probability that two randomly selected packages are both more than 4.5 pounds is 0.25

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PLEASE HELP SOON

1. Solve the system. 3x+y = 10 y = 6x+1 Enter your answer by filling in the blanks. The solution is ( , )

2. Solve the system. 6x - y = -15 x + 2y = 17 Enter your answer as a coordinate pair in the blank.

Answers

Answer:

1. ( 1,7)

2. (17, 39)

Step-by-step explanation:

1.  Replace all occurrences of y with 6x+1, and we get

9x + 1 = 10

x = 1

y = 6x + 1

y = 7

So, the answer for number 1 is (1,7)

2. 6x - y = -15x + 2y = 17

We subtract 2y and get

6x - 3y = 15x = 17

Replace all occurrences of x with 17, and we get

102 −3y = −15

x = 17

y = 39

So, the answer for number 2 is (17, 39)

Write a recursive formula for an,the nth term of the sequence 125, -25, 5, ...

Answers

Recursive formula for a(n) , the nth term of the sequence is

⇒ a(n) = 125 × (5)ⁿ⁻¹

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

We have to given that;

The sequence is,

⇒ 125, - 25, 5 , ....

Clearly, The sequence is a geometry sequence with common ratio - 5 and first term 125.

We know that;

The nth term of geometry sequence is,

⇒ a(n) = a rⁿ⁻¹

Where, 'r' is common ratio and 'a' is first term of the sequence.

Substitute all the values, we get;

The nth term of the given sequence is,

⇒ a(n) = a rⁿ⁻¹

⇒ a(n) = 125 × (5)ⁿ⁻¹

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A vegetable store sold 3 fewer tons of vegetables on the first day than on the second, and on the third day it sold 5 9 of the amount sold in the first two days. How many tons of vegetables did the store sell on each of the days if it sold a total of 98 tons of vegetables on those three days

Answers

On solving the provided question, we can say that by equation

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

What is equation?

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).

[tex]x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882[/tex]

solution

[tex]x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35[/tex]

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

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28.2, 27.22, 27.62 , 27.54 , 27.5 in Greatest to Least

Answers

Answer:

28.2, 27.63, 27.54, 27.5, 27.22

Answer: 28.2, 27.62,27.5,27.22

Step-by-step explanation:

Mai bought some party supplies from an online store. For shipping, the shop charges a flat fee of $7.95 or 6.25% of the total purchase, whichever is greater. Suppose Mai's total purchase is $128. How much shipping will she pay?

Answers

Answer:

8

Step-by-step explanation:

if we do 128+7.95 we get 135.95. but when we do 128+8(wich is 6.25% of 128) we get 136. so she will pay 8 dollars in shipping

Hope this helps.

(i) Write 3^-2 as a fraction
(ii) Find the value of 3X^0 when X=5

Answers

ans Is here i) 1/9

ii) 3

tq brainlest?

Simplify the expression. (-3+ 4n²) - (5 - 2n²)

Answers

Answer:

2(3n^2-4) and 6n^2-8

Step-by-step explanation:

There are two different answers but try at least both of them.

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