Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.

What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?

Answers

Answer 1

The solution of the equation -x^2 + 2x + 3 = x^2 - 2x + 3 are the x-coordinates of common points on the graphs are x=0 and x=2.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

As we can see from the attached graph these graphs intersect at points (0,3) and (2,3).

The system of equation are;

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

So,

[tex]-x^2 + 2x + 3 = x^2 - 2x + 3 \\\\2x^2 - 4x = 0\\\\2x ( x - 2) = 0[/tex]

Then the solutions of the equation are x=0 and x=2.

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Trey Graphs The Equations Y = X2 + 2x + 3 And Y = X2 2x + 3 To Solve The Equation X2 + 2x + 3 = X2 2x
Answer 2

Answer:

0 and 2

Step-by-step explanation:

b on edge


Related Questions

what is the length of the base? help me please thank u ;)​

Answers

Answer:   26

=============================================================

Explanation:

a = 26 and b = 26 are the congruent legs

angle C = 60 degrees is between sides 'a' and b

c = unknown base which is opposite angle C

We'll use the law of cosines to find this missing side.

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 26^2 + 26^2 - 2*26*26*cos(60)

c^2 = 676

c = sqrt(676)

c = 26

It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.

---------------

Here's another way to see why we have an equilateral triangle.

The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180

x+x+60 = 180

2x+60 = 180

2x = 180-60

2x = 120

x = 120/2

x = 60

Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.

If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.

[tex] \textsf{let each of those angles measure ' x ' } [/tex]

[tex]\qquad \tt \rightarrow \:x + x + 60 = 180[/tex]

[ sum of all interior angles of a triangle ]

[tex]\qquad \tt \rightarrow \:2x + 60 = 180[/tex]

[tex]\qquad \tt \rightarrow \:2x = 180 - 60[/tex]

[tex]\qquad \tt \rightarrow \:2x = 120[/tex]

[tex]\qquad \tt \rightarrow \:x = \cfrac{120}{2} [/tex]

[tex]\qquad \tt \rightarrow \:x = 60 \degree[/tex]

Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.

henceforth, all its sides are equal to one another.

[tex]\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units[/tex]

Suzy invests $2,600 in an account that earns 2.3% annual interest, compounded continuously. What is the value of the account after 10 years? Round to the nearest dollar

Answers

Answer:

$3,272

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)

Given:

P = $2,600r = 2.3% = 0.023t = 10 years

Substitute the given values into the formula and solve for A:

[tex]\sf \implies A=2600e^{(0.023 \times 10)}[/tex]

[tex]\sf \implies A=2600e^{0.23}[/tex]

[tex]\implies \sf A=3272.360026...[/tex]

Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.

how to solved theses question (4.2×7)-10.4÷2²+2.9×3-6 explain​

Answers

Answer:

29.5

Step-by-step explanation:

Use PEDMAS

P - Paraenthesis

E -Exponents

D - Divsion

M - Multiplication

A and S - Addition and subtraction respectively.

First multiply 4.2 and 7 as they are inside the parenthesis

Then find 2² which 4

(4.2 *7) - 10.4 *2² + 2.9*3 - 6 = 29.4 - 10.4 ÷2² + 2.9*3 - 6   {Parenthesis}

                                              = 29.4 - 10.4÷4 + 2.9*3 - 6   {Exponents}

                                               = 29.4 - 2.6 + 2.9*3 - 6    {Division}

                                              = 29.4 - 2.6 + 8.7 - 6   {Multiplication}

                                              = 29.5

WILL GIVE BRAINLIEST!!!! *20 points*

Answers

Answer:

g(-0.0001) = -9

g(0.0001) = -1

g(0) = -1

g(9) undefined

Step-by-step explanation:

g(9) undefined .because the graph have an empty circle

at (9 , 0) which means g is not defined at 9.

Please help due tomorrow

What transformations could have been used to map ABCE onto A’B’C’D’E?

Answers

Answer: This looks like it is a reflection of the y-axis and then an enlarging dilation.

The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2

Answers

A function assigns the values. The inverse of the function in terms of the area will be b=(a/7)-5.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is,

The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2. Write a function in terms of area to find the length of the other side.

The given is the function of the area of the trapezoid, a(b)=14 x b+5/2.

The area of a trapezoid is given as,

Area = Height × [(Sum of parallel sides)/2]

The given function can be written in terms of area as,

[tex]a = 14\times \dfrac{(b+5)}{2}\\\\\dfrac{2(a)}{14} = b+5\\\\\dfrac{2(a)}{14} -5= b\\\\\dfrac{(a)}{7} -5= b[/tex]

Hence, the inverse of the function in terms of the area will be b=(a/7)-5.

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Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.

x + y = 3,500

x – y = 2,342

Answers

Answer: x = 2921, y = 579

Step-by-Step Explanation:

I am assuming that we just have to Solve for ‘x’ and ‘y’.

‘x’ = No. Of Contemporary Titles
‘y’ = No. Of Classic Titles

=> x + y = 3500 (Eq. 1)
=> x - y = 2342 (Eq. 2)

Adding Eq. 1 and Eq. 2, we get :-

2x = 3500 + 2342
2x = 5842
x = 5842/2
=> x = 2921

Therefore, x = 2921

Substitute value of ‘x’ in Eq. 1 :-

x + y = 3500
(2921) + y = 3500
y = 3500 - 2921
=> y = 579

Therefore, y = 579

Hence,
No. Of Contemporary Titles = 2921
No. Of Classic Titles = 579

Find the value of x ??
A. 31
B. 5
C. 11
D. 25

Answers

Answer: 11

Step-by-step explanation:

By the trapezoid midsegment theorem, x = (9+13)/2 = 11

Can someone answer this as soon as possible.

Answers

The second one because it seems like the one that makes sense the most

solution.
5(4x + 7)-2x = ________+ 21

Answers

Answer:

18x + 14

Step-by-step explanation:

First, we need to distribute the 5:

 5(4x + 7) - 2x = __ + 21

 20x + 35 - 2x = __ + 21

Now, we can combine like terms:

 20x + 35 - 2x  = ___ + 21

  18x + 35 = ___ + 21

> subtract 21 from both sides to isolate "___"

 18x + 35 = __ + 21

          -21             -21

18x + 14 = ___

now that we have a solution, we should check that it works:

5(4x + 7) - 2x = ____ + 21

5(4x + 7) - 2x = 18x + 14 + 21  

{simplify both sides:}

20x + 35 -2x = 18x + 35

18x + 35 = 18x + 35

(TRUE)


So, we know our solution is 18x + 14

hope this helps!!

30.
10 cm
O
7 cm
10 cm
4 cm
How many triangles are needed to draw the net of this object?

Answers

There are two triangles in the figure(triangular prism) option third is correct.

What is a triangular prism?

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

The complete question is:

How many triangles are needed to draw the net of this object?

4321

For the figure please refer to the attached picture.

As we can see in the figure we have given a triangular prism:

The triangular prism has two triangles.

A triangle for the base of the prism and a triangle for the top of the prism.

The lateral faces of the prism are rectangular.

Thus, there are two triangles in the figure(triangular prism) option third is correct.

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Need help simple explanation if possible

Answers

that’s correct answer is person is correct above

Answer: 21 sqrt(43)/43

Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43

Please mark my answer as brainliest if this helped you.

Dilate the figure by the scale factor. Then enter the new coordinates.
K= 2

Answers

Answer:

A(2, 8)

B(4, 4)

C(-4, 2)

Step-by-step explanation:

Multiply all the coordinates by 2

A circle inside of a square. The square has side lengths of 5 meters.
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.

Answers

Answer:

the area is 25/4 π

Step-by-step explanation:

diameter is 5 m

area will be 25/4π

Answer:

  17.9 m²

Step-by-step explanation:

The area of the deck is the difference between the area of the square and the area of the circular hot tub.

__

square area

The area of the square is given by the formula ...

  A = s² . . . . where s is the side length

For a side length of 5 m, the area is ...

  A = (5 m)² = 25 m²

circle area

The area of a circle is found from the formula ...

  A = (π/4)d² . . . . where d is the diameter

For a diameter of 3 m, the area is ...

  A = (π/4)(3 m)² = 9/4π m² ≈ 7.069 m²

deck area

The area of the deck is the difference between the square area and the circle area:

  deck area = 25 m² -7.069 m² ≈ 17.9 m²

The area of the deck surrounding the hot tub is about 17.9 m².

Find the length of side BC.
Give your answer to 3 significant figures.
C
A
71°
B

Answers

Answer:

BC ≈ 19.4 cm

Step-by-step explanation:

using the cosine ratio in the right triangle

cos71° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{6.3}{BC}[/tex] ( multiply both sides by BC )

BC × cos71° = 6.3 ( divide both sides by cos71° )

BC = [tex]\frac{6.3}{cos71}[/tex] ≈ 19.4 cm ( to 3 sig. figs )

Answer:

19.4°

Step-by-step explanation:

I put the image of how I did it if you don't understand let me know

In one class, homework is worth 10% of the final grade, each of 3 projects is worth 20%, and a final exam is worth 30%.
(a) If a student has an 81 homework average and a 95 on the first project, what is the student's grade at this point?
(b) If the same student from part (a) gets a 72 on the second project and a 71 on the third project, what is the lowest grade the student can get on the final exam to get an 80 overall in the course?
(a) The grade at this point is_____
(Simplify your answer. Round to the nearest tenth as needed.)
(b) The lowest possible grade is____
(Simplify your answer. Round to the nearest integer as needed.)

Answers

a) At this point, the grade is 27.1

b)  The lowest possible grade is 81

How to get the grades of the student?

a) At this point the student has 81 in homework and 95 on the first project.

Remember that the homework is worth 10% of the final grade, and each project is worth 20%, then at this point the final grade is:

F = 0.10*81 + 0.20*95 = 27.1

b) The student gets 72 on the second project and 71 on the third project, at this point the final grade is:

F = 27.1 + 0.20*72 + 0.20*71 = 55.7

Now the student wants to get a final grade of 80, then if we define x as the grade on the final exam (which is worth 30%) we must have that:

55.7 + 0.30*x = 80

Now we can solve this for x:

x = (80 - 55.7)/0.30 = 81

The lowest possible grade that he must get is 81.

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How tall is the tree?
5ft
35°
-20ft-
[? ]ft

Answers

Answer:

[tex]\boxed{\bf 19ft}[/tex]

Step-by-step explanation:

[tex]\bf tan\:\theta =\cfrac{opp}{adj}[/tex]

[tex]\bf tan(35^o)=\cfrac{x}{20}[/tex]

[tex]\bf 20\;tan (35^o)=x[/tex]

[tex]\bf 14ft=x[/tex]

The height of the tree:-

[tex]\bf x+5ft[/tex][tex]\bf 14ft+5ft[/tex][tex]\bf 19ft[/tex]

Answer:

19.00 ft to the nearest hundredth.

Step-by-step explanation:

tan 35 = h / 20

h = 20 tan 35

Now we add the man's height

Total height of the tree

=  20 tan 35 + 5

=  19.00 ft to the nearest hundredth.

Given that y varies directly as x², find the percentage increase in y when x doubles.

Answers

Answer:400%

Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)

Which is equivalent to 3√8* ?

O x √8^3
O 8 ^3/x
O 8 ^x/3
O 8^3x

Answers

Answer:

O 8 ^x/3

Step-by-step explanation:

Remember that :

[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]

………………………………

Then

[tex]\sqrt[n]{8^x} = (8^{x})^{\frac{1}{3}}[/tex]

      [tex]= 8^{x\times\frac{1}{3}[/tex]

      [tex]=8^{\frac{x}{3}[/tex]

What is the function written in vertex form? f(x) = 4(x 6)2 10 f(x) = 4(x 6)2 – 26 f(x) = 4(x 6)2 – 134 f(x) = 4(x 6)2 154

Answers

The required vertex form of the given equation is a) [tex]4(x-6)^2 +10[/tex] is correct

the function  [tex]y=4x^2+24x+154[/tex] is given,

What is vertex form?

vertex form of a equation [tex]y=ax^2+bx+c[/tex] is given by [tex]y=a(x-h)^2+k[/tex].

since [tex]y=4x^2+24x+154[/tex]
Now h = - b/2a

   h = -N

Now at x = 0
  k = 10
vector form can be given by  [tex]4(x+6)^2 +10[/tex]

The question is incomplete. The question could be:

what is the correct vertex form of equation [tex]y=4x^2+24x+154[/tex]?
a)[tex]4(x+6)^2 +10[/tex]
b)[tex]4(x-6)^2 -26[/tex]
c)[tex]4(x-6)^2 -134[/tex]
d)[tex]4(x-6)^2 +154[/tex]


Thus, the vector form of the given function is [tex]4(x+6)^2 +10[/tex]

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state one example of 2 numbers where the LCM of the 2 numbers is the product of those numbers. explain your answers​

Answers

Answer:

See below

Step-by-step explanation:

3 and 5     have a LCM of 15    which is  3 * 5

Need help (pic included)

Answers

Answer:

a = 1

Step-by-step explanation:

We have the expression:

12x² + ax - 20

3x + 4 is a factor. Therefore:

12x² + ax - 20 = (3x · 4x) + ax + (4 · (-5))

12x² + ax - 20 = (3x + 4)(4x - 5)

(3x + 4)(4x - 5) = (3x)(4x) + (3x)(-5) + (4)(4x) + (4)(-5)

= 12x² - 15x + 16x - 20 = 12x² + x - 20

a = 1

Other method:

12x² + ax - 20 = (3x + 4)(bx + c)

12x² + ax - 20 = (3x)(bx) + (3x)(c) + (4)(bx) + (4)(c)

12x² + ax - 20 = 3bx² + 3cx + 4bx + 4c

12x² + ax - 20 = 3b² + (3c + 4b)x + 4c

therefore

3b = 12

a = 3c + 4b

4c = -20

3b = 12 ⇒ b = 4

4c = -20 ⇒ c = -5

substitute to a:

a = 3 · (-5) + 4 · 4

a = -15 + 16

a = 1

Does this graph show a function? Explain how you know.

Answers

Answer:

No, the graph fails the vertical line test

Step-by-step explanation:

To determine if the graph is a function, we can use the vertical line test.

Use a vertical line, if the vertical passes through two or more points, the graph is not a function

Looking at the y axis ( which is a vertical line), it passes through two points

This means the graph is not a function

No, the graph fails the vertical line test

Polygon C and polygon D are similar. The perimeter of polygon C is 60 inches,
and the perimeter of polygon Dis 12 inches. If one side of polygon C is 4
inches, what is the length of the corresponding side in polygon D?
A. 0.3 in
OB. 20 in
OC. 4 in
OD. 16 in
k

Answers

Answer:

Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.

Step-by-step explanation:

Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.

Perimeter of polygon C = 60in

Perimeter of polygon D = 12in

Length of side of polygon C = 4in

Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.

First equation, 4n = 60

Second equation, xn = 12

Dividing second by first

(xn) / (4n) = 12 / 60

x / 4 = 1 / 5

x = 4 / 5 = 0.8in

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please answer I've got 10 mins
100 POINTS FOR BRAINLIEST

Determine if the two expressions are equivalent and explain your reasoning.
3(4n) + 2 + 6n and 13n + 2

Answers

Answer:

3(4n) + 2 + 6n

12n + 2 + 6n

12n + 6n + 2

18n + 2 is not equal to 13n + 2

hence both the expression are not equivalent

find the positive square root of 217.05 and 100.2001......with division method​

Answers

The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.

How to depict the square root?

It should be noted that square root is factor of a number that when multiplied by itself will give the original number.

In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.

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Write [tex]\frac{1}{22}[/tex] as a decimal, Also please include the working out plus anyone that includes other examples will be given brainlest!

Thank you!

Answers

Do long division (see the attachment).

[tex]\dfrac{1}{22}=0.04545\ldots=0.0\overline{45}[/tex]


In 1990, the average monthly bill for cellular telephone service was $80.90. From 1990-1997, the monthly bill decreased by 8.6% per year (in other words, each year the bill is 91.4% of
what is was the previous year (Source: Statistical Abstract of the United States).
Part a: Write a formula for the average monthly cellular telephone bill in terms of the year. Let n = 1 represent 1990.
Part b: What was the average monthly bill in 1993

Answers

A)The formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹

B)The average monthly bill in 1993 willl be $ 61.77

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.

The formula for the average monthly cellular telephone bill in terms of the year willl be,

A=P(R/100)ⁿ

A = 80.90(0.914)ⁿ⁻¹

The average monthly bill in 1993 is found as ;

n=4 for 1993

A=P(R/100)ⁿ

A = 80.90(0.914)³⁻¹

A=$ 61.77

Hence the formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹ and the average monthly bill in 1993 willl be $ 61.77.

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There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.

Answers

Answer:

11:12

Step-by-step explanation:

You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio

In ABC, CT is a median. What is the measure of AB?

Fill in the blank by enter in just a number for your answer.

Answers

Answer:

AB = 102

Step-by-step explanation:

the median CT bisects the side AB at T , then

BT = AT , that is

7x + 9 = 5x + 21 ( subtract 5x from both sides )

2x + 9 = 21 ( subtract 9 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

then

AB = 5x + 21 + 7x + 9 = 12x + 30 = 12(6) + 30 = 72 + 30 = 102

The measure of AB is 102.

How to estimate the measure of AB?

The median CT bisects the side AB at T, then

BT = AT

7x + 9 = 5x + 21

subtracting 5x from both sides of the equation, we get

2x + 9 = 21

subtract 9 from both sides, and we get

2x = 12

Divide both sides by 2, we get

x = 6

then, AB = 5x + 21 + 7x + 9

AB = 12x + 30

Substituting the value of x,

12x + 30 = 12(6) + 30

= 72 + 30

AB = 102

Therefore, the measure of AB is 102.

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