please help :(

Determine the number of solutions for the quadratic function f(x) = 3x^2 + 5x + 10.

Answers

Answer 1

Answer:

0 real solutions

Step-by-step explanation:

I guess you are looking for the number of real solutions? Correct me if I'm wrong.

There is something called the discriminant that can help us determine this without actually solving f(x)=0 for x.

The discriminant is the thing inside the square root in the quadratic formula.

It is the thing that reads b^2-4ac.

If b^2-4ac:

A) is negative, then you have 0 real solutions (you could say 2 complex solutions)

B) is positive, then you have 2 real solutions

C) is 0, then you have 1 real solution

So comparing 3x^2+5x+10 to ax^2+bx+c, you should see that a=3, b=5, and c=10.

b^2-4ac

=5^2-4(3)(10)

=25-120

=-95

That is a negative result so you have no real solutions.


Related Questions

Three vertices of a square are (–1, 2), (2, 2), and (2, –1).

What is the fourth vertex of the square?


(–1, –1)


(–1, –2)


(2, 1)


(5, 1)


Question 5
Three vertices of a square are (–1, 2), (2, 2), and (2, –1).

What is the fourth vertex of the square?


(–1, –1)


(–1, –2)


(2, 1)


(5, 1)

Answers

Answer:

(-1,-1)

Step-by-step explanation:

The square needs to be all side with the same value when you graph the vertices on x-y plot, you obtain (x is the dot that correspond a vertice and y the forth vertice )

                            x       2 |                        x

                                      1 |

                                       |                                  

      -2                  -1         |          1              2

                            y        -1|                       x

                                     -2 |

If you draw a line between vertices the value it will be 2 +  (-1) so the forth vertice has to be (-1,-1)

convert -3 degree to farenheit ​

Answers

Answer:

26.6 degrees

Step-by-step explanation:

Use the converting formula:

(-3°C × 9/5) + 32 = 26.6°F

-3 degrees to Fahrenheit would be 26.6

The formula is attached in the image below

-3 × 1.8 = -5.4

-5.4 + 32 = 26.6

The function whose graph is shown below has the following characteristics.

•Two relative minima

•Two relative maxima

○True
○False​

Answers

True true true true true true tr

Answer with explanation:

A function is said to attain maximum in the interval , if you consider any two points on the curve suppose (a,b) and (c,d)

if , c>a

Then , f(d) > f(a).

A function is said to attain minimum in the interval,

if ,c>a

Then,f(d)< f(a).

A function can have more than one relative Maximum and more than one relative Minimum.

The function whose graph is given here has following Characteristics

    •Two relative minima

     •Two relative maxima

is True .

Find the value of x in the picture please

Answers

Answer:

Option B. The value of x is 20

Step-by-step explanation:

we know that

The intersecting chords theorem  states that the products of the lengths of the line segments on each chord are equal.

so

In this problem

[tex](x)(x-11)=(x-8)(x-5)\\x^{2}-11x=x^{2}-5x-8x+40\\-11x=-13x+40\\2x=40\\x=20[/tex]

PLEASE HELP

A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

Answers

Answer:

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct

Step-by-step explanation:

step 1

Find the area of the base of the rectangular pyramid

we know that

The volume of the rectangular pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of the pyramid

we have

[tex]V=40\ units^{3}[/tex]

[tex]H=6\ units[/tex]

substitute and solve for B

[tex]40=\frac{1}{3}B(6)[/tex]

[tex]120=B(6)[/tex]

[tex]B=120/6=20\ units^{2}[/tex]

step 2

Find the volume of the rectangular prism with the same base area and height

we know that

The volume of the rectangular prism is equal to

[tex]V=BH[/tex]

we have

[tex]B=20\ units^{2}[/tex]

[tex]H=6\ units[/tex]

substitute

[tex]V=(20)(6)=120\ units^{3}[/tex]

therefore

The rectangular prism has a volume that is three times the size of the given rectangular pyramid. Shannon is correct

Answer:

C

Step-by-step explanation:

Got it right one the test! <3

Match the expression with its name.
10x2 – 5x + 10

quadratic trinomial

cubic monomial

not a polynomial

fourth-degree binomial

Answers

Answer:

[tex]\large\boxed{10x^2-5x+10\ -\ \bold{quadratic\ trinomial}}[/tex]

Step-by-step explanation:

[tex]\text{quadratic trinomial}\ -\ ax^2+bx+c\\\\\text{cubic monomial}\ -\ ax^3\\\\\text{not a polynomial}\ -\ \dfrac{a}{x}\\\\\text{fourth-degree binomial}\ -\ ax^4+bx[/tex]

[tex]10x^2-5x+10\\\\\text{the highest power of variable (x) is 2}\to \boxed{x^2}\ \to\ \bold{quadratic}\\\\\text{polynomial has 3 terms}\ \to\ \boxed{10x^2,\ -5x,\ 10}\ \to\ \bold{trinomial}[/tex]

19. x² + x = 6
the graf
Factors:
Solution(s):

Answers

For this case we must factor the following equation:

[tex]x ^ 2 + x-6 = 0[/tex]

We must find two numbers that, when multiplied, obtain -6 and when summed, obtain +1. These numbers are: +3 and -2

So, we have to:

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

The roots are:

[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]

ANswer:

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


The first diagram shows an equilateral triangle and a
square with the same side length S. Find the area of the
triangle Ar in terms of the area of the square As

Answers

Answer:

Ar = ¼√3 As

Step-by-step explanation:

Area of an equilateral triangle is:

Ar = ¼√3 s²

Area of a square is:

As = s²

Substituting:

Ar = ¼√3 As

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. solve for x and match the solutions

Answers

The solutions to the linear equations in variable x and unknown constant [tex]\alpha[/tex] are [tex]\frac{-\alpha}{6}[/tex], [tex]\frac{3}{\alpha}[/tex] and [tex]\frac{-6}{\alpha}[/tex].

What is a linear equation?

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

We are given linear equations in variable x with an unknown constant [tex]\alpha[/tex] and we have to solve for x.

[tex]4 = \frac{6}\alpha}x + 5\\\\\frac{6}{\alpha}x = - 1\\\\x = \frac{-\alpha}{6}[/tex].

[tex]7 + 2\alpha{x} = 13.\\\\2\alpha{x} = 6.\\\\x = \frac{3}{\alpha}[/tex]

[tex]-\alpha{x} - 20 = -14.\\\\-\alpha{x} = 6.\\\\x = \frac{-6}{\alpha}[/tex]

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Given the following coordinates complete the reflection transformation. A(−5,0) B(−3,3) C(−3,0) Transformation: Complete the double reflection over the lines x=−2 followed by x=1. A"( , ) B"( , ) C"( , )

Answers

Answer:

A''(1,-1) B''(3,2) C''(3,2)

Step-by-step explanation:

A(−5,0) B(−3,3) C(−3,0)

reflection over x=-2

Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 3,1 and 1

after reflections, the perpendicular distance will be 6,2,2, and the points will be at

A'(1,0) B'(−1,3) C'(−1,0)

again  reflection over x=1

Perpendicular distance between points y-coordinates of points (A', B' and C') and y=1 are 0,2,2

after reflections, the perpendicular distance will be 0,4,4 and the points will be at

A''(1,-1) B''(3,2) C''(3,2)!

Which product is equivalent to 25x2 – 16?

Answers

Answer:

The correct answer would be 34

Step-by-step explanation:

When solving an expression, we would first solve the operator with the highest precedence. In mathematics, there are four basic operators. Addition, subtraction, multiplication and division. The precedence of Division and multiplication is higher than the precedence of Addition and subtraction. So by solving this with the precedence, we would first solve the multiplication operator which is 25 * 2, it will give 50, then we will subtract 16 from it like 50-16, which will give us 34.

Answer:

(5x+4)(5x-4)

Step-by-step explanation:

The product expression can be obtained by factorizing the expression 25x²-16 provided in the question.

The expression is a difference of two squares whose factors are generally

(a-b)(a+b)

√25x² is 5x

√16 is 4

Therefore the product required is (5x+4)(5x-4)

25x²-16 is equivalent to (5x+4)(5x-4)

What value of b will cause the system to have an infinite
number of solutions?
у= 6x –b
—3х + 1/2y=-3

a) 2
b) 4
c)6
d)8

Answers

Answer:

Option C) b=6

Step-by-step explanation:

we know that

If two linear equations of a system of equations have an infinite of solutions, then both equations are identical

we have

[tex]y=6x-b[/tex] -----> equation A

[tex]-3x+(1/2)y=-3[/tex]

Multiply by 2 both sides

[tex]-6x+y=-6[/tex]

Adds 6x both sides

[tex]y=6x-6[/tex] ------> equation B

equate equation A and equation B

[tex]6x-b=6x-6[/tex]

solve for b

[tex]b=6[/tex]

Solve (x + 2<5) n (x-7>-6).
{x11 {x1x < 3 or x> 1)
{all real numbers)

Answers

For this case we must solve [tex]x + 2 <5[/tex]intersected with [tex]x-7> -6[/tex]

So, we have:

[tex]x + 2 <5\\x <5-2\\x <3[/tex]

The solutions are given by all strict minor numbers to 3.

[tex]x-7> -6\\x> -6 + 7\\x> 1[/tex]

The solutions are given by all the major strict numbers to 1.

If we intersect the solutions of both equations we have [tex]x <3[/tex] ∩ [tex]x> 1[/tex].

The intersection is given by [tex]1 <x <3[/tex]

Answer:

 The solution interval is (1,3)

What are the coordinates of point C on the directed segment from A (-8,4) to B (10,2) that partitions the segment such that AC:CB is 2:1?

Answers

Final answer:

To find the coordinates of point C, divide the x- and y-coordinates of AB in the ratio 2:1.

Explanation:

To find the coordinates of point C, we can use the concept of dividing a line segment in a given ratio. Given that AC:CB is 2:1, we can divide the x- and y-coordinates of the line segment AB in the same ratio.

The x-coordinate of point C is calculated by dividing the difference between the x-coordinates of points A and B by the sum of the ratio (2+1).

The y-coordinate of point C is calculated by dividing the difference between the y-coordinates of points A and B by the sum of the ratio (2+1).

Therefore, the coordinates of point C are (-2, 3).

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The correct option is d. [tex]\((4, 0)\)[/tex]. The coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].

To find the coordinates of point [tex]\(C\)[/tex] that partitions the segment [tex]\(AB\)[/tex] in the ratio [tex]\(AC:CB = 2:1\)[/tex], we use the section formula. Given points [tex]\(A(x_1, y_1)\)[/tex] and [tex]\(B(x_2, y_2)\)[/tex] with a ratio [tex]\(m:n\)[/tex], the coordinates [tex]\((x, y)\)[/tex] of the point dividing the segment in the ratio [tex]\(m:n\)[/tex] are given by:

[tex]\[x = \frac{mx_2 + nx_1}{m + n}, \quad y = \frac{my_2 + ny_1}{m + n}\][/tex]

For this problem:

- [tex]\(A(-8, 4)\)[/tex]

- [tex]\(B(10, -2)\)[/tex]

- Ratio [tex]\(m:n = 2:1\)[/tex]

Plugging in the values:

[tex]\[x = \frac{2 \cdot 10 + 1 \cdot (-8)}{2 + 1} = \frac{20 - 8}{3} = \frac{12}{3} = 4\][/tex]

[tex]\[y = \frac{2 \cdot (-2) + 1 \cdot 4}{2 + 1} = \frac{-4 + 4}{3} = \frac{0}{3} = 0\][/tex]

Thus, the coordinates of point [tex]\(C\)[/tex] are [tex]\((4, 0)\)[/tex].

The complete question is:

What are the coordinates of point C on the directed segment from A(−8,4) to B(10,−2) that partitions the segment such that AC:CB is 2:1 ?

A. (1,1)

B. (−2,2)

C. (2,−2)

D. (4,0)

Find the value of y.

Answers

Answer:

The answer should be the last one.

Step-by-step explanation:

Answer:

=2√2 the fourth choice.

Step-by-step explanation:

We can use the Pythagoras theorem to calculate the value of y.

a²+b²=c²

a=1

b=y

c=3

Therefore substituting for the values in the theorem above we get:

1²+y²=3²

Leave y on one side.

y²=3²-1²

y²=9-1

y²=8

y=±2√2 in surd form.

Since we expressing length, a scalar quantity, we take the modulus of our answer. Thus y=2√2

Complete the table for the given rule. Rule: y=X/4(fraction)
Table
X Y
4
2
9
What would X be i am really confused here does the fraction mean divide the numbers or something else

Answers

The complete table of values for the equation y = x/4 is

x   4   2  9

y  1   1/2  9/4

Completing the table of values for the equation

From the question, we have the following parameters that can be used in our computation:

y = x/4

The missing y values are at x = 4, 2 and x = 9

Substitute the known values in the above equation, so, we have the following representation

y = 1/4 * 4 = 1

y = 1/4 * 2 = 1/2

y = 1/4 * 9 = 9/4

So, the missing values are 1, 1/2 and 9/4

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Final answer:

The rule 'y = X/4' describes division of X by 4 to find Y. The student completes the table by dividing each X value by 4 to find the corresponding Y values, providing an organized data set.

Explanation:

The student is asking about the operation indicated by the rule y = X/4, which involves division. The fraction bar signifies division. Given this rule, we can complete the table for y when x-values are provided.

For x = 4: y = 4/4 = 1

For x = 2: y = 2/4 = 0.5

For x = 9: y = 9/4 = 2.25

To organize the data in the table, you simply divide the x-value by 4 to find the corresponding y-value.

why does 7 9/7 = 8 2/7?

Answers

Firstly see what they are in mixed fraction form:

[tex]7 \frac{9}{7} = \frac{58}{7} [/tex]

therefore, 7 9/7 is equal to 58/7

[tex]8 \frac{2}{7} = \frac{58}{7} [/tex]

One triangle has the hypotenuse of 26 and the shortest side is 10, what is the other side?

a. 22
b. 25
c. 24
d. 23

Answers

Answer:

C. 24

Step-by-step explanation:

In a right triangle, the sum of the squares of the two legs of the triangle is equivalent to the square of the  hypotenuse.

a²+b²=c²

a=10

b=?

c=26

Let us substitute with the values given in the question.

10²+b²=26²

100+b²=676

b²=676-100

b²=576

b=√576

=24

The other leg of the triangle is 24 units long.

Answer: option c.

Step-by-step explanation:

You need to use the Pythagorean Theorem. This is:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" and "c" are legs of the triangle.

In this case you know that:

[tex]a=26\\b=10[/tex]

Then, you need  to substitute values into  [tex]a^2=b^2+c^2[/tex] and then solve for "c".

So, this is:

[tex]26^2=10^2+c^2\\\\26^2-10^2=c^2\\\\576=c^2\\\\\sqrt{576}=c\\\\c=24[/tex]

plz help me plz plz plz

Answers

Answer:

195

Step-by-step explanation:

9 times 10 is 90 and 7 times 15 is 105  

so 105+90=195

Answer:

195 cm

Step-by-step explanation:

The area of ABCD is 195 cm.

Multiply the sides together:

9 ⋅ 10 = 90

7 ⋅ 15 = 105

Add them together:

105 + 90 = 195

Therefore, the area of ABCD is 195 cm.

solve 2/5+1/4+7/10= in simplest form

Answers

Answer:

1.35 or 27/20

Step-by-step explanation:

(2/5) + (1/4) + (7/10)

= 0.4 + 0.25 + 0.7

= 1.35 or 27/20

27/20 (decimal 1.35)

what is equivalent to 10/10^3/4

Answers

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\\\ ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{10}{10^{\frac{3}{4}}}\implies \cfrac{10^1}{10^{\frac{3}{4}}}\implies \cfrac{10^{\frac{4}{4}}}{10^{\frac{3}{4}}}\implies 10^{\frac{4}{4}}\cdot 10^{-\frac{3}{4}}\implies 10^{\frac{4}{4}-\frac{3}{4}}\implies 10^{\frac{1}{4}}\implies \sqrt[4]{10}[/tex]

A box can hold 24 crayons. How many boxes must be used to put all of Mr.Syed's 98 crayons into boxes?

Answers

Answer:

5 boxes

Step-by-step explanation:

Given:

Total crayons : 98

Capacity of each box : 24

Number of boxes of 24 crayons needed to hold 98 crayons,

= 98 ÷ 24

= 4.08 boxes.

However since we cannot have 0.08 of a box, we must round this up to the next larger whole number of boxes.

4.08 rounded up to next whole number = 5

Hence he will need 5 boxes to hold all 98 crayons

5. Divide 98 by 24 and you’ll get 4.08. Since you need to put all of them into boxes, you have to round that up to the next whole number.
98/24= 4 r2
So it’s be four full boxes and one with two and four plus one is five

If f(x) = 5x, what is f^-1(x)?
o f^-1(x) = -5x
o f^-1(x)= -1/5x
o f^-1(x) = 1/5x
o f^-1(x) = 5x

Answers

Answer:

Third choice

Step-by-step explanation:

They are asking us to find the inverse of y=5x. To do this you just switch x and y and then remake y the subject of the equation (solve for y.)

y=5x

x=5y (I switch x and y)

x/5=y ( I divided both sides by 5)

Then you just replace y with the f^-1(x) thing

f^-1(x)=x/5

or

f^-1(x)=1/5x

If f(x) = 5x, then the inverse of the function, f⁻¹(x) is x/5.

Given that :

f(x) = 5x

Let y = f(x).

So, y = 5x

Now, interchange the values for x and y.

Then,

x = 5y

Now, solve for y.

Divide both sides of the equation by 5.

x/5 = y

So, the inverse of the function is x/5.

Hence f⁻¹(x) = x/5.

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What is the distance between the points (2, 8) and (-7, -4) in the coordinate plane?​

Answers

This is the possible answer and if my answer is wrong then the formula i used is absolutly right so you may proceed.

The distance between the points (2, 8) and (-7, -4) is 15 units.

Using the distance formula derived from the Pythagorean theorem, the distance between the points (2, 8) and (-7, -4) is found to be 15 units.

The distance between two points in the coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. For points (2, 8) and (-7, -4), the distance can be calculated as follows:

Subtract the x-coordinates: 2 - (-7) = 9.Subtract the y-coordinates: 8 - (-4) = 12.Square each result: 92 = 81 and 122 = 144.Add the squares together: 81 + 144 = 225.Take the square root of the sum: \\sqrt{225}\ = 15.

Therefore, the distance between the points (2, 8) and (-7, -4) is 15 units.

Find the formula for (f + g)(x) and simplify your answer.

f(x) = 3x and g(x) =
[tex] \sqrt{x - 4} [/tex]

Answers

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


Prove that the diagonals of a rectangle bisect each other.

The midpoint of AC is _____

Answers

Answer:

answer is a,b

Step-by-step explanation:

I have answered ur question

The mid-point of AC is (a, b). So, option D is correct. In a rectangle, the two diagonals bisect each other at their mid-point.

How to prove that the diagonals of a rectangle bisect each other?Find the mid-points of both the diagonals of the rectangleMid-point = ((x1+x2)/2, (y1+y2)/2)If the midpoints of both the diagonals are the same then they are said to bisect each other. If they are not the same, then they are not bisecting each other.

Calculation:

The given rectangle is ABCD

Its vertices have coordinates as

A - (0, 0)

B - (0, 2a)

C - (2a, 2b)

D - (2a, 0)

The diagonals are AC and BD.

Finding their mid-points:

Mid-point of the diagonal AC = ((0 + 2a)/2 , (0 + 2b)/2)

⇒ (2a/2, 2b/2)

⇒ (a, b) ... (1)

Mid-point of the diagonal BD = ((0 + 2a)/2, (2a+0)/2)

⇒ (2a/2, 2b/2)

⇒ (a, b)  ...(2)

From (1) and (2), the midpoints of both the diagonals are equal. So, the diagonals of the rectangle ABCD bisect each other.

Hence, proved.

Therefore, the mid-point of the diagonal AC is (a, b).

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What is the range of the given function?
{(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)}
{x|x = -5, -4,-2, 0, 2)
{yly = -9, -3, 0,5,7)
{x|x= -9,-5, 4, -3, -2, 0,2 5,7}
{yly = -9, -5, -4 -3 -2,0, 2, 5, 7}

Answers

Step-by-step explanation:

range is all the y values

{y|y=-9, -3, 0, 5, 7}

The range of a function are all the ys included in the graph. In this case that would be:

(-2, 0), (-4,-3), (2, -9), (0,5), (-5, 7)

Remember to order it from least to greatest:

{yly = -9, -3, 0,5,7}

Hope this helped!

~Just a girl in love with Shawn Mendes

Which table contains the vertex of the graph represented by y=x^2-6x+4?


A
x y
-2 20
0 4
2 -4
4 -4


B
x y
-1 11
1 -1
3 -5
6 4


C
x y
-3 31
-1 12
0 4
2 12


D
x y
0 5
2 7
3 5
5 7


Answers

Answer:

Table B

Vertex is (3,-5)

Step-by-step explanation:

We are given with an equation of a parabola [tex]y=x^2-6x+4[/tex]

Let is convert it into standard form of a parabola

[tex]y=x^2-6x+4[/tex]

adding and subtracting 9 in the right hand side of the =

[tex]y=x^2-6x+9-9+4[/tex]

[tex]y=x^2-2\times 3\times x+ 3^2-9+4[/tex]

the first three terms of the right hand side forms the expression of square of difference

[tex]a^2-2 \times a \times b+b^2 = (a-b)^2[/tex]

Hence

[tex]y=(x-3)^2-5[/tex]

adding 5 on both sides we get

[tex](y+5)=(x-3)^2[/tex]

Comparing it with the standard equation of a parabola

[tex]X^2=4\times \frac{1}{4} \times Y[/tex]

where [tex]X=x-3[/tex] and [tex]Y=y+5[/tex]

The vertex of [tex]X^2=4\times \frac{1}{4} \times Y[/tex] will be (0,0)

and thus vertex of

[tex](y+5)=(x-3)^2[/tex] will be (3,-5)

Hence the Table B is our right answer

Complete the table for the given rule y=6x-4

Answers

Answer:

1 = 2

3 = 14

10 = 56

Step-by-step explanation:

y = 6x - 4

y = 6 - 4

y = 18 - 4

y = 60 - 4

Step-by-step explanation:

In first there is 2

ln second there is 14

ln third there is 56

I hope this is right answer!

which equation represents the data in the table? check all that apply

Answers

Answer:

[tex]y-6=-\frac{5}{4}(x+2)[/tex]

[tex]y-1=-\frac{5}{4}(x-2)[/tex]

[tex]y-3.5=-1.25x[/tex]

Step-by-step explanation:

step 1

Find the slope of the linear equation

with the points (-2,6) and (2,1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{1-6}{2+2}[/tex]

[tex]m=-\frac{5}{4}[/tex]

step 2

Find the equation of the line into point slope form

The equation of the line in slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{5}{4}[/tex]

1) with the point (-2,6)

substitute

[tex]y-6=-\frac{5}{4}(x+2)[/tex]

2) with the point (2,1)

substitute

[tex]y-1=-\frac{5}{4}(x-2)[/tex]

3) with the point (0,3.5)

substitute

[tex]y-3.5=-\frac{5}{4}(x-0)[/tex]

[tex]y-3.5=-\frac{5}{4}x[/tex] -------> [tex]y-3.5=-1.25x[/tex]

Answer:

A, D, E

Step-by-step explanation:

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