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3 years ago

Use the discriminant to determine which graph could represent the equation. y=x^2+4x+5

Mathematics

1 answer:

lidiya [134]3 years ago

5 0

ANSWER

See attachment.

EXPLANATION

The given function is

$y = {x}^{2} + 4x + 5$

When we compare this function to

$y = a{x}^{2} + bx + c$

We have a=1, b=4 and c=5

We put this inside the formula for the discriminant, which is

$D = {b}^{2} - 4ac$

$D = {4}^{2} - 4(1)(5)$

$D = 16 - 20 = - 4$

Since the discriminant is negative, the function has no x-intercepts.

The graph of this function is the one hanging in the air above the x-axis and opens upwards.

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Vladimir [108]

One third = two sixths

1/6 + 1/6 = 1/3

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3 years ago

Write the equation of a line:

yawa3891 [41]

a) Line parallel to the line 3x+5y=-10 is -6x-10y=9

b) Line parallel to the line 2y-4x=5 and which goes through the point

(3,7) is y= 2x-1.

c) Line perpendicular to the line 8x+6y=-1 and which goes through the

point (-2,1) is 4y= 3x+ 10

<h3>What is equation of line?</h3>

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.

a) Equation parallel to 3x+5y=-10 is

-6x-10y=9

So, it satisfies: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

b)given equation into the form of y=mx+c,

2y-4x=5

we can find the gradient of the line.

2y= 5+4x

y= $\frac{5}{2}$ + 2x

Hence, the gradient is 2.

As, Parallel lines have the same gradient

Thus the line would also have a gradient of 2.

Substitute m=2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x=3, y=7,

7= 2(3) +c

7= 6 +c

c=6-7

c= -1

So, equation of line be: y= 2x-1.

c) Given: 8x+6y=-1

6y= -1-8x

y= $\frac{-1}{6} -\frac{4}{3}x$

Hence, m= $-\frac{4}{3}$

We know, if two lines are perpendicular have m and m' as slope then,

m*m'=-1

$\frac{-4}{3} *m'=-1$

m'= $\frac{3}{4}$

Now, y= $\frac{3}{4}$ x +c

Put x= -1 and y=1

then, 1= $\frac{3}{4}$ (-2) + c

c= $\frac{5}{3}$

So, y= $\frac{3}{4}$ x + $\frac{5}{2}$

4y= 3x+ 10

Learn more about equation of line here:

brainly.com/question/14577230

#SPJ1

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3 years ago

In a recent international sport competition, the top 3 countries— Country A, Country B, and Country C— won a total of 134 medals

vlada-n [284]

Answer:

Country A = 85, Country B = 29, Country C = 20

Step-by-step explanation:

A+B+C=134 ----- eq(1)

B=C+9 ------------ eq(2)

A=36+B+C ------ eq(3)

By substituting eq(2) in eq(3), we get:

A=36+C+9+C

A=2C+45 ------- eq(4)

Now substituting eq(2) & eq(4) in eq(1), we get

2C+45+C+9+C=134

4C+54=134

4C=134-54

4C=80

C=20

Now putting the value of C in eq(2),

B=20+9

B=29

Substituting the value of B & C in eq(1), we get:

A+29+20=134

A+49=134

A=134-49

A=85

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3 years ago

Adm,Ming,and Clinton sold sandwiches in the ratio 4:7:3 to raise money for their scout troop.Ming sold 91 sandwiches. How may sa

bonufazy [111]

The ratio in which Adm, Ming and Clinton sold sandwiches = 4:7:3
Number of sandwiches sold by Ming = 91
Let us assume the common ratio to be = x
Then
7x = 91
x = 91/7
= 13
Then
The number of sandwiches sold by Adm = 4 * 13
   = 52
The number of sandwiches sold by Clinton = 3 * 13
      = 39
So
The total number of sandwiches
sold by Adm, Ming and Clinton = 52 + 91 + 39
      = 182.
So a total of 182 sandwiches were sold by Adm, Ming and Clinton.

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4 years ago

What is 105 rounded to the nearest hundred?

Kaylis [27]

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