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3 years ago

If x6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the

Mathematics

1 answer:

lys-0071 [83]3 years ago

5 0

Answer:

The discriminant is equal to zero

Step-by-step explanation:

If x=6 is the only x-intercept of the graph of a quadratic equation, the it means the quadratic equation has a repeated root.

When a quadratic equation has a repeated root, it means its discriminant is zero.

This means that

${b}^{2} - 4ac = 0$

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The solutions to the inequality y<-x+1 are shaded on the graph. Which point is a solution?

suter [353]

Answer:
B) (3, –2)

Explanation:
The inequality is y ≤ –x + 1
There are two ways to do this. You can try the four options by seeing where they lie on the graph, or by inputting them into the inequality and seeing if they check out. I am going to do a bit of both.

I know that the solution cannot have two positive coordinates because the first quadrant is not part of the solution, so I won't guess A or C.
I'll try (3, –2) (which is option B).
On the graph, (3, –2) is on the line, which means it is part of the solution because the line is solid and the inequality is a greater than or equal to sign.
Try it in the inequality:
y ≤ –x + 1
–2 ≤ –3 + 1
–2 ≤ –2 yes this checks out.

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3 years ago

Abby has 96 songs on her ipod on 8 playlists.if each playlist is the same lenght, how many songs are on each

Ludmilka [50]

12. CoryxKenshin! amazing YTer

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3 years ago

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Solve the system of equations using substitution method<br>x=y+2<br>x+2y=5<br>PLEASE HELP!!

nlexa [21]

Answer:

x=1

y=-1

Step-by-step explanation:

x = y+2

x+2y = 5

y+2 +2y = 5

3y +2 = 5

3y = 3

y=1

x=-1

6 0

3 years ago

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The circular base of a cone has a radius of 5 centimeters. The height of the cone is 12 centimeters, and the slant height is 13

shepuryov [24]

Answer:

Hence, the surface area of cone is:

282.6 cm^2 which is approx 283 cm^2.

Step-by-step explanation:

We are given:

The circular base of a cone has a radius of 5 centimeters.

i.e. r=5 cm.

The height of the cone is 12 centimeters

i.e. h=12 cm.

The slant height is 13 centimeters.

i.e. l=13 cm.

Now we know that the surface area(S.A.) of cone is given by:

$S.A.=\pi r(l+r)$

Hence by putting the value of l,r and π in the formula we get:

$S.A.=3.14\times 5\times (13+5)\\\\S.A.=15.7\times 18\\\\S.A.=282.6$

Hence the surface area of cone is 282.6 cm^2 which is approx 283 cm^2.

4 0

3 years ago

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Determine the length and midpoint of the segment whose endpoints are (–15, 9) and (–4, 11).

ch4aika [34]

$(-15,9) \\
x_1=-15 \\
y_1=9 \\ \\
(-4,11) \\
x_2=-4 \\
y_2=11 \\ \\
\hbox{the length:} \\
l=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(-4+15)^2+(11-9)^2}=\\
=\sqrt{11^2+2^2}=\sqrt{121+4}=\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5} \\ \\
\hbox{the midpoint:} (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) \\
\frac{x_1+x_2}{2}=\frac{-15-4}{2}=\frac{-19}{2}=-9.5 \\
\frac{y_1+y_2}{2}=\frac{9+11}{2}=\frac{20}{2}=10 \\
(-9.5,10)$

The length of the segment is 5√5, the midpoint of the segment is (-9.5,10).

6 0

3 years ago

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