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Determine which equation has exactly one real solution. PLS HELPP

sergey [27]

Answer:

b) $4x^2-12x+9=0$

Step-by-step explanation:

We can use the discriminant $b^2-4ac$ to determine how many real solutions a quadratic equation in the form $ax^2+bx+c=0$ has.

discriminant > 0 ⇒ 2 real solutions
discriminant = 0 ⇒ 1 real solution
discriminant < 0 ⇒ no real solutions

$5x^2+9x-4=0$

$b^2-4ac=9^2-4(5)(-4)=161 > 0\implies \textsf{2 solutions}$

$4x^2-12x+9=0$

$b^2-4ac=(-12)^2-4(4)(9)=0 \implies \textsf{1 solution}$

$-9x^2+6x+1=0$

$b^2-4ac=6^2-4(-9)(1)=72 > 0 \implies \textsf{2 solutions}$

$-2x^2-7=0$

$b^2-4ac=0^2-4(-2)(-7)=-56 < 0 \implies \textsf{no solutions}$

4 0

2 years ago

from a set of seven math books, nine science books, and five literature books, in how many ways can a student select two from ea

Over [174]

There are 7 math books, 9 science books and 5 literature books. Student has to select 2 books from each set.

This is a combination problem.

Number of ways to select 2 math books from 7 books = 7C2 = 21
Number of ways to select 2 science books from 9 books = 9C2 = 36
Number of ways to select 2 literature books from 5 books = 5C2 = 10

Total number of ways to select 2 books from each set = 21 x 36 x 10 = 7560 ways.

So there are 7560 ways to select 2 books from each set of seven math books, nine science books, and five literature books

6 0

3 years ago

Which expression models this phrase? 27 decreased by the difference of a number and 3 A. (n – 3) – 27 B. 27 – n + 3 C. 27 – (n –

inysia [295]

The answer is c because you have to say 27 minus the number minus 3

7 0

3 years ago

Read 2 more answers

Grace is an hourly employee, and the line that models her total pay in dollars

tresset_1 [31]

Answer: Hello mate!

if x is the amount of hours worked, 45 is the slope and the y intercept is 35.

A linear equation has the form of y = ax + b, where a is the slope and b is the y-intercept, then the equation that we have is:

y = 45*x + 35

this means that she wins $45 per hour, and has a plane amount of $35, indiferent of the amount of hours worked.

Then the correct answer is

C) Grace's wage is $45 an hour, and it appears that she received a signing bonus of $35.

5 0

3 years ago

Read 2 more answers

Let ABC be an isosceles triangle with AB = AC and ∠BAC=30°. Side AB and the median AD contain points Q and P respectively (point

Svet_ta [14]

Answer:

15°

Step-by-step explanation:

Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)

The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.

Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°. Angle PQC has the same measure as angle RQC, so is 15°.

Angle PQC is 15°.

5 0

3 years ago