Determine the exact value of k so that the quadratic function f(x) = x2 - kx + 5 has only one zero.

Answers

Answer 1

Answer: $f(x)=ax^2+bx+c\n\n\Delta=b^2-4ac\n\nif\ \Delta < 0-no\ zeros\nif\ \Delta=0-one\ zero\nif\ \Delta > 0-two\ zeros$

$f(x)=x^2-kx+5=0\n\na=1;\ b=-k;\ c=5\n\n\Delta=(-k)^2-4\cdot1\cdot5=k^2-20\n\none\ zero\ if\ \Delta=0\n\ntherefore\nk^2-20=0\ \ \ \ |add\ 20\ to\ both\ sides\n\nk^2=20\n\nk=\pm√(20)\n\nk=\pm√(4\cdot5)\n\n\boxed{k=-2\sqrt5\ or\ k=2\sqrt5}$

Answer 2

Answer: I like this question. When we factorise this question the brackets have to be identical.
5 has to be square rooted to become √5. From, FOIL we know that the last digit is times by the other last digit to find the 5, as our brackets are identical this number is the same. The square root of 5.
This number is doubled in identical brackets to find the middle number. so it is 2√5. As there is a minus number there the brackets are: (x-√5)(x-√5). Multiplying this out gives us: x²-2√5 x+5. k=2√5 (or -2√5, depending on if the minus is counted or not)

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Could anyone help with math?? Will up vote, thanks!If a cone-shaped vase can hold 45 cubic centimeters of water and has a radius of 2 centimeters, what is the height of the vase? Use 3.14 for pi. Round your answer to the nearest hundredth. 7.45 centimeters 10.75 centimeters 14.33 centimeters 22.50 centimeters

Find the value of 5 2^ 3.

Answers

$5* 2^3 = 5* (2* 2* 2) = 5 * 8 = \boxed{\bf{40}}$

A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like algebra or geometry. What are the correct values of a, b, c, d, and e?

a = 16, b = 29, c = 22, d = 30, e = 24

a = 29, b = 16, c = 30, d = 22, e = 24

a = 16, b = 29, c = 24, d = 22, e = 30

a = 29, b = 16, c = 24, d = 30, e = 22

Answers

Let x be the number of students that like both algebra and geometry. Then:

1. 45-x is the number of students that like only algebra;

2. 53-x is the number of students that like only geometry.

You know that 6 students do not like any subject at all and there are 75 students in total. If you add the number of students that like both subjects, the number of students that like only one subject and the number of students that do not like any subject, you get 75. Therefore,

x+45-x+53-x+6=75.

Solve this equation:

104-x=75,

x=104-75,

x=29.

You get that:

29 students like both subjects;
45-29=16 students like only algebra;
53-29=24 students like only geometry;
24+6=30 students do not like algebra;
16+6=22 students do not like geometry.

The correct choice is D.

It is very easy to find the values for a, b, c, d and e. All you have to do is use the Algebra vs. Geometry table to use the given values to find the rest. Please see attachment to see the table. For example if we want to find e we simply subtract 53 from 75. This way e = 22, then use this to find the next value which will be b.

The answer is:

a = 29, b = 16, c = 24, d = 30 and e = 22

I hope this helps, Regards.

Brian’s backyard is in the shape of a square. If the yard is 21 feet long, how much land does Brian’s backyard cover?Pleaseee helppp

Answers

Answer: 21 feet long

Could you please explain it?

Answers

Hello,
there are some words that I could not read. But:
I support evements are independants.
p(s)=0.2
p(l)=1-0.2=0.8 l=lose

1)0.8*0.2=0.16

2) 0.8²*0.2=0.128

3) 0.8^3*0.2=0.1024

4) 0.2*0.8^(n-1)

If angle A has a measurement of 42° and is complementary to angle B, what's the measure of angle B? A. 48°
B. 42°
C. 38°
D. 138°

Answers

The answer to the question is A. 48 degrees. In a complimentary angle, both of the angles have to add up to 90 degrees. For this case, with 42 degrees, the complimentary would be 48 degrees as they both add up to 90 degrees in the problem presented above.

Answer:

A:48

Step-by-step explanation:

True or False? 1. All real numbers are either rational or irrational?

2. Every real number can be represented as a decimal, and every decimal represents a real number?

Answers

"Every real number can be represented as a decimal, and every decimal represents a real number"

Every real number can be represented as a decimal --> True since non-terminating decimals are decimals too.

And every decimal represents a real number --> This is just the vice versa of the first statement. Hence true.

That's making the whole statement true.So both the statements are true.

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