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WINSTONCH [101]
1 year ago
11

6. Using the discriminant, determine the value of k that will give 1 solution (i.e. discriminant equals zero) y = kx²-4x + 4 ​

Mathematics
1 answer:
Gwar [14]1 year ago
4 0

Answer:

k = 1

Step-by-step explanation:

<u>Discriminant</u>

b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0

\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}

\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}

\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}

As we need to determine the value of k that will give <u>one solution</u>, set the <u>discriminant to zero</u>.

<u>Given equation</u>:

y=kx^2-4x+4

Therefore:

  • a = k
  • b = -4
  • c = 4

Substitute these values into the discriminant and solve for k:

\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}

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2. Name the numerator and the denominator in each fraction.
marishachu [46]

Answer:

Step-by-step explanation:

a.11/12 =11 is numerator and 12 is denominator

b.7/512 =75 is numerator and 512 is denominator

c.12/10 = 12 is numerator and 10 is denominator

d0/78 = 0 is numerator and 78 is denominator

point to remember : In fraction,upper part is always numerator and down part is denominator.

6 0
2 years ago
Josh has 4 times as many pears as leya, who has one half as many pears as amy. If josh has 32 pears how many does amy have?
arlik [135]
<h3>The number of pears Amy has is 16.</h3>

Step-by-step explanation:

Let J represent the number of pears Josh has.

Let L represent the number of pears Leya has.

Let A represent the number of pears Amy has.

From the question given above,

Josh (J) = 4 × Leya (L)

J = 4L ....... (1)

Leya (L) = ½ × Amy (A)

L = ½A ........ (2)

Next, we shall determine the number of pears Leya has. This can be obtained as follow:

From equation 1

J = 4L

But

Josh (J) = 32 pears

Thus,

32 = 4L

Divide both side by 4

L = 32 / 4

<h3>Leya (L) = 8 pears </h3>

Finally, we shall determine the number pears Amy has. This can be obtained as follow:

From equation 2

L = ½A

But

Leya (L) = 8 pears

Thus,

8 = ½A

Cross multiply

A = 8 × 2

<h3>Amy (A) = 16 pears </h3>

Therefore, Amy has 16 pears.

Learn more: brainly.com/question/20971657

6 0
2 years ago
Read 2 more answers
Please please help me with this ​
iris [78.8K]

Answer:

angle FQE= Minor sector

6 0
2 years ago
Mr. Soto plans to open a savings account. Four banks offer the annual interest rates shown. Which list shows these interest rate
Delvig [45]
Ok, so IDK if I'm about to do this problem right, but here we go;


so first, lets change these all to decimals (I more of a decimal gal)

3 1/2 = 3.5
3 2/3 = 3.6666 (repeating)
3 3/5 = 3.6
3 3/8 = 3.375

So now, just order them from greatest to least.  

3.66666, 3.6, 3.5, 3.375.  

Now, change them back to fractions.  
3 2/3, 3 3/5, 3 1/2, 3 3/8


So, if I'm correct, the answer is 3 2/3%, 3 3/5%, 3 1/2%, 3 3/8%
Hopefully I solved your problem! 
6 0
3 years ago
Suppose in the population, the Anger-Out score for men is two points higher than it is for women. The population variances for m
tatuchka [14]

Answer:

a)= 2

b) 6.324

c) P= 0.1217

Step-by-step explanation:

a) The mean of the sampling distribution of X`1- X`2 denoted by ux`-x` = u1-u2 is equal to the difference between population means i.e = 2 ( given in the question)

b) The standard deviation of the sampling distribution of X`1- X`2 ( standard error of X`1- X`2) denoted by σ_X`1- X`2 is given by

σ_X`1- X`2 = √σ²/n1 +σ²/n2

Var ( X`1- X`2) = Var X`1 + Var X`2 =  σ²/n1 +σ²/n2

so

σ_X`1- X`2 =√20 +20 = 6.324

if the populations are normal the sampling distribution X`1- X`2 , regardless of sample sizes , will be normal with mean u1-u2 and variance σ²/n1 +σ²/n2.

Where as Z is normally distributed with mean zero and unit variance.

If we take X`1- X`2= 0 and u1-u2= 2  and standard deviation of the sampling distribution = 6.324 then

Z= 0-2/ 6.342= -0.31625

P(-0.31625<z<0)= 0.1217

The probability would be 0.1217

8 0
2 years ago
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