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3 years ago

How many roots does a quadratic have if the discriminant if prime?

Mathematics

1 answer:

scZoUnD [109]3 years ago

5 0

"The discriminant is prime?" I haven't heard that one before.

Here are the general rules:

1. a positive discriminant results in two real, unequal roots.

2. a zero discr. results in two real, equal roots.

3. a negative discr. results in two complex roots, which sometimes means two imaginary roots.

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Which function is the inverse f(x)=-5x-4

Kay [80]

Answer:

f⁻¹(x) = -(x+4) / 5

Step-by-step explanation:

Given function is :

f(x) = -5x-4

We have to find the inverse of given function.

Step 1. Put y = f(x) in given function

y = -5x-4

Step 2. Add 4 to both sides of above equation

y+4= -5x-4+4

y+4 = -5x

Step 3.Divide by -5 to both sides of above equation

y+4 / (-5) = -5x / (-5)

-(y+4) / 5 = x

Step 4 . Swap sides

x = -(y+4) / 5

Step 5. Put x = f⁻¹(y) in above equation

f⁻¹(y) = -(y+4) / 5

Step 6. replace y with x

f⁻¹(x) = -(x+4) / 5 which is the inverse of f(x) = -5x-4.

8 0

3 years ago

Read 2 more answers

david is buying a cheese wheel priced at $650 before tax. the store charges 8% sales tax. what is the total price including tax,

Marina CMI [18]

I think he pays $702.

Basically,

650 • .08 (move the decimal over two to the left, that’s what you get) = 52. Then I did 650 + 52 and got $702.

6 0

3 years ago

The 2004 presidential election exit polls from the critical state of Ohio provided the following results. There were 2020 respon

lord [1]

Answer: a) $0.490\leq p\leq0.582$

b) $0.501\leq p$

Step-by-step explanation:

Given : Sample size of respondents in the exit polls : n= 2020

Number of respondents voted for George Bush = 412

Sample proportion: $\hat{p}=\dfrac{412}{768}\approx0.536$

a) Critical value for 99% confidence level : $z_{\alpha/2}=2.576$

Confidence interval for proportion:-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$=0.536\pm (2.576)\sqrt{\dfrac{0.536(1-0.536)}{768}}\\\\=0.536\pm0.046\\\\=(0.490,\ 0.582)$

Hence, the 99% confidence interval for the proportion of college graduates in Ohio that voted for George Bush: $0.490\leq p\leq0.582$

b) Critical value for 95% confidence level : $z_{\alpha/2}=1.96$

Lower confidence bound for the proportion :

$\hat{p}- z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.536-(1.96)\sqrt{\dfrac{0.536(1-0.536)}{768}}\\\\=0.536-0.035=0.501$

Hence, a 95% lower confidence bound for the proportion of college graduates in Ohio that voted for George Bush : $0.501\leq p$

7 0

3 years ago

Read 2 more answers

Malcolm is driving 1,323 miles from Wichita to Charleston for a family reunion. He drives 443 miles the first day and 409 miles

svp [43]

1323 rounds to 1320
443 rounds to 440
409 rounds to 410

1320 - (440 + 410) =
1320 - 850 =
470 <=== malcolm has about 470 miles left to go

4 0

4 years ago

Let f(x) = [infinity] xn n2 n = 1 . Find the intervals of convergence for f. (Enter your answers using interval notation.) Incor

sveta [45]

Answer:

The interval of convergence is -1<x<1

Step-by-step explanation:

To find the interval of convergence of the series, we will use the condition for convergence of a series according to Ratio test.

The solution is as shown in the attachment.

7 0

3 years ago