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3 years ago

Use the discriminant to determine the number of real solutions to the equation. −4x^2=−8−10x

Mathematics

2 answers:

ICE Princess25 [194]3 years ago

6 0

Answer:

Step-by-step explanation:

Len [333]3 years ago

6 0

Answer:

Step-by-step explanation:

You don't get a free answer. I am, after all, a high school math teacher, so there has to be a lesson in with this.

The discriminant is part of the quadratic formula. It is:

$b^2-4ac$ . If this value is found to be > 0 and a perfect square, there are 2 real roots; if this value is found to >0 and not a perfect square, there are 2 complex roots; if this value is found to be = 0, then there is 1 real root with a multiplicity of 2; and finally, if this value is found to be < 0, then there are 2 imaginary roots. Also, it would help to know that, because we are dealing with the discriminant, which comes from the quadratic formula, and quadratics, by definition, have 2 solutions, you must have 2 solutions listed as the possible roots for the equation. Our equation is:

$-4x^2=-8-10x$ but in order to determine the a, b, and c for the discriminant, that equation has to be in standard form, set equal to 0:

$-4x^2+10x+8=0$

From this we can see that a = -4, b = 10, and c = 8. Filling in the discriminant:

$10^2-4(-4)(8)$ which gives us a value of

100 - [4(-4)(8)] (don't forget orders of operation here!)

100 - (-128) = 100 + 128 = 228

This value is greater than 0 but is not a perfect square, so there are 2 complex roots. That means that there will be radicals in the solutions.

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A TV has a listed price of $647.99 before tax. If the sales tax rate is 9.75%, find the total costs of the TV with the sales tax

Lena [83]

Answer:

$647.99

Step-by-step explanation:

Divide the tax rate (9.750%) by 100 to get a decimal rate of 0.09750.

Add 1 to the decimal rate to get 1.09750.

Divide that tax-included price ($647.99) by 1.09750 price to get a pretax price of $590.42.

Subtract the pretax price from $647.99 to get the sales tax amount of $57.57.

6 0

3 years ago

The factory quality control department discovers that the conditional probability of making a manufacturing mistake in its preci

Anni [7]

Answer:

The probability that a defective ball bearing was manufactured on a Friday = 0.375

Step-by-step explanation:

Let the event of making a mistake = M

The event of making a precision ball bearing production on Monday = Mo

The event of making a precision ball bearing production on Tuesday = T

The event of making a precision ball bearing production on Wednesday = W

The event of making a precision ball bearing production on Thursday = Th

The event of making a precision ball bearing production on Friday = F

the conditional probability of making a manufacturing mistake in its precision ball bearing production is 4% on Tuesday, P(M|T) = 4% = 0.04

4% on Wednesday, P(M|W) = 0.04

4% on Thursday, P(M|Th) = 0.04

8% on Monday, P(M|Mo) = 0.08

and 12% on Friday = P(M|F) = 0.12

The Company manufactures an equal amount of ball bearings (20 %) on each weekday, Hence, the probability that a random precision ball bearing was made on a particular day of the week, is mostly the same for all the five working days.

P(Mo) = 0.20

P(T) = 0.20

P(W) = 0.20

P(Th) = 0.20

P(F) 0.20

The probability that a defective ball bearing was manufactured on a Friday = P(F|M)

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F)

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

We can obtain each of these probabilities by using the expression for conditional probability.

P(Mo n M) = P(M|Mo) × P(Mo) = 0.08 × 0.20 = 0.016

P(T n M) = P(M|T) × P(T) = 0.04 × 0.20 = 0.008

P(W n M) = P(M|W) × P(W) = 0.04 × 0.20 = 0.008

P(Th n M) = P(M|Th) × P(Th) = 0.04 × 0.20 = 0.008

P(F n M) = P(M|F) × P(F) = 0.12 × 0.20 = 0.024

P(M) = P(Mo n M) + P(T n M) + P(W n M) + P(Th n M) + P(F n M)

P(M) = 0.016 + 0.008 + 0.008 + 0 008 + 0.024 = 0.064

P(F|M) = P(F n M) ÷ P(M)

P(F n M) = P(M n F) = 0.024

P(M) = 0.064

P(F|M) = P(F n M) ÷ P(M) = (0.024/0.064) = 0.375

Hope this Helps!

4 0

3 years ago

Can someone please help, I need this done soon :))

Sonja [21]

The volume of the pyramid is $726 \mathrm\ {cm}^{3}$

Explanation:

The height of the square pyramid is 18 cm

The base of the square pyramid is 11 cm

The volume of the square pyramid can be determined using the formula,

$V=\frac{1}{3} b^{2} h$

Substituting $b=11$ and $h=18$ in the formula, we have,

$V=\frac{1}{3} (11)^{2} (18)$

Simplifying, we have,

$V=\frac{1}{3} (121)(18)$

Multiplying, we get,

$V=\frac{2178}{3}$

Dividing, we get,

$V=726 \ cm^3$

Thus, the volume of the pyramid is $726 \mathrm\ {cm}^{3}$

5 0

3 years ago

I need help with this due in 10 mins pleaseeeee

mylen [45]

Answer:

D) (2, 14)

Step-by-step explanation:

substitute each coordinates into the inequality:

(0, 0)

y > 5x

0 > 5*0

0 > 0

this is false, 0 = 0.

(3, 12)

y > 5x

12 > 5 * 3

12 > 15

this is false, 12 < 15

(-2, -10)

y > 5x

-10 > 5 * -2

-10 > -10

this is false, -10 = -10

(2, 14)

y > 5x

14 > 5 * 2

14 > 10

this is true, 14 > 10

3 0

3 years ago

Read 2 more answers

I'm not sure how to start the process....

lesantik [10]

Step 1; both side divide by 4, you'll get Ix-10I=8
step 2: x-10=8 or x-10=-8
x=18 or x=2

3 0

3 years ago