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7 days ago

Solve x2 - 8x - 9 = 0. Rewrite the equation so that it is of the form x2 + bx = c.

Mathematics

2 answers:

Svet_ta [9.5K]7 days ago

4 0

Answer:

x=9,-1 and $x^2+(-8)x=9$

Explanation:

We are given the quadratic equation $x^2-8x-9$

, which we then compare with the standard form of a quadratic. The general quadratic is identified as $ax^2+bx+c=0$

. From our given equation, it follows that a=1,b=-8,c=-9

. To calculate the discriminant, we insert these values into the formula $D=b^{2}-4ac$

$D=(-8)^2-4(1)(-9)=100$

. Now, to find the value of x

The formula is $x=\frac{-b\pm\sqrt{D}}{2a}$

. The resulting equation will be obtained by rewriting the original equation through rearranging 9 to the right side and applying negative signs within brackets to convert the expression into the form of

$x^2+bx=c$

zzz [9K]7 days ago

4 0

From the provided information, it can be observed that a = 1, b = -8, and c = -9. To move c across the equation, simply add 9 to both sides,
x² - 8x -9 + 9 = 0 + 9
This will yield the result of
x² - 8x = 9.

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Tags are placed to the left leg and right leg of a bear in a forest. Let A1 be the event that the left leg tag is lost and the e

babunello [8412]

Answer:

0.75 = 75% chance that only one tag is lost, provided at least one tag is lost

Step-by-step explanation:

Independent events:

If A and B are independent events, then:

$P(A \cap B) = P(A)*P(B)$

Conditional probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

Here

P(B|A) refers to the probability of event B occurring, given that event A has occurred.

$P(A \cap B)$ is the probability of both A and B occurring together.

P(A) is the probability of event A occurring.

In this scenario:

Event A: At least one tag is missing

Event B: Only one tag is missing.

Each tag has a 40% likelihood of being lost, which is equal to 0.4.

Probability of at least one tag missing:

The events can be considered as either no tags are missing or at least one is. Their probabilities sum to 1. Thus

$p + P(A) = 1$

p is the probability that none are lost. Each tag has a 60% = 0.6 chance of not being lost, and since they are independent,

p = 0.6*0.6 = 0.36

Then

$P(A) = 1 - p = 1 - 0.36 = 0.64$

Intersection:

The intersection of at least one lost (A) and exactly one lost (B) is precisely one lost.

Then

Probability of at least one lost:

The first being lost (0.4 chance) and the second not lost (0.6 chance)

The first not being lost (0.6 chance) and the second lost (0.4 chance)

$P(A \cap B) = 0.4*0.6 + 0.6*0.4 = 0.48$

Calculate the probability that exactly one tag is lost, given that at least one tag is lost (round to two decimal places).

$P(B|A) = \frac{0.48}{0.64} = 0.75$

0.75 = 75% likelihood that precisely one tag is lost, assuming at least one tag is lost

8 0

5 days ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

Svet_ta [9500]

We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

We can substitute in the values.

$\frac{8}{sin(45)}=\frac{BC}{sin(60)}$

$BC=\frac{8}{sin(45)} \times sin(60)$

$BC=9.798$

Finding AC:

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

Now we'll input the values.

$\frac{8}{sin(45)}=\frac{AC}{sin(75)}$

$AC=\frac{8}{sin(45)} \times sin(75)$

$AC=10.928$

Calculating Perimeter:

$p=AB+BC+AC$

We substitute values here as well.

$p=10.928+8+9.798$

$p=28.726$

Calculating Area:

Using the area formula,

$A=\frac{1}{2}AB \times AC \times sin(A)$

we can then insert values.

$A=\frac{1}{2}8 \times 10.928 \times sin(60)$

$A=37.85570$ ...............Answer

6 0

1 month ago

Read 2 more answers

Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, a

zzz [9080]

A)
4(q - 10) = 76..... Tim earned 4 points for each correct answer, totaling 76 points. He got 10 answers right less than the total number of questions on the test.

b)
q = 10 + 76/4
q = 29

Thus, the overall number of questions on Tim's math test amounted to 29.

4 0

1 month ago

Read 2 more answers

Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per perso

Zina [9171]

Jada intends to provide milk and nutritious cookies at a gathering for her book club. She has planned to offer 12 ounces of milk and 4 cookies for each participant. With her included, the total number of club members is 15. Each package of cookies has 24 cookies and is priced at $4.50. A gallon of milk has 128 ounces and costs $3. Let n denote the club members, m for the ounces of milk, c for the cookies, and b for Jada's budget in dollars. Identify all equations that could represent the relevant quantities and constraints in this scenario.

â m = 12(15)

n refers to the club members

b. 3m + 4.5c = 6

c. 4n =

m stands for ounces of milk

& 44.50) = C

c indicates the cookies

e b=2(3) + 3(4.50)

b denotes Jada's budget in

currency

The equations applicable for representing the quantities and constraints in this scenario are:

a) m = 12(15)

c)4n = c

e) b = 2(3) + 3(4.50)

Detailed explanation:

Jada is set to provide milk and nutritious cookies for her book club meeting

She plans to prepare 12 ounces of milk and 4 cookies for each individual

She has 15 members in total

A pack of cookies contains 24 cookies and costs $4.50

A gallon of milk has 128 ounces and costs $3

Designate the total members by n

Ounces of milk = m

The number of cookies = c

Jada's budget in dollars = d

y = 12(15)

Each individual will receive 4 cookies

4n = c

As one pack contains 24 cookies

She requires = 15 × 4 = 60 cookies

60 ÷ 24 = 2.5

Thus, she would need to purchase 3 packs of cookies

She needs = 15 × 12 = 180 ounces of milk

A gallon of milk contains 128 ounces

180 ÷ 128 = 1.406

She will need to acquire 2 gallons of milk

It's noted: from the prompt

Each gallon of milk costs $3

Each package of cookies costs $4.50

b serves as Jada's dollar budget

b = 2(3) + 3(4.50)

<pThe relevant equations that could signify the quantities and constraints in this scenario are:

Options a, c and e are valid

3 0

26 days ago

If BD = 7x – 10, BC = 4x – 29, and CD = 5x – 9, find each value.

babunello [8412]

BD=7x-10
Solution: x=bd/7 + 10/7

BC=4x-29
Solution: x=Bc/4 + 29/4

CD=5x - 9
Solution: x= cd/5 + 9/5

4 0

1 month ago