X2 -2x + 1= 0. Solve the equation using the quadratic formula. Then solve the equation by factoring to check your solutions

To find the total grams of saturated fat in 12 ounces of cream cheese, multiply the grams per ounce (7.8) by the total ounces (12), which equals 93.6 grams.

To answer this question, we need to multiply the amount of saturated fat in one ounce of cream cheese by the total number of ounces you have. Since one ounce of cream cheese contains 7.8 grams of saturated fat, you would multiply 7.8 by 12 (the total number of ounces) to get the total amount of saturated fat.

7.8 grams of saturated fat per ounce × 12 ounces = 93.6 grams

So, 12 ounces of cream cheese contains 93.6 grams of saturated fat.

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$4.5 per service x 8 = $36.00

$18.00 x 8 = $144 x 20% = $29.00

$65.00

Answer:

You can expect $65.00 to earn on such a day.

Step-by-step explanation:

The price of shampoo, cut and style  = $18.00

you generally get a tip from each customer  = 20%  of $18.00

0.20 × 18.00 =  $3.60

Salon owner pays 1/4 of each job's cost = [tex]\frac{1}{4}[/tex] of $18.00

[tex]\frac{1}{4}[/tex] × 18.00 = $4.50

Total earning from each customer = 3.60 + 4.50 = $8.10

On a typical day, you serve 8 customers,

so the earning of each day = 8.10 × 8 = $64.80 ≈ $65.00

You can expect $65.00 to earn on such a day.

The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]

Further explanation:

Given:

The function is [tex]y = {e^{rx}}.[/tex]

The differential equation is [tex]y'' - 6y' + 2y = 0\,\,\,\,\,or\,\,\,\,\dfrac{{{d^2}y}}{{d{x^2}}} - 6\dfrac{{dy}}{{dx}} + 2y = 0[/tex]

Explanation:

The given function can be expressed as follows,

[tex]y = {e^{rx}}[/tex]

Differentiate the above equation with respect to [tex]x[/tex].

[tex]\begin{aligned}\frac{{dy}}{{dx}} &= \frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&= {e^{rx}} \times \frac{d}{{dx}}\left( {rx} \right)\\&= {e^{rx}} \times r\\&= r{e^{rx}}\\\end{aligned}[/tex]

Again differentiate with respect to [tex]x[/tex].

[tex]\begin{aligned}\frac{{{d^2}y}}{{d{x^2}}} &= \frac{d}{{dx}}\left( {r{e^{rx}}} \right)\\&= r\frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&=r\times {e^{rx}} \times\frac{d}{{dx}}\left( {rx} \right)\\&= {r^2}{e^{rx}}\\\end{aligned}[/tex]

Now solve the differential equation.

[tex]\begin{aligned}y'' - 6y' + 2y &= 0\\{r^2}{e^{rx}} - 6r{e^{rx}} + 2{e^{rx}} &= 0\\{e^{rx}}\left( {{r^2} - 6r + 2} \right) &= 0\\{r^2} - 6r + 2 &= 0\\\end{aligned}[/tex]

Solve the quadratic equation [tex]{r^2} - 6r + 2 = 0.[/tex]

[tex]\begin{aligned}D&= {b^2} - 4ac\\&={\left( { - 6} \right)^2} - 4\left( 1 \right)\left( 2 \right)\\&= 36 - 8\\&= 28\\\end{aligned}[/tex]

The value of [tex]r[/tex] can be obtained as follows,

[tex]\begin{aligned}r&= \frac{{ - b \pm \sqrt D }}{{2a}}\\r&=\frac{{ - \left( { - 6} \right) \pm \sqrt {28} }}{{2 \times 1}} \\ r &= \frac{{6 \pm 2\sqrt7 }}{2}\\r&= 3 \pm \sqrt7\\r&= 3 - \sqrt 7 \,\,\,\,\,\,\,or\,\,\,\,\,\,\,r = 3 + \sqrt7 \\\end{aligned}[/tex]

The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Derivatives

Keywords: Derivative, value of x, function, differentiate, minimum value, dy, compute, given value of [tex]x, y=6x, x=4, x=1[/tex]

Two ways to make the number 100 by inserting operations between the sequence 123456789 are 1+2+3-4+5+6+78+9=100 and 123-45-67+89=100.

To create the number 100 by inserting mathematical operations (+, -, ×, ÷) between the numbers 1 to 9 sequenced as 123456789, we can approach the problem in several ways. Here are two solutions:

In the first solution, we primarily use addition, with a single subtraction to adjust the total to 100. The second solution uses both subtraction and addition, combining smaller numbers to form larger numbers that eventually add up to 100.

7200 / 800 = 9

9*200 = 1800

he walked 1800 m

The solution to the given equation (1/2)(3g - 2) = g/2 is g = 1 using the distributive property.

The equation is given as follows:

(1/2)(3g - 2) = g/2

Apply the distributive property by multiplying (1/2) to both terms inside the parentheses:

(1/2)(3g - 2) = g/2

(3g/2) - (2/2) = g/2

(3g/2) - 1 = g/2

Multiply both sides of the equation by 2 to eliminate the denominators:

2[(3g/2) - 1] = 2(g/2)

3g - 2 = g

Simplify the equation by moving all terms with g to one side and the constant terms to the other side:

3g - g = 2

2g = 2

Divide both sides of the equation by 2 to solve for g:

(2g)/2 = 2/2

g = 1

Therefore, the solution to the equation (1/2)(3g - 2) = g/2 is g = 1.

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The area of the deck that is built around the pool is 1352 ft².

A rectangle is a 2-dimensional quadrilateral with four right angles.  

Area of a rectangle = length x width

Area = 26 x 52 = 1352 ft²

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Answer:

There is exactly one plane containing points W, X, and Y

Step-by-step explanation:

The answer relies on whether the balls are different or not. If they are not, which is almost certainly what is intended.

If they are, the perceptive is a bit different. Your expression gives the likelihood that a particular set of j balls goes into the last urn and the other n−j balls into the other urns. But there are (nj) different possible sets of j balls, and each of them the same probability of being the last insides of the last urn, so the total probability of completing up with exactly j balls in the last urn is if the balls are different.

See attached file for the answer.

To calculate the probability that the last urn contains j balls when n balls are distributed randomly into k urns, consider the number of ways to distribute the balls among the k-1 urns and multiply it by the probability of the last urn containing j balls.

To calculate the probability that the last urn contains j balls, we need to consider the number of ways to distribute the n balls among the k-1 urns (excluding the last urn) and multiply it by the probability of the last urn containing j balls.

Let's assume that the number of ways to distribute the n balls among the k-1 urns is denoted by C. The probability of the last urn containing j balls is then given by P(j) = C * (1/k).

For example, if there are 10 balls distributed randomly into 4 urns and we want to find the probability that the last urn contains 3 balls, we need to calculate the number of ways to distribute the 10 balls among the first three urns (C) and multiply it by the probability of the last urn containing 3 balls (1/4).

Final answer:

Using grouping symbols helps organize and clarify information in mathematical expressions.

Explanation:

Grouping symbols are essential in organizing information effectively. By using grouping symbols like parentheses, brackets, or braces, you can prioritize operations, clarify relationships, and maintain accuracy in mathematical expressions. For example, in the expression 2 x (3 + 5), the grouping symbols clarify that the addition inside the parentheses should be done first before multiplying the result by 2.

The average height of a 5 year old baby can be obtained by substituting the x and y values into the regression equation ; Hence, the average height of the baby is 98.9 cm

Given the linear regression equation :

The average height of a 5 year old baby is thus :

y = 6.3(5) + 67.4

y = 31.5 + 67.4

y = 98.9

Hence, the average height a 5 year old baby will be 98.9cm

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the expression which represents how much money they make per pound of crawfish they catch is 3.3573x.

Given that, the restaurant pays them $3.80 a pound for live crawfish that is large enough 5% of the crawfish die before they can deliver to the restaurant 7% of the live crawfish are too small.

We need to write an expression for the given situation.

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

Let "x" be the number of crawfish they catch.

Now, the expression is

Money earned=3.80× (1-5%)× (1-7%)× x

=3.80× (1-0.05)× (1-0.07)× x

=3.80× 0.95× 0.93× x

=3.3573x

Therefore, the expression which represents how much money they make per pound of crawfish they catch is 3.3573x.

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Your question is incomplete, probably the complete question/missing part is:

Henry and Holly catch crawfish which they sell to a local Cajun restaurant. The restaurant pays them $3.80 a pound for live crawfish that are large enough. 5% of the crawfish die before they can deliver to the restaurant and 7% of the live crawfish are too small.

Identify an expression which represents how much money they make per pound of crawfish they catch.

13 +2 = 15 -5= 10 -15 = -5

To divide 300 by a ratio of 3:7, calculate the value of each part by dividing 300 by the sum of the ratio parts (10) and then multiply by each part of the ratio to get 90 and 210, respectively.

To divide 300 in a ratio of 3:7, first add the parts of the ratio together to determine how many parts you will split 300 into.

In this case, 3 + 7 equals 10 parts.

Then, you divide 300 by 10 to find out how much one part is worth.

This gives 300 ÷ 10 = 30. Now, to find the amounts corresponding to the ratio, multiply the single part value by the numbers in the ratio. For the first part (ratio 3), multiply 30 by 3 to get 90.

For the second part (ratio 7), multiply 30 by 7 to get 210.

So, 300 divided in a ratio of 3:7 gives us 90 and 210, respectively.

To find the measure of angle 6, we can use the fact that angles 3 and 6 are vertical angles (opposite angles formed by the intersection of two lines). Therefore, their measures are equal.

Given that[tex]\( m\angle 3 = 105^\circ \), we have \( m\angle 6 = m\angle 3 = 105^\circ \).So, the measure of angle 6 is \( \boxed{105^\circ} \).[/tex]

The measure of angle 6 is 105 degrees. This is because angles 3 and 6 are vertical angles, meaning they are formed by intersecting lines and are opposite each other. According to the Vertical Angles Theorem, vertical angles are congruent, meaning they have the same measure. Therefore, if angle 3 measures 105 degrees, angle 6, being its vertical angle, also measures 105 degrees. This principle holds true regardless of the specific configuration of lines or shapes, as long as the angles are formed by intersecting lines. Hence, in this case, the measure of angle 6 directly corresponds to the measure of angle 3 due to their relationship as vertical angles, resulting in both having a measure of 105 degrees.