Find the discriminant. 2p^2-9p+8=0

Final answer:

The dilution ratio of a solution when 150 microliters of it contains 90 microliters of saline is 3:5. This means there are 3 parts saline to every 5 parts of the total solution.

Explanation:

If 150 microliters of a solution contains 90 microliters of saline, the dilution ratio of the solution can be described as the volume of saline to the total volume of the solution. To find this ratio, divide the volume of saline by the total solution volume:

Ratio = Volume of Saline / Total Volume of Solution

Ratio = 90 µL / 150 µL

By dividing the two volumes, you get a ratio of 0.6, which can also be expressed as 3:5 after multiplying both numerator and denominator by 10 to eliminate the decimal. This means there are 3 parts of saline to every 5 parts of the total solution.

The dilution ratio is therefore 3:5.

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of [tex]x-49[/tex] meters and the distance from the top of the tree to the end of the shadow is [tex]x+1[/tex] meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

[tex]x^{2}+(x-49)^{2}=(x+1)^{2}[/tex]

Expanding, we get,

[tex]2 x^{2}-98 x+2401=x^{2}+2 x+1[/tex]

[tex]2 x^{2}-98 x+2400=x^{2}+2 x[/tex]

[tex]2 x^{2}-100 x+2400=x^{2}[/tex]

[tex]x^{2}-100 x+2400=0[/tex]

Solving the equation using the quadratic formula [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex], we get,

[tex]x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}[/tex]

Simplifying, we have,

[tex]x=\frac{100\pm\sqrt{10000-9600}}{2}[/tex]

[tex]x=\frac{100\pm\sqrt{400}}{2}[/tex]

[tex]x=\frac{100\pm{20}}{2}[/tex]

Thus,

[tex]x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60[/tex]  and  [tex]x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40[/tex]

where the value [tex]x=40[/tex] is not possible because substituting the value [tex]x=40[/tex] in [tex]x-49[/tex] results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

Answer:

$120

Step-by-step explanation:

2/3 of Mary's money + 1/2 of Mary's money is equal to 7/6 of Mary's money

7/6 of Mary's money = $210

Mary's money = m

210 = 7/6*x

180 = x

Mary's money = $180

Suzy's original money = 2/3 of 180

2/3 * 180 = 120

The monthly rate is $45 for this cellphone plan.

Step-by-step explanation:

Given,

Amount charged for cell phone = $60

Amount paid by Regina for 24 month plan = $1140

Number of months = 24

Let,

m be the monthly rate for cellphone plan

Number of months * Monthly rate + cellphone charges = Amount paid

[tex]24m+60=1140\\24m=1140-60\\24m=1080[/tex]

Dividing both sides by 24

[tex]\frac{24m}{24}=\frac{1080}{24}\\m=45[/tex]

The monthly rate is $45 for this cellphone plan.

Keywords: subtraction, division

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Answer:

392 students

Step-by-step explanation:

Given: 3/8 of the seventh grade students were taking advanced math at the beginning of the year.

          Seven dropped out by the end of the year.

          There are 140 students taking advanced math at the end of the year.

Lets assume total number of students of seventh grade be "x".

As given, 3/8 of the seventh grade students were taking advanced math at the beginning of the year.

∴ Number of student took advanced maths at the beginning= [tex]\frac{3}{8} \times x= \frac{3x}{8}[/tex]

We know, 7 student dropped out of advanced math by the end of the year.

Now, forming an equation to determine number of students taking advanced math at the end of the year.

⇒ [tex]\frac{3x}{8} -7= 140[/tex]

Solving the equation  to find number of student in seventh grade.

⇒ [tex]\frac{3x}{8} -7= 140[/tex]

Adding both side by 7

⇒ [tex]\frac{3x}{8} = 140+7[/tex]

Multiplying both side by 8

⇒[tex]3x= 147\times 8[/tex]

Dividing both side by 3

⇒[tex]x= \frac{147\times 8}{3}[/tex]

∴ [tex]x= 392[/tex]

Hence, there are 392 students in seventh grade.

Answer:

isnt it n 24

Step-by-step explanation:

[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]

Solution:

Given that,

[tex](14x+21y)(6ab-3a)[/tex]

We have to factor out terms and write as a product of 2 binomials and monomial

A monomial is a mathematical expression with only one term, while a binomial is a mathematical expression with two terms.

From given expression,

[tex](14x+21y)(6ab-3a) = (14x + 21y)(3 \times 2ab -3a)[/tex]

3 and a are common factors in second bracket

[tex](14x+21y)(6ab-3a) = 3a(2b - 1)(14x + 21y)[/tex]

Hence, the product of two binomial is written in two binomial and a monomial

Marlie's federal unsubsidized student loan will accrue $3,627.34 in interest over a 4.5-year non-payment period, given a 4.29% annual interest rate.

The subject of this problem is calculating interest accrued on an unsubsidized student loan. First, we need to understand that the 4.29% interest is an annual rate. So, for 4.5 years, the rate would become: 4.29% * 4.5 = 19.305%.

To calculate the amount of interest that will accrue during this period, we simply multiply this by the principal loan amount ($18,800). So, $18,800 * 19.305% = $3,627.34. Therefore, Marlie will accrue $3,627.34 in interest over this 4.5-year period.

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Marlie, who took a Federal Unsubsidized student loan that accumulates interest over time, will accrue $3,628.83 in interest during her 4.5 years of non-payment.

The subject of this question is about interest calculation on a Federal Unsubsidized student loan. Interest on an unsubsidized loan like Marlie's accumulates from the time the loan is disbursed until it's paid in full, including during the non-payment period. The interest that will accrue can be calculated using the formula I = PRT, where 'I' is the interest, 'P' is the principal amount (the initial amount of loan), 'R' is the annual interest rate in decimal, and 'T' is the time the money is borrowed for in years.

In Marlie's case, P = $18,800, R = 4.29/100 = 0.0429, and T = 4.5. Therefore, the interest accrued will be I = 18800 * 0.0429 * 4.5. After performing the calculation, the total interest that Marlie will accrue over the non-payment period is $3,628.83.

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Answer:

the right answer is b

Step-by-step explanation:

since its square root does not result in an integer

Final answer:

Using a system of equations, we established that there are 8 pigs and 11 ducks among the 19 animals with a total of 54 legs.

Explanation:

To solve the problem of determining how many pigs and ducks there are when there are 19 animals in total and 54 legs, we set up two equations. Let's assume the number of pigs is x and the number of ducks is y. Pigs have 4 legs, and ducks have 2 legs. We can summarize this information in the following system of equations:

Equation 1: x + y = 19 (because there are 19 animals total)

Equation 2: 4x + 2y = 54 (because the total number of legs is 54)

We can solve this system using the substitution or elimination method. Simplifying Equation 2 by dividing every term by 2 gives us 2x + y = 27, which we'll call Equation 3.

Equation 3: 2x + y = 27

We can now subtract Equation 1 from Equation 3 to find the value of x:

(2x + y) - (x + y) = 27 - 19

(2x - x) + (y - y) = 8

x = 8 (number of pigs)

Substitute x back into Equation 1:

x + y = 19

8 + y = 19

y = 19 - 8

y = 11 (number of ducks)

Therefore, there are 8 pigs and 11 ducks among the 19 animals.

Answer:

Always write it except if distributing 1. This does NOT apply for -1!

Step-by-step explanation:

Polynomial functions with an even degree have y-axis symmetry is a true statement.

Explanation:

A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function. f(x). Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.

So a function that has an even degree in it, be it a polynomial function, has a y-axis symmetry always. The equations with odd degrees may or may not have a y axis symmetry.

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=−3x+5;5x−4y=−3

Step: Solve: y=−3x+5for y:

Step: Substitute: −3x+5foryin5x−4y=−3:

5x−4y=−3

5x−4(−3x+5)=−3

17x−20=−3 (you have to simplify both sides of the equation)

17x−20+20=−3+20(then add 20 to both sides)

17x=17

17x

17

=

17

17

(Divide both sides by 17)

x=1

Step: Substitute1forxiny=−3x+5:

y=−3x+5

y=(−3)(1)+5

y=2( again Simplify both sides of the equation)

The Answer Is:

x=1 and y=2

Am I incorrect?

Answer:32

Step-by-step explanation:

The pattern seems to double each time there is a new week. By the fourth week he saved $8, and it asks how much he saved by the sixth week. We know $8 x 2 = 16 and 16 x 2 = 32, SO, by the sixth week Mikhail saved $32!

Answer:

5 (for c only)

Step-by-step explanation:

for c:

1st cleaning company: [tex]y=17x+15[/tex]

2nd cleaning company: [tex]y=20x[/tex]

set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)

it will look like:

[tex]y=17x+15[/tex]

[tex]-y=-20x[/tex]

make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with

[tex]0=-3x+15[/tex]

then you will add 3x to both sides to get [tex]3x=15[/tex] then divide both sides by 3 to get [tex]x=5[/tex]

if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5

Answer:

c. 43*

Step-by-step explanation:

1) 180-133= 47

2) 80-90= 90

3) 90+47= 137

4) 180-137= 42*

Answer:

Vestigial.

Step-by-step explanation:

It might have had a use in the past and man's evolution has rendered it of no known use.

Answer:

112.5

Step-by-step explanation:

25/100 x450/1 =

11250/100=112.5

The estimated value of 19% of 44 is 8 as per the percentage rule and rounding decimals rule.

The correct option is 8.

To estimate 19% of 44, we can start by finding 10% of 44, which is simply moving the decimal point one place to the left. So, 10% of 44 is 4.4.

Next, we can estimate 5% of 44 by dividing 10% by 2. This gives us 2.2.

Now, to estimate 19% of 44, we can add the estimates for 10% and 5%. So, 4.4 + 2.2 equals 6.6.

Given the options of 8, 9, 9.5, and 10, we can see that the estimate of 19% of 44 is closest to 9.

Therefore, the estimated value of 19% of 44 is 8.

It's important to note that this is an estimation, and the actual value of 19% of 44 is 8.36. The estimation technique used here is a quick approximation that can be useful in situations where an exact calculation is not required or when a rough estimate is sufficient.

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The complete question:

Estimate 19% of 44.
The available options are:

8, 9, 9.5, and 10.

Answer:

1.5,

Step-by-step explanation:

The examples of rational numbers are: a, d, and e.

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Let's evaluate each option:

a. [tex]\( \sqrt{4} + \sqrt{16} = 2 + 4 = 6 \)[/tex]

This is a rational number because it can be expressed as the integer 6.

b. [tex]\( \sqrt{5} + \sqrt{36} = \sqrt{5} + 6 \)[/tex]

This is not a rational number because it involves the irrational square root of 5.

c. [tex]\( \sqrt{9} + \sqrt{24} = 3 + 2\sqrt{6} \)[/tex]

This is not a rational number because it involves the irrational square root of 6.

d. [tex]\( 2 + \sqrt{4} = 2 + 2 = 4 \)[/tex]

This is a rational number because it can be expressed as the integer 4.

e. [tex]\( \sqrt{49} + \sqrt{81} = 7 + 9 = 16 \)[/tex]

This is a rational number because it can be expressed as the integer 16.

f. [tex]\( 3\sqrt{12} = 3 \times \sqrt{4 \times 3} = 3 \times 2\sqrt{3} = 6\sqrt{3} \)[/tex]

This is not a rational number because it involves the irrational square root of 3.

So, the examples of rational numbers are: a, d, and e.

The complete Question is given below:

Which of the following are examples of rational numbers? Select all that apply

a. √4+√16

b. √5+√36

c. √9+√24

d. 2+√4

e. √49+√81

f. 3√12

Answer:50%

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer:

$98.00

Step-by-step explanation:

$2000.00 x .049=$98.00

Answer:

Yes each side will always be of the same size unless you are purposely trying to make an uneven shape

Step-by-step explanation:

Expression: [tex]\((x - 3)(x + 5)\)[/tex]. If original is 10 × 10, new is 105 sq ft. New is 5 sq ft larger.

1. **Expression representing the two binomials for the area of Talia's new bedroom:**

Let [tex]\( x \)[/tex] represent the original length of the square bedroom.

The original bedroom's dimensions: [tex]\( x \times x \)[/tex]

The new bedroom's dimensions: [tex]\( (x - 3) \times (x + 5) \)[/tex]

So, the expression representing the two binomials would be: [tex]\((x - 3)(x + 5)\)[/tex]

2. **Finding the difference in size between old and new bedrooms:**

If the original bedroom measured 10 feet by 10 feet, then [tex]\( x = 10 \)[/tex] (since it's a square).

Substituting into the expression: [tex]\( (10 - 3)(10 + 5) = (7)(15) = 105 \)[/tex] square feet.

So, the new bedroom's area is 105 square feet.

The original bedroom's area is [tex]\( 10 \times 10 = 100 \)[/tex] square feet.

The difference is: [tex]\( 105 - 100 = 5 \)[/tex] square feet.

Therefore, her new bedroom will be 5 square feet larger than her old bedroom.

The complete question is here:

Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction and 5 feet longer in the other direction. Write an expression that represents the two binomials you would multiply together to find the area of Talia's new bedroom.

2nd Part

If Talia's old bedroom measured 10 feet by 10 feet, how much larger or smaller will her new bedroom be?

Answer:

B. The probability that the second dart hits the center given that the

first dart hits the center

Step-by-step explanation:

P(BA) is also called the "Conditional Probability" of B given A.

B. The probability that the second dart hits the center given that the first dart hits the center

The following information should be considered;

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