9 people audition for a choir. The choir director must choose one soprano, one alto,
and one tenor.
In how many ways can the director fill these positions?

When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1

The values of variables satisfying the given quadratic equation are called its roots.

if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta

alpha + beta = -b/a and

alpha × beta = c/a

when the roots are reduced by 2

alpha-2+ beta-2 = -b/a

(alpha+beta)-4 = -b/a

alpha+ Bata = -b/a + 4

the resulting equation is x²-2x+1 = 0

a = 1, b = -2 and c = 1

therefore alpha +beta = -b/a = -(-2)/1 = 2

therefore 2 = -b/a+4

a = 1

2 = -b+4

b = 4-2 = 2

alpha×beta = c/a = 1/1

(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1

therefore b = 2 , c = 1

learn more about root of quadratic equation from

https://brainly.com/question/1214333

#SPJ1

The given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to

10x + 0.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the expression as follows -

8.5x + 0.5 + 3.5x - 2x

The given expression is -

8.5x + 0.5 + 3.5x - 2x

(8.5x + 3.5x - 2x) + 0.5

12x - 2x + 0.5

10x + 0.5

Therefore, the given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to

10x + 0.5.

To solve more questions on expressions, visit the link below -

brainly.com/question/29358298

#SPJ1

The three sides of a triangle are referred to as the base, the height, and the hypotenuse.

The base and height of a triangle can be used to calculate the area of the triangle using the formula:

Area = (Base x Height) / 2

To calculate the hypotenuse of a triangle, the Pythagorean Theorem is used. The theorem states that the sum of the squares of the lengths of the two sides of a right triangle is equal to the square of the length of the hypotenuse.

The formula for the Pythagorean Theorem is:

a2 + b2 = c2

where a and b are the two sides of the triangle and c is the hypotenuse.

To calculate the hypotenuse of a triangle, the following steps are taken:

1. Measure the length of each side of the triangle.

2. Square the length of each side (multiply the length by itself).

3. Add the two values together.

4. Find the square root of the sum. This is the length of the hypotenuse.

Learn more about Pythagorean Theorem here:

https://brainly.com/question/28361847

#SPJ4

The solution for given question of algebra are 10, -42, -38 for question 1st, 2nd and 3rd.

There are several sub-branches of algebra, including commutative algebra, abstract algebra, linear algebra, and elementary algebra.

x + 6/x + 3 = 4/7

7x + 42 = 4x + 12

7x - 4x = 42-12

3x = 30

x = 10

2/x+8 = 3/x+9

2x - 18 = 3x + 24

x = -42

x+2/6 = x-4/7

7x+14 = 6x-24

x = -38

To know more about algebra visit:-

brainly.com/question/24875240

#SPJ1

Rotation of PQRS by 90 degree.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location. What are the four mathematical transformations?

Translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.

To know more about geometric figure visit:-

brainly.com/question/11266123

#SPJ1

The complate table is,

Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                      CPCTC

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

K is the midpoint of segments RM and JL.

Now,

Since, K is the midpoint of segments RM and JL.

Hence, We get;

   Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                       CPCTC

Thus, The complete table is shown above.

Learn more about the line segment visit:

https://brainly.com/question/280216

#SPJ1

Answer:

Step-by-step explanation:

We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.

5/15 = 1/3

5*3 = 15*1

15 = 15

as the left-hand side is equal to the right side. So, these fractions are in proportion.

Answer:

9978

Step-by-step explanation:

10000 - 22 = 9978

9978 is the answer

Answer: 9978

Step-by-step explanation:

Stack the numbers up like this 10000

                                                          22

     borrow from the one make the zero a ten, and then borrow from that to make the next one and make it a nine and then do it to the last one and subtract. Hope this makes sense

The margin of error and the sample mean of the confidence interval are given as follows:

The confidence interval is defined as follows:

(12.7, 19.5).

The definition of a confidence interval is that it is obtained as the sample mean plus/minus the margin of error.

Hence the sample mean is calculated as the mean of the bounds of the interval, hence:

(12.7 + 19.5)/2 = 16.1.

The margin of error is calculated as the absolute value of the difference of each bound from the sample mean, hence:

|19.5 - 16.1| = |12.7 - 16.1| = 3.4.

More can be learned about confidence intervals at https://brainly.com/question/25890103

#SPJ1

The ratio of days in May and days in a year is 31 to 365 or 31:365

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We need to find the days in May and days in a year as a ratio

Therefore, Days in may = 31

Days in a year = 365

Thus, the expected ratio = 31/365

Or

31:365

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ1

Answer:

D

Step-by-step explanation:

I think it would be D hope this helps!

The best definition of a decimal is decimals are whole counting numbers.

Suppose that the number is abcdefg and belongs to the decimal numerical system.

Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.

Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.

Thus, we write abcd.efg as:

[tex]a \times 10^3 + b \times 10^2 + c \times 10^1 + d \times 10^{0} + e \times 10^{-1} + f \times 10^{-2} + g \times 10^{-3}[/tex]

We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.

Therefore, the definition will be Decimals are whole counting numbers,

Learn more about decimal here:

https://brainly.com/question/17983725

#SPJ2

An equation that shows what the cost of renting a car will be: C=R+mc.

Let the rental cost = R

consider m to be the number of miles driven= m

let c be the cost per mile

And C is the total cost of renting;

Then C = R+mc

the given equation $40 + $0. 10 per mile

Now, in the above equation consider:

R =$40 ( the rental cost)

c = $0.10 ( the cost per mile)

The total cost is C = $40+$0.10m

Ex:

if m is known assume m=1000 miles

Then the total cost C = $40+($0.10/mile)(1000miles)

then  C = $40+$100=$140

To know more about the equation of cost of renting:

https://brainly.com/question/16404189

#SPJ4

Answer:

sry i dont no

Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

p(x)=6x+2

for p(-2)

p(-2) = 6(-2) + 2

p(-2) = -12 + 2

p(-2) = -10

for p(4)

p(4) = 6(4) + 2

p(4) = 24 + 2

p(4) = 26

p(-2) < p(4)

Learn more about functions here: https://brainly.com/question/11624077

#SPJ1

Answer:

(B) "The value of p(-2) is smaller then the value of p(4)" is True

Step-by-step explanation:

p(x)=6x+2

p(-2) = 6*(-2)+2

p(-2) = -12+2

p(-2) = -10

p(4) = 6*(4)+2

p(4) = 26

====

p(-2) = -10

p(4) = 26

===

(A) The value of p(-2) is larger then the value of p(4).   False

(B) The value of p(-2) is smaller then the value of p(4).  True

(C) The value of p(-2) is the same as the value of p(4).  False

(D) The values of p(-2) and p(4) cannot be compared.   False

The average rate of driving from Newyork to Boston is d. 54 mph.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The distance you drive is proportional to the time.

We know, The arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Therefore,

The average rate of driving is,

= (216/4) mph.

= 54 mph.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ1

Read the link attached.

I have written it down on the word doc

The statement whether each data set is likely to be distributed nor not:

Number of minutes required to complete a marathon - Yes.

Number of miles in a marathon: - No.

Average age of a person who runs a marathon: No.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Let n miles in marathon.

To normally distribute, number of minutes required to complete a marathon:

The number of minutes required to complete a marathon is likely to be normally distributed with small amounts in tails (very slow, very fast) and large amount in middle.

So, yes.

To normally distribute,  number of miles in a marathon:

The number of miles is a fixed number, not normally distributed.

So, no.

To normally distribute, average age of a person who runs a marathon:

The average age is a fixed number

Average age is not likely to be normally distributed.

So, no.

Therefore, the first one is yes, and the other two are no.

To learn more about the distributions;

https://brainly.com/question/29062095

#SPJ1

Answer: B

Step-by-step explanation:

B) 180−m180-m180−m

Answer:22 days

Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,

Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)

so, 2000/90 = we will get number of days

therefore 22.22 days

Which emplies 22 days.

Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

What is an Algebraic expression ?

Algebraic expression can be defined as combination of variables , constants and exponents.

Radical expression, in which if the expression contains square root than it called as the radical expression.

Examples are  : - [tex]\sqrt{7}[/tex] , [tex]\sqrt{x}[/tex] and etc .

Rational exponent , in which it is in the form of p/q is called as the rational exponent .

Examples are :- 5/8 , 6/9,8/7 and etc .

Hence, Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

To learn more about Algebraic expression from the given link.

https://brainly.com/question/953809

#SPJ1

Answer:

(n - 6)(n -4)

Step-by-step explanation:

Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.

Answer:

y = -x + 5

Step-by-step explanation:

The equation is y= mx + b

m = the slope or rise/run or (y2 - y1) / (x2 - x1)

b = y-intercept

The slope here is -1, and the y-intercept is 5, so our equation is

y = -x + 5

The correct option regarding the surface area of the solid is given as follows:

d. 45 square inches.

The surface area of a solid is composed by the sum of the areas of all the pars of the figure.

The composition of the figure in this problem is given as follows:

Thea area of a triangle is given by half the multiplication of the base by the height, hence the area of the four triangles in this problem is given as follows:

At = 4 x 1/2 x 3 x 6

At = 36 square inches.

The area of a square is given by the square of the side length, hence:

As = 3³

As = 9 square inches.

Thus the surface area of the solid in this problem is given as follows:

S = At + As

S = 36 + 9

S = 45 square inches.

Meaning that option d is correct.

More can be learned about surface area at https://brainly.com/question/16519513

#SPJ1

The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

-28, -31, -34, -37, ...

The general formula of an arithmetic sequence:

aₙ= a₁ + (n)d,

where a₁ is the first term and d is the common difference.

First, we will find the common difference between consecutive terms.

Here,

a₁ = -28

To find the common difference:

a₂ - a₁ = -31 + 28 = -3

a₃ - a₂ = -34 + 31 = 3

a₄ - a₃ = -37 + 34 = 3

Hence, d = -3.

Substitute the values to the formula,

aₙ= a₁ + (n)d,

aₙ= -28 + (-3)d,

aₙ= -28 -3d

Therefore, aₙ= -28 -3d is the required sequence.

To learn more about the arithmetic sequence;

https://brainly.com/question/29616017

#SPJ1

The expected time until the tourist arrives in the city is 4.75 hours.

The expected time until the tourist arrives at the city can be calculated by using the formula for the expected value:

Expected value = (probability of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...

In this case, there are two possible outcomes: the tourist takes road A or road B.

If the tourist takes road A, the expected time until he arrives in the city is the average of the two possible travel times (4 hours and 8 hours). The probability of this outcome is 0.5 (the tourist has an equal chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.

If the tourist takes road B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this outcome is (0.5) x 7 = 3.5 hours.

To find the overall expected time until the tourist arrives in the city, we add up the expected values for each outcome:

Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours

So the expected time until the tourist arrives in the city is 4.75 hours.

To learn more about the probability, visit:

brainly.com/question/30034780

#SPJ4

The two angles that have the sum of angles as 90° are called as Complementary Angles .

What are Complementary Angles ?

The two angles are said to be complimentary Angles when the sum of two angles is 90° .

In other words, we can say that if the measure of two angles add up to form a right angle, then these angles are called as Complementary Angles.  We can also say that  the two angles complement each other.

For Example : the angles having the measure of 30 degree and 60 degree can be called as Complimentary as their sum adds up to 90 degree .

Learn more about Complimentary Angles here

https://brainly.com/question/1425570

#SPJ4

The value of x is 7 and value of y is 8

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given data set is {4, 6, x, y, 10}

The mean and the median are the same value.

The median is the middle value, which is x, and the mean is:

M = (4 + 6 + x + y + 10)/5

Then we have that:

(4 + 6 + x + y + 10)/5 = x

Now let's solve this:

(4 + 6 + x + y + 10) = 5x

20 + x + y = 5x

20 + y = 4x

And x and y are whole numbers. Then we can take x = 7 to get:

20 + y = 4*7

y = 28 - 20 = 8

Then we have x = 7 and y = 8.

Hence, the value of x is 7 and value of y is 8 in the data set 4 6 x y 10

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ1

The linear equation f(x) is  4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.

The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:

m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4

The y-intercept (b) can be found using one of the points and the slope:

b = y - mx = 2 - 4(3) = -10

So the linear equation in standard form is:

f(x) = 4x - 10

For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.

Let's (3,2) point 1 and (7,18) point 2.

f(k) = ak^2 + bk + c....(1)

point 1: f(3) = 2 = 9a + 3b + c...(2)

point 2: f(7) = 18 = 49a + 7b + c...(3)

Now we have 2 equations and 3 unknowns.

using theirs first equation and substitute it in the second and third equation

18 = 49a + 7b + c

2 = 9a + 3b + c

c = 2 - 9a - 3b

18 = 49a + 7b + (2 - 9a - 3b)

18 = 49a + 7b + 2 - 9a - 3b

18 = 40a + 4b + 2

16 = 40a + 4b

now this equation is used to solve for a and b

b = (16 - 40a) / 4

so a,b and c are

a = -5/2

b = 4

c = -1

so the quadratic equation in standard form is:

f(k) = -5/2k^2 + 4k - 1

4x - 10 is the linear equation f(x)  and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.

To know more about quadratic equation :

https://brainly.com/question/28038123

#SPJ4