Combining like terms in a quadratic Simplify the following expression. 12x^(2)+9-8x-6x^(2)-14x

If Allister’s father measures 180 cm, then the height of Allister would be 150 cm

Let us assume that 'h' represents the height of Allister and 'm' represents the height of Allister’s father.

Here, Allister’s father is 120% of Allister’s height.

This means that m is 120 percent of 'h'

Using the formula of percentage,

m = 120% of h

m = 120/100 × h

m = 6h/5

But Allister’s father actually measures 180 cm

This means m = 180

so , 180 = 6h/5

We solve this equation to find the value of h.

⇒ h = 180 × 5/6

⇒ h = 150 cm

Therefore, Allister's height = 150 cm.

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The complete question is:

Allister’s father is 120% of Allister’s height. If his father measures 180 cm, how tall is Allister?

Answer: 3

Step-by-step explanation:

To find the x value, we must plug 6 in for y

6 = 15 - 3x

-9 = -3x

3 = x

Hope this helps!

Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.

A figure can be expressed as a fraction of 100 using a percentage. It is frequently utilised to compare two values or to convey a portion of a whole. "%," which stands for "per hundred," is the symbol used to indicate percentages. 50%, for instance, is 50/100, or 50 out of 100. Calculating percentages involves dividing a portion by a whole and multiplying the result by 100. For instance, if a bag contains 75 blue spheres and 25 red balls, the proportion of red balls is as follows:

(Number of red balls / Total Number of Balls) times 100% equals the percentage of red balls.

Red ball percentage equals (25/100) times 100%

25% of the balls are crimson.

given

You can compute the cost as follows:

Loss is calculated as Initial Price - Selling Price ($210 - $139).

Loss = $71

We must divide the loss by the initial price and multiply by 100 to determine the percentage loss:

(Loss / Original price) times 100 equals the percentage of loss.

($71 / $210) times 100 equals the percentage loss.

Loss as a percentage: 33.81%

Therefore, Han's loss amounts to 33.81% of the original cost because he spent $210 on a chest of drawers before selling it for $139 four years later.

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We get the cartesian equation of the plane:

-48x - 28y + 20z = -240

To find the cartesian equation of a plane using the given vectors u and v, we need to find a normal vector to the plane. A normal vector is a vector that is perpendicular to the plane. We can find a normal vector by taking the cross product of u and v. The cross product of two vectors u and v is given by:

n = u x v = <(u2*v3 - u3*v2), (u3*v1 - u1*v3), (u1*v2 - u2*v1)>

Plugging in the values for u and v, we get:

n = <-6,8,4> x <2,-6,-9> = <(8*-9 - 4*-6), (4*2 - -6*-6), (-6*-6 - 8*2)>

n = <-72+24, 8-36, 36-16> = <-48, -28, 20>

Now that we have a normal vector to the plane, we can use it to find the cartesian equation of the plane. The cartesian equation of a plane is given by:

n1(x-x0) + n2(y-y0) + n3(z-z0) = 0

where n =  is the normal vector and (x0, y0, z0) is a point on the plane. We can use the vector u as a point on the plane, so (x0, y0, z0) = (-6, 8, 4). Plugging in the values for n and (x0, y0, z0), we get:

-48(x+6) - 28(y-8) + 20(z-4) = 0

Simplifying, we get the cartesian equation of the plane:

-48x - 28y + 20z = -240

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The equation of total time taken by the commuter in travelling is 14x + 11, thus the correct option (b).

An algebraic equation can be defined as a mathematical statement in which two expressions are equivalent. Algebraic equations usually consist of variables, coefficients and constants .

Algebraic equations are also called polynomials because they contain polynomials on both sides of the equality sign. Algebraic equations consist of variables, coefficients, constants, and algebraic operations such as addition, subtraction, multiplication, division, and exponentiation.

According to the question:

(4x + 13) + (10x - 2) = 4x + 10x + 13 - 2

                               = 14x + 11

Thus, the equation for the total time taken is 14x + 11.

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The volume of the prism would be h(60 - hp/2) cubic feet.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is that the surface area of the right prism is 120 feet.

The formula for finding the surface area for the right prism is -

A = 2b + hP

2b + hp = 120

We can write the base area as -

2b = 120 - hp

b = 60 - hp/2

The volume of the prism would be -

V = base area x height

V = (60 - hp/2) x (h)

V = h(60 - hp/2)

Therefore, the volume of the prism would be h(60 - hp/2) cubic feet.

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Answer:

The two numbers are 90 and 59

Step-by-step explanation:

Let's call the two numbers x and y.

From the problem statement, we know that:

x + y = 149 (the sum of two numbers is 149)

x - y = 31 (the difference of the two numbers is 31)

To solve for x and y, we can use the method of elimination. Adding the two equations together eliminates the y term:

(x + y) + (x - y) = 149 + 31

2x = 180

x = 90

Substituting x = 90 into one of the original equations, we can solve for y:

x + y = 149

90 + y = 149

y = 59

Therefore, the two numbers are 90 and 59.

Using the unitary method, we found that one yellow token is worth 13.57 points and one blue token is worth 8.57 points.

Let's first find the value of one yellow token. We know that Jillian has collected 7 yellow tokens and has a total of 95 points. Therefore, the value of 1 yellow token can be found using the unitary method as follows:

1 yellow token = 95 / 7

1 yellow token = 13.57

Therefore, one yellow token is worth 13.57 points.

Therefore, the value of 4 blue tokens can be found using the unitary method as follows:

4 blue tokens = 75 - (3 x 13.57)

4 blue tokens = 34.29

Now, we know that 4 blue tokens are worth 34.29 points. To find the value of one blue token, we can use the unitary method again as follows:

1 blue token = 34.29 / 4

1 blue token = 8.57

Therefore, one blue token is worth 8.57 points.

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The stopping distance for a car traveling at 50 mph is 208.3 feet.

We can set up a proportion using the given information and the formula for stopping distance:

D = k s²

where D is the stopping distance, s is the speed of the car, and k is a constant of proportionality.

Using the given information, we can solve for k:

75 = k * 30²

k = 75 / (30²) = 0.0833

Now we can use this value of k to find the stopping distance for a speed of 50 mph:

D = 0.0833 * 50² = 208.3 feet

Therefore, the stopping distance for a car traveling at 50 mph is 208.3 feet.

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According to the question the resulting table would have 109 rows.

Table is a piece of furniture with a flat top and one or more legs, used as a surface for working at, eating from or on which to place things. Tables come in a variety of materials, shapes, and sizes and are used in many different settings, including homes, offices, and commercial establishments.

This is because all 90 players who played for 1 day would be joined, plus the 10 players who played across 2 days. Of the 90 players who played for 1 day, 82 would have 1 row each from the join, 7 would have 2 rows from the join, and 1 would have 0 rows from the join (since it was not in Table B). Of the 10 players who played across 2 days, 9 would have 1 row each from the join, and 1 would have 2 rows from the join. This adds up to a total of 109 rows.

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The dosage of Jack and Jill is obtained using geometric series formula which is 500 mg and 225 mg respectively.

What is geometric series?

A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. A geometric series is typically expressed as a + ar + ar² + ar³ + ..., where r is the common ratio between neighbouring terms and a is the coefficient of each term.

Let's start by finding the amount of medication that Jack takes in total.

Each hour, Jack takes a dosage that is 80% of the previous dosage (since it drops by 20%).

So his dosages form a geometric sequence with first term 100 and common ratio 0.8 -

100, 80, 64, 51.2, 40.96, ...

The sum of an infinite geometric series with first term a and common ratio r (where |r| < 1) is given by -

sum = a / (1 - r)

In this case, a = 100 and r = 0.8, so the sum is -

sum = 100 / (1 - 0.8) = 500

Therefore, Jack takes a total of 500 mg of medication.

Now let's find the original dosage for Jill.

If Jill takes half the amount of medication that Jack eventually took, then she takes -

500 / 2 = 250 mg

Let's call Jill's original dosage x.

Then her dosages form a geometric sequence with first term x and common ratio 0.7 (since it drops by 30%).

The sum of this sequence must be 250.

x + 0.7x + 0.49x + 0.343x + ... = 250

This is an infinite geometric series with first term x and common ratio 0.7, so we can use the formula for the sum of an infinite geometric series -

sum = x / (1 - 0.7) = x / 0.3

Simplifying the equation from before -

x / 0.3 × (1 + 0.7 + 0.49 + 0.343 + ...) = 250

x / 0.3 × (1 / (1 - 0.7)) = 250

x / 0.3 × 3.333... = 250

x = 250 / 1.111... = 225

Therefore, Jill's original dosage was 225 mg.

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Solving the given radical equation [tex]\sqrt{(4x+5)} = x-4[/tex] ,  the solution set is {11}

To solve the radical equation, we need to isolate the radical on one side of the equation and then square both sides to eliminate the radical. We can then solve for x and check our proposed solutions. Here are the steps:

Step 1: Isolate the radical on one side of the equation:
[tex]\sqrt{(4x+5)} = x-4[/tex]

Step 2: Square both sides of the equation to eliminate the radical:
[tex](\sqrt{(4x+5))^2} = (x-4)^2\\4x+5 = x^2-8x+16[/tex]

Step 3: Rearrange the equation and solve for x:
[tex]x^2-12x+11 = 0\\(x-11)(x-1) = 0[/tex]

Step 4: Solve for x:
[tex]x-11 = 0 , x-1 = 0\\x = 11 , x = 1[/tex]

Step 5: Check the proposed solutions by plugging them back into the original equation:
[tex]\sqrt{(4(11)+5)} = 11-4\\\sqrt{49 } = 7[/tex]
7 = 7 (True)

[tex]\sqrt{(4(1)+5) } = 1-4\\\sqrt{9} = -3[/tex]
3 = -3 (False)

Therefore, the solution set is {11}.

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The conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.

So the answer is ????(????|???? = y) = 1/y.

The question asks us to find the conditional density function ????(????|???? = y) given the joint density function ????(x, y) = 6y(1 − y), 0 ≤ x ≤ y ≤ 1.

To find the conditional density function, we need to divide the joint density function by the marginal density function of y.

The marginal density function of y can be found by integrating the joint density function with respect to x:

????(y) = ∫????(x, y) dx = ∫6y(1 − y) dx = 6y(1 − y) ∫dx = 6y(1 − y) (x) |0≤x≤y = 6y(1 − y) (y - 0) = 6y^2(1 − y)

Now we can find the conditional density function by dividing the joint density function by the marginal density function:

????(????|???? = y) = ????(x, y)/????(y) = 6y(1 − y)/6y^2(1 − y) = 1/y

Therefore, the conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.

So the answer is ????(????|???? = y) = 1/y.

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So, the solution to the system of equations is:

x = -26/7
y = -25/7
z = -37/7

Solving a system of linear equations by the Matrix Inversion method involves finding the inverse of the coefficient matrix, multiplying it by the constant matrix, and solving for the variables.

First, we need to write the system of equations in matrix form:

[ 2 6 2 ] [ x ] [ 8 ]
[ 6 6 3 ] [ y ] = [ -3 ]
[ 2 3 1 ] [ z ] [ 3 ]

Next, we need to find the inverse of the coefficient matrix:

A = [ 2 6 2 ]
[ 6 6 3 ]
[ 2 3 1 ]

The determinant of A is:

det(A) = 2(6-9) - 6(2-6) + 2(18-6) = -6 + 24 + 24 = 42

The adjoint of A is:

adj(A) = [ (6-3) (-2+6) (-18+6) ]
[ (-6+3) (2-4) (12-6) ]
[ (6-18) (-2+12) (2-18) ]

= [ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]

The inverse of A is:

A' = (1/det(A))adj(A) = (1/42)[ 3 4 -12 ]
[ -3 -2 6 ]
[ -12 10 -16 ]

= [ 1/14 2/21 -4/7 ]
[ -1/14 -1/21 2/7 ]
[ -4/7 5/21 -8/21 ]

Now, we can multiply the inverse of A by the constant matrix to find the solution:

[ x ] [ 1/14 2/21 -4/7 ] [ 8 ]
[ y ] = [ -1/14 -1/21 2/7 ] [ -3 ]
[ z ] [ -4/7 5/21 -8/21 ] [ 3 ]

= [ (8/14) + (16/21) + (-32/7) ]
[ (-8/14) + (-3/21) + (-6/7) ]
[ (-32/7) + (15/21) + (-24/21) ]

= [ -26/7 ]
[ -25/7 ]
[ -37/7 ]

So, the solution to the system of equations is:

x = -26/7
y = -25/7
z = -37/7

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Answer:

21.5

Step-by-step explanation:

The expression can be expanded as a difference of two logarithms:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

What is the logarithms?

Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.

We can use the properties of logarithms to expand the expression as follows:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]ln(x^2) - ln(y^5/2)[/tex]

Next, we can simplify each logarithm using the property that log(a^b) = b log(a):

[tex]ln(x^2) - ln(y^5/2)[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

Hence, the expression can be expanded as a difference of two logarithms:

[tex]ln(\sqrt\frac{x^2}{y^5})[/tex] = [tex]2 ln(x) - (5/2) ln(y)[/tex]

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Answer:

If it costs 5% of $75  it would be $3.75

If it is 5% off $75 it would be $71.25

How we find the answer.

To find 10% of an item you move the decimal point once to the right

If we do this to 75.00 it would be 7.500

We can remove the two 0's

7.5

We are not looking for 10% though we are looking for 5%

Half of 10 = 5 so half 7.5

3.75 is 5% of 75

---------------------------------------

Now if we want to find out 5%  off of 75 we subtract

75.00 - 3.75

71.25

Hope i could help

Answer:

$3.75

Step-by-step explanation:

If the item was on sale and cost 5% of its original price, to find the answer we would have to find 5% of 75 and to do this we have to do 5 ÷ 100 × 75

This means that the price would be $3.75

Hope this helps, have a lovely day! :)

The coordinates (2,1) will be on graph but (1,3) is not on graph.

What is a coordinate?

A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.

This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.

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The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.

What is Subtraction?

One of the four arithmetic operations, along with addition, multiplication, and division, is subtraction, which is denoted by the minus sign. The operation of subtraction represents the removal of items from a collection. In the adjacent image, for instance, there are 5 2 peaches, which means 5 peaches with 2 subtracted, making a total of 3 peaches.

As a result, 5 minus 2 equals 3, or the difference between 5 and 2. Although subtraction is most often used in mathematics with natural numbers, it can also be used with other types of objects, such as negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices, to remove or decrease physical and abstract quantities.

The difference in inches between 7 3/4 and 8 whole numbers is 1/4 inch.

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Answer: $15

Step-by-step explanation:

Remember percent makes the decimal move two places

The cost of Frank's shirt is 12 + 12(0.25)

12 + 3 = $15

Hope this helps!

The mass of suitcase D is 2x -2 kg.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the names given to these symbols because they lack fixed values.

As per the given data:

mass of A = x kg

B has a mass 6 kg less than A.

C has a mass twice of B

total mass = 6x - 20 kg

Let's consider mass of D as M.

mass of B = x - 6

mass of C = 2(x - 6)

For the total mass:

x + x - 6 + 2(x - 6) + M = 6x - 20

2x - 6 + 2x - 12 + M = 6x - 20

4x - 18 + M = 6x - 20

M = 2x - 2 kg

Hence, mass of suitcase D is 2x -2 kg.

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From the equation of the least squares regression line, we can say that the height of the flower compared to the soil line, in the beginning, is 3.16 units and it grows by 0.56 units each day.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. Two expressions joined by an equal sign form a mathematical statement known as an equation. The expression on the left and the expression on the right is shown to be equal in relation to one another.

LHS = RHS (left-hand side = right-hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" symbol in the statement. It will be taken into account as an expression.

Given,

The predicted height = 0.56

Days in soil = 3.16

The y-axis of the plot is the height of the line compared to the soil line.

The x-axis gives the number of days.

from the equation of the least squares regression line, we get the above predicted height and the days in the soil.

y  = mx+b is the equation of a line.

Then, we can say that,

m = slope = 0.56

b = y-intercept = 3.16

Therefore from the equation of the least squares regression line, we can say that the height of the flower compared to the soil line, in the beginning, is 3.16 units and it grows by 0.56 units each day.

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Kim Chung owes $176 in federal income taxes.

What is the interest?

In finance, interest refers to the fee that a borrower pays to a lender for the use of money or assets. It is a cost of borrowing money, usually expressed as a percentage of the principal amount borrowed (or invested).

To calculate the federal income tax owed by Kim Chung, we need to first determine his taxable income.

Kim Chung's taxable income is calculated as follows:

Total Income = $2,897 (wages) + $57 (interest) = $2,954

Adjustments = $0

Adjusted Gross Income (AGI) = Total Income - Adjustments = $2,954 - $0 = $2,954

Since Kim Chung's parents claim him as a dependent, his standard deduction for tax year 2022 is $1,150.

Taxable Income = AGI - Standard Deduction = $2,954 - $1,150 = $1,804

To determine the federal income tax owed, we need to use the tax tables provided by the IRS for tax year 2022.

According to the tax tables, the tax on $1,804 of taxable income is $176.

Therefore, Kim Chung owes $176 in federal income taxes.

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[tex]y =ax+b[/tex]

[tex]x = 0 \iff a(0) + b = 3 \implies b = 3[/tex]

[tex]x = 1 \iff a(1) + 3 = 5 \implies a = 2\\[/tex]

[tex]\implies \bf y = 2x + 3[/tex]

___________

[tex]x = 2 \iff 2(2) + 3 = 4 + 3 = 7[/tex]

[tex]x = 3 \iff 2(3) + 3 = 6 + 3 = 9[/tex]

The percent of powdered sugar in mixture B is 25.82%.

To solve this problem, we can use a table to organize the information and find the percent of powdered sugar in mixture B.

MixturePoundsPercent Powdered SugarPounds of Powdered SugarA520%1B11x%0.11xTotal1624%3.84

From the table, we can create an equation to find the percent of powdered sugar in mixture B:

1 + 0.11x = 3.84

Solving for x:

0.11x = 2.84

x = 25.82%

Therefore, the percent of powdered sugar in mixture B is 25.82%.

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The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

A mathematical statement is a sentence that can be either true οr false and cοntains mathematical expressiοns οr variables, such as numbers, variables, οperatiοns, relatiοns, οr lοgical cοnnectives.

Mathematical statements can take many fοrms, such as equatiοns, inequalities, geοmetric theοrems, and lοgical prοpοsitiοns. Fοr example, "2 + 2 = 4" is a mathematical statement that is true, while "1 + 1 = 3" is a mathematical statement that is false.

Nοw,

Given statement can be written as

Twο times=2x

six less than 2 times=2x-6

is nο mοre than 17= 2x-6≤17

where x is the number.

Hence,

          The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

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The exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).

The exact value of the following trig expression tan(11pi/12) can be found using trig identities and the special points on the unit circle.

First, we can use the double angle formula for tangent:

tan(2x) = 2tan(x)/(1-tan^2(x))

We can then use this formula to rewrite the given expression:

tan(11pi/12) = tan(2*11pi/24) = 2tan(11pi/24)/(1-tan^2(11pi/24))

Next, we can use the sum formula for tangent to rewrite the expression in the numerator:

tan(11pi/24) = tan(7pi/24 + 4pi/24) = (tan(7pi/24) + tan(4pi/24))/(1-tan(7pi/24)*tan(4pi/24))

We can then use the special points on the unit circle to find the exact values of these expressions:

tan(7pi/24) = tan(pi/3 + pi/8) = (tan(pi/3) + tan(pi/8))/(1-tan(pi/3)*tan(pi/8)) = (sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))

tan(4pi/24) = tan(pi/6) = sqrt(3)/3

Plugging these values back into the original expression, we get:

tan(11pi/12) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(1-(sqrt(3)/3)^2) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(8/9) = (2(sqrt(3) + sqrt(2-sqrt(2))))*(9/(8-9sqrt(3)*sqrt(2-sqrt(2))))

Simplifying further, we get:

tan(11pi/12) = (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2)))

Therefore, the exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).

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The present value of A = $35,000, r = 7% compounded monthly, t = 6 years is $24,036.89.

The present value is the amount of money that is needed today in order to produce a specified future value at a specified interest rate and time period. It is calculated using the formula: PV = A / (1 + r/n)^(n*t), where A is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the time period in years.

Given that A = $35,000, r = 7%, n = 12 (since the interest is compounded monthly), and t = 6 years, we can plug these values into the formula to calculate the present value:

PV = $35,000 / (1 + 0.07/12)⁷²
PV = $35,000 / (1.00583)⁷²
PV = $35,000 / 1.45558
PV = $24,036.89

Therefore, the present value is $24,036.89.

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