To decorate a cake, you make a shade of orange icing using 24 drops of red food coloring for every 8 drops of yellow. How many drops of yellow food coloring would you need if you use 9 drops of red food coloring?.

As per the given 4 x 5 matrix, the reduced row echelon form of A is [tex]\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right][/tex]

The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have the 4 x 5 matrix.

And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.

Now, we have to apply the value of

a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.

Then we get the matrix of 3 x 3 looks like the following,

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

Now, we have to do the following steps in order to get the reduced row echelon form of A,

The first and foremost steps is to take the non-zero number in the first row is the number 1.

Then we have to place any non-zero rows are placed at the bottom of the matrix.

This steps are repeated until the final row becomes zero.

Then we get the resulting matrix as [tex]\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right][/tex]

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The equation of the line that passes through the points (0,3) and (2,7) in slope intercept form is y = 2x + 3  .

The Slope Intercept form of the line is written as y = mx + c ; where c is the y intercept and m is the slope of the line .

to find the equation , we first need to find the slope ,

So , slope (m) = (7-3)/(2-0) = 4/2 = 2 ;

next we need to find the y intercept ;

So , putting the values , we get ;

3 = 2(0) + c

c = 3 .

putting the values of y intercept and slope in the equation ,

we get ;

the equation as ; y = 2x + 3 .

Therefore , the equation of the line is y = 2x + 3 .

The given question is incomplete , the complete question is

How do you write an equation of a line that passes through the points (0,3) and (2,7) in slope intercept form ?

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Constant, variable, operator and terms are four types of expression.

A constant term in mathematics is a term in an algebraic expression whose value is fixed or cannot change since it lacks any variables that may be changed. As the component is not yet included in the new term, a constant term that has a constant applied as a multiplicative coefficient likewise indicates a constant term. The term identify themselves as constants because the phrase has been modified. 5 is a constant term, in the quadratic polynomial 2x^2 + 5.

Is -4 a constant?

Yes, negative sign have nothing to do with the definition of constant. -4 is still a constant.

There are four types of expression in mathematics:

1. Constant: any numeric value e.g. 6

2. Variable: any alphabetic/unknow value e.g. x,y etc.

3. Operators: +,-, *, / (addition, subtraction, division, multiplication)

4. Term: it can be constant, variable, constant multiplied by variable. It is separated by an operator.

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Answer:

2.) the answer is D, because 12 hours is the closest number between 10 and 15

No, your cousin is not correct. 5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

When you round a number to the nearest hundred, you look at the tens place to determine which hundred to round to. In this case, the tens place is 9, which means that 5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

To round to the nearest hundred, you can follow these steps:

Look at the tens place (the digit in the ones place).

If the tens place is 0, 1, 2, 3, or 4, round down.

If the tens place is 5, 6, 7, 8, or 9, round up.

For example, if you want to round 4,567 to the nearest hundred, you would look at the tens place, which is 6. Since the tens place is greater than 5, you would round up to 4,600. Similarly, if you want to round 5,432 to the nearest hundred, you would look at the tens place, which is 3. Since the tens place is less than 5, you would round down to 5,400.

∴5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

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To round to the nearest hundred, you can follow these steps:

Look at the tens place (the digit in the ones place).

If the tens place is 0, 1, 2, 3, or 4, round down.

If the tens place is 5, 6, 7, 8, or 9, round up.

For example, if you want to round 4,567 to the nearest hundred, you would look at the tens place, which is 6. Since the tens place is greater than 5, you would round up to 4,600. Similarly, if you want to round 5,432 to the nearest hundred, you would look at the tens place, which is 3. Since the tens place is less than 5, you would round down to 5,400.

5,953 should be rounded up to 6,000 when rounded to the nearest hundred.

Answer:

Your answer is B

Step-by-step explanation:

Answer in image.

Answer:

Below

Step-by-step explanation:

From the graph, the zeroes are at -4 and - 0.5 so the equation starts like this:

a (x+4)(x+.5) = 0    now ya need to sub in a point to calculate 'a'

 ......  point 0,4 results in this:

a (0+4)(0+.5) = 4

 2a = 4

   a = 2

so the equation becomes  2 ( x+4)(x+.5) = 0

                                2 ( x^2 + 4.5x +2) = 0

                                   2 x^2 + 9x + 4 =0  

Answer:

-2

Step-by-step explanation:

plug both equations in desmos graphing calculator website

and you can see that the solution (where both equations intersect)

is (-2,6)

solutions are (x,y)

so the x coordinate of the solution is -2

The system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, the search for a way to respond to them has spurred the development of mathematics.

Here,

Given data:

Time taken by Latanya to solve a problem = 1.5 minute.

Time to read one page = 2 minutes.

Number of problems completed = x problems.

Total time used for reading = y  minutes.

Using the data to consider:

Let x be the the number of math problems that Latanya solved.

Let y be the number of pages that Latanya read.

thus,

1.5x +2 y = 48

and

x = 4 + y

Thus, we can conclude the the system of equations obtained from the given information are 1.5x +2 y = 48 and x = 4 + y respectively.

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The Nature of roots of the quadratic equation "5x² -3x +2 = 0" is  imaginary and conjugate   .

To find the Nature Of Roots of the Quadratic Equation ax² + bx + c = 0 , we find the discriminant(D) by the formula ; D = b² - 4ac .

the quadratic equation is given as 5x² -3x +2 = 0 ;

On comparing , we get , a = 5  , b = -3 and c = 2 .

Substituting the values in the Discriminant formula mentioned above , we get

D = (-3)² - 4×5×2

= 9 - 40

= -36 .

Since the value of the discriminant is less than 0 ,

Therefore  , the roots will be imaginary and conjugate .

The given question is incomplete , the complete question is

What is the nature of the roots of the equation 5x² -3x +2 = 0  ?

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Answer:

3x + 2y = 6

Step-by-step explanation:

When you solve for y in this equation, it is in the same format as the slope-intercept equation.

3x + 2y = 6

2y = -3x + 6

y = -3/2 x + 3  

The slope intercept equation is ...

y = mx + b

(m can be any number)

The slope-intercept equation is for linear functions!

The initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours  of flight.

The linear model that can be used to predict the amount of jet fuel present on the Boeing 747-8 Intercontinental jet after 18 hours of flight without refueling is given by the equation

F = 63,500 - (800 x 18),

where F is the amount of jet fuel in gallons and 18 is the number of hours of flight. This equation indicates that after 18 hours of flight, the jet would have an estimated amount of jet fuel of 42,400 gallons remaining. This amount is significantly lower than the initial amount at the start of the flight, which was 63,500 gallons, indicating that the jet would need to refuel soon after the 18 hours of flight.

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Domain is the input of a function and range is the output of a function, for f(x) = sin(x), domain will be (-inf, +inf) and range will be [0,1].

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Domain is the input of a function and range is the output of a function.

Examples:

f(x) = sin(x), domain =  (-inf, +inf) and range = [0,1].

f(x) = cos(x), domain =  (-inf, +inf) and range = [0,1].

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The probability that the sample proportion is more than 40% is approximately .0001.

What is Probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To find the probability that the sample proportion is more than 40%, we need to use the normal distribution and the central limit theorem.

The central limit theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To find the probability that the sample proportion is more than 40%, we need to first calculate the mean and standard deviation of the sample proportion. The mean of the sample proportion is equal to the population proportion (38%), and the standard deviation of the sample proportion is equal to:

  [tex]standard\ deviation = sqrt((population\ proportion * (1 - population\ proportion)) / sample\ size)\\\\= \sqrt{((.38 * .62) / 400)}\\\\= .048[/tex]

Next, we need to standardize the sample proportion of 40% by subtracting the mean and dividing by the standard deviation:

z = (40% - 38%) / .048 = 4.17

The probability that it is less than or equal to 40% is approximately .9999.

The probability that the sample proportion is more than 40% is then equal to 1 - .9999 = .0001.

So, The probability that the sample proportion is more than 40% is approximately .0001.

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A vertical straight line is not a function. It is a relation, but not a function as it does not follow the condition to be a function.

A condition for a function is that a unique input gives a unique output, that is a unique output can trace back to only one unique input.

In the case of a vertical straight line, it is of the form x = a, where a is a constant. That is for x = a, there is infinitely many values for y, therefore it does not follow the condition of a function and hence a vertical straight line is not a function.

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Answer:440

Step-by-step explanation:

Answer:

To find the number of nickels in $22, we need to first convert the amount of money from dollars to cents and then divide this number by the value of a nickel in cents. Since 1 dollar is equal to 100 cents, we can convert $22 to 2200 cents.

Next, we need to find the value of a nickel in cents. Since a nickel is worth 5 cents, the value of a nickel in cents is 0.05 * 100 = 5 cents.

Finally, we can divide the total number of cents by the value of a nickel in cents to find the number of nickels:

2200 cents / 5 cents/nickel = 440 nickels

Therefore, there are 440 nickels in $22. Solving the equation 22 ÷ 0.05 gives the same result.

The number of students that failed the examination in the class is 64

information from the problem

there are 160 students in a class

60% of students passed in examination

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

if 60% of the students passed the examination then the percentage that failed is solved by subtraction from 100. This is done by

= 100 - 60

= 40%

The number of failed students is solved by converting the 40% to a factor by diving by 100 such that 40% = 40 / 100 = 0.04

= 0.4 * 160

= 64

The total number of failed students is 64

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The mode of a set of numbers is the number that appears most often in the set. In the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there is no number that appears more often than any other, so the mode of this set is not defined.

The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group. The mode is the one that is most prevalent.

The value that appears most frequently in a set of values is referred to as the mode. It is the value that shows up the most frequently. Example: Since the number 5 appears twice in the provided data set of 2, 4, 5, 6, and 7, it is the mode of the data set. 2

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The value of polynomial 5x - 4x² + 3 at x=0 is equal to 3

Given that,

The polynomial is 5x - 4x² + 3

To find : The value of polynomial 5x - 4x² + 3 at x=0

A combination of more than two algebraic expressions, particularly when they each contain a distinct power of the same variable (s).Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

Given : x = 0

→ 5x - 4x² + 3

→ 5 ( 0 ) - 4 ( 0) ² + 3

→ 0 - 0 + 3   ( ∵ here + 0 - 0 cancels )

→ 3

Therefore, The value of polynomial 5x - 4x² + 3 at x=0 is 3.

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Identify the denominator of the function and set it equal to zero. Solve the equation to find the x-values of the asymptote. Substitute the x-values found in step two into the original equation to determine if the vertical asymptote is a true asymptote.

The first step when finding vertical asymptotes is to identify the

denominator of the function and set it equal to zero. This creates an equation which can then be solved to find the x-values of the asymptote. The second step is to solve the equation, using methods such as factoring or completing the square, to find the x-values of the asymptote. The final step is to substitute the x-values found in step two into the original equation and determine if the vertical asymptote is a true asymptote. If the limit of the function as x approaches the x-value found in step two is either positive or negative infinity, then the vertical asymptote is a true asymptote. If, however, the limit of the function as x approaches the x-value found in step two is not infinity, then the vertical asymptote is not a true asymptote. This process of finding vertical asymptotes can be used to find the vertical asymptotes of any function.

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Answer:

2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]\sqrt{5}[/tex] * [tex]\sqrt{8}[/tex] =

[tex]\sqrt{5*8}[/tex] =

[tex]\sqrt{40}[/tex] =

[tex]\sqrt{4*10}[/tex] =  ==> 4 has a square root: [tex]\sqrt{4}[/tex] = 2

2 * [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex].

The roots of the quadratic equation 2x² + 5√3x - 6 = 0 are imaginary.

To solve this equation, we can use the Quadratic Formula. The Quadratic Formula is:

x = [ -b ± Â√(b2 - 4ac) ] / 2a

In this equation, a = 2, b = 5√3, and c = -6.

Plugging these values into the formula, we get:

x = [ -(5√3) ± Â√((5√3)2 - 4(2)(-6)) ] / (2(2))

Simplifying, we get:

x = [ -(5√3) ± Â√(25*3 + 24) ] / 4

Simplifying further, we get:

x = [ -(5√3) ± Â√(75) ] / 4

Since √75 is an irrational number, the roots of the equation are imaginary.

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The state income tax owed on the $40,000 salary should be $1,800.

An income tax is a tax levied on persons or companies based on their earnings or profits. In most cases, income tax is calculated as the result of a tax rate multiplied by the taxable income. Taxation rates may differ depending on the taxpayer's attributes and the source of income.

Given:

Income Progressive Range ($)                  Tax Rate

                        0-  10,000                                 3%

                       10-001- 50000                           5 %

                      50001- 100000                          5.5%

The calculation of the state income tax owed on $40,000 salary

= 3% of $10,000 + 5% of $30,000

= $300 + $1,500

= $1,800

Hence, the state income tax owed is $1,800.

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The solutions to the equation 2x^2 = 100 is  [tex]x=\pm 5 \sqrt{2}[/tex].

How do you find all solutions of a quadratic equation?

The solutions of a quadratic equation ax2 + bx + c = 0 are given by the quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula, just get the equation into standard form ax2 + bx + c = 0, and apply the quadratic formula.

[tex]$$2 x^2=100$$[/tex]

Divide both sides by 2

[tex]\frac{2 x^2}{2}=\frac{100}{2}$$[/tex]

Simplify

[tex]x^2=50$$[/tex]

For [tex]$x^2=f(a)$[/tex] the solutions are [tex]$x=\sqrt{f(a)},-\sqrt{f(a)}$[/tex]

[tex]$$x=\sqrt{50}, x=-\sqrt{50}$$[/tex]

[tex]$$\begin{aligned}& \sqrt{50}=5 \sqrt{2} \\& -\sqrt{50}=-5 \sqrt{2} \\& x=5 \sqrt{2}, x=-5 \sqrt{2}\end{aligned}$$[/tex]

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The level of a line's slope indicates its steepness, for the line y = 3x + 1 the graph is looks like:

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

Now, given that,  

Y = 3x + 1 ........ (1)

slope intercept form equation is: y = mx+c ........... (2)

next, if we compare (1) and (2)

it comes out to be

m = 3 representing slope

and c = 1 representing y-intercept.

now, slope angle: tan θ = m (slope)

tan θ = 3              [putting the value of m]

θ = [tex]tan^{-1/3}[/tex]

The graph is shown as:

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The complete question is as follows:

What does y = 3x + 1 look like on a graph?

BC is equal to 24cm.Now, by applying the Pythagoras theorem i.e. in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides, we can find BC.

Find BC ?

So, we can apply the Pythagoras theorem here, if it is right-angled at C then the side opposite to C will be the hypotenuse of the triangle that is AB = 25 cm, and the other two sides are AC = 7 cm and BC.

AB = 25 cm, AC = 7 cm and BC =?

In triangle ACB, By Pythagoras theorem, (Hypotenuse)2 = (Perpendicular)2 + (Base)2

AB)2 = (AC)2 + (BC)2

(25)2 = (7)2 + (BC)2

625 = 49 + (BC)2

(BC)2 = 625 – 49

(BC)2 = 576

BC = 24 cm

Thus, BC is equal to 24cm

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No, 1 is not a real number.

Real numbers are numbers that can be used to measure or describe anything, such as a quantity or distance. Real numbers can be either rational (e.g. fractions, decimals, and integers) or irrational (e.g. roots and pi). Real numbers are usually represented on a number line, where points to the right of 0 represent positive numbers and points to the left of 0 represent negative numbers.

Real numbers include all the rational and irrational numbers. They can be integers, fractions, decimals, and even imaginary numbers. 1 is an integer, so it is not considered a real number. Real numbers are those that have a decimal representation, which 1 does not.
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Answer:

Option C

1 and 5

Step-by-step explanation:

So,

as you can see here,

are the vertical angles.

According to the calculation used to compute it, [tex]3\frac{1}{3}[/tex] liters of water are required to water all the indoor plants.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. An expression in mathematics is a combination of digits and operations. A mathematical expression that performs an operation has the following components: Operations and Operands

The amount of water needed to water all the indoor plants is 1/3 liter, according to the calculation used to determine this.

[tex]= 4/3 / 2/5\\ = 4/3 X 5/2\\ = 3\frac{1}{3}[/tex]

Consequently, 3 1/3 liters are needed.

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On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)

The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.

The answer to the question is that all real numbers or (−∞,∞)

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