for what values of k does the quadratic equation (k 4)x -3kx-4(k -2) = 0 have two roots which differ by 1?

By the property of exponents, the value of the above equation is 2*10^7.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

=1.2 x 10^5/6 x 10^-3

=(12/6)*10^7

=2*10^7

The value of given expression is 2*10^7 by property of exponents.

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The value of the original fraction is expressed as; 36/45

Let the numerator be x and let the denominator be y. Thus;

Original fraction = x/y

Reciprocal of fraction = y/x

x/y = 4/5

Cross multiply to get;

5x = 4y

4y - 5x = 0   -----(1)

The numerator is now increased  by 9 and the new fraction equals the reciprocal of the value of the original fraction. Thus;

(x + 9)/y = 5/4

Cross multiply to get;

4x + 36 = 5y

5y - 4x = 36    ------(2)

Multiply eq 1 by 4 and eq 2 by 5 to get;

16y - 20x = 0   -----(3)

20y - 20x = 180  ----(4)

Subtract eq 3 from 4 to get;

4y = 180

y = 180/4

y = 45

5x = 4y

x = (4/5) * 45

x = 36

Original fraction is; 36/45

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Answer:

To find the apothem of a regular polygon, we can use the formula:

A = (ns^2)/(4tan(180°/n))

Where A is the area, n is the number of sides, s is the length of each side, and tan(180°/n) is the tangent of half of the central angle.

First, we need to find the number of sides of the polygon. To do this, we can use the formula for the sum of the interior angles of a polygon:

(n - 2)180° = 1080°

Solving for n:

n = 6

So the polygon has 6 sides.

Next, we can plug in the values we have into the formula for the apothem:

A = (6s^2)/(4tan(180°/6)) = 160

Expanding the right side:

A = (6s^2)/(4tan(30°)) = 160

Using the tangent identity:

A = (6s^2)/(4(√3/3)) = 160

Multiplying both sides by 4(√3/3) to isolate s^2:

4(√3/3)A = 6s^2

Expanding the left side:

4(√3)A/3 = 6s^2

Dividing both sides by 6:

2(√3)A/3 = s^2

Taking the square root of both sides:

s = √(2(√3)A/3)

Plugging in the value for A:

s = √(2(√3) * 160/3)

Calculating:

s = √(106.667) = 3.25

So the length of each side is 3.25 inches.

Finally, we can find the apothem using the formula:

a = s/2tan(180°/n)

Expanding the right side:

a = 3.25/2tan(30°)

Using the tangent identity:

a = 3.25/2(√3/3)

Dividing both sides by √3/3:

a = 3.25√3

Calculating:

a = 5.5

So the length of the apothem is 5.5 inches.

Answer:

3+[tex]\frac{1}{4}w[/tex]  represents the distance ran on week w

The marks in paper 2 would be 100.

Given is a pupil who scored 50 in his paper 1 exam got ill and missed paper 2.

Assume the equation of the line of best fit is of the form -

y = mx + c

Let {c} = 0

Now, for the point (1, 50), we can write -

50 = m

So, the equation will be of the form -

y = 50x

Now, for {x} = 2, we can write -

y = 100

Therefore, the marks in paper 2 would be 100.

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Answer:

80

Step-by-step explanation:

Hope it helps! =D

Answer: 80

Step-by-step explanation: When rounding to the nearest 10, you need to examine the number you are trying to round. If the number has a 1's place that is 4 or lower, you round to 70, but if the 1's position is 5 to 9, you round to 80. In this case, 77 can be rounded to 80, since the 1's place number is between 5 and 9.

Hope this helps! :)

The percent increase in the height of the seedling is, 23%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

A seedling Jeffery planted in 2009 was 5cm tall in 2010 it was 120 cm

i.e. increase in the height = 120-5

                                           =115 cm

now,

the percent increase in the height of the seedling is,

115/5*100

=23%

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Same amount of money can buy 95 dinners after 12 years.

Inflation is a decrease in the purchasing power of money, reflected in a general increase in the prices of goods and services in an economy.

Given,

Purchasing power of a fixed quantity of money decreases by 5% every year

It can buy 175 frozen dinners today,

Principal value P = 175 frozen dinners

Rate of decrease R = 5% = 0.05

Time n = 12 years

Equation for the future value

A = P (1- R)ⁿ

Frozen dinners that can be bought in 12 years with same amount

A = 175 ( 1 - 0.05 )¹²

A = 175 (0.95)¹²

A = 175 × 0.540360088

A = 94.5630154 ≈ 95

Hence, 95 frozen dinners can be bought after 12 years with same amount of money.

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from the given information in the question we have found that all the three sets form a partition from the universal sets

What is a set?

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

As it is given that there are 3 sets where the first set A1 has 10 or more elements, A2 has 20 or more elements, and A3 has 15 or more elements.

1. If A1 ⊆ A2 and A2 ⊆ A3 then the union of these three will contain the same number of elements as that of A3.

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The provided Product 9/10 * 20/21 has the simplest form, which is 6/7.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given a fraction multiplication 9/10 × 20/21

Simplification Using PEMDAS

=>  9/10 × 20/21

=> 9* 20 /21 *10

=> 6/7

Therefore, the simplest form of the given Product 9/10 × 20/21 is 6/7.

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 2 }{ 2 } \implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 1}(x-\stackrel{x_1}{1})\implies y-1=x-1\implies \boxed{y=x}[/tex]

Answer: y=x+2

Step-by-step explanation: to find the slope use the formula y2-y1/x2-x1 which will get 3-1/3-1= 2/2= 1 so the slope is one. then take formula (y-y1)=m(x-x1) m is slope so you will get (y-3)=1(x-1) distribute the one y-3=x-1 add three to both sides to get y=x+2

Answer:

16/2

Step-by-step explanation:

2 2/7  = 16/2

2 times 7 = 14 + 2 = 16/2

So, the answer is 16/2

Answer:

2 2/7 = 17/7

Step-by-step explanation:

The way I learnt it is that when you take 2 2/7 we just have to multply the denominator (7) by the whole number (2) which gives us 14 and then we have to add the numerator (2) which gives us our numerator which is 16 and the denominator stays the same meaning our answer would be 17/7. (It is the simplest form)

Ximena wants to decrease 350 by 4%, here the complete statement is:

350 × 4% = 14.

When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.

b)

= 350 × 4%

= 350 × (4/100)

= 14

19. a)

5 (x - 6) = 15

or, 5x - 30 = 15

or, 5x = 45

or, x = 9

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Answer:

Where are the choices?

Step-by-step explanation:

An example of a pure exact number is "3".

In mathematics, pure exact numbers are also known as mathematical constants or closed-form numbers. Unlike approximations, such as those obtained through measurement or estimation, exact numbers have a fixed and well-defined value.

A pure exact number is a number that has a fixed, precise value and is not subject to any estimation or measurement error.

Examples of pure exact numbers include integers (e.g. 3, 42), rational numbers (e.g. 1/2, -3/7), and some real numbers that can be expressed as a ratio of integers (e.g. pi, e).

These numbers have a definite value and do not change, regardless of the measurement or calculation method used.

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The two numbers that multiply to -60 and add up to -7 are:

[tex]-12,5[/tex]

We can multiply -12 by 5 and get -60:

[tex]-12\times5=-60[/tex]

We can also add -12 and 5 to get -7:

[tex]-12+5=-7[/tex]

So therefore, the two numbers that multiply to -60 and add to -7 are:

[tex]\fbox{-12 and 5}[/tex]

Answer:

answer for the expression 5(–4+k) + –2(–3+–10k) is -5k - 6.

To arrive at this answer, we used the order of operations (PEMDAS) as follows:

Parentheses first: (–4+k) = k-4 and (–3+–10k) = –10k-3

Next, the multiplication: 5(k-4) = 5k-20 and -2(-10k-3) = 20k+6

Finally, the addition: -5k-20 + 20k+6 = -5k - 6 + 20k

And then we simplify further by combining the like terms:

-5k - 6 + 20k = -5k + 20k - 6 = 15k - 6

So the final answer is -5k -6

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Marna thinks is wrong. Thus Marna's think is incorrect.

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.

Given that Marna thinks that about 35% of her mail is junk mail.

Thus out of 100 emails, 35 emails are junk.

Thus the ratio of regular emails to junk mail is

100:35

= 20:7

Again given that she gets about twice as much regular mail as junk mail.

Assume that the number of junk mail is x.

Then the regular mail is 2x.

Thus the ratio of regular emails to junk mail is

2x:x

=2:1

The ratio  20:7 ≠ 2:1

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Each person eats at least one fruit. Hence 39% of people eat both orange and apple using the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. From the given data

n(O)=0.63

n(A)=0.76

n(A∪O)=1 as every person eats at least one fruit

n(A∪O)=n(A)+n(O)−n(A∩B)

1=0.63+0.76−n(A∩B)

n(A∩B)=1.39−1

n(A∩B)=0.39

A∩B=0.39×100=39

Hence 39% of people eat both orange and apple

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The statement that best describes the graph of linear Inequality in two variables is a straight line graph. That is option A.

A linear Inequality is defined as the expression that can be used to represent the relationship between two variables using inequality symbols such as '<', '>', '≤' or '≥'.

When a linear Inequality between two variables are being represented in a graph, a straight line graph is obtained because the inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

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The initial amount a is 1250 and the rate of decay r is 0.865 (86.5%). When t = 3, the function h(t) = 1250(0.865)3 = 587.356. Rounded to the nearest tenth, the answer is 587.4.

To solve this exercise, you need to use the equation

h(t) = a(r)^t,

Where a is the initial amount and r is the rate of decay.

In this example,

Plugging in t = 3 into the equation gives

h(t) = 1250(0.865)^3 = 587.356.

To round this to the nearest tenth, you need to look at the number to the right of the decimal point, which is the 6 in 587.356. Since the 6 is 5 or greater, you need to round the 587.356 up to 587.4.

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Each polynomial given is associated with the given factoring technique in the second column. a. GCF b. grouping c. none d. the difference of two squares e. Sum and product f. Perfect square trinomial.

To factorize an algebraic statement, we first identify the terms' highest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic expression gets expanded in the opposite direction.

Each polynomial given is associated with the given factoring technique in the second column.

a. grouping

b. GCF

c. none

d. the difference of two squares

e. Sum and product

f. Perfect square trinomial

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The graph of the sequence may pass toward the vertical line test.

Functions are defined as a fundamental part of the calculus in mathematics. These are the special types of relations. A function is visualized as a rule, which gives a unique output for every input x.

Given the information that, he gives two away on day 1, four away on day 2, and eight away on day 3. He continues this pattern for 10 days.

Let x be the number of days and f(x) be the number of cards.

So, the pattern is

f(x)=2, when x=1

f(x)=4, when x=2

f(x)=8, when x=3

Then, the function will be f(x)=2ˣ

The equation of the graph is passing through a vertical line.

The vertical line test is a graphical method that determines whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

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The required solution for the given inequalities has been shown in the graph.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
4x + y < 8
x - y > 3

Illustrate the graph of the inequality, the overlapped region on the graph is the solution of a system of inequalities.

Thus, the required solution for the given inequalities has been shown in the graph.

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The required number of songs that can be put in the final CD are 5 song.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A band expects to put 16 songs on their next CD. The band writes and records ​25% more songs than they expect to put on the CD. During the editing​ process, 75​% of the songs are removed.

According to the question,
Song added to CD = 16 + 25% of 16
                               = 20 songs

Song added to Final CD = 20 - 75% of 20
                                        = 5 songs

Thus, the required number of songs that can be put in the final CD are 5 song.

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Height is a interval - level variable typically in statistics.

Height is typically considered an interval-level variable in statistics. This means that height has a meaningful zero point, but the difference between two height measurements does not have a meaningful interpretation. For example, if one person is 6 feet tall and another person is 5 feet tall, the difference of 1 foot is meaningful, but the ratio of their heights is not.

In contrast, ratio-level variables have a meaningful zero point and the ratio of two values also has a meaningful interpretation. For example, weight is a ratio-level variable because a weight of 0 pounds has a well-defined meaning, and the ratio of two weights (such as two people each weighing 150 pounds) is meaningful and can be compared.

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The interquartile range (IQR) is a measure of spread in a dataset and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

The IQR of the ‘gre’ variable can be calculated using the formula IQR = Q3 - Q1. This tells us the range of values that lie between the 25th and 75th percentile.

In this case, the IQR of ‘gre’ is calculated to be 210 - 340 = 70. This means that 70% of the distribution data falls within the interquartile range of ‘gre’. This can be further visualized on a boxplot, which shows the median, upper and lower quartiles. The IQR is represented by the box and the whiskers that extend out from it, indicating the range of values that lie within the interquartile range.

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The area of the state of Nevada which had the shape of a right trapezoid would be = 110,622 miles²

The area of a trapezoid can be calculated using the formula of the following;

A = ( a + b ) x h/2

where;

a = 205

b = 511

h = 309

Area (A) = (205+511) × 309/2

= 716 × 154.5

= 110,622 miles²

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The area of the state of Nevada with the shape of a right trapezoid is; 110622 miles²

The area of a trapezoid can be calculated with the formula :

Area = ¹/₂(a + b) * h

where;

a and b are parallel sides

h is height

The parameters are;

a = 205

b = 511

h = 309

Thus;

Area = ¹/₂(205 + 511) * 309

Area = 716 * 154.5

Area = 110622 miles²

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The required simplified value of the given expression is [A × B] ×10².

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
=  A x 10 ×  B × 10

Applying distributive property, a (bc) = (ab) c
= A × B × 10 × 10

Applying associative property in the exponents of 10, 10 × 10 = 10²
= [A × B] × 10²

Thus, the required simplified value of the given expression is [A × B] ×10².

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