For what values of k will the following pair of linear equations have infinitely many?

The required way to plot the graph of log function is described.

It can be represented graphically as follows: The graph of any function's inverse function is the reflection of the function's graph about the line y=x. The reflection of the preceding graph about the line y=x is the graph of the logarithmic function y=log3(x), which is the inverse of the function y=3x.

The function loglog(X, Y) shows the x- and y-coordinates on the x- and y-axes, respectively, using a base-10 logarithmic scale. Specify X and Y as vectors of the same length in order to visualise a set of coordinates connected by line segments. You must provide at least one of X or Y as a matrix in order to plot several sets of coordinates on the same set of axes.

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An acute triangle is a sort of triangle in which all three internal angles of the triangle are less than 90°. Acute triangles are also named acute-angled triangles.

A triangle is a fundamental polygon with three sides and three vertices. Since the triangle has three sides, it also has three interior angles. An angle which measures between 0° to 90° is called an acute angle. An acute triangle is a kind of triangle in which all three internal angles of the triangle are less than 90°.

Acute triangles are also called acute-angled triangles. Even though the length of the sides of acute triangles varies, the interior angles are never more than 90°.

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69Answer:

Step-by-step explanation:

because I love 69

Answer:

Depth after 9 minutes is -253 feet

Step-by-step explanation:

Since we can find the submarine's depth as a function of time, m (in minutes), lets use the function to calculate the answer.

We are given the equation for depth: Depth(m) = -370+13m

Depth(x) means that the equation will tell us the submarine's depth after m minutes. The equation is missing the units, but we know from the statement that the initial depth is -370 feet and the rate of ascention is +13 feet/min. So we can enhance the equation by rewriting it with the units.

Depth(m) = -370ft+13(feet/minute)*m [m is minutes]

The sub's depth after 9 minutes is:

Depth(9) = -370ft+13(feet/minute)*(9 minutes)

Depth(9) = -370ft + 13*(9)

Depth(9) = -370+117

Depth(9) = -253 feet

The slope of y = -2x is -2.

The slope of a linear equation is a measure of how steep the line is. In other words, it represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

In the equation y = -2x, the coefficient of the x term is -2, which means that for every unit increase in x, the value of y will decrease by 2 units. So the slope of this line is -2.

The slope can also be thought of as the tangent of the angle the line makes with the x-axis. In this case, the slope being -2, means the angle of the line with the x-axis is negative, which means the line is going downward and to the left.

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So, the person's blood-alcohol level is estimated to be 40 mg/dL after 4 hours.

An exponential model for the person's blood-alcohol level can be represented by the function f(t) = A * e^(-kt) where A is the initial blood-alcohol level, k is the decay constant and t is the time in hours.

To find the decay constant k, we can use the known information that after 2 hours, 112.5 mg/dL remains. We can substitute the known values into the exponential function, and solve for k:

f(2) = A * e^(-2k) = 112.5

A = 200 mg/dL

200 mg/dL = 112.5 * e^(-2k)

k = ln(200/112.5)/(-2)

Using this value of k, we can now find the blood-alcohol level after 4 hours:

f(4) = A * e^(-kt) = 200 * e^(-k*4)

f(4) = 200 * e^(-1.6) = 200 * 0.20 = 40 mg/dL

Therefore, the person's blood-alcohol level is estimated to be 40 mg/dL after 4 hours.

It's worth noting that this model is based on the assumption that the blood-alcohol level decays exponentially, and many other factors like body weight, gender, metabolism, and the amount of alcohol consumed can affect the actual blood-alcohol level.

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Answer:

2 & 4 (36 and 12)

Step-by-step explanation:

[tex]\frac{y}{3} \leq 12\\y\leq 36\\12\leq 36\\36 = 36[/tex]

Length of YZ = 29.5

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

Given,

∵ ABCD ~ WXYZ

∴ By the figure ΔADC ~ ΔYWZ

∴ AD/DC = WZ/YZ

AD = 8, DC = 4, and WZ = 59

⇒ 8/4 = 59/YZ

⇒ 2 = 59/YZ

⇒ 2YZ = 59

⇒ YZ = 29.5

Hence, 29.5 is the length of YZ.

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Answer: I believe it is infinitely many solutions

Step-by-step explanation:

2023

Answer:

Step-by-step explanation:

The first equation is already in slope intercept form - y=mx+b

the second equation we would to get y by itself.

so 7x - 6y = 12  subtract 7x from both sides

-6y= -7x + 12    I put the 7x first to keep the y=mx+b form

y = (-7x + 12) / -6  divide both sides by -6

y = 7/6 x -2

so your two equations are now

y = 7/6x + 2

y = 7/6x - 2

you can graph the equation by putting a point in for x and solving for y.

y = 7/6 (0) +2

y = 2

so your first point is (0,2)

try a different value for x

y = 7/6 (6) + 2

y = 7 + 2 (multiplying by 6 cancels out the 6 denominator)

y = 9

so another point is (6, 9)

in the formula y = mx + b , b is the y intercept

so the line will intercept Y at 2 and there will be a point at (6,9)

Do the same for the other equation.  It will be exactly the same except that the y intercept will be at -2, not 2.

We have found more than one solution, so the answer can not be one solution or no solutions.   By process of elimination we have infinitely many solutions.

Qualitative variables allow for the classification of individuals based on some attribute or characteristic.

A qualitative variable, additionally referred to as categorical, is one wherein the variable categories aren't described as numbers but alternatively by using verbal groupings. There are classifications of specific statistics: nominal and ordinal. Nominal variables have “names,” not numerical values.

Quantitative variables are any variables in which the facts constitute amounts (e.g. height, weight, or age). specific variables are any variables wherein the information constitutes companies. Qualitative Variables. additionally referred to as specific variables, qualitative variables are variables without a natural feel of order. They're consequently measured on a nominal scale. Qualitative records are information describing the attributes or homes that an object possesses. The residences are categorized into training that may be assigned numeric values. but, there may be no significance to the statistics values themselves, they genuinely constitute attributes of the object worried.

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When w = 2 and x = 3, the value of the expression 10w - 9x will be -7.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, w = 2 and x = 3, the value of 10w - 9x will be:

= 10w - 9x.

= 10(2) - 9(3)

= 20 - 27

= -7

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Complete question

Given w = 2 and x = 3, what does 10w - 9x equal?

The difference between the y-intercepts of the lines y = 5x + 3 and

y = (17/2)x - 19 is  22 units.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The given equation of the line in slope intercept form is y = 5x + 3.

The slope of the line given in the table is,

m = (32 - 15)/(6 - 4).

m = 17/2.

Now, 15 = (17/2)×4 + b.

15 = 34 + b.

b = - 19.

So, The required equation of the line is y = (17/2)x - 19.

The difference between the y-intercepts of the lines y = 5x + 3 and

y = (17/2)x - 19 is 3 - (- 19) = 22 units.

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Answer:

To find the percent of increase in the cost of season tickets, we can use the following formula:

(New cost - Old cost) / Old cost x 100 = % increase

Using the given information:

(1,441 - 1,310) / 1,310 x 100 = 10.06%

So, the percent of increase in the cost of season tickets is 10.06%.

The number of weeks that he will be able to buy the game will be 6 weeks.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Marcus starts with $5 in his piggy bank. He receives a $10.00 allowance each week. Each week he saves $7.00 of his allowance in his piggy bank. His goal is to save at least $47.00 to buy a game.

Let 'x' be the number of weeks. Then the inequality is given as,

$5 + $7x ≥ $47

Simplify the inequality, then we have

$5 + $7x ≥ $47

$7x ≥ $42

x ≥ 6 weeks

The number of weeks that he will be able to buy the game will be 6 weeks.

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The probability that:

(a) at least one of these students is in class is:  0.88

(b) exactly one of them is there is:  0.44

(a) To find the probability that at least one of the students is in class, we need to know the probability that Alice is in class and the probability that Betty is in class, which is given as 0.8 and 0.6 respectively.

Since we know that the students' absences are independent, we can use the formula for the probability of the union of two events:

This means that the probability of both of them being absent is:

    (1-0.8) * (1-0.6) = 0.04.

So the probability that at least one of them is in class is P(A) + P(B) - P(A and B) = 0.8 + 0.6 - 0.04 = 0.88.

(b) To find the probability that exactly one of the students is in class, we need to consider the probability that Alice is in class and Betty is absent and the probability that Betty is in class and Alice is absent. These events are mutually exclusive which means they can't happen at the same time.

The probability that Alice is in class and Betty is absent is

       (0.8 * 0.4) = 0.32.

The probability that Betty is in class and Alice is absent is

       (0.6 * 0.2) = 0.12.

So, by adding these two probabilities we get the probability that exactly one of them is in class:

     0.32 + 0.12 = 0.44.

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Answer:

-5/8+67/8. -5+67/8. 62/8

Step-by-step explanation:

The expression that represents the correct factorization of the polynomial 8x³  +  125 exists (2x + 5) (4x²  -  10x  +  25)

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

A polynomial is not an expression that contains a variable with exponents that are negative or fractional, divides by a variable, or has a variable inside a radical.

Let the given polynomial expression be 8x³  +  125

The expression 8x³  +  125 can be rewritten as (2x)³ + 5³

By using the sum of cubes formula, we get

(2x)³ + 5³  =  (2x  + 5)( ((2x)² - 2x(5) + 5²)

8x³  +  125 = (2x + 5) (4x²  -  10x  +  25)

Therefore, the expression that represents the correct factorization of the polynomial 8x³  +  125 is (2x + 5) (4x²  -  10x  +  25)

The complete question is:

A polynomial expression of degree three is shown below. 8x^3 + 125 Which expression represents the correct factorization of the polynomial?

A (2x + 5)(4x + 10x + 25)

B (2x + 5)(4x + 10x-25)

C (2x + 5)(4x - 10x +25)

D (4x + 25)(2x - 10x+5)

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The inequality that represents the situation is 15c + 5b ≥ 165.

What is inequality?

Inequality means not equal. Generally, if two values are not equal, we use the “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

We can start the inequality by using the following equation:

15c + 5b ≥ 165

This equation represents the total number of daisies used in the floral arrangements.

The left side of the inequality is the total number of daisies used in centerpieces (15c) plus the total number of daisies used in bouquets (5b), and it must be greater than or equal to 165 (the minimum number of daisies needed for the wedding).

Hence, the inequality that represents the situation is 15c + 5b ≥ 165.

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Answer: 2/3, or 0.6666666667

Step-by-step explanation:

Answer:

The simplest form of 6/9 is 2/3.

Step-by-step explanation:

1) Divide both the numerator and denominator by three(does not apply to all situations).

2) Outcome should be 2/3 or .666

The spoken statement "six metres less than four times the width is 4w -6" has an algebraic equivalent.

An algebraic expression:

An expression that has been created utilizing integer variables, constants, and algebraic operations is known as an algebraic expression. 3x 2 2xy + c is a nice illustration of an algebraic expression.

As per the data given in the above question are as bellow,

Let's say the value is v.

To get: the product of w multiplied by four.

As a consequence, we must multiply w and 4 the result we get 4w.

To get: the subtract 6 meter less than four times the width.

As a consequence, we must subtract 6 meter less than four times the width the result we get 4w -6.

The following is the mathematical expression.

4w-6

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The value of x is 2.5.

The centroid theorem states that, the centroid of a triangle equals two-third of the distance from each midpoint of a triangle to each vertex.

Given;

BD = 6x+4

DF = 4x-1

Now,

BD = 2/3(BF)

BD = 2/3(BD+DF)

Substituting the values of BD and DF

4x + 5 = 2/3(6x+4+4x-1)

4x + 5 = 2/3(10x+3)

4x - 6x -20x/3 = 1

(-6x-20x)/3=1

26x/3=1

x=3/26

Therefore, based on the centroid theorem, the value of x will be 3/26.

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Answer:

length = 15x + 6

Step-by-step explanation:

given the length is 3 times the width, then

length = 3(5x + 2) ← distribute parenthesis by 3

          = 15x + 6

The sales tax paid 1.15=3y/23

What is Sales tax?

Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. Typically, a sales tax is assessed at the point of sale, paid to the store, and then forwarded to the government. A company is responsible for paying sales taxes in a specific jurisdiction if it has a nexus there. Depending on the local rules, this could be a physical location, a worker, an affiliate, or some other kind of presence.

Step by step Explaination:

Sales tax: 15%

Converting 15%=15/100

                         =0.15

To show sales tax paid is 3y/23

0.15=3y/23

Multiply both side by 23

23*0.15=3y

3.45=3y

Divide both sode by 3

3.45/3=y

y=1.15

The sales tax paid 1.15=3y/23(as the purchase price includes sales tax).

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The statement also says that t finishes after p and before q. This means that t cannot have finished third, as that position is already occupied by q.

In a race involving five runners, p, q, r, s, and t, it is possible to deduce the order of finish based on the information given. According to the statement, p beats q and p beats r, indicating that p finished first in the race. Additionally, q beats s, so q must have finished second.

Therefore, t must have finished either fourth or fifth.One could also deduce that T could not have finished fourth in the race.

As T finishes before Q who is in the 2nd place and after P who is in the first place.It is important to note that this conclusion is based on the information given and cannot be confirmed without additional information.

For example, if it were specified that t finished just milliseconds after p and just before q, it would not be possible to determine whether t finished fourth or fifth.

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The slope represented in terms of the given context will be 2 minutes per mile. Then the correct option is D.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a constant speed. The table below represents the time it takes the car to travel several distances.

The slope of the car is given as,

Slope = 30 / 15

Speed = 2 minutes per mile

The slope represented in terms of the given context will be 2 minutes per mile. Then the correct option is D.

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Individuals can be categorized using qualitative (or categorical) factors based on a trait or characteristic. Individuals are measured numerically through quantitative variables.

There are counts of the participants or observations in each category in qualitative or categorical data. Frequently, percentages or other ratios are used to describe this data (eg, risks). There are two types of categorical data: nominal and ordinal. Nominal variables don't have numerical values; instead, they have two or more categories with "names" (from the Latin nominalis, which means belonging to names). Furthermore, they lack any inherent or natural order. Sex (male or female), marital status (single, married, or divorced), and the reason for a spinal cord injury are examples of nominal variables.

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Answer:

The appropriate form for this equation is B. 6x - 30 = 84. This equation can be used to calculate the number of t-shirts Lashanda sold. By solving the equation, we can determine that she sold 14 t-shirts.

Step-by-step explanation:

Answer:

The misplaced modifier in the sentence is "sitting in the back of the fridge."

Step-by-step explanation:

It implies that Fabiola Torres is stale and sitting in the back of the fridge, rather than the Skittles.

The correct sentence would be: "Fabiola Torres found some stale Skittles in the back of the fridge."

The endpoints of the line segment after translation will be (−5, 2) and (−3, −2). Then the correct option is A.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The translation does not change the shape and size of the geometry. But changes the location.

The endpoints of the line segment are (−2, 7) and (0, 3).

Translate the points 5 units down and 3 units left. Then the points are given as,

(−2 − 3, 7 − 5) and (0 − 3, 3 − 5)

(−5, 2) and (−3, −2)

The endpoints of the line segment after translation will be (−5, 2) and (−3, −2). Then the correct option is A.

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The ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594 is 7,140:18.

The greatest common factor (GCF) of 180 and 594 is 18.

The least common multiple (LCM) of 180 and 594 is 7,140.

Therefore, the ratio of the LCM to the GCF is 7,140:18.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number.

180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17.

Then, you need to identify the greatest common factor among the prime factors of each number. The prime factors of 180 and 594 that are common to both are 2 and 2, which means that the GCF of 180 and 594 is 18. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number. 180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17. Then, you need to identify the least common multiple among the prime factors of each number. The LCM of 180 and 594 is 2 x 2 x 3 x 3 x 5 x 7 x 17, which is 7,140.

Therefore, the ratio of the LCM to the GCF is 7,140:18.

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