What is the solution to this inequality?

−16x<64

x<−4

x≥−4

x≤−4

x>−4

For the system of equations to have a unique solution the value of k must not be 6

Now, According to the question:

The given equations are,

kx + 2y = 5

3x + y = 1

The above equations can be written as,

kx + 2y – 5 = 0

3x + y – 1 = 0

We need to find the value of k.

So, we know that if the two equations are \(a_1x+b_1y+c_1=0\), \(a_2x+b_2y+c_2=0\) Then we will compare the coefficients such that

\(\frac{a_1}{a_2},\frac{b_1}{b_2} and \frac{c_1}{c_2}\).

If \(\frac{a_1}{a_2}\neq \frac{b_1}{b_2}\)  then the equations have unique solution, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2} = \frac{c_1}{c_2}\)

then the equations have infinitely many solutions and if \(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

then the equations have no solutions.

Here we can clearly see that,

\(a_1=k,b_1=2,c_1=-5\\\\\\a_2=3,b_2=2,c_2=-1\)

So, \(\frac{a_1}{a_2},\frac{b_1}{b_2} , \frac{c_1}{c_2}\)

\(\frac{a_1}{a_2}=\frac{k}{3}, \frac{b_1}{b_2}=\frac{2}{1} , \frac{c_1}{c_2}=\frac{5}{1}\)

We know that if the system of equation has unique solution then \(\frac{a_1}{a_2}\neq \frac{b_1}{b_2}\)

So, we solve on putting their values and we get,

\(\frac{k}{3}\neq \frac{2}{1}\)

\(k\neq 6\)

Hence, for the system of equations to have a unique solution the value of k must not be 6.

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The given question is incomplete, complete question is:

Find the value of k for which the following system of equation has the unique solution:-

kx + 2y = 5

3x + y = 1.

Answer:

On the y axis

Step-by-step explanation:

If x is zero, it automatically has to be on the y axis because x=0 is where the x and y axis intersect.

Answer:

210

Step-by-step explanation:

According to this question, y varies directly with x. Mathematically, This means that:

y =kx

Where k is the constant variable

If y=30 and x=0.75, then k will be;

k = y/x

k = 30/0.75

k = 40

Since k = 40,

y = 40x

Therefore, when x=5.25, the value of y will be:

y = 40x

y = 40 × 5.25

y = 210.

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

Answer:- 1/100 degrees Fahrenheit

Step-by-step explanation:

The directions say decreasing so it has to be negative, and the slope is showing how much it is decreasing every meter. y=mx+b. The mx is the slope which is where the answer is located.

The mixed number on rounding to the nearest whole gives 8. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

With the help of the four fundamental operations, often known as "arithmetic operations," any real number may be described. Operations like quotient, product, sum, and difference come after operations like division, multiplication, addition, and subtraction in mathematics.

We are given a mixed number as 8 \(\frac{4}{27}\).

Now, we will convert it into fraction.

⇒ [(27 * 8) + 4] ÷ 27

⇒ [216 + 4] ÷ 27                               (Using multiplication operation)

⇒ 220 ÷ 27                                      (Using addition operation)

⇒ 8.14                                               (Using division operation)

Hence, the number nearest to the mixed number is 8.

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Answer:

565.2cm³

Step-by-step explanation:

the radius= 6/2= 3 cm

the height= 20cm

the volume= 3.14× 3²×20

= 3.14×180= 565.2 cm³

Check the picture below.

Answer:

Step-by-step explanation:

Thus if you are not allowed to repeat a digit the number of possible 4 digit numbers you can construct from 1,2,3,4 is 4 3 2 1 = 24.

The number of 4-digit numbers can you write if you can use only digits 1 and 2 is 16.

Given that, using only digits 1 and 2 form 4-digit numbers.

Digits are the single symbols used to represent numbers in Maths. For example, in number 89, 8 and 9 are two digits. Hence, the numerals such as 0, 1, 2, 3,4, 5,6,7,8,9, and 0 are the form of digits which are used to represent a combination of numbers and do arithmetic operations in our day to day life.

Here,

For the first digit you are picking from 2 digits.

For the second digit you are picking from 2 digits.

For the third digit you are picking from 2 digits.

For the fourth digit you are picking from 2 digits.

2×2×2×2=16

4-digit numbers

1111, 2111, 1211, 1121, 1112, 1221, 2112, 1122, 2211, 1212, 2121, 2221, 1222, 2122, 2212 and 2222.

Therefore, the number of 4-digit numbers can you write if you can use only digits 1 and 2 is 16.

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The required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

The concept of the equation model is a fundamental part of mathematics, and it is used in a wide range of applications. Here are some ways in which the equation model is used,
1. Solving equations    2. Modeling real-world situations 3.Understanding relationships between variables.

here,
According to the question let the Pokémon cards Mark intially had be c,
So as per the given condition, Mark has c + 24 card and he gives 1/6 of his card to his little brother, which is 15 cards
The equation model of the situation is given as,
1/6(c + 24) = 15

Thus, the required equation model for the given situation is 1/6 (c + 24) = 15. Option C is correct.

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The correct option is (d) interval/ratio, nominal with 2 or more levels.

In ANOVA (Analysis of Variance), the independent variable is interval/ratio with 2 or more levels, and the dependent variable is nominal with 2 or more levels. Here, ANOVA is a statistical tool that is used to analyze the significant differences between two or more group means.

ANOVA is a statistical test that helps to compare the means of three or more samples by analyzing the variance among them. It is used when there are more than two groups to compare. It is an extension of the t-test, which is used for comparing the means of two groups.

The ANOVA test has three types:One-way ANOVA: Compares the means of one independent variable with a single factor.Two-way ANOVA: Compares the means of two independent variables with more than one factor.Multi-way ANOVA: Compares the means of three or more independent variables with more than one factor.

The ANOVA test is based on the F-test, which measures the ratio of the variation between the group means to the variation within the groups. If the calculated F-value is larger than the critical F-value, then the null hypothesis is rejected, which implies that there are significant differences between the group means.

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Answer:

The balance after 6 years, assuming the deposit of 5000 earns 4% interest compounded yearly, would be 7400. This is calculated by using the formula A=P(1+r/n)^nt, where A is the balance, P is the principal (5000), r is the interest rate (0.04), n is the number of times the interest is compounded per year (1), and t is the number of years (6).

There are 130 positive integers less than 1000 that are divisible by 7 but not by 11.

The rule used to find the number of positive integers less than 1000 that are divisible by 7 but not by 11 is the inclusion-exclusion principle. This principle states that if we want to find the number of elements that belong to at least one of two sets, we can add the sizes of the sets together and then subtract the size of the intersection of the sets. In this case, we first find the number of positive integers less than 1000 that are divisible by 7 (which is 142), then the number that are divisible by 11 (which is 90), and finally the number that are divisible by both (which is 12). Using the inclusion-exclusion principle, we can find the number of positive integers less than 1000 that are divisible by 7 but not by 11 by subtracting the number that are divisible by both from the number that are divisible by 7: 142 - 12 = 130. Therefore, there are 130 positive integers less than 1000 that are divisible by 7 but not by 11.
To find the number of positive integers less than 1000 that are divisible by 7 but not by 11, you can use the Inclusion-Exclusion Principle.

First, find the number of integers divisible by 7: there are 999/7 = 142.71, so 142 integers are divisible by 7.

Next, find the number of integers divisible by both 7 and 11 (i.e., divisible by their LCM, which is 77): there are 999/77 = 12.97, so 12 integers are divisible by 77.

Now, apply the Inclusion-Exclusion Principle: Subtract the number of integers divisible by both 7 and 11 from the number of integers divisible by 7: 142 - 12 = 130.

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Answer:

32 x 2
---------- = 16
.....4


To start off we can do 32 x 2.
32 x 2 = 64


Next, we divide 64 by 4 to equal the fraction 32 x 2 / 4.
64 divided by 4 = 16


In conclusion the fraction 32 x 2 / 4 is equal to 16.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer: hii

Step-by-step explanation:

In symmetric multiprocessor (SMP) scheduling using private queues, the specific type of action performed when the scheduler running on a processor seeks to change its workload because it has no tasks to run is called a "pull migration."

In pull-migration, the scheduler on a processor actively requests or "pulls" a task from another processor's queue when its local queue is empty or low on tasks. This allows the scheduler to obtain a new workload from a different processor within the SMP system.

The "Pull-Migration" enables dynamic load balancing in SMP systems by allowing processors to actively request tasks from each other when their local queues are depleted. This approach helps ensure that workloads are distributed evenly among processors, minimizing idle time and maximizing resource utilization across the system.

By utilizing pull-migration, SMP schedulers can effectively manage task distribution and adapt to changing workloads, resulting in improved performance and efficient utilization of resources within the SMP system.

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When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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Answer:

D. (-1, 3/2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define System

4x + 2y = -1

3x + 4y = 3

Step 2: Rewrite System

4x + 2y = -1

Step 3: Redefine Systems

-8x - 4y = 2

3x + 4y = 3

Step 4: Solve for x

Step 5: Solve for y

Answer:

To determine the number of sheets of cardboard in a stack, we need to use the information given in the problem.

We know that each sheet of cardboard is 1 inch thick, and 16 sheets are stacked on top of each other in packages. The height of each stack is 21 inches.

Using the model of a ruler, we can divide the height of the stack (21 inches) by the thickness of each sheet (1 inch) to find the number of sheets in the stack.

21 ÷ 1 = 21

So, there are 21 sheets of cardboard in a stack.

To write an expression that can be used to determine the number of sheets of cardboard in a stack, we can use:

Number of sheets = height of stack ÷ thickness of each sheet

Or, substituting the given values: Number of sheets = 21 ÷ 1 = 21

This expression is simply a representation of the model we used earlier. It shows that we can determine the number of sheets in a stack by dividing the height of the stack by the thickness of each sheet. In this case, the expression yields the same result as the model, which is 21 sheets.

Answer:

25:75 = 1:3 in simplest form

Step-by-step explanation:

you are comparing the # of ppl who said thay visited to the # of people who did not go. 100-25=75. then you simplify.

Answer:

e

Step-by-step explanation:

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

a. the number of patients in a hospital

A discrete random variable is a variable that can only take on a finite or countably infinite set of distinct values. In this case, the number of patients in a hospital can only be whole numbers (e.g., 0, 1, 2, 3, etc.), which is a countable set of values. Therefore, it is a discrete random variable.

b. the average amount of electricity consumed

The average amount of electricity consumed is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range, and it is not restricted to specific distinct values.

c. the amount of paint used in repainting a building

The amount of paint used in repainting a building can be measured in continuous quantities (e.g., liters or gallons). It is not restricted to specific distinct values, and therefore, it is not a discrete random variable.

d. the average weight of female athletes

Similar to the average amount of electricity consumed, the average weight of female athletes is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range and is not restricted to specific distinct values.

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

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Lateral surface area = 2H(L + W)

Total surface area = 2 LW + 2 WH + 2 HL

We need to know the prism's dimensions in order to determine its lateral and total surface area for a rectangular base prism. The rectangular prism's length, width, and height are assumed to be L, W, and H, respectively.

The sum of the areas of the rectangular prism's four lateral faces determines its lateral surface area. Since every sidelong face is a square shape with a level of H and a width of one or the other L or W, the parallel surface region is given by:

Lateral Surface Area = 2H(L + W)

The sum of the areas on each of the six faces creates the rectangular prism's total surface area. This incorporates the four sidelong faces, as well as the top and base faces, which are additionally square shapes with aspects L x W. Consequently, the all out surface region is given by:

Total Surface Area = 2(LW + LH + WH)

So, if you know the dimensions of the rectangular prism, you can use these formulas to find its lateral and total surface area.

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Answer:

63/16 or 3 15/16.

Step-by-step explanation:

Solve: 3/8[-8 + 16 - (-2 and 1/2)]  Using order of operations (PEMDAS):

=3/8[-8 + 16 - (-2.5)]

= 3/8( 8 + 2.5)

= 3/8(10.5)

= 31.5/8

= 63/16.

Answer:

20 cm

Step-by-step explanation:

Answer:

The answer is 5 cm

Step-by-step:

5 x 5 = 25 cm^2

hope this helps

Answer:f(4)=g(4)

Step-by-step explanation:We see that when x= 4, we see that f(4) intersects g(4)

Answer: f(-3) = -4

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given expression

f(n) = 3n + 5

Substitute values into the expression

f(-3) = 3(-3) + 5

Simplify by multiplication

f(-3) = -9 + 5

Simplify by addition

f(-3) = \(\boxed{-4}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

$74.5

Step-by-step explanation:

7(10) + 1.50(3) =

70 + 4.5 = 74.5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: x=39

Step-by-step explanation:

You would subtract 107 and 68 to get your answer. Therefore, your answer would be 39.

Answer:

X=39

Step-by-step explanation:

180 - 107 = 73

180 - 68 = 112

73 + 68 = 141

180 - 141 = 39

The value of dw/dt at t = 3 is  -0.282.

Given, the functions are:

w = 4x² + 3y, x = cos(t), and y = sin(t).

Let's find the expressions for w with respect to t using the chain rule.Using the chain rule, we have:

dw/dt = ∂w/∂x × ∂x/∂t + ∂w/∂y × ∂y/∂t...[1]      Here, ∂w/∂x = 8x, and ∂w/∂y = 3.

Substituting these values in [1], we get:

dw/dt = 8x × (-sin(t)) + 3 × cos(t)

dw/dt = -8cos(t)sin(t) + 3cos(t)dw/dt = cos(t)(3 - 8sin(t))...[2]

Now, let's find the expression for w in terms of t and differentiate directly with respect to t.Using w = 4x² + 3y, we get:

w = 4cos²(t) + 3sin(t)dw/dt = 8cos(t)(-sin(t)) + 3cos(t)dw/dt = -8cos(t)sin(t) + 3cos(t)dw/dt = cos(t)(3 - 8sin(t))

dw/dt = cos(t)(3 - 8sin(3)) = -0.282

Since, we have to evaluate at t = 3

Therefore, w = 4cos²(3) + 3sin(3) = 0.416

dw/dt = cos(3)(3 - 8sin(3)) = -0.282

Hence, the expression of dw/dt as a function of t using the chain rule is cos(t)(3 - 8sin(t)).

The expression of dw/dt as a function of t by expressing w in terms of t and differentiating directly with respect to t is -0.282.

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