Assume all vectors are in R" Mark each statement True or False. Justify each answer a. Not every orthogonal set in R" is linearly independent A Every orthogonal set of nonzero vectors is linearly independent but not every orthogonal set is linearly independent. B Orthogonal sets with fewer than n vectorsin Rare not linearly independent C. Every orthogonal set of nonzero vectors is linearly independent and zero vectors cannot exist in orthogonal sets D. Orthogonal sets must be linearly independent in order to be orthogonal

The treatments by the researcher are:

The new high-fiber diet and original diet

A randomized block design is defined as an experimental design whereby the experimental units are in groups referred to as blocks. The treatments are usually randomly allocated to the experimental units inside each block. When all treatments appear at least once in each block, we will have a completely randomized block design.

Now, from the question, we see that the researcher is testing the effects of a new high-fiber diet on cholesterol.

We also see that half are being tested on the original diet.

Thus, we can easily infer that the treatment here is the new high-fiber diet and original diet because that is what we are using to find the get a research on the testing.

Read more about Research Treatments at: https://brainly.com/question/28386316

#SPJ1

The 80s series of nasal consonants, including /m/, /n/, and /ŋ/, is the best option for testing for hyponasality. These consonants require adequate nasal resonance for accurate articulation, making them effective for identifying individuals with this speech disorder. Option D is correct.

Hyponasality is a speech disorder characterized by reduced nasal resonance during speech production. To test for hyponasality, a series of nasal consonants can be used, as they require appropriate nasal resonance for accurate articulation.

Among the options given, the best series of numbers to use when testing for hyponasality is the 80s. This series includes nasal consonants that are commonly used in the English language, and their production requires adequate nasal resonance. The nasal consonants in the 80s series include /m/, /n/, and /ŋ/, which are produced with varying degrees of nasal airflow.

/m/ is a bilabial nasal consonant, which requires the closure of the lips and the lowering of the velum to allow air to flow through the nasal cavity. /n/ is an alveolar nasal consonant, which requires the tongue to contact the alveolar ridge while the velum is lowered. /ŋ/ is a velar nasal consonant, which requires the back of the tongue to contact the soft palate while the velum is lowered.

Using the 80s series of numbers to test for hyponasality can help identify individuals who have difficulty producing nasal consonants correctly due to reduced nasal resonance. This information can be used to develop appropriate speech therapy interventions to help improve nasal resonance and overall speech production.

To learn more about hyponasality

https://brainly.com/question/31662331

#SPJ4

Complete question:

What is the recommended series of numbers to use for testing hyponasality?

a) 50s,

b) 60s,

c) 70s,

d) 80s,

e) 90s

Answer:

Root square is a proper method

Step-by-step explanation:

√72 =+-(m+8)

and m+8>= 0<=>m>=-8

=>m= √72 -8

Answer:

C

Step-by-step explanation:

To represent the system of equations step by step using matrices, we'll start by setting up the coefficient matrix and the constant matrix. Let's go through the process:

Step 1: Write down the equations:

Equation 1: y = 10

Equation 2: 4x - 5y = 3

Step 2: Set up the coefficient matrix (matrix A):

Coefficients of Equation 2: 4 and -5

Coefficients of Equation 1: 0 and 1

A =

| 4 -5 |

| 0 1 |

Step 3: Set up the constant matrix (matrix B):

Constants of Equation 2: 3

Constants of Equation 1: 10

B =

| 3 |

| 10 |

Step 4: Combine the coefficient matrix and constant matrix into an augmented matrix (matrix [A|B]):

[A|B] =

| 4 -5 3 |

| 0 1 10 |

This augmented matrix represents the system of equations:

4x - 5y = 3

0x + 1y = 10

Each row in the augmented matrix corresponds to an equation in the system. The first column represents the coefficients of x, the second column represents the coefficients of y, and the last column represents the constants.

Therefore, the matrix that represents the system of equations is:

C.

0 1 3

4 -5 10

Part A: The scale factor is 4/3

Part B: The surface area of prism B is 300 square yards

Scale factor is simply described as a measure for similar figures, with similarity in appearance but have different scales or measures.

It is used to scale shapes in different dimensions.

The formula for scale factor is expressed as;

Scale factor = Dimension of the new shape/Dimension of the original shape

Now, substitute the values, we have;

Scale factor = 8/6

Divide the values

Scale factor = 4/3

Then, the surface area of Prism B would be;

Prism A × 4/3

Substitute the values

225 × 4/3

300 yd²

Learn more about scale factor at: https://brainly.com/question/10253650

#SPJ1

The arc PS is 120

The measure of angle ∠R is 60.

We have,

If an angle is inscribed in the circle and its vertex is on the circle, then the measure of the inscribed angle is half the intercepted arc.

Now,

We see that,

∠Q and ∠R are both inscribed angles for the intercepted arc PS.

So,

Arc PS = 60 x 2 = 120

And,

∠R = 60

Thus,

The arc PS is 120

The measure of ∠R is 60.

Learn more about arc lengths here:

https://brainly.com/question/16403495

#SPJ1

The estimated true population variance in leasing rates for the car dealer is between 3436.02 and 9512.46 with 90% confidence.

To estimate the true population variance in leasing rates with 90% confidence, we can use a confidence interval formula with the t-distribution. The formula for the confidence interval is:

CI = (n-1)*s^2 / chi2(alpha/2, n-1) to (n-1)*s^2 / chi2(1-alpha/2, n-1)

Where CI is the confidence interval, n is the sample size, s is the sample standard deviation, alpha is the level of significance, and chi2 is the chi-squared distribution.

Given the sample of leasing rates, the sample size is 6 and the sample standard deviation is approximately 31.27.

Using a chi-squared distribution table or calculator, we can find the critical values for chi2(0.05, 5) and chi2(0.95, 5) to be approximately 11.07 and 0.83, respectively.

Plugging in the values into the confidence interval formula, we get:

CI = (6-1)*31.27^2 / 11.07 to (6-1)*31.27^2 / 0.83

Simplifying the equation gives:

CI = 3436.02 to 9512.46

Therefore, with 90% confidence, the true population variance in leasing rates for the car dealer is between 3436.02 and 9512.46.

Visit here to learn more about variance:

brainly.com/question/25639778

#SPJ11

A tile is drawn and replaced, and then a second tile is drawn. Therefore, option A and B are correct answers.

The first two events would be considered independent because the drawing and replacing/removing of one tile does not affect the outcome of the next tile. The third event would not be considered independent because how the first tile is drawn will affect the second one being drawn (since only one of each color is available). The fourth event would also not be considered independent because the outcome of the first tile drawn will affect the second one.

Therefore, option A and B are correct answers.

Learn more about the independent variable here:

brainly.com/question/29430246.

#SPJ1

(a) (-1, 5), (b) (0, 4), and (f)  (-6, 7) are the solution to the inequality.

To check which ordered pairs are solutions to the system of inequalities:

{ x + 5y > 8

{ 4x - y < 6

We can substitute each ordered pair into both inequalities and check if they are true or false.

a. (-1, 5)

x + 5y > 8 becomes -1 + 5(5) > 8 which is true

4x - y < 6 becomes 4(-1) - 5 < 6 which is true

Since both inequalities are true, (-1, 5) is a solution to the system of inequalities.

b. (0, 4)

x + 5y > 8 becomes 0 + 5(4) > 8 which is true

4x - y < 6 becomes 4(0) - 4 < 6 which is true

Since both inequalities are true, (0, 4) is a solution to the system of inequalities.

c. (10, 2)

x + 5y > 8 becomes 10 + 5(2) > 8 which is true

4x - y < 6 becomes 4(10) - 2 < 6 which is false

Since the second inequality is false, (10, 2) is not a solution to the system of inequalities.

d. (2, -3)

x + 5y > 8 becomes 2 + 5(-3) > 8 which is false

4x - y < 6 becomes 4(2) - (-3) < 6 which is true

Since the first inequality is false, (2, -3) is not a solution to the system of inequalities.

e. (-4, 1)

x + 5y > 8 becomes -4 + 5(1) > 8 which is false

4x - y < 6 becomes 4(-4) - 1 < 6 which is true

Since the first inequality is false, (-4, 1) is not a solution to the system of inequalities.

f. (-6, 7)

x + 5y > 8 becomes -6 + 5(7) > 8 which is true

4x - y < 6 becomes 4(-6) - 7 < 6 which is true

Since the second inequality is false, (-6, 7) is a solution to the system of inequalities.

Therefore, the solutions are (a) (-1, 5), (b) (0, 4), and (f)  (-6, 7).

Learn more about inequalities here:

https://brainly.com/question/30231190

#SPJ1

Answer:

Step-by-step explanation:

To find the area of the shaded region, we must first find the area of the square. The side length of the square is 8ft, so the area is 8ft x 8ft = 64 square feet.

Next, we need to find the area of the circle. The diameter of the circle is the same as the side length of the square, which is 8ft. Therefore, the radius of the circle is half of the diameter, which is 4ft.

Using the formula for the area of a circle, we get:

Area of circle = π x (radius)^2
Area of circle = 3.14 x (4ft)^2
Area of circle = 3.14 x 16ft^2
Area of circle = 50.24 square feet

Now, we can find the area of the shaded region by subtracting the area of the circle from the area of the square:

Area of shaded region = Area of square - Area of circle
Area of shaded region = 64 square feet - 50.24 square feet
Area of shaded region = 13.76 square feet

Therefore, the area of the shaded region is 13.76 square feet.

Least Integer are -

(a) n = 7

(b) n = 9

(c) n = 0

(d) n = 4

What is a polynomial?

A mathematical statement made up of variables, coefficients, and non-zero integer exponents is known as a polynomial. A sum of terms is represented by this algebraic equation, where each term is the product of a coefficient and one or more variables raised to non-negative integer exponents. Any symbols or letters, such as x, y, or z, can be used as the variables.

What is a degree of a polynomial?

The degree of a polynomial is the highest exponent/power of the variable (or variables) in the polynomial expression. It represents the degree of the highest term in the polynomial.

The smallest integer n with which f(x) is O(([tex]x^{n}[/tex]) for the given functions, we need to determine the highest power of x in each function. Let's analyse each function separately:

(a) f(x) = 2x² + x⁷log(x)

The highest power of x in this function is x⁷. Therefore, n = 7.

(b) f(x) = 3x⁹ + (log(x))⁴

The highest power of x in this function is x⁹. Therefore, n = 9.

(c) f(x) = (x⁴ + x² + 1)/(x⁴ + 1)

In this function, both the numerator and denominator have the highest power of x as x⁴. When we simplify the function, we can see that the highest power of x cancels out, resulting in a constant value of 1. So, f(x) is O([tex]x^{0}[/tex]) or simply O(1). Therefore, n = 0.

(d) f(x) = (x³ + 5log(x))/(x⁴ + 1)

The highest power of x in the numerator is x³, and the highest power of x in the denominator is x⁴. When we simplify the function, we can see that the x³ term becomes negligible compared to the x⁴ term as x approaches infinity. Therefore, f(x) is O(x⁴). Hence, the least integer n such that f(x) is O([tex]x^{n}[/tex]) is n = 4.

Therefore:

(a) n = 7

(b) n = 9

(c) n = 0

(d) n = 4

To know more about polynomials follow the given link:

https://brainly.com/question/1496352

#SPJ4

By failing to reject the null hypothesis with an observed p-value of 0.18% in a 2-tailed test with an alpha level of 0.05, the researcher runs the risk of a Type II error.

In hypothesis testing, a Type II error occurs when the null hypothesis is not rejected even though it is false. It means that the researcher fails to detect a significant effect or relationship that actually exists.

By accepting the null hypothesis when it should be rejected, the researcher may overlook an important finding or draw incorrect conclusions. In this case, with a low observed p-value of 0.18%, the researcher is likely to commit a Type II error by not rejecting the null hypothesis and missing a potentially significant result.


To learn more about Type II Error click here: brainly.com/question/30403884

#SPJ11

Therefore, p(1) = -1, p(2) = -1, p(3) = -2, and p(4) = 0. The recurrence relation is given by p(n) = 0 if n = 0 and [p(n-1)]^2 - n if n > 0.

We can use this to compute p(1), p(2), p(3), and p(4) as follows:

p(1) = [p(0)]^2 - 1 = 0^2 - 1 = -1

p(2) = [p(1)]^2 - 2 = (-1)^2 - 2 = -1

p(3) = [p(2)]^2 - 3 = (-1)^2 - 3 = -2

p(4) = [p(3)]^2 - 4 = (-2)^2 - 4 = 0

Therefore, p(1) = -1, p(2) = -1, p(3) = -2, and p(4) = 0.

To compute p(n) for larger values of n, we would need to use the recurrence relation repeatedly, plugging in the value of p(n-1) each time. However, it is worth noting that the recurrence relation leads to a sequence that grows very quickly in magnitude,

as each term is the square of the previous term minus a constant. Therefore, the values of p(n) for large values of n will be very large (in absolute value), and it may be difficult to compute them explicitly.

To know more about value click here

brainly.com/question/30760879

#SPJ11

Answer:

Angle 11 = 100°

Step-by-step explanation:

As angle 7 = 100°

Using corresponding angle property

7 is correspond to 11

So, 11=100°

Hope the answer was correct

Thank You!

Pls rate my answer!!

Answer:

f= 3s

Step-by-step explanation:

f= s+3

3 = 1+3

3 ≠ 4

s = 3f

1 = 3(3)

1 ≠ 9

f = -3s

3 = -3(1)

3 ≠ -3

f = 3s

3 = 3(1)

3 = 3

Therefore answer is f = 3s

The process for identifying adverse consequences and their associated probability is B. Risk assessment.

Risk assessment is the systematic process of identifying, analyzing, and evaluating potential risks and their associated consequences. It involves identifying hazards, determining the likelihood of occurrence,

and assessing the potential impacts or adverse consequences. The goal of risk assessment is to quantify and understand the risks involved in a particular situation or activity.

During risk assessment, various factors are considered, including the probability or likelihood of a risk occurring and the potential severity or impact of the consequences.

This process helps in making informed decisions and implementing appropriate risk management strategies to mitigate or reduce the identified risks.

Hazard identification (A) is a component of risk assessment, where hazards or potential sources of harm are identified.

Cost-effective analysis (C) refers to evaluating the costs and benefits of different options or alternatives. Exposure assessment (D) involves assessing the extent and duration of exposure to a specific hazard or risk factor.

Therefore, the process specifically focused on identifying adverse consequences and their associated probability is known as risk assessment (B).

To know more about probability click here

brainly.com/question/15124899

#SPJ11

The vectors (1, k) and (k, 4k+5) are linearly independent precisely when k does not equal -1 or 5/4.

Two vectors are linearly independent if neither can be expressed as a linear combination of the other. In this case, we can test linear independence by setting up a system of equations and determining whether there is a unique solution.

Specifically, we want to find values of a and b such that a(1,k) + b(k,4k+5) = (0,0). This gives us two equations:

a + bk = 0

ak + 4bk + 5a = 0

We can solve for a and b by row-reducing the augmented matrix [1 k | 0 ; k 4k+5 | 0]. If the system has a unique solution (a=0, b=0), then the vectors are linearly independent. If the system has infinitely many solutions or no solutions, then the vectors are linearly dependent.

After row-reducing the matrix, we get the reduced row echelon form [1 0 | 0 ; 0 1 | 0], which corresponds to the unique solution a=0, b=0.

Therefore, the vectors are linearly independent, except when k=-1 or k=5/4. In those cases, the second vector is a scalar multiple of the first vector, and the two vectors are linearly dependent.

To understand why k=-1 and k=5/4 are the exceptions, we can substitute those values into the equations and see that they result in a second equation that is a scalar multiple of the first equation.

This means that one of the vectors can be expressed as a linear combination of the other, and the vectors are linearly dependent.

To know more about matrix click here

brainly.com/question/30389982

#SPJ11

The end behaviour of the graph of the Polynomial as required to be determined in the task content is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

By observation of the polynomial equation; the degree is 3 which is odd and the leading coefficient is; positive.

Therefore, it follows that the end behaviour is; As x tends negative infinity, y tends to negative infinity and As x tend to infinity, y tends to infinity.

Read more on end behaviour of polynomial functions;

https://brainly.com/question/1365136

#SPJ1

The end behavior of the polynomial y = 2x³ + x² - 45 is:

As x approaches negative infinity, y approaches negative infinity. As x approaches positive infinity, y approaches positive infinity.

The degree of the polynomial and the sign of the leading coefficient  describe the end behavior.

Below are rules for determining the end behavior of a function:

a. Even and Positive: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches positive infinity

b. Even and Negative: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches negative infinity

c. Odd and Positive: As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

d. Odd and Negative: As x approaches negative infinity, y approaches positive infinity. Also, as x approaches positive infinity, y approaches negative infinity.

Given: y = 2x³ + x² – 45

The degree (largest exponent) of the polynomial = 3 (odd)

Leading coefficient (coefficient of largest exponent) = 2 (positive)

Since the degree and leading coefficient are positive and negative respectively.

Therefore, the end behavior of the graph of the polynomial is:

As x approaches negative infinity, y approaches negative infinity. Also, as x approaches positive infinity, y approaches positive infinity.

Learn more about end behavior on:

brainly.com/question/1365136

#SPJ1

The statement below that describes the probability that a student chosen at random prefers blue is this: A. The probability that a student chosen at random prefers blue is less than the probability that a student chosen at random does not prefer green.

To determine the probability that when a student is chosen at random, they will prefer the color blue, we first determine the probability of choosing blue and this is 100 students out of 400 and this is 100/400 = 0.25.

Next, we determine the probability of not choosing green is 250/400 = 0.625.

So, the probability of preferring blue is less than the probability of not chosing green.

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

(a), there are 160 non-French books that are not about mathematics, and in scenario (b), there are 130 non-French books that are not about mathematics.

To find the number of non-French books not about mathematics, we need to subtract the total number of French books and mathematics books from the total number of books, and then subtract the specific category mentioned in each scenario.
(a) If there are 40 French mathematics books, we subtract 40 from the total of 70 French books to get 30 non-French books. We also subtract 100 mathematics books and 40 French mathematics books, which leaves us with 160 non-French books that are not about mathematics.
(b) If there are 60 French non-mathematics books, we subtract 60 from the total of 70 French books to get 10 French mathematics books. We also subtract the 100 mathematics books and the 10 French mathematics books, which leaves us with 190 non-mathematics books. We then subtract the 60 French non-mathematics books mentioned in the scenario, which gives us a total of 130 non-French books that are not about mathematics.
Therefore, in scenario (a), there are 160 non-French books that are not about mathematics, and in scenario (b), there are 130 non-French books that are not about mathematics.

Learn more about mathematics here:

https://brainly.com/question/29129702

#SPJ11

Thus,  if SSE = 2,578 and SST = 20,343, then s2 = 322.25 and se = 17.95 using the simple linear regression model.

In a simple linear regression model, SSE represents the sum of the squared errors of the regression line, while SST represents the total sum of squares of the data points.

To calculate s2, we can use the formula:
s2 = SSE / (n - 2)

where n is the number of data points used in the regression analysis. Since you haven't provided the value of n, I'll assume it's 10 for the sake of this example.
So, s2 = 2,578 / (10 - 2) = 322.25 (rounded to 2 decimal places).

Next, we can calculate se, which represents the standard error of the estimate. It's calculated using the formula:
se = sqrt(s2)

Therefore, se = sqrt(322.25) = 17.95 (rounded to 2 decimal places).

In summary, if SSE = 2,578 and SST = 20,343, then s2 = 322.25 and se = 17.95. These values can be used to evaluate the goodness of fit of the regression model and to make predictions about future data points.

Know more about the linear regression model

https://brainly.com/question/30401933

#SPJ11

The graph for the inequalities is attached below.

To solve the system of inequalities without graphing, we can use algebraic manipulation and logical reasoning.

Solve the first inequality:

3x + y ≤ 1

Subtract 3x from both sides:

y ≤ 1 - 3x

Solve the second inequality:

x - y < 3

Add y to both sides:

x < y + 3

Now we have the following system of inequalities:

y ≤ 1 - 3x

x < y + 3

Learn more about inequalities here:

https://brainly.com/question/30231190

#SPJ1

The limit of (1 + (a/x))^(bx) as x approaches infinity is e^(ab), where e is the base of the natural logarithm.

To see why this is the case, we can use the fact that the limit of (1 + 1/n)^n as n approaches infinity is e. We can rewrite the expression (1 + (a/x))^(bx) as [(1 + (a/x))^x]^(b/a) and let n = x/a. As x approaches infinity, n also approaches infinity, and we have:

(1 + (a/x))^x = [(1 + (1/n))^n]^a

Taking the limit as n approaches infinity, we have:

lim n→[infinity] [(1 + (1/n))^n]^a = e^a

Therefore, we can rewrite the original expression as:

lim x→[infinity] (1 + (a/x))^(bx) = lim x→[infinity] [(1 + (a/x))^x]^(b/a) = (e^a)^(b/a) = e^b

Thus, the limit of the expression is e^b, which is independent of the value of a. We do not need to use l'Hospital's Rule in this case because the limit evaluates to a simple exponential function of the parameter b.

Learn more about logarithm here: brainly.com/question/32066434

#SPJ11

so we have two investments, one compounding annually and another compounding semi-annually, let's check both

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &11 \end{cases} \\\\\\ A = 5000\left(1+\frac{0.05}{2}\right)^{2\cdot 11} \implies \boxed{A \approx 8607.86} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &11 \end{cases}[/tex][tex]A = 5000\left(1+\frac{0.05}{1}\right)^{1\cdot 11} \implies \boxed{A \approx 8551.70} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ semi-annually }{8607.86}~~ - ~~\stackrel{ annually }{8551.70} ~~ \approx ~~ \text{\LARGE 56.16}[/tex]

The equation for the given question will be 3x - 4 = 14. Trevor worked for 6 hours last week.

To find the equation for this question, firstly we will let the number of hours he worked last week be x,

Now it is given that he worked for 14 hours this week.

We also know that this 14 hrs is equal to three times he worked last week minus 4 hrs.

So, the equation will be:

3x - 4 = 14

On solving the equation, we will get the number of hours Trevor worked last week.

3x - 4 = 14

3x = 14 + 4

3x = 18

x = 18 / 3

x = 6

Hence, Trevor worked for 6 hours last week.

To know more about equation:

https://brainly.com/question/14686792

#SPJ1

For hypothesis testing involving proportions, the appropriate distribution to use is the binomial distribution.

For hypothesis testing involving proportions, the appropriate distribution to use is the binomial distribution.

This is because we are interested in the number of successes (students who work part-time jobs) out of a fixed number of trials (students in the sample), which is the definition of a binomial experiment.

The proportion of students who work part-time jobs can be estimated using the sample proportion, which is the number of students who work part-time jobs divided by the total number of students in the sample.

We can then perform a hypothesis test to determine whether this sample proportion is significantly different from the hypothesized true proportion.

To learn more about the hypothesis;

brainly.com/question/29519577

#SPJ1

Answer:

The units digit of a number is the rightmost digit of the number.

Step-by-step explanation:

the sum of the digits in the unit's place of all numbers formed with the help of 3,4,5,6 taken all at a times is 18+24+30+36=108.

This inequality states that x is less than -2. In other words, any value of x that is smaller than -2 will satisfy the inequality solution to the inequality 14 < -7x is:

x < -2. OB.

To solve the inequality 14 < -7x, we can start by isolating the variable x.

Dividing both sides of the inequality by -7, we have:

(14)/(-7) > x

Simplifying the left side, we get:

-2 > x

This means that any value of x that is less than -2, such as -3, -4, -5, and so on, will make the inequality true.

On the number line, these values will lie to the left of -2.

It's important to note that the options given in the question are not all correct.

Option OA (x > -2) is incorrect because the inequality states that x is less than -2, not greater than -2.

Option OC (x > 9) is also incorrect because the value of x that satisfies the inequality is less than -2, not greater than 9.

Option OD (x > 7) is also incorrect because the value of x that satisfies the inequality is less than -2, not greater than 7.

For similar questions on inequality

https://brainly.com/question/30238989

#SPJ8

Given the center (-1, 2) and the point (-6, -3).So equation of the circle is (x + 1)^2 + (y - 2)^2 = 50                                            

Find the equation of a circle, we use the standard form:
(x - h)^2 + (y - k)^2 = r^2

 Step 1: Determine the center (h, k) of the circle.
The center of the circle is given as (-1, 2). Therefore, h = -1 and k = 2.

Step 2: To find the radius, we use the distance formula between the center (-1, 2) and the point (-6, -3) that the circle passes through:
r = √((x₂ - x₁)² + (y₂ - y₁)²)
r = √((-6 - (-1))² + (-3 - 2)²)
r = √((-5)² + (-5)²)
r = √(25 + 25)
r = √50

Step 3: The standard form of the equation of a circle is (x - h)² + (y - k)² = r². Plug in the values for h, k, and r from steps 1 and 2:
(x - (-1))² + (y - 2)² = (√50)²
(x + 1)² + (y - 2)² = 50

So the equation of the circle with center (-1, 2) and passing through the point (-6, -3) is:

(x + 1)² + (y - 2)² = 50

Learn more about circle here:
https://brainly.com/question/29142813

#SPJ11