f(x) = 2x² - 6
Find f(7)

Answer:

Reflection across x = -5

Answer:

1. I,P,M,P

2. P,I,P,M

3. M,P,P,I

4. P,I,M,P

The solutions of the trigonometric equation are x₁ = π / 6 and x₂ = 5π / 3.

In this problem we find a trigonometric equation which has to be simplified and solved for x to find the family of solutions within the given interval:

csc x · tan x = 2√3 / 3

(1 / sin x) · (sin x / cos x) = 2√3 / 3

1 / cos x = 2√3 / 3

cos x = 3 / 2√3

cos x = √3 / 2

Then, by inverse trigonometric functions:

x₁ = π / 6, x₂ = 5π / 3

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(a) The quantity of gas in the tank of a car on a journey between New York and Newark is a continuous function of time.

(b) The number of students enrolled in a class during a semester is also a continuous function of time.

(a) The quantity of gas in the tank of a car on a journey between New York and Newark is a continuous function of time.

As the car travels, the amount of gas in the tank changes continuously without any abrupt jumps or discontinuities.

(b) The number of students enrolled in a class during a semester is also a continuous function of time. The enrollment count can change gradually as students join or leave the class, and there are no sudden jumps or interruptions in the enrollment process.

Therefore, both (a) the quantity of gas in the tank of a car and (b) the number of students enrolled in a class during a semester are continuous functions of time.

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Answer:

true for A P E X

Step-by-step explanation:

Answer:

x = 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Equation

2(x + 2x) = 36

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 36 does indeed equal 36.

∴ x = 6 is the solution to the equation.

Answer :

2(x+2x)=36

2x + 4x =36

6x =36 is the answer

Hope it helped

Given:

The arrow diagram of a relation.

To find:

Whether the given relation is a function or not.

Solution:

A relation is a called a function it there exist a unique y-value or unique output value for each x-value or input value.

From the given arrow diagram it is clear that y=2 and y=-1 for x=-1.

Since we have more than one value of y at x=-1, therefore, the given relation is not a function.

Hence, the correct option is B.

Answer:

Step-by-step explanation:

Division by zero is undefined, so the only restriction on the domain, the values of x is that x cannot equal 9. So the domain is all real numbers except 9. Or in interval notation

x=(-oo,9),(9,+oo)

Answer:

All real numbers

Step-by-step explanation:

y = (x+1)(x-9)

y = x² - 8x - 9

There are no asymptotes, restrictions of x, or holes.

We've run into a problem. If the height is zero, then the trapezoid is actually a rectangle, not a trapezoid. So we can't find the height of the trapezoid with the given information.

To find the height of a trapezoid with bases of 3.2ft and 7ft, we need to use the formula for the area of a trapezoid, which is (b1 + b2) * h / 2, where b1 and b2 are the lengths of the two bases and h is the height.

We can rearrange the formula to solve for h by multiplying both sides by 2 and dividing by (b1 + b2):

h = 2 * area / (b1 + b2)

To find the area of the trapezoid, we need to know the length of at least one of its sides. If we don't have any other information, we can't find the height of the trapezoid.

However, if we assume that the trapezoid is a right trapezoid (i.e. one of the bases is perpendicular to the height), we can use the Pythagorean theorem to find the length of the other leg.

Let's call the height h and the length of the leg adjacent to the shorter base x. Then we have:

h^2 + x^2 = (7-3.2)^2
h^2 + x^2 = 12.96
x^2 = 12.96 - h^2

Now we can substitute this expression for x^2 into the formula for the area of the trapezoid:

A = (3.2 + 7) * h / 2
A = 5.1h

And then substitute this expression for A into the expression for x^2:

5.1h = (3.2 + 7) * h / 2
5.1h = 5.1h
h = 0

We would need either the length of one of the legs or the angle between the two legs to solve the problem.

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Given :

To find :-

Solution :-

First term :-

Second term :-

Third term :-

Answer:ndjsoalwjjdlq bc hxlansbdlmdnwb

Step-by-step explanation:

Answer:

x≥-4

Like this I believe

Step-by-step explanation:

6x ≥ -24

-24/6

-4

x≥-4

========================================================

Explanation:

We have a triangle with sides a,b,c where a = 3 and b = 3 are given. The side c is unknown, but using the variation of the triangle inequality theorem allows us to say the following:

b-a < c < b+a

3-3 < c < 3+3

0 < c < 6

The missing side c is between 0 and 6 units long, but cannot be equal to 0 and can't be equal to 6 either. Therefore, the answers must be A) 4, C) 5, and D) 2. All of these values satisfy the inequality 0 < c < 6.

Something like c = 12 is too large. I recommend cutting out two slips of paper that are 3 inches long, and you'll find it impossible to form a triangle that has a third side of 12 inches. The longest side you can form is 3+3 = 6 inches, but you wouldn't have a triangle at that point (it would be a straight line instead). This is a visual way to rule out choice E, and it also rules out choices B and F for similar reasoning.

The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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Answer:

624 rounded 624.3 not rounded

Step-by-step explanation:

hope this helps <3

Answer:

r = c/x

Step-by-step explanation:

We should allocate the workers as follows: {HLH,LHL} {HLL,LHH} {HHH,LLL} to get the maximum output.

The O-ring model states that production output depends on the quality of each worker. The quality of the final product is determined by the lowest quality worker working on the project.

In the given case, we have two types of workers: H-type and L-type.

The H-type workers have a quality of q=0.6, and the L-type workers have a quality of q=0.4.

We are to determine how to allocate the workers to get the maximum output.

The answer is all of the above.{HLH,LHL} {HLL,LHH} {HHH,LLL} is the allocation we need to get maximum output.

Here's how we arrive at the solution:

For the O-ring model, we need to group the workers in a way that minimizes the number of low-quality workers in a group.

We can have two possible groupings as follows:

{HLH,LHL} - This group has a minimum q of 0.4, which is the quality of the L-type worker in the middle of the group.

{HLL,LHH} - This group also has a minimum q of 0.4, which is the quality of the L-type worker on the left of the group.

The other grouping, {HHH,LLL}, has all low-quality workers in one group and all high-quality workers in another group. This is not ideal for the O-ring model as the low-quality workers will negatively affect the output of the high-quality workers.

Thus, to get the maximum output, we should allocate the workers as follows:

{HLH,LHL} {HLL,LHH} {HHH,LLL} all of the above

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Answer:

95,85

Step-by-step explanation:

x-10+x=180

190=2x

95

95-10=85

According to the discount, the price of the tablet computer after the markup is $610.30.

In this problem, a store offered a 30% discount on a tablet computer that originally sold for $670. We can calculate the discounted price of the tablet computer by finding 30% of its original price and subtracting it from the original price.

Discounted price = Original price - Discount

Discounted price = $670 - 30% of $670

Discounted price = $670 - $201

Discounted price = $469

So, the discounted price of the tablet computer is $469.

The problem then asks us to find the price of the tablet computer after it is marked up by 30%. To do this, we need to add 30% of the discounted price to the discounted price.

Markup price = Discounted price + Markup

Markup price = $469 + 30% of $469

Markup price = $469 + $141.30

Markup price = $610.30

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Answer:

$32.09

Step-by-step explanation:

Um....yeah I just used an online calculator lol

Answer:

Slope= -7/9

rise= 7

run=-9

Step-by-step explanation:

Answer

Slope= -7/9 rise= 7 run=-9

step explanation:

Since the p-value (0.0179) is less than the typical significance level of 0.05, we reject the null hypothesis. We have evidence to suggest that the true proportion of uninjured occupants in head-on collisions exceeds 0.25 based on the sample data.

To test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25, we can perform a hypothesis test using the given sample data.

Let's set up the null and alternative hypotheses:

Null Hypothesis (H₀):

The true proportion of uninjured occupants in head-on collisions is 0.25 or less.

Alternative Hypothesis (H₁):

The true proportion of uninjured occupants in head-on collisions exceeds 0.25.

To test these hypotheses, we can use the proportion test, assuming the conditions for the test are met (e.g., the sample can be considered random and independent, and the sample size is sufficiently large).

Let's calculate the test statistic (z-score) and p-value based on the sample data.

Sample proportion of uninjured occupants:

p = 95/319 = 0.2978

Sample size:

n = 319

Under the null hypothesis, assuming the true proportion is 0.25 or less, the expected proportion of uninjured occupants is 0.25.

The test statistic (z-score) can be calculated as:

z = (p - p₀) / sqrt((p₀ * (1 - p₀)) / n)

where p₀ is the assumed proportion under the null hypothesis (0.25), and n is the sample size.

Substituting the values:

z = (0.2978 - 0.25) / sqrt((0.25 * (1 - 0.25)) / 319)

z = 2.1185

To determine the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator. The p-value is the probability of observing a test statistic as extreme as the calculated z-value, assuming the null hypothesis is true.

The p-value associated with a z-score of 2.1185 is approximately 0.0179.

Finally, we can compare the p-value to the significance level (α) to make a decision. If the p-value is less than α (typically 0.05), we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

In this case, since the p-value (0.0179) is less than the typical significance level of 0.05, we reject the null hypothesis. We have evidence to suggest that the true proportion of uninjured occupants in head-on collisions exceeds 0.25 based on the sample data.

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The value of the expression v(x) = 12 - 2x - 5.8, At x= - 2,0, and 5 are

10.2, 6.2, and - 3.8 respectively.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression, v(x) = 12 - 2x - 5.8.

v(x) = - 2x + 6.2.

Now, Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.

At, x = -2,

v(-2) = - 2(- 2) + 6.2.

v(-2) = 10.2.

Similarly,

v(0) = - 2(0) + 6.2.

v(0) = 6.2.

v(5) = - 2(5) + 6.2

v(5) = - 3.8

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Answer:

a=3

Step-by-step explanation:

p(x)=x^2-x-6 and f(x)=x^2+3x-18

they have a common factor x=a

so, when they are devided by x-a leave 0 as the remainder ( by remainder theorem)

p(a) =0

f(a)=0

SO, p(a) =f(a)

a^2-a-6=a^2+3a-18

a^2-a^-a-3a= -18+6

-4a= - 12

a=3

The measure of center that would best summarize the plot is given as follows: Median of 11.

The measure of variability is given as follows: IQR of 1.5.

A box and whisker plots shows these five features from a data-set, listed as follows:

From the plot, these features are given as follows:

The median is the best measure of center of the data-set.

There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:

IQR = 11.5 - 10

IQR = 1.5.

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The data set is approximately symmetric. The data set is not positively skewed. The data set is not negatively skewed. The data set is unimodal. The data set is not bimodal.

(a) The stem-and-leaf display organizes the data in a tabular format. The stems represent the tens digit, and the leaves represent the ones digit. For example, the stem 1 with leaves 2 and 8 represents the values 12 and 18.

(b) To determine if the data set is symmetric, we examine the distribution of values. In this case, the stem-and-leaf display shows that the values are roughly evenly distributed on both sides of the median, indicating symmetry.

(c) Positive skewness occurs when the tail of the distribution is longer on the right side. In this data set, there is no long tail on the right side, suggesting that it is not positively skewed.

(d) Negative skewness occurs when the tail of the distribution is longer on the left side. Since there is no long tail on the left side in this data set, it is not negatively skewed.

(e) A data set is considered unimodal if it has a single peak or mode. In this case, the stem-and-leaf display shows that the value 75 appears three times, making it the mode. Thus, the data set is unimodal.

(f) A data set is considered bimodal if it has two distinct modes. In this data set, although the value 66 appears twice, it is not significantly higher than the surrounding values and does not constitute a separate mode. Therefore, the data set is not bimodal.

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