Glven: -7x < -21. Choose the solution set.​

Hello!

Answer:

2 pies ÷ 4 people (including himself ) = 2/4 = 1/2

Each person get 1/2 of a pie

Hope this helps!! :)

Answer: y = 16807

Step-by-step explanation:

7 * 7 * 7 * 7 * 7 * 7 = 117649

7^16807 = 117649

Hello There!!

I think the best answer is:

A. \(12p^3r\)

D. \(54p^3\)

\(GoodLuck!!\)

\(_{Loserbrazts}\)

Answer:

x=12

Step-by-step explanation:

LM = RS

9x+27 = 135

Subtract 27 from each side

9x+27-27 =135-27

9x=108

Divide each side by 9

9x/9 = 108/9

x = 12

the boxes are equivalent so the one with a single dash is equal to the other with a single dash.

the one with 2 dashes is equal to the other with 2 dashes so on and so forth

SR=LM

LM=9x+27

RS=135

9x+27=135

so I solve it in my own weird way but you can solve it differently. 135-27=108

108/9=12

so your answer is 12

The graph of the function f(x) = –x^2 – 4x +2 are true options 1 and 4 are correct.

We have the given,

The graph of the function f(x) = –x^2 – 4x+ 2

The statements that agree with the graph of the equation are as follows:

1. The domain is {x|x ≤ –2}.

The set of points at which function is defined.

4. The function is decreasing over the interval (−4, ∞).

From the given graph,

We can say that the above statements are true.

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Answer:

yes

Step-by-step explanation:

Answer:

\(\cot(\theta)=\sqrt{2}\)

\(\implies \dfrac{1}{\tan(\theta)}=\sqrt{2}\)

\(\implies \tan(\theta)=\dfrac{1}{\sqrt{2}}\)

\(\implies \theta=35.26438968...\textdegree \pm180\textdegree n\)

\(\implies \theta=215.26438968...\textdegree\)

⇒ Opposite side to angle = 1,  Adjacent side to angle = √2

⇒ Hypotenuse = √(1² + √2²) = √3

\(\implies \cos(\theta)=\dfrac{A}{H}=-\dfrac{\sqrt{2}}{\sqrt{3}}=-\dfrac{\sqrt{6}}{3}\)

\(\implies \sin(\theta)=\dfrac{O}{H}=-\dfrac{1}{\sqrt{3} }=-\dfrac{\sqrt{3}}{3 }\)

\(\implies \tan(\theta)=\dfrac{O}{A}=\dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2}\)

From the power rules, the matching of  each expression with its equivalent expression is:

\(5^{-3}=\frac{1}{125}\)

\(-5^{-3}=-\frac{1}{125}\)

\((-5^{-3})^{-1}=-125\)

\((-5^{-3})^{0}=1\)

There are different power rules, see some them:

1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

\(4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}\)

2. Power. For this rule, you should repeat the base and multiply the exponents. See the  example, \((2^{2})^3=2^6=64\).

3. Zero Exponent. When you have an exponent equals to zero, the result must be 1.  See the  example, \(2^0=1\).

From this for your question, you have:

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Yes, it is possible to write 7 as a linear combination of the given vectors V1, V2, and V3 with coefficients that are not all zero.

One such linear combination can be given as follows:7 = -3V1 + 4V2 + V3To prove that this is indeed a linear combination of the given vectors, we can substitute the given vectors and coefficients in the above expression and verify that it gives the desired result.

So, we have:RHS = -3V1 + 4V2 + V3= -3(2i - 3j + k) + 4(-i + 2j + 3k) + (i - j - k)= -6i + 9j - 3k - i + 8j + 12k + i - j - k= 7j + 8kSince this result matches with the given vector 7, we can conclude that 7 can be written as a linear combination of the given vectors with coefficients that are not all zero.Hence, the required linear combination is:7 = -3V1 + 4V2 + V3.

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The lengths of the three sides of the right Triangle are 6, 8, and 10.

The smallest side (or leg) of the right triangle is 6. Let's call the other two sides x and x+2, where x is the smaller of the two consecutive even integers.

According to the Pythagorean theorem, in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. The hypotenuse is the longest side of the triangle.

Applying the Pythagorean theorem, we can set up the equation:

6^2 + x^2 = (x+2)^2

Expanding the equation, we have:

36 + x^2 = x^2 + 4x + 4

Simplifying the equation, we can cancel out the x^2 terms:

36 = 4x + 4

Subtracting 4 from both sides of the equation:

32 = 4x

Dividing both sides of the equation by 4:

8 = x

So, the smaller of the two missing sides (the second leg) is 8

the length of the other missing side (the hypotenuse), we can substitute the value of x back into the equation:

x+2 = 8+2 = 10

Therefore, the lengths of the three sides of the right triangle are 6, 8, and 10.

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Answer:

3/9

Step-by-step explanation:

P(G,G) = 1/3 × 1/3 = 1/9

P(B,B) = 1/9

P(Y,Y) = 1/9

P(same colour) 1/9 + 1/9 + 1/9 = 3/9

Using the distance formula, Jet will take 2.2 hours to catch up with the airplane.

We will find the solution using distance formula.

distance formula is a formula that is used to find the distance between two points. These points can be in any dimension.

d=rt where

d is distance r is rate or speed and t is time

"distance airplane traveled" = "distance jet traveled"

Let x = hours "airplane" was flying

x-1 = hours "jet" was flying

.

180x = 330(x-1)

180x = 330x - 330

180x + 330 = 330x

330 = 150x

330/150 = x

2.2 hours = x

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if a set S contains a countable set, then it is in one-to-one correspondence with a proper subset of itself.

To prove that if a set S contains a countable set, then it is in one-to-one correspondence with a proper subset of itself, we can use Cantor's diagonal argument.

Let's assume that S is a set that contains a countable set C. Since C is countable, we can list its elements as c1, c2, c3, ..., where each ci represents an element of C.

Now, let's construct a proper subset E of S as follows: For each element ci in C, we choose an element si in S that is different from ci. In other words, we construct E by taking one element from each pair (ci, si) where si ≠ ci.

Since we have chosen an element si for each ci, the set E is constructed such that it contains at least one element different from each element of C. Therefore, E is a proper subset of S.

Now, we can define a function f: S → E that maps each element x in S to its corresponding element in E. Specifically, for each x in S, if x is an element of C, then f(x) is the corresponding element from E. Otherwise, f(x) = x itself.

It is clear that f is a one-to-one correspondence between S and E. Each element in S is mapped to a unique element in E, and since E is constructed by excluding elements from S, f is a proper subset of S.

Therefore, we have proved that if a set S contains a countable set, then it is in one-to-one correspondence with a proper subset of itself.

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The 14th term of the arithmetic sequence x-1x−1, 7x-77x−7, 13x-13, ...13x−13,... is  -79.

The nth term of a particular arithmetic sequence can be found by,  an = a + (n – 1)d. So in order to find the nth term, substitute the given values \(a_{1}\) and d  into the formula. So to find the 14th term, substitute n = 14 into the equation which is the nth term.

Given,

 \(a_{1}\)= x-1x-1

 \(a_{2}\)= 7x-77x−7

 \(a_{3}\)= 13x-13

 n=  14

We have to find the common difference d from differences in adjacent terms \(a_{1}\),\(a_{2}\),\(a_{3}\) . That is,

\(a_{2}-a_{1} =a_{3} -a_{2}\)

\(7x-77x-7-(x-1x-1)=13x-13-(7x-77x-7)\)

\(7x-77x-7-x+x+1=13x-13-7x+77x+7\\-70x-8x=-6+6\\-78x=0\\ x=0\)

Put x=0 in x-1x-1, 7x-77x-7, 13x-13

Therefore,

\(a_{1}\) = -1

\(a_{2}\) = -7

\(a_{3}\) = -13

Then,  d will be \(-7-(-1)\) or \(-13-(-7)\)

So, d= -6

Put  \(a_{1}\), d, and n in the equation \(a_{n} =a+(n-1)d\)  to find the 14th term.

Therefore,

\(a_{14}=-1+(14-1)-6\\ =-1-78\\=-79\)

The 14th term of the given arithmetic sequence is -79

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Answer:

A. Radical 12, not a pythagroean triple. B. 5, yes, it is a pythagorean triple.

Step-by-step explanation:

Use the pythagroean theorem ^^

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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The difference in Logan and Rita's account balances after 4 years will be $113.22. To calculate the difference in their account balances, find the future value of their deposits using the given interest rates.

For Logan's account, which pays simple interest, we can use the formula: Future Value = Principal + (Principal x Rate x Time).

Given:

Principal (P) = $8,100

Rate (R) = 5% = 0.05 (expressed as a decimal)

Time (T) = 4 years

Future Value of Logan's account = 8,100 + (8,100 x 0.05 x 4)

                           = 8,100 + 1,620

                           = $9,720

For Rita's account, which pays compound interest annually, we can use the formula: Future Value = Principal x\((1 + Rate)^Time\).

Given:

Principal (P) = $8,100

Rate (R) = 5% = 0.05 (expressed as a decimal)

Time (T) = 4 years

Future Value of Rita's account = 8,100 x \((1 + 0.05)^4\)

                           = 8,100 x 1.21550625

                           = $9,833.50

The difference in their account balances = Future Value of Rita's account - Future Value of Logan's account

                                      = 9,833.50 - 9,720

                                      = $113.22

Therefore, the difference in their account balances after 4 years will be $113.22.

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Answer:

11x^2 + x - 1 (answer)

Step-by-step explanation:

To add polynomials, combine like terms:

11x^2                - 5

              +x      +4

--------------------------

11x^2 + x - 1 (answer)

The probability of choosing a left-handed student was determined by observing a sample of students and calculating the proportion of left-handed students in that sample.

The given probability is an empirical probability. This is because it is based on actual data obtained by observing or measuring the occurrence of an event, in this case, the proportion of left-handed students in a certain population. Empirical probabilities rely on empirical evidence and can vary from one sample to another.

In contrast, classical probability is based on theoretical probabilities calculated by assuming that all outcomes are equally likely, while subjective probability is based on personal judgments or beliefs about the likelihood of an event.

In this case, the probability of randomly choosing a left-handed student is not based on theoretical assumptions or personal judgments but rather on actual data obtained from observation, making it an empirical probability.

The probability of choosing a left-handed student was determined by observing a sample of students and calculating the proportion of left-handed students in that sample.

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No, the line passing through  (-4, 26) and (-2, 0) is  not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.

Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.

We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.

Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)

So, for first line we have (x₁, y₁)=(-4,26)

and (x₂, y₂)=(-2,0)

So, slope(m₁) of first line is =(0-26)/(-2 - (-4))

                  =>m₁ = -26/2

                   =>m₁ = -13     ----(eq1)

Similarly, for second line, we have (x₁, y₁)=(10,18)

and (x₂, y₂)=(5,3)

So, slope(m₂) of second line is =(3-18) / (5-10)

                =>m₂ = -15/-5

                 =>m₂=     3   -------(eq2)

On comparing eq1 and eq2,we get

 =>m₁≠m₂.

Hence, the given lines are not parallel.

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(Complete question) is:

Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?

Answer:

10 boxes

Step-by-step explanation:

hope this helps! :)

The total height in feet of the  piece of plywood is 14 foot.

The theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the square of the other two sides.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

13² = 5²  + h²

169 = 25 + h²

h²  = 169 - 25

h²  = 144

h = √144

h = 12 foot

12 + 2 = 14 foot

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Answer:

12%

Step-by-step explanation:

P(cold, med) = 25/100 x 12/25 = 12/100 or 12%

The probability that a customer ordered a small given that he or she ordered a cold drink is, 32%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Since, The probability is represented as:

P(Small | Cold)

This is calculated using:

P(Small | Cold) = n(Small and Cold)/n(Cold)

Using the data on the given table, we have:

P(Small | Cold) = 8/(8 + 12 + 5)

Evaluate

P(Small | Cold) = 0.32

Express as percentage

P(Small | Cold) = 32%

Hence, the probability that a customer ordered a small given that he or she ordered a cold drink is 32%

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Answer:

AB is similar to YZ.

AC is similar to YX.

CB is similar to XZ.

Step-by-step explanation:

Answer:

To find the equivalent positive angle of a negative angle, just add 360 to it until it becomes positive and is between 0 and 360 degrees. -244 + 360 = 116.

Step-by-step explanation:

The coordinates of the endpoint is ( 5 , 20 ).

Given data:

To find the coordinates of the other endpoint, let's assume the coordinates of the unknown endpoint are (x, y).

Given the midpoint of the segment, which is (-1, 17), and one endpoint, which is (-7, 14).

Using the midpoint formula, the two equations based on the x-coordinates and y-coordinates are:

Equation 1: (x1 + x2) / 2 = x

Substituting the known values:

(-7 + x) / 2 = -1

Equation 2: (y1 + y2) / 2 = y

Substituting the known values:

(14 + y) / 2 = 17

Solving these equations will give us the values of x and y, which represent the coordinates of the other endpoint.

Let's solve the equations step by step:

Equation 1:

(-7 + x) / 2 = -1

-7 + x = -2

x = -2 + 7

x = 5

Equation 2:

(14 + y) / 2 = 17

14 + y = 34

y = 34 - 14

y = 20

Hence, the coordinates of the other endpoint are (5, 20).

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