A data set has a mean of x = 75 and a standard deviation of 11.4. Find the z-score for each of the following.

A Data Set Has A Mean Of X = 75 And A Standard Deviation Of 11.4. Find The Z-score For Each Of The Following.

Answers

Answer 1

Part (a)

[tex]z=\frac{85-75}{11.4} \approx \boxed{0.88}[/tex]

By similar logic, the answers to the other parts are

(b) 1.75

(c) -2.19

(d) 0

A Data Set Has A Mean Of X = 75 And A Standard Deviation Of 11.4. Find The Z-score For Each Of The Following.

Related Questions

3a²+ab²-b² x a²-2ab²-3b²
/a+b

Answers

Answer:

It might be  - c² or  b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)

Step-by-step explanation:

I agree with the person above ^^^

Which of the following is not irrational? (a) (2-√3)2 (b)(√2+√3)2 (c) (√2-√3)(√2+√3) (d)27√7​

Answers

Answer: (c)

(√2-√3)(√2+√3)

Step-by-step explanation:

An irrational number is one that cannot be expressed as the ratio of two integers. In other words it cannot be expressed as [tex]\frac{x}{y}[/tex] where x and y are integers

[tex]\sqrt{2}[/tex] is irrational

[tex]\sqrt{3}[/tex] is irrational

In fact the square root of any prime number is irrational. So [tex]\sqrt{5}[/tex], [tex]\sqrt{7}[/tex] etc are irrational. But [tex]\sqrt{9}[/tex] is not irrational since it evaluates to 3 which can be expressed as [tex]\frac{3}{1}[/tex]

Any expression that contains the square root of a prime number is also irrational

Looking at the choices we see that choices (a), (b) and (d) all evaluate to expressions containing square roots of primes

(a)  (2-√3)2 = 4 - 2√3  . Hence irrational

(b) √2+√3)2 = 2√2+2√3. Hence irrational

(d) 27√7​ is irrational

Let's look at choice (c)

(√2-√3)(√2+√3)

An expression [tex](a+b)(a-b)[/tex]  can be evaluated as [tex]a^{2} - b^{2}[/tex]

Here a = √2, [tex]a^{2}[/tex] =[tex]a = \sqrt{2}\\ a^2 = (\sqrt{2} )^2 = 2\\\\b = \sqrt{3} \\b^2 = (\sqrt{3} )^2 = 3\\\\a^2 - b^2 = 2-3 = -1\\[/tex]

This is a whole number(integer) and all integers are rational numbers

Hence correct answer is (c)

The length and width of a rectangle must have a sum of 60. Find the dimensions of the rectangle that will have the maximum area. [Hint: Let x and 60-x be the length
and width. The area can be described by the function f(x)=x(60-x).]
The length is… and the width is…

Answers

If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.

Given that the sum of length and breadth of rectangle is 60.

We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.

Let the length of rectangle be x.

According to question the breadth will be (60-x).----2

Area of rectangle=Length *Breadth

A=x(60-x)

A=60x-[tex]x^{2}[/tex]

Differentiate A with respect to x.

dA/dx=60-2x

Again differentiate with respect to x.

[tex]d^{2} A/dA^{2}[/tex]=-2x

-2x<0

So the area is maximum because x cannot be less than or equal to 0.

Put dA/dx=0

60-2x=0

60=2x

x=30

Put the value of x in 2 to get the breadth.

Breadth=60-x

=60-30

=30

Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.

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Why are angles opposite each other when two lines cross called vertical angles? (

Answers

Angles is known to be opposite each other when two lines cross called vertical angles  due to the fact that they are opposite each other at a vertex.

What angles are opposite to each other when two lines cross?

Vertical Angles are known to be often called Vertically Opposite Angles and this is described as the scenario when two lines intersect one another, then the opposite angles, is made as a result of the intersection which is known to be called vertical angles or what we say as vertically opposite angles.

Note that A pair of vertically opposite angles are said to be often always equal to one another.

Hence, based on the scenario above, Angles is known to be opposite each other when two lines cross called vertical angles  due to the fact that they are opposite each other at a vertex.

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5) What problems have a negative slope?

Answers

A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.

What is a negative slope

It should be noted that a negative slope implies that two variables are negatively related.

This implies that when x increases, y decreases, and also when x decreases, y increases.

Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.

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Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2 R: rectangle with vertices (0, 0), (0, 5), (2, 5), (2, 0)

Answers

It looks like the function is

[tex]f(x,y) = 3 + 4x^{3/2}[/tex]

We have

[tex]\dfrac{\partial f}{\partial x} = 6x^{1/2} \implies \left(\dfrac{\partial f}{\partial x}\right)^2 = 36x[/tex]

[tex]\dfrac{\partial f}{\partial y} = \left(\dfrac{\partial f}{\partial y}\right)^2 = 0[/tex]

Then the area of the surface over [tex]R[/tex] is

[tex]\displaystyle \iint_R f(x,y) \, dS = \iint_R \sqrt{1 + 36x + 0} \, dA \\\\ ~~~~~~~~ = \int_0^5 \int_0^2 \sqrt{1+36x} \, dx \, dy \\\\ ~~~~~~~~ = 5 \int_0^2 \sqrt{1+36x} \, dx \\\\ ~~~~~~~~ = \frac5{36} \int_1^{73} \sqrt u \, du \\\\ ~~~~~~~~ = \frac5{36}\cdot \frac23 \left(73^{3/2} - 1^{3/2}\right) = \boxed{\frac5{54} (73^{3/2} - 1)}[/tex]

3. What is the measure of angle B from the right triangle below?

Answers

Answer:

angle B = 78.46°

Step-by-step explanation:

Use the cosine ratio

[tex]cosB=\frac{2}{10} =0.2[/tex]

[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]

Hope this helps

What is the area of the actual square window
shown in the scale drawing?

Answers

Answer:

2.25m²

Step-by-step explanation:

if 1in = 2m then 0.5in = 1m

so 0.75in = 1.5m

area = 1.5 x 1.5

a = 2.25m²

What insult is meat shield I never understood it if someone calls a person a meat shield what does the insult mean

Answers

Answer: someone who is viewed as obsolete or a person you can use to save yourself from any problem/situation

Step-by-step explanation:

Answer:

The term "meat shield" is often used as an insult to refer to someone who is used by others as a protective barrier, especially in a dangerous or violent situation. The implication is that the person being referred to is expendable and not valued for their own merits or abilities.

Here are a few examples of insults that use the term "meat shield":

"You're nothing more than a meat shield for your boss."

"You're just a disposable meat shield to your friends."

"You're nothing but a human meat shield to your team."

"You're just a weak and pitiful meat shield."

"You're just a coward who hides behind others like a meat shield."

Again, it's important to remember that using insults is never a productive or kind way to communicate with others. It's always better to try to address the issue in a respectful and constructive manner.

The next two terms of 2;6;18;54

Answers

Hello there! The next two terms in this arithmetic sequence are 162 and 486.

This set of terms has a rule that for each corresponding number, we multiply by 3.

2 x 3 = 6

6 x 3 = 18

18 x 3 = 54

By following this rule, we can multiply our last used number by 3 to get what our next term is.

54 x 3 = 162

Our terms now look like this:

2; 6; 18; 54; 162

Again, we multiply the last used number.

162 x 3 = 486

Now our set looks like this:

2; 6; 18; 54; 162; 486

By multiplying each corresponding term by 3, we have identified the rule and the next two terms in our set.

The next two terms of 2; 6; 18; 54 are 162 and 486. If you need any extra help, let me know and I will gladly assist you.

Round 219.371 to the nearest one tenth and hundredths

Answers

Answer:

219.4

Step-by-step explanation:

Find the number in the tenth place 3 and look at the one place to the right for rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5. So the answer is 219.4

What is the standard form equation of an ellipse that has vertices (−2,−18) and (−2,8) and foci (−2,−14) and (−2,4)?

Answers

Answer:

Hello,

Step-by-step explanation:

All is in the picture.

B=(-2,8), O=(-2,-5)

b=BO=8+5=13

F_1=(-2,4)   O=(-2,5)  Focus distance=4+5=9
Horizontal half axis=√(b²-f²)=√88

Juan bought a table on sale for $459. This price was 32% less than the original price. What was the original price?

Answers

Answer:

675

Step-by-step explanation:

100%-32%=68%

459/0.68= 675

Hope this helps! :)

Consumer math. send help

Answers

Mean = 402.5.

Variance = 77,556.3

Standard deviation = 278.5

See attachment for the complete table.

What is the Mean?

The mean of a data is the sum of all data values divided by the number of data values we have in the data set.

What is the Variance?

Variance is calculated by finding the sum of the squares of the deviations from the mean, find the average, then find the average.

What is the Standard Deviation?

The standard deviation = the square root of variance.

The mean of the data given would be: 402.5.

402.5 is subtracted from each of the data points to get the deviations which are squared.

It is the sum of the deviations that gives us 310,225.2.

To find the variance, divide 310,225.2 by the number of data values which is 4.

Variance = 310,225.2/4

Variance = 77,556.3

Standard deviation = √77,556.3

Standard deviation = 278.5

The complete table containing the missing values is given in the image attached below.

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Put the events in order of what is most likely to happen, to least likely to happen. If you were to win a million dollars for winning one of these events, which would you pick to play? Use probability to explain your answers.

Winning the Lottery: If the six numbers on the lottery ticket match the six numbers drawn, then you win. The numbers can range from 1-49.
Rolling a 7: Roll two dice numbered 1-6 then add the numbers that are face up to get 7.
Drawing the Ace of Spades: In a deck of 52 cards, what is the likelihood of drawing the Ace of Spades in one try.
2 Heads in a Row: Using a coin with a heads-side and tails-side, what is the likelihood of flipping a heads twice in a row?
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of pulling out a red marble 3 times in a row, assuming you put each marble back into the bag before drawing another?

Answers

The order of the probabilities from the highest to the least would be

4 > 2 > 3 > 5 >1. This tells us tgat the highest probability is number 4 while the lowest is 1.

What is probability?

In mathematics, this is the concept that is used to talk about the likelihood of having an event occurring.

The probability of these items have been calculated below

1. Winning the Lottery

probability = 1/49P6

= 0.00000000009932

2. Rolling a 7:

we have to find the group of 7's

= (2,5) (1,6), (3,4), (4, 3), (6,1), (5,2)

= 6/36 = 0.1666

3. Drawing the Ace of Spade

1/52 = 0.019

4. 2 Heads in a Row:

1/2 x 1/2

= 0.25

5. Marbles:

3 + 4+ 5 = 12

3/12 * 3/12 * 3/12

= 0.01562

Hence the order of the probabilities from the highest to the least would be

4 > 2 > 3 > 5 >1

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QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP

Answers

a. Central angle in the circle is: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. m(arc BEC) = 260°.

e. m(arc BC) = 100°.

What is the Central Angle Theorem?

The central angle theorem states that: the central angle measure of a circle equals the measure of the intercepted arc.

What is a Central Angle?

A central angle is formed by two radii of a circle, and the vertex of the angle is at the center of the circle.

What is a Major Arc?

Any arc that is more than half a circle (semicircle) or has a measure that is greater than 180 degrees, is referred to as a major arc of that circle. The measure of the major arc > 180 degrees.

What is a Minor Arc?

Any arc that is not more than half a circle (semicircle) or has a measure that is less than 180 degrees, is referred to as a minor arc of that circle. The measure of the minor arc < 180 degrees.

a. One central angle that can be identified in circle A is: Angle BAC

b. A major arc that can be identified in circle A is: Arc BEC

c. A minor arc that can be identified in circle A is: Arc BC.

d. According to the central angle theorem, we have:

m(arc BEC) = 360 - 100

m(arc BEC) = 260°

e. We are given that m(angle BAC) = 100°, therefore, according to the central angle theorem, we have:

m(arc BC) = m(angle BAC )

m(arc BC) = 100°

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can someone help me on this question with step by step explaination
and reasoning

Answers

Answer: Same

Step-by-step explanation:

Given formula

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

Given information

Troop A:

Original (2010) = 14New (2011) = 16

Troop B:

Original (2010) = 21New (2011) = 24

Substitute values into the formula (Troop A)

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{(16)~-~(14)}{(14)}*100\%[/tex]

Simplify the fraction

[tex]Percent~of~change~=~\Large\frac{2}{14}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]

[tex]Percent~of~change~\approx~14.29\%[/tex]

Substitute values into the formula (Troop B)

[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{(24)~-~(21)}{(21)}*100\%[/tex]

Simplify the fraction

[tex]Percent~of~change~=~\Large\frac{3}{21}*100\%[/tex]

[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]

[tex]Percent~of~change~\approx~14.29\%[/tex]

Compare the two percent of change

[tex]Troop~A~v.s.~Troop~B[/tex]

[tex]14.29\%~=~14.29\%[/tex]

Therefore, they are [tex]\Large\boxed{Same}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is same.

Finding the percentage of change for Troop A :

New - Original / Original × 100%

16 - 14 / 14 × 100%1/7 × 100%14.29%

Finding the percentage of change for Troop B :

24 - 21 / 21 × 100%1/7 × 100%14.29%

Both the troops have the same percent change in membership.


If h(x) = 3x - 1 and j(x) = -2x, solve h[j(2)]

Answers

Answer:

-13

Step-by-step explanation:

First, we will find the value of j(2) first.

j(2) = -2(2) = -4

next, we will solve h[j(2)].

h[j(2)] = h(-4) = 3(-4) - 1 = -12 - 1 = -13

Peter have twice as many stickers as Joe. Joe has 40 more stickers than Emily. They have 300 stickers together. How many stickers does Peter have?

Answers

Answer:

  170

Step-by-step explanation:

The given relations can be used to write and solve an equation for the number of stickers Peter has.

Setup

Let p represent the number of stickers Peter has. That is twice as many as Joe, so Joe has (p/2) stickers. Joe has 40 more stickers than Emily, so the number of stickers Emily has is (p/2 -40).

The total number of stickers is 300:

  p +p/2 +(p/2 -40) = 300

Solution

  2p = 340 . . . . . . . . . . . . . . add 40, collect terms

  p = 170 . . . . . . . . . . . divide by 2

Peter has 170 stickers.

__

Additional comment

Joe has 170/2 = 85 stickers. Emily has 85-40 = 45 stickers.

We could write three equations in three unknowns. Solving those using substitution would result in substantially the same equation that we have above. Or, such a system of equations could be solved using a calculator's matrix functions, as in the attachment.

  p +j +e = 300

  p -2j +0e = 0

  0p +j -e = 40

(-4,2) (5,0) midpoint

Answers

Answer:

[tex]M = (0.5, 1)[/tex]

Step-by-step explanation:

The midpoint can be found using the formula: [tex]x, y = (\frac{x_2+x_1}{2}, \frac{y_2 + y_1}{2})[/tex]

So plugging in the values we get: [tex]M = (\frac{-4+5}{2}, \frac{2+0}{2})\\M = (\frac{1}{2}, \frac{2}{2})\\M = (0.5, 1)[/tex]

Answer: [tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]

Step-by-step explanation:

Given information

(x₁, y₁) = (-4, 2)

(x₂, y₂) = (5, 0)

Given formula for midpoint

[tex]Midpoint~=~(\frac{x_1~+~x_2}{2} ,~\frac{y_1~+~y_2}{2} )[/tex]

Substitute values into the formula

[tex]Midpoint~=~(\frac{-4~+~5}{2} ,~\frac{2~+~0}{2} )[/tex]

Simplify by addition

[tex]Midpoint~=~(\frac{1}{2} ,~\frac{2}{2} )[/tex]

Simplify fractions if necessary

[tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

louizah baked 8 dozen muffins and sold them all at the school for R5,50. if louizah bought the ingredients for R12,50. Determine louizahs profit​

Answers

Answer:

3550

Step-by-step explanation:

C.P=Rs 1250

S.P=8(12)(50)

Rs4800

P=S.P-C. P

=Rs4800-Rs1250

= Rs3550

What is the distance from (-3,8) and (13,-6)?

Answers

Answer:

d ≈ 21.26 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 3, 8 ) and (x₂, y₂ ) = (13 - 6 )

d = [tex]\sqrt{13-(-3))^2+(-6-8)^2}[/tex]

   = [tex]\sqrt{(13+3)^2+(-14)^2}[/tex]

   = [tex]\sqrt{16^2+196}[/tex]

   = [tex]\sqrt{256+196}[/tex]

   = [tex]\sqrt{452}[/tex]

   ≈ 21.26 units ( to 2 dec. places )

Answer:

The distance is 21.3

Step-by-step explanation:

The solution is in the attached image

A recursive rule for an arithmetic sequence is a1=4;an=an−1−3.

What is the explicit rule for this sequence?



Enter the simplified answer in the box.

an=

I NEED HELP ASAP

Answers

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

What is the arithmetic sequence?"Arithmetic means" refers to repeatedly adding a fixed number to produce a series. Let n be "the number." Because the numbers in the sequence are becoming progressively negative, we might conclude that n is negative.We can locate a particular term in an arithmetic series using the method for locating the nth term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.The Arithmetic Mean or Mean of the Group is the sum of all the numbers in a group divided by the total number of items in the list. For instance, since 5 + 7 + 9 = 21 and 21 divided by 3 [there are three numbers] is 7, the mean of the digits 5, 7, and 9 is 4.The difference between each succeeding pair of terms in an arithmetic series is always the same. The following is the explicit guideline for formulating any arithmetic sequence: a = a1 + d (n - 1)

The explicit rule for this sequence:

The obvious rule for an arithmetic sequence is given as follows:

[tex]a_{n}=a_{1} +(n-1)d[/tex]

The first term = [tex]a_{1}[/tex].

The number of terms = n.

The common difference for two consecutive terms = d.

A recursive rule for an arithmetic sequence: [tex]a_{1} =4[/tex].

[tex]a_{n} =a_{n-1}-3[/tex]

The arithmetic sequence is given by:

[tex]a_{n} =a_{n-1}+d[/tex]

We get: d = -3

Substitute the given values:

[tex]a_{n} =4+(n-1)(-3)[/tex]

[tex]a_{n} =4-3n+3[/tex]

=7-3n

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

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The explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference of the arithmetic sequence.For example, [tex]2,5,8,11,...[/tex] is an arithmetic sequence with the first term [tex]a=2[/tex] and the common difference [tex]d=3[/tex].The formula for the nth term [tex]a_n[/tex] of an arithmetic sequence whose first term is [tex]a[/tex] and the common difference is [tex]d[/tex] can be given by [tex]a_n=a+(n-1)d[/tex].

Given the recursive formula for an arithmetic sequence: [tex]a_1=4, a_n=a_{n-1}-3[/tex].

Thus, the first term of the arithmetic sequence is [tex]a=a_1=4[/tex]. using the recursive formula, we can get the 2nd term by putting [tex]n=2[/tex], [tex]a_2=a_1-3=4-3=1[/tex].

So, the common difference of the given arithmetic sequence is [tex]d=a_2-a_1=1-4=-3[/tex].

Thus, the nth term of the arithmetic sequence is given by [tex]a_n=a+(n-1)d\\\Longrightarrow a_n=4+(n-1)\times(-3)\\\Longrightarrow a_n=7-3n[/tex]

Therefore, the explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

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Please help me quick. I don’t understand please give me the answer

Answers

Answer:

m = -2

Step-by-step explanation:

to find the answer you must put rise over run

rise is (y2 - y1) and run is (x2 - x1)

lets use the bottom two points for thisd

y2 is 0 and y1 is 2

x2 is 1 and x1 is 0

0 - 2 = -2

1 - 0 = 1

-2/1 = -2

that is the slope

Find the points of intersection of the equation: xy=2 and x+y =4

Answers

Answer:[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~xy=2[/tex]

[tex]2)~x+y=4[/tex]

Divide x on both sides of the 1) equation

[tex]xy=2[/tex]

[tex]xy\div x=2\div x[/tex]

[tex]y=\dfrac{2}{x}[/tex]

Current system

[tex]1)~y=\dfrac{2}{x}[/tex]

[tex]2)~x+y=4[/tex]

Substitute the 1) equation into the 2) equation

[tex]x+(\dfrac{2}{x} )=4[/tex]

Multiply x on both sides

[tex]x\times x+\dfrac{2}{x}\times x=4\times x[/tex]

[tex]x^2+2=4x[/tex]

Subtract 4x on both sides

[tex]x^2+2-4x=4x-4x[/tex]

[tex]x^2-4x+2=0[/tex]

Use the quadratic formula to solve for the x value

[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)} }{2(1)}[/tex]

[tex]x=2\pm\sqrt{2}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]xy=2[/tex]

[tex](2+\sqrt{2} )y=2[/tex]

[tex]y=2-\sqrt{2}[/tex]

[tex]OR[/tex]

[tex]xy=2[/tex]

[tex](2-\sqrt{2} )y=2[/tex]

[tex]y=2+\sqrt{2}[/tex]

Therefore, the points of intersection are

[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) and (2 + [tex]\sqrt{2}[/tex], 2 - [tex]\sqrt{2}[/tex] )

Step-by-step explanation:

xy = 2 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

x(4 - x) = 2

4x - x² = 2 ( multiply through by - 1 )

x² - 4x = - 2

using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = - 2 + 4

(x - 2)² = 2 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{2}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{2}[/tex] , that is

x = 2 - [tex]\sqrt{2}[/tex] , x = 2 + [tex]\sqrt{2}[/tex]

substitute these values of x into (2) for corresponding values of y

x = 2 - [tex]\sqrt{2}[/tex] , then

y = 4 - (2 - [tex]\sqrt{2}[/tex])

  = 4 - 2 + [tex]\sqrt{2}[/tex]

  = 2 + [tex]\sqrt{2}[/tex] ⇒ (2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) ← 1 point of intersection

x = 2 + [tex]\sqrt{2}[/tex] , then

y = 4 - (2 + [tex]\sqrt{2}[/tex] )

   = 4 - 2 - [tex]\sqrt{2}[/tex]

   = 2 - [tex]\sqrt{2}[/tex] ⇒ (2 + [tex]\sqrt{2}[/tex] , 2 - [tex]\sqrt{2}[/tex] ) ← 2nd point of intersection

Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLU X = 6 X = -x + 6 = x - 6 Identify any extraneous solution. (If there is no extraneous solution, enter NO SOLUTION.) 2​

Answers

Taking squares on both sides leads to

[tex]\sqrt{-x + 6} = x - 6[/tex]

[tex]\left(\sqrt{-x + 6}\right)^2 = (x - 6)^2[/tex]

[tex]-x + 6 = x^2 - 12x + 36[/tex]

[tex]x^2 - 11x + 30 = 0[/tex]

[tex](x - 5) (x - 6) = 0[/tex]

Solving for [tex]x[/tex], we get

[tex]x - 5 = 0 \text{ or } x - 6 = 0[/tex]

or

[tex]x = 5 \text{ or } x = 6[/tex].

Evaluating both sides of the starting equation at these solutions, we have

[tex]\sqrt{-6 + 6} = 6 - 6 \implies 0 = 0[/tex]

which is true, so [tex]\boxed{x=6}[/tex] is a valid solution. However,

[tex]\sqrt{-5 + 6} = 5 - 6 \implies \sqrt1 = -1 \implies 1 = -1[/tex]

which is not true, so [tex]\boxed{x=5}[/tex] is an extraneous solution.

Find the surface area of the cone in terms of pie 18 height 12 radius

Answers

144π cm²

Answer:

Solution given:

diameter (d)= 12cm

radius (r)=12/2=6 cm

slant height(l)=18cm

Now

Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²

could anyone help me solve this?

Answers

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

After 3 minutes, a submarine had descended to −550 feet. After 8 minutes, the submarine had descended to −600 feet. Assuming a linear function, write an equation in the form d(t)=mt+b that shows the depth, d(t), after t minutes.

Answers

Answer:

d(t)=-10t-520

Step-by-step explanation:

First you have to find the gradient (m) using the formula [tex]m=\frac{d(t)2-d(t)1}{t2-t1}[/tex]

using the two points you have been given: 1(3,-550) and 2(8,-600)

so you substitute these points into the equation [tex]m=\frac{-600+500}{8-3}[/tex]

m=-10

Now that you have found the m-value you need to find the b-value by using one of the points you already have, I will use Point 2 (8,-600), and substitute it into the equation and solve

d(t)=-10t+b

-600=-10*8+b

-600=-80+b

-520=b

Therefore, the equation is d(t)=-10t-520

just for fun cuz I've heard of different answers.. what's:

6÷2(1+2) = ??​

Answers

Answer:9

Step-by-step explanation:1+2=3 6/2=3

3x3=9

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