a linear system in three variables has no solution. Your friend concludes that it is not possible for two of the three equations to have any points in common. is your friend correct? Explain your reasoning.

Answer:

Step-by-step explanation:

g(x)= -2 x^2 + 3 x - 5

g(-2) = -2 . (-2)^2 + 3. (-2) - 5 = -2 . 4 - 6 - 5 = - 8 - 6 - 5 = - 19

g(0) = -2 . (0)^2 + 3 . 0 - 5 = -2 . 0 + 0 - 5 = 0 + 0 - 5 = - 5

g(3) = -2 . (3)^2 + 3 . (3) - 5 = -2 . 9 + 9 - 5 = -18 + 9 - 5 = - 14

The value of g(x) is the input values are  –2, 0, and 3 are -19, -5 and -14

Given the following function

g(x) =  –2x² + 3x – 5

For the input value of -2

g(-2) =  –2(-2)² + 3(-2) – 5

g(-2) = -8 - 6 - 5

g(-2) =-19

If the value of x is 0

g(0) =  –2(0)² + 3(0)– 5

g(0) = -5

If the vaue of x is 3

g(3) =  –2x² + 3x – 5

g(3) = -2(3)² + 3(3)– 5

g(3) =-18 + 9 - 5

g(3) = -14

Hence the value of g(x) is the input values are  –2, 0, and 3 are -19, -5 and -14

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Answer:

A.A line segment consist of two points and all points in between .

Step-by-step explanation:

Definition of  a line segment : It is a portion of a line .It has two end points and all point contain between them.It is shortest distance between two points.

A.A line segment consist of two points and all points in between .

By definition of  a line is is true.

Hence, option A is true.

B.A line segment is a set of a points that extend infinitely far in one direction.

No, line segment can not be extend infinitely in any direction.

Therefore, option is false.

C.A line segment is a set of points that extend far in both directions.

No, by definition of line segment , it is false.

D.A line segments is the set of points in a plane that are equidistant from a given point.

By definition of line segment , it is false.

Answer:

264.

Step-by-step explanation:

Let x represent the number of trout in the lake.

We have been given that a group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged.

Using proportions, we will get:

[tex]\frac{\text{Total trouts}}{\text{Tagged trouts}}=\frac{48}{22}[/tex]

[tex]\frac{x}{121}=\frac{48}{22}[/tex]

[tex]\frac{x}{121}*121=\frac{48}{22}*121[/tex]

[tex]x=\frac{24}{11}*121[/tex]

[tex]x=24*11[/tex]

[tex]x=264[/tex]

Therefore, there would be approximately 264 trout in the lake.

264 trouts are estimated to be in the lake.

Using proportion, we write: Tagged trout/Total Trout

This becomes 22/48.

In order to use cross multiplication, we write another fraction using x, the total number of trout in the lake: 121/x.

Now we have 121/x=22/48.

We cross multiply.

121*48=22x.

(121*48)/22 becomes:

264.

Answer:

6

Step-by-step explanation:

In a square, all diagonals, vertices, sides, and angles are congruent, and since 36 is its area, take the square root of 36, giving you 6.

* When we are talking about length, we want the NON-NEGATIVE root.

I am joyous to assist you anytime.

Answer:

  -$5,500

Step-by-step explanation:

  The change in the one year from 2009 to 2010 was ...

  18,500 -24,000 = -5,500

The annual rate of change in the boat's value was -$5,500.

Thus, the annual rate of change of the boat's value is $5,500 per year.

To find the annual rate of change of the boat's value, we need to determine how much the value decreased from 2009 to 2010 and then calculate the yearly decrease. The boat's value in 2009 was $24,000; in 2010, it was $18,500.

First, calculate the decrease in the boat's value from 2009 to 2010:

Decrease = Initial Value - Final Value

Decrease = $24,000 - $18,500 = $5,500

Since this decrease occurred over one year, the annual rate of change in the boat's value is $5,500 per year.

Therefore, the annual rate of change of the boat's value is $5,500 per year.

Step-by-step explanation:

seriously i am not understanding your question

The two region under whose we have to find area is

 f(x)=x

 [tex]g(x)=x^{\frac{1}{n}}\\\\x \geq 0\\\\n\geq 2[/tex]

The Point of Intersection of two curves is always , x=0 and x=1.

Area of the Region

    =Area under the line - Area Under the curve g(x), when n take different value, that is ≥2.

[tex]\rightarrow[- \int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{2}} \, dx]+[ -\int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{3}} \, dx]+[ -\int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{4}} \, dx]+[ -\int\limits^1_0 {x} \, dx + \int\limits^1_0 {x^{\frac{1}{5}} \, dx]+......[/tex]

[tex]=\int\limits^1_0({x^{\frac{1}{2}}+x^{\frac{1}{3}}+x^{\frac{1}{4}}+x^{\frac{1}{5}}+.......+x^{\frac{1}{200}}}) \, dx -\int\limits^1_0 ({x}+{x}+{x}+{x}...........+200\text{times}) \, dx[/tex]

When, n=200, the first quadrant is completely occupied by the curve

       [tex]g(x)=x^{\frac{1}{n}},x\geq 0\\\\2\leq n \leq 200[/tex]

[tex]=\int\limits^1_0{x^{\frac{1}{n}} \, dx=\frac{n\times x^{(\frac{1}{n}+1)}}{n+1}\left \{ {{x=1} \atop {x=0}} \right.}\\\\= \frac{n}{n+1}\\\\\int\limits^1_0{x^{n} \, dx=\frac{x^{n+1}}{n+1}\left \{ {{x=1} \atop {x=0}} \right.}\\\\=\frac{1}{n+1}[/tex]

[tex]=\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...........+\frac{200}{201}-199 \times \frac{1}{2}\\\\=1-\frac{1}{3}+1-\frac{1}{4}+1-\frac{1}{5}+...........+1-\frac{1}{201}-99.5\\\\=199-99.5+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...........+\frac{1}{201}\\\\=99.5+1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...........+\frac{1}{201}-1-\frac{1}{2}\\\\=98+\frac{1}{d} \times\ln(\frac{2a+(2n-1)d}{2a-d})\\\\=98+\ln(\frac{2 \times 1+(2\times 201-1)\times 1}{2\times 1-1})\\\\=98+\ln 403\\\\=98+6({\text{approx}})\\\\=104 \text{square units}[/tex]

Sum of n terms of Harmonic Progression is

     [tex]=\frac{1}{a}+\frac{1}{a+d}+\frac{1}{a+2d}+\frac{1}{a+3d}+\frac{1}{a+4d}.....+\frac{1}{a+(n-1)d}\\\\=\frac{1}{d} \times \ln(\frac{2a+(2n-1)d}{2a-d})[/tex]    

Answer:

The Recursive Formula of sequence is: 8, 5, 2, -1, -4,...

Step-by-step explanation:

Arithmetic Sequence is a sequence in which every two neighbor digits have equal distances.

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

We have given that,

a₁₇ = -40  ⇒ a₁₇ = a + (17 - 1)d

⇒ -40 = a + 16d        →      (1)

Also, a₂₈ = -73  ⇒ a₂₈ = a + (28 - 1)d

⇒ -73 = a + 27d           →    (2)

Solving, equation (1) and (2), We get  

a = 8, d = -3

Hence, First term = a = 8

Second term = a + d = 8 - 3 = 5

Third term = 5 + d = 2

Fourth term = 2 + d = -1

Thus, The Arithmetic Sequence is: 8, 5, 2, -1, -4,...

Answer:

The difference between the given terms is

–73 – (–40) = –33.

The difference between the term numbers is 28 – 17 = 11.

Dividing –33 / 11 = –3.

The common difference is –3.

The recursive formula is the previous term minus 3, or an = an – 1 - 3 where a17 = -40.

Step-by-step explanation:

explanation is the answer above ^

edg answer

correct aswell

To find the percentage rate of growth, calculate the percentage change in enrollment from one year to the next using the graph. Perform these calculations for each pair of consecutive years to determine the overall percentage rate of growth.

To determine the percentage rate of growth, we need to analyze the graph showing the enrollment growth of the school. Exponential growth is represented by a curve that increases more and more steeply over time. To find the rate of growth, we can calculate the percentage change in enrollment from one year to the next.

For example, if the enrollment was 100 in Year 1 and 200 in Year 2, the percentage change would be (200-100)/100 * 100 = 100%. This means the enrollment doubled from Year 1 to Year 2.

By performing similar calculations for each pair of consecutive years, we can find the percentage rate of growth over the entire period represented by the graph.

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The percentage rate of growth for the school's enrollment is approximately 24% per year.

To determine the percentage rate of growth, we need to find the common ratio and the common difference in the exponential function that represents the school's enrollment. From the given graph, we can see that the enrollment doubles approximately every three years. This means that the common ratio is 2. The initial enrollment is 500, which is represented by the value "a" in the exponential function. The final enrollment, which is approximately 4000, is represented by "an". Using these values, we can write the exponential function as follows:

[tex]an = a * 2^(n-1)[/tex]

Substituting the initial enrollment and final enrollment in this equation, we get:

[tex]4000 = 500 * 2^(n-1)[/tex]

Dividing both sides by 500 and simplifying, we get:

[tex]8 = 2^(n-1)[/tex]

Taking the logarithm of both sides with base 2, we get:

(n-1) = log2(8)

(n-1) = 3

Adding 1 to both sides, we get:

n = 4

This means that it takes approximately four years for the school's enrollment to double. To find the percentage rate of growth per year, we need to find the common difference in the exponential function. The common difference is calculated as follows:

Common difference =[tex]ln(y2 / y1) / (x2 - x1)[/tex]

Here, x1 and x2 are two consecutive years, and y1 and y2 are their corresponding enrollments. Using this formula, we can calculate the common difference as follows:

Common difference = ln(4000 / 3200) / (7 - 4) = 0.263975 (approximately 24%) per year. This means that every year, the school's enrollment grows by approximately 24%.

-200,-100,-25,0,30

Step-by-step explanation:

negatives will always be less than positives with negatives you put greatest to least and then 0 and then positives from least to greatest

In order to get the answer you have to remember that bigger negatives are actually less then smaller negatives so -200 would be less then -25.

[tex]-100, -200, 0, -25, 30[/tex]

[tex]-200 < -100[/tex]

[tex]-100 <-25[/tex]

[tex]-25 < 0[/tex]

[tex]0 <30[/tex]

[tex]= -200,-100,-25,0,30[/tex]

Therefore your answer is "-200,-100,-25,0,30."

Hope this helps.

Check the picture below.

Answer:

1). Option E

2). Option H

3). Option C

4). Option J

5). Option C

Step-by-step explanation:

1). (5x + 3xy + 4y) + (4x - 2xy - 2y)

= (5x + 4x) + (3xy - 2xy) + (4y - 2y)

= 9x + xy + 2y

Option E. is the answer.

2). 5y + 2z + 3x²- (2y - 2z + 4x)

= 5y - 2y - 4x + 2z + 2z + 3x²

= 3y - 4x + 4z + 3x²

Option H is the answer.

3). (x - 1)(x + 1)(x - 1)

= (x² - 1)(x - 1)    [Since (a - b)(a + b) = a² - b²]

= x²(x - 1) - 1(x - 1)

= x³ - x² - x + 1

Option C is the answer.

4). (2a + 6)²

= 4a² + 24a + 36

[Since (a + b)² = a² - 2ab + b²]

Option J. is the answer.

5). For subtraction,

(6 - 1)³ - (4 - 1)²

= 5³ - 3²

= 125 - 9

= 116

But the result is 200 so operation subtraction is not the answer.

For Multiplication,

(6 × 1)³ - (4 × 1)²

= 6³ - 4²

= 216 - 16

= 200

For division,

(6 ÷ 1)³ - (4 ÷ 1)²

= 6³ - 4²

= 216 - 16

= 200

Therefore, Option C. is the answer.

Answer:

SAS (side angle side)

Step-by-step explanation:

We have a pair of corresponding sides and the included angle. The angle is equal, but the sides are a fraction of the other triangle's side and has an equal rate.

2AC=DF

2AB=DE

The triangles are congruent

Answer:

SAS

Step-by-step explanation:

Answer:  At least 3

Step-by-step explanation:

Lets solve this problem by the pidgeon hole principle. Suppose that Matt pulls out 2 socks, if he gets a matching pair then he is done and that's it. But now suppose that he gets one black sock and one white sock, if he then pulls out a third sock it will be either white or black, in either case he would have gotten with a 100% certainty a matching pair, since he already has a black and a white sock. So the minimum number to ensure he gets a matching pair is 3 socks.

Answer:

The drawer contains 40 nickels, 20 dimes and 14 quarters.

Step-by-step explanation:

Let d, q and n represent number of dimes, quarters and nickels respectively.

We have been given that there are twice as many nickels as dimes.

[tex]n=2d...(1)[/tex]

Further, the number of dimes and quarters sum to 34.

[tex]d+q=34...(2)[/tex]

As the change drawer contains $7.50 made up entirely of quarters, nickels, and dimes.

[tex]0.10d+0.25q+0.05n=7.50...(3)[/tex]  

From equation (2), we will get:

[tex]q=34-d[/tex]

Substituting equation (1) and equation (2) in equation (3), we will get:

[tex]0.10d+0.25(34-d)+0.05(2d)=7.50[/tex]  

[tex]0.10d+8.50-0.25d+0.10d=7.50[/tex]  

[tex]-0.05d+8.50=7.50[/tex]  

[tex]-0.05d+8.50-8.50=7.50-8.50[/tex]  

[tex]-0.05d=-1[/tex]  

[tex]\frac{-0.05d}{-0.05}=\frac{-1}{-0.05}[/tex]  

[tex]d=20[/tex]  

Therefore, drawer contains 20 dimes.

Substitute [tex]d=20[/tex] in equation (1):

[tex]n=2d[/tex]

[tex]n=2(20)[/tex]

[tex]n=40[/tex]

Therefore, drawer contains 40 nickels.

Substitute [tex]d=20[/tex] in equation (2):

[tex]20+q=34[/tex]

[tex]20-20+q=34-20[/tex]

[tex]q=14[/tex]

Therefore, drawer contains 14 quarters.

Answer:

There are 40 nickels, 14 quarters and 20 dimes.

Step-by-step explanation:

A change drawer contains $7.50

Let the number of quarters in the drawer = q

let the number of nickels in the drawer = n

and number of dimes = d

So, (0.25q + 0.05n + 0.10d) = 7.5

By dividing the equation by 0.50

5q + n + 2d = 150 ---------(1)

Now statement says " There are twice as nickels as dimes"

n = 2d -------(2)

And "the number of dimes and quarters sum to 34"

d + q = 34 -------(3)

We replace n = 2d from equation (2) in equation (1)

5q + 2d + 2d = 150

5q + 4d = 150 ---------(4)

Multiply equation (3) by 4 and subtract it from equation (4)

(5q + 4d) - 4(d + q) = 150 - 34×4

5q - 4q + 4d - 4d = 150 - 136

q = 14

We plug in the value of q in equation (3)

d + 14 = 34

d = 34 - 14

d = 20

Since n = 2d

So n = 2×20

n = 40

Therefore, there are 40 nickels, 14 quarters and 20 dimes.

Answer:

  $13

Step-by-step explanation:

Fill in the given values and solve for the unknown.

  110 = 10A -20

  130 = 10A . . . . . add 20

  13 = A . . . . . . . . divide by 10

You spent $13 on advertising.

Answer:

Step-by-step explanation:

Answer:

Malia's allowance changed from $10.00 to $([tex]10-2x[/tex]) after buying ice cream cones.

Step-by-step explanation:

We are given the following information:

Malia's allowance to spend at carnival = $10.00

Ice cream ordered by her = 2

Let x dollars be the cost of one ice cream cone.

Total money spent on ice creams = [tex]2x[/tex]

Formula:

[tex]\text{Change in Malia's allowance} = \text{Total allowance} - \text{Money spent on ice cream cones}\\= 10 - 2x[/tex]

Thus, Malia's allowance changed from $10.00 to $([tex]10-2x[/tex]) after buying ice cream cones.

Final answer:

The terms in the expression 3 + 5 + 7b – 18a are the individual elements consisting of constants and variables with their coefficients: 3, 5, 7b, and -18a, with the correct response being option b.

Explanation:

The terms in the expression 3 + 5 + 7b – 18a are individual elements that are added or subtracted within the expression. These are individually known as terms. In an algebraic expression, coefficients and variables combined as a product (like 7b or -18a) are considered single terms. On the other hand, numbers without variables, such as 3 and 5, are also terms but are called constants because their values do not change. Consequently, each number or variable or product of a number and a variable that is separated by a plus or a minus sign is a separate term.

In this expression, we have four distinct terms which are 3, 5, 7b, and -18a. The correct answer is thus option b: The terms are 3, 5, 7b, and -18a.

Answer:

Step-by-step explanation:

(a) You use the fact that the lengths RS and ST total the length RT.

  RS +ST = RT

  (6y+3) +(3y+5) = 80 . . . . . substitute the given values

  9y +8 = 80 . . . . . . . . . . . . .simplify

  9y = 72 . . . . . . . . . . . . . . . .subtract 8

  72/9 = y = 8 . . . . . . . . . . . .divide by the coefficient of y

___

(b) Now, the value of y can be substituted into the expressions for RS and ST to find their lengths.

  RS = 6y +3 = 6·8 +3

  RS = 51

  ST = 3y +5 = 3·8 +5

  ST = 29

___

Check

  RS +ST = 51 +29 = 80 = RT . . . . the numbers check OK

Answer:

  9 m

Step-by-step explanation:

  ∠CAB = 90° -∠ABC = 90° -30° = 60°

Since AL bisects angle A, we have ...

  ∠LAC = ∠LAB = 60°/2 = 30°

Then ∠BAL = ∠ABL = 30° and ΔABL is isosceles with AL = LB = 18 m.

The 30°-60°-90° triangle ALC has sides in the ratio ...

  CL : CA : AL = 1 : √3 : 2

so

  CL/AL = 1/2

  CL = AL/2 = (18 m)/2 = 9 m

_____

It can help to draw a diagram

In triangle BCL, since it is a 30-60-90 triangle, the side opposite the 60-degree angle is √3 times the side opposite the 30-degree angle. Thus, the length of side CL is 18√3 meters.

In triangle ABC, you're told that angle C is 90 degrees and the angle ABC is 30 degrees. Therefore angle ACB (or BAC) is 60 degrees because the sum of all angles in a triangle is 180 degrees.

You're also given that LB, a line that bisects angle B, is 18 meters.  The triangle BCL is a 30-60-90 triangle, a special type of triangle where the sides are in the ratio 1:√3:2.

In this case, LC (the side opposite the 60-degree angle) is √3 times the side opposite the 30-degree angle (LB), which is 18 meters. So, the length of CL = 18√3 meters.

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Answer:

x = 3+1/2 y -----Equation-1

-2x-y = 2 -------Equation-1

Multiplying equation 1 by 2  we get

2x = 2*(3+1/2y)

2x = 6+y

y = 2x-6

substituting the value of of y in equation2

-2x - (2x-6) = 2

-2x -2x +6 = 2

-4x = 2-6

-4x = -4

x = -4/-4 = 1

y = 2x-6 = 2-6 = -4

x = 1

y = -4

Step-by-step explanation:

Answer:

x=0.75 and Y=-4.5

Step-by-step explanation:

let x=3+1/2y.....(1)

-2x-y=3.......(2)

substitute (1) into (2)

-2(3+1/2y)-y=3

-6-y-y=3

-2y=9

y=-9/2

put y=-9/2 into (1)

x=3+(1/2)(-9/2)

x=-4.5

Answer:

Hello my friend! The answer is ZERO!

Step-by-step explanation:

If we substitue the values of "a" and "b" on the equation, will have:

3*(a*b)  + 5(b)  -6 =

3 * (-1 * 3)  +   5*(3)   - 6 =

-9 + 15 - 6 = 0

Answer:

Step-by-step explanation:

As the problem statement suggests, look up the rules if you have to.

In the case of trailing zeros, the decimal point makes them significant.

__

In a number without a decimal point, such as 300, the zeros are sometimes significant. (Different authors may tell you the zeros are never significant in such a number. The problem comes when, for example, you're trying to represent 296 rounded to the nearest 10. That is 30. tens--with 2 significant digits, just as 286 rounded to the nearest 10 would be 290--with 2 significant digits. In some numbers, you cannot tell the difference between a 0 that is a placeholder and a 0 that is present because the value of the number cannot be represented exactly any other way.)

Answer:

The magnitude of A is 17.46 m and B is 1.50 m

Step-by-step explanation:

If the vector sum A+B+C =0, then the sum of the projection of the vector in axes x- is zero and the sum of the projection of the vector in the axes y- is also zero.

Ax+Bx+Cx = 0

Ay+By+Cy = 0

|Ax| = cos 41.9 * |A|

|Ay| = sin 41.9 * |A|

|Bx| = cos 28.2 * |B|

|By| = sin 28.2 * |B|

|Cx| = 0

|Cy| = 22.2

Ax+Bx+Cx = 0

|Ax|-|Bx|+0 =0

the vector Ax is in the positive direction of the x- axes and Bx in the negative direction and C do not have a component in the x- axes

cos 41.9 * |A| - cos 28.2 * |B| = 0 (I)

Ay+By+Cy = 0

|Ay|+|By|-|Cy|=0

the vector Ay and By are the positive direction of the y- axes and Cy in the negative direction

sin 41.9 * |A| + sin 28.2 * |B| - 22 =0 (II)

Now we have a system of 2 (I and II) equations and 2 variables (|A| and |B|)

cos 41.9 * |A| - cos 28.2 * |B| = 0

sin 41.9 * |A| + sin 28.2 * |B| = 22

cos 41.9 * |A| = cos 28.2 * |B|

|A| = cos 28.2 * |B| / cos 41.9

sin 41.9 * |A| + sin 28.2 * |B| = 22

sin 41.9 *  cos 28.2 * |B| / cos 41.9 + sin 28.2 * |B| = 22

tg 41.9 * cos 28.2 * |B| + sin 28.2 * |B| = 22

(tg 41.9 * cos 28.2 + sin 28.2) * |B| = 22

|B| = 22 / (tg 41.9 * cos 28.2 + sin 28.2)

|B| = 17.46

|A| = 1.50

The magnitude of vector A and the magnitude of vector B is 20.6198 and 17.4146 respectively.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

Given

Vector C has a magnitude of 22.2 m and points in the negative y‑direction.

Vectors A and B both have positive y‑components and make angles of α=41.9° and β=28.2° with the positive and negative x-axis.

Let the vectors A, B, and C be concurrent.

Then vectors can be resolved in x-direction and y-direction.

Vectors in y-direction

[tex]\rm A\ sin 41.9^o + B \ sin28.2^o = C\\0.6678\ A\ \ +\ 0.4726\ B \ = 22[/tex].....eq(1)

Vectors in x-direction

[tex]\rm A \ cos41.9^o = B \ cos 28.2^o\\0.74431 \ \ A = B \ \ 0.8813[/tex].....eq(2)

From equations 1 and 2, we get

A = 20.6199 and B = 17.4147

Thus, the magnitude of vector A and the magnitude of vector B is 20.6198 and 17.4146 respectively.

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Answer:

y = - [tex]\frac{3}{4}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (4, 0) ← 2points on the line

m = [tex]\frac{0-3}{4-0}[/tex] = - [tex]\frac{3}{4}[/tex]

Note the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - [tex]\frac{3}{4}[/tex] x + 3 ← equation of line

Answer:

The total change in the stock market from the beginning of the day to the end of the day is [tex]-89\frac{3}{4}[/tex] or the stock market goes down [tex]89\frac{3}{4}[/tex]

Step-by-step explanation:

At the beginning of the day the stock market goes up [tex]30\frac{1}{2}[/tex] points. This means, we have to add [tex]30\frac{1}{2}[/tex]

At the end of the day the stock market goes down [tex]120\frac{1}{4}[/tex] points. This means, we have to subtract [tex]120\frac{1}{4}[/tex]

Change [tex]=+30\frac{1}{2}-120\frac{1}{4}=(30-120)+\left(\frac{1}{2}-\frac{1}{4}\right)=-90+\frac{1}{4}=-89\frac{3}{4}[/tex]

So, the total change in the stock market from the beginning of the day to the end of the day is [tex]-89\frac{3}{4}[/tex] or the stock market goes down [tex]89\frac{3}{4}[/tex]

Answer 89 3/4

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Answer:

(a) The linear formula that models the lean of the renovated tower is:

I = (17 / 300)t + 162

In 2150, the tower will lean 170.44 inches off the perpendicular.

Step-by-step explanation:

Data:

(a)

A linear formula has the form:

where

In this case, the dependent variable is the tilt of the tower, measured as the number of inches from the perpendicular. Let´s call "I" this variable. And what does it depend on? It depends on the variable time. The tilt of the tower varies over time.

Therefore, the time (in years) is the independent variable. Let´s call "t" this variable.

The slope (m) is the change in the dependent variable for each unit of the independent variable. So, it is the change in the number of inches from the perpendicular, for each year elapsed.

Officials forecast that it would take 300 years for the tower to return to its 1990 tilt. In other words, 300 years to the tower to lean 17 inches. Or, the tower will lean 17 inches in 300 years. That is the slope (m).

m = (17 / 300) inches per year

The y-axis interception (b) is the value of the dependent variable (I) when the independent variable (t) is equal to zero.

Our t=0 occurs when the tower was reopened, in 2001.

At that time, the tower leaned 162 inches off the perpendicular.

b = 162

Then, the linear formula that models the lean of the renovated tower is:

I = (17 / 300)t + 162

or

I = 162 + (17 / 300)t

To predict the lean of the tower in 2150, let´s substitute the independent variable t in the formula for the time elapsed from 2001 (our t=0) to 2150.

Time elapsed = 2150 - 2001 = 149 years

I = 162 + (17 / 300) * 149

I = 170.44

In 2150, the tower will lean 170.44 inches off the perpendicular.

Final answer:

To predict the lean of the Tower of Pisa in 2150, plug 149 years into the formula l = 162 + (17/300)t, resulting in approximately 170.45 inches lean from the perpendicular.

Explanation:

The question involves constructing a linear model and making a prediction based on that model. Given the information, the linear formula to model the lean of the renovated Tower of Pisa is [tex]\l = 162 + (17/300)t[/tex], where l represents the lean of the tower inches away from the perpendicular, and t represents the number of years since 2001.

To predict the lean of the tower in 2150 using the formula, we need to first calculate the number of years from 2001 until 2150, which is 2150 - 2001 = 149 years. Plugging this value into the formula, we get:

[tex]\[ l = 162 + (17/300) \times 149 \][/tex]

Now, let's calculate the result:

[tex]\[ l = 162 + 0.0567 \times 149 \][/tex]

[tex]\[ l = 162 + 8.4483 \][/tex]

[tex]\[ l = 170.4483 \][/tex]

Therefore, rounding to two decimal places, the predicted lean of the tower in 2150 would be approximately 170.45 inches off the perpendicular.

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Answer:

  segment EF over segment LM equals segment FG over segment MN

Step-by-step explanation:

The triangles are similar, not congruent, so any answer choice with the word "congruent" can be ignored.

The sequence of letters in the triangle name tells you the corresponding segments:

Corresponding segments have the same ratio, so ...

  EF/LM = FG/MN . . . . . . matches the first answer choice

  EF/LM = EG/LN . . . . does not match the 3rd answer choice

Answer:

segment EF over segment LM equals segment FG over segment MN