the equation of the normal to the 2x² + 2y² -4x +4y =12 at the point (-1,1) is​

Based on a system of equations, the number of seats in the upper section of the racetrack is 3,600.

A system of equations or simultaneous equations is two or more equations concurrently or simultaneously solved.

There are four methods for solving simultaneous equations:

The charge per lower-section seat = $85

The cost per upper-section seat = $60

The fee per field ticket = $35

Let the number of lower-section seats = x

Let the number of upper-section seats = 3x

Let the number of field tickets = y

Equation 1: x + 3x + y = 22,800 or 4x + y = 22,800

85x + 60(3x) + 35y = 948,000

Equation 2: 85x + 180x + 35y = 948,000

From equation 1, y = 22,800 - 4x ...Equation 3

Substitute Equation 3 in Equation 2 to eliminate y:

85x + 180x + 35(22,800 - 4x) = 948,000

85x + 180x + 798,000 - 140x = 948,000

125x = 948,000 - 798,000

125x = 150,000

x = 1,200

The number of seats for each racetrack section:

Lower section seats, x = 1,200

Upper section, 3x = 3,600 (1,200 x 3)

Field tickets, y = 22,800 - 4x

y = 22,800 - 4(1,200)

= 18,000

Check:

85x + 180x + 35y = 948,000

85(1,200) + 180(1,200) + 35(18,000) = 948,000

102,000 + 216,000 + 630,000 = 948,000

948,000 = 948,000

Total revenue:

Lower section seats = $102,000 (85 x 1,200)

Upper section seats = $216,000 (60 x 3 x 1,200)

Field tickets = $630,000 (35 x 18,000)

Total revenue = $948,000

Thus, based on simultaneous equations, we can conclude that there are 3,600 seats in the upper section.

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The value of y that satisfies the equation is 41.

What is the arithmetic operation?

Arithmetic operations involve the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

To solve this equation for y, you can divide both sides by 4:

4y/4 = 164/4

This simplifies to:

y = 41

Hence, the value of y that satisfies the equation is 41.

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Answer:

[tex]W=\frac{A}{L}[/tex]

Step-by-step explanation:

Divide both sides of the equation by [tex]L[/tex].

To prove parallelograms is a parallelograms we have show that, diagonals cut each other in half, and one angle adds to both following angles .

One particular type of quadrilateral that is created by parallel lines is a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel.

The sum of all the sides' lengths determines a rhombus' perimeter. A rhombus's perimeter is equal to four times the length of each side because all of its sides are equal. A diamond's perimeter is given in 4x units, for instance, if one of its sides is x units.

P=4a

The two opposing side pairs must be parallel, the two opposite side pairings must coincide, the two opposite angle pairs must coincide, the diagonals must cut each other in half, the first angle must add to both the following angles, and one set of opposing sides must be both parallel AND congruent. These are the six basic properties of parallelograms.

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well, as you already know, to check if a function is EVEN, we simply check what's f( -x ), if f( -x ) = f( x ), then voila!!.  and if f( -x ) = -f( x ), then oddly enough, is an ODD function.

well, let's plug in " -x " to see what we get anyway

[tex]f(x)=-5x^2 + |2x|\implies \boxed{f(x)=-5x^2 + 2x} \\\\[-0.35em] ~\dotfill\\\\ f(-x)=-5(-x)^2 + |2(-x)|\implies f(-x)=-5(-x)(-x) + |-2x| \\\\\\ f(-x)=-5(+x^2) +2x\implies \boxed{f(-x)=-5x^2 + 2x}~\hfill \stackrel{\textit{\LARGE Even}}{f(-x)=f(x)}[/tex]

Answer:

The answer is in the picture

Step-by-step explanation:

The explanation is in the picture

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of x is 6.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4(x + 11/3) = 9(2/3)

Divide both sides by 4.

x + 11/3 = 29/3

Subtract 11/3 on both sides.

x = 29/3 - 11/3

x = (29 - 11) / 3

x = 18/3

x = 6

Thus,

The value of x is 6.

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Median won't change, however Mean will fall by 180.

By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.

African elephants total 555 in number.

Elephants had a 3800 kg average mass.

Elephants had a 3600 kg median mass.

Lola, the elephant that was the smallest, weighed 2700 kg.

Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.

What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.

now 2700 becomes 1800

so Median remains the same as 3600

No change in Median

The mean mass of the elephants was  3800 kg

=> total weight = 5 x 3800 = 19000 kg

2700 kg becomes 1800 kg

Hence new total mass = 19000 - 2700 + 1800 = 181000 kg

New Mean = 18100/5   = 3620  kg

Mean reduced by 3800 - 3620  = 180 kg

No change in Median weight

Mean reduced by 180 kg

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Answer:

f(3) = 10

Step-by-step explanation:

f (x) = x +7

plug in 3

f (3) = 3 + 7

add

f(3) = 10

The amount of money left on the gift card, in term of the number of cups, a Lauren has bought is represented by the equation would be A = 10 - 2a.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that from the task content that the total amount of money Lauren has initially is $10.

Hence, each cup of coffee costs $2.

Since the amount of money Lauren has left each time,

That is related to the number of coffee cups bought by the equation;

A = 10 -2a.

where a ranges be between 0 and 5.

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Answer:

Step-by-step explanation:

d. 0 to 4 seconds, None, 4 to 6 seconds.

Based on the data in the table, the speed of the car is increasing for the interval of time from 0 to 4 seconds. After 4 seconds, the speed remains constant at 23 mph for the remainder of the time period. Therefore, the speed is not decreasing at any point in the given time interval.

Answer:

A. 20

Step-by-step explanation:

300 ÷ 2.5= 120

So

50÷2.5 = 20

Answer: 68

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex], meaning that [tex]m\angle TRS +m\angle TSR=136^{\circ}[/tex].

Furthermore, since [tex]\triangle TSR[/tex] is isosceles, [tex]m\angle TRS=m\angle TSR[/tex].

Therefore, [tex]m\angle TSR=68^{\circ}[/tex].

Answer:

2sin²0 + 2sin0 - 1/2 = 0

(2sin0 + 1)(sin²0 - 1/2)= 0

2sin0 + 1 = 0 or sin²0 - 1/2 = 0

2sin0 = -1 or sin0 = ±1/√2

Answer:

increase of 100%

Step-by-step explanation:

50 cents to 1 dollar is an increase.

The percent increase can be calculated by dividing the increased amount by the original amount.

$1.00 - $0.50 = $0.50 increase

% increase = 100%

Answer:

y=1, x=1

Step-by-step explanation:

no need for step by step cause i know

The correct statements for the triangle are given as follows:

The vertices of the triangle are given as follows:

A(0,0), B(8,12), C(16,6).

The midpoints of each side are given by the mean of the coordinates at the extrema of these sides, hence:

The segment BE is a vertical segment, as the x-coordinate is fixed at x = 8, hence ti is parallel to the y-axis.

Given two points, the slope is given by the change in y divided by the change in x. Then the slope of CF is given as follows:

m = (6 - 6)/(16 - 4) = 0.

The length of the segment AD is given as follows:

Length of AD = square root(12² + 9²) = 15 units.

(formula for the distance between two points).

The centroid of a triangle is given by the mean of it's three coordinates, hence:

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Answer:

To find the dimensions of a rectangle

Step-by-step explanation:

perimeter=302

let width=x

length=x+47

p=2(L+W)

302=2(x+x+47)

302=2(2x+47)

302=4x+94

subtracting 94 from the other side we have

302-94=4x

208=4x

x=52

length=99

width=52

The correct answer is c) iii only as statement 1 and statement 2 are false.

What do mean and standard deviation tell us?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilized. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

What is relationship between mean and standard deviation?

The standard deviation is a measure that summarizes how far away from the mean each observation is. The positive would exactly balance the negative if the discrepancies themselves were totaled together, making their aggregate equal to zero. The squares of the discrepancies are then added as a result.

What is median?

The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Statement 1: False, it only works if distributiion is syummetric, for non- symmetric distribution, median is not unbiased estimator population in mean.

Statement 2: False standard deviation is not equal to IQR, and is heavily influenced by sample mean and outliers.

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Step 1: Figure out when Savannah will double her account value:

We need to solve [tex]140000 = 70000\left(1+\frac{0.01375}{4}\right)^{4t}[/tex].

Divide by 70000:

       [tex]2 = \left(1+\frac{0.01375}{4}\right)^{4t}[/tex]

Take the natural log of both sides and bring the exponent down:

      [tex]\ln(2) = 4t\cdot\ln\left(1+\frac{0.01375}{4}\right)[/tex]

Divide by that mess multiplied by t:

      [tex]\dfrac{\ln(2)}{4\ln\left(1+\frac{0.01375}{4}\right)} = t[/tex]

Throw that into a calculator and you get about 50.497297884.

Depending on how picky your teacher is, we'd need to round this to the next time the interest is compounded, since it's only compounded each quarter, so t = 50.5.  (The fact is that Savannah's account will never exactly double in value.)

Step 2:

Now, we need to evaluate Carter's continuously compounded investment for 50.5 years:

    [tex]B = 70000e^{0.01125\cdot(50.5)}\approx123546.825994[/tex]

    B ≈ 123547 to the nearest dollar.

As a comparison, here's the other calculation with the more precise t value.

    [tex]B = 70000e^{0.01125\cdot(50.497297884)}\approx123543.070375[/tex]

    B ≈ 123543 to the nearest dollar.

Again, I would say the 50.5 calculation is actually more correct, since Savannah's account only compounds the interest each quarter, but you'll have to decide what your teacher would say.

Answer:

$123,543 (nearest dollar)

Step-by-step explanation:

Find the length of time Savannah has to invest her money for it to double.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies 140000=70000\left(1+\dfrac{0.01375}{4}\right)^{4t}[/tex]

[tex]\implies 140000=70000\left(1.0034375\right)^{4t}[/tex]

[tex]\implies2=\left(1.0034375\right)^{4t}[/tex]

[tex]\implies \ln2=\ln\left(1.0034375\right)^{4t}[/tex]

[tex]\implies \ln2=4t\ln\left(1.0034375\right)[/tex]

[tex]\implies t=\dfrac{\ln 2}{4 \ln\left(1.0034375\right)}[/tex]

[tex]\implies t=50.49729788[/tex]

Therefore, it would take approximately 50.5 years for Savannah's principal investment to double.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\ \phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula along with the found value of t and solve for A:

[tex]\implies A=70000e^{0.01125 \times 50.4972...}[/tex]

[tex]\implies A=123543.0704...[/tex]

Therefore, the amount of money that Carter would have in his account when Savannah's money has doubled in value is $123,543 (nearest dollar).

Answer:

83 degrees

Step-by-step explanation:

17^2 = 8^2 + 16^2 - 2 * 8 * 16 * cos (X)

289 = 64 + 256 - 16 * 16 * cos(X)

289 = 320 - 256 cos(X)

289-320 = -256 cos(X)

- 31 = -256 cos(X)

31 = 256 cos(X)

31/256 = 256/256 cos(X)

0.121094 = cos (X)

x = arccos 0.121094

x = 83.04475538

. Each lemon bar must be covered in decorative icing. A picture of the lemon bar is shown below.

Answer:

The answer to your question is,

B) It isn’t true that corresponding cross-sections have the same area.

Step-by-step explanation:

They have the same areas and the same heights. but the corresponding cross-section is not the same

{The top of the first figure is a point, but the second one is a flat}

I hope this helps :)

Answer:

B)  It isn’t true that corresponding cross-sections have the same area.

Step-by-step explanation:

Cavalieri's principle

If two three-dimensional figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

From inspection of the given diagram:

The cross-sectional area at every point along the height is not the same in both figures.

Answer:

Step-by-step explanation:

3 small tiers + 5 medium tiers= 291 guests

1 small tier+5 medium tiers=247 guests

The 2 cakes have the same medium tiers(5 medium tiers). If we subtract  291-247 we will have the number of guest that  2 small tiers serve.

291-247= 44 guests serve per 2 small tiers

44:2=22 guests serve per one small tier.

So if we subtrack the number of guest that one small tier one the cake that has only one small tier we will obtain the number of guests that the 5 medium tiers serve.

247-22=225 guests serve per 5 medium tiers

225:5= 45 guests per 1 mediem tier.

Sorry, because english isn't my mother tongue.

Answer:

18.2

Step-by-step explanation:

20 + (n-1)-.2

n is the number of the term.

-.2 is the common difference

20 + (10-1) -.2

20 + 9(-.2)

20 - 1.8

18.2

The measure of PQ in the given triangle is 24.

What is triangle?

PQ = ST

7x-2 = -2x+32

7x + 2x = 32 + 2

9x = 34

x = 34/9

The measure of PQ:

PQ = 7x-2

= 7(34/9) - 2

= (238 - 18) / 9

= 24.4

PQ ≅ 24

Hence, the measure of PQ in the given triangle is 24.

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The circumference of the circle with the dimensions radius = 6 and π = 3.14 is 37.68

The circumference of a circle refers to the line that bounds a circle or other two-dimensional figure.

Circumference of a circle = 2πr

Where,

Circumference of a circle = 2πr

= 2 × 3.14 × 6

= 37.68

Therefore, the circumference of the circle is given by 37.68

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On solving the provided question, we got to know that -  the points (0,1) and (1,0) to be used to plot the graph .

An algebraic equation of the form y=mx+b (where m is the slope and b is the y-intercept) with one constant and only one first-order (linear) term is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.

To draw a straight line, just two points are needed.

Finding the points where the graph intersects is one approach.

[tex]the intercepts of the x and y axes[/tex]

[tex]Let x = 0 in the y-intercept equation.\\ Let y = 0 in the x-intercept equation.[/tex]

x =0→y=0+y=1⇒y=1←y-intercept

y =0→x+0=1⇒x=1←x-intercept

plot the points (0,1) and (1,0)

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