In the xy-plane, what is the slope of the line tangent to the graph of x² + xy + y2 = 7 at the point (2,1)? -4/3 -5/4 -1 -4/5 -3/4

Total number of red marbles that John owns is 44.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. The expression on the left and the expression on the right are shown to be equal in reference to one another. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase. 

How to solve?

Let the number of blue marbles be x.

x + x + 12 + x + 34 = 76

3x + 46 = 76

3x = 30

x = 10

Therefore, total number of red marbles = x + 34 = 44

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Answer:

at one gas station, gas costs $2.75 per gallon. write and equation that relates the total cost, C, to the number of gallons of gas purchased:  2.75 g  

Answer:

Step-by-step explanation:

either 150.7 or 40

Cheri collected 145 number of 5 peso coin and 156 number of 10 peso coin during her family's annual outreach

An equation is used to show the relationship between numbers and variables.

Let x represent the number of 5 peso coins and y represent the number of 10 peso coin

At the end of the year, she has saved a total of Php 2285, hence:

5x + 10y = 2285    (1)

Also, she has 11 more 10 pesos than 5 peso coins, hence:

y = x + 11    (2)

Solving both equations using elimination method gives:

x = 145, y = 156

Cheri had 145 number of 5 peso coin and 156 number of 10 peso coin.  

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If the point (x, y) is in Quadrant IV, the x-coordinate is positive, the y-coordinate is negative, and the absolute value of y is greater than the absolute value of x.

If the point (x, y) is in Quadrant IV, the following must be true:

The x-coordinate (horizontal value) of the point is positive: Since Quadrant IV is to the right of the y-axis, the x-coordinate of any point in this quadrant will be positive.

The y-coordinate (vertical value) of the point is negative: Quadrant IV is below the x-axis, so the y-coordinate of any point in this quadrant will be negative.

The absolute value of the y-coordinate is greater than the absolute value of the x-coordinate: In Quadrant IV, the negative y-values are larger in magnitude (greater absolute value) than the positive x-values.

These three conditions must be true for a point (x, y) to be located in Quadrant IV on a Cartesian coordinate system.

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The required values of x and y that allows these two triangles to be similar are x=(32±√239)/5, y=(19±2√239)/5.

Let the first triangle be called ABC where A(-1, 4), B(-3, 5) and C(-6, 1).

Let the second triangle be called LMN where L(-2, 8), M(-6, 10) and N(x, y)

Now if the 2 triangles are similar then the ratio of the lengths of corresponding sides will also be equal.

AB: BC= \(\sqrt{(-1+3)^{2}+(4-5)^{2} }\):\(\sqrt{(-1+6)^{2}+(5-1)^{2} }\) = √5:√41

AC: BC= \(\sqrt{(-1+6)^{2}+(4-1)^{2} }\): \(\sqrt{(-1+6)^{2}+(5-1)^{2} }\)=√34:√41

Now,

LM: MN= \(\sqrt{(-2+6)^{2}+(8-10)^{2} }\):\(\sqrt{(x+6)^{2}+(y-10)^{2} }\)

=2√5:\(\sqrt{(x+6)^{2}+(y-10)^{2} }\)

Comparing LM: MN to AB: BC we get \(\sqrt{(x+6)^{2}+(y-10)^{2} }\)=2√41

∴ \((x+6)^{2}+(y-10)^{2}\) = 164...... (1)

Again, LN: MN= \(\sqrt{(x+2)^{2}+(y-8)^{2} }\) : \(\sqrt{(x+6)^{2}+(y-10)^{2} }\)= AC: BC= √34:√41

Applying (1) to this rati we get: \(\sqrt{(x+2)^{2}+(y-8)^{2} }\)=2√34....(2)

Solving (1) and (2) we get: 8x-4y=32-68=-36

∴ 2x-y=9

Substituting y=2x-9 in (1) we get: \((x+6)^{2}+(2x-9)^{2}\)=164

Solving we get x=(32±√239)/5, y=(19±2√239)/5

Hence we get the required answers.

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Answer:

(3, 5 )

Step-by-step explanation:

y = 2x² - 7x + 8 → (1)

y = 2x² - 18x + 41 → (2)

substitute y = 2x² - 7x + 8 into (2)

2x² - 7x + 8 = 2x² - 18x + 41 ( subtract 2x² from both sides )

- 7x + 8 = - 18x + 41 ( add 18x to both sides )

11x + 8 = 41 ( subtract 8 from both sides )

11x = 33 ( divide both sides by 11 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

y = 2(3)² - 7(3) + 8 = 2(9) - 21 + 8 = 18 - 13 = 5

solution is (3, 5 )

Answer:

(3, 5)

Step-by-step explanation:

Solution given by jimrgrant1 is absolutely correct. I am just offering another solution strategy without using substitution.

We have the equations

\(y = 2x^2 - 7x + 8 \quad\quad [1]\\\\y = 2x^2 - 18x + 41 \quad\quad [2]\)

Since the left side in both equations is y, set the right sides equal to each other;
\(2x^2 - 7x + 8 = 2x^2 - 18x + 41\)

Subtract \(2x^2\) from both sides:
\(- 7x + 8 = - 18x + 41\)

\(\text{Add 7x to both sides:}\\\)
\(- 7x + 7x + 8 = - 18x +7x + 41\\\\8 = -11x + 41\\\\\text{Subtract 41 from both sides:}:\\\\8 - 41 = -11x\\\\-33 = -11x\\\\\text{Switch sides:}\\\\-11x = -33\\\\\text{Divide by -11}:\\\\\dfrac{-11x}{-11} = \dfrac{-33}{-11}\\\\x = 3\\\\\)

Looking at the answer choices, we see only one answer choice has x = 3 and this is the third option. So we need not calculate for y.

The correct answer is (3, 5)

{If curious we can plug into any of the two equations and see that y evaluates to 5

This has been done for you by user jimrgrant1  so I won't repeat

The point that is a solution of the line is the point marked  (-6, 0).

We know that the equation of a line would take the general form y = mx + c. The m is the slope of the line and c is the vertical intercept of the line. This is the pattern that we can use to be able to obtain the equation of every other line that we have.

In this case, the equation that we have is the equation; 4x + y = -24. We now have to rearrange the equation in the form; y = -4x - 24. This now looks exactly like the equation of a straight line graph.

We would go straight to test the solution (-6, 0) and see if it is a solution for this line.

When we do that;

y = -4 (-6) - 24

y = +24 - 24

y = 0

Hence this is a solution.

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Answer:  

∠A= 60

Step-by-step explanation:  

SinA = 13/15  

SinA = 0.866  

A = inverse sin (0.866)  

A = 59.997

A = 60

An increase in the rate of inflation will increase the nominal interest rate while lowering the real interest rate.

When the rate of inflation rises, it affects both the nominal and real interest rates. The nominal interest rate is the stated or observed interest rate, while the real interest rate is adjusted for inflation and represents the purchasing power of the interest earned or paid. Inflation erodes the purchasing power of money over time.

As inflation increases, lenders and investors demand higher nominal interest rates to compensate for the expected loss in purchasing power. However, while the nominal interest rate rises, the real interest rate, which takes inflation into account, decreases because the purchasing power of the interest earned or paid is reduced.

In summary, an increase in the rate of inflation will result in an increase in the nominal interest rate but a decrease in the real interest rate due to the erosion of purchasing power caused by inflation.

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Answer: Y= -5x+4

Step-by-step explanation:

Given data:Width of flume (B) = 3 mDepth of flume (D) = 1.5 mChezy’s constant (C) = 0.013Slope of the bed (S) = 0.0025We know that,Q = (1/C) * A * R^(2/3) * S^(1/2)

Where,Q = Discharge of rectangular flumeA = Area of cross-sectionR = Hydraulic radiusS = Slope of the bedCalculation:Area of cross-section, A = B * D = 3 * 1.5 = 4.5 m²Wetted perimeter, P = B + 2 * D = 3 + 2 * 1.5 = 6 mHydraulic radius,

R = A / P = 4.5 / 6 = 0.75 mSubstituting the given values,Q = (1 / 0.013) * 4.5 * 0.75^(2/3) * 0.0025^(1/2)Q = 0.796 m³/sBoundary shear stress, τo = ρ * g * R * Sρ = Density of water = 1000 kg/m³g = Acceleration due to gravity = 9.81 m/s²Substituting the given values,τo = 1000 * 9.81 * 0.75 * 0.0025τo = 18.23 N/m²

The discharge of a rectangular flume 3 m wide and 1.5 m deep on a slope of 0.0025 is 0.796 m³/s and the boundary shear stress is 18.23 N/m².

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To determine the largest possible complete map that can fit on a 4x6 index card, we need to find the scale factor by which the original map needs to be reduced.

The scale factor can be calculated by dividing the dimensions of the index card by the dimensions of the map:

Scale factor = (Index card width / Map width) = 4 / 9 = 0.444

Scale factor = (Index card height / Map height) = 6 / 15 = 0.4

Since we want to ensure that the entire map fits on the index card, we need to choose the smaller scale factor, which in this case is 0.4.

Now, we can find the dimensions of the largest possible complete map on the index card by multiplying the scale factor by the original map dimensions:

Largest possible map width = Map width * Scale factor = 9 * 0.4 = 3.6 inches

Largest possible map height = Map height * Scale factor = 15 * 0.4 = 6 inches

Therefore, the largest possible complete map that can fit on the 4x6 index card would have dimensions of approximately 3.6 inches by 6 inches.

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Answer:

i know arts

Step-by-step explanation:

False. let a be a real square matrix. if a is diagonalizable then a is symmetric

Explanation: Diagonalizability and symmetry are two different properties of a square matrix. A real square matrix A is diagonalizable if it can be transformed into a diagonal matrix D through a similarity transformation with an invertible matrix P, i.e., A = PDP^(-1). A matrix is symmetric if A = A^T, where A^T is the transpose of A.

While it is true that every symmetric matrix is diagonalizable, the converse is not necessarily true. In other words, not every diagonalizable matrix has to be symmetric.

Conclusion: The statement "if A is diagonalizable then A is symmetric" is false because diagonalizability does not guarantee symmetry.

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Answer:

x=17 3y=13+10-3

x=17y=20

Step-by-step explanation:

answer to the questions

Answer:

x = 3 y = 46

Step-by-step explanation:

8x+13 = 9x+10

-8x          -8x

13 = x+10

-10     -10

3 = x

180-37 = 143

3y+5 = 143

-5          -5

3y = 138

/3      /3

y = 46

Answer:

B, C, A.

Step-by-step explanation:

In order to find the angles of triangle KLM and their order from least to greatest, we need to use the Law of Cosines and the perimeter equation of the triangle. The Law of Cosines states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of these sides and the cosine of the angle between them.

Let's assume that the length of sides KL, LM, and KM are x - 4, x + 4, and 2x - 1, respectively. We can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (x - 4)^2 + (2x - 1)^2 - (x + 4)^2 / 2 * (x - 4) * (2x - 1)

Next, we can use the perimeter equation of the triangle, which is

KL + LM + KM = 27, to find the value of x:

x - 4 + x + 4 + 2x - 1 = 27

4x = 36

x = 9

So, the lengths of the sides of the triangle are

KL = x - 4 = 5, LM = x + 4 = 13, and KM = 2x - 1 = 17.

Next, we can use the Law of Cosines to find the cosine of the angle between KM and KL:

cos A = (5)^2 + (17)^2 - (13)^2 / 2 * (5) * (17)

cos A = 74 / 60

A = cos^-1 (74/60) = approximately 49.7°

Finally, we can use the perimeter equation of the triangle and the Law of Sines to find the other two angles of the triangle:

B + C = 180° - 49.7° = 130.3°

B / sin B = LM / sin A

B = sin^-1 (sin B / sin A) * LM / sin A

C = 130.3° - B

The angles of triangle KLM in order from least to greatest are approximately:

B, C, A.

Answer:

24

Step-by-step explanation:

hope this help if it dont sorry i tried

Hence, the minimum number of at-the-door tickets she needs to sell to make her goal is (B) 334.

Given information: Anna is in charge of the alumni fundraiser for her alma mater. She is selling pre-sale tickets for $10 and at-the-door tickets $25. The venue has the capacity to hold 400 people.

The graph represents the number of tickets Anna needs to sell to offset her upfront costs and raise at least $5,000 for her school.

The minimum number of at-the-door tickets she needs to sell to make her goal can be calculated as follows;

Let's suppose that x represents the number of pre-sale tickets, and y represents the number of at-the-door tickets Anna needs to sell.

Then the following equation represents the total amount of money Anna will earn after selling the given number of tickets;

10x + 25y ≥ 5,000

If she sells all the tickets, she will have sold a total of x + y tickets. But, we know that the venue has a capacity of 400 people.

So, we also know that;

x + y ≤ 400

Solving the two equations for y gives;

10x + 25y ≥ 5,00025y ≥ 5,000 - 10x y ≥ (5,000 - 10x)/25y ≥ 200 - 0.4xy ≤ 333.3 - 0.4x

Answer: B.334.

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The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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Answer:

12bloz

Step-by-step explanation:

9lb x4oz-2lb x 12oz

36bloz-24bloz

12bloz

$390 represent 100%. To find what percentage $7.80 represent, we can use the next proportion:

Solving for x,

The sales tax rate is 2%

Answer: 420.25in^2

Step-by-step explanation:

Area of Square = s^2

20.5^2 = 420.25

The simple linear regression line is found to be y = a + bx.

In a simple linear regression model, y = ß0 + ß1x + ε, the parameter ß1 represents the slope of the true regression line.

ß1 is used in simple linear regression to represent the change in y for each unit increase in x.

When x changes by 1 unit, ß1 represents how much y will change.

The slope is positive when y and x are both increasing and negative when y decreases as x increases.

This is why the slope is negative.

When the slope is zero, there is no correlation between y and x.

This would be demonstrated by a scatter plot in which the points are dispersed randomly around the horizontal axis without following any discernible trend.

When the slope is positive, the data points are rising from left to right. This may be seen as a line sloping upward. If the slope is negative, the points are descending from left to right and form a line sloping downward.

Therefore, we may correctly infer that ß1 represents the slope of the true regression line.

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Answer:

-3, -1, 2 i belive sorry if I'm wrong

The height of the curve for a given value of x is closely related to the probability of an observation falling in an interval around x.

The height of the curve, also known as the probability density function (PDF), represents the relative likelihood of different values occurring in a distribution. In probability theory, the area under the curve within a specific interval represents the probability of an observation falling within that interval.

Therefore, the height of the curve at a particular value of x reflects the probability of an observation being close to that value.

The concept of the PDF and its relationship to probability is fundamental in statistical analysis. By examining the height of the curve at different points, we can assess the likelihood of observing specific values or ranges of values.

This information is crucial for making inferences, estimating probabilities, and conducting hypothesis testing in various fields such as finance, biology, and social sciences.

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Answer:

D

Step-by-step explanation:

Replace R1 with 1 and R3 with 0 you have -2(1)+0 which equals 0 and that matches matrix II. Repeat the process with the other numbers in R1 and R3 and they all come out equal therefor the answer is D.

The correlation coefficient between the number of volunteers x and the number of bags of trash collected y, so the percentage of variation in the number of bags of trash collected is 92.92 %.

You may gauge how closely two variables are related by looking at their correlation coefficients. Pearson's correlation coefficient is the most often used of the several correlation coefficient types. Often employed in linear regression, Pearson's correlation (also known as Pearson's R) is a correlation coefficient. It's likely that you'll learn about Pearson's R first if you're just getting started in statistics. Actually, Pearson's is typically mentioned when someone mentions the correlation coefficient.

According to the question,

The correlation coefficient i.e., r between x and y is 0.964.

r = 0.964

Squaring on both sides :

r² = 0.964²

r² = 0.9292

Now, convert this into percentage form by multiplying it will 100.

⇒0.9292 × 100

= 92.92 %.

Hence, the percentage of the variation will be 92.92 %.

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