What is the slope of a line that cobennects the points (7,5) and (12,15)

Answer: 3 hours

Step-by-step explanation:

The value of b = -3/2 and c = -5/4

To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:

(x + b)² = x² + 2bx + b²

Comparing this to the given expression x² - 3x + 1, we see that we need:

2bx = -3x, so b = -3/2

b² + c = 1, so substituting b = -3/2 gives:

(9/4) + c = 1

so c = 1 - 9/4

= 4/4 - 9/4

= -5/4

The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).

Therefore, the value of b = -3/2 and c = -5/4

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Given question is incomplete, the complete question is below

the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?

Answer:

19

Step-by-step explanation:

Using number line method:

-8+19=11

11+8=19

Answer:

19 is the answer

19 -8+8=19

(i) y = ±√(-x² + 2ax - a² + (b² - r²)) + b

(ii) y = ±√(-25)

The square root of a negative number is not real, there are no real y-coordinates for the given values of a, b, r, and x. There are no points on the circle with those coordinates.

(i) To express y in terms of a, b, x, and r, we can rearrange the equation of the circle as follows:

(x - a)² + (y - b)² = r²

Expanding the square terms, we get:

x² - 2ax + a² + y² - 2by + b² = r²

Rearranging the equation to isolate the y term, we have:

y² - 2by = r² - x² + 2ax - a² - b²

Completing the square by adding (b² - r²) to both sides, we obtain:

y² - 2by + (b² - r²) = -x² + 2ax - a²

Factoring the left side as a perfect square, we have:

(y - b)² = -x² + 2ax - a² + (b² - r²)

Taking the square root of both sides, we get:

y - b = ±√(-x² + 2ax - a² + (b² - r²))

Finally, isolating y, we have:

y = ±√(-x² + 2ax - a² + (b² - r²)) + b

(ii) Given a = 2, b = 3, r = 5, and x = 5, we can substitute these values into the equation we derived in part (i). Plugging in the values, we have:

y = ±√(-(5)² + 2(5)(2) - (2)² + (3)² - (5)²) + 3

Simplifying the equation:

y = ±√(-25 + 20 - 4 + 9 - 25) + 3

y = ±√(-25)

Since the square root of a negative number is not real, there are no real y-coordinates for the given values of a, b, r, and x. Therefore, there are no points on the circle with those coordinates.

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The probability of winning the game before the fourth turn is \(\frac{19}{54}\).

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur. The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability of winning the game before the fourth turn, we need to calculate the probability of winning on the first, second, or third turn and then add them together.

On each turn, rolling a standard die has 6 equally likely outcomes (numbers 1 to 6), and tossing a fair coin has 2 equally likely outcomes (heads or tails).

1.Probability of winning on the first turn: To win on the first turn, we need the die to show a 1 or a 6, and the coin to show heads. Probability of rolling a 1 or 6 on the die:  \(\frac{2}{6} =\frac{1}{3}\)

Probability of tossing heads on the coin: \(\frac{1}{2}\)

Therefore, probability of winning on the first turn: \(\frac{1}{3} *\frac{1}{2}\) = \(\frac{1}{6}\)

2.Probability of winning on the second turn: To win on the second turn, we either win on the first turn or fail on the first turn and win on the second turn. Probability of winning on the second turn, given that we didn't win on the first turn:

\(\frac{2}{3} *\frac{1}{3} *\frac{1}{2} \\=\frac{1}{9}\)

3.Probability of winning on the third turn:

To win on the third turn, we either win on the first or second turn or fail on both the first and second turns and win on the third turn. Probability of winning on the third turn, given that we didn't win on the first or second turn:

\(\frac{2}{3} *\frac{2}{3} *\frac{1}{3} \\=\frac{2}{27}\)

Now, we can add the probabilities together:

Probability of winning before the fourth turn =

\(\frac{1}{6}+\frac{1}{9}+\frac{2}{27}\\\\=\frac{9}{54}+\frac{6}{54}+\frac{4}{54}\\\\=\frac{19}{54}\\\)

Therefore, the probability of winning the game before the fourth turn is  \(\frac{19}{54}\).

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Answer:

The area is 196π, or 615.752160 when evaluated to 6 decimal places.

Step-by-step explanation:

There is an equation for the area of a circle:

A=π\(r^{2}\), Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:

A=π(\(14^{2}\))

A=196π

If we write out π and evaluate with an (un)reasonable amount of decimal places:

π≅3.1415926536

A=196×(3.1415926536)

A≅615.752160

Answer:

A = \(\pi ^{2}\)

Step-by-step explanation:

A≈615.75

Answer:

2/3 or 0.6

Step-by-step explanation:

Note that the r-value of the above data is : -0.903 (Option A)

In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.

With regard to the above data:

A) Find the Sum of the X values: 4 +5+8+9+13 = 39

B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56

C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355

D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858

E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339

N = number of sets = 5

Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8

Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =

SQRT(355-39^2/5) x SQRT(858-56^2/5) =

SQRT(50.8) x SQRT(230.8) =

7.1274 x 15.1921 =

108.2803

r = -97.8 / 108.2803

r = -0.903

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a) The linearized function is 2x - 1. b) The linearized function is ex. c) The linearized function is 1. d) The linearized function is 5x - 5.

To linearize the given functions around the specified points, we can use the first-order Taylor series expansion. The linearized function will be in the form f(x) ≈ f(a) + f'(a)(x - a), where a is the specified point.

a) f(x) = \(x^1\) + x', around x = 2

To linearize this function, we evaluate the function and its derivative at x = 2:

f(2) = \(2^1\) + 2' = 2 + 1 = 3

f'(x) = 1 + 1 = 2

Therefore, the linearized function is f(x) ≈ 3 + 2(x - 2) = 2x - 1.

b) f(x) = \(e^x\), around x = 1

To linearize this function, we evaluate the function and its derivative at x = 1:

f(1) = \(e^1\) = e

f'(x) = \(e^x\) = e

Therefore, the linearized function is f(x) ≈ e + e(x - 1) = e(1 + x - 1) = ex.

c) f(x) = cos(x), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = cos(0) = 1

f'(x) = -sin(x) = 0 (at x = 0)

Therefore, the linearized function is f(x) ≈ 1 + 0(x - 0) = 1.

d) f(x) = sin(x)(cos(x) - 4), around x = 0

To linearize this function, we evaluate the function and its derivative at x = 0:

f(0) = sin(0)(cos(0) - 4) = 0

f'(x) = cos(x)(cos(x) - 4) - sin(x)(-sin(x)) = \(cos^2\)(x) - 4cos(x) + \(sin^2\)(x) = 1 - 4cos(x)

Therefore, the linearized function is f(x) ≈ 0 + (1 - 4cos(0))(x - 0) = 5x - 5.

To compare the linearized functions with the actual functions, we can use MATLAB's "taylor" and "plot" commands. Here is an example of how to perform the comparison for the given functions:

% Part (a)

syms x;

f = x^1 + diff(\(x^1\), x)*(x - 2);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (a):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (b)

syms x;

f = exp(x);

taylor_f = taylor(f, 'Order', 1);

x_vals = -0.5:0.2:0.5;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (b):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

% Part (c)

x_vals = 0:0.1:1;

actual_f = cos(x_vals);

linearized_f = ones(size(x_vals));

disp("Part (c):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

figure;

plot(x_vals, actual_f, 'r', x_vals, linearized_f, 'b');

title("Comparison of Actual and Linearized f(x) for Part (c)");

legend('Actual f(x)', 'Linearized f(x)');

xlabel('x');

ylabel('f(x)');

grid on;

% Part (d)

syms x;

f = sin(x)*(cos(x) - 4);

taylor_f = taylor(f, 'Order', 1);

x_vals = 0:0.1:1;

actual_f = double(subs(f, x, x_vals));

linearized_f = double(subs(taylor_f, x, x_vals));

disp("Part (d):");

disp("Actual f(x):");

disp(actual_f);

disp("Linearized f(x):");

disp(linearized_f);

This MATLAB code snippet demonstrates the calculation and comparison of the actual and linearized functions for each part (a, b, c, d). It also plots the actual and linearized functions for part (c) using the "plot" command with the "hold" command to combine the graphs in one plot.

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Answer:

{2, 6, 14}

Step-by-step explanation:

Using f(x) = 4x + 6 with a domain of {-1, 0, 2 }, find the range.

To get the range, we will substitute the values of the domain into the given function as shown;

when x = -1

f(-1) = 4(-1)+6

f(-1) = -4+6

f(-1) = 2

when x = 0

f(0) = 4(0)+6

f(0) = 0+6

f(0) = 6

when x = 2

f(2) = 4(2)+6

f(2) = 8+6

f(2) = 14

Hence the required range are {2, 6, 14}

Answer:

It falls between 7 and 8.

Step-by-step explanation:

Since the \(\sqrt{49}\) = 7 and the \(\sqrt{64}\) = 8 it would make the \(\sqrt{50}\) fall in between 7 and 8.

To find the circumference we have to calculate

where r=6

therefore we have that the answer is

To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees.

How to find the sum of interior angles ?

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This is a decay problem,

The equation is written as start value x (1 - rate)^tike

Using the information given in the problem:

a) Total = 120(1-0.12)^Hours

b) Replace hours with 19 and solve:

Total = 120(1-0.12)^19

Total = 120(0.88)^19

Total = 10.57674 mg

Round the answer as needed.

Answer:

8

Step-by-step explanation:

(Refer to picture)

Plug in the value of A and the value of B into the expression

The correct option  A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.

The statement made by Xavier that the product of two odd integers always results in an even integer should be noticed.

For the given case, conjecture that the sum of two odd integers is always an even integer is -

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The complete question is-

Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?

Select option;

A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.

B: Look at these different examples: 3 + 5 = 8, 13 + 5 = 18, 23 + 5 = 28. So the sum of two odd numbers must be even.

C: Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.

D: Every time you add two odd numbers, the sum is an even number.

Alyssa and Caleb ate 5/6 of the nachos together.

To calculate the fraction of nachos that Alyssa and Caleb ate together, add the fractions representing the portions that they each ate. However, because the fractions have different denominators, we must first find a common denominator.

2 and 3 share a common denominator of 6. With a denominator of 6, we can rewrite 1/2 and 1/3 as follows:

1/2 = 3/6

1/3 = 2/6

We can now add these fractions:

3/6 + 2/6 = 5/6

As a result, Alyssa and Caleb shared 5/6 of the nachos.

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Answer:

x = 11

Step-by-step explanation:

6x - 21 = 3x + 12

6x - 3x = 21 + 12

3x = 33

x = 33/3

x = 11

Answer:

B. Andre babysat 5 times this past month and earned the same amount each time. To thank him, the family gave him an extra $4 at the end of the month. Andre earned $99 from babysitting.  and C. A family of 5 drove to a concert. They paid $4 for parking, and all of their tickets were the same price. They paid $99 in total.

Step-by-step explanation: B and C are the right answers

Answer:

let people=x

and shoes=y

now,as per the question

2x-4=y

Answer:

A

Step-by-step explanation:

It's when points intersect.

To determine the sinusoidal expression for the current in a capacitor, we will use the following equation:

I(t) = C * (dV(t)/dt)

Where I(t) is the current at time t, C is the capacitance (1 μF in this case), and dV(t)/dt is the derivative of the voltage function V(t) with respect to time.

Let's examine both voltage expressions:

a) V(t) = 30sin(200t)

b) V(t) = 60×10^(-3)sin(377t)

Now, let's find the derivatives:

a) dV(t)/dt = 30 * 200 * cos(200t)

b) dV(t)/dt = 60 * 10^(-3) * 377 * cos(377t)

Next, we will multiply each derivative by the capacitance C (1 μF):

a) I(t) = 1×10^(-6) * 30 * 200 * cos(200t)

b) I(t) = 1×10^(-6) * 60 * 10^(-3) * 377 * cos(377t)

Finally, we can simplify the expressions:

a) I(t) = 6 * 10^(-3) cos(200t) A

b) I(t) = 22.62 * 10^(-6) cos(377t) A

Thus, the sinusoidal expressions for the current in each case are:

a) I(t) = 6 * 10^(-3) cos(200t) A

b) I(t) = 22.62 * 10^(-6) cos(377t) A

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The amount of soil needed to fill the garden box is given as follows:

1728 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

V = 19 x 12 x 6 + 10 x 3 x 12

V = 1728 ft³.

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Answer:

Mathematics Solutions Solutions for Class 8 Math Chapter 14 Construction Of Triangles are provided here with simple step-by-step explanations. These solutions for Construction Of Triangles are extremely popular among Class 8 students for Math Construction Of Triangles Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 8 Math Chapter 14 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Step-by-step explanation:

Construct a triangle ABC in which AB = 5 cm and BC = 4.6 cm and AC = 3.7 cm.

ANSWER:Steps of construction:

ANSWER:Steps of construction:(1) Draw a sufficiently long line segment using a ruler.

ANSWER:Steps of construction:(1) Draw a sufficiently long line segment using a ruler.(2) Locate points A and B on it such that AB = 5 cm.

ANSWER:Steps of construction:(1) Draw a sufficiently long line segment using a ruler.(2) Locate points A and B on it such that AB = 5 cm.(3) With A as the centre and radius 3.7 cm, draw an arc.

ANSWER:Steps of construction:(1) Draw a sufficiently long line segment using a ruler.(2) Locate points A and B on it such that AB = 5 cm.(3) With A as the centre and radius 3.7 cm, draw an arc.(4) With B as the centre and radius 4.6 cm, draw another arc that cuts the previous arc at C.

ANSWER:Steps of construction:(1) Draw a sufficiently long line segment using a ruler.(2) Locate points A and B on it such that AB = 5 cm.(3) With A as the centre and radius 3.7 cm, draw an arc.(4) With B as the centre and radius 4.6 cm, draw another arc that cuts the previous arc at C.(5) Join AC and BC.

ANSWER:Steps of construction:(1) Draw a sufficiently long line segment using a ruler.(2) Locate points A and B on it such that AB = 5 cm.(3) With A as the centre and radius 3.7 cm, draw an arc.(4) With B as the centre and radius 4.6 cm, draw another arc that cuts the previous arc at C.(5) Join AC and BC.Then, ABC is the required triangle.

Answer:

Try khan academy! It’s free and is really good. Has subjects from k-g12!

Step-by-step explanation:

Answer:

slader is great for science and math and for English paper hacker is pretty good

Answer:

ok, i hate questions like these because i don't want to answer them

Step-by-step explanation:

Answer:

x = 1.08 and x = -2.08

Step-by-step explanation:

We can solve this equation using the quadratic formula.

\(ax^2+bx+c=0\)

Thus, in the equation given, 4 is our a value, 4 is (also) our b value and -9 is our c value.

The formula for the positive solution of the quadratic formula is

\(x=\frac{-b+\sqrt{b^2-4ac} }{2a}\)

The formula for the negative solution of the quadratic formula is

\(x=\frac{-b-\sqrt{b^2-4ac} }{2a}\)

Positive solution:

\(x=\frac{-4+\sqrt{4^2-4(4)(-9)} }{2(4)}\\ \\x=\frac{-4+\sqrt{160} }{8}\\ \\x=1.08113883\\\\x=1.08\)

Negative solution:

\(x=\frac{-4-\sqrt{4^2-4(4)(-9)} }{2(4)}\\ \\x=\frac{-4-\sqrt{160} }{8}\\ \\x=-2.08113883\\\\x=-2.08\)