200-123+289-2/2=????

Answer:

y-intercept: 1

slope: -2

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given

\(x^2 - 10x + 4 = 12\\\)

get it all to one side equaling zero

\(x^2 - 10x - 8 = 0\)

now, we want to find the factors of 8 that either add up to of have a difference of 10

Factors of 8:

\(1, 8, 2, 4\)

None of the factor pairs add up to or have a difference of 10.

So, we can use the quadratic formula

\(x = \frac{-b\pm\sqrt{b^2-4ac} }{2a} \\x = \frac{10\pm\sqrt{100-4*8} }{2}\\x = \frac{10\pm\sqrt{132} }{2}\\\\\\x = \frac{10 + \sqrt{132} }{2}= 10.74456265\\x = \frac{10 - \sqrt{132} }{2} = -0.7445626465\)

When dividing the same dividend by 0.1 and 0.01, the quotient obtained by dividing by 0.1 is greater than the quotient obtained by dividing by 0.01. This is because dividing by a smaller decimal results in larger parts

The quotient obtained by dividing the same dividend by 0.1 and 0.01 can be compared by understanding the concept of dividing by decimals.

Let's say the dividend is 10. When we divide 10 by 0.1, we are essentially dividing it by 1/10 or 1 ÷ 10. This means we are dividing 10 into 10 equal parts. Each part would be 1, so the quotient is 1.

When we divide 10 by 0.01, we are dividing it by 1/100 or 1 ÷ 100. This means we are dividing 10 into 100 equal parts. Each part would be 0.1, so the quotient is 0.1.

Comparing the two quotients, we can see that 1 is greater than 0.1. This is because dividing by a smaller decimal results in a larger quotient. In other words, dividing by 0.01 gives smaller parts than dividing by 0.1.

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Here's how you can use the Trapezoidal Rule to approximate the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 in MATLAB:

```matlab

a = -2;    % Lower limit

b = 2;     % Upper limit

n = 1000;  % Number of subintervals (increase for higher accuracy)

h = (b - a) / n;   % Step size

x = a:h:b;         % Generate evenly spaced x values

y = 1 ./ (25 + x.^2).^1.5;  % Evaluate the function at x

approximation = h * (sum(y) - (y(1) + y(end)) / 2);  % Trapezoidal Rule approximation

fprintf('Approximation: %.6f\n', approximation);

```

1. We define the lower limit `a` as -2, the upper limit `b` as 2, and the number of subintervals `n` as 1000 (you can adjust `n` for higher accuracy).

2. We calculate the step size `h` by dividing the range (`b - a`) by the number of subintervals (`n`).

3. We generate an array `x` of evenly spaced values from `a` to `b` using the step size `h`.

4. We evaluate the function `f(x)` at each point in `x` and store the results in the array `y`.

5. Finally, we use the Trapezoidal Rule formula to approximate the integral by summing the values in `y` and adjusting for the endpoints, multiplying by the step size `h`.

The Trapezoidal Rule approximation for the integral of the function \(f(x) = \frac{1}{{(25+x^2)}^{\frac{3}{2}}}\) from -2 to 2 is the value calculated using the MATLAB code above.

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Answer:

5 rooms

Step-by-step explanation:

4 rooms = 9 hours

9 hours = 540 minutes

1 room = 540 ÷ 4 = 135 minutes

60 x 12 = 720 minutes (12 hours)

720 ÷ 135 = 5.33333

5.3333 estimated to nearest whole number = 5

Answer:

Angle 1 or Angle 3

Step-by-step explanation:

They are the only two that are immediately next to angle 2

Answer:

angle 1

Step-by-step explanation:

The equation of the osculating plane is 24x + 12√10(y-π) - 3z - 6π√10 = 0.

Given curve,  x=5sin(3t), y=t, z=5cos(3t); (0, π,-5).

To find the normal plane equation, the unit normal vector of the curve at the point must first be found. The unit tangent and unit binormal vectors are both derived from the unit tangent vector.

To calculate the tangent vector, the following steps are taken:

Equation of the curve is given as,

x=5sin(3t),

y=t,

z=5cos(3t).

Differentiating above equation with respect to t, we get;

dx/dt = 15 cos(3t)

dy/dt = 1

dz/dt = -15 sin(3t)

The unit tangent vector T is given by,

T = 1/√(dx/dt² + dy/dt² + dz/dt²) (dx/dt i + dy/dt j + dz/dt k)

Substituting the given values, we get

T = (3√10/10) i + (1/√10) j - (3/√10) k

Since we have to find the normal vector, we will differentiate the unit tangent vector,T, to get the unit normal vector N.

Let's differentiate T to obtain N:

dn/dt = 1/√(dx/dt² + dy/dt² + dz/dt²) [d²x/dt² i + d²y/dt² j + d²z/dt² k] + {(-1/2)(2t)(2t')/√(dx/dt² + dy/dt² + dz/dt²)³} [dx/dt i + dy/dt j + dz/dt k]

On substituting, we get,

N = (-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the normal plane equation is given by,(-9/√10)(x) + (3√10/10)(y-π) + (9/√10)(z+5) = 0.

To find the osculating plane equation, the coordinates of the point of tangency (P) and the principal normal vector, N, are required.

The equation of the osculating plane is then written as follows:

xT + yN = c,

where c is a constant value that is calculated by substituting the coordinates of P into the equation.Let us calculate the value of P and N,

To find the value of P, we substitute t=π in the given curve,

Thus,

x(π) = 5sin(3π) = 0,y(π) = π,z(π) = 5cos(3π) = -5

Therefore, the point of tangency P is (0, π, -5).

From the above derivation, we know that the unit normal vector N is(-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the unit principal normal vector is given by,

B = T x N= [(3√10/10) i + (1/√10) j - (3/√10) k] x [- (9/√10) i + (3√10/10) j + (9/√10) k]

= [(3√10/10) (9/√10) + (3/√10) (3/√10)] i + [(9/√10) (1/√10) - (3√10/10) (- 3/√10)] j + [(1/√10) (- 3/√10) - (3√10/10) (3√10/10)] k

= (24/√10) i + (12√10/10) j - (3/√10) k

The osculating plane equation is given by,

xT + yB = c

Now substituting x=0, y=π and z=-5 in above equation, we get

c = π(12√10/10) = (6π√10/5)

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The coordinate points of the point P is (-3.5, 2.3).

What is a coordinate plane?

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line.

The ratio in which the point 'P' divides the line segment RQ is -

a:b = 5:1

The coordinates of the end-points of line segment RQ are -

R(4, -1)  and  Q(-5, 3).

The coordinates of the point H are obtained when a point H divides a line segment with end points (p, q) and (s, t) in the ratio a:b -

H = [(as + bp)/(a + b)], [(at + bq)/(a + b)]

H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]

H = (-21/6, 14/6)

H = (-3.5, 2.3)

Therefore, the coordinate points are obtained as H = (-3.5, 2.3).

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Step-by-step explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.

Answer: x = y + −3/2

Step-by-step explanation:

Let's solve for x.

−3+5y=2x+3y

Step 1: Flip the equation.

2x+3y=5y−3

Step 2: Add -3y to both sides.

2x+3y+−3y=5y−3+−3y

2x=2y−3

Step 3: Divide both sides by 2.

2x/2 = 2y - 3/2

ANSWER: x = y + -3/2

The height of the  building which casts a 103-foot shadow is 95.5 foot.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow

We need to find the height of the building.

Let us consider x be the height of building.

Form a proportional equation.

x/103=32/34.5

Apply cross multiplication

34.5x=32×103

34.5x=3296

Divide both sides by 34.5

x=3296/34.5

x=95.5

Hence, 95.5 foot be the height of the  building which casts a 103-foot shadow.

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Answer:

x = 8\(\sqrt{3}\) in

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 22² = 26²

x² + 484 = 676 ( subtract 484 from both sides )

x² = 192 ( take square root of both sides )

x = \(\sqrt{192}\) = \(\sqrt{64(3)}\) = \(\sqrt{64}\) × \(\sqrt{3}\) = 8\(\sqrt{3}\) in

The absolute value equation is:

|M - 430g| = 20g

And the solutions are M = 410g and M = 450g

b) No, the mass is not acceptable.

We know that the recomended mass is 0.43kg, with an accepted error of 20 grams.

Where:

0.43kg = 0.43*1000g = 430g

Then the minimum mass accepted is: 430g - 20g = 410g

The maximum mass accepted is: 430g + 20g = 450g

These are the solutions, and the absolute value equation is, if M is the mass:

|M - 430g| = 20g

b) If the ball has a mass of 423g it is in the accepted range, if now it loses 0.016kg:

0.016kg = 0.016*1000g = 16g

The new mass is:

423g - 16g = 407g

This is smaller than the minimum accepted mass, then this mass is not acceptable.

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Answer:

Step-by-step explanation:

Recursive formula is used to represent the terms using the previous term of the sequence.

Using the explicit equation find the first two terms and their difference:

The recursive formula for this sequence is:

Answer:

C

Step-by-step explanation:

hope it helps

would appreciate brainly

Answer:

C!

Step-by-step explanation:

Answer:

1.2 (if that’s wrong then it’d 1.3)

Step-by-step explanation:

Divide first since it’s rounding and when you get the answer round to the nearest tenth.

Answer:

26

Step-by-step explanation:

This is what I got! I hope this helps!

(A) Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

(A) Average speed = Distance / Time

Average speed = 200 meters / 19.30 seconds

Average speed = 10.36 meters per second

Therefore, Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) 1 mile = 2580 feet

Converting the distance from meters to miles:

Distance in miles = Distance in meters / (1 meter / 3.28 feet) / (1 mile / 5280 feet)

Distance in miles = 200 meters / 3.28 / 5280 miles

Time in hours = Time in seconds / (60 seconds / 1 minute) / (60 minutes / 1 hour)

Time in hours = 19.30 seconds / 60 / 60 hours

Average speed = Distance in miles / Time in hours

Average speed = (200 meters / 3.28 / 5280 miles) / (19.30 seconds / 60 / 60 hours)

Average speed = 23.35 miles per hour

Therefore, Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

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The missing number in 6 17 37 10 10 25 12 32 ? is 37.

Based on the provided sequence, the missing number can be determined by observing the pattern within the given numbers. Let's analyze the sequence:

6 17 37 10 10 25 12 32 ?

By examining the sequence, we can identify the following pattern:

The first number, 6, increases by 11 to become 17.

The second number, 17, increases by 20 to become 37.

The third number, 37, increases by 27 to become 64.

At this point, we can see that the pattern alternates between adding the square of an increasing increment and subtracting that same increment from the previous number. So, to continue the pattern:

The fourth number, 10, decreases by 6 to become 4.

The fifth number, 10, decreases by 1 to become 9.

The sixth number, 25, increases by 3 to become 28.

The seventh number, 12, decreases by 4 to become 8.

The eighth number, 32, increases by 5 to become 37.

Therefore, the missing number in the sequence is 37.

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Answer:

512 cm3

Step-by-step explanation:

Answer:

512 cm3 (cubic centimeters)

Step-by-step explanation:

Answer:

.72

Step-by-step explanation:

9 rounds up because 1-4 stay the same and 5-9 round up

Answer: 0.719 to the nearest hundredth is 0.72

Answer:

2x - 10=65-x

2x+x=65+10

3x=75

x=75/3

x=25 (1.)

2x - 10

2*25-10

50-10

40 (2.)

The number that satisfies the given condition is 1 1/2 or 3/2.

The number that is less than 7/4 but greater than 9/8 is 1 1/2 or 3/2. To understand this, let's convert the fractions into a mixed number or a decimal.

7/4 is equal to 1 3/4, which means it is greater than 1.

9/8 is equal to 1 1/8, which means it is less than 2.

Therefore, the number we are looking for must be greater than 1 but less than 2.

In decimal form, 1 1/2 is equal to 1.5.

So, the number that satisfies the given condition is 1 1/2 or 3/2.

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The equation of each line in slope‐intercept form are y = -4x+2 and y = -x+4

The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

GIven are two graphs of lines, we need to find the slope‐intercept form of the lines,

We know that, the slope‐intercept form of the line is given by:

y = mx+c, where m is slope and c is the y-intercept,

m = y₂-y₁ / x₂-x₁

1) The line is passing through two points (0.5, 0) and (0, 2) :-

y-0 = 2-0 / 0-0.5 (x-0.5)

y = -4(x-0.5)

y = -4x+2

2) The line is passing through two points (4, 0) and (0, 4) :-

y-0 = 4-0 / 0-4 (x-4)

y = -1(x-4)

y = -x+4

Hence, the equation of each line in slope‐intercept form are y = -4x+2 and y = -x+4

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Answer:

A

Step-by-step explanation:

check the above attachment to verify the answer.

Answer:

side BC or maybe its side AD

Step-by-step explanation:

The equation for g(x) that matches the graph is g(x) =| -x - 3| +3

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that function, g(x), is shown below. It is a shifted graph of y = |x|.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged.

The equation for g(x)  is g(x) =| -x - 3| +3

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Answer:

b

Step-by-step explanation:

Answer:

A translation by 2 units to the left and 6 units up.

Step-by-step explanation:

Answer:

(5,-2)

Step-by-step explanation:

(x, y)=(y, -x)

(2,-5)=(5,-2)

90° clockwise=(5,-2)

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