What is the best estimate of -15/16 + (-1/2)

To find the vector equation of the plane containing the two intersecting lines, we can first find the normal vector of the plane by taking the cross product of the direction vectors of the two lines. The normal vector will be orthogonal to both direction vectors and thus will be parallel to the plane.

Direction vector of the first line: (2, 4, 3)

Direction vector of the second line: (-1, -1, 3)

Taking the cross product of these two vectors, we get:

(2, 4, 3) x (-1, -1, 3) = (9, -3, -6)

This vector is orthogonal to both direction vectors and thus is parallel to the plane. To find the vector equation of the plane, we can use the point-normal form of the equation, which is:

N · (r - P) = 0

where N is the normal vector, r is a point on the plane, and P is a known point on the plane. We can choose either of the two given points on the intersecting lines as the point P.

Let's use the point (4, 7, 3) on the first line as the point P. Then the vector equation of the plane is:

(9, -3, -6) · (r - (4, 7, 3)) = 0

Expanding and simplifying, we get:

9(x - 4) - 3(y - 7) - 6(z - 3) = 0

Simplifying further, we get:

9x - 3y - 6z = 0

Dividing by 3, we get:

3x - y - 2z = 0

Therefore, the vector equation of the plane containing the two intersecting lines is:

(3, -1, -2) · (r - (4, 7, 3)) = 0

or equivalently,

3x - y - 2z = 0.

Answer:

Step-by-step explanation:

a) 9.80- 98/10

b) 7.3- 73/10

a) 7/100- 0.07

b) 82/10- 8.2

Hope this helps

Fraction:

a) 98/100

b) 73/10

Decimal:

a) 0.07

b) 8.2

Answer:

<3 is the same as <1 : 143°

<4 is the same as <2: 37°

Step-by-step explanation:

They look the same

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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The scale factor used in the dilation is 1/2

From the question, we have the following parameters that can be used in our computation:

The scale factor is calculated as

Scale factor  = A'/A

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (-1, 3)'/(-2, 6)

Evaluate

Scale factor  = 1/2

Hence, the scale factor is 1/2

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Andy to get to Willie's house = 15 ways

Andy to get to Willie's house = 45 ways

From the information given, we have that from

Andy's house to Billy's  hometown = 3 roads

Billy's hometown to Willies house = 5 ways

To travel from Andy's house to Willies house, we should multiply the number of ways

= 3 × 5

= 15 ways

Dan's ranch to Andy's house = 1 road

To Willie's house = 2 roads

For Andy to get to Willie's house, we have;

= 3 × 15

= 45 ways

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The value of a should be 2 for the function to be composite.

What is composite function?

When two functions, f and g, are combined to create a third function, h, the result is such that h(x) = g(f(x)).

Main Body:

A commutative function means that when you insert one function in space of x in the other function, they will equal x. The equation is

f(g(x)) = g(f(x)) = x

So, 2(\(\frac{x+1}{a}\)) - 1 = \(\frac{(2x-1)+1}{a}\)

If you multiply both sides by a, you get   2a(\(\frac{x+1}{a}\)) - a = (2x-1)+1

Simplify it                                                   2a(\(\frac{x+1}{a}\)) - a = 2x

Add a to both sides                                    2a(\(\frac{x+1}{a}\))  = 2x +a

The two as on the left cancel out                   2(x+1)=2x+a

Distribute the 2:                                              2x+2=2x+a

Then subtract 2x from both sides                        2 = a

Therefore, a = 2

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Answer:

B. 2

Step-by-step explanation:

Right on Edge

We have shown that every string in S contains exactly one a.

(a) We can prove that every string in S begins with the character a by induction.

Base case: a is in S, and a begins with the character a.

Inductive step: Suppose that every string in S of length k or less begins with the character a. We want to show that every string in S of length k+1 also begins with the character a.

Let w be a string in S of length k+1. We have two cases to consider:

Case 1: w is of the form x b, where x ∈ S.

Since x ∈ S, by the inductive hypothesis, x begins with the character a. Therefore, w begins with the character a.

Case 2: w is of the form x a, where x ∈ S.

In this case, w begins with the character a by definition.

Therefore, we have shown that every string in S begins with the character a.

(b) We can prove that every string in S contains exactly one a by induction.

Base case: a is in S, and a contains exactly one a.

Inductive step: Suppose that every string in S of length k or less contains exactly one a. We want to show that every string in S of length k+1 also contains exactly one a.

Let w be a string in S of length k+1. We have two cases to consider:

Case 1: w is of the form x b, where x ∈ S.

Since x ∈ S, by the inductive hypothesis, x contains exactly one a. Therefore, w contains exactly one a.

Case 2: w is of the form b x, where x ∈ S.

In this case, w contains exactly one a if and only if x contains exactly one a. But x ∈ S, so by the inductive hypothesis, x contains exactly one a. Therefore, w contains exactly one a.

Therefore, we have shown that every string in S contains exactly one a.

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The answer of the given question based on the code is , the output of the code will be: The root of x³ + 2x - 2 between 0 and 1 is 0.771

MATLAB code:
To show that `x³ + 2x - 2` has a root between 0 and 1 and,

to find the root to 3 significant digits using the Newton Raphson Method,

we can use the following MATLAB code:  

Defining the function

f = (x)x³ + 2*x - 2;

Plotting the function

f_plot (f, [0, 1]);

grid on;

Defining the derivative of the function

f_prime = (x)3*x² + 2;

Implementing the Newton Raphson Method x0 = 1;

Initial guesstol = 1e-4;

Tolerance for erroriter = 0; % Iteration counter_while (1)

Run the loop until the root is founditer = iter + 1;

x1 = x0 - f(x0)

f_prime(x0);

Calculate the next guesserr = abs(x1 - x0);

Calculate the error if err < tol

Check if the error is less than the tolerancebreak;

else x0 = x1;

Set the next guess as the current guessendend

Displaying the resultfprintf('The root of x³ + 2x - 2 between 0 and 1 is %0.3f\n', x1));

The output of the code will be: The root of x³ + 2x - 2 between 0 and 1 is 0.771

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When you run the above code in MATLAB, it will display the root of x^3 + 2x - 2 to 3 significant digits.

MATLAB code:

Show that x^3 + 2x - 2 has a root between 0 and 1:

Here is the code to show that x^3 + 2x - 2 has a root between 0 and 1.

x = 0:.1:1;y = x.^3+2*x-2;

plot(x,y);

xlabel('x');

ylabel('y');

title('Plot of x^3 + 2x - 2');grid on;

This will display the plot of x^3 + 2x - 2 from x = 0 to x = 1.

Find the root to 3 significant digits using the Newton Raphson Method:

To find the root of x^3 + 2x - 2 to 3 significant digits using the Newton Raphson Method, use the following code:

format longx = 0;fx = x^3 + 2*x - 2;dfdx = 3*x^2 + 2;

ea = 100;

es = 0.5*(10^(2-3));

while (ea > es)x1 = x - (fx/dfdx);

fx1 = x1^3 + 2*x1 - 2;

ea = abs((x1-x)/x1)*100;

x = x1;fx = fx1;

dfdx = 3*x^2 + 2;

enddisp(x)

When you run the above code in MATLAB, it will display the root of x^3 + 2x - 2 to 3 significant digits.

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As per the query, we have to find a number which is divided by 8 that answers 27, i.e., quotient is 27, and remainder is 4. The number is 220.

In this case, we used it to find the number that was divided by 8 and gave a quotient of 27 and a remainder of 4. As we know the rule:

Dividend = Divisor × Quotient + Remainder

x = 8 × 27 + 4 x = 216 + 4 x = 220.

Hence, the number is 220.

The formula I used is called the division algorithm. It’s a way to divide two numbers and get a quotient and remainder. We can use this formula to solve other division problems with remainders as well.

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Answer:

perfect square

Step-by-step explanation:

It is not positive because it is negative.  

Answer:

D. IMAGINARY

Step-by-step explanation:

That is an imaginary number.

Answer:

If you were to multiply the percentages by the numberws your using to the AB formula you can get the answer 252 B

Step-by-step explanation:

Answer:

5-hour reunion at Picnic Place will cost $250.

5-hour reunion at Total Tent will cost $350.

15 hours for both choices to cost the same.

Explanation:

Let x represent the number of hours.

Let y represent the total cost.

For Picnic Place, our equation can be written as;

For a 5-hour reunion at Picnic Place, the charge will be;

For Total Tent, our equation can be written as;

For a 5-hour reunion, the cost will be;

To determine how many hours onwill need to reserve both shelters for both choices to cost the same, we just need to equate both equations and solve for x;

Answer:

<L = <E

<MFL = <DFE

vertical opposite

angles are same

by, AA simillary postulate triangles are similar.

Answer:

X=35

Step-by-step explanation:

6X =45 SO ANSWER TO THE QUESTION IS 35

The value of (double)(5/2) is 2.0. In the expression (double)(5/2), the division operation 5/2 is performed using integer division because both 5 and 2 are integers.

Integer division truncates the decimal part of the result and returns the quotient as an integer. In this case, 5 divided by 2 is equal to 2.

However, by explicitly casting the result to a double (using the (double) operator), we convert the integer value 2 to a double value, which becomes 2.0.

Therefore, the value of (double)(5/2) is 2.0, as the division is performed as an integer division followed by a casting to a double.

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Answer:

No

Step-by-step explanation:

Simplify both terms and compare.

3x + 12 + x = 3x + x + 12 = 4x + 12

4(3x + x) = 4(4x) = 16x

4x + 12 ≠ 16x for all x

The length of overline A'B' after the dilation is 1/2 of the length of overline AB. The measure of angle A′ is 28°.

Given:AABC is dilated by a factor of to produce 1/2 triangle A′B′C′. A (62 degrees), B (16), C. To find:A′B′ and the measure of angle A′.Using the concept of dilations:Now, we need to find the measure of angle A′.Here, A′ is the image of A after the dilation.Since AABC is dilated by a factor of to produce 1/2 triangle A′B′C′.Therefore, the measure of angle A′ = 28°.Hence, the main answer is,The length of overline A'B' after the dilation is 1/2 of the length of overline AB. The measure of angle A′ is 28°.

As we know that, Dilations are like scaling and resizing. It is a transformation that changes the size of a shape but not its orientation or position. It is also called scaling by a factor. There are two types of dilations. They are:Enlargement: The new shape is larger than the original. The scaling factor is greater than 1.Reduction: The new shape is smaller than the original.The length of A′B′ is 1/2 of the length of AB.Measure of angle A′:Here, A′ is the image of A after the dilation.Since AABC is dilated by a factor of to produce 1/2 triangle A′B′C′.Therefore, the measure of angle A′ = 28°.The length of overline A'B' after the dilation is 1/2 of the length of overline AB. The measure of angle A′ is 28°.

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The growth rate of the herd of cattle is 90 when t = 5 years.

The population of a herd of cattle over time is given byp(t) = 100(9+0.4t+0.005t^2)

The growth rate when t = 5 years:

We need to differentiate the given equation with respect to t to find the growth rate,dp/dt = 100(0+0.4+0.01t)Put t = 5 years in above equation,dp/dt = 100(0+0.4+0.01x5)dp/dt = 100(0.9)dp/dt = 90

The growth rate when t= 5 years is 90. Therefore, the growth rate of the herd of cattle is 90 when t = 5 years.

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The expression  5w + 2w²   represents the area, in square feet, for each cabin size

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Area of a rectangle = length * width = l*w

length is equal to 5 feet more than twice the width.

=> l= 5+2w

So, area = ( 5+2w  ) *w

             = 5w + 2w²  

Thus, the expression  5w + 2w²   represents the area, in square feet, for each cabin size

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cutei mo boy Chad bleehhh

Answer:

I can't post a graph, but I will explain how to do it.

Step-by-step explanation:

The y intercept is 3, so we know we can place a point at the coordinates (0,3). The y intercept is the point where your line crosses the y axis.

The slope is -3, which is the same as -3/1. The top number is the y axis, the bottom number of the slope is the x axis. This tells us that for every 1 space we move on the x axis, we move -3 spaces on the y axis. You should therefore have a second point located at (1,0).

You should end up with a line with a point at (0,3) and (1,0) which slopes down from left to right. Hope that helps.

The line of the graph is y=-3x+3

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope is -3 and y-intercept is 3.

y=-3x+3

Now we have to plot the graph

x   0      1     2    3     4

y    3     0    -3   -6   -9

Hence, the line of the graph is y=-3x+3

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Answer:

12

Step-by-step explanation:

48/4=12

perimeter of squre is 4l so the length of a squre side is 12 (4*12=48)

First we add 0.3 to 3.7, that way we will have an integer and it would be more easy to make the operations. Then we have 4.

Then we can substract the 4 to the 9.4, getting 5.4.

Finally we add once again 0.3 (because in the difference we have an extra .3) to the 5.4, getting 5.7.

Then Tamela swims 5.7 more than Blake every day.

Answer;

40%

Explanation;

h = 100 * 45 - 75  / 75 = -3000 / 75 = -40 / 1 = 40%

Answer:

1 5/3 or 3/5

2. 25/9 or 9/25

3.9/25*15=5.4

Answer:

h < -13/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Inequality

h - 8 > 4h + 5

Step 2: Solve for h

Here we see that any value h smaller than -13/3 would work as a solution to the equation.

Answer:

(0, -2)

(-3, 1)

(3, -4)

Step-by-step explanation:

The constraints given as;

x + y ≥ -2

3x - y ≤ 2

x - y ≥ -4

Since we want to find vertices of the feasible region, we will ignore the less than or greater than sign and use the equal to sign to some simultaneously.

Let's add first and third constraint together to get;

2x = -6

x = -6/2

x = - 3

Put - 3 for x in equation 1 to get;

-3 + y = -2

y = 3 - 2

y = 1

Thus, vertex here is; (-3, 1)

Lets add first and third equations to get;

4x + 0 = 0

Thus, x = 0

Putting this for x in eq 1;

0 + y = -2

y = -2

vertex here is; (0, -2)

Lets subtract eq 3 from eq 2 to get;

2x = 6

x = 6/2

x = 3

Put 3 for x in eq 3;

x - y = -4

vertex here is; (3, -4)

From the table, we have:

• The first column (Value),: indicates the # of correct answers,

• The second column (Frequency),: indicates the # of students that answer the # of correct answers to the left in the table,

• The third column (Relative Frequency),: indicates the proportion of the # of students to the total,

• The fourth column (Cumulative Frequency),: gives the sum of the previous frequencies up to that row.

Using these data, we answer the questions:

a) Looking at the column Frequency for Value = 3, we find that 2 students answered exactly 3 answers correct.

b) Looking at the column Cumulative Frequency for Value = 2 (the previous value to 3), we find that 18 students answered less than 3 questions correctly.

c) Looking at the column Relative Frequency for Value = 4, we find that 0.3 = 0.3 * 100% = 30% of the students answered exactly 4 questions correctly.

a) 2

b) 18

c) 30%