Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She
starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to
write and simplify expressions for the lengths of the diagonals.

What is the length of one of the diagonals of the rectangle?

A: 12.4
B: 6
C: 6.3
D: 8

y = x², y = 4  are  the region enclosed by the given equations is revolved about the y -axis.

What exactly is a closed area?

All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.

What do you mean by the region that a closed curve encloses?

The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.

Whether contained or not?

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The translated and reflected function is:

g(x) = f(-x) - 3 = 3x + 1.

Here we want to transform a function f(x)=  -3x + 4.

First, remember that a vertical translation is written as:

g(x) = f(x) + N

Then a translation of 3 units down is written as:

g(x) = f(x) - 3

Now we want to do a reflection across the y-axis, this just changes the sign of the variable, so we get:

g(x) = f(-x) - 3

Now we replace the actual function f(x) by -3x + 4, we will get:

g(x) = -3*(-x) - 3 + 4 = 3x + 1

g(x) = 3x + 1

We conclude that the transformed function is 3x + 1.

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Answer:

perimeter: 14.5

Step-by-step explanation:

The two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.

It should be noted that decimals simply means.the numbers that aren't whole numbers.

It should be noted that this is a straight forward question.

Here, the two decimal numbers that are greater than 5.06 and less than 5.13 are 5.09 and 5.1.

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Answer:

value of k is 3 to make it perfectly

The right-angle triangle on the coordinate plane will be drawn. Then the third length of the right triangle will be 2√(a² - b²) units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The right triangle ΔABC with legs AC and AB so that AC is 2a units long and leg AB is 2b units long.

We know that the angle ABC is a right angle which means 90°.

Then the third length of the right triangle will be

H² = P² + B²

(2a)² = (2b)² + B²

B² = 4a² - 4b²

B² = 4(a - b²)

B = 2√(a² - b²)

The right-angle triangle on the coordinate plane will be drawn.

The diagram is attached below.

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Answer:

48

Step-by-step explanation:

ANSWER:

19.54

Step-by-step explanation:

23.7-8.3

=15.4

15.4+4.14

=18.54

Answer:

b=v

Step-by-step explanation:

Answer:

I got b=v so it would be 0

Step-by-step explanation:

I'm sorry if I'm wrong

Answer:

Step-by-step explanation:

b) Figure 1 is 2² = 4 (which is also 2x2=4 or if you count all the squares = 4)

Figure 2 is 3² = 9 (which is also 3x3=9 or if you count all the squares = 9 )

Figure 3 is 4² = 16 (which is also 4x4=16 or if you count all the squares = 16 )

Figure 4 is 5² =25(which is also 5x5=25 or if you count all the squares = 25)

Figure 5 is 6² = 36(which is also 6x6=36 or if you count all the squares =36)

c) Figure 1 add squares in a horizontal row which is your x-coordinate (2)

then add squares in a vertical row which is your y-coordinate (2)

so (x,y) = (2,2). Graph those points. Do the same for each and your line is a diagonal straight line traveling diagonally upward equally.

f) Equation: a² = a x a

Answer:

ue7e7373777 is is and 88877376363778

Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

And, The vertices on a coordinate are plot in figure.

Here,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

And, Plot the vertices on a coordinate grid to model the problem.

What is Isosceles triangle?

When two sides of a triangle are equal then the triangle is said to be isosceles triangle.

Now,

The vertices of a triangle are A (0, 0), B (2a, b) and C (4a, 0)

We have to check the triangle is isosceles.

For this we use distance formula and prove that the two sides of triangle are equal.

Distance between the points A (0, 0) and B (2a, b) is;

[tex]D_{AB} = \sqrt{(2a - 0)^2 + (b-0)^2} = \sqrt{4a^2+b^2}[/tex]

And, Distance between the points B (2a, b) and C (4a, 0) is;

[tex]D_{BC} = \sqrt{(4a - 2a)^2 + (0-b)^2} = \sqrt{4a^2+b^2}[/tex]

Hence, Distance between the points A and B are equal to distance between points B and C.

So, The given triangle is isosceles.

a. The vertices are plot in coordinate grid to model the problem in figure.

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How is the Additive Identity Property similar to the Multiplicative Identity Property?

How is it different?

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The ordering of the number is 6.286  , 6.628 , 6.826

According to the question we have been given three numbers which are

     6.826 , 6.628 and 6.286

We need to arrange in ascending order that is from least number to the greatest number.

when we arrange number in ascending order for decimal number we first look at the number before the decimal point then if they are all same then we look at the number after the decimal point. After the decimal point the first number is compared which is closest to the decimal point.

If we look into this question the number before decimal points are all same thus we will look the numbers after the decimal point. Therefore we will arrange according to the first  number after the decimal that is 8 , 6 and 2

Hence the ordering the number we get:

      6.286  , 6.628 , 6.826

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Answer/Step-by-step explanation:

2.

5x + 3y = 15

3y = -5x + 15

÷3   ÷3    ÷3

y = (-5/3)x + 5

* = coordinate: (0, 5), (3, 0)

                5  *

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----*----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 -

4.

10x + 8y = -40

8y = -10x - 40

÷8     ÷8    ÷8

y = (-5/4)x - 5

* coordinate: (0, -5), (4, -10)

                5  -

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 *

                 -6 -

                 -7 -

                 -8 -

                 -9 -

                 -10 -                    *

6.

-3x + 6y = 12

6y = 3x + 12

÷6   ÷6   ÷6

y = (1/2)x + 2

* coordinate: (0, 2), (2, 3)

                5   -

                4   -

                3   -          *

                2   *

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -

                 -5 -

8. x - y = 5

-y = -x + 5

÷-1   ÷-1  ÷-1

y = x - 5

* coordinate: (0, -5), (1, -4)

                5  -

                4   -

                3   -

                2   -

                 1   -

-------------------0----|----|----|----|---|------

                 -1  -     1    2   3   4   5

                 -2 -

                 -3 -

                 -4 -     *

                 -5 *

I hope this helps!

When Olga turns 18, she will have $3032.89 in her account, which earned a monthly compound interest rate of 1.75%.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula of monthly compound interest is:

B = P(1 + r)^t

where B is the ending balance, P is the principal amount or original balance, r is the monthly interest rate in decimal form, and t is the number of months.

If Olga's uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly, using the formula, solve for the ending balance after 2 years.

B = P(1 + r)^t

B = 2000(1+ 0.0175)^24

B = $3032.89

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Answer: x=1

Step-by-step explanation:

x-5=2x-6

x-5+6=2x-6+6

x+1=2x

x-x+1=2x-x

2x-x=1

x=1

Answer: x = 1

Step-by-step explanation:

fewer or less than means minus -

difference of x and 5 = x - 5

6 fewer = - 6

twice the number of x = 2x

x - 5 = 2x - 6

x = 2x - 6 + 5

x -2x = - 6 + 5

- x = - 1

x = 1

checking

1 - 5 = 2(1) - 6

4 = 2 - 6

4 = 4

The value of b is b=p-a.

Given the equation is p=a+b.

A pair of inverse operations is defined as two operations to be performed on a number or. variable,  always returns the original number or variable And inverse means opposite.

equation means a mathematical statement with the symbol "equal" between two expressions of equal value. This is represented by '='.

The given equation is p=a+b.

Now, we will apply the inverse operations on both sides.

Subtract a from both sides, we get

p-a=a+b-a

Now, we will simplify the above equation, we get

p-a=b

Hence, the value of b from the given equation p=a+b is b=p-a.

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Answer:

x =7

Step-by-step explanation:

hope it helped

Answer:

x=7

Step-by-step explanation:

i just saw that this has been answered but i want to give an explanation incase it is needed:

•3x+4=5x-10

first move the like terms to one side of the = sign. (its best to move the smaller x value to the bigger one.

•4+10=5x-3x

then you just solve the equation on both sides:

• 14=2x

then you have to being the 2 over the = sign so that x is by itself. when you bring a divide value over the = sign it will turn into the opposite operation.

so basically you are dividing 14 by 2

•14/2 = x or 14÷2=x

which finally gives you :

x=7

hope that makes sense...

Answer:

Pon tu tarea aquí para que podamos ayudarte con ella :)

Answer:

d = 13

Step-by-step explanation:

19d - 16d - d - d - 1 = 12

19d + (-16 - 1d - 1d) - 1 = 12

19d + (--18d) - 1 = 12

19d - 18d - 1 = 12

1d = 12 + 1

d = 13

Check:

19*13 - 16*13 - 13 - 13 - 1 = 12

247 - 208 - 26 - 1 = 12

39 - 27 = 12

If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

Given,

The total amount you had = $150

The amount you spend in each day = $2

Consider the number of days = x

Then the algebraic expression for this situation is 150-2x

Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

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For the given parabola, we have that:

a) The equation is: f(x) = -16(x - 0.75)² + 18.

b) The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

For this problem, the vertex is at (0.75,18), hence:

h = 0.75, k = 18.

f(x) = a(x - 0.75)² + 18.

When x = 0, y = 9, hence:

9 = 0.5625a + 18

a = -9/0.5625

a = -16.

Hence:

f(x) = -16(x - 0.75)² + 18.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

It is increasing between x = 0 and x = 0.75, in which f(0) = 9, f(0.75) = 18, hence:

r = 9/0.75 = 12.

The function is increasing at a rate of 12 feet per second, while the don't have the final point for the decrease, hence we cannot compute the average rate of change.

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Answer:

k <−33

Step-by-step explanation:

The student walked 58.58 meters more than the total displacement from the starting point.

Given that a student walked 100 meters north, then 100 meters west.

We are required to find the number of meters, the student travelled more as compared to the total displacement from the starting point.

We have to find the distance from the starting point to ending point. We have to apply pythagoras theorem to find that distance.

Pythagoras theorem basically says that the square of hypotenuse of right angled triangle is equal to the sum of squares of base and perpendicular.

[tex]H^{2} =P^{2} +B^{2}[/tex]

In our case P is 100 meters and B is 100 meters and we have to find H from the formula given above.

[tex]H^{2} =100^{2} +100^{2}[/tex]

H=[tex]\sqrt{10000+10000}[/tex]

H=[tex]\sqrt{20000}[/tex]

H=141.42 meters

Difference=100+100-141.42

=200-141.42

=58.58 meters

Hence the student walked 58.58 meters more than the total displacement from the starting point.

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Answer:

860.9 m³

Step-by-step explanation:

We can obtain the volume of the composite figure by subtracting the volume of cylinder from the volume of cuboid.

     l = 10 m

     w = 10 m

    h = 12 m

[tex]\sf \boxed{\text{ \bf Volume of cuboid = l *w * h}}[/tex]

                                    = 10 * 10 * 12

                                    = 1200 m³

      r = 3 m

      h = height of the cuboid = 12 m

    [tex]\sf \boxed{\text{\bf Volume of cylinder = $\pi r^2h$}}[/tex]

                                         = 3.14 * 3 * 3 * 12

                                         = 339.1 m³

Volume of composite figure = 1200 - 339.1

                                                = 860.9 m³

The recursive formula for the given sequence is a(n) = 2 a(n-1) - a(n-2) + 1

A recursive formula is an equation that express the nth term as a function of preceding term(s), i.e. as function of (n-1)th term, (n-2)th terms, and so on. Mathematically it can be written as:

a(n) = f(a(n-1), a(n-2), ..., a(1))

The given sequence: 1,3,6,10, . . .

Here a(1) = 1. Notice that:

a(2) = 3 = 1 + 2

a(3) = 6 = 3 + 3

a(4) = 10 = 6 + 4

Notice that the differences between terms increase by 1.

Further, we can write:

a(2) = 3 = 1 + (1 - 0) + 1

             = a(1) + a(1) + 1

             = 2a(1) + 1  

a(3) = 6 = 3 + (3 -1) + 1

             = a(2) + a(2) - a(1) + 1

             = 2a(2) - a(1) + 1

a(4) = 10 = 6 + (6 - 3) + 1

               = a(3) + a(3) - a(2) + 1

               = 2 a(3) - a(2) + 1

We can continue this recursive pattern to find a(n),

a(n) = 2 a(n-1) - a(n-2) + 1

We can find next term for n = 5:

a(5) = 2a(4) - a(3) + 1

       = 2. 10 - 6 + 1 = 15

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