A square is cut in half on the diagonal, creating two equal triangles. each triangle has an area of 0.32 square units. what is the side length, in units, of the original square?

Answer:

  congruent triangles

Step-by-step explanation:

The complete reason is, "corresponding parts of congruent triangles are congruent." This reason is sometimes abbreviated CPCTC.

It can be helpful to note that the previous step concluded that the relevant triangles are congruent.

Answer:

5. Congruent triangles

Step-by-step explanation:

Congruent Triangles : When two triangles are congruent, all its three sides are equal and have the same angles.

So in conguent traingles,

ΔADB ≅ BDC

Therefore, AB = DC and AD = BC

Thus this completes the missing information that proves that the quadrilateral ABCD ia a parallelogram, then its opposite sides are congruent.

Answer:

  n(n+1)

Step-by-step explanation:

Only the last two formulas work for n=1; only the last formula works for n=2.

For n=1

  3n = 3 ≠ 2

  n² -1 = 0 ≠ 2

  n² +1 = 2

  n(n+1) = 2

For n=2

  n²+1 = 5 ≠ 6

  n(n+1) = 6 . . . . . this last formula works for the given sequence

Answer:

sqrt of 2/2

Step-by-step explanation:

Answer:

The exact value of cos 45° is: [tex]\frac{\sqrt{2} }{2}[/tex].

Step-by-step explanation:

Answer:  272

Step-by-step explanation:

f(x) = 4x         g(x) = 3x - 5

(g × f)(x) = (4x)(3x - 5)

             = 12x² - 20x

(g × f)(-4) = 12(-4)² - 20(-4)

               = 12(16) + 80

               = 192 + 80

              = 272

Answer:

You add them together and divide it by how many number there are.

Step-by-step explanation:

For example lets say we need to find the average of 12, 15, 18, and 24.

You would do 12+15+18+24

You will get a sum of 69

Then since there are 4 numbers you do 69 divided by 4 and get a quotients of 17.25.

Therefore 17.25 is the average of all four numbers.

The equation of Bunny hill ski resort is z = 10x + 35 while z = 5x + 40  for the Black diamond ski resort at the point and at point (1,45) the cost of both will be the same.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say x number of hours a men sky

Then,

Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour

So,

Total cost

z = 35 + 10x

Now,

Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski

So,

Total cost

z = 40 + 5x

Now point where the cost of both resorts will same is

35 + 10x = 40 + 5x

x = 1

So,

z = 40 + 5(1) = 45

Hence, at point (1,45) the cost of both will be the same.

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Final answer:

To find when the costs are the same for both ski resorts, set up an equation based on their rates and solve for the number of hours, which in this case is 1 hour.

Explanation:

To determine at what point the cost of both Bunny Hill Ski Resort and Black Diamond Ski Resort is the same, we can set up an equation based on the given rates.

Let x be the number of hours spent skiing. Then the total cost at Bunny Hill Ski Resort is $35 (ski rental) plus $10 per hour (hourly rate), which is expressed as 35 + 10x.

Similarly, the cost at Black Diamond Ski Resort is $40 (ski rental) plus $5 per hour (hourly rate), or 40 + 5x. To find when the costs are equal, we set the two expressions equal to each other:

35 + 10x = 40 + 5x

Now we can solve for x:

35 + 10x = 40 + 5x
10x - 5x = 40 - 35
5x = 5
x = 1

Thus, after 1 hour of skiing, the cost of skiing at both resorts becomes the same.

Answer:

  y = 3

Step-by-step explanation:

The solution is the point where the lines intersect, (x, y) = (6, 3). The y-coordinate of that point is 3.

Answer:

y = 3

Step-by-step explanation:

You must count the lines from the intersection to the Ox axis down.

Answer:

Step-by-step explanation:

No solution

Answer:

First, before I answer, he or she forgot the n/3.

So the problem is n/3 + (-4) = 2

The answer is 6

Step-by-step explanation:

First, simply + -4 to -4, because different signs subtract

Second subtract -4 + 2 which equals 2

Now multiply 3 ( came from n/3) with 2

And its 6

I hope I helped you!!!

Hi!

To solve this, first let's decide what quadrant the 135 degrees lies in. Starting in quadrant one, it would end up landing in quadrant 2.

Coordinates:

(cos, sin)

In quadrant 2, the y value (sin) as a coordinate would be positive, therefore our final answer should be positive.

180 - 135 = 45

Therefore our reference angle will be sin45.

We should know that sin45 is equal to [tex]\cfrac{\sqrt{2} }{2}[/tex]

Now, remember that our final answer should be positive. We don't have to change this because it's already positive, so your final answer is:

[tex]\cfrac{\sqrt{2} }{2}[/tex]

The exact value of sin 135 degrees is - (√2)/2.

The unit circle and trigonometric identities can be used to calculate the sine of 135 degrees.

We can determine the location of the point on the unit circle that corresponds to an angle of 135 degrees by utilizing the unit circle. It is located in the third quadrant.

In the first and second quadrants, the sine function is positive; however, the third and fourth quadrants are where it is negative.

We can use the fact that the sine of an angle equals the y-coordinate of the point on the unit circle corresponding to that angle to determine the precise value.

The sine of 135 degrees is negative because the third quadrant's y-coordinate is negative.

We can determine the precise sine value of 135 degrees by using a reference angle.

In the third quadrant, the reference angle for 135 degrees is 45 degrees (180 degrees - 135 degrees).

The sine of a 45-degree angle is (2)/2 or 1/sqrt(2).

The sine of 135 degrees is a negative number because the reference angle is in the third quadrant.

Consequently, (2)/2 is the precise value of sin 135 degrees.

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Answer:

Step-by-step explanation: You are given the equation of -7x+6y=9 and -2x-5y=16 and you are asked to find what x=? and what y=?

First step is to write down the problem

-2x-5y=16

next add 5y over the equal sign.

-2x=5y+16

Next is too divide by -2

-2x/-2=5y+16/-2

after solving you get

x=-2.5y-8

now you substitute the equation into the other formula to get

-7(-2.5y-8)+6y=9

then solve by doing -7*-2.5y and -7*-8 to get 17.5y and 56 which will give you

17.5y+56+6y=9

Next you subtract 56 to the other side to get 9-56 or -47 now you have

17.5y+6y=-47

next is too add the 17.5y and 6y together to get 23.5y

23.5y=-47

next is too divide by 23.5

23.5y/23.5=-47/23.5

solve to get y=-2, now this is half you the problem

Step two is too substitute what y=-2 into the equation of x=-2.5y-8 to get

x=-2.5(-2)-8

Solve to get

x=5-8

Solve again to get

x=-3

Your answers are x=-3 and y=-2

Answer:

x = -3 and y = -2

Step-by-step explanation:

It is given that,

-7x + 6y = 9

   ----(1)

-2x - 5y = 16    -------(2)

To find the solution of given equations

eq(1) * 2 ⇒

-14x + 12y = 18 ------(3)

eq(2) * 7 ⇒

-14x - 35y = 112   ---(4)

eq (3) - eq(4) ⇒

-14x + 12y = 18 ------(3)

-14x - 35y = 112   ---(4)

    0   4y = -94

y = 94/(-47) = -2

Substitute the value of y in eq (2)

-2x - 5y = 16    -------(2)

-2x - 5*-2 = 16

-2x +10 = 16

-2x = 6

x = 6/-2 = -3

Therefore x = -3 and y = -2

Answer:

b 125

Step-by-step explanation:

first you know that you have 2 and 5 as similar numbers you both square them so that they become a ratio of area which is 4/25 after you do 4/25=20/x and you do cross multiply then you find 125. hope that helped understand.

Answer:

B.

Step-by-step explanation:

o find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.

[tex]\begin{array}{c|c|c}\underline{\quad (x,y)\quad}&\underline{\quad y=2x\quad }&\underline{\quad Answer\quad }\\(-1, a_o)&a_o=2(-1)&a_o=-2\\(0, a_1)&a_1=2(0)&a_1=0\\(1, a_2)&a_2=2(1)&a_2=2\\(2, a_3)&a_3=2(2)&a_3=4\\(3, a_4)&a_4=2(3)&a_4=6\\(4, a_5)&a_5=2(4)&a_5=8\end{array}[/tex]

Answer:

b = √(c^2 - a²)

Step-by-step explanation:

Start with the given c = √a^2 + b^2.  Squaring both sides, we get:

c² = a² + b².

We want to iosolate b² and then b.

So:  subtract a² from both sides, resulting in:

c² - a² = b²

Taking the square root of both sides, we get:

√b² = √(c² - a²)

and so:

b = √(c^2 - a²)

To solve the Pythagorean theorem equation for b, isolate b on one side by first squaring both sides. Move the a^2 term to the other side of the equation, then take the square root of both to solve for b. The solution is b = √(c^2 - a^2).

The formula mentioned, c = √a^2 + b^2, represents the application of the Pythagorean theorem for right-angled triangles. To solve this equation for b, you would have to isolate b on one side. Start by squaring both sides of the equation, which gives: c^2 = a^2 + b^2. Then, move a^2 to the other side of the equation to isolate b^2 assuming c^2 > a^2. This gives you: b^2 = c^2 - a^2. Then, take the square root of both sides, which gives: b = √(c^2 - a^2).

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The  fraction of the animals at the shelter are dogs 74/100 or 37/50

A relative value indicating hundredth parts of any quantity.

Given:

74% of the animals at an animal shelter are dogs.

We know the percent is considered as 100.

If we need to estimate anything in percent we compare it with 100%.

So,  fraction of the animals at the shelter are dogs be,

=74% of 100%

=74/100*100/100

= 74/100

=37/50

Hence,  fraction of the animals at the shelter are dogs be is 74/100 or37/50.

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Step-by-step explanation:

This equation is written in standard form, y = ax² + bx + c.

a = 1 , b = -2 , c = -4

First, the x² tells you that this is going to be a parabola. Since the a is positive, the parabola will be facing up (with the ends pointing up).

Next, you find the axis of symmetry, or vertex, which is where the middle of the parabola is. The formula for this is [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-(-2)}{2(1)}[/tex]   Simplify

[tex]\frac{2}{2}[/tex]   Simplify

1

So, the middle of your parabola will be at x = 1.

Now, find the x-intercept. Since the x-intercept of a graph is where y = 0, just plug 0 into the equation for y.

y = x² - 2x - 4   Plug in 0

0 = x² - 2x - 4   Factoring won't work, so use the Quadratic Formula.

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]   Plug in[tex]$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$[/tex]   Simplify

[tex]$x=\frac{2\pm\sqrt{4+16}}{2}$[/tex]   Simplify

[tex]$x=\frac{2\pm\sqrt{20}}{2}$[/tex] The square root of 20 is about 4.47.

[tex]$x=\frac{2+4.47}{2}$[/tex] and [tex]$x=\frac{2-4.47}{2}$[/tex]   Simplify

x = 3.235 and -1.235

These are your x-intercepts, where your parabola crosses the x-axis.

Now, just put all of this information together on a graph!

Answer:

144, 36, 9, 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex]

Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give

Multiply both sides by 4, then

[tex]a_{n-1}[/tex] = 4[tex]a_{n}[/tex]

Given a₄ = 2 [tex]\frac{1}{4}[/tex], then

a₃ = 4 × a₄ = 4 × 2[tex]\frac{1}{4}[/tex] = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

The first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.

The recursive formula allows us to find a term in a sequence from the previous term.

Given

[tex]a_n=\dfrac{a_n-1}{4}[/tex]

Given the fourth term, we require to work back to the third term, second, and so on. Rearrange the formula to give.

Multiply both sides by 4, then

a[tex]_{n-1}[/tex] = 4a[tex]._n[/tex]

Given a₄ = 2, then

The first four terms will be calculated as given below:-

a₃ = 4 × a₄ = 4 × 2 = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144

Therefore, the first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.

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Answer:

The value of slope m = -1

Step-by-step explanation:

x = -2 + 4t

and y = 1 + 4t

Solving the both equations

x +2 = 4t

=> t = (x+2)/4     eq(1)

y-1 = 4t

=> t = (y-1)/4      eq(2)

Putting eq(1) = eq(2) as left hand side of both equations are same

(x+2)/4 = (y-1)/4

Cross multiplying

4(x+2) = 4(y-1)

4x + 8 = 4y -4

4x +4y = -4 -8

4x + 4y = -12

4(x+y) = -12

x+y = -12/4

x+y = -3

y = -x -3

The slope intercept form of line is:

y = mx + b

where m is the slope. Comparing with y = -x-3

The value of slope m = -1

The slope of the line defined by the parametric equations x=-2+4t and y=1+4t is mathematically given as

m = -1

Question Parameter(s):

the parametric equations x=-2+4t and y=1+4t

Generally, the equation for the Equations   is mathematically given as

x=-2+4t

y=1+4t

Therefore

t = (x+2)/4..1

t = (y-1)/4 ...2

 Hence

(x+2)/4 = (y-1)/4

4(x+2) = 4(y-1)

y = -x -3

In conclusion, slope intercept

y = mx + b

Hence

y = -x-3

The slope is m = -1

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The answer is 4. All of the above I googled it

Step-by-step explanation:

A number cubed is equal to the product of 52 and the square of the number.

Answer:

[tex](p - 19) \geqslant 47[/tex]

[tex]p \geqslant 66[/tex]

Answer: The required interval notation of the solution is [66, ∞).

Step-by-step explanation:  We are given to translate and solve the following inequality :

"Nineteen less than p is no less than 47".

Also, to write the solution in interval notation.

According to the given information, the inequality can be written as follows :

[tex]p-19\geq47.[/tex]

The solution of the above inequality is as follows :

[tex]p-19\geq47\\\\\Rightarrow p\geq47+19\\\\\Rightarrow p\geq 66.[/tex]

Thus, the required interval notation of the solution is [66, ∞).

Answer:

Step-by-step explanation:

1. Each term has an even coefficient, so a factor of 2 can be removed:

  2(3x^2 +7x -15)

The remaining quadratic factor is prime.

__

2. Each of these two terms is a square, so this is the difference of two squares.

__

3. This cubic has one irrational negative real root. It is prime.

__

4. This trinomial factors in the usual way: (x +15)(x -2). It is factored by "factoring trinomials."

__

5. The magnitude of the x-coefficient is double the square root of the (positive) constant, so this is a perfect square trinomial.

Answer:

4th option

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{1+\sqrt{3}}[/tex]

In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with [tex]1-\sqrt{3}[/tex], as shown below:

[tex]\frac{1}{1+\sqrt{3}}\\=\frac{1}{1+\sqrt{3}} \times \frac{1-\sqrt{3}}{1-\sqrt{3}}\\=\frac{1-\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}\\\\ =\frac{1-\sqrt{3}}{1-3}\\\\ =\frac{1-\sqrt{3}}{-2}\\\\ =\frac{-1(1-\sqrt{3})}{2}\\\\ =\frac{-1+\sqrt{3}}{2}[/tex]

Thus, 4th option gives the correct answer.

Answer:

The right option is D -1+√3/2

Step-by-step explanation:

To find the quotient of the sure function 1/1+√3, we will rationalize the surd function by multiplying the numerator and the denominator of the surd by the conjugate of its denominator.

Given he denominator to be 1+√3, the conjugate of 1+√3 is 1-√3

Multiplying by 1-√3 will result in the following;

1/1+√3×1-√3/1-√3

= 1-√3/(1+√3)(1-√3)

= 1-√3/1-√3+√3-√9

= 1-√3/1-√9

= 1-√3/1-3

= 1-√3/-2

= -(1-√3)/2

= -1+√3/2

The right option is D -1+√3/2

I'm only doing these because it's about a pet pig named Hammy.

5.

rate = distance / time

a.

rate: 36 inches per 3 seconds

b

unit rate: 12 inches per second

c

5 seconds × 12 inches per second = 60 inches

d

144 inches / 12 inches per second = 12 seconds

6.

a.

[tex] \frac 4 7 \div \frac 3 5 = \frac 4 7 \times \frac 5 3 = \dfrac{20}{21}[/tex]

b.

[tex]2 \frac 2 5 \div 1 \frac 7 9 = \frac{12}{5} \div \frac{16}{9} = \frac{12}{5} \times \frac{9}{16} = \dfrac{27}{20} [/tex]

c

[tex]3.24 \div 1.5 = 3.24 \div \frac 3 2 = 3.24 \times \frac 2 3 = 6.48/3 = 2.16[/tex]

d

[tex] \frac 8 9 \div 3\frac 1 3 = \frac 8 9 \times \frac{3}{10} = \dfrac{4}{15}[/tex]

Answer:

Step-by-step explanation:

(a) Hammy's rate is 36 inches in 3 sec.

(b) Hammy's unit rate is (36 inches) / (3 sec) = 12 in/sec

(c) In 5 sec Hammy can run (12 in/sec)(5 sec) = 60 in

(d) time = distance/rate, so here the time is (144 in) / (12 in/sec) = 12 sec

(6a) 4/7 divided by 3/5 is equivalent to 4/7 times 5/3, which comes out to 20/21.

(6b) Convert 2  2/5 to 12/5 and 1  7/9 to 16/9.  Then invert the second improper fraction and multiply:  12/5 times 9/16 = 108/80, or 27/20.

(6c)  3.24 divided by 1.5 is equivalent to 3.24 times 2/3:  2.16, or 2  4/25

(6d) 8/9 divided by 3  1/3 is equivalent to 8/9 times 3/10, or 24/90, or 4/15.

Answer:

216°

Step-by-step explanation:

Both chords are the same length, so the left and right arcs are both 72°.  The whole circle is 360°, so:

72° + 72° + x = 360°

x = 216°

Perimeter of the square backyard=56m

Perimeter of a square=4*side

Side=

56=4*side

56/4=side

side=14 cm

Area of a square=side*side

=14*14

=196cm^2

So,the area of the square backyard is 196m^2.

Answer:

A=196

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

  (x, y) = (-3, 5)

Step-by-step explanation:

There are many ways to solve a system of two equations with two unknowns. Almost all of them involve reducing the system to one equation in one unknown. (Graphical solution, as in the attachment, bypasses that algebraic manipulation.)

In general, the first step is to look at the equations to see if ...

If the first condition is true, then the system may be easily solved by "substitution." The expression you have for one of the variables can be substituted for that variable in the other equation.

If the second condition is true, you can add the equations to eliminate the variable with opposite coefficients. (Opposites add to give zero.)

Here, the third condition holds: the coefficient of x in the first equation (4) is simply related to the coefficient of x in the second equation (8) by a factor of 2.

___

So, we can eliminate the x-variable from the system of equations by multiplying the first equation by -2 and adding that result to the second equation:

  -2(4x +2y) +(8x +5y) = -2(-2) +(1)

  -8x -4y +8x +5y = 4 +1 . . . . eliminate parentheses

  y = 5 . . . . . . . . . . . . . . . . . . . collect terms

Now, we can substitute this value into either equation to find the value of x. Using the first equation, we get ...

  4x +2(5) = -2

  4x = -12 . . . . . . . subtract 10

  x = -3 . . . . . . . . . divide by 4

The solution to the system of equations is (x, y) = (-3, 5).

Answer:

(-2, 4)

Step-by-step explanation:

One of the equations is already solved for y, so let's solve the other one for y and by the transitive proprerty of equality, if y = y, then what those y's are equal to are equal to each other.  Solving the first equation for y:

x + y = 2 so

y = -x + 2

Let's fill that in for y in the second equation.  Where

[tex]y=\frac{1}{2}x+5[/tex], making the substitution,

[tex]-x+2=\frac{1}{2}x+5[/tex]

Combining like terms and getting the x on one side and the constant on the other side of the equals sign:

[tex]-\frac{3}{2}x=3[/tex]

The product of a fraction and its reciprocal is 1 so we will multiply both sides by

[tex]-\frac{2}{3}[/tex] to get:

[tex](-\frac{2}{3})(-\frac{3}{2})x=(3)(-\frac{2}{3})[/tex]

and we end up with x = -2.

Now that we know that, we can sub that in for x in either one of the original equations.  I chose the first one:

If x + y = 2, then -2 + y = 2

and y = 4

Therefore, the solution set is (-2, 4)

ANSWER

[tex]x = 140 \degree[/tex]

EXPLANATION.

The two tangents each meet the radius at 90° each.

This implies that,

[tex]x + 40 + 90 + 90 = 360[/tex]

The sum of interior angles of a Quadrilateral is 360°

We simplify to get

[tex]x + 40 = 180[/tex]

[tex]x = 180 - 40[/tex]

[tex]x = 140 \degree[/tex]

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-4}{2(1)}~~,~~6-\cfrac{(-4)^2}{4(1)} \right)\implies (2~~,~~6-4)\implies (2~,~2)[/tex]

Answer:

B. (2,2).

Step-by-step explanation:

Convert to vertex form y = a(x - b)^2 + c where (b, c) is the vertex.

y =x^2 - 4x + 6

y = (x - 2)^2 - 4 +6

y = (x - 2)^2 + 2.

Therefore the vertex is (2, 2).