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So the 45-45-90 triangle is considered to be a "special triangle" and has a rule with it. If the legs are x, then the hypotenuse is x√2. Since we know that the hypotenuse is 18, this means we can set up our equation as such:

[tex]x\sqrt{2} =18[/tex]

From here we can solve for x. Firstly, divide both sides by √2.

[tex]x=\frac{18}{\sqrt{2}}[/tex]

Next, we want to simplify this expression and to do that we first have to rationalize the denominator. With the right side, multiply the numerator and denominator by √2:

[tex]\frac{18}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{18\sqrt{2}}{2}\\\\\\x=\frac{18\sqrt{2}}{2}[/tex]

Next, divide:

[tex]x=9\sqrt{2}[/tex]

In short, the length of one leg of the triangle is 9√2 cm.

A 45-45-90 triangle is a special triangle: If the legs of the hypotenuse each equal x then the length of the hypotenuse is equal to x√2.

To find the length of one of the legs, all we need to do is find the value of "x".

The hypotenuse in a 45-45-90 triangle is equal to x√2.

In this case we are given the hypotenuse which equals 18cm.

x√2 = 18

to find the value of x divide both sides by √2

x√2 / √2 = 18 / √2

x = 18/√2 or 9√2 (the most simplified form)*

x is the length of one of the legs of a 45-45-90 triangle.

Answer:

B) −1/4

Step-by-step explanation:

The slope represents the change in y values divided by the change in x values.  We can use the formula

slope = (y2-y1)/(x2-x1)

(2,4)  (-2,5)

slope = (5-4)/(-2-2)

        = 1/-4

slope = -1/4

Answer:

B. -1/4

Step-by-step explanation:

To get the slope you have to use the formula: y2-y1/x2-x1

y2-y1/x2-x1 = 4.47-5/-1-(-2)

4.75-5 = -.25

-1 - (-2) = 1

-.25/1 = -.25 or -1/4

Answer:

84.78 cm

Step-by-step explanation:

The circumference = pi * d

d = 27

The circumference = 27 * pi

p = 3.14

The circumference = 84.78

If that is not among your choices, list what is.

Answer:

20 watermelons

Step-by-step explanation:

28/1.4 = 20

Plz give me brainiest!!!!

y-coordinate is 3 times the x-coordinate → y = 3x

Substitute to the equation 3x - 4y = 9:

3x - 4(3x) = 9

3x - 12x = 9

-9x = 9     divide both sides by (-9)

x = -1

y = 3(-1)

y = -3

The point of x and y-coordinate after solving the equation is (-1, -3).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.

Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given equation in the question,

3x - 4y = 9  (i)

It is given that y is three times the x-coordinate,

y = 3x

Substitute it in equation (i)

3x - 4(3x) = 9

3x - 12x = 9

-9x = 9

x = -1

Substitute x = -1 in equation (i)

3(-1) - 4y = 9

-4y = 12

y = -3

Therefore, the point is (-1, -3).

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Answer:

2x² - 3x - 8

Step-by-step explanation:

note that (f - g )(x) = f(x) - g(x)

= 2x² - 5 - (3x + 3) = 2x² - 5 - 3x - 3 = 2x² - 3x - 8

Answer:

25% of 1000 > 15% of 1500

Step-by-step explanation:

Lets calculate how much money you could receive

15% of 1500

.15 * 1500 = 225

25% of 1000

.25*1000 = 250

250>225

Final answer:

After calculating 15% of $1,500 and 25% of $1,000, it is evident that choosing the latter provides more money, amounting to $250 compared to $225 from the former option.

Explanation:

Choosing between percentages of different amounts involves straightforward arithmetic. To determine which option gives you more money, calculate the numerical value of each percentage. Option one is 15% of $1,500, which can be calculated as follows:

Convert the percentage to a decimal: 15% = 0.15.

Multiply the decimal by the total amount: 0.15 x $1,500 = $225.

Option two is 25% of $1,000:

Convert the percentage to a decimal: 25% = 0.25.

Multiply the decimal by the total amount: 0.25 x $1,000 = $250.

Now, compare the two amounts: $225 from the first option and $250 from the second option. It is clear that you would receive more money by choosing the 25% of $1,000, as it gives you a total of $250 compared to the $225 from the first option.

Answer:

(u + 7) + 13 = u + (7 + 13)

Step-by-step explanation:

The associative property moves the parenthesis.  We are doing addition , so we need to look for the problem that moves the parenthesis on addition.

Answer:

b

Step-by-step explanation:

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Initial value of the property = P

Rate of growth = 275%

So, we need to find the property's current value:

We will use "compound interest ":

Answer:

- 648, 1944, - 5832

Step-by-step explanation:

the terms form a geometric sequence with

common ratio r = [tex]\frac{-72}{24}[/tex] = [tex]\frac{24}{-8}[/tex] = - 3

to obtain the next term in the sequence multiply the previous term by r

216 × - 3 = - 648

- 648 × - 3 = 1944

1944 × - 3 = - 5832

the next 3 terms are - 648, 1944, - 5832

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ y=a(x- h)^2+ k \qquad\qquad vertex~~(\stackrel{2}{ h},\stackrel{-7}{ k}) \\\\\\ y=a(x-2)^2-7~\hspace{4em}\stackrel{\textit{y-intercept}}{(0, -3)}~~ \begin{cases} x=0\\ y=-3 \end{cases}\implies -3=a(0-2)^2-7 \\\\\\ 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a~\hfill y=1(x-2)^2-7 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y(x-2)^2-7~\hfill[/tex]

The quadratic function with the vertex (2,-7) and y-intercept -3 is f(x) = x² - 4x - 3.

To find the quadratic function given the vertex (2,-7) and the y-intercept -3, we can use the vertex form of a quadratic equation, which is f(x) = a(x - h)² + k, where (h, k) is the vertex.

Substituting the vertex into the equation, we get f(x) = a(x - 2)² - 7. To find 'a', we can use the fact that the y-intercept is -3, which occurs when x = 0. Thus, we substitute x = 0 into the equation to get -3 = a(0 - 2)² - 7.

Simplifying further,

-3 = 4a - 7

4a = 4

a = 1

With this value of 'a', the quadratic function is f(x) = (x - 2)² - 7, or in expanded form f(x) = x² - 4x + 4 - 7, which simplifies to f(x) = x² - 4x - 3.

This function has a vertex at (2, -7) and passes through the y-axis at y = -3, confirming that we calculated the correct equation for the parabola.

Answer: Lins Family would drive 75 miles.

Hope this helps!!!!

Step-by-step explanation:

Answer:

5,340

Step-by-step explanation:

Hi there:)

Amount invested in stock

=5000×0.6=3000

Amount invested in a saving account

5000-3000=2000

The stock increases 9% in the first year

3,000×(1+0.09)=3,270

and loses 4% of its value the second year

3,270×(1−0.04)=3,139.2

Amount of a saving account after two years

2,000×(1+0.049)^(2)=2,200.8

the total amount gained during the 2 years

3,139.2+2,200.8=5,340...answer

Hope it helps

Answer: B) 1/4

The greatest common factor of 4 and 16 is 4. This is the largest factor that goes into both numerator and denominator

Divide the numerator and denominator by the GCF

4/4 = 1

16/4 = 4

This means 4/16 reduces to 1/4

Thinking in reverse, you can multiply top and bottom of 1/4 by 4 to get 4/16.

Answer:

The scale factor of dilation is: 5

Step-by-step explanation:

" A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

If the scale factor is greater than 1, the image is an enlargement (a stretch) " .

Whenever we multiply an coordinates or for some figure if all the coordinates get multiply by same factor 'a' then 'a' is called as scale factor in the dilation.

Here in this question:

(-3,-4) is moved to (-15,-20).

Here when (-3,-4) is multiplied by 5 we get the coordinate as: (-15,-20).

Hence, the scale factor is 5.

Answer:

8 HOURS  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

NY TO CHICAGO = 3.5 HOURS

CHICAGO TO LA = 4.5 HOURS

NY  TO   CHICAGO            CHICAGO TO LA

        3.5                     +                4.5              =  8 HOURS

The point-slope form of line:

[tex]y-y_1=m(x-x_1)[/tex]

The fomula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the coordinates of the points:

[tex]m=\dfrac{7-3}{2-(-2)}=\dfrac{4}{2+2}=\dfrac{4}{4}=1\\\\y-7=1(x-2)[/tex]

[tex]y-7=x-2[/tex]       subtract y from both sides

[tex]-7=x-y-2[/tex]     add 2 to both sides

[tex]-5=x-y\to\boxed{x-y=-5}[/tex]

Answer:

1.) y = -4x + 10

2.) y = 3x - 7

Step-by-step explanation:

Since they're asking for slope-intercept form we must make our equation look like this:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

1.) [tex]4x+y=10[/tex]

[tex]4x+y=10\\\\4x-4x+y=-4x+10\\\\y=-4x+10[/tex]

Note that we just need to subtract 4x on both sides.  In this case the slope is -4 and the y-intercept is 10.

2.)

[tex]3x-y=7\\\\3x-3x-y=-3x+7\\\\\frac{-y}{-1}=\frac{-3x+7}{-1}\\\\y=3x-7[/tex]

Note that we subtracted 3x on both sides then divided by -1 to get rid of the negative y.  In this case our slope is 3 and our y-intercept is -7

Answer:

ASA congruence and CPCT property

Step-by-step explanation:

There are two triangles PRQ and SRT given

In these two triangles we have

QR=TR, Angle Q = angle T and angle PRQ = Angle SRT

i.e. two angles and corresponding side are congruent.

Hence by ASA congruence for triangles the two triangles

PRQ and SRT are congruent

By CPCT property for congruent triangles,

we have corresponding sides are equal.

Hence PR = SR

Proved.

The graph of a proportional relationship passes through origin (0, 0).

Therefore your answer is B).

Answer:

The answer is B

Step-by-step explanation:

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Answer:

x=22

Step-by-step explanation:

In the top lines, it is given they are perpendicular, in the bottom case, you don't know that. However, it is given that the line from the center intersects halfway the chord (I looked that up). By definition that means that these lines are also perpendicular. Since the line from the center is 12 units in both cases, the top chord must be the same size as the bottom chord.

x seems to denote the total length, so that's twice 11, x=22

Answer:

11

Step-by-step explanation:

if you folded the circle in help the 12s would line us and so would x and 11 so x = 11

Final answer:

A line with a slope of -4/3 passes through the point (-6, 1) can be represented by the equation y = -4/3x - 7.

Explanation:

A line with a slope of -4/3 passes through the point (-6, 1).

To find the equation of the line, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values into the equation, we get y - 1 = -4/3(x - (-6)).

Simplifying, we have y - 1 = -4/3(x + 6).

Expanding, y - 1 = -4/3x - 8.

Moving the constant term to the other side, we get y = -4/3x - 7.

Answer:

Eliza travels 54 minutes.

Step-by-step explanation:

Let's use the variable r to represent the number of minutes Ricky travles to school.

Eliza travels 6 times as many minutes as Ricky, so Eliza travels 6r minutes.

Altogether, they travel r + 6r minutes, or 7r minutes.

We are told they travel 63 minutes altogether, so 7r must equal 63.

7r = 63

Divide both sides by 7.

7r/7 = 63/7

r = 9

Ricky travels 9 minutes.

Eliza travels 6r minutes.

6r = 6 * 9 minutes = 54 minutes

Eliza travels 54 minutes.

x is a placeholder for a number. Think of it as a box. Inside the box, we're told that 2 is there.

So we'll replace every x with 2 and use PEMDAS

5*x - 3*x = 5*2 - 3*2 = 10 - 6 = 4

After simplifying, the answer is 4.

Answer:

4

Step-by-step explanation:

5x-3x

We can simplify this expression

2x

Now we can substitute x=2

2(2)

=4

The interest Tamika earns after 15 years with an annual deposit of $1,750 in a money market account with a 4.25% annual compound interest rate is $9,449.40.

This is a problem of calculating compounded interest over time. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. But since Tamika is depositing $1,750 each year, this becomes an annuity problem. So, the future value of an annuity formula is used, which is FV = P * [(1 + r)^nt - 1] / r.

Here, P = $1,750, r = 4.25% or 0.0425, n = 1 (since interest is compounded annually), and t = 15 years. Substituting these into the formula, we find FV = $1,750 * [(1 + 0.0425)^15 - 1] / 0.0425 = $35,699.40.

The total amount after 15 years is $35,699.40, but this includes her contributions which total $26,250 (1750 * 15). So, the interest she earned is $35,699.40 - $26,250 = $9,449.40.

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Joe paid $1,260 in interest over 2 years.

To calculate the amount of interest Joe paid in 2 years, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $9,000, the rate is 7% (which is equivalent to 0.07), and the time is 2 years. Plugging these values into the formula gives: Interest = $9,000 * 0.07 * 2 = $1,260. Therefore, Joe paid $1,260 in interest over 2 years.

Answer:

400/500

48 to 60

both  are correct

Step-by-step explanation:

4/ 5

Multiply top and bottom by 100

4*100/ 5* 100 =400/500

400:500

4/5  

Multiply top and bottom by 12

4/5 * 12/12 = 48/60

we can rewrite as 48:60

Answer:

 2x+10 // 2 • (x + 5)  

Step-by-step explanation:

Final Result :

     y + 10  

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