simplify:
[tex] \sqrt[5]{3} + \sqrt{12} + \sqrt{32} [/tex]

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:

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: Lins Family would drive 75 miles.

Hope this helps!!!!

Step-by-step explanation:

Answer:

70 seconds

Step-by-step explanation:

Answer:

70 seconds

Step-by-step explanation:

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

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.

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

Answer:

nth term =  523 + 24(n - 1

Step-by-step explanation:

This is modelled by an arithmetic series where first term a1 = 523 and common difference d = 24.

nth term = a1 + d(n - 1).

Here it is  523 + 24(n - 1)   (answer)

Answer:

The answer is:24n+499

Step-by-step explanation:

As we know Henry's grandfather gave him a box of 523 baseball cards in the first month.

from the second month Henry start to collect 24 baseball cards each month.

if the total process took n months, so Henry himself collected 24 baseball cards for 'n-1' months.

so total cards collected by Henry in (n-1) months is=24(n-1)

hence, Henry's total collection is=number of baseball cards his grandfather gave him+number of baseball cards collected by Henry himself

=523+24(n-1)

=523+24n-24

=24n+499

Answer:

A

Step-by-step explanation:

C and D are both wrong for the same reason. The denominator should be (x +1)*5 which means that either A or B is correct.

C and D have an error seldom seen on Brainly. It means that the denominator has been added rather than multiplied but even the addition is a little strange. Frankly, I don't know what has to be done to get either of them.

So the answer is

numerator: 5*(x + 9) +  (x + 1)(x - 2)

denominator: 5*(x + 1)

Simplify the numerator. Remove the brackets.

numerator: 5x + 45 + x^2 - 2x + x - 2               Gather like terms

numerator: x^2 + 5x - 2x + x + 43                      Simplify

numerator: x^2 + 4x + 43

Answer

x^2 + 4x + 43

==========

5(x + 1)

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:

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:

your question does not make any sense.

Step-by-step explanation:

Answer:

(6+2n-7)÷4

Step-by-step explanation:

Answer:

Step-by-step explanation:

8x6= (4x6)+(4x6)

48=24+24

48=48

Answer:

[tex]6\cdot{(4+4)}=6\cdot{8}[/tex]

Step-by-step explanation:

We can break apart he arrau as follows:

We can take a common number from (4x6)+(4x6). The common term is 4 and 6. We can take 6 out:

[tex](4\cdot{6})+(4\cdot{6})=6\cdot{(4+4)}=6\cdot{8}[/tex]

Which equals 8x6

Answer:

A

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

subtract the sum of the 2 given angles from 180

x = 180° - (90 + 16)° = 180° - 106° = 74° → A

Answer:

Step-by-step explanation:

the sum of the interior angles of a triangle is 180°, you have a 90° angle and a 16° angle, take away the know angles from 180°

180 - 90 - 16 =

74°

----------------

check

90 + 16 + 74 = 180°

the answer is good

Answer:

 2x+10 // 2 • (x + 5)  

Step-by-step explanation:

Final Result :

     y + 10  

Processing ends successfully

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: 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.

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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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:

please click the thanks button

Answer:

20 watermelons

Step-by-step explanation:

28/1.4 = 20

Plz give me brainiest!!!!

Answer: 31 & 42

Step-by-step explanation:

1st #: x

2nd #: x + 11

1st# + 2nd# = sum

 x    +  x + 11 =  73

         2x + 11 = 73

         2x        = 62

           x          = 31

2nd #: x + 11   = 31 + 11   = 42

The problem is solved by creating two equations from the given conditions and then solving them to find the numbers. The result is that the two numbers are 31 and 42.

We are looking for two numbers, let's call them x and y. According to the problem, one number exceeds the other by 11, so we can say that y = x + 11. Moreover, their sum is 73, so x + y = 73.

Now, we need to substitute y from the first equation into the second one. So x + (x + 11) = 73, which simplifies to 2x + 11 = 73. Subtracting 11 from both sides gives us 2x = 62. Dividing by 2, we find that x = 31. From the first equation, we can now determine the value for y as y = 31 + 11 = 42. Therefore, the two numbers are 31 and 42.

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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).

To know more about expression:

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Answer:

-1

Step-by-step explanation:

11 minus 3 is 8

8 minus 3 is 5

5 minus 3 is 2

2 minus 3 is -1

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.

[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:

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.