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The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    [tex]?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12[/tex]

Thus the missing side length is 12 cm

Hope that helps!

Answer:

Step-by-step explanation:

Arithmetic sequaence:

[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]

[tex]a_2 = -3*4^2-1\\[/tex]

    = -3*16 -1

     = -48 - 1

    = -49

difference = second term - first term

                 = -49 -(-13)

                = -49 + 13

             d = -36

[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]

[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]

= 5*(-135)

= -675

Answer:

They'll each want a quarter of a cupcake.

Step-by-step explanation:

The number of people in the family is 14.

The number of cupcakes ordered is 4.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Number of cakes for the family = 3 (1/2)

Number of friends = 2

Now,

Each person's amount of cake = 1/4

The number of people in the family.

= 3(1/2) ÷ 1/4

= 7/2 x 4

= 14

The total number of cupcakes ordered.

= 2 x 1/4 +3(1/2)

= 1/2 + 3(1/2)

= 1/2 + 7/2

= 8/2

= 4

Thus,

There are 14 people in the family.

The total number of cupcakes ordered is 4.

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The complete question is:

Hello, id like to order3 halves of a cupcake for my family plus some extra for my 2 friends.

They'll each want a quarter of a cupcake.

Answer:

48

Step-by-step explanation:

one pound equals 16 ounces so multiply each side by three and you get that 3 lb equals 48 ounces

Answer:

48 oz

Step-by-step explanation:

We know 1 lb = 16 oz. That means that to find how many oz are in 3 lbs, you have to multiply 16 by 3. That equals 48.

Answer:

[tex]\sf (x+9)^2+(y-5)^2=16[/tex]

Step-by-step explanation:

Standard equation of a circle:  [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]

(where (h, k) is the center of the circle and r is the radius)

Given:

Substituting given values into the equation:

[tex]\sf \implies (x-(-9))^2+(y-5)^2=4^2[/tex]

[tex]\sf \implies (x+9)^2+(y-5)^2=16[/tex]

Equation:-

Answer:

3 > x

Step-by-step explanation:

3 is larger than all of the values on the line, of which the arrow is pointing. The circle is open, so it means that it is not greater than or equal to.

I hope this helps!

-No one

Answer:

567 ghbvc. the high but

Step-by-step explanation:

solve accordingly to the picture

hope it helps

Answer: See attached

Step-by-step explanation:

     Coordinate points come in (x, y) so we graph them as so.

(4, 1) - Starting at (0, 0), also known as the origin, move four units right and one unit up. Plot point A here.

(5, 4) - Starting at (0, 0), also known as the origin, move five units right and four units up. Plot point B here.

(9, 4) - Starting at (0, 0), also known as the origin, move nine units right and four units up. Plot point C here.

(9, 1) - Starting at (0, 0), also known as the origin, move nine units right and nine units up. Plot point D here.

Answer:

Assuming a vertical axis of symmetry, the equation would be of the form y = ax^2 + bx + c which can also be written as y = a(x - h)^2 + k. Case 1: If the two points have the same y value, then the axis of symmetry will pass through the midpoint of the segment between them.

Step-by-step explanation:

An equation is formed of two equal expressions. The given equation can be simplified for y as y=(x²-14x+114)/10.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation √[(x-7)²+(y-9)²]=(y-4) can be simplified for y as shown below,

[tex]\sqrt{\left(x\:-\:7\right)^2\:+\:\left(y\:-\:9\right)^2}=\left(y\:-\:4\right)[/tex]

(x - 7)² + (y - 9)² = (y - 4)²

(x - 7)² = (y - 4²) - (y - 9)²

(x² + 49 - 14x) = (y² + 16 - 8y) - (y² + 81 - 18y)

x² + 49 - 14x = y² + 16 - 8y - y² - 81 + 18y

x² + 49 - 14x = 10y - 65

x² - 14x + 49 + 65 = 10y

x² - 14x + 114 = 10y

y = (x² - 14x + 114)/10

Hence, the given equation √[(x-7)²+(y-9)²]=(y-4) can be simplified for y as y=(x²-14x+114)/10.

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Answer:

4x+4=16

4x= 16–4

4x= 12

x= 12/4

x= 3

Alternatively,

4x+4=16

Taking 4 common,

4 (x+1) = 16

x+1 = 16/4

x+1 = 4

x = 4–1

x = 3

Step-by-step explanation:

The value of x is 68.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

Given equation:

4/(x - 4) = 1 /16

Now, solving for x

4/(x - 4) = 1 /16

64 = x - 4

x= 68

Hence, the value of x is 68.

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The probability of not drawing C in neither draw is P = 0.5

All the cards have the same probability of being drawn, in this case, our set of cards is {F, D, C, G}

The probability of not drawing C is equal to the probability of drawing F, D or G. So we have 3 options out of 4, then the probability is:

p = 3/4.

Now we draw another, this time there are 3 cards, one of these is C, and the other two cards are not C. Then the probability of not drawing C again is equal to 2 over 3.

q = 2/3.

The joint probability (for both of these events to happen) is equal to the product of the individual probabilities:

P = p*q = (3/4)*(2/3) = 0.5

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Answer:

1 quick fix            2 solving               3 result

Step-by-step explanation:

hope it helps

Answer:

B

Answer:

In physics the standard unit of weight is Newton, and the standard unit of mass is the kilogram. On Earth, a 1 kg object weighs 9.8 N, so to find the weight of an object in N simply multiply the mass by 9.8 N. Or, to find the mass in kg, divide the weight by 9.8 N.Divide the object's weight by the acceleration of gravity to find the mass.

Step-by-step explanation:

this is what i think

Answer:

Q. Equal

Step-by-step explanation:

"The same" means equal. Its kind of like equations.

1 is equal to 1 they are the same number

answer: Equal

Step-by-step explanation: being the same in quantity, size, degree, or value.

Answer:

The bother's weight is 46.5 lb.

Step-by-step explanation:

Let the brother's weight be b.

Antonio's weight is 2b + 4.

Antonio's weight is 97 lb.

2b + 4 = 97

2b = 93

b = 46.5 lb

Answer: The bother's weight is 46.5 lb.

Answer:

I-9I

Step-by-step explanation:

Absolute value (the straight brackets) is how far away the number is from zero, this makes -9 into positive 9

Answer:

C. |-9|

Step-by-step explanation:

|-9| = 9

9 > 7 > |5| (5) > -12

Answer:

B)1, 2, 3, 6, 9, 18

Step-by-step explanation:

1×18

2×9

3×6

HOPE IT HELPS YOU

Answer:

529/55 and 57/2

Step-by-step explanation:

By taking the integral of the difference between the two given lines, we will see that R = 0.75.

Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]

Then we just need to compute:

[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]

Solving that we will get:

[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]

[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]

So the area of region R is 0.75 square units.

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Step-by-step explanation:

AC= 8x-14

AC+14=8x

x=(AC+14)÷8

EC=2x+11

EC-11=2x

x=(EC-11)÷2

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Using a system of equations, it is found that the correct option is:

A) 1389x+1660y=787x+1121y.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, considering the amounts in each olympics(1389 men and 787 women participated on the 19th, 1660 men and 1121 women in the 22th), the system is:

A) 1389x+1660y=787x+1121y.

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[3 6 3]

( 3 3. 3]

THIS ANSWER IS CORRECT

Solution:

[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]

[tex]\sf \left[\begin{array}{ccc}3&6&3\\-3&3&3\\\end{array}\right][/tex]

The rule for a reflection over the x -axis is (x,y) → (x,−y)

===============================================================

or multiply the matrix with:      [tex]\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right][/tex]

[tex]\dashrightarrow \ \sf \begin{pmatrix}1\cdot \:3+0\cdot \left(-3\right)&1\cdot \:6+0\cdot \:3&1\cdot \:3+0\cdot \:3\\ 0\cdot \:3+\left(-1\right)\left(-3\right)&0\cdot \:6+\left(-1\right)\cdot \:3&0\cdot \:3+\left(-1\right)\cdot \:3\end{pmatrix}[/tex]

[tex]\sf \left[\begin{array}{ccc}3&6&3\\3&-3&-3\end{array}\right][/tex]

Answer:

Step-by-step explanation:

YES IS THE ANSWER BECAUSE X=9

AND 11+3=87

Answer:

f(x)= (x-3)^2-3

Step-by-step explanation:

Vertex Form: y= a(x-h)^2+k

a is the reflection

h and k are the vertex so in an ordered pair (x,y) = (h,k)

Since it is translating 3 units down it is going to be a negative 3.  If it was translating up it would be positive 3.  This represents the "k" because it is moving on the y-axis.

Since it is translating 3 units to the right it is going to be positive 3.  If it was translating left it would be negative 3. This represents the "h" because it is moving on the x-axis.

After plugging it into the vertex form formula: f(x)= (x-3)^2-3

*notice when I plugged the "h" in it became negative because x-(3)= x-3*

Step-by-step explanation:

there is the rule

outside length × (outside length + inside length) is the same for all lines originating from the same point.

so, we have

CD(CD + x) = BC(BC + AB) = 6(6+20) = 6×26 = 156

8(8 + x) = 156

8 + x = 19.5

x = 11.5

Answer:

6 students

Step-by-step explanation:

Let x = number of students

Let y = total number of pens

Given:

⇒ 5x = y

Given:

⇒ 3x = y - 12

Substitute  5x = y  into  3x = y - 12  and solve for x:

⇒ 3x = 5x - 12

⇒ 12 = 5x - 3x

⇒ 2x = 12

⇒ x = 6

Therefore, there are 6 students.

Answer:

75.062

Step-by-step explanation:

just add and multiply then remember that 1/100 or 1/1000 is just 0.001 or 0.01