If x/3 = 5/6, then x =

The area of triangle ABC is 23.5 square units and the perimeter is 20.4174 units.

To find the area and perimeter of the given triangle ABC, we need to apply the following formulas:Formula for Distance between two points:

The distance between two points (x1, y1) and (x2, y2) is given by:

AB = √(x2-x1)²+(y2-y1)²BC = √(x3-x2)²+(y3-y2)²AC = √(x3-x1)²+(y3-y1)²

Formula for Area of Triangle: If we know the length of the three sides of a triangle then,

using Heron's formula, we can calculate the area of the triangle as:

area = √s(s-a)(s-b)(s-c)where a, b, and c are the lengths of the sides of the triangle and s is the semi-perimeter of the triangle, which is given as s = (a+b+c)/2

Formula for Perimeter of Triangle: The perimeter of the triangle is the sum of the lengths of its sides.

That is: perimeter = AB + BC + ACArea of ΔABCAB

= √(1 - (-2))² + (5 - (-4))²AB

= √3²+9² = √90BC

= √(2 - 1)² + (2 - 5)²BC

= √1²+3² = √10AC

= √(2 - (-2))² + (2 - (-4))²AC

= √4²+6²

= √52Semi-Perimeter (s)

= (AB + BC + AC)/2

= (√90 + √10 + √52)/2

= 12.8572Area of ΔABC

= √s(s-a)(s-b)(s-c)

= √12.8572(12.8572-√90)(12.8572-√10)(12.8572-√52)

= 23.5

Perimeter of ΔABC = AB + BC + AC = √90 + √10 + √52 = 20.4174

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Answer:

Subtraction property of equality

Step-by-step explanation:

Given the equation;

2x + (x+5) = 41

open the parenthesis;

2x+x + 5 = 41 (Associative property)

3x+5 = 41

Subtract 5 from both sides

3x + 5 = 41

3x + 5- 5 = 41 - 5 (Subtraction property of equality)

3x = 36

Divide both sides by 3;

3x/3 = 36/3

x = 12 (Division property of equality)

Hence the required property is Subtraction property of equality

Answer:

62cm

Step-by-step explanation:

You were told the perimeter of the triangle is 38

but two sides are added to make a Pentagon. and that Pentagon is made up of a triangle and a square.

so if we find the side of the square, we can equally get the other two sides of the triangle.

hint: (because it's a square, we would be getting an isosceles triangle, meaning two sides are equal)

because one side of the pentagon added to the other two sides of the triangles gives us the perimeter of the triangle.

we first find the sides of the square with all sides equal by diving by 2

\( \frac{48}{2} = 12\)

the sides of the square making the perimeter of the square 12cm.

now we subtract 12 from the perimeter of the triangle 38

\(38 - 12 = 26\)

now that we have gotten one side we can get the other two by dividing the result by 2

\( \frac{26}{2} = 13\)

so the other two sides of the triangle are 13cm.

now since we have the sides of the square and the triangle, we can find the perimeter of the pentagon by adding.

all the sides of the triangle without the base which is also the top of the square.

so instead of adding 4 times of 12, we add 3 times of 12 and 2 times of 13.

3(12)+2(13) = 62

or

12 + 12 + 12 + 13 + 13 = 62cm

Answer:

Bryce is 10 years old

Step-by-step explanation:

The age of Brice is given by B = 10 years old

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as B

Now , the value of B is

Substituting the values in the equation , we get

The age of Aida = 15 years

The age of Brice = 5 years younger than Aida

On simplifying the equation , we get

So , age of Brice = 15 - 5 = 10 years

The age of Henry = three years younger than Aida

So , the age of Henry = 15 - 3 = 12 years

Hence , the age of Brice is 10 years old

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The bell-shaped curve, also known as a Gaussian curve or a symmetrical distribution , showcases a central peak with data symmetrically distributed around it .

Revered for its iconic shape, the bell curve enchants the discerning observer with its symmetrical countenance, reminiscent of a resonant chime.

This majestic distribution unveils its true essence through its discernible apex, a testament to central tendency , where the mean, median, and mode converge, bestowing upon it an air of distinction .

The rough sketch of the curve having the bell shape is shown attached to the question.

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Answer:

arithmitic

Step-by-step explanation:

Answer:

i think its 3 im not sure

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30/30

→ [ x = -1 ]

Hence, the value of x is -1.

Answer:

The equation of the tangent line

\(y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )\)

Step-by-step explanation:

Step(i):-

Given function y = x cot (x) ....(i)

Differentiating equation (i) with respective to 'x' , we get

\(\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)\)

Step(ii):-

The slope of the tangent line

\(\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x\)

\((\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}\)

We will use trigonometry formulas

\(Cosec(\frac{\pi }{4} ) = \sqrt{2}\)

\(sec(\frac{\pi }{4} ) = \sqrt{2}\)

\(Cot(\frac{\pi }{4} ) = 1\)

Now the slope of the tangent

\(\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1\)

\(\frac{dy}{dx} =-\frac{\pi }{2} +1\)

Step(iii):-

Given

Substitute \(x=\frac{\pi }{4}\) in y = x cot (x)

               \(y = \frac{\pi }{4} cot (\frac{\pi }{4} )\)

              \(y = \frac{\pi }{4}\)

The point of the tangent line  \((x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )\)

The equation of the tangent line

\(y - y_{1} = m ( x - x_{1} )\)

\(y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )\)

The value of x is 2√14 mi

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore, if a and b are the legs of the triangle and c is the hypotenuse, then

c² = a²+b²

here, x and 5 are the legs and 9 is the hypotenuse of the triangle.

therefore;

x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = √4×14

x = 2√14

Therefore the value of the Missing side is 2√14 mi

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X intercept: 10/5

Y intercept: 0

To find the intercepts of a linear equation, you need to set either the X or Y variable to 0 and then solve for the other variable.

For example, if you have the equation 5x - 2y = 10, you can set X equal to 0 and solve for Y to find the Y intercept, or you can set Y equal to 0 and solve for X to find the X intercept.

X Intercept:

To find the X intercept, set Y equal to 0 and solve for X.

5x - 2(0) = 10

5x = 10

x = 10/5

X intercept = 10/5

Y Intercept:

To find the Y intercept, set X equal to 0 and solve for Y.

5(0) - 2y = 10

-2y = 10

y = -10/2

Y intercept = 0

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Answer:

3:7

Step-by-step explanation:

thats the ratio simplified

Answer:

12:16

Step-by-step explanation:

Answer:

a) lilla has 1/5 of the book left to read

b) lilla has 15 pages left to read

Step-by-step explanation:

a) 1/5 + 3/5 = 4/5

b) 75÷ 5= 15

15× 4= 60

75-60= 15

The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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(a) The probability that the top card is an ace or a king is \($\frac{2}{13}\)

(b) The probability that the top card is spades and the second card is clubs is \($\frac{1}{2652}\)

(c) The probability that the top card is spades and the second card is an ace is \($ \frac{1}{663}\)

(d) The probability that the top 3 cards are all spades is \($\frac{1}{132600}\)

(e) The probability that the top 4 cards include 3 different ranks, with one rank appears twice is \($\frac{2}{925}\)

As per the data given:

A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.

a) The probability that the top card is an ace or a king:

The probability that the top card is an ace \($\frac{4}{52} = \frac{1}{13}\)

The probability that the top card is an king \($\frac{4}{52}=\frac{1}{13}\)

The probability that the top card is an ace or a king is \($\frac{1}{13} +\frac{1}{13} =\frac{2}{13}\).

b) The probability that the top card is spades is \($\frac{1}{52}\)

Already a card is drawn then the probability that the second card is clubs is \($\frac{1}{51}\)

The probability that the top card is spades and the second card is clubs is \($\frac{1}{52}\times\frac{1}{51} = \frac{1}{2652}\)

c) The probability that the top card is spades is \($\frac{1}{52}\)

Already a card s drawn then the probability that the second card is an ace is \($\frac{4}{51}\)

The probability that the top card is spades and the second card is an ace  is \($\frac{1}{52}\times\frac{4}{51} = \frac{4}{2652} = \frac{1}{663}\)

d) The probability that the top 3 cards are all spades is \($\frac{1}{52}\times\frac{1}{51}\times\frac{1}{50} = \frac{1}{132600}\)

e) There are C(52, 4) ways to choose 4 cards from the deck, and the 4 ways to choose the rank that appears twice.

So, the total number of ways to choose 4 cards with 3 different ranks and one rank appearing twice is 4 C(52, 4) = 4 × 270725.

The number of ways to choose the 4 cards such that they include 3 different ranks, with one rank appearing twice is 4  C(13, 2)  C(4, 2) = 672.

Hence, the probability is \($\frac{672}{270725} =\frac{2}{925}\)

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A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit. The deck is randomly arranged. What is the probability that

(a) the top card is an ace or a king.

(b) the top card is spades and the second card is clubs.

(c) the top card is spades and the second card is an ace.

(d) the top 3 cards are all spades.

(e) the top 4 cards include 3 different ranks, with one rank appears twice (for example, an ace of hearts, a 3 of clubs, a 3 of hearts, and a 7 of spades).

Answer:

total=$260 tax=$10

Step-by-step explanation:

total:

250x104%

= 250x1.04

=260

tax:

4%*250

=$10

Answer:

32778

Step-by-step explanation:

76543-43765=32778

Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

The proof is given as follows:

The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".

The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.

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The diagram of the required shaded region of the Venn representing the set of elements (A ∩ B)' ∪ C, created with MS Word, is attached.

A Venn diagram consists of circles or curved enclosures, representing sets, located in a universal set which is a rectangle.

The sdets shown in the Venn diagram = Set A, Set B, and Set C

The required region to be shaded in the Venn diagram = (A ∩ B)' ∪ C'

A ∩ B (A intersection B) is the set of elements common to both Set A and Set B

(A ∩ B)' (A intersection B) complement is the set of all elements which are not in the set of elements common to both Set A and Set B

(A ∩ B)' ∪ C (A intersection B)  comliment union C; The set of elements not in the intersection of Set A and Set B, but contains the elements in Set C

(A ∩ B)' ∪ C' (A intersection B)  comliment union C complement; The set of elements not in the intersection of Set A and Set B, but includes elements in the universal set, excluding all elements in the Set C.

The required shaded region is; A ∩ (B ∪ C)', B ∩ (A ∪ C)' and (A ∪ B ∪ C)'

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The reflection of the point (–4, 6) across both axes is (b) (4, -6)

From the question, we have the following parameters that can be used in our computation:

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

Using the above as a guide, we have the following:

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Answer:

H

Step-by-step explanation:

Answer:

H. 3.9

Step-by-step explanation:

5.6 - 1.7 = 3.9

Answer:

140 ft³

Step-by-step explanation:

imagine the prism is standing on one of its triangular sides.

then it becomes a regular object with the volume

base area × height

the base area is the area of the triangle

baseline × inner height / 2

in our case

4 × 7 / 2 = 14 ft²

so for the volume we have

14 × 10 = 140 ft³

Answer:

70

Step-by-step explanation:

1+9+40-40+40+10*2

----------------------- 20

10+40-40+40+20

50 (-40+40 cancels out to 0) +20

50+20= 70

(Following PEMDAS)

Multiply, add, subtract.

if you were to instead go through it left to right, you would get 120, which is incorrect.

The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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