given that у=6 cm and θ=15 °, work out x rounded to 1 decimal place.

(the diagram is not drawn to scale.)

Answer: 80

Step-by-step explanation:

We can use the formula [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals.

By the distance formula,

[tex]AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}[/tex]

So, the area is [tex]\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}[/tex]

Answer:

30°

Step-by-step explanation:

This right triangle has :

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

Solving :

We know the angle sum of a triangle is 180°.

⇒ x + 90° + 60° = 180°

⇒ x + 150° = 180°

⇒ x = 30°

We know the angle sum of a triangle is 180° so

= 180°

= 180°

⇒x = 30°

[tex]\boxed{\blue{ » \: Lear \: math \: with \: Kareninajovanka \: « コ:彡}}[/tex]

The probability of picking two snacks of the same type is 0.308.

The probability of picking 2 potato will be:

= 6/14 × 5/13

= 0.429 × 0.385

= 0.165

The probability of picking 2 doritos will be:

= 5/14 × 4/13

= 0.357 × 0.308

= 0.110

The probability of picking 2 corn curls will be:

= 3/14 × 2/13

= 0.214 × 0.154

= 0.033

Therefore, the probability of picking two snacks of the same type will be:

= 0.165 + 0.110 + 0.033

= 0.308

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The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7​ is given in the image attached.

This is known to be that which is created by two part that are known to give the latitude and longitude position of a person or place.

Therefore, The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7​ is given in the image attached.

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The area of the entire rectangle is 4x² + 12x + 8

The given parameters are:

height = 4

Width = x² + 3x + 2

The area of the rectangle is:

Area = Width * Height

So, we have:

Area = (x² + 3x + 2) * 4

Expand

Area = 4x² + 12x + 8

Hence, the area of the entire rectangle is 4x² + 12x + 8

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The error interval for the length of the piece of wood is 293.5 ≤ length < 294.5

Error Interval can be defined as the limit of Accuracy when a number has been truncated.

It is given that the length of the piece of wood is 294 cm truncated to the nearest centimeter.

To determine the error interval for the length of the piece of wood

length ≥ 293.5

length < 294.5

293.5 ≤ length < 294.5

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The tension in the cable is given by the newton's first law will be 163.622 N.

The summation of the force is equal to zero.

The formula is given as

ΣF = 0

Where m is the mass of the body and a is the acceleration.

A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam.

Then the tension in the cable will be

Let T be the tension in the cable.

T sin 29° + T sin 53° – 210 = 0

On simplifying, we have

T (sin 29° + sin 53°) = 210

                             T = 163.622 N

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Answer:

Step-by-step explanation:

the number that is 45% greater than 90 is :

[tex]90+90\times \frac{45}{100} = 90 + 40.5 = 130.5[/tex]

Answer:

2nd option

Step-by-step explanation:

the recursive rule is

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( d is the common difference )

use the explicit rule to find a₁ and d

a₁ = 48 - 11(1) = 48 - 11 = 37

a₂ = 48 - 11(2) = 48 - 22 = 26

then

d = a₂ - a₁ = 26 - 37 = - 11

recursive rule is then

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 11

a₁ = 37

Answer:

the arrows and dots show where

Hey there!

Look at your graph… then look at your points (the green dots) and it should be there.

Your x-values are across (just think of its saying “East” and ”West”) & your y-values are up and down (just think of it as “North” and “South”)

So, based on that that information:

ANSWER:

Your x-value would be: -1 because the point landed on it whereas the y-value would be: 5 because the point landed on it.

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 247 the Answer

Answer:

see the attachment photo!

Answer:

$ 8874.11 after 5 years

Step-by-step explanation:

 Each year it is worth 85 % of its value

20 000 ( .85)^5 = 8874.11

The value of x so that lines s and t are parallel is 12

The angle are alternate exterior angles.

Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.

Hence,

7x - 20 = 4x + 16

7x - 4x= 16 + 20

3x = 36

x = 36 / 3

x = 12

Therefore, the value of x is 12.  

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The marketing team conclusion that someone between 18 and 24 years of age is more likely never to have flown on a commercial airliner than someone 25 years or older is true based on the percentage.

The percentage for someone between 18 and 24 years of age to have flown on a commercial airline will be:

= 216/279 × 100.

= 77.4%

The percentage for someone that is 25 years older to have flown will be:

= 2210/2988 × 100

= 74%

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A box plot has 5 data descriptions. The correct option is 87 and 132.

A box plot has 5 data descriptions.

Since each quartile of the box-and-whisker plot represents 25% of the data. Therefore, values between which there are 3 quartiles present will represent 75% of the data.

Hence, the correct option is 87 and 132.

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Answer:

all real numbers greater than or equal to 10,000 and less than or equal to 20,000

Step-by-step explanation:

ye

The area of the Rhombus is 162√3 sq.unit , Option A is the correct answer.

A rhombus is a polygon , which has four equal sides , its diagonal bisect each other at 90 degree.

Let x be the half of the other diagonal.

tan 60 = x / 9

x = 9 tan 60

x = 9√3

Area of the Rhombus = (d1 * d2 /2 )

d1 and d2 are the length of the diagonal.

Area of the Rhombus = (9*2)(2 *9√3)/2

Area of the Rhombus =162√3 sq.unit

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Step-by-step explanation:

Solve the following equation for x.

10 = 2 – 4(ar – 3)

OA. -

a

OB.

Oc.

OD.

5

a

The equation for the (x-4)²2 is  5. x=4± √5. Hence, option D is correct.

Due to the fact that they contain two or more algebraic terms, quadratic equations fall within the category of polynomial equations. It must equal 0 in order to solve a quadratic equation. There can be zero, one, or two (true) solutions to a quadratic equation.

To solve the equation (x - 4)² = 5, we can start by taking the square root of both sides:

√[(x - 4)²] = ±√5

This gives us two possible equations:

x - 4 = √5 or x - 4 = -√5

Now it can add 4 to both sides of each equation:

x = 4 + √5 or x = 4 - √5

So the solutions to the equation (x - 4)² = 5 are x = 4 + √5 and x = 4 - √5.

Thus, option D is correct.

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The given equation is wrong, the correct equation is given below-

(x-4)²2 = 5.

The equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4

The correct formats of the equations are:

y = 3x^5 - 5x^3 + 2x^2 - 10x + 4

y = 4x^4 + 6x^3 - 11

To determine the equation, we substitute 4x^4 + 6x^3 - 11 for y in the first equation.

So, we have:

4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4

Hence, the equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4

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[tex]2x^6y^2[/tex]The equivalent expression to the given expression is [tex]2x^6y^2[/tex] (option D)

An expression in mathematics is a fusion of numbers, variables, and operators that embodies a mathematical entity. Expressions possess the ability to symbolize magnitudes, functions, and connections, exhibiting versatility and finesse.

Expressions are used in many different areas of mathematics. They are used to represent quantities, functions, and relationships.

To determine the given expression, lets start:

[tex](12x^9y^4)/(6x^3y^2)[/tex]

= [tex](12/6) x^(^9^-^3^) y^(^4^-^2^)[/tex]

= [tex]2x^6y^2[/tex]

Therefore, the equivalent expression to [tex](12x^9y^4)/(6x^3y^2)[/tex] is [tex]2x^6y^2[/tex]

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[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

Work Shown:

2/5 - 1/3

6/15 - 5/15

(6-5)/15

1/15

Here are two ways to check the answer:

Hi Student!

Looking at the problem statement and them just asking for us to determine the difference between two numbers seems like an easy task.  The first thing that we must do is to find a common denominator so we subtract them otherwise we can not since the denominators are different.

The denominators of the fractions are 5 and 3 and we know that they both multiply up to 15 so that can be our common denominator.

Convert to common denominator

Subtract

Therefore, the final answer to the question asking the difference between 2/5 and 1/3 would be 1/15.

Answer:

u=30

x=150

z=150

y=30

Step-by-step explanation:

u=y [ being vertically opposite angle]

x+u=180[ being linear pair]

x+30=180

x=180-30

x=150

z=x[being vertically opposite angle]

z=150

y=u[ being voa]

Answer:

=40°

Step-by-step explanation:

Sorry that's all I know

^keep safe^

The number of grams of canned apple that Chantel needs for her apple-cinnamon cake is about 1400 grams.

To know the amount of canned apple that Chantel needs for her apple and cinnamon cake recipe, we must review the amount of apple that she needs for the filling of her cake.

According to the basic recipe to make this cake, we need 6 to 8 apples. Taking into account that each apple weighs about 200g, we can infer that Chantel is going to use about 1400g of canned apple as shown below.

On average we need 7 apples.

Each apple weighs 200g, so 7 apples would be 1400g.

Based on the above, Chantel needs 1400g of canned apple.

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Answer:

a = 6

Step-by-step explanation:

g(x) = 5x - 2

h(x) = √(x + 3)

g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2

g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2

5[tex]\sqrt{a+3}[/tex] - 2 = 13

5[tex]\sqrt{a+3}[/tex] = 15

[tex]\sqrt{a+3}[/tex] = 3

( [tex]\sqrt{a+3}[/tex] )² = 3²

a + 3 = 9

a = 6

Answer:

(5.5, 5 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (8, 2 ) and (x₂, y₂ ) = B (3, 8 ) , then

midpoint = ( [tex]\frac{8+3}{2}[/tex] , [tex]\frac{2+8}{2}[/tex] ) = ( [tex]\frac{11}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = (5.5, 5 )

Answer:

a = z/mb

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z=mab}[/tex]

To solve for a, divide both sides by the variables mb to isolate a-term.

[tex]\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}[/tex]

Simplify the expression and we finally have solved for a-term.

[tex]\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}[/tex]

Therefore, the answer to this question is a = z/mb.

Please let me know if you have any questions regarding my answer or explanation!