Area of perimeter of composite figures puzzle question C

Answer:

x = -30

Step-by-step explanation:

25 = -7 (x+5) +5x            expand brackets

25 = -7x -35 +5x             simplify

25 = -2x -35                    add 35 to both sides

60 = -2x                          multiply by sides by -1

-60 =2x                           divide by 2

x =-30

Answer:

-30

Step-by-step explanation:

25= -7x-35+5x

25+35= -2x

60= -2x both side by -2

-30=x

The length of the hypotenuse of the isosceles right triangle is 2.8 inches.

An isosceles right triangle is a right triangle with two equal sides. In this case, the two equal sides are each 7 8 inches long.

To find the length of the hypotenuse, we can use the Pythagorean theorem:

a^2 + b^2 = c^2, where c is the length of the hypotenuse

In this case, a = b = 7/8 inches, so:

(7/8)^2 + (7/8)^2 = c^2

(49/64) + (49/64) = c^2

98/64 = c^2

c = sqrt(98/64) inches

To the nearest tenth, c = 2.8 inches, so the length of the hypotenuse of the isosceles right triangle is 2.8 inches.

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This graph above portraiture the linear equation

The approximate area that Poseidon is searching is given as follows:

64.13 square units.

The area of a triangle is given by half the multiplication of the base length by the height.

The coordinates of the vertices of the triangle in this problem are given as follows:

(-6,1), (4,-5) and (-1,9).

Any of the three sides can be chosen as the base, and we use the equation for the distance between two points to obtain it's length.

Choosing vertices (-6,1) and (4,-5) as the base, it's length is given as follows:

b = sqrt((4 - (-6))² + (-5 - 1)²)

b = 11.66.

The midpoint of the base has the coordinates given as follows:

The height is the distance between the vertices (-1,-2) and (-1,9), hence, as they have the same x-coordinate, the height is given as follows:

h = 9 - (-2)

h = 11.

Then the area is given as follows:

A = 0.5 x 11.66 x 11

A = 64.13 square units.

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The side lengths x and y are √( 50² - y²) and √50² - x² respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In a right angle triangle, the length of one side can be determined using the Pythagorean theorem:

x² + y² = hypotenuse²

In the given triangle the length of hypotenuse is 50 cm

x² = 50² - y²

x=√( 50² - y²)

y = √50² - x²

Hence, the side lengths x and y are √( 50² - y²) and √50² - x² respectively.

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Answer:east

Step-by-step explanation:

north: LOW:-8F    HIGH:10F  this have the most change

+18F

south: LOW:-3F     HIGH:2F    this have the third most change

+5F

east: LOW:-2F    HIGH:0F    this have the least change

+2F

west: LOW:-4F    HIGH:3F    this have the second most change

+7F

the east only have +2F so it have the least change

The answers for the asked probabilities are a) 1/6, b) 5/36, c) 1/36 and d) A and B events are not independent.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, Antonia rolls a pair of fair six-sided dice. A is the event that the first die lands on 5 and B is the event that the sum of the two dice is 6.

Probability = possible outcomes / favorable outcomes

Suppose that Antonia rolls a pair of fair six-sided dice.

All possible outcomes are:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

(36 outcomes in total)

a) A = the first die lands on 5

Favorable outcomes:

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6 outcomes)

Therefore, the probability that the first die lands on 5 = P(A) = 6/36 = 1/6

b) B = the sum of the two dice is 6

Favorable outcomes:

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = (5 outcomes)

Therefore, the probability that the sum of the two dice is P(B) = 6 = 5/36

c) A∩B = the first die lands on 5 and the two dice add up to 6

Favorable outcomes:

(5, 1) = 1 outcome

Therefore, the probability that the first die lands on 5 and the two dice add up to6 = P(A∩B) = 1/36

d) Two events are independent when;

P(A∩B) = P(A) · P(B)

Since,

1/36 ≠ 5/36 · 1/36

Therefore, A and B events are not independent.

Hence, the answers for the asked probabilities are a) 1/6, b) 5/36, c) 1/36 and d) A and B events are not independent.

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The measures of the angles X, Y, and Z are 5, 50, and 125 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that in ∆XYZ, the measures of angles X, Y, and Z, respectively, are in the ratio 1:10:25.

We have to find the measure of each angle.

Let the measures can be expressed as 1x, 10x, and 25x, respectively, where x is an arbitrary value.

We know that the sum of the angles of a triangle is always 180 degrees, so:

1x + 10x + 25x = 180

36x = 180

Divide both sides by 36

x = 5

Therefore, the measures of the angles X, Y, and Z are 5, 50, and 125 degrees.

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Answer:

yes

Step-by-step explanation:

Taylor will get an offer for a free trip as within two hours (10 - 12) even before the end of the midnight show, he got the required views.

from 10: to 10:20

1 : 3

3: 3 in every five minutes i.e. 10:25, 10:30, 10:35 n so on

1: 30 in every four minutes

till 11:32

from 11:32 till 12:00

the views recorded till now doubles every three minutes!!

42 feet is the length of the guy wire.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that a pole 10 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground.

After placing the pole, Liam measures the distance from the pole to the stake and from the pole to the tower.

We have to find the length of the guy wire

Let the required distance is x and the height of the tower is t.  

Use similar triangle ratios to find the value of t:  

t / 10 = (9 + 3) / 3

t / 10 = 4

t = 40 feet

Use Pythagorean to find the value of x:  

x² = 40² + (9 + 3)²

x² = 1600 + 144

x² = 1744

x = √1744

x = 42 feet

Hence, 42 feet is the length of the guy wire.

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a. The total of the two sides of the right triangle using Algebraic expression is 3x²+7x-4.

b. The length of the missing side of the triangle is 3x³-4x²-15x+5.

c. If the value of x=2, then the length of the three sides of the triangle is

   a=11, b=11 and c= -17.

d. No, it is not possible to have these side lengths for a right triangle.

Algebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them. These symbols are referred to as variables because they don't have predetermined values. These values are usually represented in algebra by variables, which are symbols like x, y, z, p, or q. These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.

a. Let the sides of the right triangle be a, b and c.

Given, one side of the triangle is 2x² + 2x - 1 and

another side is 5x + x² -3.

So, let a = 2x²+2x-1 and b = 5x+x²-3

Now, the total of the two sides= a+b

          a+b

         =2x²+2x-1 + 5x+x²-3

         = 3x²+7x-4

Therefore, the total of the two sides of the right triangle = 3x²+7x-4.

b. Now the perimeter of the triangle is given= 3x³-x²-8x+1.

Given, a+b+c=3x³-x²-8x+1.

We already have a+b, so by simplifying the equation a+b+c=3x³-x²-8x+1

we can find the length of the third side, c.

a+b+c= 3x³-x²-8x+1

⇒3x²+7x-4 +c= 3x³-x²-8x+1

⇒c= 3x³-x²-3x²-8x-7x+1+4

⇒c= 3x³-4x²-15x+5.

Therefore, length of the missing side is 3x³-4x²-15x+5.

c. We have the three sides of the triangle with us which are:

a = 2x²+2x-1

b = 5x+x²-3

c = 3x³-4x²-15x+5

Now putting the value of x as 2 in the equations as follows:

a= 2(2²) +2(2)-1

 = 8+4-1

 =11

b=5(2) +2²-3

 = 10+4-3

 =11

c=3(2³)- 4(2²) -15(2) +5

 =24-16-30+5

 = -17

Therefore, the length of the three sides of the right triangle

are 11, 11 and -17.

d. The sides of the right triangle are.

a = 11

b = 11

c = -17

We know as per the Pythagorean theorem c² = a² + b².

Accordingly, c²= 289 & a² = 121 and b²= 121, a² + b²= 242

which shows that c² is not equal to a² + b².

As, the sides of the triangle does not follow the Pythagorean theorem, so these are not the sides of a right-angle triangle.

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Answer:

d

Step-by-step explanation:

d

Sofie will not make a profit if she sells her scarves for $5 or less.

The maximum profit Sofie can make is $200.

A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line.

According to the given problem,

y = (x - 5)(50 - 2x)

⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)

⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)

⇒ y - (x - 5)(-2x + 50) = 0

⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0

⇒ y - ( -2x² + 50x + 10x - 250) = 0

⇒ y - ( - 2x² + 60x - 250 ) = 0

⇒ y + 2x² - 60x + 250 = 0

⇒ 2x² -60x + y + 250 = 0

⇒ ( 2x² - 60x ) + y + 250 = 0

⇒ 2 ( x² - x) + y + 250 = 0

⇒ 2 ( x² - x) + y + 250 = 0

⇒ 2 ( x² - 30x ) + y + 250 = 0

⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0

⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0

⇒ 2( x - 15 )² + y = -2(-225) - 250

⇒ 2( x - 15 )² + y = 450 - 250

⇒ 2( x - 15 )² + y = 200

⇒ y = -2( x - 15 )² + 200

This equation is in the form of y =  a(x - h)² + k where the vertex of the parabola is (h , k).

Therefore the vertex of the parabola is at (15 , 200)

Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.

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Answer:Second option ( $8.04)

Step-by-step explanation:

Answer:

A cup

Step-by-step explanation:

Because a pint is smaller than a cup look it up it's true

With the value tanθ = 4/3 on the interval (π, 3π/2), using trigonometric identities sin 2θ = 24/25 , cos 2θ = -7/25 , tan 2θ = -8/7.

First, we'll find sin 2θ:

sin 2θ = 2sinθcosθ

We can use the identity tanθ = sinθ/cosθ to find sinθ and cosθ:

sinθ = 4/5 and cosθ = 3/5

So,

sin 2θ = 2(4/5)(3/5) = 24/25

Next, we'll find cos 2θ:

cos 2θ = cos^2θ - sin^2θ = 1 - 2sin^2θ

Using the values of sinθ and cosθ that we found earlier:

cos 2θ = 1 - 2(4/5)^2 = 1 - 32/25 = -7/25

Finally, we'll find tan 2θ:

tan 2θ = (2tanθ)/(1 - tan^2θ)

Using the value of tanθ that we were given:

tan 2θ = (2(4/3))/(1 - (4/3)^2) = (8/3)/(-7/9) = -8/7

So, the values of sin 2θ, cos 2θ, and tan 2θ are:

sin 2θ = 24/25

cos 2θ = -7/25

tan 2θ = -8/7

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Answer: 1

Step-by-step explanation: The Distributive Property is nothing to get confused about. It is simply just a multiplication rule. Follow out the steps in this problem in order. 1/3 * 6 = 2. 2 * 1/2 = 1, and there you go! If this helped, please consider giving this a brainiest as I am one away from the next rank!

Answer: 2

Step-by-step explanation:

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

9.3 × 3.5 / 2 = 16.275 ft²

as you can see, yes, really easy.

what was the problem ? do you need any further explanation ?

Answer:

3.19

Step-by-step explanation:

5.5% of 58 is 3.19

and is you need it,

58 - 3.19 = 54.81

I believe this is right

the sales tax on $58 at a rate of 5.5% is $3.19

How to find the tax on $58 at a rate of 5.5%?

Taxes are a mandatory contribution to the state. So sales must pay taxes, and it is stated that the rate of tax that must be paid is 5.5%

The way to calculate tax from sales is to multiply the tax rate by the income from sales.

the income = $58

the rate of tax = 5.5%

the tax to be paid by sales = the income x the tax

                                             = $58 x 5.5%

                                             = $3.19

so the answer to the question is $3.19

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Answer:

I think it's c sorry if im wrong

Answer:

x³ - 3x² + 5x - 6

Step-by-step explanation:

      1) (2x + y)(4x - 9) = 2x*(4x - 9) + y(4x - 9)

                                 = 2x*4x - 2x*9 + y*4x - y *9

                                = 8x² - 18x + 4xy - 9y

2) (3x + 5y)²

Identity : (a + b)² = a² + 2ab + b²

a = 3x and b = 5y

(3x +5y)² = (3x)² + 2 * 3x *5y + (5y)²

               = 9x² + 30xy + 25y²

3) (x -2)(x² - x + 3) = x*(x² - x + 3) - 2(x² - x + 3)

                             =x*x² - x*x + x*3 -2*x² + 2*x - 2*3

                            = x³ - x² + 3x - 2x² + 2x - 6

                            =x³ - x² - 2x² + 3x + 2x - 6

Combine like terms. Like terms have same variable with same exponent.

                           = x³ - 3x² + 5x - 6

Step-by-step explanation:

Пісяжлшорркгашанргчгаппаппвмсап

Answer:

a. To find the annual net income, subtract the annual expenses from the annual rental income.

The annual rental income = $750 * 12 months = $9,000

So, the annual net income = $9,000 - $6,890 = $2,110

b. To find the annual yield, divide the annual net income by the investment cost (the down payment) and multiply by 100 to get the answer as a percentage.

The annual yield = ($2,110 / $28,500) * 100 = 7.41%

c. To find the monthly rent required to get a yield of 90%, divide the investment cost by the desired yield and divide by 12 to get the monthly rent.

The investment cost = $28,500

The desired yield = 0.90

So, the monthly rent = ($28,500 / 0.90) / 12 = $2,306.25

Step-by-step explanation:

Answer: x=3

Step-by-step explanation:

divide by the common factor 3

3x ÷ 3 = x

9÷3 = 3

hence the reason we get x=3

Answer: 3

Step-by-step explanation:

To solve for x, you need to divide 9 by 3 which equals 3.

Since 3x = (3 ⋅ 3), x = 3.

Answer:

They are not equal

  one is  -1 times  the other   answer C

Step-by-step explanation:

for t =2     15.8t - 3.8t = 24

                    3.8t - 15.8t =  - 24

Answer:

C, 24, and -24

Step-by-step explanation:

Step 1a) No, so C

Step 1b) 15.8(2)- 3.8(2)

Step 2b) 31.6 -7.6

Step 3b) 24

Step 1c) 3.8(2)- 15.8(2)

Step 2c) 7.6 -31.6

Step 3c) -24

Answer:

[tex]y=4(x-7)^2-196[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]y=4x^2-56x[/tex]

Factor out the coefficient of the term x²:

[tex]y=4(x^2-14x)[/tex]

Add and subtract the square of half the coefficient of the term in x inside the brackets:

[tex]y=4\left(x^2-14x+\left(-\dfrac{14}{2}\right)^2-\left(-\dfrac{14}{2}\right)^2\right)[/tex]

Simplify:

[tex]y=4\left(x^2-14x+\left(-7\right)^2-\left(-7\right)^2\right)[/tex]

[tex]y=4\left(x^2-14x+49-49\right)[/tex]

Factor the perfect square trinomial created by the first three terms inside the brackets:

[tex]y=4\left((x-7)^2-49\right)[/tex]

Distribute:

[tex]y=4(x-7)^2-196[/tex]

The equation is now in vertex form y = a(x - h)² + k, where (h, k) is the vertex of the parabola (turning point).

Compare the equation with the vertex formula to identify the values of h and k:

Therefore, the coordinates of the turning point (vertex) are (7, -196).

The volume of larger solid represented by b is 3125.

The scale factor of two solids will be equal to the following formula -

volume of solid a/volume of solid b = solid a³/solid b³

Keep the values in formula to find the volume of solid b

200/ volume of solid b = 2³/5³

Rewriting the equation according to volume of solid b

Volume of solid b = 5³ × 200/2³

Performing multiplication with cube of 5

Volume of solid b = 125 × 200/8

Volume of solid b = 25000/8

Performing division on Right Hand Side of the equation

Volume of solid b = 3125

Hence, the volume of solid b is 3125.

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Given all sides are right angles, the height of the sides are equal.

left side = 12

right side = x+5

set equation equal to each other and solve for x.

12 = x +5 =>> 12-5 = x =>> x = 7

x = 7 cm

The distance between the points A and B is 209.4 feet

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12°. Let a represent distance from point A to light house:

tan(12) = 107/a

a = 503.4 feet

They measure the angle of elevation a second time from point B at some later time to be 20°. Hence, if b represent distance from point A to light house:

tan(20) = 107/b

b = 294 feet

Distance from point A to B = 503.4 feet - 294 feet = 209.4

The distance between the points is 209.4 feet

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6

Hope This Helps!

P2 = 90; 10P2 = 90. Combinations. There are also two types of combinations

Answer:

P(3, 2) = 6

Step-by-step explanation:

A permutation is an ordered combination, i.e. an arrangement in a definite order of a number of objects taken some or all at a time.

[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]

where:

Given P(3, 2):

So we need to calculate the permutations of two numbers taken from three numbers.

The numbers are 1, 2 and 3.  As order matters, the number of ways two numbers from this set can be arranged is:

Therefore, there are 6 ways two numbers from the set of three numbers can be arranged.

To prove this, substitute n = 3 and r = 2 into the permutation formula:

[tex]\begin{aligned}\implies P(3,2)&=\dfrac{3!}{(3-2)!}\\\\&=\dfrac{3!}{1!}\\\\&=\dfrac{3 \times 2 \times 1}{1}\\\\&=\dfrac{6}{1}\\\\&=6 \end{aligned}[/tex]

Therefore, P(3, 2) = 6.