What is the result when 2a - 5 is subtracted from 3a + 3?

The length of the incline of the ramp will be [h] = 12.0415 ft

According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -

h² = p² + b²

Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.

From the data given, we can consider the ramp construction as right angled triangle. We can write -

base [b] = 12 ft

height [p] = 1 ft

Using the Pythagoras theorem -

h² = (12 x 12) + (1 x 1)

h² = 144 + 1

h = √145

h = 12.0415

Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft

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Answer:

The value of x is 65 degrees.

Explanation:

To solve for x, we use the formula for an angle formed by a tangent and a secant.

Next, solve the equation for x:

The value of x is 65 degrees.

Answer:

Tip- $5.16

Total cost- $33.86

Step-by-step explanation:

To find a 18% tip, turn 18% into 0.18.

Multiply 28.67 by 0.18.

28.67x0.18=

5.16

If you add that to the bill, it would be 33.86

Answer:

A. 1/6 would be the answer I think

Take into account the following property:

Then, for the given expression you have:

Hence, the answer is approximately 3.322

3) [tex]\angle BCA \cong \angle CAD[/tex] (alternate interior angles theorem)

4) [tex]\triangle ABC \cong \triangle CDA[/tex] (AAS)

Answer:

where???????????????

Answer:

The answer is 8.27×10^4

Answer: 8.27×10^4

Step-by-step explanation:

Answer:

1) multiply and divide by 2 on right hand side

2) multiply by 24 on both sides ( LHS and RHS)

3) divide by -1 on both sides so that negative sign on RHS will be cancelled

Using a common factor, 20 - 4x³ can be rewritten as 4(5 - x³).

A common factor of two or more numbers is any number that the two numbers can be divided by and will leave no remainder.

For example, a common factor of 4 and 8 is 2. This is because:

2 into 4 will give us 2 without a remainder.

2 into 8 will give us 4 without a remainder.

To rewrite the expression, 20 - 4x³ using a common factor, find the factor that will go into each of the terms without a remainder.

4 into 20 will give us 5 without a remainder.

4 into 4x³ will give us x³ without a remainder.

Therefore, we can factor out the common factor from the expression to rewrite 20 - 4x³ as 4(5 - x³).

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Answer:

x = -5/2

Step-by-step explanation:

-15/2 = 3x

multiply both sides by 2:

2(-15/2) = 2(3x)

-15 = 6x

divide both sides by 6:

-15/6 = 6x/6

x = -15/6

this can be reduced to:

x = -5/2

The decay constant of a radioactive nuclide exists its probability of decay per unit time.

The half life of i 125 is 60 days exists 0.169 ml.

The decay constant of a radioactive nuclide exists its probability of decay per unit time. The number of parent nuclides P therefore decreases with time t as dP/P dt = −λ.

The ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.

The rate of decay is determined by the decay constant. The symbol for the decay constant is "lambda," or. The many diverse decay rates that have been seen may be caused by large variations in this constant probability among various types of nuclei.

Decay constant: [tex]$& \lambda=\frac{0.693}{t_{1 / 2}}[/tex]

Decay constant expressed in any unit of time

Such as reciprocal seconds, minutes, hours etc.

[tex]$\mathbf{N}=\mathrm{N}_o \mathrm{e}^{-\lambda t} \quad \lambda=\frac{0.693}{\mathrm{t}_{1 / 2}}$[/tex]

Half Life: [tex]$\quad t_{1 / 2}=\frac{0.693}{\lambda}$[/tex]

The half life of i 125 is 60 days exists 0.169 ml.

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In triangle  ABC, BC = 29 units.

Given,

In Δ ABC, ∠A = 45°.

A perpendicular line segment traced from a triangle's vertex to its opposite side is said to be the triangle's altitude.

Let altitude meet AB on D.

So, AD = 20 units and DB = 21 units and ∠ADC = ∠BDC = 90°

In ΔADC,

tan A = DC/AD

tan 45° = DC/20

          1 = DC/20

      DC = 20 units

In ΔBDC,

BC² = BD² + DC²     (Pythagorean Theorem)

      = 21²  + 20²

      = 441 + 400

      = 841

BC  = √841

      = 29  

Hence, BC = 29 units.

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About 50% of Americans households have a tv except  who live in low-income, single-parent, or disadvantaged homes

Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole

Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.

however, about 50% of Americans households have a tv

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Answer:

1) trinomial

2) binomial

3) binomial

4) trinomial

5) monomial

Step-by-step explanation:

Monomial: 1 term

Binomial: 2 terms

Trinomial: 3 terms

Terms are separated by plus and minus signs.

1) trinomial

2) binomial

3) binomial

4) trinomial

5) monomial

The east of the base is 6.3 km far from B.

The bearing of B, as measured from the base is 73°.

The base is 73° south vest of the B.

What is sin?

Sin is a periodic function with a period of 2π, and the domain of the function is (−∞, ∞) and the range is [−1,1]. Sin formula is used to find sides of a triangle.

Given, the distance between soldier and base is 3 km. and the bearing is 50°.

He then walked a further 4 km due east to point B.

1) the east of the base to point B = 3 sin 50° +4

= 6.3 km

2) The bearing of B is solved as

3(cos 50°) = 1.9km

then, bearing is 6.3/1.9

= 73°

3) the base is 73° south vest of the B

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Answer:

$32,000

Step-by-step explanation:

We have that:

then, in this case, we have:

therefore, the velocity of the cart is 0.9 meters per second.

The rule for the given function f /g when the function f(x) = -3x -6 and

g(x) = x² -x - 6 is identified as  f(x) / g(x) = -3 / (x -3).

As given in the question,

Given function are:

f(x) = -3x -6

g(x) = x² -x - 6

Rule to identify for the function f(x) / g(x) we get,

Substitute the value of f(x) and g(x) in the required rule we have,

f(x) / g(x) = (-3x -6 ) / ( x² -x - 6 )

Now simplify the function to get the rule:

f(x) / g(x) = -3(x+2) / (x² -3x +2x -6)

⇒ f(x) / g(x) = -3(x+2) /(x-3)(x+2)

⇒ f(x) / g(x) = -3 / (x-3)

Therefore, the rule for the given function f /g when the function f(x) = -3x -6 and g(x) = x² -x - 6 is identified as  f(x) / g(x) = -3 / (x -3).

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The triangles are similar. The smaller is isosceles, so the 3 of them are as well.

Let's Start by finding the hypotenuse of the smaller one:

a² = 2

EXPLANATION

Let's see the facts:

shoot = 20 feet

goal = 5 foot

Let's draw the statement:

Since we are finding the side opposite the given angle and know the side adjacent, we can use the Pythagoras Theorem to find the needed value.

Replacing terms:

Isolating x:

Switching sides and simplifying:

The player will not score because 5.4 is greater than 5

Hello! We can prove this with some statements, look:

• Notice that CD is parallel to AB;

• angle 1 ≅ angle 2

• M is the midpoint of AB;

Statement 1:

Reasoning 1:

As M is the midpoint of AB and we have two similar lines starting in M, we can divide the angle M into two equal angles m1 and m2.

definition of midpoint

Statement 2:

Reasoning 2:

As we already know that angle 1 ≅ angle 2, let's calculate the sum of the angles C and D, look:

angle C:

90º + angle 1

angle D:

90º + angle 2

so, 90º + angle 1 ≅ 90º + angle 2, it means that angle C ≅ angle D.

Statement 3:

Reasoning 3:

The sum of the internal angles of a triangle must be equal to 180º, right? So, knowing it we can say that angles A and B are equal, look:

m1 + A + C = m2 + B + D = 180º

remember, m1 ≅ m2 and C ≅ D, so A ≅ B too.

According to the explanation and image, we can prove that triangle CAM ≅ triangle DBM.

Table:

Answer:

Acute scalene triangle.

More Information:

Sides: a = 10   b = 11   c = 12

Area: T = 51.521

Perimeter: p = 33

Semiperimeter: s = 16.5

Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad

Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad

Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad

Height: ha = 10.304

Height: hb = 9.367

Height: hc = 8.587

Median: ma = 10.368

Median: mb = 9.579

Median: mc = 8.631

Inradius: r = 3.122

Circumradius: R = 6.405

Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]

Centroid: CG[5.708; 2.862]

Coordinates of the circumscribed circle: U[6; 2.242]

Coordinates of the inscribed circle: I[5.5; 3.122]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad

∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad

∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad

How to Solve:

The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

1. Input data entered: sides a, b, and c.

a=10

b=11

c=12

We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.

a=10

b=11

c=12

2. The triangle perimeter is the sum of the lengths of its three sides

3. Semiperimeter of the triangle

The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.

4. The triangle area using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

5. Calculate the heights of the triangle from its area.

There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.

6. Calculation of the inner angles of the triangle using a Law of Cosines

The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.

7. Inradius

An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

8. Circumradius

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

9. Calculation of medians

A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.

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We have the polynomial:

We have to factorize it.

We know that 216 is the cube of 6.

We then applied the property for the difference of cubes.

The answer is Option C.

Difference of cubes property:

x^3-y^3 = (x-y)(x^2+xy+y^2)

Explanation

Step 1

let x represents the numbers of days you can stay at the beach

then,

You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.

so

but, you have only $1200, so the total needs to be smaller or equal than 1200

Step 2

solve the inequality

it means you can stay maximum 6 days

I hope this helps you

Two parallel lines in the coordinate system share the same slope, this means that if you have two parallel lines:

For the given equations, the slopes are:

The slopes are different, so this lines are not parallel.

Two lines are perpendicular, when the slope of one of them is the negative inverse of the first one, this is for the perpendicular lines:

For the given equations, using y=17x-8 as reference, the slope of a line perpendicular to this one must be:

The slope of a perpendicular line to y=17x-8 is different from the slope of the second given line, so you can conclude that these lines are not perpendicular.

The correct choice is Neither

Given that April has 30 days, Luke used, on average, 20.05 kilowatt-hours of electricity per day during April.

The average is the mean value obtained by dividing the total value of a data set by the number of items.

In this situation, we can divide the total electric bill for April by 30 to obtain the average daily charge.

In addition, we can divide the average charge per day by the cost per kilowatt-hour to obtain the number of kilowatt-hours used per day.

The total electric bill for April = $84.21

The charge per kilowatt-hour (kWh) = $0.14

The number of days in April = 30

The bill per day = $2.807 ($84.21/30)

The kilowatt-hours per day = 20.05 kWh ($2.807/$0.14)

Thus, Luke used an average of 20.05 kilowatt-hours per day in April.

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Answer:

(if am not wrong)