The mixed number 1 1/2 is between which two numbers? 2 and 3 and 1 3 and 4 1 and 2

Answer:

Step-by-step explanation:

Directions

Draw a line from B to C. A can be anywhere above 132 degrees and it would have the same value as long as its endpoints are B and C

The actual value is 1/2 the central angle which is given as 132 degrees.

Givens

<BOC = 132 degrees.

<BOC is the central angle.

Solution

<BAC = 1/2 <BOC

<BAC = 1/2 132 degrees

<BAC = 66 degrees.

Answer

<BAC = 66 degrees

Answer:

4 hours

Step-by-step explanation:

Answer:

the answer is 4 HOURS

Step-by-step explanation:

i took the exam

In conclusion Equality in Euclidean geometry is determined by isometries - transformations preserving shape and size of geometric figures.

why it is?

In Euclidean geometry, equality is determined by the application of isometries. An isometry is a transformation that preserves the shape and size of a geometric figure. Examples of isometries include translations, rotations, and reflections.

When we say that Euclidean geometry relies on isometries for equality, we mean that two geometric figures are considered equal in Euclidean geometry if there exists an isometry that maps one figure onto the other. In other words, two figures are considered equal in Euclidean geometry if they can be transformed into each other using isometries.

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Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

Answer:

$21,038.28

Step-by-step explanation:

Use the equation 15000(1.07)^5 since 1.07 equals to 7% and you are loaning more money to Tony's account for 5 years.  You should get $21,038.28 as your result.

Answer: 21286

Step-by-step explanation:

answer/explanation:

hope this helps

The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

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Answer:

C. 115.2

Step-by-step explanation:

First, divide what you know, 4,000 seeds by 8 lbs. This gives us 500. From here, divide the 57,600 by 500 to get 115.2 :) hope this helps lmk if you need clarification

The sum of the 2 smallest angles in a right angled triangle be \(90^{0}\).

"The angle sum property of a triangle states that the sum of the angles of a triangle is equal to 180º."

"A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle."

As we know the sum of the three angles of a right angled triangle is 180 degrees.

<A + <B + <C = \(180^{0}\)

We also know the right angled triangle have a 90 degrees angle among the three angles.

So the sum of the 2 smallest angles in a right angled triangle be

<A + <B + <C = \(180^{0}\)

<A + <B  = \(180^{0}\) - <C

<A + <B = \(180^{0}-90^{0}\)

<A + <B = \(90^{0}\)

Hence, the sum of the 2 smallest angles in a right angled triangle be \(90^{0}\).

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My Question:

Is there any answer choices?

Answer:

a triangle

Step-by-step explanation:

when looking at a triangular prism it is made of 4 triangles, so any way you cut it, it will be a triangle

The exponential equation that models the population of Lime County would be: y = 711,500(0.979)^x

We can use the information from the question. When Leslie moved to Lime County, the population was 711,500, i.e.:

Let's then use this information to set up two equations:

Let's now substitute the value of a into the second equation:

Therefore, we find the exponential equation that models the population of Lime County, which is:

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Answer:

x = 1, y = 2

Step-by-step explanation:

this system is set up nicely to just add because then the y-value will be eliminated and you will have:

8x = 8

x = 1

get y value:  2(1) - 6y = -10

                    2 - 6y = -10

                     -6y = -12

                      y = 2

Answer:

O A. PQ = SU

Step-by-step explanation:

When two triangles are congruent then by CPCTC,

their corresponding parts ( angles and sides )  must be congruent.

In triangles PQR and STU,

Side PQ, QR and RP are corresponding to the sides ST, TU and US respectively,

Also, angles P, Q and R are corresponding to angles S, T and U respectively.

Here, Δ PQR ≅ Δ STU,

Thus, by the above property,

PQ ≅ ST, QR ≅ TU and RP ≅ US,

∠P ≅ ∠T, ∠Q ≅ ∠T and ∠R ≅ ∠U

The required equivalent expression to 12⁻⁷ x 12⁵ is 12⁻².

Given that,
To determine the equivalent expression for  12⁻⁷ x 12⁵.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= 12⁻⁷ x 12⁵
Simplifying
=  12⁻⁷ x 12⁵
Since, when the same value has a difference in the exponent in the product then it retains the base value and the addition of the exponent takes place.
= 12⁻⁷⁺⁵
=12⁻²

Thus, the required equivalent expression to 12⁻⁷ x 12⁵ is 12⁻².

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Answer: 3 tons

Step-by-step explanation: first I figured out how much 2 tons was which is 4000 pounds and then I divided 4000 by 8 which told me that each foot can hold 500 pounds So then I just did 500×10 which is 5000 pounds which is 3 tons

If an 8-foot column can hold 2 tons, then a 10-foot column can hold 1.28 tons.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The maximum weight that a circular column can hold is inversely proportional to the square of its height.

∴ w ∝ 1/h² or w = k(1/h²).

An 8-foot column can hold 2 tons which is,

2 = k(1/8²).

2 = k(1/64).

k = 128.

Now, 10 feet column can hold,

w = 128(1/10²).

w = 128/100.

w = 1.28 tons.

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Answer:

y = 3x + 4

Step-by-step explanation:

✔️First, find the slope using any two given pairs form the table, say (2, 10) and (5, 19):

Slope (m) = ∆y/∆x = (19 - 10) / (5 - 2) = 9/3

m = 3

✔️Find y-intercept (b) by substituting (x, y) = (2, 10) and m = 3 into y = mx + b

10 = 3(2) + b

10 = 6 + b

10 - 6 = b

4 = b

b = 4

✔️Write the equation by substituing m = 3 and b = 4 into y = mx + b

y = 3x + 4

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Regarding the functions in the context of the cylinder, it is found that:

a) The domain of r is: r ≥ 0.

b) The inverse function is: r = A/(2πr + 8)

The function for the surface area of the cylinder is defined as follows:

A(r) = 2πr² + 8πr.

In which r is the radius of the cylinder, representing the input of the function.

The domain of a function is the set containing all possible values of the function. Hence, in the context of this problem, it is the set containing the values of the radius.

Length measures such as the radius do not assume negative values, hence the domain is defined as follows:

r ≥ 0.

To find the inverse function, we have to isolate the variable r in the given definition of A(r), hence:

A(r) = 2πr² + 8πr.

2πr² + 8πr = A

2πr(r + 4) = A

r = A/(2πr + 8) (implicit definition).

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Answer:

Step-by-step explanation:

A=πr2

= (3.14)(27)2

= 2289.06

Answer:

Radius or r = \(\frac{diameter}{2}\) = \(\frac{27}{2}\) = 13.5 m

Area of the circle = π r²

                              = 3.14 x 13.5²

                              = 3.14 x 182.25

                              = 572.265 m²

Answer:

28 are 6th

14 and 7th

40% are 8th

Step-by-step explanation:

Answer:

28= 6th grader

14= 7th grader

28= 8th grader

40% were 8th graders

Step-by-step explanation:

28= 6th grader

14= 7th grader

28= 8th grader

40% were 8th graders

The fraction of the area of polygon H of polygon G's area would be: 1/16.

When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.

The scale factor = new dimension/original dimension

Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:

Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation

Area of polygon H/Area of polygon G = 1²/4² = 1/16

This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².

Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.

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The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line