Solve the given initial-value problem. 2y'' + 3y' − 2y = 10x2 − 8x − 13, y(0) = 0, y'(0) = 0
y(x)=

a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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Domain: {-15, 0, 9, 33, 44, 45}

Range: {15, 21, 33, 46, 57, 97}

The domain and range describe the x and y-values of a function.

Domain

The domain of a function shows the x-values covered by a function. Since the function cannot be proved to be continuous, we have to list the domain as a discrete list of values. We cannot say that the values between the listed x-values are a part of the domain. Any x-value included in the function is a part of the domain. As stated in the question, we should list our answer as an ordered list with braces.

Range

The range of a function shows the y-values covered by the function. Similar to the domain, we cannot assume that the y-values between those listed are included in the range. This means that the range will also be a list of values. Range and domain should be listed from least to greatest. So, we can create a list of all the y-values in numerical order.

Rhett's house is a rectangular prism

Given data ,

Let the figure be represented as A

Now , the value of A is

Rhett made a simple drawing of his house.

And , It is a three dimensional figure with four faces that are rectangular and two that are square

So , the figure is represented as a rectangular prism

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Hence , the figure is rectangular prism

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Option A shows the Venn diagram representing the union of these two events.

A Venn Diagram divides a data-set into separate regions, which are correspond to each activity in the context of the problem.

The intersection region is the region that corresponds to the people sharing both features, with are M and B.

The union region is the region showing at least one of the two features, M and B, hence it is the region in which all the circles are painted.

Hence option a is the correct option in the context of this problem.

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The classroom coin box required less than 11.11 Square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient

The 100 square feet of cardboard is enough to build the new coin box with a scale factor of 3 times the classroom coin box, we need to consider the relationship between the areas of the two boxes.

The area of the original classroom coin box is unknown, as it is not given in the problem. However, since we know that the new coin box has a scale factor of 3 times the original, we can infer that its area will be 3^2 = 9 times greater than the original.

Let's assume that the area of the classroom coin box is A square feet. In that case, the area of the new coin box would be 9A square feet.

Now, we are given that 100 square feet of cardboard is available. To determine if it's sufficient, we need to compare this value to the area of the new coin box, which is 9A.

If 100 square feet is greater than or equal to 9A, then it would be enough to build the new coin box. Conversely, if 100 square feet is less than 9A, it would not be enough.

Since we do not have a specific value for A, we cannot determine the exact answer. However, we can provide the argument to defend our solution.the classroom coin box required less than 11.11 square feet of cardboard (100 square feet divided by 9), then 100 square feet would be sufficient.

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Note the question be like :

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn from the bag without replacement, what is the probability that both marbles are red?

1) sin θ + tan θ is equal to 5/6. 2) sin θ is 5/12. 3) sec θ + cosecc^2 θ = 12/√119 + 144/25 4) cot θ + sin θ is equal to 169/60.

1) To find sin θ + tan θ, we need to find the value of sin θ. Using the identity tan θ = sin θ / cos θ, we can rewrite tan θ as sin θ / cos θ.

tan θ = 5/12 = sin θ / cos θ

Since we are given that 0 < θ < 90, both sin θ and cos θ are positive.

Using the Pythagorean identity[tex]{sin^2}[/tex] θ + [tex]cos^2[/tex] θ = 1, we can solve for cos θ:

[tex]cos^2[/tex] θ = 1 - sin^2 θ

[tex]cos^2[/tex] θ = [tex]1 - (5/12)^2[/tex]

[tex]cos^2[/tex]θ = 1 - 25/144

[tex]cos^2[/tex] θ = 119/144

cos θ = √(119/144)

cos θ = √119/12

Now, we can find sin θ using the relationship [tex]sin^2[/tex] θ + [tex]cos^2[/tex]θ = 1:

[tex]sin^2[/tex] θ = 1 - [tex]cos^2[/tex] θ

[tex]sin^2[/tex]θ = 1 - (119/144)

[tex]sin^2[/tex]θ = 25/144

sin θ = √(25/144)

sin θ = 5/12

Finally, we can substitute the values of sin θ and tan θ into the expression sin θ + tan θ:

sin θ + tan θ = (5/12) + (5/12) = 10/12 = 5/6

Therefore, sin θ + tan θ is equal to 5/6.

2) The value of sin θ is already calculated as 5/12.

3) To find sec θ + [tex]csc^2[/tex] θ, we need to find the values of sec θ and csc θ.

Since sec θ is the reciprocal of cos θ, we can calculate sec θ as:

sec θ = 1/cos θ = 1/(√119/12) = 12/√119

csc θ is the reciprocal of sin θ, so:

csc θ = 1/sin θ = 1/(5/12) = 12/5

Now, we can substitute these values into the expression sec θ + [tex]csc^2[/tex]θ:

sec θ + [tex]csc^2[/tex]θ = (12/√119) + [tex](12/5)^2[/tex]= 12/√119 + 144/25

4) To find cot θ + sin θ, we need to calculate the value of cot θ.

cot θ is the reciprocal of tan θ, so:

cot θ = 1/tan θ = 1/(5/12) = 12/5

Now, we can substitute the values of cot θ and sin θ into the expression cot θ + sin θ:

cot θ + sin θ = 12/5 + 5/12

To add these fractions, we need a common denominator:

cot θ + sin θ = (12/5)(12/12) + (5/12)(5/5)

              = 144/60 + 25/60

              = 169/60

Therefore, cot θ + sin θ is equal to 169/60.

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In mathematics, notation is used to simplify and make our understanding of equations and problem statements easier.

Mathematical notation makes use of various symbols in order to represent operations, unspecified numbers, relations, and any other mathematical objects or entities, and proceeds to assemble them into understandable expressions and formulas.

A notational convention is a set of representatives consisting of symbols that are used to express mathematical equations, in this case, the notational convention adopted is that all the free variables of a formula are among u1, u2, u3 . . . un. as shown in the image provided.

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The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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Answer:

B

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer:

19.24 ft

Step-by-step explanation:

x = length of ramp

sin12 = 4/x

x = 4/sin12 = 19.24 ft

Answer:

7, 14

Step-by-step explanation:

Look at the first column of numbers: 2.8 m in 2 min.

We can get a unit rate from those numbers:

2.8 m / 2 min = 1.4 m/min

He walks at a rate of 1.4 m/min

Now multiply the unit rate by each number of minutes to find the number of meter.

Let's do the second column as a check: time = 3 min

1.4 m/min × 3 min = 4.2 m

4.2 m is the number on the table, so our unti rate is correct.

5 min:

1/4 m/min × 5 min = 7 m

10 min:

1.4 m/min × 10 min = 14 m

5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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The rays in Tiffany’s design are EA, FB, GC, GH, ED

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

Tiffany’s design

By definition, the rays in Tiffany’s design are lines that have one fixed endpoint and the other endpoint extends indefinitely

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

The rays in Tiffany’s design are EA, FB, GC, GH, ED

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physical sciences 2023

Given that in circle S, a sector is shaded and ZTSU measures 40°. We are to find out what fraction of the interior of the circle is shaded and simplify the answer.The correct answer is 16π/9 cm².

To find out the fraction of the interior of the circle that is shaded, we need to determine the measure of the central angle that intercepts the entire circle.The total measure of a circle is 360 degrees.

To find the fraction of a circle shaded, divide the number of degrees in the sector by

360.4x = (40/360) × πr² = (1/9) × πr².

We simplify the answer: 4x = πr²/9 Fraction of the interior of the circle that is shaded = 40/360 = 1/9.Expression for the area of the shaded sector in square centimeters is:

A = (40/360) × πr² = πr²/9 =  π(4²)/9 = 16π/9 cm²

Therefore, the correct answer is 16π/9 cm².

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The figures paired are given as follows:

| -3| = 3

|-2| >  1

0 < |-1|

The left over is 2. This is based on the principle of absolute values.

The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.

A number's absolute value can be conceived of as its distance from zero along the real number line.

As a result, the absolute value of -3 is 3, which suggests that |-3| = 3.

-2 in absolute terms equals 2. That is |-2| greater than 1.

the inverse value of -1 equals 1. This equals 0 |-1|.

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Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

The diagram represents the trajectory of an airplane at take off the angle representing the airplane's trajectory is approximately 147.83 degrees.

To solve this problem, let's denote the angle of the airplane's trajectory as x degrees. According to the given information, the angle representing the trajectory of the jet is 15% greater than the airplane's trajectory.

The angle representing the trajectory of the jet can be calculated as:

x + 0.15x = 1.15x

Therefore, the angle representing the trajectory of the jet is 1.15x degrees.

Given that the airplane's trajectory is at 170 degrees, we can set up the following equation:

1.15x = 170

To solve for x, divide both sides of the equation by 1.15:

x = 170 / 1.15 ≈ 147.83

Thus, the angle representing the airplane's trajectory is approximately 147.83 degrees, and the angle representing the jet's trajectory is approximately 1.15 * 147.83 ≈ 170 degrees.

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Answer:

b=2

Step-by-step explanation:

You are given:

[tex]b^{3} =8[/tex]

What does [tex]b^3[/tex] mean?

It is simply, b·b·b

Therefore:
b·b·b=8

What number could be multiplied by itself three times and equal 8?

...

2

Yay! That's great!

The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.

To find the area of a sector, we can use the formula:

Area of Sector = (Central Angle / 360 degrees) × π ×  (Radius²)

Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:

Area of Sector = (285 degrees / 360 degrees) ×  π ×  (6²)

Area of Sector = (19/24) ×  π × 36

Area of Sector = (19/24) ×  36π

Area of Sector = (19 × 36π) / 24

Area of Sector = 684π / 24

Area of Sector = 28.5π

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Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Accrued amount A = $174,000

Compounded daily n = 365

Time t = 19 years

Interest rate r = 4.3%

Principal P = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 4.3/100

r = 0.043

Plug these values into the above formula and solve for principal P.

[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]

Therefore, the principal that needs to invested is $76,869.06.

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The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20

The simple interest formula is J = C ∙ i ∙ t, where J is interest, C is principal, i is interest rate, and t is time. To calculate the simple interest, just substitute the values ​​in the formula and perform the calculation.

Calculate the deposit:

[tex]D=R4.80 + 1.20% of R5,000\\=R4.80 + (1.20/100) * R5,000\\= R4.80 + R60\\= R64.80[/tex]

Now, the deposit amount for the branch:

[tex]DB=R8.00 + 1.50% of R5,000\\= R8.00 + (1.50/100) * R5,000\\= R8.00 + R75\\= R83.00[/tex]

The difference will be:

[tex]Difference = R64.80 - R83.00\\Difference = -R18.20[/tex]

The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20. Therefore, John's statement is incorrect.

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Answer: x=15.6

Step-by-step explanation:

An isosceles triangle has two congruent sides. (1 pair). So, the other side (not x) must equal 11.

Using the Pythagorean Theorem; a^2+b^2=c^2, you can substitute the values in as follows

11^1+11^2=x^2

121+121=x^2

242=x^2

15.55634918610405=x

round to the nearest tenth as said in the question...

x=15.6

Step-by-step explanation:

This is a quadratic with vertex at (2,1) ....write the equation first in vertex form, then expand to the form requested

  y = ( x -2)^2  + 1

  y = x^2 -4x +4    + 1

 y = x^2 -4x + 5     Done.      a = -4   b = 5

Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.

Therefore, AC is congruent to DB.

Given: AB is parallel to BC

DC is parallel to BC

Angle 1 is congruent to Angle 2

Prove:

AC is congruent to DB

Proof: AB is parallel to BC and DC is parallel to BC.

Therefore, AB is parallel to DC.

Angle 1 is congruent to Angle 2.

Angles 1 and 2 are alternate interior angles, so they are congruent.

Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.

Therefore, AC is congruent to DB.

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Answer:

6* 2.2lb = 13.2 lb

Step-by-step explanation:

If 1 bag weights 2.2lb than 6 bags will weight 6 times more or:
2.2 lb * 6 = 13.2 lb

We can use the provided conversion factor, which states that 1 kg is equal to 2.2 pounds, to determine the weight of the cat food in pounds.

Since each bag of cat food weighs 6 kg, we can calculate the weight of 5 bags as follows.

5 bags of 6 kg each equal the total weight = 30 kg.

Now, we can convert the total weight from kilograms to pounds using the conversion factor:

Total weight multiplied by the conversion factor equals total weight in pounds.

= 30 kg x 0.2 lb/kg.

= 66 lbs.

Consequently, the cat food has a 66-pound weight when measured in pounds.

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Answer: 30

Step-by-step explanation:

18/5 divided by 3/25 is the same thing as multiplying 18/5 with the reciprocal of 3/25 (25/3).

[tex]\frac{18}{5} *\frac{25}{3} =\frac{450}{15}[/tex]

And when multiplying out you get 450/15.

Simplifying (by dividing 450 by 15) this you will get 30.

The value of the variable x in the right angle triangle is: 9

Pythagoras Theorem is defined as the way in which we can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

The tangent forms a right angle with the circle and as such using Pythagoras theorem, we have:

8 + x = √(15² + 8²)

8 + x = √289

8 + x = 17

x = 17 - 8

x = 9

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