Rewrite 96 X8 = 768 using the Commutative Law of Multiplication.

The triangles  ΔPQR ≈ ΔXYZ are similar by Angle-Angle Similarity.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are items that feature more than two figures that are the same shape but different sizes.

Given two triangles, ΔPQR and ΔXYZ

both the triangles are right triangles,

∠P = ∠Z = 90°

and given ∠R = ∠Y = 62°

A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.

From the above-described figure

ΔPQR ≈ ΔXYZ

so triangles are similar to Angle-Angle Similarity.

Hence the triangles are similar.

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The boat and the whale are about 218.5 miles apart.

Using the Pythagorean theorem to calculate the distance between the boat and the whale.

Let's call the distance between the boat and the whale "d" and the time they moved apart "t".

1st movement:

d = 45t

2nd movement:

d = (45t + 25(t+35))²

To calculate the final distance, we need to square d from the second movement and add the result from the first movement.

d² = (45t)² + (25(t+35))²

We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.

d² = (4535)² + (2560)²

Taking the square root of the result and get the final distance between the boat and the whale.

d =  ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])

d ≈ 218.5 miles

Hence, the boat and the whale are about 218.5 miles apart.

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The factorization of the expressions gives 2(l + w), -2ab(b + 2a), (3x+2)(3x−2) and 3(x²+2x−6)

Factorization, also known as factoring, is the process of breaking a mathematical expression down into its individual factors. In algebra, factorization refers to the process of expressing a polynomial as a product of simpler polynomials, known as its factors.

To factorize an expression, you need to look for factors of that expression. That is:

1. 2l+2w

2l+2w = 2(l + w)

2. -2ab²-4a²b

-2ab²-4a²b = -2ab(b + 2a)

3. 9x²-4

9x²-4 = (3x+2)(3x−2)

4. y²+7x+12

This cannot be factorized

5. 3x²+6x-18​

3x²+6x-18​ = 3(x²+2x−6)

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Answer:

Step-by-step explanation:

B i guess

The convergence of the series ∑∧∞ 4.7.10…(3n+1) /1.2.3….n is π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106

You should understand that any series that is not convergent is said to be divergent or to diverge

The reciprocals of the positive integers produce a divergent series

This can be written as π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106 .... For x ∈ R, the (infinite) geometric series ∑n≥0 xn converges if |x| < 1 and ...

This is to say that the convergence series is the reciprocal of the series.

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Answer:

2 * 1 ==> 1st option

Step-by-step explanation:

Matrix dimensions are:

number of rows by number of columns

The number of rows is 2   :   ( 2 and 12 are the rows)

The number of columns is 1   :  ( 2      

                                                    12 )    

Hence, the dimensions is 2 * 1.

Answer: The total fee for an item priced at $300 is $80.

Step-by-step explanation:

We can use the two given points to find the slope (m) and one point to find the y-intercept (b) of the line representing the consignment fee equation.

We know the two points are (500, 120) and (800, 180)

slope (m) = (y2-y1)/(x2-x1) = (180-120)/(800-500) = 60/300 = 0.2

Now we can use one of the point to find y-intercept (b)

120 = 0.2(500) + b

b = 20

Now we can use point-slope equation to find the total fee for an item priced at $300

y - 120 = 0.2(x - 500)

y = 0.2x + 20

The actual distance between towns on the map is 350km

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given;

The scale on the map is 1:5,000,000

Which implies that 1 cm on the map represent 5,000,000 cm in the actual;

Remember that;

1km = 1000m

1m= 100cm

1km= 100000cm

Convert cm to Km;

Divide by 100,000

5,000,000cm= 5,000,000/100,000= 50km

Now 1:5,000,000= 1cm/50km

That means

1 cm on the map represent 50 Km in the actual

So, 7 cm apart on the map

Multiply by 50

7 x 50= 350km

Hence, the answer to this question in kilometers is 350km

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Answer:

15500 Paise

In 1 rupee there are 100 paise therefore, 155 rupees after multiplying by 100 you will get the answer as 15500 paise

155×155=

24,025 p

This is the correct answer

Answer:

The slope is 3

Step-by-step explanation:

y = mx + b  The slope is the m.  It is the number before the letter x.

Answer:

Step-by-step explanation:

A heptagon is a polygon with 7 sides.

Sum of all angles of a polygon with n sides = 180(n-2) = 180 x 5 = 900°

So, the degree of each angle will be 900/7 = 128.57 or ≈129°.

Thanks

The displacement of the particle from time t = 0 and t = 5, with the velocity function, v(t) = arctan(t² + t - 1), using numerical integration which is the difference in the values of the indefinite integral at t = 0 and t = 5, we get option B

B. 5.504

The indefinite integral of a function is the antiderivative of the function, which does not have limits.

The function for the velocity is; v(t) = arctan(t² + t -1)

The position of the particle at time t = 0 is x = 0.085

The duration of the required displacement (between time t = 0 and t = 5)

The displacement = The area under the velocity time graph, therefore;

Displacement = ∫v(t)

Using substitution method, which is the similar to the inverse of chain rule, we get;

[tex]\int\limits {arctan(t^2+t-1)} \, dt = t\cdot arctan(t^2+t-1)-\int\limits {\frac{t\cdot (2\cdot t+1)}{(t^2+t-1)^2+1} } \, dt[/tex]

The value of ∫v(t), using manual steps on an online calculator, is a large expression, however, using numerical integration, we get;

[tex]\int\limits^5_0 {arctan(t^2+t-1)} \, dt \approx 5.504[/tex]

The displacement of the particle from time t = 0 to time t = 5 is about 5.504. The correct option is therefore;

B. 5.504

The displacement is the change in the position of the particle, and is the shortest distance between the particle's current position and the initial position of the particle

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Considering the properties of the angles of the given triangle, the required prove is explained below.

When it can be observed that two sides and measure on internal angles of a given triangle are equal, then it can be inferred that it is an isosceles triangle. Thus the measure of the internal angles that are opposite to the equal sides are the congruent angles.

Considering the given isosceles triangle, the properties of angles required for the prove are:

             STATEMENT                                   REASON

1. LO ≅ NO                                 Congruent sides of isosceles triangle.

2. <LOM ≅ <NOM                      Angle bisector property.

3. LM ≅ NM                                Definition of midpoint.

4. <LMO ≅ <NMO                      Definition of a perpendicular bisector.

5. <OLM ≅ <ONM                      Congruent angles of an isosceles triangle.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{b + b + b + b + b}\\\mathsf{= 1b + 1b + 1b + 1b + 1b}\\\mathsf{= 2b + 2b + 1b}\\\mathsf{= 4b + 1b}\\\mathsf{= 5b}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{5b}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

b+b+b+b+b is 5b

The number-finding assignment to a subset of the numbers depending on the age and arithmetic proficiency .

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x.

given

It is possible to locate more numbers in the challenge in some years than in others.

You might want to limit the number-finding assignment to a subset of the numbers depending on the age and arithmetic proficiency of your pupils as well as the amount of class time you want to allot to this task. The 2023 Challenge is available in 6 distinct iterations this year, which you can print and utilize with your pupils. Using the digits in 2023, set a challenge for your students to discover the numbers 1-10, 1-20, 1-30, 1-40, 1-50, or 1-100.

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Answer:

Step-by-step explanation:

The solutions to the equation −2x+2=(1/3)^x+1 can be found by finding the values of x that make the two sides of the equation equal. To solve this equation, we need to find the x values where the graphs of f(x) and g(x) intersect.Since the two functions are not linear and have different forms, it's hard to find the exact solutions. One way to find the solution is to graph the functions and find the x values where the two graphs intersect.It's not possible to find the exact values of x that make the two sides of the equation equal, because the two functions don't intersect at any specific point. It's not possible to find an exact solution to this equation, so none of the options are correct.

Answer:105

Step-by-step explanation:

let the number is x

Then 15% of x = 0.15x = 45 .

x= 45/0.15

x = 300

now 50 % of x = 0.5x =150

x = 150/0.5

x= 300 (crosscheck correct)

now 35% of 300 = 0.35 ×3000

= 105

Answer:

[tex]\huge\boxed{18 + 0i}[/tex]

Step-by-step explanation:

= (3 + 3i)(3 - 3i)

= 3(3 - 3i) + 3i(3 - 3i)

= 9 - 9i + 9i - 9i²

= 9 - 9(-1)

= 9 + 9

In the form a + bi:

[tex]\rule[225]{225}{2}[/tex]

The solution of the equation (x - 5)² + 3(x - 5) + 9 = 0 is x = -7 ± √35/2. Option B

From the information given, we have the equation as;

(x - 5)² + 3(x - 5) + 9 = 0

To solve the equation, take the following steps;

(x -5)(x-5) + 3x - 15 + 9 = 0

x² - 5x - 5x + 25 + 3x - 15 + 9 = 0

Now, collect like terms

x² - 5x - 5x + 3x + 25 - 15 + 9 = 0

add or subtract the like terms

x² - 7x + 21 = 0

The quadratic formula is is given as;

x =[tex]-b[/tex] ± [tex]\frac{\sqrt{b^2 - 4ac} }{2a}[/tex]

substitute the values

x = -(7) ± [tex]\frac{(-7)^2 - 4(1)(21)}{2(1)}[/tex]

expand the bracket

x = -7 ± [tex]\sqrt{\frac{49 - 84}2} }[/tex]

x = -7 ± √35/2

Hence, the value is x = -7 ± √35/2

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Answer:

Step-by-step explanation:

The tractor-trailer rig is a fixed input under the circumstances described because it is necessary for the business to service this profitable market and it cannot be replaced with any other type of capital equipment. The tractor-trailer is a quasi-fixed input because it has a five-year contract that requires monthly lease payments, so it is not completely fixed in the sense that the business can replace it with another piece of capital equipment at any time.

The zeros of f(x) = 4x³ + 4x² -37x + 44, using the Factor Theorem, are given as follows:

x = -4, x = 1.5 + 0.707i and x = 1.5 - 0.707i.

The function for this problem is defined as follows:

f(x) = 4x³ + 4x² -37x + 44.

The first linear factor is given as follows:

x + 4 = 0

x = -4 is the first zero.

The Factor Theorem states that the polynomial can be written as a product of it's linear factors.

x + 4 is of the first degree, while the polynomial is of the third degree, hence the remaining linear factors form a second degree polynomial, thus:

(x + 4)(ax² + bx + c) = 4x³ + 4x² -37x + 44.

Then, multiplying on the left side, we have that:

ax³ + (4a + b)x² + (4b + c)x + 4c = 4x³ + 4x² -37x + 44.

Then the coefficients are given as follows:

Inserting these coefficients into a quadratic function calculator, the remaining zeros are given as follows:

x = 1.5 + 0.707i, x = 1.5 - 0.707i.

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[tex]\vec A = \left[\begin{array}{cccc}- 3&- 14&7 &18\\-13&-2&-5 & -6\end{array}\right][/tex]

In this problem we find a matrix as result of the addition of two matrices. According to linear algebra, matrix addition is performed between matrices with same number of rows and columns. There, matrix A must have two rows and two columns to make addition operation possible, that is:

[tex]\vec A + \left[\begin{array}{cccc}3&9&-1 &-8\\16&- 2&3 & 13\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}3 + a_{11}&9+a_{12}&-1+a_{13} &-8+a_{14}\\16+a_{21}&- 2+a_{22}&3+a_{23} & 13+a_{24}\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]

And we shall solve the following equations:

First row

3 + a₁₁ = 0

9 + a₁₂ = - 5

- 1 + a₁₃ = 6

- 8 + a₁₄ = 10

Second row

16 + a₂₁ = 3

2 + a₂₂ = 0

3 + a₂₃ = - 2

13 + a₂₄ = 7

The solutions to the equations are: a₁₁ = - 3, a₁₂ = - 14, a₁₃ = 7, a₁₄ = 18, a₂₁ = - 13, a₂₂ = - 2, a₂₃ = - 5, a₂₄ = - 6.

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Answer:

16

Step-by-step explanation:

Basically one-half of 32

one-half = 1/2

Hence, 1/2 x 32 = 16

The rest of the information is not needed, it is a trick.

Answer:

Step-by-step explanation:

volume  of cylinder is

[tex]V = \pi r^{2}h[/tex]

In your cylinder, r = 20 and h =20

V = 3.14 x 20^2 x 20

   =25 120.00 ft^3

Please note: The numbers in the question seem wrong if your teacher wants you to round to the nearest hundredth.  Double check if the information.  They might have said " 0.1 times" instead of 1 times or they meant the nearest hundred instead of the nearest hundredth.  Please check.

Answer:

-------------------------------

As per given drawing PQ is the segment bisector of XY.

The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.

XW = 13 units, hence:

The value of the specified finite sum is -15.

The correct option is D.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The finite sum,

[tex]\sum^n_{k=1}{a_k = 5[/tex],

and [tex]\sum^n_{k=1}{b_k = 10[/tex].

Now,

[tex]\sum^n_{k=1}{a_k -2b_k = \sum^n_{k=1}{a_k -2\sum^n_{k=1}{b_k[/tex]

Substituting the values,

[tex]\sum^n_{k=1}{a_k -2b_k[/tex] = 5 - 20

                      = -15

Therefore, the value is -15.

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Answer: 27,800.0 cm[tex]^{3}[/tex] / 1,696.5 cu in.

Step-by-step explanation:

So Basically, If the Diameter is 12 and the height is 15 inches, the radius will be 6 inches making the Volume of the cylinder 1696.46 cu in.

Now if we were to round that to the nearest place it'd be 1,696.5 cu in.

However, If you want the answer in cm[tex]^{3}[/tex] it would be 27,800 cm making the rounded value 27,800.0 cm[tex]^{3}[/tex].

Hope that helped!

Answer: The answer would be $96.

Step-by-step explanation: $78 increasing dramatically by $1.50 every month, 78+1.50x12=$96.

Answer:

$96

Step-by-step explanation:

78+1.5m is the expression, with m representing months. Since one year has 12 months, the expression is now 78+1.5*12, which equals 96.

Answer:

C. Flipping a two-sided coin with one side green and the other side blue

Step-by-step explanation:

The sample space, S, is a list of tge possible outcomes (results) of an event (coin-flipping, dice-rolling etc)

Unless its a trick question and you can argue that g and b also stand for heads/tails and A/B, then the answer C.

Answer: C: Flipping a two-sided coin with one side green and the other side blue

Step-by-step explanation: :)