Which rule explains why these triangles are congruent?

Answer:

16 inch³

Step-by-step explanation:

Given that :

Length = 2 2/6 = 14/6 inches

Width = 3 3/7 = 24 /7 inches

Height = 2

The volume of a rectangular prism is given by :

Volume = Length * width * height

Volume = (14/6) * (24/7) * 2

Volume = 16 inch³

Answer:

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]

(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]

Step-by-step explanation:

Let [tex]f(x) = g(x)[/tex], [tex]f(x) = \ln (x+5)-1[/tex] and [tex]g(x) = x^{3}-2\cdot x + 1[/tex], then we have the following implicit equation:

[tex]\ln (x+5)-x^{3}+2\cdot x -2 = 0[/tex] (1)

This equation cannot be solved by analytical means. There are two different strategies to solve this expression: (i) Numerical methods, (ii) Graphical methods. We decide to use the second method:

Let suppose that we use this function [tex]h(x) = \ln (x+5) -x^{3}+2\cdot x - 2[/tex]. By the help of a graphing tool, we find the smallest solution such that [tex]h(x) = 0[/tex]. There are three possible solutions: [tex](x_{1},y_{1}) = (-1.577,0)[/tex], [tex](x_{2},y_{2}) = (0.18,0)[/tex], [tex](x_{3}, y_{3}) = (1.376, 0)[/tex]

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of [tex]x[/tex] has the smallest distance with respect to origin: [tex](x_{2},y_{2}) = (0.18,0)[/tex]

(ii) The smallest solution is the most negative value: [tex](x_{1},y_{1}) = (-1.577,0)[/tex]

The smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

Given functions;

f(x) = ln(x + 5) – 1

g(x) = x³ – 2x + 1

After graphing both the function, we get the three solutions of the given equation,

[tex]\rm \left(-1.577,0.223\right)[/tex]

[tex]\left(0.18,0.645\right)[/tex]

[tex]\left(1.376,0.853\right)[/tex]

Hence,the smallest smallest solution of f(x) = g(x) will be [tex]\rm \left(-1.577,0.223\right)[/tex]

To learn more about the function, refer to:

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Answer: Nick needs to sell 20 treats to break even.

Answer:

the answer is B

Step-by-step explanation:

when you take the first answer and subtract the second answer from it you get a negitive number of -1.1080325x10+28

Answer:

(a + b) / n

Step-by-step explanation:

Pounds of apple in box = a

Pounds of plum in box = b

Number of boxes used in packing = n

The amount fruit in pounds that are in each box :

Total pound of fruits / number of boxes used

Total pounds of fruit = a + b

Number of boxes used = n

Hence, we have ;

(a + b) / n

I'm pretty sure you have to write how much they are

Pink heart is 2

Green square is 2

Blue moon 1

Answer:

Pink Heart = 2 Green Square = 6  Blue Moon = 4

Step-by-step explanation:

h ( h x g) = (b x g) = 24    left side of table

2 (2 x  3)  = (4 x 6) = 24   right side of table

h(h x g ) = 2(2 x 3) = (4 x 6) = (b x g) = 24   equivalent outcomes

Answer:

The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].

Step-by-step explanation:

Let be a binomial of the form [tex](a+b)^{n}[/tex], where [tex]a, b\in \mathbb{R}[/tex] and [tex]n\,\in\mathbb{N}^{+}[/tex]. The expansion of this polynomial is defined below:

[tex](a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})[/tex] (1)

Where:

[tex]n[/tex] - Number of terms of the expanded polynomial.

[tex]k[/tex] - Index associated to [tex]k[/tex]-th term of the expanded polynomial.

For all [tex]n[/tex]-th binomial, we a sum of [tex]n+1[/tex] terms. If the given binomial has a term of [tex]20[/tex], then we have 21 terms and the fifteenth term of the polynomial corresponds to the [tex]14[/tex]-th term. Then, the fifteenth term of the binomial is:

[tex]c_{14} = \frac{20!}{14!\cdot 6!}\cdot (a^{6}\cdot b^{14})[/tex]

[tex]c_{14} = 38760\cdot a^{6}\cdot b^{14}[/tex]

The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].

since -15/16 is a negative number, we can add both sides by 15/16 or subtract both sides by -15/16. Either way works.

p = 1/8 + 15/16

Use common denominator, which is 16:

p = 1(2)/8(2) + 15/16

p = 2/16 + 15/16

p = 17/16

17/16 is an improper fraction. If you want to use a mixed number for your answer, then:

17/16 becomes 1 1/16 (one and one-sixteenth, with 1 being a whole number and 1/16 being a fraction)

Answer:

[tex]25x^{2} -30x+10[/tex]

Step-by-step explanation:

Plug in 5x-3 into f(x) so

[tex](5x-3)^2 + 1 = 25x^2 -30x+10[/tex]

Answer:

[tex]1\frac{7}{10}[/tex] kg of sugar

Step-by-step explanation:

Amount of sugar on Wednesday: [tex]3\frac{2}{3}[/tex] kg

Convert the mixed number fraction to an improper fraction (multiply the whole number by the numerator)

[tex]3\frac{2}{3}[/tex] ⇒ [tex]\frac{6}{3}[/tex] ⇒ [tex]2[/tex]

Therefore, Emila bought 2 kg of sugar on Wednesday.

Because Emila bought [tex]\frac{3}{10}[/tex] kg less sugar on Thursday, subtract [tex]\frac{3}{10}[/tex] from [tex]2[/tex].

[tex]2-\frac{3}{10}[/tex]

Convert 2 into a fraction with 10 as the denominator

[tex]=\frac{20}{10} -\frac{3}{10}\\=\frac{17}{10}[/tex]

Convert the fraction into a mixed number

[tex]= 1\frac{7}{10}[/tex]

Therefore, Emila bought [tex]1\frac{7}{10}[/tex] kg of sugar on Thursday.

I hope this helps!

Answer:

27.5 mph

Step-by-step explanation:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. I

After you add up all the numbers you get : 330 mph

330 mph divided by 12 is 27.5

27.5 mph is the answer :)

Answer:

I put the answer as a picture because it wouldn't let me write out the equations and use some characters :(

Step-by-step explanation:

Hopefully this helped :))

9514 1404 393

Answer:

  x = 1

Step-by-step explanation:

The axis of symmetry is the vertical line halfway between the zeros.

  x = (4 -2)/2

  x = 1 . . . equation of axis of symmetry

Answer:

The distance in one sweep is 100 cm approximately

Step-by-step explanation:

Here, we want to calculate the distance the wiper covers in one sweep

Mathematically;

we have a structure like an arc of a circle. It is the length of this arc we want to calculate.

The formula for the length of an arc is;

theta/360 * 2 * pi * r

r is the radius which in this case is 50 cm

We have ;

115/360 * 2 * 3.1412 * 50 = 100 cm approximately

Answer:

Number of boys = 12

Number of girls = 36

Step-by-step explanation:

Number of boys = x

Number of girls = 3*x = 3x

Total students = 48

x + 3x = 48

   4x = 48

    x = 48/4

    x = 12

Number of boys = 12

Number of girls = 3*12 = 36

Answer: 38

Step-by-step explanation:

3 (2/3) +(9)(4)

3 (2/3) +(9)(4) Again=38

If I Helped Please Mark Me As Brainliest, Have A Great Day :D

Answer:

A. UPS- $7 Fed Ex- $6

B. 4 pounds

C. UPS by one dollar

Step-by-step explanation:

Answer:

It's B

Step-by-step explanation:

Answer:

$12,150

Step-by-step explanation:

I = Prt

I = (40500)(0.03)(10)

I = 12150

Answer:

2(b+6)

Step-by-step explanation:

Answer:

B) obtuse triangle

Step-by-step explanation:

Answer:

x= - 7/2

Step-by-step explanation:

Decimal Form: -3.5

Mixed Number Form: -3 1/2

Answer:

It's 230 feet squared! (aka B)

Step-by-step explanation:

I just took the test :)

Answer:

B.) 230 feet squared.

Step-by-step explanation:

I hope this helps!! :)

Answer:

I think it would be 216cm

Step-by-step explanation:

how I got this answer?:

cubes are mostly the same in all sides due to all the sides being equal

Answer:

54 ÷ 18

18 x 3

Step-by-step explanation:

54 ÷ 18 is 3

and 18 x 3 is 54

We can write the multiplication expression and a division expression as

Given are the numbers as 54, 18, 18, 18.

We can write the multiplication expression and a division expression as-

(54 ÷ 18)

(18 x 18)

Therefore, we can write the multiplication expression and a division expression as

To solve more questions on multiplication and division, visit the link below -

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Answer:

Step-by-step explanation:

mean = total / amount of numbers

= 15/5 = 3

median = 4 middle number

mode = most common numbers = 3,2