Boxes of Valentine’s Day chocolate truffles come in a variety of sizes. The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches. If each truffle in this box has a volume of 2 cubic inches, how many truffles are included in the box?

To complete the given proof, we need to select the missing statement and reason that correctly demonstrates the congruence of angles in the triangles ΔKLN and ΔMNL.

The correct option is:

C. \(\displaystyle\sf \angle KLN \cong \angle MLN\), and \(\displaystyle\sf \angle KNL \cong \angle MNL\)

by the corresponding angles theorem

The corresponding angles theorem states that if two parallel lines are intersected by a transversal, then the corresponding angles formed are congruent. In this case, \(\displaystyle\sf KL \parallel NM\) and \(\displaystyle\sf KN \parallel LM\), so the corresponding angles \(\displaystyle\sf \angle KLN\) and \(\displaystyle\sf \angle MLN\), as well as \(\displaystyle\sf \angle KNL\) and \(\displaystyle\sf \angle MNL\), are congruent. Therefore, option C is the correct choice to complete the proof.

Answer:

  P = -16(x -28)² +1024

Step-by-step explanation:

The equation can be written in vertex form as ...

  P = -a(x -h)² +k

where (h, k) is the vertex, and 'a' is a scale factor. We are given the vertex (h, k) = (28, 1024) and another point (x, P) = (10, -4160). Using these points, we can find the value of 'a'.

  -4160 = -a(10 -28)² +1024

  -5184 = -324a . . . . simplilfy

  a = 5184/324 = 16 . . . . divide by the coefficient of 'a'

A suitable quadratic relation is ...

  P = -16(x -28)² +1024

temperature. ?????? don't understand

is 3 square root / 2

Answer:

(1, 2)

Step-by-step explanation:

Hi there!

We are given two points - (4, 7) and (-2, -3)

We want to find the midpoint between these two points

The midpoint can be found using the formula \((\frac{x_1 + x_2}{2}, \frac{y_1+y_2}{2})\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We have everything we need to find the midpoint, but let's label the values of the points to avoid any confusion & mistakes

\(x_1=4\\y_1=7\\x_2=-2\\y_2=-3\)

Now substitute into the formula

\((\frac{x_1 + x_2}{2}, \frac{y_1+y_2}{2})\)

\((\frac{4+ -2 }{2}, \frac{7+-3}{2})\)

The pluses can be replaced with minus signs:

\((\frac{4 -2 }{2}, \frac{7-3}{2})\)

Now subtract

\((\frac{2 }{2}, \frac{4}{2})\)

Divide

(1,2)

The midpoint is (1, 2)

Hope this helps!

Answer:

y= 10

Step-by-step explanation:

-3x-5y=4

+3x        +3x

-5y=7x

+5y     +5y

y= 10

Answer:

y= -3/5 x + 27/5

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u

Speed of current = v

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045

v = 0.5205

Now the time taken by the un powered raft to cover this distance

Because un powered raft travel with the speed of the current.

T = 192.12 hr

Therefore the  time taken by the un powered raft to cover this distance is

T = 192.12 hr

Answer:

\(6\text{ mph}\)

Step-by-step explanation:

To find the the distance between A and B, use \(d=rt\), where \(d\) is distance, \(r\) is rate/speed, and \(t\) is time.

The raft travels from A to B in 6 hours at a rate of 3 mph. Thus, the distance from A to B must be:

\(d=3\cdot 6=18\) miles.

Since the motorboat travels the same distance in 2 hours, its rate/speed must be:

\(18=2r,\\r=\frac{18}{2}=9\text{ mph}\)

Because the raft is drifting, the speed of the current must be \(3\text{ mph}\) in the direction of the raft (from A to B). Thus, let the motorboat's speed be \(m\):

\(m+3=9,\\n=\boxed{6\text{ mph}}\)

That is correct.

Sqrt 5 x sqrt20

Apply the radical rule to get sqrt( 5 x 20)

Simplify to get sqrt(100)

Sqrt(100) = 10

After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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Answer:

\(\frac{2}{\frac{1}{24} }\)

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

\(\frac{2}{\frac{1}{24} }\) = 48

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.

A motor oil store has two tanks: one holds 12 gallons of oil, and the other holds 2 gallons of oil. In order to determine which tank will require to fill the bottles, the following computation must be done:

Quarts to gallons is 4 to 1.

1/4 x 60 = X

60/4 = X

15 = X

Since the motor oil vendor requires 15 gallons of oil, he must use both tanks but will still be short by 1 gallons

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Answer:

4

Step-by-step explanation:

2*2=4

Hope this helps!

:)

Answer: Monke.

Step-by-step explanation:

get good.

Answer:

mark is making $4,575, Carlos is makeing 457.50

Option 3 yielded the most money after 10 years is 171.7

Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

A solution of an equation is a value or set of values that satisfy the equation, meaning that when the value(s) is substituted for the variable(s) in the equation, both sides of the equation are equal.

Based on the given equations, Option 1 yielded the most money after 10 years, and Option 3 yielded the most total money by the time you were 60 years old.

After 10 years:

Option 1: 50×(1.09)¹⁰ - 30 =  88.36

Option 2: 50×(1.08)¹⁰ - 20 =  87.94

Option 3: 100×(1.07)¹⁰ - 25 =  171.71

Therefore, Option 3 yielded the most money after 10 years is 171.7

By the time you were 60 years old:

Option 1: 50×(1.09)⁶⁰ - 30 =  8,771.56

Option 2: 50×(1.08)⁶⁰ - 20 =  5,042.85

Option 3: 100×(1.07)⁶⁰ - 25 =  5,769.64

Therefore, Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

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We know that the circumference (C) of a circle can be calculated using the formula:

C = 2πr, where r is the radius of the circle.

We are given that the circumference of the circle is 2.20 cm, so we can use this to solve for the radius (r):

C = 2πr

2.20 = 2πr

r = 2.20 / (2π)

r ≈ 0.350 cm

Therefore, the radius of the circle is approximately 0.350 cm.

To find the area (A) of the circle, we can use the formula:

A = πr^2

Substituting the value we found for r:

A = π(0.350)^2

A ≈ 0.385 cm^2

Therefore, the area of the circle is approximately 0.385 cm^2.

Please mark this answer as brainliest if possible.

Answer:

Step-by-step explanation:

Question :-

The circumference of the circle is 220 cm.

Find :

a) Radius

b) Area of the Circle

Solution :

a)

Circumference of circle = 2πr

\( \longrightarrow \: \: 220 = 2 \pi r \\ \\ \longrightarrow \: \: \frac{220}{2} = \pi r \\ \\ \longrightarrow \: \: 110 = \frac{22}{7} × r \\ \\ \longrightarrow \: \: r = 110 \times \frac{7}{22} \\ \\\longrightarrow \: \: r = \frac{770}{22} \\ \\ \longrightarrow \: \: r = 35 \: cm \\ \)

b)

Area of circle = πr²

\(\longrightarrow \: \: \frac{22}{7} \times 35 \times 35 \\ \\ \longrightarrow \: \:22 \times 5 \times 35 \\ \\ \longrightarrow \: \:3850 \: {cm}^{2} \\ \)

Hence,

a) Radius of circle is 35 cm.

b) Area of the Circle is 3850 cm²

Answer:

Answer is A

Step-by-step explanation:

100× x is 100x

100 × 10 is 1000

Answer:

A is the answer

Step-by-step explanation:

PLZZZ give me brainliest

The value of B, the area of the base include the following: C. 1,542 m².

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

Volume of rectangular prism = base area × Height

26,214 = B × 17

Base area, B = 26,214/17

Base area, B = 1,542 m²

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Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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part a.

There is  a 49.1% chance that HRC finds a sample mean between $477 and $527.

part b.

There is a 20.9% chance that the sample mean falls between $492 and $512.

The standard error (SE) of the sample mean.

SE = σ / √(n)

σ = $80 and n = 68.

SE = 80 / √(68)

z1 = (X1 - μ) / SE

z2 = (X2 - μ) / SE

for first scenario:

X1 = $477, X2 = $527, and μ = $499.

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

For the range $477 to $527:

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

z1 = -0.275

z2 = 0.35

Probability 1 =  0.4909 = 49.1%

We have a 49.1% chance that HRC finds a sample mean between $477 and $527.

For the second scenario

X1 = $492, X2 = $512, and μ = $499.

z1 = (492 - 499) / Standard Error

z2 = (512 - 499) / SE

We have a 20.9% chance that the sample mean falls between $492 and $512.

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Compute the derivative of y = (x² + x - 2)² using the chain rule:

dy/dx = 2 (x² + x - 2) d/dx [x² + x - 2]

dy/dx = 2 (x² + x - 2) (2x + 1)

Evaluate the derivative at x = -1 :

dy/dx (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4

This is the slope of the tangent line to the function at (-1, 4).

Use the point-slope formula to get the equation for the tangent line:

y - 4 = 4 (x - (-1))   →   y = 4x + 8

Answer:

1 2  −  1 9 8

Step-by-step explanation:

Answer:

wednesday

Step-by-step explanation:

Answer:

Wednesday

Step-by-step explanation:

you'd just have to count the days!

It will take 140 seconds for the decay of 88% of the sample.

Given,

Radium-221 has a half-life of 30 sec.

Half life of Radium;

The half-life is the amount of time needed for a radioactive substance to decay and lose half of its radioactivity. The most prevalent radium isotopes have half lifetimes of 3.5 days, 1,600 years, and 6.7 years, respectively, after which each produces an isotope of radon.

We have to find the time taken for 88% of a sample to decay;

Here,

We can calculate how long the decay by using the half-life equation. It is expressed as:

A = Ao e^-kt

Where A is the amount left at t years

Ao is the initial concentration, and k is a constant.

From the half-life data, we can calculate for k.

1/2(Ao) = Ao e^-k(30)

k = 0.023

0.04Ao = Ao e^0.023(t)

t = 140 sec

That is,

The 88% of sample will decay in 140 seconds.

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Answer:

Find the area of all of the different shapes (2D)

and then add them up together to find the surface area.

3×2

6×2

6×2

5×3

6×3

1×3

1×4

1×4

4×3

Then you add them up together.

6+12+12+15+18+3+4+4+12=ANS.

How will I answer that, the image isn't showing luv

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Answer:

191.67 feets

Step-by-step explanation:

From. The attached picture :

Height x can be obtained using trigonometry :

Tan 22 = x / 200

0.4040262 = x / 200

x = 0.4040262 * 200

x = 80.805245 feets

For height, y :

Tan 29 = x / 200

0.5543090 = x / 200

y = 0.5543090 * 200

y = 110.86181 feets

Building height = x + y

Building height = 80.805245 + 110.86181 = 191.67 feets

Answer:

12 -20

30 - 5

Step-by-step explanation:

12 × 20 = 240

30 × 5 = 150

240 + 150 = 390

then 5 has 8 more than 20

5 × 8 = 40

30 +8 = 38

38 × 5 = 190

240 + 190 = 430

please mark as brainlist answer

Answer:

6x - 5 = 8x + 2

or -5-2 = 8x-6x

or -7 = 2x

or -7 / 2 = x

this is correct answer because in fraction form if one number is negative whole fraction is negative

Hey there!

IF YOUR EQUATION IS:

6x - 5 = 8x + 2
THEN:

SUBTRACT 8x to BOTH SIDES

6x - 5 - 8x = 8x + 2 - 8x

SIMPLIFY IT!

-2x - 5 = 2

ADD 5 to BOTH SIDES

-2x - 5 + 5 = 2 + 5

SIMPLIFY IT!
-2x = 2 + 5

-2x = 7

DIVIDE -2 to BOTH SIDES

-2x/-2 = 7/-2

SIMPLIFY IT!
x = -7/2

The step you had a partial mistake was step 2 because that’s not what had to simplify to get the 7/-2. You should’ve converted your equation to: -2x - 5 = 2 (as I put for STEP 1.1) but your overall result is correct x DOES equal to 7/-2.

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)