are these two right triangles congruent??

Answer:

24 units²

Step-by-step explanation:

The area of the given triangle is 24 unit², calculated by the area of the right-angle triangle formula.

What information do we have?

Base of triangle = 12

Height of triangle = 4

Area of triangle = (1/2)(b)(h)

Area of the given triangle = (1/2)(12)(4)

Area of the given triangle = (1/2)(48)

Area of the given triangle = 24 unit²

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Answer:

The solutions are,

x=0 and x= 5

(I don't know if you have to write both of these or only one, sorry)

Step-by-step explanation:

\(x^2-3x+6=2x+6\\solving,\\x^2-3x-2x+6-6=0\\x^2-5x+0=0\\x^2-5x=0\\x(x-5)=0\\\\x=0, x-5=0\\x=0,x=5\)

So, the solutions are,

x=0 and x= 5

6370 in3

Step-by-step explanation:

Answer:

The answer is -7. This equation only has one solution. It makes the equation -2 = -2.  

For the second part, you can use a number like 7 and then that would make it be 2 = -2. Hope this Helps!

Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.

Answer:

It would be 2 1/3!

Step-by-step explanation:

Answer:

I’d go with number 2 and number 4.

Answer:

Correct. 16 when 4x4=16 or just count the inside.

Step-by-step explanation:

Grogg can order 1024 different pizzas from the pizzeria, considering all possible combinations of the ten toppings.

To determine the number of different pizzas Grogg can order, we need to consider the choices for each topping. Since Grogg can choose any combination of toppings, including no toppings, we can use the concept of combinations.

For each topping, Grogg has two choices: either include it on the pizza or exclude it. This means that for each topping, there are 2 possibilities. Since there are 10 toppings in total, the total number of different pizzas can be calculated as:

Number of Pizzas = 2^10

Calculating this value, we find:

Number of Pizzas = 1024

Therefore, Grogg can order 1024 different pizzas from the pizzeria, considering all possible combinations of the ten toppings.

what is combinations?

In mathematics, combinations refer to the selection of items from a larger set without considering the order of the selected items. Combinations are used when the arrangement or order of the selected items is irrelevant.

The number of combinations, denoted as nCk or C(n, k), represents the number of ways to choose k items from a set of n distinct items without regard to their order. It is often calculated using the binomial coefficient formula:

C(n, k) = n! / (k! * (n - k)!)

Where n! (read as "n factorial") represents the factorial of a number, which is the product of all positive integers from 1 to n.

For example, if you have a set of three elements {A, B, C}, the possible combinations of selecting two items from this set would be {AB, AC, BC}.

Combinations are widely used in various areas of mathematics, statistics, and combinatorics, including probability theory, counting principles, and permutations.

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The definite integral for this function is given as follows:

\(\int_{0}^{6} f(x) dx = 18\)

The definite integral represents the area of the function in the interval composed by the bounds of the definite integral.

This means that the definite integral in this problem can be found merely obtaining the area of the function.

The function is composed as follows:

Hence the area of the figure is given as follows:

A = 2 x 2² + 2 x 5 = 8 + 10 = 18 units.

Which is the result of the definite integral.

The figure is given by the image shown at the end of the answer.

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The measure of the angles 2 and 3 are 70°

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles also were generated when plane cross. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.

Given, angle 1 = 40°

and, angle 2 = angle 3 = x

In a triangle, sum of angles = 180°

or, m∠1 + m∠2 + m∠3 = 180°

or, 2x = 180-40

or, 2x = 140

or, x = 140/2 = 70°

Hence, the measure of the angles 2 and 3 are 70°

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By brute force, we will see that the smallest 4-digit number that meets the conditions is 2,064.

To do it, we just need to multiplicate 24 by integers (increasing the value of these integers) until we find the first product that has 4 digits. This is called brute force.

For example:

24*50 = 1,200

Nice, but we can only use even numbers, so we must be in the 2 thousand range.

Then let's multiply by 100

24*100 = 2,400

Now we need to go down, until we find the first product that meets the conditions, for example if we use 85 instead of 100, we get:

24*85 = 2040

Each digit can be used once, and here the zero appears twice, let's go to the next one:

24*86 = 2,064

Nice, this is the smallest 4-digit number that meets the conditions.

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Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.

1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.

2. Calculate side BC using the Law of Cosines:

BC = (2(AB)(AC)cosB) + (AB)(AC)2

3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)

4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)

5. Determine BC =. (2095 - 1539.07)

6. Condense: BC = 556.93

7. Determine BC as 23.701 cm.

8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.

By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.

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Answer:

\(d=2\) and \(d=3\)

Step-by-step explanation:

\(d^2-5d+6=0\)

\((d-2)(d-3)=0\)

\(d=2\) and \(d=3\)

Answer:

a. four and thirty four thirty fifths

The statement " It can be read as "eight squared." It has a power of 256. " is true. Option A

This is further explained below.

Generally, A product in mathematics is either the end result of performing the operation of multiplication or an expression that indicates the elements that are going to be multiplied.

For instance, 30 is the product of the numbers 6 and 5, while x's dot product is x multiplied by itself.

In conclusion, It may also be interpreted as "eight times eight." It might be interpreted as "two raised to the power of eight," which is a mathematical expression. It may be expressed as a problem of multiplication with eight factors of 2, as shown below.

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Hope this answer image helps you ...

By Benjemin

Answer:

m = 2b - 45000

m + b = 111000

Substitute to get

2b - 45000 + b = 111000

3b                      =  156000

b                        = 52000

So m = 59000

Step-by-step explanation:

(Go Answer my question pls! Thanks!)

The number which is greater is 75% of 200 over 7 over 9 of 180.

7 over 9 can be written as 7/9

So 7/9 of 180 can be calculated as,

7/9 x 180

= 0.777 x 180

= 140

Therefore, the value of 7 over 9 of 180 is 140

Now we have to calculate 75% of 200,

= 75/100 x 200

= 0.75 x 200

= 150

Therefore, the value of 75% of 200 is 150

So the value greater is 150 that is 75% of 200 is greater than 7 over 9 of 180.

Greater or less than and equal in math assist students comprehend how one number differs from another. If one number is more than the other, less than the other, or if both numbers are equal.

Important symbols or signs are used to distinguish between bigger, smaller, and equal numbers so that people can understand them.

We utilise the greater than symbol (>) to indicate that one number is larger than another.

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9514 1404 393

Answer:

  C.  3x² +24

Step-by-step explanation:

Use the given function definitions and simplify.

  \(g(f(x))=g\left(\dfrac{1}{3}x^2+4\right)\\\\=9\left(\dfrac{1}{3}x^2+4\right)-12\\\\=3x^2+36-12\\\\\boxed{g(f(x))=3x^2+24}\qquad\textbf{matches C}\)

Answer:

B

Step-by-step explanation:

\(v = \pi {r}^{2} h \\ = 8 \\ v = \pi {8}^{2} \times 3 = 3.14 \times 64 \times 3 = 602.88 = 602.9\)

The volume of the cylinder is 2411.5 cm³ in the given figure. which is the correct answer would be an option (A).

The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder.

V = πr²h

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

As per the given figure,

The radius of a cylinder is 16 cm and the height of the cylinder is 3 cm.

The volume of a cylinder = πr²h

The volume of a cylinder = π(16)² × 3

The volume of a cylinder = 3.14(256) × 3

The volume of a cylinder = 2411.5 cm³

Thus, the volume of the cylinder is 2411.5 cm³ in the given figure.

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Answer:

The Area of the regular polygon=65.35 inches²

Step-by-step explanation:

We are given:

Length of side of polygon = 10 inches

Apothem = 13.07

We need to find area of the regular polygon.

The formula used is: \(Area \of \ the \ regular \ polygon=\frac{1}{2}\times (apothem) \times(Perimeter) \\\)

\(Perimeter = Sum \ of \ length \ of \ all \ sides\)

The polygon has 8 sides. so,

\(Perimeter = 10+10+10+10+10+10+10+10\\Perimeter = 80\)

Now, finding area of Polygon

\(Area \of \ the \ regular \ polygon=\frac{1}{2}\times (apothem) \times(Perimeter) \\\\Area \of \ the \ regular \ polygon=\frac{1}{2}\times (13.07) \times(10)\\Area \of \ the \ regular \ polygon=\frac{1}{2}\times (130.7)\\Area \of \ the \ regular \ polygon=65.35 \ inches^2\)

So, the Area of the regular polygon=65.35 inches²

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Step-by-step explanation:

Every hour, the cars are 43 + 38 = 81 miles further apart.

Therefore 2904/81 = 35.85 hours.

They will take around 35.85 hours for them to be 2,904 miles apart.

The derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹ * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

To find the derivative of the given function g(x), we can apply the product rule and the chain rule. Let's break down the function into its constituent parts: f(x) = (x² - x + 1\()^1^0\) and h(x) = (tan(x))³.

Using the product rule, the derivative of g(x) can be calculated as g'(x) = f'(x) * h(x) + f(x) * h'(x).

First, let's find f'(x). We have f(x) = (x² - x + 1\()^1^0\), which is a composite function. Applying the chain rule, f'(x) = 10(x² - x + 1\()^9\) * (2x - 1).

Next, let's determine h'(x). We have h(x) = (tan(x))³. Applying the chain rule, h'(x) = 3(tan(x))² * sec²(x).

Now, we substitute these derivatives back into the product rule formula:

g'(x) = f'(x) * h(x) + f(x) * h'(x)

       = 10(x² - x + 1)² * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\)* (tan(x))² * sec²(x).

In summary, the derivative of the function g(x) = (x² - x + 1\()^1^0\) * (tan(x))³ is g'(x) = 10(x² - x + 1)⁹  * (2x - 1) * (tan(x))³ + 3(x² - x + 1\()^1^0\) * (tan(x))² * sec²(x).

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9514 1404 393

Answer:

  499 1/3 miles

Step-by-step explanation:

Let m represent the number of miles the car can travel on 14 gallons. We assume distance is proportional to gas usage, so ...

  m/14 = 107/3

Multiplying by 14, we have ...

  m = 14(107/3) = 1498/3 = 499 1/3

The car can travel 499 1/3 miles on a full tank of gas.

Answer:

0.5

Step-by-step explanation: