Determine whether each pair of triangles is congruent. If yes, include the theorem or
postulate that applies and describe the series of rigid motions that map one triangle onto the
other.
A.
4
B.
ΔΔ
C.
D.

Answer:43.289

Step-by-step explana

The step which contains the first error in calculation is: B. Step 2 - the sine ratio was applied incorrectly.

The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

Mathematically, the law of sines is given by this equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]

For any right-angled triangle, the ratio of the length of its opposite sides to the length of its hypotenuse is generally referred to as sine ratio. Thus, sine ratio is given by this formula:

cos(θ) = Opp/Hyp

Where:

In this context, we can infer and logically deduce that the step which contains the first error in calculation is step 2:

sin(W) = y/XZ; XZsin(W) = y.

In conclusion, the correct step should have been written as follows:

sin(W) = XZ/y; ysin(W) = XZ.

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Answer:

step 2 is incorrect

Step-by-step explanation:

B. Step 2 - the sine ratio was applied incorrectly

Answer:

= – 5 – 7

Step-by-step explanation:

= –5 – 7

Answer:

"a[b(b + 6) +7(a²-2)]" (the third one)

Step-by-step explanation:

Multiply 9 with 9, and we get:

9 × 9 = 81

Multiply 10 with 10, and we get:

10 × 10 = 100

We get the final result as:

Hope this helps :)

Answer:

x=1

Step-by-step explanation:

2/3(9x-6) = 1/4(12-4x)

We want to solve for x

Distribute

6x-4=3-x

Add x to each side

6x-4+x = 3-x+x

7x-4 = 3

Add 4 to each side

7x-4+4 = 3+4

7x=7

Divide by 7

7x/7 = 7/7

x=1

Answer:

x = 1

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] (9x - 6) = [tex]\frac{1}{4}[/tex] (12 - 4x) ← distribute parenthesis on both sides

6x - 4 = 3 - x ( add x to both sides )

7x - 4 = 3 ( add 4 to both sides )

7x = 7 ( divide both sides by 7 )

x = 1

Answer:

12:1

Step-by-step explanation:

each pack contains 12 eggs

108/9 = 12

Hope this helps

The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

Recursive functions are functions that is used to determine the next term of a given sequence giving the common difference.

Given the recursive function shown below;

f(1) = 1/5

f(n) = f(n-1) + 1/5

For the second term;

f(2) = f(1) + 1/5

f(2) = 1/5 + 1/5

f(2) = 2/5

For the third term;

f(3) = f(2) + 1/5

f(3) = 2/5 + 1/5

f(3) = 3/5

For the fourth term;

f(4) = f(3) + 1/5

f(4) = 3/5 + 1/5

f(4) = 4/5

For the fifth term;

f(5) = f(4) + 1/5

f(5) = 4/5 + 1/5

f(5) = 5/5 = 1

Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

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The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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If the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.

Given that the vertices of parallelogram ABCD is A(-6,-4),B(0,-4)

,C(3,4),D(-3,4).

We are required to find the area of parallelogram ABCD.

Let the point of intersection of height of parallelogram from point A is point E.

When we see the graph on which the parallelogram then we will be able to know that point E has coordinates of (-3,-4).

Area of parallelogram=Base*Height

=AB*DE

DE=[tex]\sqrt{(-4-4)^{2} +(-3+3)^{2} }[/tex]

=[tex]\sqrt{64}[/tex]

=8 units

AB=[tex]\sqrt{(-4+4)^{2} +(0+6)^{2} }[/tex]

=[tex]\sqrt{36}[/tex]

=6 units

Area=6*8

=48 square units.

Hence if the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.

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Answer:

See below.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

Given statement:  If n is an even integer, then 2n + 1 is an odd integer.

Converse:  If 2n + 1 is an odd integer, then n is an even integer.

Given statement:  If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

Converse:  If a transversal intersects two lines such that each pair of corresponding angles is equal, then the two lines are parallel to each other.

Given statement:  If each pair of opposite sides of a quadrilateral is equal, then the quadrilateral is a parallelogram.

Converse:  If a quadrilateral is a parallelogram, then each pair of opposite sides of the quadrilateral is equal.

Given statement:  If the decimal expansion of a real number is terminating, then the number is rational.

Converse:  If a real number is rational, then the decimal expansion of the number is terminating.

Answer:

[tex] {216 \: in}^{3} [/tex]

Step-by-step explanation:

Split the chimney into 2 rectangular prisms. One is the short one, and the other is the tall one.

The dimensions of the short prism are 4 x 3 x 2. The volume of that prism is found by multiplying those numbers together, which is 24.

The dimensions of the tall prism are 4 x 4 x 12. The volume of that prism is 192.

Adding those 2 volumes together, you will get the volume of the composite figure. 192 + 24 = 216

Volume is always in cubic units

Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.

The formula exists:

[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]

The parameters exists:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters are: p = 0.5 and n = 13

The probability that at most eleven of the thirteen babies are girls is:

[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then

[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]

By using the binomial distribution formula

[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]

substitute the values in the above equation, we get

[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]

[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]

So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]

[tex]=0.0016+0.0001=0.0017 \\[/tex]

[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]

[tex]=1-0.0017=0.9983[/tex]

0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.

Therefore, the correct answer is option c. 4089/4096

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Answer:

0.075

Step-by-step explanation:

to convert a fraction to a decimal fraction

divide the numerator by the denominator, that is

[tex]\frac{3}{40}[/tex] = 3 ÷ 40 = 0.075

The term "altitude" is the same as "height of a triangle". It is perpendicular to the base. Since we can rotate the triangle to have any side be horizontal, there are effectively 3 possible bases. Hence, there are 3 heights. It all depends how you look at it.

Let h1, h2, and h3 be the three altitudes or heights.

Without loss of generality, we'll focus on the first two heights h1 and h2. Their respective bases are b1 and b2.

If we use b1 as the base, then the area is...

area = 0.5*base*height = 0.5*b1*h1

Similarly, the other base gives the area of:

area = 0.5*b2*h2

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

Since both formulas refer to the same area (because we're working with the same triangle), we can set the expressions equal to one another

0.5*b1*h1 = 0.5*b2*h2

b1*h1 = b2*h2

Let's see what happens when b1 = b2, so,

b1*h1 = b2*h2

b1*h1 = b1*h2

b1h1 - b1h2 = 0

b1(h1 - h2) = 0

b1 = 0 or h1 - h2 = 0

b1 = 0 or h1 = h2

If the bases b1 and b2 were equal, then either those bases must be 0 which isn't possible, or the altitudes must be equal. However, the initial premise is that the heights must be different from one another.

Therefore, the bases b1 and b2 can't be the same length.

We could follow the same steps and logic to conclude that if the altitudes h1 and h3 were different, then the bases b1 and b3 can't be the same. Similarly, we would conclude that b2 and b3 can't be the same. This is where the "without loss of generality" kicks in.

In other words, we only need to focus on one subcase to extend the logic to the other cases, without having to actually do every single step. That would be a bit tedious busywork.

In conclusion, we've shown that if the heights are different, then their respective bases must be different. This leads to wrapping up the proof that we have a scalene triangle.

Side note: I used an indirect proof or proof by contradiction. I assumed that a non-scalene triangle was possible and it led to a contradiction of h1 = h2.

Using it's concept, the approximate perimeter of pentagon ABCDE is given as follows:

34.4 units.

The perimeter of a figure is given by the sum of the lengths of it's outside dimensions.

In this problem, the vertices are in a coordinate-plane, hence the distances are found using the formula for the distance between two points.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The length of segment AB is:

[tex]AB = \sqrt{(6 - 0)^2+(0 - 7)^2} = 9.2[/tex]

The length of segment BC is:

[tex]BC = \sqrt{(6 - 3)^2+(0 + 4)^2} = 5[/tex]

The length of segment CD is:

[tex]CD = \sqrt{(-3 -3)^2+(-4 + 4)^2} = 6[/tex]

The length of segment DE is:

[tex]DE = \sqrt{(-6 + 3)^2+(0 + 4)^2} = 5[/tex]

The length of segment EA is:

[tex]EA = \sqrt{(-6 +0)^2+(0 - 7)^2} = 9.2[/tex]

Hence the perimeter is:

P = AB + BC + CD + DE + EA = 9.2 + 5 + 6 + 5 + 9.2 = 34.4 units.

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Answer:

Exact form: 78√2 - 17√3 / 54

Decimal form: 1.49747766

Step-by-step explanation:

Rationalize and simplify the expression.

Answer:

2

Step-by-step explanation:

→ Find 2 points from the line

( 0 , 6 ) and ( - 3 , 0 )

→ Find the change in y coordinates

0 - 6 = -6

→ Find the change in x coordinates

-3 - 0 = -3

→ Divide the 2 results

-6 ÷ -3 = 2

The general soultion of the given differential equation  12y'' − 5y' − 3y = 0 is

y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].

According to the given question.

We have a differential equation

[tex]12y^{"} -5y^{'} -3y = 0[/tex]

The above equation can be written as

[tex](12D^{2} -5D -3)y = 0[/tex]

The auxillary equation for the above differential equation is

[tex]12m^{2} -5m-3 = 0[/tex]

[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]

⇒ 3m(4m - 3) +1(4m - 3) = 0

⇒ (3m + 1)(4m -3) = 0

⇒ m = -1/3 or 3/4

Therefore,

[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]

Here, P.I = 0

As we know that the general solution of the differential equation is given by

y = PI + CF

Thereofre, the general soultion of the given differential equation  12y'' − 5y' − 3y = 0 is

y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].

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**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.

Answer: None of above

Step-by-step explanation:

Given formula

S = r θ

Given information

radius = 19 ft

Angle = 2π / 3

Substitute values into the formula

S = r θ

S = (19) (2π / 3)

Simplify by multiplication

[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The value of the solution is 3π/2.

What is a trigonometric equation?

An equation involving one or more trigonometric ratios of unknown angles is called a trigonometric equation.

tan x/2 = -1

tanx/2 = tan(-π/4)

tanx=tanФ

⇒ The general equation of tanx=tanФ is

⇒ x=nπ+Ф

x/2=nπ+(-π/4)

at n=0

x/2=-π/4

x=-π/2

at n=1

x/2=π-π/4

x/2=3π/4

x=3π/2

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Questions: Which value is a solution for the equation tan x/2 = -1?

A. 5pi/4

B. 7pi/4

C. 3pi/4

D. 3pi/2

The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.

The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.

From the given information:

y = 2x + 4  --- (1)

y = 4x + 1  --- (2)

Using the slope-intercept formula:

y = mx + b

From the first equation, the slope is 2 and in the second equation, the slope is 4.

Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.

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Answer:

9/41

Step-by-step explanation:

Cosine represents adjacent / hypotenuse.

When A is the reference angle, AB is the adjacent side (9) and AC is the hypotenuse (41).

9/41 is already simplified.

a. log₈8 = 1

b. log₇6/5

c. log₉3¹

1. log₈ 2 * 4 would produce an integer

= log₈8 = 1

The output is an integer

2. log₇6/5 would give us an irrational number

= log₇1.2

This would give us an irrational number

3. log₉3¹ would give us a rational number

= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9

= 1/2

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Answer:

Step-by-step explanation: This example is saying that adding a negative number is the same as subtracting a positive number. For example 2-3 = 2 + (-3).

The solution for the initial value problem is [tex]y_{g} = e^{-2x} (-12cos(x) + 5sin(x)) + 7e^{-4x}[/tex]

Given,

y" + 4y' + 5y = 35[tex]e^{-4x}[/tex]

y(0) = -5

y'(0) = 1

Solve this homogenous equation to get [tex]y_{h}[/tex]

According to differential operator theorem,

[tex]y_{h}[/tex] = [tex]e^{ax}[/tex]( A cos (bx) + B sin (bx)), where A and B are constants.

Therefore,

y" + 4y' + 5y = 0

([tex]D^{2}[/tex] + 4D + 5)y = 0

D = -2± i    

[tex]y_{h} = e^{-2x} ( A cos (x) + B sin (x))[/tex]

Now, solve for [tex]y_{p}[/tex]

A function of the kind [tex]ce^{-4x}[/tex] is the function on the right, we are trying a solution of the form [tex]y_{p} =ce^{-4x}[/tex], here c is a constant.

[tex]y_{p} " + 4y_{p} ' + 5y_{p} = 35e^{-4x} \\=16ce^{-4x} -16ce^{-4x} +5ce^{-4x} = 35e^{-4x} \\= 5ce^{-4x} =35e^{-4x} \\c=\frac{35}{5} =7\\y_{p} =7e^{-4x}[/tex]

Then the general solution will be like:

[tex]y_{g} =y_{h} +y_{p} \\[/tex]

    = [tex]e^{-2x} (Acos(x)+Bsin(x))+7e^{-4x}[/tex]

[tex]y_{g}(0)=-5=A+7=-12\\y_{g} '(0)=e^{-2x} (-Asin(x)+Bcos(x))-2e^{-2x} (Acos(x)+Bsin(x))-28e^{-4x} \\y'_{g} (0)=1=B-2A-28\\[/tex]

       B = 1 - 24 + 28 = 5

Then the solution for the given initial value problem is

[tex]y_{g} =e^{-2x} (-12cos(x)+5sin(x))+7e^{-4x}[/tex]

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There is only one statement that is true: B. The graph of the function is a parabola.

In this question we have a quadratic equation, whose characteristics have to be inferred and analyzed. We need to prove each of the five choices presented in the statement:

Choice A:

If we know that x = - 10, then we evaluated it at the function:

f(- 10) = (- 10)² - 5 · (- 10) + 12

f(- 10) = 162

False

Choice B:

By analytical geometry we know that all functions of the form y = a · x² + b · x + c always represent parabolae.

True

Choice C:

The quadratic function opens up as its leading coefficient is greater that 0.

False

Choice D:

If we know that x = 20, then we evaluate it at the function:

f(20) = 20² - 5 · (20) + 12

f(20) = 312

False

Choice E:

If we know that x = 0, then we evaluate it at the function:

f(0) = 0² - 5 · (0) + 12

f(0) = 12

There is only one statement that is true: B. The graph of the function is a parabola.

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The volume of the cone is  84.9 km³

Volume of a cone = 1 / 3 πr²h

where

Therefore,

radius = 3 km

height = √9.5² - 3²

height = √81.25

height = 9.01387818866

height = 9.014 km

Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014

volume of the cone = 254.732197612 / 3

volume of the cone = 84.9107325372

volume of the cone = 84.9 km³

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Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.

In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

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