If Three Angles In A Triangle Are A -x^2, B-x+40, And C-x+60, What Is Angle C? (2024)

Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’. Option D is correct .

What is a trapezoid simple definition?

A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides.

A trapezium's parallel bases and non-parallel legs are referred to as its bases and legs, respectively.

1) We have and isosceles trapezoid DEFG and and another trapezoid D'E'F'G' dilated.

2) E'F'G'H' is not congruent to EFGH (due to its legs) Besides that, E'F'G'H has undergone not to rigid motions. Rigid motions are better known as translations and rotations and they preserve length and angles. That was not the case.

3) So it's d, the only correct choice:

d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

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The complete question is -

The coordinates of the vertices of trapezoid EFGH are E(-8, 8), F(-4, 12), G(-4, 0), and H(-8, 4). The coordinates of the vertices of trapezoid E’F’G’H’ are E’(-8, 6), F’(-5, 9), G’(5, 0), and H’(-8, 3). Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E’F’G’H’? a) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions. b) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions c) Trapezoid EFGH is congruent to trapezoid E’F’G’H’ because you can map trapezoid EFGH to trapezoid E’F’G’H’ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions d) Trapezoid EFGH is not congruent to trapezoid E’F’G’H’ because there is no sequence of rigid motions that map trapezoid EFGH to trapezoid E’F’G’H’.

The total number of pennies you have at the end are 2^26 pennies

Imagine, at the first day have only one penny. Then tomorrow have 2 pennies, next day have 4 (2x2), next day have 8 (4x2), next day have 16 (8x2) and so forth.

Geometric Sequence

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio

It looks like geometric sequence (the ratio between the number of pennies that from the 2nd day and the 1st day is 2)

So, by using geometric sequence theorem can total those pennies until day 27

S (total pennies at day-27) = (1)(2^27-1) / 2-1 = 2^26 pennies

So, have 2^26 pennies.. a big number of pennies=))

The formula is: S = a( r^n-1) / r-1

a= the number of pennies that have got at the 1st day

n= number of days spent to collect those pennies)

r= the ratio of the number of pennies

2^26 pennies

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The figure in the question is a kite and the value of the angle 4 is equal to 40°

Interior angles of a kite

A kite has4 interior anglesand the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equa

Let us represent the angle 3 with x, so that;

angle 1 = 2x,

angle 2 = x + 20

angle 1 + angle 4 = one of the pair of opposite angles

angle 1 + angle 3 + 90° = 180° {sum of interior angles of a triangle}

2x + x + 90°= 180°

3x = 180° - 90° {subtract 90° from both sides}

x = 90°/3 {divide through by 3}

x = 30°

so;

angle 1= 60°

angle 2 = 50°

sum of interior angles of kite (quadrilateral) = 360°

2(angle 3) + 2(angle 2) + 2(angle 1 + angle 4) = 360°

60° + 100° + 2(60° + angle 4) = 360°

60° + 100° + 120° + 2(angle 4) = 360° {open bracket}

280° + 2(angle 4) = 360°

2(angle 4) = 360° - 280° {subtract 280° from both sides}

2(angle 4) = 80°

angle 4 = 80°/2 {divide through by 2}

angle 4 = 40°

Therefore, the angle 4 of the kite is equal to the value of 40°.

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The number= -25

Step-by-step explanation:

To solve this equation, you can start by expressing the difference between the number and 9 as 2 times the sum of the number and 8 divided by 3. This gives you the equation:

2 * (x + 8) / 3 = x - 9

You can then multiply both sides of the equation by 3 to get rid of the fraction:

6 * (x + 8) = 3 * (x - 9)

This simplifies to:

6x + 48 = 3x - 27

You can then combine like terms on both sides of the equation to get:

3x + 48 = -27

You can then add 27 to both sides of the equation to get:

3x + 75 = 0

You can then subtract 75 from both sides of the equation to get:

3x = -75

You can then divide both sides of the equation by 3 to get the solution:

x = -25

Therefore, the number x is equal to -25.

Hope this helps you??

When y be the number of heads obtained then the value of [tex]$E(Y)=\frac{1}{8}[/tex].

As per question roll one fair six-sided die and then flip as many coins as the number showing on the die.

Let [tex]$Y$[/tex] be the number of heads obtained.

[tex]$E(Y)=\Sigma_{y=1}^{y=6} y P_y(y)$[/tex]

We will define X as the number on the die.

Therefore

[tex]$$E(Y)=\sum_{y=1}^{y=6} y P_y(y)\\\\=\sum_{y=0}^{y=6} \sum_{x=1}^{x=6}(y) P(X=x, Y=y)\\\\=\sum_{y=0}^{y=6} y \sum_{x=1}^{x=6}(1 / 6)\left(\begin{array}{l}x \\y\end{array}\right)(1 / 2)^x$$[/tex]

This inner equation is valid:

[tex]$(1 / 6)\left(\begin{array}{l}x \\ y\end{array}\right)(1 / 2)^x$[/tex]

Basically, it says that if I roll a 3 , and I get 1 head only, what is the probability of that occurring [tex]=\frac{1}{6}[/tex]

From 3 rolls, we choose one head [tex]=\frac{1}{8}[/tex]

Therefore

[tex]$E(Y)=\frac{1}{8}[/tex]

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The correct answer is (c): "The hypothesis that 33% of Canadians exercise regularly cannot be rejected at significance level α = 0.05".

The confidence interval [0.30;0.42] represents our estimate of the true proportion of Canadians who exercise regularly, with a confidence level of 95%. This means that if we were to repeat the survey multiple times, using the same sampling method and sample size, we would expect the confidence interval to contain the true proportion of Canadians who exercise regularly 95% of the time.

Based on the confidence interval provided, we can say that we are at least 95% confident that more than 30% and fewer than 42% of Canadians exercise regularly. This means that statements (a) and (d) are both true. However, statement (c) is false because the hypothesis that 33% of Canadians exercise regularly is not contained within the confidence interval, and therefore cannot be rejected at significance level α = 0.05.

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Given any set of seven integers, there are no two numbers that have the same remainder when divided by 6.

The remainder is the value left after the division. If a number is not completely divisible by another number then we are left with a value once the division is done. This value is called the Remainder.

Given any set of seven integers, there must be at least two numbers that have the same remainder when divided by 6.

So there can be six remainders when divided by 6 i.e. 0,1,2,3,4 and 5.

According to the Pigeonhole principle,

in any set of seven integers, two must have the same remainder when divided by seven.

Consider the set of integers 0,1,2,3,4,5 and 66. All of these have different remainders upon division by 8.

Hence there need not be two numbers such that they have the same remainders when divided by 6.

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The power series representation for f(x)=x15x2+1f(x)=x15x2+1 is a series of terms of the form (−1)n(15x2)n+1, starting with x and going up to the nth power of x. The coefficients of each term are determined by alternating signs and multiplying the previous term by 15x2.

The power series representation for f(x)=x15x2+1f(x)=x15x2+1 can be calculated as follows: The first term is x, as this is the first power of x. The second term is -15x3, which is obtained by multiplying the first term by -15x2. The third term is 45x5, which is obtained by multiplying the second term by -15x2. The fourth term is -135x7, which is obtained by multiplying the third term by -15x2, and so on. This process is repeated for each successive term, alternating between multiplying the previous term by -15x2 and changing the sign.

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The doubles to find the sum is 1+1+1

How to find doubles?

We should know that the double is the figures when added to the original figure, will give us exact value

So by definition, a double is any amount of number which is twice as large as the given amount of a number.

The give parameter is 1+2

We can write 2 as 1+1

So this means that 1+2 can be written as

1+2=1+1+1=3

Since 1+2=3

Therefore 1+1+1=3

Hence a double is any amount of number which is twice as large as the given amount of a number,

In conclusion the doubles to find the sum of 1+2 is 1+1+1

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To find the area under the standard normal curve that lies to the right of -0.91, we can use a z-table to look up the corresponding probability. We find that the area to the right of -0.91 is approximately 0.1587.

To find the z-score for the value 76.00, we can use the formula for a z-score: (x - μ) / σ. Plugging in the values given, we get: (76.00 - 61.00) / 13.00 = 2.77. So the z-score for the value 76.00 is approximately 2.77.

To find the area under the standard normal curve that lies between -5.10 and 1.0, we can use a z-table to find the corresponding probabilities for each of these values and then subtract the probability for -5.10 from the probability for 1.0. We find that the probability of -5.10 is approximately 0.0000, and the probability of 1.0 is approximately 0.8413. Subtracting these values gives us an area of approximately 0.8413.

To find the z-value that has an area of 0.9922 to the left, we can use a z-table to look up the corresponding z-value. We find that the z-value that corresponds to an area of 0.9922 to the left is approximately 2.33.

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The expression √(7x) × (√x − 7√7) in the simplified form will be x√7 − 49√x.

What is simplification?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ √(7x) × (√x − 7√7)

Simplify the expression, then the expression is written as,

⇒ √(7x) × (√x − 7√7)

⇒ x√7 − 7 × 7√x

⇒ x√7 − 49√x

The expression √(7x) × (√x − 7√7) in the simplified form will be x√7 − 49√x.

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Answer:

I hope this helps

Step-by-step explanation:

solving for the price of y

6x + 3y = 15

3y = 15 – 6x

=

[tex]y = \frac{15 - 6x}{3} [/tex]

Answer:

the slope is 1, the coefficient of x.

Step-by-step explanation:

You want to know the mistake in declaring the slope of y=x is 0, because there is no coefficient.

Coefficient

In algebra, a coefficient of 1 is usually not written. We let 1 times something be represented by the something itself. Its existence is indication there is one of it. No multiplier is needed.

y = x ⇔ y = 1·x

Whether the 1 is there or not, there is still exactly one 'x'.

So, the coefficient of x is 1 in y=x, meaning the slope is 1, not zero.

False, If A is row equivalent to the identity matrix, then A is invertible.

Given :

if a is a square matrix that is row equivalent to the identity matrix then a is diago - nalizable.

Identity matrix :

An identity matrix is a square matrix having 1s on the main diagonal, and 0s everywhere else .

Invertible matrix :

An invertible matrix is a matrix for which matrix inversion operation exists, given that it satisfies the requisite conditions.

so given statement is false if A is row equivalent to the identity matrix, then A is invertible.

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Answer:

The answer is B

Step-by-step explanation: A trick I use for these type of problems is pick a point from the highest part of the graph, then make a right triangle. A right triangle with this graph will make the answer -2/3 since it goes down 2 right 3

The value of X=8 when the bases have lengths of 2x+4 and 8x-50

A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The nonparallel sides are referred to as the legs of the trapezoid.

A median of a trapezoid is the segment that joins the midpoints of the nonparallel sides (legs). The median is also parallel to the two bases, and it is the average length of the two bases.

The formula to find the median is

median=a+b/2

where a and b are the lengths of the bases or parallel sides.

we have the values of a=2x+5 b=8x-50 m=17 now substitute the values in the above formula and we get x value:

(17)=2x+4+8x-50/2

17=10x-46/2

2(17)=10x-46

10x=80

x=8

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170= x + (x *2+5) + (x *2+5-15).
x = 35

Day 1 = 35
Day 2 = 75
Day 3 = 60

The remainder when the sum of 1⁹⁹ + 2⁹⁹ + 3⁹⁹ +.... + 2022⁹⁹ is divided by 2023 is 0.

How to determine the reminder?

We can use the formula for the sum of an arithmetic series to find the sum of the series 1⁹⁹ + 2⁹⁹ + 3⁹⁹ +.... + 2022⁹⁹. The formula is:

Sum = (n/2) (2a + (n - 1)d)

Where n is the number of terms in the series, a is the first term, and d is the common difference.

In this case, the first term is 1, the common difference is 1, and the number of terms is 2022.

Plugging these values into the formula, we have:

Sum = (2022/2)(2×1 + (2022 - 1) × 1) = (2022/2)(2 + 2021)

We can simplify this to:

Sum = (2022/2)(2023) = (2022/2)(2023) = (2022 × 2023)/2

To find the remainder when this sum is divided by 2023, we can use the property of modular arithmetic:

(a + b) mod n = ((a mod n) + (b mod n)) mod n

Applying this property to the sum we have:

(Sum mod 2023) = (((2022 × 2023)/2 mod 2023) + (0 mod 2023)) mod 2023

The remainder when 2022 × 2023 is divided by 2023 is 0, so the expression simplifies to:

(Sum mod 2023) = (0 + 0) mod 2023 = 0

Thus, the remainder is 0

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Answer:

Slope: 1/3 ---- y-intercept: (0,-3)

Step-by-step explanation:

Let A be the set of all prime numbers, B be the set of all even prime numbers, and C is the set of all odd prime numbers, then A = BUC, B is a singleton set and A = CU{2}. Hence, the correct option for this question is option D - All of the mentioned.

We have,

A = set of all prime numbers

A = {2, 3, 5, 7, 11, 13, ...}

B = the set of all even prime numbers

B = {2}

C = the set of all odd prime numbers

C = {3, 5, 7, 11, 13, ...}

We know that 2 is the only even prime number. hence, Set B is a singleton set, containing only one element.

Also, if we take the union of set B and set C, we will get the set of all the prime numbers, which is set A. Hence, we get, A = B U C.

If we have A = B U C, we can also say A = C U {2}, since B = {2} is a singleton set.

Hence, all the options mentioned above are correct.

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Part 1

[tex]a=\sqrt{12^2 + 21^2 -2(12)(21) \cos 35^{\circ}} \approx \boxed{13}[/tex]

Part 2

[tex]\frac{\sin B}{b}=\frac{\sin A}{a}\\\\\sin B=\frac{b\sin A}{a}\\\\\sin B=\frac{12 \sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}}\\\\B=\sin^{-1} \left(\frac{12\sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}} \right)\\\\B \approx \boxed{32^{\circ}}[/tex]

Part 3

[tex]\angle C=180^{\circ}-\angle A -\angle B=\boxed{113^{\circ}}[/tex]

The radius of the semicircle having an arc of length equal to 8.5 [tex]\pi[/tex] in a right-angle triangle ABC is equal to 7.5 cm.

Given:

Angle ABC of triangle ABC is a right angle. The sides of ABC are the diameters of semicircles.

The area of the semicircle on AB equals 8[tex]\pi[/tex].

Area of a semicircle = [tex]\pi r^2/2[/tex]

Therefore:

[tex]\pi r^2/2[/tex] = 8[tex]\pi[/tex]

[tex]r^2 = 16[/tex]

[tex]r = 4[/tex]

Next, the arc of the semicircle on AC has a length of 8.5[tex]\pi[/tex].

Length of the arc of a semicircle = [tex]\pi r[/tex]

[tex]\pi r[/tex] = 8.5[tex]\pi[/tex]

[tex]r = 8.5[/tex]

Using Pythagoras theorem

[tex]8.5^{2} = 4^{2} + x^{2}[/tex]

[tex]x^{2} = 8.5^2 - 4^2\\[/tex]

[tex]x^{2} = 56.25[/tex]

[tex]x = \sqrt{56.25}[/tex]

[tex]x = 7.5[/tex]

The radius of the semicircle of BC = 7.5 Units.

Refer to this complete question for this:

Angle ABC of triangle ABC is a Right angle. The sides of ABC are the diameters of semicircles as shown. The area of the semicircle on AB equals 8pi and the arc of the semicircle on AC has a length of 8.5pi. What is the radius of the semicircle of BC?

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The correct option is 3

Step-by-step explanation:

Multiple inputs can give the same output, but not vice versa.

The two case given below are disjoint and cover all the cases for n length strings, hence the numbers add up to give [tex]a_{n} =a_{n-1}+a_{n-2}[/tex].

In the given question we have to find a recurrence relation for the number of n-digit binary sequences with no pair of consecutive.

Be sure to include the initial conditions Solution an [tex]a_{n-1}+ a_{n-2}[/tex] Initial condition: [tex]a_{1}=2,a_{2}=3[/tex]

Clearly [tex]a_{1}[/tex] = 2 (0,1) and [tex]a_{2}[/tex] = 3 (00,10,01). Now for the case of n. Suppose we are given a string with no consecutive 1's. There are two cases:

Case 1: the given string starts with a 0. In this case the n-1 length string after the first bit can be any string without consecutive 1's of length n-1. Hence there are n-1 of those.

Case 2: the given string starts with a 1. In this case the second bit has to be a 0 since we don't want consecutive 1's. Not the last n-2 length string can be any string without consecutive 1's of length n-2. Hence there are [tex]a_{n-2}[/tex] of those.

These two case are disjoint and cover all the cases for n length strings, hence the numbers add up to give [tex]a_{n} =a_{n-1}+a_{n-2}[/tex].

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The coordinates of the other endpoints is (-4, -9).

What is midpoint of a line segment?

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

Midpoint: (2, -7) = (x, y)

Endpoints: (a, b) and (8, -5) = (c, d)

Now,

x = (a + c)/2

2 = (a + 8)/2

4 = a + 8

a = 4 - 8

a = -4

y = (b + d)/2

-7 = (b - 5)/2

-14 = b - 5

b = -14 + 5

b = -9

Thus,

The other endpoint is (-4, -9).

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Each element in B is an infinite sequence (b1, b2, b3, ...), where each

bi ∈ {0, 1}.

Infinite Sequence:

An infinite sequence (sometimes simply called a sequence) is a function with a domain of all positive integers. At the beginning of calculus, the domain of infinite sequences is usually the set of real numbers, but the domain can also include complex numbers.

The general form of the infinite sequence is

f(1), f(2), f(3),…f(n),…

where:

… = continues indefinitely,

n = Positive integer (input),

f(n) = real number (output).

Diagonalization:

Converting a matrix to diagonal form is called diagonalization. The eigenvalues ​​of a matrix are clearly represented by a diagonal matrix. A diagonal matrix is ​​a square matrix in which all elements except the main diagonal are zero. In this article, let's take a look at the definition, process, and example solution of diagonalization.

[tex]\left[\begin{array}{ccc}4&0&0\\0&5&0\\0&0&6\end{array}\right] = I_3 \left[\begin{array}{ccc}4&0&0\\0&5&0\\0&0&6\end{array}\right] I_{3} ^-1[/tex]

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Hello,

I hope you and your family are doing well!

DeShawn will owe 9% tax on the first $30,000, which is $30,000 * 9% = $2,700.

The remaining $66,000 - $30,000 = $36,000 will be taxed at 15%.

So DeShawn will owe an additional $36,000 * 15% = $5,400 in tax.

In total, DeShawn will owe $2,700 + $5,400 = 8,100 in tax.

Please consider giving this 5 stars and brainliest if you find this answer helpful.

Happy Holidays!

The tax DeShawn has to pay is $8100

What is Tax?

Taxes are mandatory contributions levied on individuals or corporations by a government entity.

Given that, DeShawn earned $66,000 last year and the first $30,000 is taxed at 9% and income above that is taxed at 15%,

DeShawn will owe 9% tax on the first $30,000, which is $30,000×9% = $2,700.

The remaining $66,000 - $30,000 = $36,000 will be taxed at 15%.

So DeShawn will owe an additional $36,000 * 15% = $5,400 in tax.

In total, DeShawn will owe $2,700 + $5,400 = $8,100 in tax.

Hence, The tax DeShawn has to pay is $8100

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