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The congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

For the given triangles ABC and triangle LMN we can see that:

Line segment AB = LM

Segment AC= LN

and, CB = MN

Hence, the congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.

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Answer:

see below

Step-by-step explanation:

tricycles = x

bicycles = y

x+y =10 so y=10-x

3x+2y=23

so 3x + 2(10-x) =x+20 =23

so x=3

y = 7

Step-by-step explanation:

The probability of selecting a defective watch is 400/10,000 = 2/50.

The probability of selecting 50 defective watches out of 100 selected is given by the binomial distribution:

(100 choose 50) * (2/50)^50 * (1/2)^(100-50) = 0.072.

So the probability that exactly 50 out of 100 selected watches are defective is approximately 0.072.

The solution to the integral ∫ [csc x · (cot x + csc x)] dx is - (csc x + cot x) + C. (Correct choice: A)

In this problem we find the case of an integral involving trigonometric functions, this can be solved quickly by means of algebra properties and integral tables. Integral tables are an useful resource to find the result of integrals that require a lot of time to be solved.

First, write the function within the integration operator and simplify by algebra properties:

csc x · (cot x + csc x)

csc x · cot x + csc² x

Second, rewrite the integral by integral properties:

∫ [csc x · (cot x + csc x)] dx = ∫ csc x · cot x dx + ∫ csc² x dx

Third, use integral tables to find the solution to the integral:

∫ [csc x · (cot x + csc x)] dx = - csc x - cot x + C

∫ [csc x · (cot x + csc x)] dx = - (csc x + cot x) + C

Where is C is the integration constant.

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Answer:

28 different selections

Step-by-step explanation:

The number of ways in which k items can be drawn from a larger sample of n items is given by:

[tex]nC_k\;[/tex] pronounced as "n choose k" relates to a class of problems known as combinatorics

[tex]nC_k\;[/tex] is given by the formula
[tex]nC_k\; =\dfrac{n!}{k!(n-k)!}[/tex]

where ! stands for the factorial of a number

n! = n x (n-1) x ...... x 3 x 2 x 1

Plugging values of n and k into the equation we get

[tex]8C_2\; =\dfrac{8!}{2!(8-2)!} = \dfrac{8!}{2!\;6!}[/tex]

We can rewrite 8! as 8 x 7 x 6!

So
[tex]8C_2\; =\dfrac{8\cdot 7 \cdot 6!}{2!\; 6!} = \dfrac{8 \cdot 7}{2 \cdot 1} = \dfrac{56}{2} = 28[/tex]

Answer: t=-5

Step-by-step explanation:

Multiply by -6 on both sides to get rid of the -1/6

Subtract 12 on both sides
Divide 18 by -90 on the other side

[tex](-1/6(12+18t))(-6)=13(-6)\\12+18t=-78\\18t=-90\\\\t=-5[/tex]

Answer:

81

Step-by-step explanation:

[tex]2\frac{1}{4}*36\\ \\\frac{9}{4}*\frac{36}{1} \\ \\\frac{324}{4} =81[/tex]

If you already chopped 4 walnuts and you have only gotten 1/4 cup of the chopped walnuts, it means that each walnut yields 1/4 cup / 4 walnuts = 1/16 cup of chopped walnuts.

To find out how much more chopped walnuts you need, we can subtract the amount you have from the total amount the recipe calls for:

1 cup - 1/4 cup = 3/4 cup

So you need 3/4 cup of chopped walnuts more.

To find out how many more walnuts you should chop, divide the amount you need by the amount each walnut yields:

3/4 cup / (1/16 cup/walnut) = 12 walnuts

So you should chop 12 more walnuts to get the desired amount.

Answer:

5, second choice

Step-by-step explanation:

When x is 3, the purple line's y-value is between 4 and 6, which is 5.

Answer:

B

Step-by-step explanation:

You have two black lines with the arrows at the end. The one going left and right is your X-Axis. The one going up and down is the Y-Axis.

What they want to know is what is f(x) when x = 3

f(x) is another term for y

So they want to know, what is the value of the y-axis when x is 3 on the x-axis.

So on the line going left and right you find the line 3, between 2 and 4, then going up until you hit the purple line. Once you hit the purple line, go left until you hit the up and down line. That will give you an answer of 5

"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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The decimal number 0.4 is greater than 0.25.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

There are 25 out of 100 shaded cubic part.

That means, the number is 0.25.

From the given choices:

0.4 > 0.25.

Therefore, 0.4 is the required decimal number.

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The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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Therefore , the solution of the given problem of triangle comes out to be m∠x = 30° they are congruent.

Triangles are included in polygons because they have four aspects or more. It is simple and geometric in design. The triangle formed by the letters ABC has a square angle. A single rectangles or square is produced by euclidean geometry when the sides are not coinciding. Triangles are polygons because they have three parts and three corners. The intersection of a triangle's three sides forms its corners. A triangle has 180 degrees of angles in all.

Here,

Given :

=> ΔEFG ≅ ΔXYZ

In ΔEFG

=> 90° + 60° + x = 180°

=> 150° + x = 180°

=> x = 180° - 150°

=> x = 30°

Since . they are congruent .

So m∠x = 30°

Therefore , the solution of the given problem of triangle comes out to be m∠x = 30° they are congruent.

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a) The locus of points that are less than 5 cm from P is (A)

b) The  locus of points that are closer to Q than to P is (F)

c) The locus of points that are more than 5 cm from Q is (D),

A locus is a curve or other shape created in mathematics from all the points that meet a specific equation describing the relationship between the coordinates, or from a point, line, or moving surface. The locus defines all shapes as a set of points, including circles, ellipses, parabolas, and hyperbolas.

Given:

a) The point A is less than 5cm away from point P is int he circle centered on P.

b) The option E is point closer to P than Q.

The option F is point closer to Q than P.

c) The option D point more than 5 cm away from Q on the outside of the circle centered on Q.

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Answer:

3.844, 3.840, 3.836, 3.832, 3.828 ,3.824, 3.820 - minus by 4

30.565, 31.065, 31.565, 32.065, 32.565, 33.065, - minus 0.5 , -0.5 , 0.5 .......

Answer: We can use the Law of Cosines to find the length of side k in ΔJKL:

k^2 = j^2 + l^2 - 2 * j * l * cos(m∠K)

k = √(j^2 + l^2 - 2 * j * l * cos(m∠K))

Substituting the given values, we get:

k = √(1.7^2 + l^2 - 2 * 1.7 * l * cos(47°))

k = √(2.89 + l^2 - 2.94 * l * cos(47°))

To the nearest 10th of an inch, k = √(2.89 + l^2 - 2.94 * l * cos(47°)) = 3.3 inches.

Step-by-step explanation:

Answer: [tex]11a+16[/tex] feet

Step-by-step explanation:

The perimeter is equal to the sum of the lengths of the sides.

[tex]2a+2a+2a+8+5a+8=11a+16[/tex]

if Fred has 40 balls in his room then there are 7 pits in his room.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that there are 12 balls to every 2 pits

Fred has 40 balls in his room

We have to find the number of pits for 40 balls

Let x be the number of pits for 40 balls.

Form an proportional equation

12/2=40/x

6=40/x

x=40/6=20/3

x=6.667=7

Hence, if Fred has 40 balls in his room then there are 7 pits in his room.

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The algebraic representation of the sentence the sum of 3x and 70 exceeds 13x is: 3x + 70 > 13x.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given that the sum of 3x and 70 exceeds 13x, this is represented as:

3x + 70 >13x

Hence, the algebraic representation of the sentence the sum of 3x and 70 exceeds 13x is: 3x + 70 > 13x.

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If the economy is producing 12 units of guns and 4 units of butter, the opportunity cost of increasing the production of butter from 4 units to 11 units is 4 units of guns.

In Economics, an opportunity cost is sometimes referred to as alternative forgone and it can be defined as the value, profit or benefits that are given up and forfeited by an individual or business organization, in order to choose or acquire something that is deemed most significant at a particular point in time.

This ultimately implies that, the opportunity cost of owning or earning a thing is the alternative that is foregone in the attainment or earning of another value, profit or benefits.

Cost increase = 11 units - 4 units = 7 units of butter.

In this context, we can reasonably infer and logically deduce that the opportunity cost of 7 more units of butter would be 4 units of guns.

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Step-by-step explanation:

To find the probability of getting an even number, we need to count the number of even numbers and divide it by the total number of sides of the die:

Number of even numbers = 10 (2, 4, 6, 8, 10, 12, 14, 16, 18, 19)

Total number of sides = 19

P(even number) = Number of even numbers / Total number of sides = 10/19 = 0.526 (or 52.6%)

The given function

F(x)  = √(8 - x²)/ (2x² - 5)

is continuous at  x = -2,

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  = √(8 - x²)/ (2x² - 5)

To check whether it is continuous at x = -2

First taking LHL,

[tex]\lim_{h \to \00}[/tex] √[8 - ( -2 -0)²]/ [2(-2-0)² - 5]

⇒ √4/(8-5)

⇒   2/3

Now, taking RHL

[tex]\lim_{h \to \00}[/tex]  √[8 - ( -2 +0)²]/ [2(-2+0)² - 5]

⇒ √4/(8-5)

⇒   2/3

The value at x = -2

F(3)  = √[8 - ( -2 +0)²]/ [2(-2+0)² - 5]

⇒ √4/(8-5)

⇒   2/3

RHL = LHL =  F(-2)

Hence Proved,  the function is continuous at x = -2

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On solving the provided question, we can say that In rectangle, the two diagonals are in congruence , the diagonals bisect each other. PT=TR=ST=TQ=1/2PR=1/2QS =1/2×22.8=11.4

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Rectangle, two diagonals are in congruence

⇒PR=QS=22.8

The diagonals bisect each other.

⇒PT=TR=ST=TQ=1/2PR=1/2QS

=1/2×22.8=11.4

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Answer:

slope:m=5m=5

Step-by-step explanation:

Step-by-step explanation:

y-y1=m (x-x1)

y-4=5 (x-3)

y-4=5x-15

5x-y=11

Answer:

Step-by-step explanation:

To show that x-3 and x+5 are factors of x^4+2x^3-16x^2-2x+15, we can use polynomial division, synthetic division, and the Remainder theorem.

Using long division, we can divide x^4+2x^3-16x^2-2x+15 by x-3:

x^4 + 2x^3 - 16x^2 - 2x + 15

÷ x - 3

_________________________

  x^3 + 5x^2 - 14x - 12

   |__________

      -3x^3 + 17x^2 + 26x + 36

          |_________

                -14x^2 - 23x - 36

                     |_________

                          -15x + 72

                               |___

                                  57

So, the remainder is 57, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x - 3)(x^3 + 5x^2 - 14x - 12) + 57.

Using synthetic division, we can divide x^4 + 2x^3 - 16x^2 - 2x + 15 by x+5:

1   2    -16   -2   15

   x + 5 |x^4 + 2x^3 - 16x^2 - 2x + 15|

____________________________

        x^3 - 3x^2 + 21x + 75

So, the remainder is 0, which means x^4 + 2x^3 - 16x^2 - 2x + 15 = (x + 5)(x^3 - 3x^2 + 21x + 75).

Using the Remainder theorem, we know that if a polynomial p(x) is divided by x-a, the remainder is p(a). So, when we plug in x=3, the remainder should be p(3) = 57. When we plug in x=-5, the remainder should be p(-5) = 0. This confirms that x-3 and x+5 are indeed factors of x^4 + 2x^3 - 16x^2 - 2x + 15.

Answer:lmkmonmklmlkmlkn

Step-by-step explanation:;lmklmlkmlkm

Answer:

if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months. you will have 800,000 after 20 years.

Step-by-step explanation:

rate of return is 5.3% compounded monthly.

number of years = 40.

future value = 800,000

interest rate per month is 5.3% / 12 = .4416666....%

number of time periods if 40 * 12 = 480

payment required at the end of each month is equal to 484.5267545

your total payments are 480 * 484.5267545 = 232,572.8422

total interest earned would be 800,000 minus 232,572.8422 = 567,427.1578

if you want to achieve your goal in 20 year, you would have to invest 1879.790424 at the end of each month for 240 months.

you will have 800,000 after 20 years.

if you deposit that money for an additional 10 years at the same rate of interest per year compounded annually, then you will have 1,357,560.674.

you can use an online calculator to get the results similar to this.

they might not be right on because of possible rounding errors, but they'll be close.

The angle θ that is coterminal with angle 14π/3, is 20π/3

Coterminal angles are the angles that have the same initial side and share the terminal sides. These angles occupy the standard position, though their values are different. They are on the same sides, in the same quadrant and their vertices are identical.

Given that, we need to find a coterminal angle of 14π/3,

The formula to find the coterminal angles is, θ ± 2πn where, n is an integer and it denotes the number of rotations around the coordinate plane.

For finding one coterminal angle: n = 1 (anticlockwise)

Then the corresponding coterminal angle is,

= 14π/3 + 2πn

= 14π/3 + 2π(1)

= 14π/3 + 2π

= 20π/3

Hence, the angle θ that is coterminal with angle 14π/3, is 20π/3

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Answer:

∠YPV = 50°

∠XPV = 130°

∠WPZ = 85°

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc.

6. Arc ZVW is a major arc.

7. Arc YWZ is a major arc.

8. Arc ZXW is a major arc.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc.  

Step-by-step explanation:

As WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.

As VW is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPX + ∠XPV = 180°

⇒ 50° + ∠XPV = 180°

⇒ ∠XPV = 130°

As XY is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°

⇒ ∠WPZ + 45° + 50° = 180°

⇒ ∠WPZ + 95° = 180°

⇒ ∠WPZ = 85°

Add the central angles to the given circle diagram (see attachment).

Note that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.

Note that three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.

As WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle.

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 50° + 45° = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.

6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.

7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.

8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.  

The answers to the respective arcs are given as follows:

The arcs are defined as follows:

It is to be noted that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.

Also, three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.

To solve for the arcs:

Given that WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.

As VW is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPX + ∠XPV = 180°

⇒ 50° + ∠XPV = 180°

⇒ ∠XPV = 130°

Since XY is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°

⇒ ∠WPZ + 45° + 50° = 180°

⇒ ∠WPZ + 95° = 180°

⇒ ∠WPZ = 85°

Given that WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle. Thus,

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 50° + 45° = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.

6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.

7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.

8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.  

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The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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