In the diagram below, \overline{MN}
MN
is parallel to \overline{JK}
JK
. If MNMN is 1212 more than LNLN, LK=33LK=33, and JK=55JK=55, find the length of \overline{LN}
LN
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

Answer:

The angle in the sector is 180°.

Because the area of circle is 36 pie cm². So the angle is the half of 360°.

[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]

No, the sine ratio of an acute angle cannot be greater than 1. The sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio will always be less than one.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

It's important to note that if you were to give an angle value greater than 90 degrees, the sine of the angle will be a negative value, but the ratio will still be less than one.

The sine ratio is a value between -1 and 1, and it is impossible for the sine of an acute angle to be greater than 1.

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Three variable lines are drawn in the three dimensional coordinate system.

Three-dimensional coordinate system is also called rectangular coordinate system. The system has three reference axes named X, Y and Z axis which are perpendicular to each other.

The above three axes intersect at the origin.

In the analytical geometry, location of each point is represented by three coordinate system. They give mathematical statement by using three-dimensional space.

In order to plot in the three-dimensional plane, we need to determine the value of x, y and z. At first, we start from the origin and approach to the positive x direction if our x value is positive, otherwise we need to go to the negative x direction. After identifying the x coordinate, we need to move parallel to y direction and locate the y coordinate and finally we identify the z coordinate in the same way. In the last, we will join the points.

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Answer:

a2 = b2 + c2 2bc cos(0)

Step-by-step explanation:

In the circle below the  suppose m WXU=102° and mL XWV=68° then the following is m ZXUV = 88°.

Four-sided shapes with all four corners on the same circle are known as cyclic quadrilaterals. A cyclic quadrilateral's internal angles are always added up to 360 degrees.

(a) m / WXU = 102° (Given)

(b) To find m ZXUV, we can use the property that the angles in a cyclic quadrilateral add up to 360°. Since WXU, XWV, and XLV are all inscribed angles that intercept the same arc, they are congruent. Therefore, m WXU = m XWV = m XLV = 102°. Adding these angles together, we have:

102° + 102° + 68° + m ZXUV = 360°

Solving for m ZXUV, we get:

m ZXUV = 360° - (102° + 102° + 68°)

m ZXUV = 88°

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The terms of the expression are 5x², 9x and 6

Algebraic expressions are described as expressions that are composed of variables, factors, constants, coefficients and terms.

They are also known to be made up of arithmetic operation, such as;

It is also important to note that terms in algebraic expressions are seen as summands in a sum that may be different only by a actor.

They can be regrouped by the addition of  their coefficients. Like terms are those that has the same variables to the same powers or coefficients.

The types are;

5x², 9x and 6

Thus, they are 5x², 9x and 6

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The largest side of the length is 26cm.

Now, According to the question:

Three consecutive even numbers can be expressed in terms of n. If n is an even number then,

(n -2), (n), (n + 2)

are three consecutive even numbers.

Therefore,

(n -2)+ (n)+ (n + 2) = 72cm.

We can simplify so...

3n + 2 - 2 = 72 cm.

3n + 0 = 72 cm.

3n = 72cm.

Divide both sides by 3 to solve for n

n = 24 cm.

24 is an even integer. Input 24 into the original equation.

(n -2)+ (n)+ (n + 2) = 72cm.

(24 - 2) + 24 + (24 + 2) = 72cm

22 + 24 + 26 = 72

72 = 72

Hence, The largest side of the length is 26cm.

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In the case of a 24-pack for $5. 49, the cost of the unit is the lowest.

The cost per item is nothing to the amount of money invested in buying one item.

As we have 3 different scenarios:

Case A. 6- pack for $2. 49

As here. cost of 6 packs is $2.49, so for determining the cost of one pack we will divide $2.49 by 6.

So, the cost of 1 pack will be = 2.49/6 = 0.415 $/pack

B. 12-pack for $3. 99

As here. cost of 12 packs is $3.99, so for determining the cost of one pack we will divide $3.99 by 12.

So, the cost of 1 pack will be = 3.99/12 = 0.3325 $/pack

C. 24-pack for $5. 49

As here. cost of 24 packs is $4.49, so for determining the cost of one pack we will divide $5.49 by 24.

So, the cost of 1 pack will be = 5.49/6 = 0.22875 $/pack

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Answer:

$220

Step-by-step explanation:

first let's make the $12 bracelets as Type1 and the $8 bracelets as Type2,

then we calculate the amount she made by selling each type.

Eq.1 : No. of Type1 bracelets Selena made = 9

         Amount she sold them for = $12

         Amount she made by selling them = 9*12

                                                                                   = $108

Eq.2 : No. of Type2 bracelets Selena made = 14

          Amount she sold them for = $8

          Amount she made by selling them = 14*8

                                                                               = $112

Now we calculate the Total Amount she made

we add both of the amounts

$108 + $112

= $220

Hope this helps :)

The two examples of the solution are sugar water, and soda water.

The term solution is defined as a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.

Here according to the definition of solution, here we know that Common examples of solutions are sugar in water and salt in water solutions, soda water, etc.

As we all know that the solutions have two components, one is solvent and the other is solute.

Here the components, that is the component that dissolves the other component is called the solvent where as the component(s) that is/are dissolved in the solvent is/are called solute(s).

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The effective annual rate of interest if you do not make any payments for a year is 35%.

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.

We can write -

A = 500(1 + 0.3/12)¹²⁽¹⁾

A = 500(1 + 0.025)¹²

A = 500 x (1.025)¹²

A = 675

Effective annual interest rate for a year is as follows -

A = 500(1 + r/1)⁽¹⁾⁽¹⁾

675 = 500(1 + r)

1 + r = 675/500

1 + r = 1.35

r = 0.35

r = 35%

Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.

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Answer:

C. Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles)

Step-by-step explanation:

The student first made a mistake in step 2. In order to check if the sum of the measures of the two remote interior angles of a triangle is equal to the measure of the exterior angle, it is necessary to use the property of alternate exterior angles. Alternate exterior angles are angles that are on opposite sides of the transversal and between the same parallel lines, so they are congruent. The measure of alternate exterior angles is always equal to 180 degree. Therefore, the correct statement in step 2 is that m∠o + m∠p = 180 degrees (alternate exterior angles)

Hope this helps

Answer:

Stretch the graph of f(x) = x + 3 vertically by a factor of 2.

The "same" transformations result in f(x) = 2x + 5

The "different" transformation results in f(x) = 2x + 6

Step-by-step explanation:

Transformation Rules

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

Carry out the given transformations.

Given function:

[tex]f(x) = 2x + 3[/tex]  

Translation of 2 units up:

[tex]\begin{aligned}\implies f(x) + 2&= 2x + 3 + 2\\&=2x+5\end{aligned}[/tex]

Given function:

[tex]f(x) =x + 3[/tex]

Vertical stretch by a factor of 2:

[tex]\begin{aligned}\implies 2f(x)&=2(x+3)\\&=2x+6\end{aligned}[/tex]

Given function:

[tex]f(x) = x + 5[/tex]

Horizontal shrink by a factor of 1/2:

[tex]\implies f\left(\dfrac{1}{\frac{1}{2}}x\right)=f(2x)=2x+5[/tex]

Given function:

[tex]f(x) = 2x + 3[/tex]

Translation of 1 unit left:

[tex]\begin{aligned}\implies f(x+1) &= 2(x+1) + 3\\&=2x+5\end{aligned}[/tex]

Three of the transformations result in the same function f(x) = 2 + 5.

Therefore, the transformation that does not belong with the other three is:

Answer:

33.75

Step-by-step explanation:

1.75*95 = 16 6.25

200 - 166.25 = 33.75

Answer:

150-c

Step-by-step explanation:

150= total

c= children

adults=x

x=150-c

Answer:

a) 3

b) 16 Celsius

Answer:

A. -4°C

B. 16°C

Step-by-step explanation:

A. (-7°C)-(-3°C)= -4°C

Therefore Paris is -4°C colder than Malé.

B. 23+(-7°C)=16°C

Therefore the temperature in Rome is 16°C

Hope it helps you

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The amount of eroded rock in cubic kilometres is 1 km3.

To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.

In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:

20 m / 1000 = 0.02 km

Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:

10 km * 5 km * 0.02 km = 1 km3

So the amount of eroded rock in cubic kilometres is 1 km3.

Complete Question:

The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?

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The value of x that will make aob a straight line equation is x = -6.

To make aob a straight line, we need to make the gradients of both lines equal.

The gradient of the first line is 3x20 = 60.

The gradient of the second line is 4x-36 = 4x-36.

To make the gradients equal, we need to solve the equation 4x - 36 = 60.

Subtracting 36 from both sides gives us: 4x = 96.

Dividing both sides by 4 gives us x = -6.

Therefore, the value of x that will make aob a straight line is x = -6

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Isosceles Triangle has 50°, 65°, 65°

An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.

Properties of Isosceles Triangle:

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Answer: A

Step-by-step explanation:

Based on the graph, we know that it is decreasing if it is going down from left to right.

A: correct

Looking at choice A, it says the interval is from -4<x<-3. This means we have to find x=-4 and x=-3. On the graph, that interval is going down from left to right, so it is decreasing.

B: incorrect

Looking at choice B, it says the interval is from -2<x<0. This means we have to find x=-2 and x=0. On the graph, that interval is going up from left to right, so it is increasing.

C: incorrect

Looking at choice C, it says the interval is from 0<x<2. This means we have to find x=0 and x=2. On the graph, that interval is going up from left to right, so it is increasing.

D: incorrect

Since we have identified A as decreasing, then none of the above can't be the answer.

Therefore, A is the correct answer.

The standard form of linear function y = - (1 / 2) · x + 6 is (1 / 12) · x + (1 / 6) · y = 1.

In this question we find a linear function in slope-intercept form:

y = m · x + b

Where:

From which we must obtain the linear function in standard form:

a · x + b · y = c

Where:

We can derive the standard form of the linear equation by algebra properties:

y = m · x + b

(1 / b) · y = (m / b) · x + 1

- (m / b) · x + (1 / b) · y = 1

If we know that m = - 1 / 2 and b = 6, then the equation of the line in standard form is:

- [(- 1 / 2) / 6] · x + (1 / 6) · y = 1

(1 / 12) · x + (1 / 6) · y = 1

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x>9 perfectly describes the situation.

In mathematics, inequalities characterise the connection between two non-equal numbers. Inequality implies being unequal. If two values are not equal, we use the "not equal symbol ()". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.

Let x be the amount of hot cocoa in fluid ounces that each mug contains.

Since each mug has more than 9 fluid ounces of hot cocoa, we can write the inequality as:

x > 9

We also know that the total amount of hot cocoa made is 8 mugs * the amount of hot cocoa in each mug = 8x.

So the inequality can be written as:

8x > 9*8 = 72

or

x>9

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The length of HG can be expressed as HG = b√2.

Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the most basic shapes in geometry and is found in nature in the form of mountains, icebergs and even the human face. It has a variety of applications in mathematics, engineering, and other fields. Triangles are also used to define angles and even the area of a plane.

This is because the triangle is a right triangle, and the Pythagorean Theorem states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Therefore,
HG2 = b2 + b2 = 2b2,
which reduces to HG = b√2.

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A triangle is said to be acute if the sum of the squares of its two shorter sides is greater than the square of its longest side.

Less than 90 degree angles are considered acute. Right angles have a 90 degree angle. Angles that are obtuse exceed 90 degrees.

See samples of various angles and learn about them. If and only if side lengths a, b, and c satisfy a2 + b = c2, a right triangle will be formed. These numbers are referred to as a Pythagorean triple. When the square of a triangle's longest side equals the sum of the squares of its other two sides, the triangle is said to be a right triangle. So, in the ABC equation, if c2=a2+b2, then C is a right triangle, with PQR serving as the right angle.

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According to fraction and ratio, second dog is 3/2 feet long.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

First dog is 5 feet long.

then,

5 feet is equal to 4/5 of the second dog's length.

multiply both sides by 5/4.

5/4 x 5 feet is the second dog's length.

The second dog is 25/4 feet long.

The second dog is 6(1/4) feet long.

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The standard way to solve 3 linear equations with 3 variables is to use elimination or substitution.

-Elimination: To solve the 3 equations using elimination, add or subtract equations together to eliminate one of the variables. Keep repeating this process until you are left with one equation with one variable. Solve the equation and then use the value of the variable to substitute back into the other equations to find the values of the other variables.

-Substitution: To solve the 3 equations using substitution, pick one of the equations and solve it for one of the variables. Then substitute the value of the variable into the other equations. Keep repeating this process with the other equations and variables until you have a system of equations with one variable that you can solve. Once you have the value of the variable, substitute it back into the other equations to find the value of the other variables.

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Answer:

85.71% probability

Step-by-step explanation:

30 of 35 of the students are in abc range so take 35/100% or 0.35 and go 30/0.35 and you get 85.71%

Answer:

there's one solution bc the lines have one point in common

Answer: b

Step-by-step explanation:

4-3

——-

13.40- 10.05

= 1/3.35

=b

If Jason missed 3 goals and made 9 goals in one practice session the prediction we can make if the number of tries is 24 , then (c) Jason will make 18 goals .

Jason is practicing for making soccer goals and keeping a track of the results ;

the number of goals missed by Jason is = 3 goals ;

the number of goals that Jason made is = 9 goals ;

So , the total number of goals is = 12 goals ;

the ratio of making a goal to the total goals is = [tex]\frac{9}{12}[/tex] ;

So , the number of goals that Jason will make in 24 tries can be calculated as = [tex]\frac{9}{12} \times 24[/tex]

= [tex]9 \times 2[/tex]

= 18 .

Therefore , the Jason will make 18 goals in 24 tries .

The given question is incomplete , the complete question is

Jason practiced making soccer goals and kept track of the results. he missed 3 goals but made 9 in one practice session. What can Jason predict regarding goals made if his next practice session has 24 tries?

(a) Jason will make 8 goals.

(b) Jason will make 16 goals.

(c) Jason will make 18 goals.

(d) Jason will make 21 goals.

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