Angle J and Angle M are base angles of isosceles trapezoid JKLM. If angle j= 23x+5, and angle m = 13x+15 , find measure k .

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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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

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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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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Answer:

33.75

Step-by-step explanation:

1.75*95 = 16 6.25

200 - 166.25 = 33.75

Answer:

a2 = b2 + c2 2bc cos(0)

Step-by-step explanation:

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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a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.

b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.

An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).

The cost per gallon of regular unleaded gas = $4.65

The cost of premium gas per gallon = $4.95

The total cost for gas = $874.80

Let gallons of regular unleaded gas = r

Let gallons of premium gas = p

4.65r + 4.95p = 874.8

If r = 87, the value of p is:

4.65(87) + 4.95p = 874.8

404.55 + 4.95p = 874.8

4.95p = 470.25

p = 95 gallons

Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.

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The polynomial which has a degree of  7 can be known as a polynomial of class 7.

Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.

The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.

Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.

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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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Answer:

150-c

Step-by-step explanation:

150= total

c= children

adults=x

x=150-c

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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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 :)

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: b

Step-by-step explanation:

4-3

——-

13.40- 10.05

= 1/3.35

=b

The transformation is shifted up 2 units.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=-2x+3.

Here, the slope m of a line is -2 and y-intercept is 3

A) If the function g(x)=f(x)+k, where k=2.

Now, g(x)=-2x+3+2

g(x)=-2x+5

Here, the slope m of a line is -2 and y-intercept is 5

B) The slope of both functions are same

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Shifted up 2 units

Therefore, the transformation is shifted up 2 units.

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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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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]

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:

b

Step-by-step explanation:

I think number B is the answer. because the square becomes root when it crosses the = . So, the answer is B

Answer:

  b.  ±√60

Step-by-step explanation:

You want to know the solution to x² = 60.

In general, the process of solving for a variable's value requires you to "undo" what is done to the variable. This generally means you use inverse operations. The inverse of the squaring operation is the square root operation.

Taking the square root of both sides, we get ...

  √(x²) = √60

  |x| = √60 . . . . . . simplify the left side

  x = ±√60 . . . . . . . write the equivalent without the absolute value bars

__

Additional comment

As with any operation performed on an equation, it must be done to both sides of the equal sign.

You will get a ±(radical) result whenever you take an even-index root: square root, fourth root, sixth root, and so on. Odd-index roots will have the same sign as the value under the radical.

  √64 = ±8

  ∛64 = 4; ∛-64 = -4

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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Answer: To estimate the tip, you can first round the bill to the nearest ten dollars. In this case, $706.03 rounded to the nearest ten dollars is $710.

Next, you can calculate the tip by multiplying the rounded bill amount by the tip percentage, 15% in this case.

15% of $710 is 15/100 * 710 = 106.50

So the amount of the tip is approximately 106.50

It's worth mentioning that this method of approximation is not always precise, but it can be a quick and easy way to calculate an estimate when you don't need a very precise answer.

Step-by-step explanation:

The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds

To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.

Given the starting altitude of the balloon, we know:

h(0) = 1200 feet

The rate of change of the altitude, or the speed at which the altitude is changing, is given as:

dh/dt = −712 feet/second

This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:

h(t) = h(0) + dh/dt * t

We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:

310 = 1200 + (−712) * t

This equation can be solved for t by isolating t on one side and then dividing both sides by −712:

t = (1200 - 310) / −712

t = (890) / (−712)

t = 1.25 seconds.

So it will take 1.25 seconds for the balloon to drop below 310 feet.

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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.

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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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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Answer: William Wordsworth, a prominent figure in the Romantic movement, believed that nature had an immense value and could have a profound impact on the human spirit. In his poem "I Wandered Lonely as a Cloud," he wrote, "Nature never did betray the heart that loved her," which is a claim that nature is a constant source of comfort and inspiration. In this poem he praises nature and its ability to be a source of beauty and joy.

One could argue that Wordsworth's claim is true based on the evidence that nature can have a positive impact on mental and physical health. Studies have shown that spending time in nature can reduce stress, improve mood, and boost overall well-being. Additionally, nature can be a source of inspiration for many artists and poets, including Wordsworth himself, who drew inspiration from the natural world for his poetry.

On the other hand, one could argue that Wordsworth's claim is idealistic and may not apply to everyone or every situation. Some people may not find nature as comforting or inspiring, especially those who live in urban areas with limited access to natural spaces. Additionally, there are negative impacts of human activities on nature, such as pollution and deforestation, which can make it harder for some people to find value in nature.

Overall, while Wordsworth's claim that "Nature never did betray the heart that loved her" is a strong statement, and it holds true for many people, but it's a personal perspective that may not apply to everyone. Each individual has their own relationship with nature and it's not always a constant source of comfort, however, it's a treasure that we should take care of, respect and appreciate in order to achieve a better quality of life.

Step-by-step explanation:

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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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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