Find the weighted average of the numbers -3 and 5 with 3/5 lf the weight on the first number and 2/5 on the second number.

The completed two-column table that proves ΔQTU is congruent to ΔRSU can be presented as follows;

Statement          [tex]{}[/tex]                           Reasons

1. [tex]\overline{RS}[/tex] ⊥ [tex]\overline{RT}[/tex]                          [tex]{}[/tex]          Given

2. [tex]\overline{QT}[/tex] ⊥ [tex]\overline{QS}[/tex]                         [tex]{}[/tex]          Given

3. [tex]\overline{QU}[/tex] ≅ [tex]\overline{RU}[/tex]                              [tex]{}[/tex]    Given

4. ∠Q ≅ ∠R [tex]{}[/tex]                                  All 90° angle are congruent

5. ∠QUT ≅ ∠RUS [tex]{}[/tex]                        Vertical Angle Theorem

6. ΔQTU ≅ ΔRSU [tex]{}[/tex]                        ASA

Congruent triangles are triangles that have the same size and shape.

The details of the reasons that are used to prove that the triangles ΔQTU and ΔRSU are congruent, can be presented as follows;

All 90° angle are congruent

The segments [tex]\overline{RS}[/tex] and [tex]\overline{RT}[/tex] are perpendicular, which indicates that the angle ∠R is a 90° angle. Similarly, segments [tex]\overline{QT}[/tex] and [tex]\overline{QS}[/tex] are perpendicular, therefore, ∠Q is a 90° angle, which indicates that we get;

m∠Q = m∠R = 90°

The definition of congruent angles, indicates; ∠Q ≅ ∠R

Vertical Angle Theorem

The vertical angle theorem states that the vertical angles formed by two intersecting lines are congruent.

ASA

The Angle-Side-Angle, (which can be abbreviated as ASA) congruence postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Learn more about triangle congruence rules here: https://brainly.com/question/21474941

#SPJ1

The required equation which intersects the points (12, -2) and (6, -8) in the point-slope form is y+2 = x-12.

The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

To understand more about it and see some instances, watch this video.

Both the slope-intercept form and the point-slope form can be used to write the equation of a straight line.

The slope and ANY point on the line are highlighted using the point-slope form.

Slope intercept form merely shows the slope and the y-intercept of a line.

So, we have:

m = 1

And points are (12, -2) and (6, -8)

We need to use the points: (12, -2)

Now, form the equation as follows:

y - (-2) = m (x-12)

y + 2 = 1(x-12)

y+2 = x-12

Therefore, the required equation which intersects the points (12, -2) and (6, -8) in the point-slope form is y+2 = x-12.

Know more about the point-slope form here:

https://brainly.com/question/24907633

#SPJ1

Answer:

Step-by-step explanation:

If I see this correctly it would be about 16 minutes he played football.

Answer:

Ben had given away 3/5 of his fraction.

Step-by-step explanation:

total number of marbles Ben give away,

= 65+80+35

= 180

180/300= 3/5

Answer:

Yes, the lines y = -5x + 1 and y = -5x + 8 are parallel. This is because they have the same slope (-5) but different y-intercepts (1 and 8). Parallel lines have the same slope, and different y-intercepts.

Answer:

For y = -5x + 1

x = [tex]\frac{1-y}{5}[/tex].

And

y = 1 - 5x.

Put on a graph: look at picture 1.

The for y = -5x + 8

x = [tex]\frac{8-y}{5}[/tex]

And

y = 8 - 5x.

Put on a graph: look at picture 2.

These two lines are parallel.

Answer:

28

Step-by-step explanation: 4+3+7=14

                                              56/14=4

                                              7*4=28

Answer:

28

Step-by-step explanation:

4x+3x+7x = 56

14x=56

x=4

7x ---> 7(4) ---> 28

So there are 28 lemon lime skittles in a bag

Required, after 12 days Claire will have the day where she has gone to the gym and the park an equal number of times.

The least common multiple (LCM) of two numbers represents the smallest multiple that is divisible by both numbers.

Here,
In this case, the LCM of 4 and 6 is 12, which is the smallest number that is divisible by both 4 and 6. This means that after 12 days, Claire will have gone to the gym and the park an equal number of times, and will thus be back at the same point. Therefore, the answer is LCM.

Thus, the required, after 12 days Claire will have the day where she has gone to the gym and the park an equal number of times.

Learn more about Least common multiple (LCM) here:
https://brainly.com/question/14617090
#SPJ9

The binary number will be equal to 14 in base 6

1001₂ = 14 (base 6)

Base is defined as a set of digits used to represent numbers. There are different number systems which make use of different combinations of digits as the base.

One of the most common which is the binary number system uses only 2 digits, i.e., 0 and 1 to represent numbers, while the Octal number system uses 8 digits, i.e., 0 to 7, to represent numbers.

The most common number system that is in use is the decimal number system that uses the base 10, which includes digits from 0 to 9 for writing numbers.

1001₂ = 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0

1001₂ = 1 x 8 + 1 x 1

1001₂ = 8 + 1

1001₂ = 9

Converting 9 into base 6

6 9

6 1 r 3

  0 r 1

From downwards pointing up

9 = 13 (base 6)

Learn more about number bases here: https://brainly.com/question/19460684

#SPJ1

Answer: Logarithmic differentiation when the logarithm of an expression can be written in a form for which we can find the derivative more simply. Or, for which we can find the derivative at all.

Answer:

Step-by-step explanation: 320 cm sq

The two missing angles of the quadrilateral are 10.5° and 2.47°, calculated from the given angles of 232° and 86°, and a ratio of 4:17.

The angle sum of a quadrilateral is 360°. Therefore, we need to find the sum of the two missing angles.We can start by subtracting the two known angles from the total angle sum and then dividing the difference by the ratio given.

360° - 232° - 86° = 42°

To find the two missing angles, divide the sum by the ratio given.

42° ÷ 4:17

The find the measure of the first angle, divide 42° by 4:

42° ÷ 4 = 10.5°

To find the measure of the second angle, divide 42° by 17:

42° ÷ 17 = 2.47°

Therefore, the two missing angles of the quadrilateral are 10.5° and 2.47°.

Learn more about quadrilateral here:

https://brainly.com/question/29934291

#SPJ4

Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer.

The equation is typically written in algebraic form and includes numerical values.Verifying Identity with a calculator requires an individual to enter specific numerical values into a calculator and then solve a given equation. This can be used to prove the validity of an equation, or the accuracy of a given answer. For example, if an individual is asked to verify the identity [tex]sin^2x + cos^2x[/tex]= 1, they will be given numerical values to plug into the equation. For example, if they are given x = 60, they would enter[tex](sin60)^2 + (cos60)^2[/tex] into the calculator and solve. This should result in an answer of 1, proving the equation is accurate.

Learn more about Identity here:

https://brainly.com/question/30339186

#SPJ4

two equations are: v = u + 0.5a and (v)² = (u)² + 4a.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the distance traveled by an object in t = 30 minutes is 2 miles

Let "v" be the final velocity of an object,

"u" be the initial velocity of an object,

and "a" be the acceleration of an object.

From the standard velocity equation:

final velocity = initial velocity + acceleration * time.....(1)

(final velocity)² = (initial velocity)² + 2*acceleration * distance....(1)

From equation (1)

v = u + a*30 minutes

time in hours,

v = u + 0.5a

From equation (2)

(v)² = (u)² + 2*a* 2

(v)² = (u)² + 4a

therefore, two equations are: v = u + 0.5a and (v)² = (u)² + 4a.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²

The length and breadth of the rectangle are 25.33 meters and 12.67 meters,

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

We are given that the breadth of the rectangle is half of its length, so we can write:

B = 0.5L

We are also given that the perimeter of the rectangle is 76m. The perimeter of a rectangle is the sum of the lengths of all four sides, which in this case is:

Perimeter = 2(L + B)

Substituting the value of B from the first equation, we get:

Perimeter = 2(L + 0.5L)

Perimeter = 2(1.5L)

Perimeter = 3L

Now we can solve for L:

3L = 76

L = 25.33

So the length of the rectangle is 25.33 meters.

To find the breadth, we can substitute this value of L back into the first equation:

B = 0.5L

B = 0.5(25.33)

B = 12.67

So the breadth of the rectangle is 12.67 meters.

Therefore, the length and breadth of the rectangle are 25.33 meters and 12.67 meters, respectively.

To know more about rectangles follow

https://brainly.com/question/30755636

#SPJ9

If there are 10 days of sleeping a month then in a year there are 120 days of sleeping.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Sleeping 8 hours a day is the same as sleeping 10 days a month.

In according to hours the number of hours sleeping in month will be

= 8 x 30

= 240 hours

= 240 / 24

= 10 days

So, in a year the number of days of sleeping is

= 10 x 12

= 120 days

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ9

The probability P(red pen, purple pen) without replacement is 10/33.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that a container holds 5 red pens, 4 purple pens and 3 blue pens.

We need to find the probability P(red pen, purple pen) without replacement.

P(red pen, purple pen) = (number of ways to select a red pen and a purple pen) / (total number of ways to select two pens)

Total number of ways to select two pens=¹²C₂=66 ways.

Number of ways to select a red pen and a purple pen = (number of ways to select a red pen) x (number of ways to select a purple pen from the remaining pens)

Number of ways to select a red pen = 5

Number of ways to select a purple pen from the remaining pens = 4

Therefore, the number of ways to select a red pen and a purple pen without replacement is:

Number of ways to select a red pen and a purple pen = 5 x 4 = 20

P(red pen, purple pen) =20/66

=10/33

Hence, the probability P(red pen, purple pen) without replacement is 10/33.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ9

The triangle represents 1/4 of the whole trapezoid, the rhombus represents 1/2 of the whole trapezoid, and the hexagon represents 1/1 of the whole trapezoid.

Each of the shapes represent a different fraction of the whole trapezoid.

The triangle represents 1/4 of the whole trapezoid. This is because there are four triangles in the trapezoid, and each one is equal in size. Therefore, each triangle is 1/4 of the whole trapezoid. The rhombus represents 1/2 of the whole trapezoid. This is because there are two rhombuses in the trapezoid, and each one is equal in size. Therefore, each rhombus is 1/2 of the whole trapezoid.

The hexagon represents 1/1 of the whole trapezoid. This is because there is only one hexagon in the trapezoid, and it is equal in size to the whole trapezoid. Therefore, the hexagon is 1/1, or the whole trapezoid.

In conclusion, the triangle represents 1/4 of the whole trapezoid, the rhombus represents 1/2 of the whole trapezoid, and the hexagon represents 1/1 of the whole Hexagon. These fractions can be used to determine the value of each shape in relation to the whole trapezoid.

Learn more about hexagon at https://brainly.com/question/3295271

#SPJ11

All the answers to the questions except which are impossible are illustrated below.

A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.

Each line of the polygonal circuit's segments are referred to as its edges or sides.

9. We know, The sum of all the interior angles of a 'n' sided polygon is,

= 180(n - 2).

= 180(10 - 2).

= 180×8.

= 1440°.

11. 180(n - 2) = 1260.

180n - 360 = 1260.

180n = 1620.

n = 9.

13. Mesure of exterior angles is,

= 360/n.

= 360/5.

= 72°.

14. 360/60 = 6 sides, As EA = 360/n, n = 360/EA.

learn more about polygons here :

https://brainly.com/question/24464711

#SPJ1

The original fraction described in the question is; 25/31

Let the numerator be x and let the denominator be y.

We are told that the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. Thus;

4x/(y - 2) = 4

4x = 4y - 8

4x - 4y = -8   -----(1)

The numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Thus;

(x + 15)/(2y - 2) = 5/4

4x + 60 = 10y - 10

4x - 10y = - 70   ----(2)

Subtract eq 2 from eq 1 to get;

6y = 62

y = 31/3

Thus;

4x - 4(31/3) = -8

Multiply through by 3 to get;

12x - 124 = -24

12x = 100

x = 25/3

Thus, the fraction is;

(25/3)/(31/3) = 25/31

Read more about simplifying fractions at; https://brainly.com/question/6109670

#SPJ1

A statement which best describes the function include the following: A. f(x) is a linear function because x and f(x) are both increasing.

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

Next, we would determine the slope by using the points contained in the table as follows;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 1)/(0 + 1)

Slope (m) = 4.

Slope (m) = (13 - 5)/(2 - 0)

Slope (m) = 4

Slope (m) = (21 - 13)/(4-2)

Slope (m) = 8/2 = 4.

Read more on slope here: brainly.com/question/23086745

#SPJ1

The length of RT is 13 units

A triangle is a three-sided polygon that consists of three edges and three vertices.

As T is the centroid of the given triangle.

TN=TP

x+10=4x-17

Now solve for x

27=3x

x=9

Now TP=4(9)-17

TP=36-17

TP=19

Now from pythagoras theorem we find the length of RT

19²=14²+RT²

361-196=RT²

165=RT²

Take square root on both sides

RT=13

Hence, the length of RT is 13 units

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

Answer:

What are the outliers in this data set?

26, 51, 53, 57, 57, 62, 65, 71, 93

Select EACH correct answer.

Step-by-step explanation:

Tell me if I'm wrong, You're welcome.

The x-intercept and the y-intercept of the line 5x - 2y = 10 include the following ordered pairs:

x-intercept = (2, 0).

y-intercept = (0, -5).

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, the y-intercept is sometimes referred to as an initial value (base value) and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.

Read more on y-intercept here: brainly.com/question/6240745

#SPJ1

a) There are 36 sample points that are possible.

b) The probability of obtaining a value of 7 is 1/12.

c) The probability of obtaining a value of 8 or greater is 1/6.

(a) When rolling a pair of dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. The possible outcomes for the pair of dice can be represented by the set of all ordered pairs (a, b), where a and b represent the outcomes of the first and second die, respectively.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes for rolling a pair of dice.

(b) To obtain a sum of 7, we must have one die showing 1 and the other die showing 6, or one die showing 2 and the other die showing 5, or one die showing 3 and the other die showing 4, for a total of three possible outcomes.

Since each die has six possible outcomes, there are a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 3/36, or 1/12.

(c) We must have one die showing 2 and the other die showing 6, or one die showing 3 and the other die showing 5, or one die showing 4 and the other die showing 4, or one die showing 4 and the other die showing 5, or one die showing 5 and the other die showing 3, or one die showing 6 and the other die showing 2, for a total of 5 + 1 = 6 possible outcomes.

Therefore, the probability of obtaining a sum of 8 or greater is 6/36, or 1/6.

To learn more about probability click on,

https://brainly.com/question/15036514

#SPJ4

A continuous random variable can take all values in an interval, assuming that the interval is unbounded.

This is because a continuous random variable has an infinite number of possible outcomes, and the probability density function (PDF) of a continuous random variable is defined over a range of values rather than specific values.

For example, consider the normal distribution, which is a common continuous probability distribution. The PDF of a normal distribution is a bell-shaped curve that extends from negative infinity to positive infinity.

This means that a continuous random variable following a normal distribution can take any value on the real number line, with some values being more likely than others.

However, if the interval is bounded, then it is possible for a continuous random variable to not take all values within the interval. In this case, the probability density function is zero outside of the interval, and the random variable is restricted to the range of values within the interval.

To learn more about continuous random variable click on,

https://brainly.com/question/4362384

#SPJ4

Answer:

g=4f-k+h

Step-by-step explanation:

f=g-h+k

4

4f=g-h+k

4f-k=g-h

4f-k+h=g

According to the information, we need 107.42ft of black cord and 26 yards of fabric to make the design.

To find the amount of black cord that we need in this design we must calculate the perimeter of all the figures as shown below:

rectangle

Square

triangle

Circle

Total

To calculate the amount of fabric, we must find the visible area of the figures and calculate what the area is in yards.

rectangle:

Square:

Triangle:

Circle:

Learn more about inches in: brainly.com/question/16311877

#SPJ1

The area of the basement will be 576 square feet.

The area is defined as the space covered by the object in a two-dimensional plane. The area of the rectangle is calculated by the multiplication of the length and the width.

Given that a basement floor plan for a house is being created by an architect. He drew the plans as they are seen. On the plan, one-fourth of an inch corresponds to four feet in the house.

The area of the basement will be calculated as:-

Area = 12 x 6

Area = 72 square inches

Area = 72 x 8 feet

Area = 576 square feet

To know more about an area follow

https://brainly.com/question/12203483

#SPJ9

Scatter plot Answ

Step-by-step explanation: