Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.

Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.

Answer:

Step-by-step explanation:

5.40/12= 0.45

6.72/16=0.42

Answer:

The 16 pack

Step-by-step explanation:

Pack 1: $5.40 for 12

Pack 2: $6.72 for 16

Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.

After 10 days, the expected number of shoppers at the shopping mall is 163.

It is given that the number of shoppers increases daily by 5% from the number of shoppers the previous day.

As we can see that the increase in the number of shoppers is going to change every day, and the above case is compounded daily.

The formula of compound increase is

Amount = Base X (1 + r/n)ⁿˣ

where,

Base = original amount

r = rate of change

n = no. of times the change occurs in the time period

t = time

Here,

Base = 100

r = 5/100

n = 1, since it changes once every day

x = 10

Therefore we get

100 X (1 + 5/100)¹⁰

= 100 X 1.05¹⁰

162.88

Since the number of people cannot be in decimal,

the expected number of people is 163

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Answer: 16.4, 16 1/2, 16 3/5 16.625,

Step-by-step explanation: 16.4, 16 1/2, 16 3/5 16.625,

16 1/2 = 16.5, 16 3/5 = 16.6

The values are not equivalent to 2.2 include

2.6 - 0.6

1.8 + 2.5

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, 2.6 - 0.6 will be:

= 2.6 - 0.6

= 2.0

Also, 1.8 + 2.5 will be:

= 1.8 + 2.5

= 4.3

Therefore, they're not equivalent to 2.2

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Complete question

During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2

1.2 + 1.0

2.6 - 0.6

0.9 + 1.3

1.8 + 2.5

The graph has no vertex and the transformations from the parent function are

By definition, the vertex of a function is the maximum or the minimum of the function

From the graph, we can see that the graph only has a turning point; it has no maximum or minimum

So, we can conclude that there is no vertex in the graph

Here, we have:

We can see that:

The graph is 4 units to the left of the origin and 2 units below the origin

This means that the function has been shifted down and shifted to the left

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Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

The ratio of an object's mass to its volume is its density. Grams per cubic centimeter, or g/cm³, are frequently used to measure density. Keep in mind that a volume is measured in cubic centimeters, not gram (the same volume as 1 milliliter). More particles will make a box denser than fewer particles in the same box. Despite the fact that the SI unit of density is kg/m³, we instead use g/cm³ for solids, g/ml for liquids, and g/L for gases out of convenience. The relationship between a substance's mass and the volume it occupies is known as its density.

Given,

Volume = 2.5 cm³

Mass = 10 g

For density:

Mass ÷ volume

10 ÷ 2.5

4

Density of the mass of a test sample is 10g, and it has the volume of 2.5cm^3 is 4 g/cm³.

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The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

Let length be l and width be b of garden .

According to question ,

l + 2b = 1040

Area of garden = l * b

Substituting value of l in formula for area ,

Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]

Taking derivative of Area wrt. b and putting it equal to 0 ,

1040 - 4b = 0

b = 1040 / 4

b = 260 feet

Therefore , l = 1040 - 520 = 520 feet .

Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .

Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

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Answer:

Your first option is correct but your second is wrong

Step-by-step explanation:

In option b-

when an employee receives 10% additional for each of the following weeks:

10% of 200=  10/100 x200= 20

it means he will get $20 in extra in every week

so it will be- 220,240,260

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.

Given : The quadrilateral prism

Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

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Brian has  £63 Initially, by using the ratio and proportion method.

What are Ratio and Proportion?

In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.

An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".

In the question, It is given that:

The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.

Let 7x denotes the amount in Brian's wallet and 2x denote the amount in  Colin's wallet on that day.

we know that:

Brian spent £39 that day.

Amount left in Brian's wallet = 7x- 39

Brian now had £4 less than Colin.

⇒ 2x -4= 7x- 39

⇒  7x-2x=4+39

⇒  5x=35

⇒  x=7   [Divide both sides by 5 ]

So , The initial amount in Brian's wallet  = 7(7)= £49

The initial amount in Colin's wallet = 2(7)= £14

The amount they had together =  £49+£14 = £63

So, They had £63 altogether initially.

Therefore, Brian has  £63 Initially.

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Answer: £14

The value of the function g(x) when x = -2 is 6

The definition of the function is given as

g(x)=x to the power of 2 minus x

Rewrite the above function properly

So, we have the following representation

g(x) = x² - x

To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2

This is represented by

Calculate g(x), when x = -2

Substitute -2 for x in the equation g(x) = x² - x

So, we have the following equation

g(-2) = (-2)² - (-2)

Evaluate the exponents

This gives

g(-2) = 4 - (-2)

Evaluate the sum

g(-2) = 6

Hence, the value of the function is 6

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The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:

40.01.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

Hence the quotient of the division is the numerator divided by the denominator.

In this problem, interpreting the blank variable as x, the fraction that represents the situation is:

x/40.01 = 1.

Applying cross multiplication, the numeric value of the variable x is obtained as follows:

x = 40.01 x 1

x = 40.01.

The complete problem asks for which number divided by 40.01 is close to 1.

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The length of the given isosceles triangle legs is 1.9 feet.

A linear equation is a equation that has degree as one.

To find the solution of n unknown quantities n number of equations with n number of variables are required.

Given that,

The perimeter of an  isosceles triangle is 4.9 feet.

And, legs of the triangle are 0.3 foot less than twice the base.

Suppose the base of the triangle be x.

Then, its legs are 2x - 0.3.

As per the question the expression for the perimeter of the triangle is,

2x - 0.3 + 2x - 0.3 + x = 4.9

=> 5x - 0.6 = 4.9

=> 5x = 5.5

=> x = 1.1

Thus, the legs can be found by substituting x = 1.1 in 2x - 0.3 as below,

2 × 1.1 - 0.3

= 1.9

Hence, the length of one of the triangle’s legs is 1.9 feet.

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The number of kilometers in 5 square gigameters is  5. 0 × 10^18

Proportion can be described as an expression or equation in which two ratios are made equal to each other.

It is also known as the mathematical comparison between two numbers or elements.

From the information given, we have;

1 gigameter = 1.0×10^6 kilometers

But,

5 square gigameters = 5. 1.0×10^6 . 1.0×10^6

Add the powers

5 square gigameters = 5..0×10^12

If 1 gigameter = 1.0×10^6 kilometers

Then 5. 1.0×10^12 gigameter = x

cross multiply

x = 5.0×10^12 ×  1.0×10^6

x = 5. 0 × 10^18 kilometers

Hence, the value is 5. 0 × 10^18 kilometers

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The given system of equations has no solution.

The given system of equations are A-B =2 and A+2= B.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

A-B =2 --------(I) and A+2= B --------(II)

From equation (II) substitute B=A+2 in the equation (I), we get

A-(A+2)=2

⇒ A-A-2=2

⇒ 0-2=2

Hence, the given system of equations has no solution.

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Broccoli and peppers occupy 11/12 of the gardenAs a result, 11/12 of the garden is filled with vegetables.

1,Let's add up those two fractions to determine how much of the entire garden contains broccoli and peppers since we know that 1/4 of the garden has broccoli and 2/3 of the garden contains peppers.

Consequently, 1/ 4 + 2/3 =?

It is necessary for the denominator to match.

Consequently, 1/4 x 3/ 3 = 3 / 12.

2/3 × 4 /4 = 8 / 12

Hence, 3 / 12 + 8 / 12 = 11 / 12

2  ,Amount of flour needed to complete both recipes =2+1/4+1

3,  Baked cake 1 /8 +3/4,

6  , Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes

= 54 / 12 x 5¹/₄

= 23 ⁵/₈ meters

7,   24 brownies = 9/2 cups of walnuts

    8 brownies =1 1/2 cups of walnuts

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The value of x is 25

What is congruent polygons ?

A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.

Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.

1. Pairs of congruent corresponding parts

 ∠A = ∠C     AB = CD

 ∠B = ∠D    AH = CF

 ∠H = ∠F    HG = FE

 ∠G = ∠E    GB = ED

To find the value of x

4x + 5 = 105

4x = 105 - 5

4x = 100

 x = [tex]\frac{100}{4}[/tex]

    = 25

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The value of 'm' in the absolute value equation is 3

A linear equation can be described as an equation having the highest power of the variable as 1.

It is also referred to as a one-degree equation.

Example;

x + 1 = 4

Absolute value of a number can be defined as the value of that number irrespective of its direction to zero on the number line.

The value must take a positive sign.

The symbol used to represent the absolute value of a number is '| '

We have the equation;

|m-2|-1=4

Let's take the absolute value

m + 2 - 1 = 4

Now, collect like terms, we get;

m = 4 - 1

Add or subtract like terms

m = 3

Hence, the value is 3

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Answer:

86

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

given mean mark for class of 30 is 70 , then

[tex]\frac{sum}{30}[/tex] = 70 ( multiply both sides by 30 )

sum = 2100

given the mean mark for 20 boys is 62, then

[tex]\frac{sum}{20}[/tex] = 62 ( multiply both sides by 20 )

sum = 1240

the sum for the 10 girls is then 2100 - 1240 = 860

then mean score for the 10 girls is

mean = [tex]\frac{860}{10}[/tex] = 86

Answer:

23.29 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.

To find how high up the wall the ladder reaches, use the sine trigonometric ratio:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

where:

The angle of elevation is 76°, so θ = 76°.

Let x be the height the ladder reaches up the wall, so O = x.

H is the length of the ladder, so H = 24.

Substitute the given values into the sine ratio and round the answer to the nearest hundredth:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]

[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]

[tex]24 \sin(76^{\circ})= x[/tex]

[tex]x=24 \sin(76^{\circ})[/tex]

[tex]x=23.28709743...[/tex]

[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]

Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.

The y-coordinate is 2 when x=0.

The slope or gradient of the line is a mathematical term used to describe the direction and steepness of a line. The ratio of the change in the y coordinate to the change in the x coordinate is known as the slope of a line. Δ y and Δx are the net changes in the y and x coordinates, respectively.

The slope of a line is calculated as the proportion of the rise to the run, or the increasing divide by the run. The coordinate plane, it describes the slope of the line. Finding the slope between two different points and calculating the slope of a line are similar tasks.

The slope-intercept form is y= mx +c

Here, given that slope m=2

Let us consider that the above equation is passing through (2,2)

2=2(2)+c

c=2

y=2x+2

Therefore, when x=0,

y=2(0)+2

y=2

Therefore, the y-coordinate is 2 when x=0

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About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.

A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.

arbitrary sample size, n = 1228

number of those who were dropped or dismissed, x = 856

The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785

Level of confidence = 0.99

Level of significance α = 0.01

The population proportion's 99% confidence interval estimate is calculated as follows:

p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]

Using the Excel function or the z-distribution table for calculation

[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]

=NORMSINV(0.05)

[tex]z_{0.01/2}[/tex] ≅ ±2.58

The interval's computation is as follows:

0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]

= 0.7785 ± 2.58 * 0.0118

= = 0.7785 ± 0.0306

(0.7479, 0.8091)

As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].

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The percent decrease in the travel time after getting a new job is 36%.

Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".

First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.

decrease in time = 48 - 30.72

decrease in time = 17.28

Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.

percent decrease = (17.28 / 48) x 100

percent decrease = 36%

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Answer:

1300 and 750

Step-by-step explanation:

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By solving the linear equations we get the final values of x = 4 & y = 4.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order  term are included.

We have,

               2x + 7y = -20           ----------(i)

                x - 3y = 16               ----------(ii)

By multiplying equation (ii) with 2 we get,

               2x + 7y = -20 ---------(III)

               2x - 6y = 32 -----------(IV)

taking subtraction of equations (III) and (IV), we get

               y = 4

by putting value of y in equation (ii) we get,

               x = 4

Hence by solving the linear equations we get the values of x = 4 & y = 4.  

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Answer:

3 ¹/₃ years

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 500=3000 \times 0.05 \times t[/tex]

[tex]\sf \implies 500=150t[/tex]

[tex]\sf \implies t=\dfrac{500}{150}[/tex]

[tex]\implies \sf t=3\frac{1}{3}[/tex]

Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.

0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2

P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)

= P(Z ≥0.66)

= 0.7475

normsdist(0.666666) =0.7475

The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.

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The required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

The quadratic function is defined as a function containing the highest power of a variable is two.

The quadratic function is given in the question:

2y² + 2y - 5 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -5

Using the quadratic formula to solve the above quadratic function

[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 2, b = 2 and c = -5 in the above formula

[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]

Separate the solutions as:

[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

Therefore, the required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

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