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Answer:

4. 1), 2), 4) are true

5. x = 7

Step-by-step explanation:

In question 4.

1), 2), and 4) are true

Triangles ABD and CBD are congruent by AAS. Then by CPCTC, 1) and 4) are true. 2) is true by definition of altitude and all right angles are congruent.

5.

Your drawing is good.

Since IF is a median, then IE = IG = (1/2)GE

IE = (1/2)GE

x + 6 = (1/2)(3x + 5)

2x + 12 = 3x + 5

-x = -7

x = 7

Using ratios and proportions, the time it takes for both of them to wash both cars is 24 minutes

Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.

When two or more such ratios are equal, they are said to be in proportion.

The time it takes for Jason to wax the car in 1 minute = 1/30 minutes

The time it takes for Kevin to wax the car in 1 minute = 1/120

The time it takes for both of them to do it will be in 1 minute = 1/30 + 1/120 = 1/24.

The time it takes for both of them to wax the car = 24 minutes

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Answer:

ABC

Step-by-step explanation:

Think of a plane as a piece of paper that went on forever in all directions.  Which points would be on the paper?  Three examples would be points A, B and C.

Answer: 2 gallons

Step-by-step explanation:

If they drink 12 gallons of milk every 6 weeks, to find how many gallons they drink per week, you need to divide the number of gallons by the time.

So,

12/6 = 2 gallons

Thus, they drink 2 gallons per week.

Answer:

the numbers are 53 and 24.

Step-by-step explanation:

let x be the positive number (x>0) and y the other number

one positive number is 5 more than twice another number x = 5 + 2y

their product is 1272

x*y = 1272

plug x = 5 + 2y into the last equation (5 + 2y)y = 1272 by solving we find y= 24 x = 5 + 2*24

x = 53

the numbers are 53 and 24.

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Answer:

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The Prime factorization of 144 is  ([tex]2^4[/tex]) x (3²).´

What is a factor?

A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.

Factors of 144:

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.

Prime factorization:

144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written as

144 = ([tex]2^4[/tex]) x (3²).´

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Each element in the domain of a function corresponds to exactly one

element in the range.

What is an element ?

A pure substance made entirely of one species of atoms, or a chemical element, is a species of atoms with a specific number of protons in their nuclei. Chemical elements, in contrast to chemical compounds, cannot be converted through any chemical reaction into simpler substances.

The items in a set are its elements. A property that all the objects share may serve to define a set. Consider the set E, which consists of all positive even integers. E is equivalent to 2, 4, 6, 8, or 10 dots. E={2,4,6,8,10…}.

A function is a relation in which each element of the domain corresponds to exactly one element of the range.

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Hello..!

¿What is consumidores terciarios?

They are the ones that feed on carnivores and their parasites.

An example:

When we see a dead bird, a week goes by and then there are only the bones, since as it says they feed on dead birds, that is, they eat everything without leaving anything, whether they are birds, cows or people.

Organisms that eat secondary consumers are called tertiary consumers and are carnivores that eat carnivores, such as eagles or large fish.

Producers, or autotrophs, make their own organic molecules. Consumers, or heterotrophs, obtain organic molecules by eating other organisms.

A food chain is a linear sequence of organisms through which nutrients and energy pass from one organism to another through consumption.

Answer:B

Step-by-step explanation:

A is equal to 6.3'.

none of the others are equal to 3.3 exactly.

Answer: 30kg

Step-by-step explanation:

100% = 60kg

50% = 100% /2

60kg(100%)/2 = 30kg(50%)

Answer:

Step-by-step explanation:

Proportion:

60 kg  -   100%

X kg - 50%

X = 60·50% / 100% = 30 kg

Answer: 7/5

Step-by-step explanation:

[tex]12x-15=6-3x\\\\15x-15=6\\\\15x=21\\\\\boxed{x=21/15 \ or\ 7/5}[/tex]

The needed probability that Jason will take home all three awards is 2.96%.

Jason purchased 10 of the 30 tickets for the raffle, which was a drawing.

If a raffle ticket wins a prize and is then discarded, we must calculate the likelihood that Jason will win all three of the prizes.

Let A stand for the scenario in which Jason wins all 3 prizes, and let S stand for the sample area for the experiment in which 3 tickets are drawn at random from 30 raffle tickets.

Since a lottery ticket is discarded after winning a prize,

[tex]n(S) = ^{30} P_{3} = \frac{30!}{(30-3)!} =\frac{30!}{27!} = 24360\\\\n(A) = ^{10} P_{3} = \frac{10!}{(10-3)!} =\frac{10!}{7!} = 720\\[/tex]

Therefore, the probability of event A is given by

P(A) = [tex]\frac{n(A)}{n(S)} = \frac{720}{24360} =0.029955 = 2.96[/tex]%

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The rate of change of the parabola on the interval [0, 4] is 0.

For any function f(x), we define the rate of change on an interval [a, b] as:

R = (f(b) - f(a))/(b - a)

Here we want to get the rate of change on the interval [0, 4], and we know that the graph has the points:

(0, 4), (2, -4), (4, 4)

Then:

f(0) = 4

f(4) = 4

Replacing that in the rate of change formula we get:

R = ( f(4) - f(0))/(4 - 0)

R = (4 - 4)/4 = 0

The rate of change on that interval is 0.

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Answer: -2.4x-3

Step-by-step explanation:

The plant's height after x months is 11.25 + 15x.

From the information illustrated, the plant is already 11.25 meters tall, and it will grow 15 centimeters every month.

In this case, let the plant's height be H (in meters)

Let the number of months be x.

The plant height will be:

= 11.25 + (15 × x)

= 11.25 + 15x

This is the height.

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Complete question

A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. When is the plant's height, H (in meters), after x months?

Answer:

Step-by-step explanation;

In this congruent of the triangle its proven that AB = CD.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Given BC || AD

Both triangles are congruent.

We know the distance between parallel lines always remains the same. So As it is given that BC || AD, AB, and CD both are just distances og the parallel lines

So we can say that both are equal AB = CD

Hence the side AB = CD, in this given figure,

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Answer:

----------------------

Given is the quadratic equation.

A quadratic equation has two real solutions if the discriminant is positive.

Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.

What is mean, median and mode?

The sum of the numbers is added, and the result is divided by the total number of numbers in the list to determine the arithmetic mean. An average usually refers to anything like this. In a list with values ranging from smallest to largest, the median is the middle value. On the list, the mode appears the most frequently.

As given, a high school basketball player is creating a scout summary of their sophomore season.

The points are,  29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27.

Arrange these numbers in ascending order,

0, 20, 22, 24, 27, 28, 29, 29, 30, 32, 33, 34.

So,

Mean = (0 + 20 + 22 + 24 + 27 + 28 + 29 + 29 + 30 + 32 + 33 + 34) / 12

Mean = 308 / 12

Mean = 28

Median = 29

Mode = 29 (2 times repeating)

Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.

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Answer:

The answer is 48

Step-by-step explanation:

First you have to get the number or crayons ehich is 12 then you can multiply it by the denominator in 1/4 so 12x4=48

Answer: 3, -1/3x - 1

Step-by-step explanation:

Answer:

y= -1/3x-1

Step-by-step explanation:

Find the slope of the line by plugging two points into the slope formula

[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]

[tex]\frac{-1-0}{0-(-3)}[/tex]

m= -1/3

Find the y-intercept by seeing where the graph intersects the y-axis

b = -1

y=mx+b

y= -1/3x-1

The distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.

The given points are (2,3) and (5, -2)

The distance (D) between two points [tex](x_{1} ,y_{1} )[/tex]  [tex](x_{2} ,y_{2} )[/tex] is

D = [tex]\sqrt{(x_{1} -x_{2} )^{2} +(y_{1} -y_{2} )^{2} }[/tex]

For evaluating the distance between the points (2,3) and (5, -2)

The distance (D) = [tex]\sqrt{(2 - 5)^{2} +(3 -(-2) )^{2} } = \sqrt{(-3)^{2} +5^{2} } = \sqrt{9+25} = \sqrt{34}[/tex]

Hence, the distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.

Distance is a numerical or occasionally qualitative dimension of how a ways apart objects or points are.

In normal utilization, distance may additionally discuss with a bodily duration or an estimation primarily based on different standards.

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The compound interest after 7 years is $2701.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/12)[tex].^{n/12}[/tex]

A = 2100(1+3.6/12)[tex].^{7/12}[/tex]

A=2701

Hence the compound interest after 7 years will be $2701.

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The values are given below,

Left Hand Limit i.e.  [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 ,

Right Hand Limit i.e.  [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 ,

Function value at x = 1  [tex]f(1)[/tex] = 1 ,

Left Hand Derivative [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and

Right Hand Derivative [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6.

So, the function f(x) is neither continuous nor differentiable at x = 1.

Given, a piecewise function

              3㏑(3 - 2x) + 3                for x < 1

f(x) =

                    -3x² + 4                     for x ≥ 1

Now, for  [tex]\lim_{x \to 1^-} f(x)[/tex] we will consider the function  3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.

[tex]\lim_{x \to 1}[/tex] 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3

= 3 ㏑(1) + 3

= 0 + 3

= 3

Now, for [tex]\lim_{x \to 1^+} f(x)[/tex] we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.

[tex]\lim_{x \to 1}[/tex] -3x² + 4 = -3(1)² + 4

= -3 + 4

= 1

Now, for [tex]f(1)[/tex] we will consider the function -3x² + 4,

[tex]f(1)[/tex] = -3(1)² + 4

= -3 + 4

= 1

Now, for [tex]\lim_{x \to 1^-} f'(x)[/tex] we will consider the derivative of the function

3㏑(3 - 2x) + 3,

[tex]\lim_{x \to 1}[/tex] -6/(3 - 2x) = -6/(3 - 2(1))

= -6

Now, for [tex]\lim_{x \to 1^+} f'(x)[/tex] we will consider the derivative of the function

-3x² + 4,

[tex]\lim_{x \to 1}[/tex] -6x = -6(1)

= -6

So, the function f(x) is neither continuous nor differentiable at x = 1.

Hence,  [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 ,  [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 ,  [tex]f(1)[/tex] = 1 ,  [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and  [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6

The function is neither continuous nor differentiable at x = 1.

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In the decimal for, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42

Decimal

Decimal means a number that has a decimal point followed by digits that show the fractional part.

Given,

Here we have the expression 13 tenths + 8 tenths + 32 hundredths

Now, we need to find the value of this expression.

We know that, Tenths means we have one digit after the decimal point and the hundredths have two digits after the decimal point.

So, in the given expression 13 tenths is written as 1.3

And the  8 tenths is written as 0.8

And finally, the 32 hundredths is written as 0.32

Now, we have to add these numbers, then we get,

=> 1.3 + 0.8 + 0.32

=> 2.42

Therefore, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42

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Answer:

9 miles

Step-by-step explanation:

90 min = 1hr and 30 min

6(miles)*1(hr) = 6

6(miles)*0.5(hr) = 3

[ remember we multiply by 0.5 because half of 1 hour is 30 min. ]

Answer: 9 miles

Step-by-step explanation:

convert 90 minutes into hours: 90 mins/60 mins in an hour = 1.5 hours

find how far the team ran: 6mph * 1.5 hours = 9 miles

answer: the team ran 9 miles in 90 minutes

The error in balancing the equation is that the although the number terms on both sides of the equation are the same, the operation on the 1 on the left is an addition while the operation on the number 1 on the Right Hand Side of the equation is a subtraction

A balanced equation is one in which the values or amounts on both sides of the equation are the same.

The unbalanced equation is presented as follows;

16 ÷ 8 = 16 ÷ 8 - 1

The form balanced equation in the question is; 16 ÷ 8 + 1 = 16 ÷ 8 - 1

The error is that in the balanced equation a 1 was added to the Left Side of the equation, while in the unbalanced equation, the difference between the left and right side of the equation is a subtraction of a 1 from the Right Hand Side of the equation.

The step to correctly balance the unbalanced equation involves the subtraction of a 1 from the Left Hand Side as follows;

The unbalanced equation 16 ÷ 8 = 16 ÷ 8 - 1 can be balanced by applying the addition (or subtraction) property of equality, which states that the when the same quantity is added (or subtracted) from two quantities that are initially equal, the resulting quantities that have a different amount following the addition (or subtraction) will remain equal.

The expression, 16 ÷ 8 and 16 ÷ 8 are the same.

Subtracting the same amount of 1 from both sides will result in two new expressions that are also equal in amount as follows;

16 ÷ 8 = 16 ÷ 8

16 ÷ 8 - 1 = 16 ÷ 8 - 1

The error is therefore in adding rather than subtracting a 1 from the Left Hand Side of the equation to balance the equations.

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The polynomial function  p(x) = x³ - 7x + 6 divided by x - 2 =  x² + 2x - 3

Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.

We can represent the division of two polynomials in the form:

p(x)/q(x) = Q(x) + R/(q(x))

where,

The polynomial function p(x) = x³ - 7x + 6 is divided by x - 2

x³ - 7x + 6 ÷ x - 2 = (x - 1)(x + 3)

x² + 3x - x - 3 = x² + 2x - 3

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An equation to represent this situation x is 37/12. The components of a whole or group of items are represented by fractions.

Here 7 is lessoned by 2 of a number.

Consider x be the number.

we get 2x - 7

the result is same as 3 subtracting of the number from 10.

therefore, we get 10 ( 3 - x )

from this two equations we get,

⇒ 2x - 7 = 10 ( 3 - x )

⇒ 2x - 7 = 30 - 10x

Simplifying we get,

⇒ -37 = - 12x

⇒ x = 37/12

Therefore, An equation to represent this situation x is 37/12.

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