The sides of a triangle are measured at a = 4, b = 5 and c = 6. What is the length of Median A?

Question 6:

The relationship between ∠2 and ∠7 is that they are corresponding angles.

Question 8:

Since ∠1 and ∠2 are alternate exterior angles, m∠2=m∠1 so 180°

Question 9:

Options A, C, and D are correct.

*Note*

For option B the angles are supplementary.

For option E the angles are vertical angles.

Question 10:

∠1 and ∠2 lie in the interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal.

If Jason planted 11 packs of seeds in his 4 garden's he planted the same amount of seeds in each garden then the number of packs of seeds were planted is 2.74 pack for each garden  .

the number of packs of seed planted by Jason is = 11 packs  ;

the number of gardens in which the seeds are planted is = 4 garden ;

the amount of packs planted in each garden can be calculated by the expression on dividing "number of seed packs" by "number of gardens" ;

⇒ (number of seed packs)/(number of gardens) ;

Substituting values of number of seed pack and number of garden ,

we get ;

= 11/4 = 2.74 .

Therefore , Jason planted 2.74 packs of seed in each garden .

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The original price of the sofa before the discount is $241.11.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Let the original price of the sofa be x.

Given that 72% of the original price is $173.60, this can be written mathematically as follows:

72/100 × x = 173.60

72x = 17360

x = 241.11

Hence, the original price of the sofa before the discount is $241.11.

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Kelly's brothers age after 4 2/3 is 23 12/24 years.

What is Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. 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.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

We have  ;

Kelly's Brother is 18 7/8 year old.

We have to calculate;

His age after 4 2/3 years.

So,  

⇒ 18 7/8 + 4 2/3

⇒ 151/8 + 14/3

⇒151 x 3 + 14 x 8/24

⇒453 + 112 /24

⇒565/24

⇒23 13/24 year old

Hence , his age after 4 2/3 is 23 13/24 years.

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The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]

A positive exponent indicates that the base should be multiplied by that many.

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. Negative exponents like xn can be rewritten as 1 / rs. As an illustration, qr^-4  s^6 q ^-8 s^6 q^-1 rs^6

The Power Rule for Exponents is a further exponent rule that follows from this. You multiply the exponents while keeping the base constant to simplify a power of a power. As an illustration, b for any positive s^6 q ^-8 s^6 q^-1 rs^6 number x and integers q and s.

⇒ qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹

⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹

⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹

⇒ qr⁻⁸ × r⁻⁴ × s⁹

[tex]$ \Rightarrow \frac{1}{q^8} \times \frac{1}{r^4} \times s^9[/tex]

[tex]$ \Rightarrow \frac{s^9}{q^8r^4}[/tex]

Thus , The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]

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The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

where, [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points.

Now putting the values

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)[/tex]

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)[/tex]

[tex]\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)[/tex]

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = [tex]\sqrt{(-2-1)^2+(3-1)^2}[/tex]

r =[tex]\sqrt{(-3)^2+(2)^2}[/tex]

r = [tex]\sqrt{9+4}[/tex]

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

The equation has one solution

The solution to the equation is  x = 3

4(2x – 5) = 4

To solve this, we would first have to open the bracket.

4 * 2x - 4*5 = 4

8x - 20 = 4

We would want to have the variable x stand on its own

so we take like terms

8x = 4 + 20

8x = 24

To get the value of x divide through the equation by 8

x = 24 / 8

x = 3

The solution is just one at x = 3

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For the given similar triangles, the value of x = 5.

Similar triangles share the same associated angle measurements and proportional side lengths.

Due to their similar shapes, two figures that are not always the same size can appear comparable. We might claim, for instance, that all circles are equivalent. Squares and equilateral triangles share similar characteristics. Although similar figures need not be congruent in order to be comparable, congruent figures are always comparable.

Despite having the same shape, similar triangles have different diameters. In identical triangles, corresponding angles are equal. In analogous triangles, the ratio of the corresponding sides is the same. Any pair of equivalent sides' squares and any comparable triangle's area have the same ratio.

As the given triangles are similar,

the sides are in same ratio,

⇒ 56 / 8x - 5 = 24 / 15

⇒ 8x - 5 = 35

⇒ 8x = 40

⇒ x = 5

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The possible prices of the new dress must be any value less than or equal to $45.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Start with the inequality x ≤ 45

This inequality states that x must be less than or equal to 45.

Therefore, the possible prices of the new dress must be any value less than or equal to $45.

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Answer

  5518

28/154504

154504

1 4 0      

 1 4 5    

 1 4 0    

     5 0  

     2 8  

     2 2 4

     2 2 4

         0

She would be doing 9 hours of studying per day and 6 hours of other activities. This is because 15 hours divided by 9 hours of studying and 6 hours of other activities would equal the same amount of time allocated to each activity.

The amount of studying she is going to do per day is 9 hours, and the amount of other activities she is going to do per day is 6 hours.   This means that she will be dedicating roughly 60% of her waking hours to studying and 40% to other activities. This is a good balance between the two activities, and it will ensure that she is able to adequately focus on both her studies and other activities.

This balance will also help her to stay motivated and not become overwhelmed by her studies. Having a set amount of time for both activities will also help her to organize her day and stay on track. It will give her a sense of structure and allow her to plan her day accordingly.

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The intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric function is given below.

3 sec2x − 2 tan 2x − 4 = 0

Simplify the equation, then we have

3 sec2x − 2 tan 2x − 4 = 0

3 / cos 2x − 2 sin 2x / cos 2x = 4

3 − 2 sin 2x = 4 cos 2x

(3 − 2sin 2x)² = 16 cos² 2x

The graph of the functions is drawn below.

From the graph, the intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.

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The time that it would take for the population to decrease by one fourth is 3 years. Option C

We know that when we talk about population growth, we are talking about the increase in the population of the species and this can be regarded as a kind of an exponential growth problem.

We know that we can write;

P = Poe^-rt

P = population at time t

Po = initial population

r = population growth rate

t = time taken

Then we have that at the said time, P = 1/4Po

Hence;

1/4Po = Poe^-0.365t

1/4 = e^-0.365t

0.25 = e^-0.365t

ln0.25=ln e^-0.365t

-1.386 = -0.365t

t = 3 years

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The time it takes for the country's population to double is 1000 years. The total population would be 10 million people.

We can calculate the population growth by

P = P₀ × r × t

Where

Suppose that immigration is the only factor of population growth. We have

Find the time that takes the country's population to double!

To make the country's population double, the population growth should be also 5 million people.

The formula would be

5,000,000 = 5,000,000 × 1/000 × t

t = 1,000/1

t = 1,000 years

Hence, the country's population will be double after 1,000 years.

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In the expression 2t+8, 8 represents the number of seats at each table.

An expression is combination of variables, numbers and operators.

Given that A coffee shop has a group of seats at the counter and t individual tables.

where each able has the same number of seats.

2t + 8 represents the total number of seats in the restaurant.

8 represents the number of seats at each table and 2t is the number of individual seats.

Hence, in the expression 2t+8, 8 represents the number of seats at each table.

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Answer:

Step-by-step explanation: using the y-intercept form, I see the y-intercept is 40 , at the point (0,40)

and we have a point (4,160), so

slope = (160-40)/(4-0) = 30

equqtion: y = 30x + 40 or 30x - y = -40

Answer: 8y-56

Step-by-step explanation: the equivalent expression is 8y-56

Answer: 8y - 56

Step-by-step explanation: Hello! Here are the steps to solve this:

8(y - 7)            Use the distributive property, distribute 8 to y and 8 to -7

8y - 56           8 x y = 8y, 8 x -7 = -56

8y - 56 is an equivalent expression to 8(y - 7) because it is simplified.   I hope this helps!

To complete the piece of work Kieron needs 12.42 workers. He able to complete the work in 7 days.

What is the unitary method?

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that 6 workers would take 14 and a half days.

In other words, to complete a piece of work in 14.5 days he needs 6 workers.

Now apply the unitary method,

To complete a piece of work in 1 day he needs 6×14.5 workers.

To complete a piece of work in 7 days he needs (6×14.5)/7 workers.

                                                                                  = 12.42

He has 13 workers and to complete the piece of work he needs 12.42 workers. Thus he was able to complete the work in 7 days.

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The distance travelled by Jasmine in 3 1/5 hours is 108 miles.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

Plug in given values into the above equation and solve for distance.

Speed = Distance / time

Distance = Speed × Time

Distance = 33 3/4 × 3 1/5

Convert to improper fraction

Distance = (33 × 4 + 3)/4 × ( 3 × 5 + 1)/5

Distance = 135/4 × 16/5

Distance = 2160 / 20

Distance = 108 miles

Therefore, the distance covered is 108 miles.

Option D) 108 miles is the correct answer.

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Answer:

24 days = 1500 tables

25 days = Fewer than 1500 tables

Step-by-step explanation:

So we have the inequality of < which is fewer than. Let's start by labeling all the numbers given.

What we want to find is how many days, so we'll make days = x

2100 is the initial and they sell 25 a day... 25 a x.

Combining them all we get a basic inequality of:

2100 - 25x < 1500

Let's get X alone.

Subtracting 2100 from both sides gives you

-25x < -600.

We have negatives on both sides. For me, if I see that, I make both of them positive;

25x < 600

Last step is to divide the 25 out of the X which means you'll divide 25 by 600 also

X = 24

Which means day 24 will be exactly 1500. We wanted fewer though, so adding a day gives you an answer of 25 days.

Answer: $5.55

Step-by-step explanation: 15% = 0.15

                                             37 / 0.15 = 5.55

Answer: 70

Step-by-step explanation:

70 kilometers if 3.5 centimeters is the distance and each centimeter represents 20 kilometers, 3.5 times 20 is equal to 70

well, the selling price is simply $30 plus 120% of that, hmmm what's 120% of 30 anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{120\% of 30}}{\left( \cfrac{120}{100} \right)30}\implies 36~\hfill \underset{selling~price}{\stackrel{30~~ + ~~36}{\text{\LARGE 66}}}[/tex]

The inequality of the statement is y/4 ≤ 19

From the question, we have the following parameters that can be used in our computation:

A mathematical statement represented as

the quotient of y and 4 is at most 19

The variable in the above statement is y

This means that the quotient of y and 4 cannot exceed 19

The term cannot exceed implies less than or equal to

So, we have the following representation

y/4 ≤ 19

Hence, the statement is

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Answer: $960

Step-by-step explanation:

Regular Price = x

x*0.5 = 480

x = 960

Answer:

$960

Step-by-step explanation:

Since 480 dollars is half (50%) of the regular price...

you can find the total price by dividing 480 by 0.50 (50%)

or multiplying 480 by 2. You end up getting an answer of $960.

Answer: C.

Step-by-step explanation:

since the four friends are SPLITTING the rental cost, it would be dividing.

Then, since it says NO MORE THAN it would be less than or equal to as the symbol for the inequality.

Answer:

5 hours

OR

300minutes

Step-by-step explanation:

1 degree lost 1 hour

5 degrees lost (5×1) hours

5hours

1 hour=60 minutes

5hours= (5×60)

300minutes