In triangle ABC, A is the point (4; 3) and C is the point (8; 5). The equations of AB and BC are y = 5x-17 and y = -x + 13 respectively. Calculate the equation of median BD.​

Answer:

D. 2

Step-by-step explanation:

The table represents a linear relationship between the variables x and y, where y is proportional to x. This means that for each increase in x by 3 units, y increases by 2 units. The constant of proportionality is the coefficient that relates the change in x to the change in y, and it can be calculated as the ratio of the change in y to the change in x. In this case, the constant of proportionality is equal to (4-2)/(6-3) = 2. Therefore, the correct answer is D: 2.

Answer:

Step-by-step explanation:

Substituting the value of x in the given function:

On solving the provided question, we can say that Therefore, you would need multiply  approximately 27.84 pounds of food each day for your horse.

One of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."

First, we need to convert the weight of the horse from kilograms to pounds, so:

678 kg x 2.20462 lbs/kg = 1495.69 lbs

Next, we need to calculate how many Mcal the horse needs per day:

0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day

Then, we can convert the Mcal to kcal:

22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day

Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:

22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day

Therefore, you would need approximately 27.84 pounds of food each day for your horse.

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Answer:

-11

Step-by-step explanation:

(6−1)2−(9)(4)

=52−(9)(4)

=25−(9)(4)

=25−36

=−11

Answer: Subtract: 6 - 1 = 5

Exponentiation: the result of step No. 1 ^ 2 = 5 ^ 2 = 25

Multiple: 9 * 4 = 36

Subtract: the result of step No. 2 - the result of step No. 3 = 25 - 36 = -11

===================================================

Explanation:

Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).

Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:

20*cos(x)+25

20*(-1) + 25

-20 + 25

5

The height of the fan tip is 5 cm when it is the closest to the table.

Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is \(5 \le y \le 45\)

Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

The solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.

We are given:

y = 1/8 x − 1                 ..............equation i.

− 5x + 4y = − 13          ..............equation ii.

We will use the substitution method to solve the given equation.

substitute the value of y from equation i in equation ii, and we will get;

− 5x + 4(1/8 x − 1) = − 13

− 5x + 1/2 x − 4 = − 13

(-10 + 1) / 2 x = -13 + 4

-9/2 x = -9

x = -9 * 2 / -9

x = 2

Put the value of x in equation i, we will get;

y = 1/8 *2 − 1

y = 1/4 - 1

y = 1 - 4 / 4

y = -3 / 4

So, the value of x = 2 and the value of y = -3 / 4.

Thus, the solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.

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Answer:

Step-by-step explanation:

45

Answer:

m /_PTS = 55°

Step-by-step explanation:

Just took the quiz..

The measure of angle m∠PTS from the given figure is 55°.

From the given figure, the two angles are 11(y-10)° and (4y-5)°.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

Now, 11(y-10)° = (4y-5)°

⇒ 11y-110 = 4y-5

⇒ 11y-4y = -5+110

⇒ 7y = 105

⇒ y = 15

So, m∠PTS = 11(15-10)

= 55°

Therefore, the measure of angle m∠PTS from the given figure is 55°.

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The value of a, b and c are found as 6, 10 and 2 respectively.

Values for exponents, commonly referred to as powers, indicate how many often to multiply a quantity by itself.

The given expression is;

\(4x^{8} y^{c} = \frac{24x^{b}y^{-3} }{ax^{2} y^{-5} }\)

Solving expression using the law of indices.

\(x^{8} y^{c} = \frac{6x^{b-2}y^{-3+5} }{a}\)

\(ax^{8} y^{c} = {6x^{b-2}y^{2} }\)

Comparing powers of both sides:

a = 6

8 = b-2 : b = 10

c = 2

Thus, the value of  a, b and c are found as 6, 10 and 2 respectively.

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Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Answer:

I have no idea I'm sorry

Step-by-step explanation:

I just need to ask a question

No solution.

Step-by-step explanation:

1) Simplify 2 + 2 to 4.

\(4 + 5 = 0\)

2) Simplify 4 + 5 to 9.

\(9 = 0\)

3) Since 9 = 0 is false, these is no solution.

\(no \: solution\)

Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

\(\huge\blue{\mid{\fbox{\tt{\:ANSWER\:}}\mid}}\)

____________________

The graph,

Answer:

see below

Step-by-step explanation:

are the rational numbers a subset of all real numbers?

yes of course

by definition the real numbers is the union of the rational numbers and the irrational numbers

so we can say that the rational numbers are a subset

and every rational number is part of the real number

are the rational numbers a subset of the irrational numbers?

No

the rationals numbers are all those numbers that you can write as p/q with q different of 0, and the irrationals numbers are those that you cannot write as a fraction

so as you can see those are two completely different types of number, to be a subset every rational number must be in the irrationals , and by the definition we know it can't happen

Rational numbers are a subset of all real numbers while rational numbers are not a subset of irrational numbers.

Real numbers encompasses all rational and irrational numbers, integers, whole numbers and natural numbers with the exclusion of complex numbers usually written in the form 8+i, √-1.

Hence, real numbers include numbers such as 1/4, 0.444, 0, 1, - 4, √6 and so on.

Hence, rational numbers are a subset (a part) of all real numbers .

Rational numbers are not a subset of irrational numbers as they are complement (a rational number cannot be irrational and vice versa) of one another.

• Rational numbers are numbers which can be expressed in the form a/b where b ≠ 0. While ;

• Irrational numbers are numbers which o cannot be expressed in the format a/b. Irrational numbers include √6, 0.13412... e.t.c

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Answer:

124/4= 31

93/3=3

Answer is 3!

Step-by-step explanation:

I hope this helps <33

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{3 \: boxes}}}}}\)

Step-by-step explanation:

\( \sf{ time \: ( \: in \: minutes}) \: \: \: \: \: \: \: \: \: \: no.of \: boxes\)

\( \sf{124 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 4}\)

\( \sf{93 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x( \: suppose)}\)

In case of Direct proportion

\( \sf{ \frac{124}{93} = \frac{4}{x} }\)

Do cross multiplication

\( \longrightarrow{ \sf{124x = 93 \times 4}}\)

Multiply the numbers: 93 and 4

\( \longrightarrow{ \sf{124x = 372}}\)

Divide both sides by 124

\( \longrightarrow{ \sf{\frac{124x}{124} = \frac{372}{124}}} \)

Calculate

\( \longrightarrow{ \sf{x = 3}}\)

Thus, It takes him 93 minutes to fit 3 boxes in a lorry.

Hope I helped!

Best regards! :D

Answer:It's 18

Step-by-step explanation:Multiply 7 and 6 to get 42

Subtract 10 from 13 to get 3

Divide 42 by 3 to get 14

Add 14 and 4 to get 18

Answer:

18

Step-by-step explanation:

First do the ones inside the bracket (13-10)=3

Second divide 6 by the answer you get from the first part 6÷3=2

Third multiply the answer from second with 7×2=14

Then add the answer you get from the third one to 4+14=18

Mathematically

7×6÷(13-10)+4

= 7×6÷3+4

= 7×2+4

= 14+4

= 18 Answer

Answer:

the one under 00 for (x,y)

                                    3,2

                                    6,4

                                   9,6

and then you just plot the points on the graph.

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Substitute the values so (3-2(-1/2))3

Then distribute so (3-(-1))3

Add since it's a double negative to get (4)3

And 4 cubed is 64

Answer:

The printing rate for Printer B is 10 pages more than the rate of printer A because the rate of 25 pages per minute is 10 pages more than the rate 15 pages per minute for Block A

Step-by-step explanation:

From the graph of the printing rate of Printer A, we can see that;

At 1 minute, number of pages printed = 15

At 2 minutes, number of pages printed = 30 minutes

At 3 minutes, number of pages printed = 45

Thus printing rate for printer A is; 15/1 = 30/2 = 45/3 = 15 pages per minutes

Since printer B can print 25 pages per minute, we can conclude that;

The printing rate for Printer B is 10 pages more than the rate of printer A because the rate of 25 pages per minute is 10 pages more than the rate 15 pages per minute for Block A

Answer:

the greatest density is glycerin

the least density is olive oil  

Step-by-step explanation:

i hope you get ahead in your assignments! good luck!:)

Answer:

6 h + 2 y + 4 is your answer

Step-by-step explanation:

Hope this helps! :)

Answer:

6h+2y+4

Step-by-step explanation:

so all you do is just subtract common factors so for 10h you just do 10h -4h and get 6h and do that for the rest

If Joshua drove at a constant rate, he drove 24 miles in one hour since he could drive 22 miles in 55 minutes or 0.4 miles per minute (driving speed).

Joshua's driving speed is the quotient of the total distance and the time.

The quotient is the result of a division operation, where a numerator (distance) is divided by the denominator (time) to obtain the unit rate or constant rate.

This constant rate (speed) is multiplied by the time (one hour), according to the distance, time, and speed formula, to obtain the distance to be covered.

The distance covered in 55 minutes = 22 miles

Constant driving speed or rate = 0.4 miles per minute (22/55)

1 hour = 60 minutes

For one hour, the distance Joshua could cover = 24 miles (60 x 0.4)

Thus, we can assert that in one hour, Joshua traveled 24 miles, given his constant driving rate.

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