One ferret digs 465 cubic centimeters of soil from a burrow on 5 minutes. Based on this digging rate, write an equation that can be used to predict the amount of soil,s,in cubic centimeters the ferret can dig from a burrow in m minutes

Answer:

One solution                    

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

[tex]\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }[/tex]

Simplify

[tex]x = \dfrac{ 53 }{ 30 }[/tex]

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

[tex]\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}[/tex]

[tex]\mathrm{Now\:lets\:solve\:for\:"y"\:then}[/tex]

[tex]y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}[/tex]

[tex]\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}[/tex]

[tex]y = \dfrac{ -5 \times 53 }{ 30 } +8[/tex]

[tex]\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }[/tex]

[tex]y = \dfrac{ -265 }{ 30 } +8[/tex]

[tex]\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }[/tex]

[tex]y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]y = - \dfrac{ 53 }{ 6 } +8[/tex]

[tex]\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}[/tex]

[tex]\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}[/tex]

[tex]\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}[/tex]

[tex]\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}[/tex]

[tex]y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }[/tex]

[tex]\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}[/tex]

[tex]y = \dfrac{ -53+48 }{ 6 }[/tex]

[tex]\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}[/tex]

[tex]y = - \dfrac{ 5 }{ 6 }[/tex]

[tex]\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}[/tex]

So there is only one solution to the equation.

Answer:

v/lw=h

Step-by-step explanation:

I hope this helps and have a good day

Answer:

(a) 28π cm

(b) 88 cm

Step-by-step explanation:

Part A — Give an exact answer in terms of π.

To find circumference of a circle, our formula is:

[tex]\displaystyle \large{C=2\pi r}[/tex]

Where:

Radius is,the line segment or value from center to one of endpoints. Our radius is given as 14 cm in the shown attachment.

Henceforth, our circumference is:

[tex]\displaystyle \large{C=2\pi \cdot 14}\\\displaystyle \large{C = 28\pi}[/tex]

So for part A, the circumference is 28π cm.

Part B — Use π ≈ 22/7 and express your answer as a fraction in lowest terms.

For this part, use the circumference that we solved from part A:

[tex]\displaystyle \large{C=28\pi}[/tex]

Substitute π = 22/7 in.

[tex]\displaystyle \large{C \approx 28\cdot \frac{22}{7}}\\\displaystyle \large{C \approx 4\cdot 22}\\\displaystyle \large{C \approx 88 \ cm}[/tex]

Henceforth, the circumference in Part B is approximately 88 cm.

Answer:

1.5

Step-by-step explanation:

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction.

Mark me brainliest!!

Answer:

The value of Mary's investment after two years = £12362.7

Step-by-step explanation:P = Principal / initial amountR = rate of interest per cent per yearT = number of yearsA = final amount at the end of T yearsThen:A = P*(1 + R/100)^2In our example:P = £12000R = 1.5 per cent per yearT = 2 yearsThus:A = 12000*(1 + 1.5/100)^2   = 12000*(1 + 0.015)^2   = 12000*(1.015)^2    = 12000*(1.030225)    = 12362.7Value of investment after two years = £12362.7

Answer:

sum of 22nd = 1,428.05

sum of 23 to 40 is 932.53

Step-by-step explanation:

A(n)=20(1.1)^n-1

20 is the first term or a1

1.1 is the common ratio or r

A(22) = 20(1.1)^22-1

22nd term = 20(1.1)^21

22nd term = 148.00

sum of geometric sequence

formula

Sn = a1(1-r^n)/1-r

Sn = sum

a1 = first term

n = number of term

r = constant ratio

sum of 22nd = 1,428.05.

23 to 40 is 17 terms

Sequence: 23, 25.3, 27.83, 30.613, 33.6743, 37.04173, 40.745903 ...

The 17th term: 105.684378686

Sum of the first 17 terms: 932.528165548

socratic

miniwebtoolcomgeometricsequencecalculator

His sister challenged him to find the sum of the first 22 terms of geometric series is 1428.05.

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

Antonio is working with a new geometric series generated by the equation that is

[tex]A_{n}=20(1.1)^n-1.[/tex]

His sister challenged him to find the sum of the first 22 terms will be given as

[tex]Sn = \dfrac{a(r^n - 1) }{ (r - 1)}[/tex]

We have

a = 20

r = 1.1

n = 22

Then

[tex]\rm S_n = \dfrac{20(1.1^{22} - 1) }{ (1.1 - 1)}\\\\\\S_n = \dfrac{20(8.14 - 1) }{ 0.1}\\\\\\S_n = \dfrac{20*7.14 }{0.1}\\\\\\S_n = 1428.05[/tex]

His sister challenged him to find the sum of the first 22 terms of geometric series is 1428.05.

More about the series link is given below.

https://brainly.com/question/10813422

Answer:

hope u understand

180°-142°=38°

x=38°

here is your answer

mark as brilliant and follow pls

Answer:

142

Step-by-step explanation:

because it is an obtuse angle and it is equvilent to an exteroir angle which is also 142 degrees

pls mark brainliest

113 in .8 hours

113 / 4 in .2 hours

28.25 in .2 hours

28.25 * 5 in 1 hour

141.25 in 1 hour

141.3 mph

Answer:

220

Step-by-step explanation:

First you divide 15 by 2 then you take the answer and multiply the 1750 . Last but not least you divide the answer by 60 to get your answer

Answer:

114 minutes

Step-by-step explanation:

samara runs 4 miles in 38 minutes

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

time taken to cover a distance of 12 miles:

many minutes will it take her to run 12 miles is 114 minutes

Answer:

x=1

Step-by-step explanation:

f(x) = 2x + 1

g(x) = 5x – 2

f(x) = g(x)

2x+1 = 5x-2

Subtract 2x from each side

2x+1 = 5x-2-2x

1 = 3x-2

Add 2 to each side

1+2 =3x-2+2

3 = 3x

Divide by 3

3/3 =3x/3

1 =x

Answer:

8/9 x 5

5 x 1/9 x 8

5 x 8 divided by 9

Step-by-step explanation:

5/9 = 0.5555*8 =4.444

8/9 = 0.8888*5 =4.444

5*1/9 = 0.5555*8 =4.444

5*8 = 40/9 =4.444

Answer:

10

Step-by-step explanation:

30 x 1/3 = 10

aka if you do something 30 times and every 3 times it happens you do it 10 times.

Answer:

Subtract 1/4x from each side (Yes)

Answer:

no, yes, yes, no, no, yes

Step-by-step explanation:

Answer:

The number is -3

Step-by-step explanation:

First, let's translate the statement into an equation.

Step 1: Subtract 2x from both sides.

Step 2: Divide both sides by 2.

Therefore, the number is -3/

If the number times four is six less than twice the number then the number will be -3.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

let the number be x.

According to the questions the following equation can be made:

4x=2x-6

We have multiplied by 4 with the number and 2 with number and subtracted 6 because it is given that 4 times the number is equal to twice the number less 6.

Now we have to solve the equation for x.

4x-2x=-6

2x=-6

x=-6/2

x=-3

Hence if the number times four is six less than twice the number then the number will be -3.

Learn more about equation at https://brainly.com/question/2972832

#SPJ2

The cost of the circular glass piece will be equal to $9. 24

It is given that

The radius of the circular glass piece [tex]r= 0.8 meters[/tex]

The selling price of glass per square meter = $4. 60

Now find the area of the circular glass piece

[tex]A= \pi r^{2}[/tex]

[tex]A=\pi \times (0.8)^{2}[/tex]

[tex]A=2.01 m^{2}[/tex]

Now cost of the glass piece =

[tex]=Area \times selling price of glass pieces per square meter area[/tex]

[tex]= 2.01\times4.0=9.24[/tex]

Thus the cost of the circular glass piece will be equal to $9. 24

To know more about the area of the circle follow

https://brainly.com/question/10645610

The length of the guys wire should be = 22.1 feet

The pythagorean theorem states that the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Therefore,

[tex]c {}^{2} = 20.4 {}^{2} + 8.5 {}^{2} [/tex]

[tex]c {}^{2} = 416.16 + 72.25[/tex]

[tex]c {}^{2} = 488.41[/tex]

[tex]c = \sqrt{488.41} [/tex]

c = 22.1 feet.

Where c represents the length of the guys wire

Learn more about Pythagorean theorem here:

https://brainly.com/question/343682

Answer: An Electric Store

Step-by-step explanation: Hoped This Helped! Thx For The Points!

Answer:

B

Step-by-step explanation:

an electronics store

FATHER = 123456

That means that each letter of father represents the following numbers:

Now,

Let's see the given code

4526

Which letters are they representing, Let's see:

Thus, 4526 is the code for the word Hear...

See the attached picture with the solution.

Using conditional probability, it is found that there is a 0.5714 = 57.14% probability that the student speaks ilocano given that he speaks kankanaey.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

In this problem, the events are given as follows:

Hence, the parameters are given as follows:

[tex]P(A \cap B) = 0.4, P(A) = 0.7[/tex]

Then, the probability that the student speaks ilocano given that he speaks kankanaey is given by:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]

More can be learned about conditional probability at https://brainly.com/question/14398287

Answer:

18:1

Step-by-step explanation:

Answer:

73 is the answer 100%

Step-by-step explanation:

Hoped this helped a little at least :)

*UPDATED*

Using abosute value formulas:

|a + bi| = sqrt( a + bi)(a-bi) = sqrt(a^2 + b^2)

In the given equation a = 3 and b = 8

sqrt(3^2 + 8^2)

Sqrt(73)

Answer: sqrt(73)

Explanation:

Locate x = 0 on the x axis number line.

Then move up or down until you reach the blue curve. In this case we move upward.

You should arrive at y = 4

This means (x,y) = (0,4) is a point on the blue cubic curve, and that f(0) = 4.

The given equation is an equation of a circle because it looks similar to the general equation of a circle.

The general equation of a circle is:

x² + y² +2gx + 2fy + c = 0...........eq1

Where (-g, -f) is the center of the circle.

c is a constant

Given equation is

3x² +6x + 3y²+7y+4 = 0

Let us take 3 as common

x² + 2x+y²+7/3y + 4/3 = 0

Let us rearrange the equation

x² + y²+2x +7/3y + 4/3 = 0...........eq2

Now look at eq1 and eq2

We got that eq2 is having a similar pattern as eq1.

Therefore, The given equation is an equation of a circle.

To get more about circle visit:

https://brainly.com/question/1506955

Answer:

circle A = C

Step-by-step explanation:

Answer:

D. 35 of teenagers chose to listen to Music

Step-by-step explanation:

We are given the following info

All we have to do next is find the percentage of Teenagers that Listened to music which is already given to us: 28%

Now we find 28% of 125 and we get 35 teenagers

Hope I could help

Answer:

35

Step-by-step explanation:

28%of 125 = 35

16% of 125 = 20

24% of 125 = 30

32% of 125 = 40

Let's verify

As LHS not equal to RHS

Answer:

[tex]\displaystyle \frac{\sqrt{2} + \sqrt{6}}{4}[/tex]

Explanation:

If you recall the unit circle [from the polar graph], you would have no trouble at all figuring this out, but sinse you have trouble, do not worry about it. So, here is what you should have realised:

[tex]\displaystyle \boxed{\frac{\pi}{2}} = \frac{6}{12}\pi[/tex]

If you did not notise, [tex]\displaystyle \frac{7}{12}\pi[/tex]is just [tex]\displaystyle \frac{\pi}{12}[/tex]more than [tex]\displaystyle \frac{\pi}{2},[/tex]which means the exact value could possibly have a 4 in its denominatour [which obviously also has a desimal value] or could be irrational [values that cannot be written as fractions]. In this case, according to the unit circle, you will have a fraction, and that will be this:

[tex]\displaystyle \frac{\sqrt{2} + \sqrt{6}}{4}[/tex]

It is all about memorisation of the unit circle, which I know is difficult, but you will get used to it soon.

*Now, if you had to find [tex]\displaystyle cos\:\frac{7}{12}\pi,[/tex]then the exact value would be the OPPOCITE of the exact value of [tex]\displaystyle sin\:\frac{7}{12}\pi,[/tex]which is [tex]\displaystyle -\frac{\sqrt{2} + \sqrt{6}}{4},[/tex]because you would be crossing into the second quadrant where the x-coordinates are negative, accourding to both the cartesian and polar graphs.

I am joyous to assist you at any time.

Answer:

•The prime factorization of 20 using exponents is 22*5 2 2 ∗ 5 .

#Let's Study

#I Hope It's Help

#Keep On Learning

#Carry On Learning