Write 10:5 as a ratio in its simplest form

Answer:

a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n

b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n

c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n

Step-by-step explanation:

They are all arithmetic progressions (AP) with a common difference, i.e. all differences of one term from the subsequent term are identical.

The general formula is

T(n) = T(0)+n*D

where

n = the term number

T(n) = nth term (considering the first term to be the zeroth term.

D = common difference

a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n

b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n

c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n

Answer:

-1/6=-0.166

-2/3=-0.66

Step-by-step explanation:

-by looking carefully you will notice that . which number is greater and smaller.

Answer:

-1/6 is greater than -2/3

Step-by-step explanation:

Answer:

1: C) y = -x + 1

2: D) y = -3x + 8

Step-by-step explanation:

Well number 1,

c is the correct option because,

-2 -> 2

2+1 - 3

This rule applies for all the x values.

2,

X: -2, -1, 0, 1, 2

Y: 14, 11, 8, 5, 2

d is the correct option because -3*-2 is 6 + 8 = 14.

this rule applies for all x values.

Thus,

the answers are C and D.

Hope this helps :)

Question

If the CP of 15 articles equals to the SP of 12 articles, find the gain percent.

Answer:

gain percent = 25%

Step-by-step explanation:

To solve the question given, we will follow the steps below:

gain%  =   [tex]\frac{s.p - c.p}{c.p}[/tex]  ×    100%

But from the question;

"CP of 15 articles equals to the SP of 12 articles", this implies that

15 c.p  =  12 s.p

s.p = 15c.p  /   12

s.p  = [tex]\frac{15 c.p}{12}[/tex]       =   [tex]\frac{5c.p}{4}[/tex]

s.p  =  [tex]\frac{5c.p}{4}[/tex]

substitute  s.p  =  [tex]\frac{5c.p}{4}[/tex]   into the formula

gain%  =   [tex]\frac{s.p - c.p}{c.p}[/tex]  ×    100%

      =[tex]\frac{\frac{5c.p}{4} - c.p }{c.p}[/tex]     ×    100%

       =  [tex]\frac{\frac{5c.p - 4c.p}{4} }{c.p}[/tex]      ×    100%

  =   [tex]\frac{c.p}{4}[/tex]   ÷   c.p      ×    100%

= [tex]\frac{c.p}{4}[/tex]     ×   [tex]\frac{1}{c.p}[/tex]    ×    100%

=   [tex]\frac{1}{4}[/tex]  ×    100%

=  25 %

Answer:

Barry has to pay back $1150

Step-by-step explanation:

We can set up an equation to help solve this problem

x is the amount he has to pay back

x=1000+3(1000/20)

1000/20 lets us know how many times he borrowed 20 dollars

x=1000+3(50)

x=1000+150

x=1150

Barry has to pay back $1150

If Barry also looks into the cost of repaying an easy access loan for $1000. The up-front cost of the loan is $3 for every $20 borrowed, plus the original $1000. Then Barry has to pay back $1150.

Two or more expressions with an equal sign is called as Equation.

We can set up an equation to help solve this problem

x is the amount he has to pay back.

x=1000+3(1000/20)

1000/20 lets us know how many times he borrowed 20 dollars

x=1000+3(50)

x=1000+150

x=1150

Hence, Barry has to pay back $1150.

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Answer:

[tex]\large \boxed{\sf \bf \ \ \text{The solutions are }(2,4) \text{ and } (-2,-4) \ \ }[/tex]

Step-by-step explanation:

Hello, this is the same kind of question that you have already posted( brainly.com/question/17141820).

I would suggest that you check my previous answer and try to apply the same logic here. When you try it if you have any question please let me know. It will be the more efficient way for you to learn how to solve it by yourself.

As I have already provided details for the previous question I will be more succinct here.

Again we can write y = y and then we have to solve the following.

[tex](x+1)^2-5=2x\\\\x^2+2x+1^2-5-2x=0\\\\x^2-4=x^2-2^2=(x-2)(x+2)=0\\\\x=2 \ \ or \ \ x=-2[/tex]

The solutions are (2,4) and (-2,-4)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A(t) = R -5(t)

t in minuto

Step-by-step explanation:

Nesta questão, estamos preocupados em estabelecer uma lei que forneça a quantidade de água presente no reservatório a qualquer momento, usando a quantidade inicial de água no reservatório e a taxa de perda de água do reservatório.

Agora, sabemos que a taxa de perda de água é de 5 litros por minuto.

Assim, podemos estabelecer a lei da seguinte forma; vamos chamar a quantidade de água a qualquer momento no reservatório A (t);

A lei é assim; A (t) = R -5t onde t representa o tempo que estamos considerando e é em minutos, enquanto R é o volume inicial de água no tanque.

Answer: x = -2 , y = 3

Step-by-step explanation:

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3

*see attachment below showing the dot plot and box plot created by Tia

Answer:

Dot plot

Step-by-step explanation:

In a dot plot, the temperature of a day is represented by 1 dot. There are 30 dots on the box plot shown in the attachment that was made by Tia.

This dot plot display makes it easier to find how many days had a temperature that is higher than 15°.

Thus, from the dot plot, we have:

2 dots representing 2 days having a temperature of 16°C each

2 days also have daily temperature of 17°C

2 days have temperature of 18°C as well, and

1 day has temperature of 19° C.

Therefore, the number of days that had a temperature above 15°C is 7 days.

Answer:

Dot Plot, Box Plot

Step-by-step explanation:

I got the other guy's answer wrong but mine is right =)

Answer:

The height of the totem tree is approximately 172.8ft

Step-by-step explanation:

Hello,

To find the height of the totem pole, we need to use our date to make a pictorial representation so that we can know if the pole and base makes a right angle triangle with the angle of elevation.

See attached document for better illustration.

Let T represent the height of the pole.

Using trigonometric ratio,

SOHCAHTOA, we can use tangent since we have our adjacent and we're to solve for the opposite.

Tanθ = opposite/ adjacent

Opposite = T

Adjacent = 20ft

θ = 83.4°

Tan83.4 = T / 20

T = 20Tan83.4

T = 20 × 8.64

T = 172.8ft

The height of the totem tree is approximately 172.8ft

Answer:

Step-by-step explanation:

Given

u = 14 , a = 8 , t = 4

Now, let's find the value of s

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

plug the values

[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]

Reduce the numbers with G.C.F 2

[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]

Multiply the numbers

[tex] = 56 + 4 \times {4}^{2} [/tex]

Calculate the product

[tex] = 56 + {4}^{3} [/tex]

Evaluate the power

[tex] = 56 + 64[/tex]

Add the numbers

[tex] = 120[/tex]

Hope this helps..

best regards!!

Answer:

x = 3.25

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is the order of operation.

First, subtract 3 from both sides of the equation:

4x + 3 = 16

4x + 3 (-3) = 16 (-3)

4x = 16 -3

4x = 13

Next, dvide 4 from both sides:

(4x)/4 = (13)/4

x = 13/4

x = 3.25

x = 3.25 is your answer.

~

Answer:

x = 3.25

Step-by-step explanation:

4x + 3 = 16

4x + 3 - 3 = 16 - 3

4x = 13

4x/4 = 13/4

x = 3.25

Answer:

here,

money spent in 1st year =$250

money spent in 2nd year=$295

total inflated amount=$295- $250

=$45

Then,

inflation rate= ($45/ $250)×100%

=18%

Answer:

a²  + b²  = c · (e + d) =  c × c = c²

a²  + b²  = c²

Please see attachment

Step-by-step explanation:

Statement,                                                        Reason

ΔADC ~ ΔACB,          Given

AC/AD = BA/AC,        The ratio of corresponding sides of similar triangles

b/e = c/b

b² = c·e

ΔBDC ~ ΔBCA,           Given

BC/BA =  BD/BC,        The ratio of corresponding sides of similar triangles

a/c = d/a        

a² = c·d

a²  + b²   = c·e + c·d

a²  + b²   = c · (e + d)

e + d = c,                       Addition of segment

a²  + b²   = c × c = c²

Therefore, a²  + b²   = c²

Answer:

1.9cm

Step-by-step explanation:

The density d of a material is related to its mass m and volume V as follows;

d = [tex]\frac{m}{V}[/tex]             ------------------(i)

The material in question here is the lead ball.

Now, from known experiment;

the density of lead is 11.34g/cm³

From the question, the weight/mass of the lead ball is 326g

Substitute these values into equation (i) as follows;

11.34 = [tex]\frac{326}{V}[/tex]

V = [tex]\frac{326}{11.34}[/tex]

V = 28.75cm³

Now, since the ball is of course spherical, we can get the radius by using the following relation from the volume of a sphere;

V = [tex]\frac{4}{3} \pi r^3[/tex]          [V = volume, r = radius]

V = 28.75cm³

=> 28.75 = [tex]\frac{4}{3} \pi r^3[/tex]

=> 3 x 28.75 = 4 π r³

=> 86.25 = 4 π r³

=> 21.5625 = π r³      [Take π = 3.142]

=> 21.5625 = (3.142) r³      [divide both sides by 3.142]

=> 6.86 = r³              [Take the cube root of both sides]

=> ∛6.86 = ∛r³

=> 1.90 = r

Therefore, the radius is 1.9cm to the nearest tenth

Answer:

B

Step-by-step explanation:

sqrt30 -6^2 doesn't work

2.5 sqrt18 and 5 do work

Answer:

A

Step-by-step explanation:

I'm certain the answer is this, and I understand that you are in a hurry. I can update it anytime you'd like to see the explanation

Answer:

Current price $50eax135hats= $6750

Step-by-step explanation:

If he sells the hats at $52 he sells 3 less hats so $52x132=$6864

if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc

$56 x 126=$7056

Answer:

  262°

Step-by-step explanation:

The relationship between the angle at B (82°) and the arcs of the circle, CGF and CDF, is that the angle is half the difference of those arcs. Of course the sum of those arcs is 360°, since together they make a full circle. So. we have ...

  CGF +CDF = 360

  (CGF -CDF)/2 = 82

We need to solve this system of equations to find CGF.

__

Multiplying the second equation by 2 and adding the first, we get ...

  2((CGF -CDF)/2) +(CGF +CDF) = 2(82) +(360)

  2CGF = 524 . . . . . simplify

  CGF = 262 . . . . . . divide by 2

The measure of arc CGF is 262°.

_____

Alternate solution

Here's another way to get there. Arc CDF is the supplement to angle B, so is ...

  CDF = 180° -∠CBF

Of course, arc CGF is 360° minus arc CDF, so ...

  CGF = 360° -(180° -∠CBF)

  CGF = 180° +∠CBF . . . . . simplify . . . please note this is a general solution

Then ...

  arc CGF = 180° +82° = 262°.

Answer:

It will take 1 hour and they will have 11 baskets

Step-by-step explanation:

Dave

6 + 5h = b

Emily

9 + 2h=b

where h = hours  and b = baskets

Setting the equations equal to each other

6+5h = 9+2h

Subtracting 2h from each side

6+3h = 9

Subtracting 6 from each side

3h = 3

Divide by 3

h =1

Then finding b

9+2h = b

9+2 =b

11=b

It will take 1 hour and they will have 11 baskets

Answer:

D.0

Step-by-step explanation:

Our system of equations is

then we can conclude that

This is a quadratic equation so we will use the dicriminant method:

Let Δ be our dicriminant

The dicriminant is negative so this equation has no real solutions

the the system has no real solutions

Answer: 168,750 chocolates

Step-by-step explanation:

If there are 90 chocolates in a box and there are 1,875 boxes, you multiply 1,875 by 90 to get the total number of chocolates needed to complete the order.

1,875 * 90 = 168,750

There are 168,750 chocolates needed to complete the order.

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

Where m is the slope

c is the y intercept

From the question the y intercept is 3

and the slope is 2

Substituting the values into the above equation

We have

Hope this helps you

The equation of a line that passes through [tex](0,3)[/tex] and a slope [tex]2[/tex] is [tex]y=2x+3[/tex].

The equation of a line that passes through a point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is:

[tex](y-y_1)=m(x-x_1)[/tex]

Here, the point is [tex](0,3)[/tex] and the [tex]slope[/tex] is [tex]2[/tex].

So, [tex]x_1=0, y_1=3[/tex] and [tex]m=2[/tex].

So, the equation of the line is

[tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-3)=2(x-0)[/tex]

[tex]y-3=2x-0[/tex]

[tex]y=2x+3[/tex]

So, option B is correct.

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Answer:

The larger canister has 8 times the volume and 4 times the volume of the smaller one.

Step-by-step explanation:

The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.

The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.

The canisters are in the shape of a cylinder.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

The surface area of a cylinder is given as:

A = 2πr(r + h)

SMALLER CANISTER

Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres

Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres

LARGER CANISTER

Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres

Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres

By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer:

Depth of the milk = 4 cm

Step-by-step explanation:

In the figure attached,

Milk carton is in the shape of a cuboid having length = 8 cm, Width = 5 cm and Height = 15 cm

Depth of the milk in the carton = 12 cm

Milk inside the carton will have the same shape of cuboid, having same length and width but a different height.

Volume of the milk = volume of the cuboid shape of the milk

                                = Length × width × height

                                = 8 × 5 × 12

                                = 480 cm³

Now the carton is turned with its base on the shaded region.

By changing the base, dimensions of the milk inside the carton will change but the volume of the milk will remain the same.

New dimensions of the milk inside the carton will be,

Length = 15 cm

Width = 8 cm

Height = d cm (unknown side)

By using the formula of volume again,

V = l × b × h

480 = 15 × 8 × d

480 = 120d

d = [tex]\frac{480}{120}[/tex]

d = 4 cm

Therefore, depth of the milk in the carton will be 4 cm.

Answer:

30°

Step-by-step explanation:

well AEB is a straight line which is 180° and we were already given the angles that made up the straight line ,so all u had to do was subtract 60° from 90°

BED =30°

Answer:

AEC=30

BED=30

Step-by-step explanation:

We know that AEC is 30 degrees because it is on line AB, along with a right angle and 60 degrees, add 90 to 60 to get 150, and subtract it from 180 to get your answer, 30

As for BED, AEC and BED are verticle angles so they are equivalent.

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Have a good day! :)

Answer:

a) A quadrilateral with 4 right angles

Answer:

I think the answer is b

I'm sorry if I'm not correct

Answer:

Step-by-step explanation:

Given the expression after 4 has been subtracted from both sides as

1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;

1/2 x + 4 = - 1/2 x + 4

x/2 + 4 = -x/2 + 4

Find the LCM of both equation;

(x+8)/2 = (-x+8)/2

Multiplying both sides by 2 will give;

x+8 = -x+8

Collecting the like terms;

x+x = 8-8

2x = 0

x = 0/2

x = 0

Hence, the value of x is 0

Answer:

0

Step-by-step explanation:

Answer:

1. a=9     2. f=1    3. b=6

Step-by-step explanation:

1.) 4a-1=3a+8

subtract 3a from both sides

a-1+8

add 1 to both sides

a=9

2.) 1+f+3+f=f+5

combine like terms that are on the same side

2f+4=f+5

subtract f from both sides

f+4=5

subtract 4 from both sides

f=1

3.) construct a equation

b+5=11

subtract 5 from both sides

b=6

Answer:

Area of polygon D = 10 square units

Step-by-step explanation:

Given:

Polygon C has an area of 40 square units.

It is scaled with a scale factor of [tex]\frac{1}2[/tex] to form a new polygon D.

To find:

The area of polygon D = ?

Solution:

When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.

And the area becomes one-fourth of the original polygon.

Let us consider this by taking examples:

Area of a right angled triangle is given by:

[tex]A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units[/tex]

If scaled with a factor [tex]\frac{1}{2}[/tex], the sides will be 3, 4 and 5.

New area, A':

[tex]A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A[/tex]

i.e. Area becomes one fourth.

Sides be 8 and 10 units.

Area of a rectangle, A = [tex]Length \times Width[/tex] = 8 [tex]\times[/tex] 10 = 80 sq units.

Now after scaling, the sides will be 4 and 5 units.

New Area, A' = 4 [tex]\times[/tex] 5 =20 sq units

So, [tex]\bold{A' = \frac{1}4 \times A}[/tex]

Now, we can apply the same in the given question.

[tex]\therefore[/tex] Area of polygon D = [tex]\bold{\frac{1}{4}}[/tex][tex]\times[/tex] Area of polygon C

Area of polygon D = [tex]\bold{\frac{1}{4}}[/tex][tex]\times[/tex] 40 = 10 sq units

Answer:

Step-by-step explanation:

10