How to work out this linear stimultaneous equations

The rate at which the diameter decreases is 0.0159cm/min.

Given that a snowball melts and its surface area decreases at a rate of 1cm²/min.

The surface area of a solid object may be a measure of the entire area that the surface of the thing occupies.

The surface area of the snowball is A=4πr² because the snowball is spherical.

Here, r is the radius of the snowball.

Let D be the diameter of the snowball.

As the radius is half of the diameter

The surface area of a snowball can also be rewritten as

A=4π(D÷2)²

A=4π(D²÷4)

A=πD²

Given that the surface area decreases by 1cm²/min, so,

dA÷dt=-1cm²/min.

Differentiating both sides in A=πD² and get

dA÷dt=2πD(dD÷dt)

Given that the diameter is 12cm.

Substitute these values in the formula and find dD÷dt

-1=2π×12×(dD÷dt)

-1=24π×(dD÷dt)

-1÷24π=dD÷dt

-0.0159≈dD÷dt

Hence, the diameter decreases at the rate of 0.0159 cm/min when the diameter is 12 cm.

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Answer:

[tex]a_1=1\\a_n=a_{n-1}+6[/tex]

Step-by-step explanation:

So to define a recursive equation, you need to find how much each term is increasing or decreasing by. You also need to find the first term. To find the first term you can simply plug in 1 into x: [tex]a_1=6(1)-5 = 6-5 = 1[/tex]. And as you can see the slope is 6, so each term is increasing by 6. So you get the recursive function: [tex]a_1=1\\a_n=a_{n-1}+6[/tex]

Suppose you have a valid argument with a false conclusion. Given this information, what do you know about the truth value of the argument's premises? The premises must all be false. At least one premise must be false. There must be at least one true premise and at least one false premise. The premises may be any combination of true and false. The premises must all be true.

"The argument may be either valid or invalid" When trying to determine the validity of an argument in logic, the truth of a premise is a non-factor. Logic is concerned about whether or not an argument would effectively transfer truth from its premises to the conclusion if the premises were true.

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Answer:

D

Step-by-step explanation:

The domain is the x value which in this case would be the hours of training

Answer: [tex]\frac{\sqrt{3}}{3}[/tex]

Step-by-step explanation:

[tex]\tan 30^{\circ}=\frac{\sin 30^{\circ}}{\cos 30^{\circ}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]

The value of the trigonometric relation tan 30° = 1/√3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

A = tan 30°

And , tan θ = sin θ / cos θ

On simplifying , we get

sin 30° = 1/2

cos 30° = √3/2

Substituting the values in the equation , we get

tan 30° = sin 30° / cos 30°

tan 30° = ( 1/2 ) / ( √3/2 )

tan 30° = 1/√3

Hence , the value of relation tan 30° is 1/√3

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Since both the given triangles are equilateral, their interior angles are each measure 60°.

Consider triangles ADC and BEC.

We have:

According to above, two sides and the included angle of triangles ADC and BEC are congruent by ASA.

Therefore AD = BE as corresponding sides of congruent triangles, hence proved.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The difference between −9 4/5 and −3 2/3 is -6 2/15.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The difference between −9 4/5 and −3 2/3 is,

−9 4/5 − (−3 2/3)

= −9 4/5 + 3 2/3

= (−9+3) + (−4/5 + 2/3)

= −6 + (-2/15)

= -6 2/15

Hence, The difference between −9 4/5 and −3 2/3 is -6 2/15.

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Answer: 3(3)+6=15

Step-by-step explanation:

X=3 and the Y=6

( ) means multiplying so it 3 multiplied (3) and add 6 which Is the Y then you got the answer which is 15.

The interval where f is positive is [tex]0 \le x < 1.5[/tex]

The missing function is added as an attachment

From the attached graph, the function f(x) is positive from x = 0 to x = 1.5

As an interval notation, this can be represented as:

[tex]0 \le x < 1.5[/tex]

Hence, the interval where f is positive is [tex]0 \le x < 1.5[/tex]

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Answer:

7/25

Step-by-step explanation:

there are 14 numbers greater than 30 and less than 45

   31   32  33  34 ......42  43   44         <=====14 numbers

14 choices out of 50  = 14/ 50 = 7/25

Answer:

(b) 25 muffins

(c) 38 muffins

Step-by-step explanation:

Given:

Forming system of linear equations:

muffins (m) + cookies (c) = 200 treats

1.60m + 0.80c = $200

Solve by Substitution:

m + c = 200

1.6m + 0.8c = 200

using m + c = 200, solve for m by subtracting c:

m + c - c = 200 - c

m = 200 - c

we can now plug in m tot he second equation,

1.6(200 - c) + 0.8c = 200

320 - 0.8c = 200

320 - 320 - 0.8c = 200 - 320

-0.8c = -120

-0.8c/-0.8 = -120/-0.8

c = 150

plug c back in to find m,

m = 200 - c

m = 200 - 150

m = 50

(b) if you buy 200 cookies, then how many muffins?

we use this equation as we want to stay in the price limit: 1.6m + 0.8c = 200

c = 200 so 1.6m + 0.8(200) = 200

1.6m + 0.8(200) = 200

1.6m + 160 = 200

1.6m = 200 - 160

1.6m = 40

1.6m/1.6 = 40/1.6

m = 25

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Answer:

The two numbers are 23 and 56

Step-by-step explanation:

Let's say the two numbers are A and B.

We are told:

1)  A+B=79

2) 3A+5B=283

Let's take the first expression and solve for A:

A+B=79

A=79-B

Now use this value of A in the second expression:

3A+5B=283

3(79-B)+5B=283

237-3B+5B=283

2B = 46

B = 23

Since B=23, we know from 1) that

A+B=79

A+23=79

A = 56

CHECK:

Does A+B=79?  

        56+23 = 79?  YES

Does 3A+5B=283?

3(56)+5(23)=283

168  + 115 = 283?  YES

The length of each side of the base of the pyramid is 14 cm

From the question, we are to determine the length of each side of the base of the pyramid

The volume of a square-based pyramid is given by

V = 1/3(b²h)

Where V is the volume

b is the length of the base

and h is the height

From the given information,

V = 392 cm³

h = 6 cm

Putting the parameters into the equation, we get

392 = 1/3(b²× 6)

392 = b² ×2

b² = 392/2

b² = 196

b = √196

b = 14 cm

Hence, the length of each side of the base of the pyramid is 14 cm

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Answer:

104m²

Step-by-step explanation:

we can find the area of a trapezoid from its bases and height in the following formula:

[tex]A=\frac{a + b}{2}h[/tex]

where...

A: area

a: one base

b: other base

h: height

here, we can see that our two bases are 9 and 17, and that our height is 8.

Now, let's plug these values into our formula:

a: 9

b: 17

h: 8

[tex]A=\frac{a + b}{2}h[/tex]

[tex]A=\frac{9 + 17}{2}8[/tex]

Now, we can simplify:

[tex]A=\frac{9 + 17}{2}8[/tex]

[tex]A=\frac{26}{2}8[/tex]

A = 13 · 8

A = 104

so, the area of this trapezoid is 104m²

(note: we write area as squared / in square units)

hope this helps! have a lovely day :)

The cost of covering the triangular prism wedge in silver is: $108.

Surface area = (s1 + s2 + s3)L + bh.

Given the following:

Plug in the values into the formula

Surface area of the triangular prism metal wedge = (10 + 8 + 6)0.5 + (6)(8)

Surface area of the triangular prism metal wedge = 72 cm²

Cost of covering = 72/2 × 3 = $108

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The winner received 570 votes.

Let the winner candidate be c1

Let the  second-place candidate be c2

Let the  third-place candidate be c3

[tex]c2=c1-155\\[/tex].........equation 1

[tex]c2=c3+200\\[/tex]

[tex]c3=c2-200 \\[/tex]

[tex]c3=c1-155-200\\[/tex].........by equation 1

[tex]c3=c1-355[/tex]........equation 2

Now we know,

[tex]c1+c2+c3=1200[/tex]

[tex]c1+(c1-155)+(c1-355)=1200[/tex] .....by equations 1 and 2

[tex]3c1-510=1200[/tex]

[tex]3c1=1200+510\\3c1=170\\c1=570[/tex]

Hence, The winner received 570 votes.

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There are 120 6-digit numbers that can be formed

The digits are given as:

0,1,3,5,7 and 9

Since the number must be divisible by 10.

Then the number must end in 0

The other 5 digits can take any of the 0,1,3,5,7.

So, the number of combination is:

Count = 5! * 1

Expand

Count = 5 * 4 * 3 *2 * 1 * 1

Evaluate

Count = 120

Hence, there are 120 6-digit numbers that can be formed

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Answer: 2.5

Step-by-step explanation:

[tex]1 \times 3=3\\\\3-\frac{1}{2}=2.5[/tex]

Zeros of this function

ZEros of reciprocal function

The equation

Answer:

1.21x

Step-by-step explanation:

we can write 100% as 1

then 10% is 0.1

then 1.1x = is first

1.1*1.1x = 1.21x or 121% of x

The savings of $x grows 10% each year after 2 year it will become  1.21x .

Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.

The formula of Compound interest :

[tex]A= P(1+\frac{r}{100} )^{t}[/tex]

where,

A = Final amount

P = initial Principal

t = Time in years

r = rate of interest per annum  

According to the question

Principal = $x

Rate of interest per annum  =  10%

Time in years = t

By using formula of Compound interest :

[tex]A= P(1+\frac{r}{100} )^{t}[/tex]  

Now ,

Substituting the values in the formula

[tex]A= x(1+\frac{10}{100} )^{2}[/tex]

[tex]A= x(1.1} )^{2}[/tex]  

[tex]A= 1.21x[/tex]

Hence, the savings of $x grows 10% each year after 2 year it will become   1.21x .

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Answer:

I would assume you're referring to this test? if so the answer is

a, d and e

The expression that describes the slope properly are:

A. m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

D. m = rise/run

E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

We have,

The slope of a line is a measure of its steepness or inclination.

It represents the rate of change between two points on the line, specifically the ratio of the vertical change (rise) to the horizontal change (run).

Mathematically, the slope (m) is calculated as:

m = change in vertical distance/change in horizontal distance

or

m = rise/run

or

m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Thus,

The expression that describes the slope properly are:

A. m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

D. m = rise/run

E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

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Answer:

-x+3y=9

i think this is answer

The value of x in the equation [tex](x-5)^{2} +3(x-5)+9=0[/tex]is x=(7+3[tex]\sqrt{3}i[/tex])/2,

(7-3[tex]\sqrt{3}i[/tex])/2.

Given equation [tex](x-5)^{2} +3(x-5)+9=0[/tex] .

We have to find the solution of the equation.

Equation  is solved to find the value of variables. The number of values of the variable depends on the highest power of variables.

let (x-5)=u-------------------1

equation becomes [tex]u^{2} +3u+9=0[/tex]

solution of a quadratic formula

x=-b±[tex]\sqrt{b^{2} -4ac}[/tex]/2a

on comparing with general form a=1,b=3, c=9

u=-3±[tex]\sqrt{3^{2} -4*1*9} /2[/tex]

=-3±[tex]\sqrt{9-36}/2[/tex]

=-3±[tex]3\sqrt{-27}/2[/tex]

=-3±[tex]3\sqrt{3} i/2[/tex]

[tex]u_{1} =-3[/tex]+3[tex]\sqrt{3}/2[/tex] , [tex]u_{2}[/tex]=-3-3[tex]\sqrt{3}/2[/tex]

put the values of [tex]u_{1}[/tex] in equation 1

x-5=[tex]u_{1}[/tex]

x-5=-3+[tex]3\sqrt{3} /2[/tex]

x=-3+3[tex]\sqrt{3}i/2+5[/tex]

x=7+3[tex]\sqrt{3} i/2[/tex]

put the values of [tex]u_{2}[/tex] in  equation2

x-5=[tex]u_{2}[/tex]

x-5=-3-3[tex]\sqrt{3} /2[/tex]

x=7-3[tex]\sqrt{3}/2[/tex]

Hence the values of x are 7+3[tex]\sqrt{3}i/2[/tex], 7-3[tex]\sqrt{3}i/2[/tex].

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The values of the variables are x = -2, y = 6 and z = -3

The system is given as:

4x + 2y - 2z = 10 (A)

2x + 8y + 4z = 32 (B)

30x + 12y - 4z = 24 (C)

The easiest variable to eliminate is z.

Combine A and B

2[4x + 2y - 2z = 10]

⇒

8x + 4y - 4z = 20

+ 2x + 8y + 4z = 32

⇒ 10x + 12y = 52

Combine B and C

2x + 8y + 4z = 32

30x + 12y - 4z = 24

⇒ 32x + 20y = 56

Divide through by 4

8x + 5y = 14

So, we have:

10x + 12y = 52

and

8x + 5y = 14

Multiply 10x + 12y = 52 by 8/10

8/10[10x + 12y = 52]

⇒ 8x + 9.6y = 41.6

Combine 8x + 9.6y = 41.6 and 8x + 5y = 14

8x + 9.6y = 41.6

- [8x + 5y = 14]

⇒ 4.6y = 27.6

Divide

y = 6

Substitute y = 6 in 8x + 5y = 14

8x + 5 * 6 = 14

8x + 30 = 14

Subtract 30

8x = -16

Divide

x = -2

Substitute y = 6 and x = -2 in (A)

4x + 2y - 2z = 10

4(-2) + 2(6) - 2z = 10

-8 + 12- 2z = 10

Evaluate the like terms

-2z = 6

Divide

z = -3

Hence. the values of the variables are x = -2, y = 6 and z = -3

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If the population can be shown to be decreasing in size, then the lambda would be positive while the r would be negative.

When the population is decreasing, the rate would be negative because the population is shrinking. This is why r - which is rate - will be negative.

Lambda on the other hand will be positive to show that the population started from a higher value and is now decreasing.

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Answer:

y= 1/3

Step-by-step explanation:

12(x + 4) + 8 = 9

12(x + 4) + 8 -8 = 9 -8

12(x + 4) = 1

12(x + 4)/12 = 1/12

(x + 4) = 1/12

y = 4(x + 4)

y= 4(1/12)

y= 4/12

y= 1/3

This are also referred to as exponential sequence.  The common ratio if r > 0 is 2

This are also referred to as exponential sequence. Given the following sequence

(7-2x),9,(5x+17)

If they are in geometric progression, hence;

9/7-2x = 5x+17/9

Cross multiply

7-2x(5x+17) = 9(9)

Expand

35x+119-10x²-34x = 81

-10x²+x+119-81=0
10x²-x-38 = 0

Factorize

10x²-20x +19x-38 = 0

10x(x-2)+19(x-2)= 0

x - 2 = 0

x = 2

Hence the common ratio if r > 0 is 2

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Answer:

Hence, 0.0000087 can be expressed as [tex]$8.71 \times 10^{-6}$[/tex].

Step-by-step explanation:

- Given 0.00000871

- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .

- Then count n and write no. as product with a power of 10 .

Step 1 of 1

Consider 0.00000871,

8.71

Decimal has moved 6 places to right.

The power will be negative as the original no. is less than 1 .

[tex]$$\begin{array}{r}8.71 \times 10^{-6} \\0.0000087=8.71 \times 10^{-6}\end{array}$$[/tex]

Answer:

Step-by-step explanation:

Givens

Area = 59.5 in^2

Base =  7 inches

height = h

Solution

Area = Base * height                 Substitute what you know in the formula

59.5 = 7 * h                                 Divide both sides by 7

59.5/7 = 7h / 7                            

h = 8.5

Answer height = 8.5

Answer:

Answer B is correct

Step-by-step explanation:

The formula to find the area of a rectangle is :

Area = Base × Height

Given that,

Area ⇒ 59.5 in²

Base ⇒ 7 in

Height ⇒?

Let the height of the rectangle be x.

First, let us make an expression to find the value of h.

Area = Base × Height

59.5 = 7 × x

And now let us solve for x.

59.5 = 7h

Divide both sides by 7.

x = 8.5 in

By assuming the standard deviation of population 2.2 the confidence interval is 8.67 toys,8.94 toys.

Given sample size of 1492 children,99% confidence interval , sample mean of 8.8, population standard deviation=2.2.

This type of problems can be solved through z test and in z test we have to first find the z score and then p value from normal distribution table.

First we have to find the value of α which can be calculated as  under:

α=(1-0.99)/2=0.005

p=1-0.005=0.995

corresponding z value will be 2.575 for p=0.995 .

Margin of error=z*x/d

where x is mean and d is standard deviation.

M=2.575*2.2/[tex]\sqrt{1492}[/tex]

=0.14

So the lower value will be x-M

=8.8-0.14

=8.66

=8.67 ( after rounding)

The upper value will be x+M

=8.8+0.14

=8.94

Hence the confidence interval will be 8.67 toys and 8.94 toys.

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