A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

Which one is it??

Answer:

1) 150 kg

2) 97.5 kg

3) 5%

Step-by-step explanation:

Ratios of each metal to total mass of metal can be computed by dividing its corresponding value by the sum of all the values in the ratio

The ratio of zinc to metal = 6/(13 + 6 + 1) = 6/20 = 3/10

Let the total mass of the metal be X

Then mass of zinc = (3/5)X = 90 kg (given)

1) Multiplying both sides by 5/3 gives X = 5/3 x 90 = 150 kg which is the total mass of metal

2) Ratio of copper to metal mass = 13/20
Mass of copper = 13/20 x 150 = 97.5 kg

3) Mass of lead as a ratio of metal = 1/20 = 0.05

As percentage, multiply by 100 to get 0.05 x 100 = 5%

Therefore, the probability of the event happening is 1/3 or approximately 0.333 (in decimal form).

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here,

The probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes. In this case, there are 15 possible outcomes and 5 favorable outcomes, so the probability can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 5 / 15

Simplifying the fraction by dividing both numerator and denominator by 5, we get:

Probability = 1 / 3

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EXPLANATION

We need to use the Compounding Interest Equation as shown as follows:

Where P=Principal = 14,000 r=rate in decimal form = 3.4/100 = 0.034 n=number of times interest is compounded per unit 't' = 1 t= time = 2029 - 2011 = 18 years

Plugging in the terms into the expression:

Adding numbers:

Computing the power:

Multiplying numbers:

In conclusion, in the year 2029 the value will be $14,476

Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

The  largest amount of money they can borrow is $$276.268.65

The main formula used in this problem is the Present Value of an annuity Formula:

P = R[1-(1+i)⁻ⁿ]/i

Where;

The maximal monthly payment that Bethany and Samuel can afford is $1,500.

The best interest rate is %5.1 annually, and they want to sign a 30-year mortgage.

This implies that

R=1,500

t=30

r=%5.1 = 5.1 /100 = 0.051

m=12, because they make the payments monthly

i=r/m=0.051/12=0.00425

n=mt = 12*30=360

That is,

i) they will make 360 monthly payments,

ii) the largest amount of money they can borrow can be found using the formula:

P = R[1-(1+i)⁻ⁿ]/i

Substituting the known values:

P = 1500[1-(1+0.00425)⁻³⁶⁰]/0.00425

Therefore, $276.268.65 is the largest possible principal for the situation

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Answer:

\(x = 12m\)

Step-by-step explanation:

\(area = length \: \times breath\)

\(length = \frac{11}{3} m\)

\(breath \: = x \\ since \: area = 44 \\ 44 = \frac{11}{3} \times x \\ cross \: multiply \\ 44 \times 3 = 11x \\ 132 = 11x \\ divide \: both \: sides \: by \: \\ \frac{132}{11} = \frac{11x}{11} \\ 12m = x\)

The possible values for the discriminant include the following:

A. -1

D. -18

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

Since the graph of this quadratic function has no x-intercepts, we can logically deduce that the zeros, roots, or x-intercepts of this quadratic function must be an imaginary number.

Discriminant, D = b² - 4ac

In conclusion, we can reasonably infer and logically deduce that negative numbers such as -1 and -18 are possible values for the discriminant.

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Complete Question:

The graph of a certain quadratic function has no x-intercepts. Which of the following are possible values for the discriminant? Check all that apply.

A. -1

B. 3

C. 0

D. -18

Answer:

The scale of the drawing is 1 cm to 90 m. This means that every 1 cm on the drawing represents 90 m in real life. The length of the field is 450 m, so the length of the drawing will be 450 m / 90 m = 5 cm.

Therefore, the length of the dam drawing is 5 cm.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Apply the difference of two squares formula:

\(\displaystyle \large{(a-b)(a+b) = a^2-b^2}\)

Therefore:

\(\displaystyle \large{(3-\sqrt{11})(3+\sqrt{11}) = 3^2-(\sqrt{11})^2}\\\displaystyle \large{(3-\sqrt{11})(3+\sqrt{11}) = 9-11}\\\displaystyle \large{(3-\sqrt{11})(3+\sqrt{11}) = -2}\)

Therefore, -2 is the final answer.

__________________________________________________________

Summary

\(\displaystyle \large{(a-b)(a+b)=a^2-b^2}\)

\(\displaystyle \large{(\sqrt{a})^2 = a}\)

\((3 - \sqrt{11} )(3 + \sqrt{11} )\)

Use the identity (a-b)(a+b)=a²-b²

\( {3}^{2} - { \sqrt{11 }^{2} }\)

\(9 - 11\)

\( - 2\)

Thus, Option A is the correct choice!!~

Answer:

12.8

Step-by-step explanation:

Answer:

12.8452325787

Step-by-step explanation:

Answer:

Well to this you would have to simplify the ratio first

75:35:45

That can be

15:7:9

So that means thayt each troop would get 15 enegery bars, 7 drinks and 9 bottles of water

Well if you were to keep repeating that process or just do a proportion you would get 5 total troops.

15:7:9

75:35:45

15*5 is 75

7*5 is 35

9*5=45

So 5 troops

Answer:

1 1/2  hope this helped

Answer:

the answer is 7

Step-by-step explanation:

the answer is 7 no doubt about that moth

Answer:

189.27 in.

Step-by-step explanation:

15 x 10 = 150

10/2= 5 x 5= 25 x 3.14= 78.54/2= 39.27

Answer:

150

Step-by-step explanation:

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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Here we start removing the exponents, so the answer is take the square root of both sides .

Answer: (5 × 8) - (5 × 1)

Step-by-step explanation:

When you use the distributive property, you essentially distribute a number to terms it is being multiplied by in order to make the calculation process easier.

When you use the distributive property, you distribute the number outside a multiplication statement to the numbers inside. In this case, 5 is the number outside, and 8 and 1 are the numbers inside.

When you distribute the number 5 to the eight, you are left with (5 × 8). However, you must still include 1, the other number in the parentheses, to finish the equation.

With 1, you go through the same process as you did before. You distribute the number 5 to the 1 and are left with (5 × 1). However, in the original equation, you are subtracting the 8 by the 1, so you must account for the subtraction sign.

You essentially subtract the number you get from (5 × 8) by the number you get from (5 × 1). Therefore, your answer is (5 × 8) - (5 × 1).

The basic ratio of minutes of painting to minutes of instruction is 7 : 6

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

Painting = 63 minutes

Instruction = 54 minutes

The ratio can be represented as

Ratio = Painting : Instruction

When the given values are substituted in the above equation, we have the following equation

Painting : Instruction = 63 : 54

Simplify

Painting : Instruction = 21 : 18

Simplify

Painting : Instruction = 7 : 6

This  ratio cannot be simplified

Hence, the solution is 7 : 6

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Answer:  There are multiple sets that produce single triangles:

SET     RESULT

1          Single / Sides: a = 7   b = 16   c = 21.222

2         Single / Sides: a = 9.2   b = 16   c = 22.641

3         Single / Sides: a = 12.4   b = 16   c = 25.852

4         Two Solutions / with side c=31.448 and with side c=6.696

5         Single / Sides: a = 7   b = 16   c = 21.222

6         Single / Sides: a = 9.2   b = 16   c = 22.641

7         Single / Sides: a = 12.4   b = 16   c = 25.852

8         Two Solutions / with side c=31.448 and with side c=6.696

Step-by-step explanation:

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Answer:

Step-by-step explanation:

56. 6x = 132

      x = 22

57. 2/3 = -8x

     -24x = 2

        x = -2/24= -1/12

58. 5/11x = 55

      5x = 605

       x = 121

59. 4/5 = 10/16x

       4/5 = 5/8x

        23 = 25x

        23/25

60. 3 2/3x = 2/9

      11/9x = 2/9

      11x = 2

      x = 2/11

61. 4 4/5x = 1 1/5

      24/5x = 6/5

      24x = 6

     x = 6/24 = 1/4

Answer:

8n+12=36, triplets are 8 years old

Step-by-step explanation:

total age is 36

one of them is 12 years old so -> 36-12 = 24

three triplets so 24/3 = 8

there are three 8 years olds and one 12 year old. n = 3

Answer:

Step-by-step explanation:

3n + 12 = 36

3n = 24

n = 8 (the triplets)

another child: 12 years

Answer: 24

Step-by-step explanation:

The length of the largest square is either 23 or 24.

The question is incomplete. Probably the following is your question.

Rectangle PQRS is divided into eight squares, as shown in the figure below. The side length of each shaded square is 10. What is the length of the largest squares?

A) 18

B) 24

C) 16

D)23

E) 25

Rectangles with equal sides and angles are called Squares.

The side length of each shaded square is 10 which implies that the length QR  is 30.

From the diagram, we can see that the side of the large square is longer than the two side lengths of the shaded squares. This means the side length of the large square must be more than 2×10 = 20.

Thus we can discard options (A) 18 and (C) 16 as answers.

Moreover, we can also see that the smallest square has a length of more than half of the length of the shaded square. That means it must be more than 5 but less than 10.

Thus we can conclude that the length of the largest square is less than 25 but more than 20.

Thus we can discard option (E) 25

Hence, the answer is either (B) 24 or (D)23.

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Check the picture below.

Make sure your calculator is in Degree mode.

\(\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}\)

Hi! I believe your answer is 10.5779069767. I hope this helps you! Have a great day/night. ❤️✨

No actually the answer is 11.27907 but in faction form it is 485/43

97÷8.6

Then your going to turn your decimal in a faction so

86÷10= 43÷5

97÷43/5

the your going to reciprocate the number meaning turn the over so it's going to 5/43 and the division side into the multiplication side

97×5/43= 485/45 or 11.27907

Answer:

x = 1/18

Step-by-step explanation:

2/3x = 12

multiply both sides by 3x

2/3x(3x) = 12(3x)

2 = 36x

x = 1/18

Answer:

8.2cm to m= 0,082 m

Step-by-step explanation:

divide the length value by 100

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment