Solve the following system of equations using the elimination method.
5x + y = 9

–10x + 7y = 18

Answer:

Infinite solutions

Step-by-step explanation:

3x+6 = 3(x+2)

3x+6 = 3x+6

6 = 6

let x be the amount of times she visited the movie theater

[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]

Alyssa needs to make 14 visits to earn a free movie ticket.

This is our y intercept

This is our slope.

So our equation is

Here v is visits

The probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Total number of marbles = 3+4+2+1 = 10

P(Yellow) = 1/10

P(Blue) = 4/9

Probability of extracting a Yellow marble followed by a Blue marble:

= (1/10)(4/9)

= 4/90

=  2/45

Thus, the probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1

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Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

( 3 )

the given figure resembles a rectangle !

now ,

[tex]Area \: of \: rectangle = length \times breadth \\ \\ given \: - \: length = 12 \: ft \\ \therefore \:breadth = x \: ft \\ \\ Area = 108 \: ft {}^{2} \\ \\ \implies \: length \times breadth = 108 \: ft {}^{2} \\ \\ \implies \: x \times 12 = 108 \\ \\ \implies \: x = \cancel\frac{108}{12} \\ \\ \bold\red{\implies \: x = 9 \: ft}[/tex]

_____________________________

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( 4 )

the given figure resembles a parallelogram!

[tex]Area \: of \: parallelogram = height \times base \\ \\ \implies \: height = x \: cm\\ \\ \implies \: base = 16 \: cm \\ \\ \: Area \: = 96 \: cm {}^{2} \\ \\ \implies \: x \times 16 = 96 \\ \\ \implies \: x = \cancel\frac{96}{16} \\ \\ \bold\red{\implies \: x = 6 \: cm}[/tex]

hope helpful :D

[tex]\huge \underbrace \mathfrak \red{Answer}[/tex]

To find :-

To get the value of 'di in figure 3 and 4.

Figure 3

Solution :-

Area of rectangle = length × width

area = 108 ft², length = 12 ft, width = x

[tex]108 = 12 \times x \\ \frac{108}{12} = x \\ 9 = x[/tex]

[tex] \\ [/tex]

Figure 4

Solution :-

Area of parallelogram = base × height

Area = 96 cm², base = 16 cm, height = x

[tex]96 = 16 \times x \\ \frac{96}{16} = x \\ 6 = x[/tex]

The system of inequalities represents the given constraints will be x + y < 20 and 15x + 25y > 375.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A nursing student works at a doctor's office for $15 per hour and tutors other students for $25 per hour.

Let x be the number of hours for the doctor's office and y be the number of hours for the tutor.

The student cannot work more than 20 hours each week.

      x + y < 20 ...1

15x + 25y > 375 ...2

The system of inequalities represents the given constraints will be x + y < 20 and 15x + 25y > 375.

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Answer:

Step-by-step explanation:

A driver spent 45minutes to cover a distance of 120km

Convert minutes to hour

Use the distance equation

Find the speed

Substitute the distance and time value and find the value of speed

[tex]\boxed{\sf 186,000}\boxed[/tex]

Answer:

186,000

Step-by-step explanation:

1. Multiply 10 to the 5th power:

[tex]10^{5}[/tex] = 100,000

2. Multiply:

1.86 × 100,000 = 186,000

hope this helps :)

Answer:

logarithmic

Step-by-step explanation:

The perimeter of a triangle that has the side lengths is 6 + 10√3 cm

The side lengths are given as:

6 cm, 7√3 cm and √27 cm

The perimeter is the sum of the side lengths.

So, we have:

P = 6 + 7√3 + √27

Express 27 as 9 * 3

P = 6 + 7√3 + √(9 * 3)

Take the square root of 9

P = 6 + 7√3 + 3√3

Evaluate the sum

P = 6 + 10√3

Hence, the perimeter of a triangle that has the side lengths is 6 + 10√3 cm

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Answer:

Probability of getting a green ball is more than that of getting a white ball.

Step-by-step explanation:

There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.

Therefore, P(a green ball) = 5/8

In the same way,P(a white ball) = 3/8

Thus, clearly the probability of getting a green ball is more than that of getting a white ball.

[tex]\Large\texttt{Answer\::}[/tex]

Please consult the "Calculations" section of this ans .

[tex]\Large\texttt{Calculations\::}[/tex]

The information we're given is below :

As per given information , we can do the following :

Point - slope form looks like so :

y-y₁=m(x-x₁)

y-6=-1/3(x-3)

y-6=-1/3x+1

y=-1/3x+1+7

y=-1/3x+6

↑ [tex]\small\textsc{EQUATION OF THE LINE}[/tex]

[tex]\small\textit{hope\:helpful~}[/tex]

The sum of n terms is 500(1.1ⁿ - 1) and the sum of the 6th terms is 385.78

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have sequence:

50 + $50(1.1) + 50(1.1)^2 + …

The common ration r = 1.1

First term = 50

The sum of n terms:

[tex]\rm Sum = \dfrac{50(1.1^n-1)}{1.1-1}\\\\\rm Sum = \dfrac{50(1.1^n-1)}{0.1}\\\\\\\rm Sum = 500(1.1^n-1)[/tex]

If n = 6 terms

Sum = 385.78

Thus, the sum of n terms is 500(1.1ⁿ - 1) and the sum of the 6th terms is 385.78

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Answer:

3%

Step-by-step explanation:

Easy!

88 - 85 which is equivalent to 3.

Make the 3 a percentage

A = 3%

Answer:

B. 49x^10

Step-by-step explanation:

(7x^3)^2 * (x^8)^1/2

multiply the exponents

49x^6 * x^4

add the exponents

49x^10

Answer:

see below

Step-by-step explanation:

will be of the form xxxx3.x    '3' will be just to the left of the decimal point

Answer:

The answer is c

scince I am not student so I don't use book n pen sorry

Answer:

340 people did the survey in total.

What is Algebra?

Algebra is a branch of mathematics that deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they do not have predefined values.

These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to determine their values.

Given:

People who like the color purple = 187

Moreover, 45% of people prefer the color red.

Purple color enthusiasts = 100 - 45 = 55%

Let the total number of people polled be x.

So, 55% of x = 187

55/100x = 187

x= 18700/ 55

x= 340

Therefore, the answer is 340.

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Answer:

x=-6

Step-by-step explanation:

Let x be the number

A) 12x-12=-84

B) 12x=-72

x=-6

Answer:

x ≥ 6.

Step-by-step explanation:

Given : Kathy swims at least 6 laps every day.

To find: Write an inequality to show how long Kathy swims each day.

Solution : We have given that Kathy swims at least 6 laps every day.

We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.

Then we use greater than or equal to sign  ( for at least)

Since x ≥ 6.

Therefore, x ≥ 6.

Answer:

$55

Step-by-step explanation:

Given:

A pair of shoes is $50, plus 10% tax.

To Find:

What is the total amount you will pay?

Solve:

Tax = Increase - Add on

Thus,

$50 × 10% = 5

$50 + 5 = $55

Hence, the total amount you will pay is $55.

Kavinsky

Answer: 12? im pretty sure

Step-by-step explanation: 1/4 of a unit so 4 for 1 unit, 4 x 3 is 12 units for 3

Answer:

9.1

Step-by-step explanation:

To calculate the total interest payable, we use the formula

I=P0rt,

and substituting our values yields

I=$2,400×0.08×1812=$288.

Therefore the total amount he receives at loan drawdown is $2,400−$288=$2,112. To calculate the effective interest rate, we use to formula

A=P0(1+ret).

In this instance we have A=$2,400,P0=$2,112 (redefined from the value above) and t=1.5. We substitute into the formula to get

$2,400=$2,112(1+1.5re).

Solve for re.

24002112=1+1.5re

24002112−1=1.5re

24002112−11.5=re

This gives re=0.0909⋯=9.0909…%,  which is 9.1%

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

extended Pythagoras :

c² = a² + b² - 2×a×b×cos(C)

and : the sum of all angles in a triangle is always 180°.

1.

b² = 42.1² + 37² - 2×42.1×37×cos(13) =

= 105.8575002...

b = 10.28870741...

b/sin(13) = 37/sin(C)

sin(C) = 37 × sin(13)/b = 0.808963525...

C = 53.99478824...° ≈ 54°

A = 180 - 13 - 54 ≈ 113°

2.

c² = 18² + 13² - 2×18×13×cos(115) = 690.7853465...

c = 26.28279564...

c/sin(115) = 18/sin(A)

sin(A) = 18 × sin(115)/c = 0.62069273...

A = 38.36673893...°

B = 180 - 115 - A = 26.63326107...°

3.

the length of b is missing.

this cannot be solved without the missing information

Answer:

a. y is quartered.

Step-by-step explanation:

y=1/x^2

when x is doubled, the equation becomes:

y=1/(2x)^2=1/(4x^2)

Answer:

If we double x, then the new value of x becomes 2x. So we can find the effect on y by substituting 2x for x in the given function.

y = 1/x^2

When x is replaced by 2x, we get:

y' = 1/(2x)^2

= 1/4x^2

Therefore, y' = (1/4)y

So, if x is doubled, then y is quartered (option a is the correct answer)

Answer:

[tex]8\sqrt[3]{-8x^3y^6z^{13}}[/tex]

Step-by-step explanation:

[tex]8\sqrt[3]{-8x^3y^6z^{13}}\\\\=8\sqrt[3]{(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z}\\\\=8\left[(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z \right]^{\tfrac 13}\\\\=-8\cdot 2 \cdot x \cdot y^2 \cdot z^4 \cdot z^{\tfrac 13}\\\\=-16xy^2 z^4 \sqrt[3]z[/tex]

Answer:

Step-by-step explanation:

1/5 = 0.2

This is what I came up with, hopefully this helps!

Answer:

The constant of proportionality is 5/3

Step-by-step explanation:

3 * k = 5

k = 5/3

Check

9 * k = 15

9 * 5/3 = 15

3*5 = 15

15 =15

The constant of proportionality is 5/3

The ratio for both Harry and Sidnee is the same, which is 5/3.

So, the constant of proportionality (x) is 5/3.

To find the constant of proportionality between the number of granola bars and the cost, we can use the formula for direct proportionality:

Constant of Proportionality (k) = Cost / Number of Granola Bars

For Harry:

Number of granola bars = 3

Cost = $5

Constant of Proportionality (k) for Harry = 5 / 3

For Sidnee:

Number of granola bars = 9

Cost = $15

Constant of Proportionality (k) for Sidnee = 15 / 9

Since both Harry and Sidnee's values for the constant of proportionality are the same (both simplify to 5/3), we can conclude that the constant of proportionality is 5/3, which is approximately 1.67.

This means that for every granola bar purchased, the cost increases by $5/3 or about $1.67.

So, the constant of proportionality (x) is 5/3.

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