pls help ty !
question is in the pic

The algebraic solutions to the system of equations are given as follows:

\((3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)\)

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

Replacing the second equation in the first:

x² + (2x - 2)² = 25

x² + 4x² - 8x + 4 = 25

5x² - 8x - 21 = 0.

Which is a quadratic equation with coefficients a = 5, b = -8, c = -21, then:

\(\Delta = (-8)^2 - 4(5)(-21) = 484\)

\(x_1 = \frac{-(-8) + \sqrt{484}}{2(5)} = 3\)

\(x_2 = \frac{-(-8) - \sqrt{484}}{2(5)} = -\frac{7}{5}\)

Then, the solutions for y are:

Thus, the solutions are:

\((3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)\)

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Ruby and Emma can assemble one gift basket in 0.1818 minutes, together. They will finish the 54th basket at  7:27 PM.

To solve the problem, we first need to find how many gift baskets Ruby and Emma can assemble in one minute.

Ruby can assemble 2/22 = 1/11 gift basket in one minute.

Emma can assemble 4/44 = 1/11 gift basket in one minute.

Together, they can assemble 1/11 + 1/11 = 2/11 = 0.1818 (rounded to four decimal places) gift baskets in one minute.

To assemble the 54th gift basket, they need to assemble 53 gift baskets before that.

53 gift baskets / 0.1818 gift baskets per minute = 291.8181 minutes

Since they start at 1:00 p.m. and Emma starts 15 minutes later, they will finish 291.8181 minutes after 1:15 p.m., which is approximately 7:27 p.m.

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The area shaded below in circle S can be expressed as (18/125)π - (171/250)π².

To find the area shaded below in circle S, we need to calculate the area of the sector TSU and subtract the area of the triangle TSU.

Given information:

Length of TU = (6/5)π

m∠TSU = 72°

To find the area of the sector TSU, we need to find the central angle of the sector. Since the measure of angle TSU is 72°, the central angle will be twice that:

Central angle = 2 * 72° = 144°

The formula for the area of a sector is A = (θ/360°) * πr², where θ is the central angle and r is the radius of the circle.

Since the length of TU is given as (6/5)π, we can find the radius of the circle using the formula for the circumference of a circle:

C = 2πr

Given that the length of TU is (6/5)π, which represents half the circumference of the circle, we can set up the equation:

(6/5)π = 2πr

Simplifying, we find:

r = (6/5) * 1/2 = 3/5

Now, we can calculate the area of the sector TSU:

A_sector = (144°/360°) * π * (3/5)²

A_sector = (2/5) * π * (9/25)

A_sector = (18/125)π

To find the area of the triangle TSU, we use the formula A_triangle = (1/2) * base * height. Here, the base is TU and the height can be found using the sine of the angle TSU:

sin(72°) = height / TU

Rearranging the formula, we have:

height = sin(72°) * TU

Using a calculator, we find:

height ≈ 0.951 * (6/5)π

height ≈ (57/50)π

Now, we can calculate the area of the triangle:

A_triangle = (1/2) * TU * height

A_triangle = (1/2) * (6/5)π * (57/50)π

A_triangle = (171/250)π²

Finally, we can find the shaded area by subtracting the area of the triangle from the area of the sector:

Shaded area = A_sector - A_triangle

Shaded area = (18/125)π - (171/250)π²

Therefore, the area shaded below in circle S can be expressed as (18/125)π - (171/250)π².

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Answer:

3.5

Step-by-step explanation:

Answer:

$840

Step-by-step explanation:

To do this, we can use our formula for solving percents. \(\frac{Part}{Whole}\) = \(\frac{Percent}{100}\)

The part here is $714 because this is only 85% of the original price which is the whole. Our whole in this problem will be x. As for the percent, we will write 85.

We now have \(\frac{714}{x}\) = \(\frac{85}{100}\)

To solve this, we use the rules of a proportion. 714 * 100 = 71,400 and then we will divide that by 85 to find x. x = 840

So, the original price was $840.

Answer:

Step-by-step explanation:

714  is 85%

the full price P is 100%

Using the ratio method

714 /85   =  P/100

TO find P cross multiply

85P = 714*100

85P = 71400

p = 71400/85  = $840

Ans yesterday's price = $840

or

85% of P = 714

.85*P =714

p = 714/.85

p = $840

According to the given statement The eighth term in the arithmetic sequence 2/3, 1, 4/3 is 3/1.

To find the eighth term in an arithmetic sequence, we can use the formula:

an = a1 + (n - 1)d

Where:

an represents the nth term,

a1 represents the first term,

n represents the term number,

d represents the common difference.

In this case, the given arithmetic sequence is:

2/3, 1, 4/3, ...

We can observe that the common difference (d) between consecutive terms is 1/3. Therefore, we have:

a1 = 2/3 (first term)

d = 1/3 (common difference)

n = 8 (eighth term)

Now we can substitute these values into the formula to find the eighth term (a8):

a8 = (2/3) + (8 - 1)(1/3)

Simplifying the expression:

a8 = (2/3) + 7(1/3)

a8 = (2/3) + 7/3

Combining the fractions:

a8 = (2 + 7)/3

a8 = 9/3

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:

a8 = 3/1

Therefore, the eighth term in the arithmetic sequence 2/3, 1, 4/3 is 3/1.

In conclusion, the eighth term is 3/1 or simply 3.

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The complete question is-

What is the eighth term in the arithmetic sequence 2/3, 1, 4/3, ? express your answer in simplest form.

Answer:

It's the first answer. 40

Step-by-step explanation:

divide both sides by 0.5

Answer:

1. x=40

Step-by-step explanation:

x=20÷0.5

x=40

Answer: True

Step-by-step explanation:

Answer:

8 km

Step-by-step explanation: giving that

distance=10km

time=75 minutes =75/60 hours

                                15/12=5/4 hours

speed=disance=10km

             time     = 5/4hours

     =40/5km/hours

    =8km/hours

The amount Sandra will have in the account after 12 years is b. $140,181.30 if she deposits $3,000 at the end of each semiannual period

We can determine the amount she will have in the account after 12 years by using the formula for future value as follows;

FV = P(1+i)×{ (1+i)^n - 1 } / i

Here;

FV = future value of the money after n periods

P = deposit per period

i = interest rate per period

n = the number of periods

Substituting the values in this equation to find the amount after 12 years as follows;

FV = 3000(1+0.05)×( (1+0.05)^24 - 1 ) / 0.05

FV = 3000(1+0.05)×( (1+0.05)^23 ) / 0.05

FV = 140,181.296 = 140,181.30

Hence the amount after 12 years is calculated to be $140,181.30

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Answer:

1.33

Step-by-step explanation:

The value of y when the value of x is 1, can be found to be 60 miles.

As depicted in the graph, an augmented consumption of gallons of fuel by the hybrid vehicle concomitantly correlates to an increase in mileage capacity.

Concretely, according to our research data, we confirm that for every gallon expended, there is a mileage expansion rate of 60 units. Hence, when the quantity x equals 1, it implies usage of one gallon only.

Accordingly, empirical evidence suggests that traveling precisely sixty miles remains possible on utilization of one gallon which thus confirms the efficiency of using hybrid cars as a viable option.

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Answer:

Depends on the range of x

Step-by-step explanation:

Does that make sense to you

Answer:

Step-by-step explanation

Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles

the sum of the interior angles in a triangle is 180°

so

180 - 50 = 130°

130 : 5 = 26° (unit)

26 * 2 = 52°

26 * 3 = 78°

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check

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The answer is good

Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

Answer:

x = 5

y = 3

Step-by-step explanation:

x + 4y = 17

2x + 5y = 25

We multiply the first equation by -2

-2x - 8y = -34

2x + 5y = 25

-3y = -9

y = 3

Now we put 3 in for y and solve for x

x + 4(3) = 17

x + 12 = 17

x = 5

Let's Check the answer

5 + 4(3) = 17

5 + 12 = 17

17 = 17

So, x = 17 and y = 3 is the correct answer.

Answer:

answer is B)y=3x+2

Step-by-step explanation:

here ya go, have a nice day

btw if you can give me brainliest it will help a lot, thanks

Answer: John walks a total of 360 yards from school.

Step-by-step explanation:

Let's represent the total distance John walks from school as "x".

According to the problem, John has already walked 15% of the way, which can be written as:

0.15x

We also know that he has walked 54 yards so far, which means:

0.15x = 54

To find the total distance John walks from school, we can solve for "x" by dividing both sides of the equation by 0.15:

x = 54 ÷ 0.15

x = 360

Therefore, John walks a total of 360 yards from school.

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Answer:

18

Step-by-step explanation:

Intersecting Secants Theorem:

6(x + 6) = 8(8 + 10)

6x + 36 = 8(18)

6x + 36 = 144

6x = 144 - 36

6x = 108

x = 18

Answer: B would be 5.66

Step-by-step explanation:

The factored expression of the expression 4a^3b^5 - 18a^2b^3 + 8a^3b^3 is 2a^2b^3(2ab^3 - 9 + 4a)

The expression is give as:

4a^3b^5 - 18a^2b^3 + 8a^3b^3

Factor out 2

2(2a^3b^5 - 9a^2b^3 + 4a^3b^3)

Factor out a^2b^3

2a^2b^3(2ab^3 - 9 + 4a)

Hence, the factored expression of the expression 4a^3b^5 - 18a^2b^3 + 8a^3b^3 is 2a^2b^3(2ab^3 - 9 + 4a)

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Answer:

(D) 1/9

Step-by-step explanation:

9x-2=-3

9x=1

x=1/9

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Answer:

Step-by-step explanation:

X = 64.

x^(1/2) = 8

\(\sqrt{x} = 8^{2}\)

Therefore, x = 64

Answer:

D. 64

Step-by-step explanation:

x^1/2 = 8

√x = 8

√64 = 8

x = 64

Answer:

A) x = 2

y = -28

B) x = 30

y = -4

C) x = -15

y = 11

D) x = 2

y = 46

Step-by-step explanation:

Hope this helps :D I'm in class so I can't explain rn I hope you understand the concept.

have a nice day

The missing length of the triangle using Pythagoras theorem is; x = 3

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The right angle triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

The formula to find the sides is;

hypotenuse² = opposite + adjacent²

We are given;

Hypotenuse = 5

Opposite = x

adjacent = 4

Thus;

5² = x² + 4²

x² = 5² - 4²

x² = 25 - 16

x = √9

x = 3

We conclude that it is the missing length of the triangle

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Answer:

first number: 9

second number: 6

Step-by-step explanation:

15 = x + (x - 3)

2x = 15 - 3

2x = 12

x = 6

The data-set represented by the box plot is given as follows:

51, 56, 62, 63, 63, 64, 67, 68, 79, 80, 80, 89, 91, 95, 99.

The measures shown by the box plot are given as follows:

Considering the minimum and the maximum value, only the first two options can be correct.

Each of the data-sets has 15 elements, hence:

Meaning that the first option is the correct option.

The problem is given by the image presented at the end of the answer.

I don't think that the box plots are the same but the procedure to obtain the data-set is the same,

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