Write an equation for each linear relationship. Describe the graph of the linear
relationship. State the slope and y-intercept.

The weight of small box and large box is 25pounds and 55 pounds respectively.

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . Example of a Simultaneous equation include;

3x+2 = y equation 1

5x +3 = 2y equation 2

Represent the weight of small box by x and the weight of large box by y

x + y = 80 equation 1

70x + 60y = 5050 equation 2

therefore 70( 80-y) + 60y = 5050

5600 -70y +60y = 5050

-10y = 5050-5600

-10y = -550

y = -550/-10

y = 55 pounds

From equation 1

x +55 = 80

x = 80-55

x = 25 pounds

therefore the weight of small box is 25 pounds and the weight of large box is 55 pounds

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The sum of the first 5 terms of the series is 121.

An infinite number of terms with a fixed ratio between them are added to form a geometric series.

The series is a geometric series with the first term (a) equal to 1 and the common ratio (r) equal to 3.

To find the sum of the first 5 terms of the series, we can use the formula:

[tex]\rm S = a(1 - r^n) / (1 - r)[/tex]

where S is the sum of the first n terms of the series. Substituting the values we get:

[tex]\rm S = 1(1 - 3^5) / (1 - 3) \\\\= 1(1 - 243) / (-2)\\\\ = -242 / -2 \\\\= 121[/tex]

Therefore, the sum of the first 5 terms of the series is 121.

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Answer: 10/20, 8/20, 4/20, 6/20

Step-by-step explanation:

Black: 10/20

Red: 8/20

White: 4/20

Blue: 6/20

There are 20 marbles in total the amount of colored marbles is the numerator and the denominator is the total.

Have a lovely day!!

Answer:

1/4(2^3 + 4^2) = 6

Step-by-step explanation:

I

Answer:

9/4

Step-by-step explanation:

3/2 x 3/2= 9/4

Answer:

If the entire mass of the Milky Way was due to gas and stars, how would you expect the rotational speed of a star near the edge of the galaxy to compare to the rotational speed of a star near the center?

Step-by-step explanation:

The correct classification(s) of the fractional number 15/3 is: whole, integer, rational.

What is fractional number?

A fractional number, also known as a fraction, is a number that represents a part of a whole. It consists of two parts: a numerator and a denominator, separated by a slash (/). The numerator is the number above the line, and the denominator is the number below the line.

The number 15/3 is a fraction. When we simplify this fraction, we divide 15 by 3 to get:

15/3 = 5

Therefore, the number 15/3 is equivalent to the whole number 5.

An integer is a number that can be expressed without fractions or decimals, and can be positive, negative, or zero. The number 5 is also an integer, because it is a positive whole number.

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In this case, 15/3 can be expressed as the ratio of two integers (15 and 3), so it is a rational number.

Therefore, the correct classification(s) of the number 15/3 is:

whole, integer, rational.

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Answer:

[tex]P(x)=3x^4-11x^3+71x^2-275x-100[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial with real coefficients, and 5i is a root of P(x)=0, then its complex conjugate -5i is also a root of P(x)=0.

So the zeros of the function are: 5i, -5i, 4, and -1/3.

The zeros of a function P(x) are the x-values of the function such that the P(x)=0.  According to the Factor Theorem, if P(x) is a polynomial, and P(a)=0, then (x - a)  is a factor of P(x).

Therefore, the factors of the function are:

[tex]x=5i \implies (x-5i)[/tex]

[tex]x=-5i \implies (x+5i)[/tex]

[tex]x=4 \implies (x-4)[/tex]

[tex]x=-\dfrac{1}{3} \implies (3x+1)[/tex]

So the polynomial in factored form is:

[tex]P(x)=a(x-5i)(x+5i)(x-4)(3x+1)[/tex]

As we have not been given a specific leading coefficient, let us assume it is one.

[tex]P(x)=(x-5i)(x+5i)(x-4)(3x+1)[/tex]

To write the polynomial in standard form, expand and simplify.

[tex]\begin{aligned}P(x)&=(x-5i)(x+5i)(x-4)(3x+1)\\&=(x^2+5ix-5ix-25i^2)(3x^2+x-12x-4)\\&=(x^2-25(-1))(3x^2-11x-4)\\&=(x^2+25)(3x^2-11x-4)\\&=3x^4-11x^3-4x^2+75x^2-275x-100\\&=3x^4-11x^3+71x^2-275x-100\end{aligned}[/tex]

Answer: The tank starts with 10 gallons of gas

Step-by-step explanation:

so the first thing that you are going to do is divide and multiply  what might you be dividing great question, you will divide 10 in to 9 then multiplying 160 into 15.

If you want to know how i got this answer please ask me in the commets below.

Answer: one inch measured the the map represented 100 feet on the ground

Step-by-step explanation:

The range of possible values for x is approximately -14.7 to 14.7. However, since x represents a length, it cannot be negative. Thus, the range of possible values for x is approximately 0 to 14.7.

The range refers to the difference between the maximum and minimum values in a dataset.
The range is easy to calculate and provides a quick estimate of how much variation there is in the dataset.

We have:

∠ABC + ∠ABD + ∠BDA + ∠BAC = 360°

120° + 115° + ∠BDA + ∠BAC = 360° (substituting given values)

∠BDA + ∠BAC = 125°

Now, we can use the law of cosines to relate the sides and angles in each triangle:

AC² = AB² + BC² - 2ABBCcos(∠ABC)

(4x-10)² = AB² + 24² - 2AB24cos(120°)

(4x-10)² = AB² + 576 + 24AB

AD² = AB² + BD² - 2ABBDcos(∠ABD)

40² = AB² + 24² - 2AB24cos(115°)

AB² - 48AB + 496 = 0

Using the quadratic formula to solve for AB, we get:

AB = (48 ± √(48² - 4×496))/2

AB = 24 ± 2√211

Since AB = 24 + 2x, we have:

24 + 2x = 24 + 2√211 or 24 - 2√211

By Solving for x in each case, we get:

x = √211 + 0.5 ≈ 14.7 or x = -√211 + 0.5 ≈ -14.7

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You will be able to pull out approximately $1,983.45 each month from your retirement savings if you want to be able to take withdrawals for 15 years.

Interest rate is the percentage of the principal amount (a loan or an investment) that is charged or paid over a certain period of time, usually a year. It is used to calculate the amount of interest that accrues on the principal amount.

To calculate the monthly withdrawal amount that you can make from your retirement savings, we can use the present value of an annuity formula. This formula relates the present value of a series of equal periodic payments to the interest rate, the number of periods, and the payment amount.

Let's assume that you want to make monthly withdrawals for 15 years, which corresponds to 180 months. Also, let's assume that you want to withdraw the same amount each month. We can call this amount "P".

Using the present value of an annuity formula, we can solve for P:

P = PV * (r / (1 - [tex](1 + r)^(-n)[/tex]))

where PV is the present value of your retirement savings,

           r is the monthly interest rate (which is 4% / 12 = 0.00333), and

           n is the number of months over which you want to make withdrawals (which is 180 in this case).

Substituting the given values, we get:

P = 300,000 * (0.00333 / (1 - (1 + [tex]0.00333)^(-180)[/tex]))

  ≈ $1,983.45

Therefore, you will be able to pull out approximately $1,983.45 each month from your retirement savings if you want to be able to take withdrawals for 15 years. Note that this amount is an estimate and does not take into account any taxes, fees, or other factors that may affect your retirement income.

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Height of this surface if its base is 12 cm 42 tiles are required.=14400

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

Area of region = 100 cm x 144 cm = 14400 cm.sq

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COMPLETE QUESTION-

Tim has used 11 squares tiles to cover a surface. What is the height of this surface if its base is 12 cm?

Answer: $1.46 less

Step-by-step explanation:

Lets find how much each bottle is first for Store B, to do that divide 29.10 divided by 15 and you should get 1.94 meaning each bottle of juice is $1.94. Next, lets find how much each bottle costs in store A. You can take any number from the total cost and divide it by the bottles and you should get the same thing. Lets do the first one 2.40 divided by 5 equals 0.48. If you want to check you can multiply 0.48 by any number of bottles and you should get the total cost. Now we have to find how much less Store A costs, to do so we subtract store B (1.94) and store A (0.48) and you should get $1.46.

Answer:

the clock hands do not form a right angle at 5:00.

Step-by-step explanation:

Answer: The formula needed to find the amount of border needed is the perimeter formula for a rectangle:

Perimeter = 2(length + width)

Step-by-step explanation:

m∠NOP = 90° is the value of angle .

What does a math angle mean?

An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

                                           A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. The Latin word "angulus," which meaning "corner," is the source of the English term "angle". The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.

m∠NOP = 90° is the value of angle .

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The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

[tex]Area = \int\limits^b_a {y} \, dy[/tex]

[tex]Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy[/tex]

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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a. The y-intercept of the line is 4.

b. The gradient of the line is 2.

The gradient of a line is the steepness of the line, which is determined by how much the line rises or falls for each unit of horizontal distance [m = change in y / change in x], while the y-intercept is the point where the line crosses the y-axis.

a. The line cuts the y-axis at 4, therefore, the y-intercept is 4.

b. Gradient of the line = rise/run = 2/1

Gradient = 2.

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To get 10, we can create an expression which sums up the

[tex]\left(3\cdot 4+8\right)\ -\left(7\ +\ 3\right)[/tex] = 10

In mathematics, the sum refers to the result of adding two or more numbers or quantities together. It is a basic arithmetic operation that yields a total or a whole quantity.

Here, we can make a solution of 20 by

3 ×  4 + 8

= 20

We know that 20 - 10 = 10

So another expression must be 10 and it is possible by:

7 + 3

So, we have the expression which has a solution 10

(3 × 4 +8 ) - (7 + 3)

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The weight of each of the boxes are:

Large box = 15.75 kg

Small box = 18.75 kg

Let the weight of each large box be x

Let the weight of each small box be y.

Thus, if  5 large boxes and 3 small boxes have a total weight of 135 kilograms, then we have the equation:

5x + 3y = 135   -------(1)

Thus, if  7 large boxes and 9 small boxes have a total weight of 279 kilograms, then we have the equation:

7x + 9y = 279     ------(2)

Multiply eq 1 by 3 and eq 2 by 1 to get:

15x + 9y = 405   -----(3)

Subtract eq 2 from eq 3 to get:

8x = 126

x = 126/8

x = 15.75 kg

Thus:

5(15.75) + 3y = 135

3y = 135 - 78.75

3y = 56.25

y = 18.75 kg

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The solution to the differential equation dy / dx = 2 · x · y³ · sin x² is equal to - [1 / (2 · y²)] = - cos x² - 3 / 2.

In this problem we find a differential equation with separable variables, that is, an ordinary differential equation whose variables can be separated on each side of the equivalence and solved by integrals. First, write the complete expression:

dy / dx = 2 · x · y³ · sin x²

Second, separate the variables:

dy / y³ = 2 · x · sin x² dx

Third, integrate the equation:

∫ dy / y³ = ∫ sin x² · (2 · x) dx

- [1 / (2 · y²)] = - cos x² + C

Fourth, find the value of the constant of integration:

- 1 / 2 = 1 + C

C = - 3 / 2

Fifth, write the solution to the differential equation:

- [1 / (2 · y²)] = - cos x² - 3 / 2

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Two find the point in the solution set for both these functions equation the two functions (f(x)=g(x)) and solve for x. See full process below.

Explanation:

Two find the point in the solution set for both these functions equation the two functions (f(x)=g(x)) and solve for x.

Therefore:

2x−1=−43x+9

We can now solve for x:

2x−1+43x+1=−43x+9+43x+1

2x+43x−1+1=−43x+43x+9+1

2x+43x−0=0+9+1

2x+43x=10

(33×2)x+43x=10

63x+43x=10

103x=10

310×103x=310×10

3

10×103x=310×10

x=3 is the point which lies in the solution set for both functions.

There are three coefficients present in the expression: 5 for the x³ ;  2 for the x² and 6 is for x.

The integer or constant quantity put before a variable is known as a coefficient.

Thus, there are three coefficients present in the expression: 5 for the x³ ;  2 for the x² and 6 is for x.

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Complete question-

How many coefficients are in the expression 5x³ + 2x²+6x-4?

Answer:

(0,8)

Step-by-step explanation:

The slope intercept formula is set up as y=mx+b, where b is the y-intercept value. In the equation y=3x+8, we can see that 8 is the y-intercept. So we plug 8 for y in a coordinate, and 0 for x. The answer is (0,8)

the volume of the spherical globe with a radius of 9 inches is approximately 3053.63 cubic inches.

What is globe?

A globe is a three-dimensional, spherical representation of the Earth or another celestial body, such as a planet or a moon. It is typically made of a hollow sphere of material, such as paper, plastic, metal, or glass, with a map of the Earth or the celestial body printed or drawn on its surface.

Globes are often used as educational tools to help people visualize and understand the geography, topography, and other features of the Earth or other planets. They can be used in classrooms, museums, or other settings to teach geography, astronomy, or other related subjects.

Globes can also be decorative objects, used to add visual interest to a room or office. They come in a variety of sizes, styles, and designs, ranging from small desktop globes to large, ornate globes mounted on stands.

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume, π is the mathematical constant pi (approximately 3.14), and r is the radius of the sphere.

Using this formula and substituting the given radius of 9 inches, we can calculate the volume of the globe as follows:

V = (4/3)πr³

V = (4/3)π(9³)

V = (4/3)π(729)

V = 3053.63 cubic inches (rounded to two decimal places)

Therefore, the volume of the spherical globe with a radius of 9 inches is approximately 3053.63 cubic inches.

It's important to note that the volume of a sphere is a measure of the amount of space inside the sphere, so the volume represents the maximum amount of material that can fit inside the sphere. This calculation may be useful in a variety of contexts, such as designing packaging or calculating the capacity of a container.

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Answer:

Step-by-step explanation:

(a) To find the N-intercept, we set t to 0 in the equation N = -0.3t + 250:

N = -0.3(0) + 250

N = 250

Therefore, the N-intercept is (0, 250).

(b) The N-intercept is the point on the graph where the tuition is $0 and represents the number of students who would enroll in the basketball camp if it were free. In this case, if the tuition was $0, 250 students would enroll in the basketball camp.

(c) To find the t-intercept, we set N to 0 in the equation N = -0.3t + 250 and solve for t:

0 = -0.3t + 250

0.3t = 250

t = 250/0.3

t ≈ 833.33

Therefore, the t-intercept is approximately (833.33, 0).

(d) The t-intercept is the point on the graph where the number of students who enroll in the basketball camp is zero and represents the tuition that would need to be charged for no students to enroll. In this case, if the tuition was approximately $833.33, no students would enroll in the basketball camp.