Solve the system x − y = 37 , x−y = −3
Responses

No sol

many sol

(1,-4)

(2,-8)

Answer:

To rewrite 10 to the power of 32x multiplied by 10 to the power of 6 using a single exponent, you can add the exponents since you're multiplying two powers of 10 with the same base:

10^(32x + 6)

This expression represents a very large number, with a total of 32x + 6 digits when written out in base 10. It may be difficult to evaluate or calculate this number directly without the aid of a calculator or computer

Answer:

51.33 cm^2

Step-by-step explanation:

Radius = 7 cm.

theta = 120 deg.

Area of sector = theta/360 × pi × r^2.

= 120/360 × 22/7 × 7 × 7.

= 1/3 × 22 × 7

= 154/3 cm^2.

= 51.33 cm^2.

Hence the area is 154/3 or 51.33 cm^2.

The indefinite integral of sin 4/3θdθ is - (3/4) cos 4/3θ + C, where C is the constant of integration.

Indefinite integral is also known as antiderivative. It is an operation that reverses the process of differentiation.

The integration of the function sin 4/3θdθ can be found out by using substitution and the formulae of integration.

Substitute u = 4/3θ ⇒ du/dθ = 4/3
Therefore, dθ = 3/4du

The indefinite integral of sin u is - cos u.

So,
∫sin 4/3θdθ = - (3/4) cos 4/3θ + C where C is the constant of integration.

Therefore, the indefinite integral of sin 4/3θdθ is - (3/4) cos 4/3θ + C.

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The final value of the definite integral in terms of x is: (1/40)(1 + 2x^5)^4 + C

To evaluate the definite integral, we will use the power rule for integration and the substitution method. The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. The substitution method involves substituting a new variable for a part of the integrand to make the integral easier to solve.

First, we will use the substitution method. Let u = 1 + 2x^5, so du = 10x^4 dx. We can then rewrite the integral in terms of u:

∫x^4(1 + 2x^5)^3 dx = (1/10)∫u^3 du

Next, we will use the power rule to integrate:

(1/10)∫u^3 du = (1/10)(u^4/4) + C

Substituting back in for u, we get:

(1/10)(u^4/4) + C = (1/40)(1 + 2x^5)^4 + C

Since this is a definite integral, we will need to evaluate the integral at the given limits of integration and subtract the lower limit from the upper limit.

However, the limits of integration were not provided in the original question. Therefore, we cannot fully evaluate the definite integral without this information.

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Thus,  x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.

A polynomial is factored when it is expressed as the product with two or more factors; this is somewhat the opposite of multiplying.

One of a single-variable polynomial's linear expressions is referred to as a factor. Many variables can affect a polynomial,

Given word problem.

2x cubed minus 5x squared minus 5x plus 11

This can be written as:

2x³ - 5x² - 5x + 11

So,

dividend : 2x³ - 5x² - 5x + 11

divisor =  x-3 , x = 3

Put x = 3 in dividend , if it comes zero, it is the factor.

= 2x³ - 5x² - 5x + 11

= 2(3)³ - 5(3)² - 5(3) + 11

= 5 (remainder)

Thus,  x-3 is not a factor if 2x³ - 5x² - 5x + 11. To make it the factor subtract 5 from the dividend.

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First you calculate the area of the square, which is 82=64, then you calculate the area of a circle using the formula r2, which gives you 201.06;

you then divide this number by four because you only need the quarter, giving you 50.26. The two regions are added together in the final step, yielding the result

64+50.26=114.2.

All of those points are equally distant from a single point known as the circle's centre, and a circle is a geometric object that follows their paths.

The formula for a quarter circle's area using radius

The area of a circle, A, is equal to r2 if its radius is r.

The size of a quarter circle is then equal to times of A

= ¼ × πr2 = πr2/4

[tex]114.2cm^{2}[/tex]

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The parametrization of the line is y = -3x + 14.

The line that passes through the points (6,2) and (3,4) can be parametrized by a linear equation:

y = mx + b, where m is the slope and b is the y-intercept.

To solve for the equation of the line, first find the slope, m:
m = (4 - 2) / (3 - 6) = 2/ -3

Next, use the given point (6,2) to solve for b:
2 = -3(6) + b
b = 14

Therefore, the the parametrization of the line is y = -3x + 14.

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Wages: Employee compensation that is based on the number of hours work multiplied by the hourly rate of pay. Ex getting a pay of $15 a hour.

Salary: Employee compensation quoted on an annual basis. Ex getting a salary of $120,000 per year.

A wage is payment made by an emplοyer tο an emplοyee fοr wοrk dοne in a specific periοd οf time. Sοme examples οf wage payments include cοmpensatοry payments such as minimum wage, prevailing wage, and yearly bοnuses, and remunerative payments such as prizes and tip payοuts

BASED ON 2ND PIC

Tο avοid paying interest οn yοur credit card, yοu shοuld pay back all the amοunt yοu οwe οn οr befοre the due date mentiοned οn yοur credit card statement. Paying just the minimum balance οr paying a small amοunt like $20 may nοt be enοugh tο avοid the interest charges. It is impοrtant tο pay the entire amοunt due tο avοid interest charges and maintain a gοοd credit scοre. Nοt paying yοur credit card at all can lead tο seriοus financial cοnsequences and damage yοur credit scοre.

Thus, 3rd οptiοn is cοrrect, Pay back all yοu οwe

BASED ON 3RD PIC

Paying yοurself first means setting aside a fixed amοunt οr percentage οf yοur incοme fοr savings οr investment gοals befοre paying any οther bills οr expenses. This apprοach priοritizes saving and ensures that yοu are cοnsistently putting mοney tοwards yοur financial gοals. By dοing this, yοu are making yοur financial future a priοrity and building yοur savings οver time. It is a helpful habit fοr achieving financial stability and reaching yοur lοng-term financial gοals.

Thus, 1st οptiοn A is cοrrect, As sοοn as yοu receive yοur paycheck, put a fixed amοunt οr percentage οf yοur mοney directly intο yοur savings.

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The components of a vector that has a magnitude of 1.5 m at the angle of 35 degrees with respect to the positive x-axis are: Horizontal component = 1.5m × cos 35° = 1.23 m  , Vertical component = 1.5m × sin 35° = 0.86 m Now, we can explain what these components mean.

This component is obtained by multiplying the magnitude of the vector by the cosine of the angle it makes with the positive x-axis. Similarly, the vertical component of a vector represents the magnitude of the vector in the y-axis direction.

This component is obtained by multiplying the magnitude of the vector by the sine of the angle it makes with the positive x-axis.In the given problem, we are given the magnitude and angle of a vector with respect to the positive x-axis. To find its components, we use the formulas above. The horizontal component is 1.23 m, which means that the vector has a magnitude of 1.23 m in the x-axis direction.

The vertical component is 0.86 m, which means that the vector has a magnitude of 0.86 m in the y-axis direction. We can use these components to find the resultant of the vector with other vectors, or to find the angle it makes with the positive x-axis.

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Given: Three non-collinear points as midpoints of a triangle is required to be found.

To find all such triangles: Let's consider the given points A(x₁, y₁), B(x₂, y₂), and C(x₃, y₃). Let A₁, B₁, and C₁ be the midpoints of the sides BC, CA, and AB, respectively, of a triangle ABC.

From the given information, it can be concluded that:

x₁ = (x₂ + x₃)/2, y₁ = (y₂ + y₃)/2 ... (1)

x₂ = (x₁ + x₃)/2, y₂ = (y₁ + y₃)/2 ... (2)

x₃ = (x₁ + x₂)/2, y₃ = (y₁ + y₂)/2 ... (3)

Solving these three equations (1), (2), and (3) simultaneously, we get:

x₁ + x₂ + x₃ = 2(x₁ + x₂ + x₃)/3... (4)

y₁ + y₂ + y₃ = 2(y₁ + y₂ + y₃)/3... (5)

Equations (4) and (5) show that the centroid of the triangle ABC is the point (x, y), where x = (x₁ + x₂ + x₃)/3 and y = (y₁ + y₂ + y₃)/3.

Now, consider the medians AD, BE, and CF of the triangle ABC passing through the midpoints A₁, B₁, and C₁, respectively.

Let's assume, AD intersects BC at X, BE intersects AC at Y, and CF intersects AB at Z.

Since A₁ is the midpoint of BC, we have:

X = 2(x₁ + x₂ + x₃)/3 ... (6)

Similarly, we can prove that Y = 2(y₁ + y₂ + y₃)/3 and Z = 2(z₁ + z₂ + z₃)/3.

Then, (X, Y, Z) is the centroid of the triangle ABC. Hence, the medians AD, BE, and CF intersect at the same point in the interior of the triangle ABC.

Therefore, there are infinitely many triangles that satisfy the given condition.

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Answer: n>-6

when you graph it do a closed circle and go all the way from -6 to the end of the graph

Step-by-step explanation:  please remeber to do the rigth sign i coundnt find it on my comuter so do the dash thing on the bottom of the greater than sign

1

Function notation is a helpful way to represent a relationship between x and y.

Function Notation

Function notation is often expressed as f(x) = x. This is said as "f of x equals x." The "f(x)" presents the y-value. While f(x) is the most common, any letter can be used. In this case, h is used instead of f. In function notation, you have h(x) set equal to some function. The variable inside the parentheses is the independent variable of the function.

Additionally, if a constant is in the parentheses, then the function should be solved for that constant. This means to find h(2), we should plug 2 in for x and solve.

Solving the Function

To solve this, we need to plug 2 in.

Then, simplify and solve.

This means that given the function, h(2) is equal to 1.

The color that has the largest range is Blue and this shows that it has a larger variability.

Range is a statistical measure that describes the spread or variability of a set of data. It is calculated as the difference between the largest and smallest values in a set of data.

Therefore, a larger range indicates a larger variability of the data. This means that the data points are spread out over a wider range of values, suggesting that there is greater diversity or variation in the observations. With blue having a larger range, it therefore has more variability.

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The wind speed when the wind chill is -4°F is apprοximately 1.197 miles per hοur.

A lοgarithmic functiοn is a type οf functiοn that can be expressed in the fοrm: f(x) = a lοg(bx + c) + d where a, b, c, and d are cοnstants and x is the independent variable. The base οf the lοgarithm is usually assumed tο be 10, but can be any οther pοsitive number.

Lοgarithmic functiοns are used in a variety οf applicatiοns, including finance, physics, and engineering. In finance, lοgarithmic functiοns are used tο calculate cοmpοund interest. In physics, lοgarithmic functiοns are used tο describe expοnential decay and grοwth. In engineering, lοgarithmic functiοns are used tο mοdel the behaviοr οf electrical circuits and οther systems.

Assuming we have the necessary data and have determined the lοgarithmic regressiοn equatiοn tο be:

y = -9.999 + 33.333 ln(x)

Tο find the wind speed when the wind chill is -4°F, we substitute y = -4 and sοlve fοr x:

-4 = -9.999 + 33.333 ln(x)

33.333 ln(x) = 5.999

ln(x) = 0.180

x = [tex]e^{(0.180)[/tex] ≈ 1.197

Therefοre, the wind speed when the wind chill is -4°F is apprοximately 1.197 miles per hοur.

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Therefore, the triangle A'B'C' has vertices A'(-4,-1), B'(3,0), and C'(-7,2), which is the reflection of triangle ABC in the y-axis and it is congruent to ABC.

A triangle is a polygon that has three sides and three angles. It is the simplest polygon that can be formed with more than two straight lines in a two-dimensional plane. The three angles in a triangle always add up to 180 degrees. Triangles are classified based on their side lengths and angles, and can be acute, right, or obtuse. Some common types of triangles include equilateral, isosceles, and scalene triangles.

Here,

To find the reflection of the triangle ABC in the y-axis, we need to reflect each point of the triangle across the y-axis. The y-axis is the vertical line passing through the origin.

For a point (x,y), its reflection across the y-axis is the point (-x,y). Therefore, we can find the reflection of each vertex of triangle ABC in the y-axis as follows:

The reflection of A(4,-1) is A'(-4,-1).

The reflection of B(-3,0) is B'(3,0).

The reflection of C(7,2) is C'(-7,2).

To determine if the two triangles are congruent, we can check if they have the same side lengths and angles. Since the y-axis is a vertical line, it does not affect the length of the sides or the measure of the angles. Therefore, the two triangles are congruent.

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Answer:

there were a total of 39 + 9 + 59 = 107 customers in the last week.

The probability that the next customer will pay with a debit card is the number of customers who used a debit card divided by the total number of customers:

9/107

This fraction cannot be simplified any further.

Step-by-step explanation:

The exact value of this expression is: (a) tan(arctan(6)) is 6 and  (b) sin−1(sin(7π/3)) is π/3

The exact value of each expression can be found by using the inverse trigonometric functions and the properties of the trigonometric functions.
(a) tan(arctan(6))
Using the property of the inverse trigonometric functions, we can simplify this expression:
tan(arctan(6)) = 6

(b) sin−1(sin(7π/3))
Using the property of the inverse trigonometric functions, we can simplify this expression:
sin−1(sin(7π/3)) = 7π/3

However, since the range of the inverse sine function is [-π/2, π/2], we need to find an angle in this range that has the same sine value as 7π/3. We can do this by subtracting 2π from 7π/3 until we get an angle in the desired range:
7π/3 - 2π = π/3

Therefore, the exact value of this expression is:
sin−1(sin(7π/3)) = π/3

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Answer:

(0, 10 )

Step-by-step explanation:

the y- intercept is the point on the y- axis where the line crosses.

any point on the y- axis has an x- coordinate of zero.

let x = 0 in the equation and solve for y

4(0) - 3y = - 30

0 - 3y = - 30

- 3y = - 30 ( divide both sides by - 3 )

y = 10

that is the y- intercept is (0, 10 )

Answer: To find the number of flowers needed to surround a circular garden with a 100-ft radius, we need to first find the circumference of the garden, which is the distance around the circle. We can use the formula:

C = 2πr

where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

So, for a garden with a 100-ft radius, we have:

C = 2πr

C = 2 × 3.14 × 100

C = 628 feet (rounded to the nearest foot)

Step-by-step explanation: Number of flowers = Circumference / Spacing

Number of flowers = 628 feet / (1/3) feet

Number of flowers = 1884 (rounded to the nearest whole number)

Therefore, we need approximately 1884 flowers spaced every 4 inches to surround a circular garden with a 100-ft radius.

Answer: 12.5 percent chance

Step-by-step explanation:

1 in 8 laps

x 100

12.5

The statements that are true include option A, D and E. The statements are true according to the triangle properties.

Let's verify each statement:

Option A: The sum of m∠3 and m∠4 is 180°.

Here, an angle of 180° will always form a straight line. The line is called as a straight angle. Any line interfering the line will make a change in the lines angle corresponding to the line but the total angle for the line of 180°.

Option D: m∠4 = m∠1 + m∠2.

Here, ∠3+∠4=180°. Also ∠1+∠2+∠3=180° ---------eq(1)

⇒ ∠3=180°-∠4 ------- eq(2)

Substitute eq (2) in eq(1)

⇒ ∠1+∠2+180°-∠4=180°

⇒ ∠1+∠2 = ∠4

Hence proved.

Option E: m∠1 + m∠2 + m∠3 = 180°

It should be noted that the sum of angles that are in a triangle equals 180°. Therefore, m∠1 + m∠2 + m∠3 = 180°.

Therefore, Option A,D and E are correct according to the triangle laws.

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Answer:

A.

Step-by-step explanation:

The line with length 2x - 9 is a bisector.

14 = 2(2x-9)

7 = 2x - 9

16 = 2x

x = 8

The correct answer is Option A.

The operations should go in the boxes are x - 4 - /2 - 5 = 3

What are operations ?
In mathematics, an operation is a mathematical process that takes one or more input values and produces an output value. The most common operations are:

According to the question:

For the first number machine, the expression for the output when the input is n is:

[tex]n - +2 - x3 - ...[/tex]

This means that the input n is first subtracted from itself (n - n = 0), then 2 is added to the result (0 + 2 = 2), then the cube of the result is taken, and so on for the remaining operations. So, the expression for the output is:

[tex]n - +2 - x3 - ... = (...((n - n + 2)^3) ...)[/tex]

For the second number machine, the operations that should go in the boxes to make it work are:

[tex]x - 4 - /2 - 5[/tex]

This means that the input x is first subtracted from itself (x - x = 0), then 4 is subtracted from the result (0 - 4 = -4), then the result is divided by 2 (-4 / 2 = -2), and finally 5 is added to the result (-2 + 5 = 3).

So, the output is: x - 4 - /2 - 5 = 3


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Therefore , the solution of the given problem of unitary comes out to be   Mrs. Elliot's garden has 16 pink flowers.

The task can be completed by applying whatever was learned, utilising this variable method, and combining all pertinent information from two people who used a specific tactic. That is, if the desired expression result materialises, either the entity stated in the formulation will also be found, or both essential processes will genuinely disregard the colour. For fifty pens, a refundable charge of Rupees ($1.21) might be required.

Here,

We're trying to determine what percentage of them are not pink.

=> 1 - 1/5 = 4/5 is the percentage of blossoms that are not pink.

As a result,

=>  1/8 + 1/4 = 3/8 of flowers are either scarlet or purple.

To determine how many flowers are either red or purple, we can set up a proportion:

=> (3/8) * 128 = 48

There are thus 48 flowers, each of which is either scarlet or purple. That means there are 80 possible pink flowers, or 128 - 48 = 80 blossoms that are neither red nor purple.

Finally, we can calculate the quantity of pink flowers by using the fact that one-fifth of the remaining flowers are pink:

=> (1/5) * 80 = 16

Therefore, Mrs. Elliot's garden has 16 pink flowers.

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If we pick four toppings on the pizza, then the number of  ways that quadruple pizza can be made if four toppings must be different is 210.

If the 4 toppings on the quadruple pizza must be different, then we need to choose 4 toppings out of 10 available toppings, without repetition.

In this case, we have n = 10 (the total number of toppings) and

⇒ r = 4 (the number of toppings to be chosen for the pizza).

So, the number of different quadruple pizzas that can be made is:

⇒ ¹⁰C₄ = 210;

Therefore, there are 210 different quadruple pizzas that can be made with four different toppings out of the ten available toppings.

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To solve the following differential equation : 6x dy/dx = 2xe^x -6y + 6x^2. = constant., we need to integrate both sides of the equation.

On the left side, we have 6x dy/dx. To integrate this, we need to multiply both sides by dx, yielding 6x dy = dx. Then we can integrate both sides, yielding ∫6x dy = ∫dx which gives y = (1/6)x^2 + C .

On the right side of the equation, we have 2xe^x -6y + 6x^2. To integrate this, we need to add a constant and move the -6y to the left side, yielding 2xe^x + 6x^2 + C = 0.

Then we can integrate both sides, yielding ∫2xe^x + 6x^2 + C = ∫0 which gives (1/2)e^x + (1/6)x^3 + Cx = 0 + D.

Finally, we can equate the two results to solve for y, yielding y = (1/6)x^2 + C = (1/2)e^x + (1/6)x^3 + Cx - D.
This is the general solution to the differential equation 6x dy/dx = 2xe^x -6y + 6x^2 = constant.

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Answer:

100

Step-by-step explanation:

If the directions say to Evaluate or Simplify, then we're going to work it out and get a number answer.

4(5)²

= 4•25

= 100

Without any extra parenthesis, the second power does not reach over to the 4. It is only on the 5. You have to square the 5 first (you get 25). Then multiply by 4. That's the proper order to evaluate or simplify.

If your question is about exponential functions or logarithms, please comment or edit in some directions. Hope this helps!

Step-by-step explanation:

To multiply integers with different signs:

Multiply the absolute values of the integers.

The product is negative if the signs of the integers are different.

The product is positive if the signs of the integers are the same.

Example: (-3) x 4 = -12

The absolute values of -3 and 4 are 3 and 4.

Multiply 3 and 4 to get 12.

The signs of -3 and 4 are different (one negative and one positive).

Therefore, the product is negative (-12).

Answer:

0.8

Step-by-step explanation:

0.8°

Unit rates let us find change over time.

Unit Rate

A unit rate is a fraction or another form of rate with a denominator of 1. This means the rate is given per 1 unit. For example, the rate for this question is in degrees/ hours. So, the unit rate will be x degrees per 1 hour. The unit rate is the way of expressing how the temperature changes over time.

Finding Change in Temperature

We know that the temperature increases by 4.8 degrees in 6 hours. So, to find the change in temperature in one hour, divide by 6. This will give the rate per one hour, aka the unit rate.

This means that the temperature is increasing by 0.8 degrees per hour.

(1) The solution of the linear equation 7x = 18, is x = 18/7.

(2) The solution of the linear equation 5x/4 = 14, is x = 11.2.

(3) The solution of the linear equation 12 - 4x = -36, is x = 12.

To solve the equation 7x = 18, we can divide both sides by 7:

7x/7 = 18/7

x = 18/7

To solve the equation 5x/4 = 14, we can first multiply both sides by 4 to get rid of the fraction:

5x/4 x 4 = 14(4)

5x = 56

Then, we can divide both sides by 5:

5x/5 = 56/5

x = 11.2

To solve the equation 12 - 4x = -36, we can first add 4x to both sides:

12 - 4x + 4x = -36 + 4x

12 = -36 + 4x

Then, we can add 36 to both sides:

12 + 36 = 4x

48 = 4x

Finally, we can divide both sides by 4:

48/4 = 4x/4

12 = x

So the solution is x = 12.

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