The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. P=$4000, r=5% t= 1 year

Answer:

(7, -2)

Step-by-step explanation:

x + 3y = 1

-3x - 3y = -15

(x-3x) + (3y-3y) = 1-15

-2x + 0 = - 14

-2x = - 14

x = 7

x + 3y = 1

7 + 3y = 1

3y = 1-7

3y = -6

y = -2

Answer:

D: (7 , -2)

Step-by-step explanation:

Multiply each equation by the value that makes the coefficients of x

opposite.

(3)⋅(x+3y)=(3)(1)

−3x−3y=−15

Simplify

3x+9y=3

−3x−3y=−15

Add the two equations together to eliminate x

from the system.

3x+9y= 3

+     −3x−3y=−15

_____________

6y=−12

Divide each term by 6 and simplify.

y=−2

Substitute the value found for y into one of the original equations, then solve for x.

x=7

The solution to the independent system of equations can be represented as a point.

(7,−2)

The result can be shown in multiple forms.

Point Form:

(7,−2)

Equation Form:

x=7, y=−2

I hope this helps!!!!!!!

Answer:

Please give brainliest

Step-by-step explanation:

c

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

The requried, Chloe originally had 68 marbles.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

Let's assume that Chloe originally had "x" marbles.

According to the problem, Chloe added 36 marbles to her collection. This means that she now has x + 36 marbles.

And we also know that she now has a total of 104 marbles.

So, we can set up an equation:

x + 36 = 104

To solve for x, we can isolate x on one side of the equation by subtracting 36 from both sides:

x + 36 - 36 = 104 - 36

x = 68

Therefore, Chloe originally had 68 marbles.

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

Answer:

add 3 0 x+3

Step-by-step explanation:

Answer: 3x - 2

Step-by-step explanation:

First to solve this, we need to know some basic information such as:

1. (-) × (-) = +

2. (+) × (-) = -

3. (+) × (+) = +

Therefore, 6x-(3x+2)​

= 6x - 3x - 2

= 3x - 2

The answer to the question after removing the bracket will be 3x - 2.

Answer:

\(\displaystyle 3^2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

\(\displaystyle \frac{3^3 \cdot 3^3}{3^4}\)

Step 2: Simplify

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

For such more questions on Frequency Difference

https://brainly.com/question/13193436

#SPJ8

Answer:

$14.20

Step-by-step explanation:

$42.60 ÷ 3

$14.20

Lin's family has completed approximately 86.15% of the total Distance to her grandmother's house.

The percentage of the distance Lin's family has completed, the ratio of the distance they have traveled to the total distance.

The distance traveled is 325 miles, and the total distance to Lin's grandmother's house is 377 miles.

To calculate the percentage, we can use the following formula:

Percentage = (Distance Traveled / Total Distance) * 100

Plugging in the values, we have:

Percentage = (325 / 377) * 100

          = 0.8615 * 100

          = 86.15

Therefore, Lin's family has completed approximately 86.15% of the total distance to her grandmother's house.

To know more about Distance .

https://brainly.com/question/30395212

#SPJ11

Answer:

First choice

Step-by-step explanation:

Looking at the graph, as the line gets further to the right (positive x, also displayed as x-> infinity) the line continues downwards in the y (vertical) direction

Looking at the graph, as the line gets further to the left (negative x, also displayed as x-> -infinity) the line continues downwards in the y (vertical) direction

Thus, the end behavior is -infinity for both ends

The volume of the solid formed by the figure shown above is calculated as: 3,934 cm³.

The volume of the figure can easily be found by identifying the height or length of the prism, then find the product of the base area and the height of the prism.

This is:

Volume = base area * length/height of prism = 1/2 * base * height * length of prism.

Given the following:

base = √(31.4² - 14²) ≈ 28.1 cm [Pythagorean theorem]

height = 14 cm

Length of prism = 20 cm

Substitute:

Volume = 1/2 * 28.1 * 14 * 20

= 3,934 cm³

Learn more about the volume of prism on:

https://brainly.com/question/28795033

#SPJ1

Answer:

7,8.5

Step-by-step explanation:

Answer: First, take a picture that isn't blurry

Step-by-step explanation: Re-post so I can help Mr. or Ms. eeeeeeeeeeeeeeeeeeeeeeeeee

The compound inequality to represent the scenario is 60 <= 34 + 1.36x <= 85 and the range is 19 to 37.5

The given parameters are:

Charges = $34

Rate = $1.36

Recommendation = $60 to $85

The total charge on a HCF is represented as:

Total = Charge + Rate * x

So, we have

Total = 34 + 1.36x

The compound inequality to represent the scenario is then represented as:

60 <= 34 + 1.36x <= 85

Add 34 from the inequality

26 <= 1.36x <= 51

Divide by 1.36

19 <= x <= 37.5

Hence, the compound inequality to represent the scenario is 60 <= 34 + 1.36x <= 85 and the range is 19 to 37.5

Read more about compound inequality at

https://brainly.com/question/1485854

#SPJ1

Answer:

orange juice is better than Apple Juice

Answer:

87

Step-by-step explanation:

The equation 12y−9x=−36 in slope-intercept form is y=3/4x-3.

The equation 12y−9x=−36 in slope-intercept form:

First, add 9x to both sides of the equation:

12y=9x−36

Next, divide both sides by 12:

y= 9/12 x-36/12

Simplify the fractions:

y=3/4x-3

So, the equation 12y−9x=−36 in slope-intercept form is y=3/4x-3.

To know more about equation:

https://brainly.com/question/29657983

#SPJ3

Answer:

c

Step-by-step explanation:

assume base 10

-logy = x

\( \frac{1}{ log(y) } = x\)

log base x y = 5 turns into the format x^ 5 = y

implement that to get c

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

Answer:

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

triangle ABC is an is0sceles triangle because according to the figur it's two sides are equal.

angle B = angle  (because base angles of an isosceles triangle are equal)

so let angle A also be theta

now lets find the value of theta

angle A + angle B + angle C =10 degree (sum of interior angles of a triangle)

theta + theta +90 =180

2 theta =180-90

theta =90/2

theta =45 degree

therefore the value of theta is 45 degree.

so angle A =45 degree    and angle B =45 degree

to find x

Take angle B as reference angle

using sin rule

sin 45 = opposite/hypotenuse

\(\frac{1}{\sqrt{2} } =\frac{x}{5\sqrt{2} }\)

do cross multiplication

\(x * \sqrt{2 } = 5\sqrt{2} *1\)

\(x = \frac{5\sqrt{2} }{\sqrt{2} }\)  (root 2 and root 2 gets cancel)

\(x=5\)

On each roll of a 6-sided die, we have 6 possible outcomes.

Then if we roll it twice, we will have 36 outcomes.

The outcomes where the sum is 4 are:

roll 1     roll 2    sum

1             3           4

3            1            4

2           2           4

Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:

P = 3/36

P = 1/12

Learn more about probability at:

https://brainly.com/question/25870256

#SPJ1

The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

As per option (B),

Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.

Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.

Sarah rides her bike = 3/4 × 8/9

Therefore, this problem can be solved by performing the above multiplication.

Hence, the correct answer would be an option (B).

Learn more about Multiplication operations here:

brainly.com/question/25834626

#SPJ1

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

For more questions on trigonometric form

https://brainly.com/question/31744474

#SPJ8

its c please mark me as a brainliest

The polynomial 11x⁵  + x⁴ - 4x³ - 5x² + 8 denotes the expression P - Q. The correct option is option A.

What is an expression?

A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression is (Math Operator, Number/Variable, Number/Variable)

Given polynomials are:

P = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5

Q = (2x² + 1) (4x² - 3)

Simplify the polynomial Q = (2x² + 1) (4x² - 3):

Q = (2x² + 1) (4x² - 3)

Q = 2x²(4x² - 3) + 1(4x² - 3)

Q = 8x⁴ - 6x² + 4x² - 3

Add like terms:

Q = 8x⁴ - 2x² - 3

Now calculate P + Q

P + Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 + 8x⁴ - 2x² - 3

Combine like terms:

P + Q = 11x⁵ + (9x⁴ + 8x⁴) - 4x³  + (- 7x² - 2x²) + 5 - 3

P + Q = 11x⁵ + 17x⁴ - 4x³ - 9x² + 2

Now calculate P - Q

P - Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 - (8x⁴ - 2x² - 3)

P - Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 - 8x⁴ + 2x² + 3

P - Q = 11x⁵  + (9x⁴ - 8x⁴) - 4x³ + (-7x² + 2x² )+ (5 + 3)

P - Q = 11x⁵  + x⁴ - 4x³ - 5x² + 8

Now calculate Q - P

Q - P =  8x⁴ - 2x² - 3 - (11x⁵  + 9x⁴ - 4x³ - 7x² + 5)

Q - P =  8x⁴ - 2x² - 3 - 11x⁵  - 9x⁴ + 4x³ + 7x² - 5

Combine like terms:

Q - P = - 11x⁵ + (8x⁴ - 9x⁴) + 4x³ + (- 2x² + 7x²) - 3 - 5

Q - P = - 11x⁵- x⁴ + 4x³ + 5x² - 8

To learn more about operation, click on the below link:

https://brainly.com/question/22735845

#SPJ1

Answer:

(-9 - 2y) / y + 3

Step-by-step explanation:

I just simplified it because y doesnt have a value

Answer:

\(\displaystyle h(x) = x-\frac{13}{2}\)

Step-by-step explanation:

We are given that:

\(\displaystyle g(x) = \int_{-1}^x f(t)\, dt\)

And we want to write the equation for the tangent to the graph of g at x = 4.

First, determine g(4):

\(\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}\)

This is equivalent to the area of f from -1 to 4:

\(\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}\)

Note that areas under the x-axis are negative.

Find g'(4):

\(\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}\)

By the Fundamental Theorem of Calculus:
\(\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}\)

Note f is a line for 3 < x < 6 with a slope of 1.

Therefore:
\(\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}\)

In conclusion, the equation of the tangent line is:
\(\displaystyle h(x) = x-\frac{13}{2}\)

Answer:

70%

Step-by-step explanation:

Answer:

The probability of rolling a number greater than 2 two times in a row is arond 0.44

Step-by-step explanation:

Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring. In the case of rolling a 3 on a die, the number of events is 1 (there's only a single 3 on each die), and the number of outcomes is 6.

Probability formula is the ratio of number of favorable outcomes to the total number of possible outcomes. Measures the likelihood of an event in the following way: - If P(A) > P(B) then event A is more likely to occur than event B. - If P(A) = P(B) then events A and B are equally likely to occur.