zhen borrows $1,200.she borrows the money for 2 years and owes $180 in simple interest.what is the yearly simple interest rate on zhen's loan?

Step-by-step explanation:

so, the first road is 115 m long, the second is 90 m long.

we should be finished, if we multiply each road length by $100, right ?

well, not quite.

because the 2 roads overlap. for this overlap area we don't need to pay twice.

we have the choice : to which of the 2 roads do we assign the overlap area ?

let's "give" it to the longer road.

so, the cost for the longer road is simply

115 × 100 = $11,500

the cost for the shorter road is then without the overlap area (6 meters : the width of the other road)

(90 - 6)×100 = 84×100 = $8,400

in total the costs are

$11,500 + $8,400 = $19,900

The equation you provided is a linear equation that can be solved by isolating the variable y on one side of the equation. To find the solution for y, we need to follow these steps

First, we will simplify the equation by combining like terms: 2.8y + 0.2y = 5y – 14 + 6 3y = 5y – 8

Next, we need to get y alone on one side of the equation by subtracting 3y from both sides: 0 = 2y - 8

We will add 8 to both sides of the equation: 8 = 2y

Finally, we will divide both sides of the equation by 2 to find the solution for y: y = 4

So the solution for the linear equation 2.8y + 6 + 0.2y = 5y – 14 is y=4.

It's worth mentioning that this is the only solution that this equation has since it's a linear equation which has only one answer.

To learn more about the linear equation question:

https://brainly.com/question/13738061

#SPJ4

The volume of cylinder = 15,869.56 mm.

The formula for determining a cylinder's volume is the base area times the height. Volume of a cylinder is r2h cubic units.

To calculate a box's volume, you need to know its height, width, and depth. The volume can be calculated by multiplying these three dimensions.

Assume for the moment that the spherical discs are stacked h levels high. The volume of the cylinder will now be calculated by multiplying the discs' base areas by their heights, "h". Therefore, r2h is used to represent the volume of a cylinder with base radius r and height h. The amount of material required to fill an object can be calculated using the volume of the object.

We know that the volume of cylinder = πr²h

Given,

height = 14 mm

radius = 19 mm

V = π × 19 × 19 × 14

⇒  V = 15,869.56 mm

To learn more about cylinder's refer to:

brainly.com/question/76387

#SPJ1

Answer:

-26

Step-by-step explanation

1) substitute -2 for X

4(-2)(2)-3(-2)-16

2) solve

-8(2)+6-16

-16+6-16

-10-16

-26

The value of function at x= -2 is f(-2) is 54.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = 4x² - 3x - 16.

Now, to find the value of f(-2) put the value of x= -2.

so, f(-2)= 4(-2)² - 3(-2) - 16

= 4(16) + 6 - 16

= 64 -10

= 54

Learn more about Function here:

brainly.com/question/12431044

#SPJ2

The value of x using Pythagoras theorem is x = √30.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

⇒ 5² + base² = 8²

⇒ 25 + base² = 64

⇒ base = √64 - 25
⇒ base = √39

In the other triangle,

x² + 3² = 39

⇒ x² = 39 - 9

⇒ x = √30

To learn more about Pythagoras theorem from given link

https://brainly.com/question/27258382

#SPJ1

Answer:

An increase of 20

Step-by-step explanation:

-20 + 20 = 0

The change in temperature in degrees Fahrenheit required is A = 20°F

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The current temperature is -20°F, and we want to know how much it needs to increase to reach 0°F.

On simplifying the equation , we get

We can calculate this by finding the difference between the two temperatures:

0°F - (-20°F) = 0°F + 20°F = 20°F

Hence , the temperature needs to increase by 20°F to reach 0°F

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

The polynomial x° 9x* 3x 5 has a degree of 3.

The highest power of a polynomial's variable is the polynomial's degree. The maximum power of the variable in the polynomial x* 9x* 3x 5 is 3, indicating that the polynomial has a degree of 3.

The highest power of a polynomial's variable is the polynomial's degree. The polynomial x*9x* 3x 5 has a degree of 3 since the largest power of the variable is 3, which is 3. A polynomial's degree is equal to the largest power of the variable it contains. The maximum power of the variable.

The polynomial x* 9x*3x 5 is 3, indicating that the polynomial has a degree of 3. The easiest way to do this is to look at the polynomial's variable's highest exponent. The polynomial's degree reveals its level of complexity and the quantity of its solutions. In order to ascertain a polynomial's type, number of terms, and root values, it is crucial to understand the degree of the polynomial.Understanding a polynomial's degree also aids in predicting the kind of graph it will generate.

Complete question:

What type of polynomial is the expression 9x² 30x25 What degree does the polynomial x3 9x2 3x5 have?What distinguishes the two polynomials?

To know more about Polynomial visit:

https://brainly.com/question/30284197

#SPJ4

The expression 9x² + 30x + 25 is a third degree (or cubic) polynomial.

To determine the degree of a polynomial, we look at the term with the highest degree of x. In this case, the highest degree is x², which has an exponent of 2. Therefore, this polynomial is a third degree polynomial.

Another way to determine the degree is to look at the number of terms in the polynomial, which is three in this case. A polynomial with three terms is typically referred to as a cubic polynomial. In general, the degree of a polynomial with n terms is equal to n - 1.

Learn more about Polynomials:

https://brainly.com/question/24662212

#SPJ4

The required slope of the curve at the designated point P is 1/4.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the curve at point p is given as
= rise/run

From the graph,
rise = 2 and run = 8
slope of the curve at point P = 2 / 8 = 1/4

Thus, the required slope of the curve at the designated point P is 1/4.

Learn more about slopes here:
https://brainly.com/question/3605446

#SPJ1

Four rules of multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

As given in the question,

Four rules of the multiplication are given by :

1. Zero × any number = 0

0 × a = 0 , a ∈ R.

Example : 0 × 5 = 0

2. One  × any number = Number itself.

1 × a = a  , a ∈ R.

Example : 1 × 5 = 5

3. Multiply two numbers with same sign gives positive negative.

-a × -a = + a , +a × +a = + a,  , a ∈ R.

Example : -2× -2 = 4

3 × 3 = 9

4. Multiplication of two numbers in any order does not affect the result.

a × b = b × a, a and b ∈ R.

Example : 2 × 3 = 3 × 2

Therefore, the four rules of the multiplication are :

1. 0 × a = 0 , a ∈ R.

2. 1 × a = a  , a ∈ R.

3. -a × -a = + a² , +a × +a = + a²,  , a ∈ R.

4. a × b = b × a, a and b ∈ R.

Learn more about multiplication here

brainly.com/question/5992872

#SPJ4

Answer: A partition of a line segment is a point that divides the segment into a certain ratio of segments. In this case, point P partitions the segment AB in the ratio 3 to 1.

To find the coordinates of point P, we can use the following method:

Let the point P be (x,y)

The ratio of the segments AP:BP is 3:1, so we can use the proportion: (AP)/(BP) = 3/(1+3) = 3/4

We can use the coordinates of points A and B to find the coordinates of point P. The x-coordinate of P is (3/4) times the difference in x-coordinates of A and B, plus the x-coordinate of A. And the y-coordinate of P is (3/4) times the difference in y-coordinates of A and B, plus the y-coordinate of A.

So, using the coordinates of A and B:

x = (3/4)(-5 - 7) + 7 = -4

y = (3/4)(4 - (-4)) -4 = 3

Therefore, the coordinates of point P are (-4,3)

Step-by-step explanation:

Answer:

$41.04

Step-by-step explanation:

set up a proportions equation:

[tex]\frac{18.20}{2\frac{1}{3}} =\frac{x}{5\frac{1}{4}}[/tex]

cross multiply and solve for x. this gives you:

x = 41.04

hope this helped, good luck!

The value of variable, x when f(x) = 4 according to the given function expression; f(x) = -x + 3 is; -1.

It follows from the task content that the value of x is to be determined according to the given function expression; f (x) = -x + 3.

Hence, when f (x) = 4, the resulting expression is;

4 = -x + 3

Hence, to determine the value of x, we must solve for x as follows;

4 - 3 = -x

1 = -x

x = -1.

Ultimately, the value of x for which the function instance f(x) = 4 is; x = -1.

Read more on function evaluation;

https://brainly.com/question/27234947

#SPJ1

We would expect about 80 seventh-graders to attend after-school programs.

To estimate the number of seventh-graders attending after-school programs, we can use the proportion of respondents who attend after-school programs from the sample:

28 out of 140 respondents attend after-school programs, which is a proportion of

= 28 / 140

= 0.2.

We can use this proportion to estimate the number of seventh-graders attending after-school programs in the entire population of 400 seventh-graders:

400 * 0.2 = 80

Learn more about proportions at:

https://brainly.com/question/870035

#SPJ1

The Chang family has been traveling for 18 hours, thus, t-value is 18.

A significant t-score, also known as a t-value, implies that the groups are distinct, whereas a small t-score suggests that the groups are similar. Degrees of freedom are the values in a study that are open to change and are crucial for determining the significance and reliability of the null hypothesis.

D(t) = 2,280 - 60t

D(t) = 1,200; find t.

D(t) = 2,280 - 60t

1200 = 2280 - 60t

From both sides of the equation, deduct 2280.

1200 - 2,280 = 2280 - 60t - 2,280

- 1080 = - 60t

multiplied by -60 on both sides

- 1080 / -60 = - 60t / -60

18 = t

t = 18

The Chang family had travelled for 18 hours, according to this.

The Chang family has been traveling for 18 hours, t = 18.

To learn more about t-value refer to:

brainly.com/question/27192813

#SPJ1

The complete question is,

Having just returned from a cross-country road vacation, the Chang family is traveling back home. They can visualize their distance from home in miles after t hours of travel by using the function D(t) = 2,280 - 60t during the journey. If D(t) = 1,200, what does t represent? That value stands for what?

A.t = 20; the Chang family has been traveling for 20 hours.

B. t = 20, meaning the Chang family will need to travel 20 more hours to reach home.

The Chang family has been traveling for 18 hours, thus c. t = 18.

The Chang family must go home for an additional 18 hours using the formula D. t = 18.

The value of g(2) = 36 for the given function.

The given function g is defined by,

[tex]g(x) = 4(3)^{x}[/tex]

Now to find the value of g(2), put x = 2 in the given function we get,

g(2) = 4(3)²

g(2) = 4 × 3 × 3

g(2) = 36

Therefore, the value of g(2) = 36 for the given function.

To learn more about Function,

brainly.com/question/14322077

Step-by-step explanation:

x1, y1 = (-5,-2)

slope,m = -6/5

general equation, y= MX + C

(y-y1)/(x-x1)=m

(y+2)/(x+5)=-6/5

5y+10=-6x-30

5y=-6x-40

y=-(6x/5) - 8

Step-by-step explanation:

-8(-5/8x + y = -1/4)

5x - 8y = 2 is the standard form

The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³. That is why the mole is equal to Avogadro's number.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there is A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

To know more about Avagadro’s number, here

brainly.com/question/23944317

#SPJ4

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

Suppose vector "a" is given and we want to determine an expression to produce vector "b". To do this, we need to find two vectors, "c" and "d", such that:

a = c + d

where c and d are the vectors that when added together produce vector a. The expression to produce vector b can then be represented as:

b = d - c

The expression can be determined by first finding the components of vector a, and then using these components to determine the components of vectors c and d. For example, if vector a is represented as:

a = <a1, a2, a3>

We can set c and d equal to:

c = <a1/2, a2/2, a3/2>

d = <a1/2, a2/2, a3/2>

So, the expression to produce vector b can be represented as:

b = d - c = <a1/2, a2/2, a3/2> - <a1/2, a2/2, a3/2> = <0, 0, 0>

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

To learn more about vector visit : brainly.com/question/29740341

#SPJ4

Let's say vector a is represented by the expression (a1, a2), and vector b is represented by the expression (b1, b2).

Then, the expression for the resultant vector (c1, c2) can be calculated as follows:

c1 = a1 + b1

c2 = a2 + b2

So the expression for the resultant vector is (a1 + b1, a2 + b2).

To determine an expression that produces vector b from vector a, you would need to know the relationship between the two vectors. If vector b is a scalar multiple of vector a, the expression for vector b can be represented as:

b = k * a

Where "k" is the scalar factor. If vector b is a vector that is in the opposite direction of vector a, the expression for vector b can be represented as:

b = -1 * a

In this case, the scalar factor is -1.

Learn more about vectors here:

https://brainly.com/question/29740341

#SPJ4

The pair of expressions 4p + 3c and (c +2p)(2) are not equivalent because they aren't equal.

This is referred to as the expressions that work the same even though they look different.

we were given: 4p + 3c and (c +2p)(2)

: 4p + 3c = (c +2p)(2)

: 4p + 3c = 2c + 4p

They are not equal thereby making them not to be equivalent.

Read more about Equivalent expressions here https://brainly.com/question/15775046

#SPJ1

The full question:

determine whether each pair of expressions are equivalent 4p + 3c and (c +2p)(2)

The solution for the given system of equations is (5.5, 4.333).The correct option is B

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

y - y1 =m (x - x1)

We have the following set of equations -

4x − 15y = −43

2x − 3y = −2

These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graph that the solution is given by coordinate - (5.5, 4.333).

Therefore, the solution for the system of equations is (5.5, 4.333).

Learn more about system of equation here: brainly.com/question/25976025

#SPJ1

Answer:  u = sr/qut

Step-by-step explanation:

Given the equation sr = qut, we can solve for u by isolating it on one side of the equation. To do this, we divide both sides by qut. This gives us sr/qut = u. This means that u can be represented in terms of q, r, s, and t as sr/qut. This is the final result.

.........

Given the equation sr = qut, we can solve for u in terms of q, r, s, and t by isolating u on one side of the equation.

To do this, we can divide both sides of the equation by (qut)

sr/qut = u

Then we have u = sr/qut

So, u is expressed in terms of q, r, s, and t as u = sr/qut

The measure of angle C is 47.86⁰

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

C,U and B are the angles and the  c,u and b are the sides opposite to the angles  C,U and B  respectively.

Law of cosines:

c² = u² + b² - 2ub cos C

58²=78²+48² - 2(78)(48) cos C

3364=6084+2304-7488 cos C

3364 = 8388-7488 cos C

=> 7488 cos C = 8388 - 3364 = 5024

=>  cos C = 5024 /7488 = 0.6709

=> C = arccos(0.6709) = 47.86⁰

So,  the measure of angle C is 47.86⁰

To learn more about the angle from the given link

https://brainly.com/question/25716982

#SPJ1

The factors for the expression (3x+7)(3x-7)

squared the given 9x² = 3x 49 = 7 if the operation in the first unfactor form is negative the factored form's operation will be positive and negative,  = (3x+7)(3x-7)

The factored form occurs when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form may be restated in standard form.

Several strategies may be used to derive the factored form of a quadratic equation Ax2+Bx+C=0 , A x 2 + B x + C = 0.

Factored form assists us in determining the function's x-intercepts or zeros.

Learn more about to factored form;

https://brainly.com/question/29065045

#SPJ4

Gross income means all income you receive in the form of money, goods, property, and services that isn't exempt from tax.

To learn more about tax refer to:

https://brainly.com/question/26316390

#SPJ1

Answer:

the b part

Step-by-step explanation:

Answer: The y-intercept of y=mx+b is B

Step-by-step explanation:

1. Y is the y-variable

2. Mx is the slope

3. B is the y-intercept.

Answer:

no, x = -6y+30 is the right answer

Step-by-step explanation:

Correct answer:

(-1, 8)

(-2, 6)

(1, 4)

Answer:

Correct choices are:

(-1, 8)

(1, 4)

which would correspond to the second and fourth entries of your options

Step-by-step explanation:

Best way to solve this problem is to plug in x and y values for each ordered pair and see if these values result in a consistent equation. It is impossible to solve the equation since there are two unknowns and only one equation

Here is each ordered pair and resulting y value when x value is plugged in

(-1, 2) ==> y = 2, x = -1
6 - 2(-1) = 6 + 2 = 8
This is not equal to the given value of y =2. So incorrect

(-1, 8)
We figured out from above that when x = -1, y = 8 so this is a correct choice

(-2, 6) ==> x = -2, y = 6

6 - 2(-2) = 6 + 4 = 10
Does not match y-value; incorrect

(1, 4) ==> x = 1, y = 4

6 - 2(1) = 6 - 2 = 4

This matches the given value of y so correct choice