Jill made a New Year's resolution to learn how to play the cello. She bought an Introduction to
Cello class pack from the Purple Harp music shop, which covers the cost of 15 cello lessons.
She also paid $35 to rent a cello. In all, Jill paid $425.
Which equation can you use to find the cost, c, of each cello lesson?
A. 35(c +15) = 425
B. 15c + 35 = 425
C. 15(c + 35) = 425
D. 35c+15= 425

Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. 51.09 is the compound interest.

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.

Given that,

principal amount (P) = $925

number of times interest applied per time period (n) = semiannually = 6

number of time periods (t) = 1 year

Thus, formula becomes:

[tex]I = P (1 + r/n)^{nt} - P[/tex]

or, [tex]I = 925 (1 + 5.5/6*100)^{1*6} - 925[/tex]

or, [tex]I = 925 (1.009)^6 -925[/tex]

or, [tex]I = 925 *(1.055) -925[/tex]

or, [tex]I = 976.09 -925[/tex]

or, [tex]I = 51.09[/tex]

Thus, the compound interest becomes 51.09

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If you chose the letters D and H for 20 turns, the number of times you are most likely to win is; Option C: 3

We are given the probability of winning for each letter as;

A = 5%

B = 10%

C = 15%

D = 5%

E = 5%

F = 25%

G = 10%

H = 10%

I = 10%

J = 5%

Now, we want to find the number of times you can win If you chose the letters D and H for 20 turns.

Thus;

Number of times you can win if you chose Letter D = 5% * 20 = 1 time

Number of times you can win if you chose Letter H = 10% * 20 = 2 times

Thus;

Total number of ways of winning = 1 + 2 = 3 times

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The greatest common factor of 15n^5, 30n^3, and 45n^2 is 15n^2

In this question we need to find the greatest common factor of 15n^5, 30n^3, and 45n^2.

we know that the greatest common factor of given numbers is nothing but the highest number that divides given numbers.

If we look at the variable part of given monomials, then the highest power of n that divide given monomials is n^2.

And the greatest common factor os (15, 30, 45) is 15

So, we get a monomial 15n^2

Therefore, the greatest common factor is 15n^2

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Answer:

Y= 319 hope you have the best rest of the day of your life ever. can i have brainliest

Step-by-step explanation:

Steps for Solving Linear Equation

(10×12)+(5×11)+(12×12)=Y

Multiply 10 and 12 to get 120. Multiply 5 and 11 to get 55. Multiply 12 and 12 to get 144.

120+55+144=Y

Add 120 and 55 to get 175.

175+144=Y

Add 175 and 144 to get 319.

319=Y

Swap sides so that all variable terms are on the left hand side.

Y=319

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture above.

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +4}{1 +5} \implies {\Large \begin{array}{llll} \cfrac{ 1 }{ 6 } \end{array}}[/tex]

The boy should throw the ball at a speed of 17.15 m/s.

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia. If all the external forces cancel each other out, then there is no net force acting on the object.  If there is no net force acting on the object, then the object will maintain a constant velocity. His second law defines a force to be equal to change in momentum (mass times velocity) per change in time. Momentum is defined to be the mass m of an object times its velocity V.

From Newton's equations of motion,

v = u + at

Here, v = 0 m/s

a = g = -9.8 m/s²

t = 3.5/2 = 1.75 s

Put these values in the above equation:

u = v - at

u = 0 - (-9.8)(1.75)

∴ u = 17.15 m/s

Thus, the boy should throw the ball at a speed of 17.15 m/s.

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Answer: The nearest whole number is 18

Step-by-step explanation: because 18 2/6 is closer to 18 than 19.

Answer:

the water fight ended at 2:30pm

Step-by-step explanation:

the balloons lasted an hour bringing it to 2pm then they used the hoses for 30 min bringing it to 2:30pm

The scale factor of the dilation is s = 4 units .

Given :

parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'.

To find scale factor between figures, find two corresponding sides and write the ratio of the two sides.

The value of y is same through the distance of F to G.

So, FG = change in x coordinates

FG = -2 - ( -4 )

= -2 + 4

= 2

F'G' = 3 - ( - 5 )

= 3 + 5

= 8

Let s be the scale factor

s = F'G' / FG

= 8 / 2

= 4

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Comparing the two friends earning Montraie earns $ 0.5 per hour less than Serenity

The word problem that has to do with earnings of two friends Montraie and Serenity is solved by putting the problem in equation form

The equations are generated as follows

The equation for the earning for Montraie is y = 19.2x

Using the equation in 38 hours Montraie will earn

y = 19.2 * 38

y = 729.6

This means that Montraie earns 19.2 per hour

For Serenity the earning per hour is solved

= 748.60 / 38

= 19.7

comparing both earnings

Serenity earning - Montaie earning

= 19.7 - 19.2

= 0.5

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Answer:

(6,[tex]\frac{10}{3}[/tex])

Step-by-step explanation:

[tex]\frac{2+6+10}{3}[/tex], [tex]\frac{5+5+0}{3}[/tex]

(6, [tex]\frac{10}{3}[/tex]) o r(6, 3 [tex]\frac{1}{3}[/tex])

The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,

⇒ (6, 10/3)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Three vertices of the triangle are,

⇒ s(2, 5) t(6, 5) r(10, 0)

Now, We can find;

The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,

⇒ (2 + 6 + 10) / 3, (5 + 5 + 0) / 3

⇒ (6, 10/3)

Thus, The centroid of the triangle = (6, 10/3)

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Answer:

I think -1.5 -0.1 0.8 1.1

Answer:

-1.5 || -0.1 || 0.8 || 1.1

Explanation:

Since it is from least to greatest, let's compare the 2 negative numbers -1.5 and -0.1.

-1.5 has a 1 in its first place while -0.1 has a 0. This means that -1.5 is smaller because the further a number is on the negative number line the smaller it is.

So, -1.5 is the smallest, then -0.1.

-1.5 || -0.1

Now we compare the 2 positive numbers 0.8 and 1.1.

0.8 has a 0 in its first place and 1.1 has a 1 in its first place. Because the numbers are positive, the number with the biggest digit in in front of the decimal is greater.

So, in this case 1.1 is greater than 0.8.

0.8 || 1.1

In order it is:

-1.5 || -0.1 || 0.8 || 1.1

Answer:

Step-by-step explanation:

No it is not

y = 13x ,y = x - 2 and y = 2x + 11 represents a straight line which is proportional to x i.e. a linear function .

The proportional relation equation is y = kx .

The letters y and x are the variables, which can change, and the letter k is the constant of proportionality.

According to the question ,

Given: y = 13x

since y ∝ x,

Therefore the equation is said to be proportional .

Given: y = x²

Since the term y is proportional to the square of square ,so we can't say say that the equation is proportional .

Given: y = x - 2

Since ,y is in the form of the equation y = mx + c and y is proportional to x as well ,therefore we say that x is proportional to x .

Given : y = 2x + 11

Since y is in the form of y = mx + c and y is proportional to x

As the given expression represents a straight line , so its proportional to x .

Hence, all the given expressions are proportional to x except the second option which is proportional to square of x and is not forming a linear equation that is a straight line.

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Answer:

x = [tex]\frac{-14}{3}[/tex]

Step-by-step explanation:

-2(3x + 8) -2 = 10  Distribute the -2

-6x - 16 -2 = 10 Combine like terms

-6x - 18 = 10   Add 18 to both sides

-6x = 28  Divide both sides by -6

x = [tex]\frac{-28}{6}[/tex] = [tex]\frac{-14}{3}[/tex]

Answer:

-1

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define two points on the line:

Substitute the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-0}{0-(-2)}=\dfrac{-2}{2}=-1[/tex]

Therefore, the slope of the line is -1.

Answer:

A= I + P

for real? And why is high-school question

The value of x = 3 for y = 9 is a solution of the linear equation -4x = y - 21.

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalises the two sides of the equation.

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Basically, there are infinitely many solutions to a linear equation with two variables.

The solution of the equation (x,9).

For the equation -4x = y -21

here, y = 9

-4x = 9 - 21

⇒ -4x = -12

⇒ x = 3.

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After solving the given equation at g(x) = 3 the value obtained is 3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

The given equation is,

g(x) = -2x + 9

Then,

g(3) = -2(3) + 9

= -6 + 9

g(3) = 3

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Your question seems incomplete, the complete question may be:

If g(x) = -2x + 9, what is the value of x

when g(x) = 3?

Answer:

252

Step-by-step explanation:

in each minute, the wheel makes 42 turns. That means it turns 42×360=15120 degrees in one minute (60 seconds). We want to find how many degrees it will turn in one second, not one minute, so we will divide the total degrees by 60.

15120÷60=252

So our answer is 252.

Answer:

square root of 43 is irrational and thus square root of 43 + 5 is also irrational.

Step-by-step explanation:

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If the father is 22 years older than his son, and the sum of their ages is 38 years, we can set up the following equations to represent this information:

Copy code

father + son = 38

father = son + 22

We can solve for the father's and son's ages by substituting the second equation into the first equation:

Copy code

(son + 22) + son = 38

2 * son + 22 = 38

2 * son = 16

son = 8

Therefore, the son's age is 8 years, and the father's age is 8 + 22 = <<8+22=30>>30 years.

Answer:

16

Step-by-step explanation:

son=38-22

son=16

hope am correct

Based on the triangle midsegment theorem, the length of CZ is calculated as: 7.2 m.

The triangle midsegment theorem states that when two sides of a triangle are joined together by a line segment at their midpoint, the line segment is called the midsegment, and it is parallel to the third side whose measure is twice its length.

This implies that, AB is a midsegment in the image shown for triangle XYZ. It is parallel to YZ.

Therefore:

AB = 1/2(the length of YZ)

Substitute the value of AB into the equation:

7.2 = 1/2(YZ)

2(7.2) = YZ

YZ = 14.4 m.

The length of CZ = 1/2(the length of YZ) [this is because YC = CZ]

CZ = 1/2(14.4)

CZ = 7.2 m.

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Answer:

Step-by-step explanation:

You want it to be in y=mx+b form.

B= y intercept

mx= slope (3x)

Y=3x+-2

Answer:

FJ is -3/1

Step-by-step explanation:

And in order to be a trapezoid, just one pair of sides needs to be parallel.

Answer:

Step-by-step explanation:

If the discriminant of a quadratic function is 64 and its vertex is in quadrant III, here are three things you can know about the function and/or its graph:

The function has two distinct real roots. The discriminant of a quadratic function is the value under the square root in the quadratic formula:

x = (-b +/- √(b^2 - 4ac)) / 2a

If the discriminant is positive, it means that there are two real roots (values of x that make the equation equal to zero). If the discriminant is negative, it means that there are no real roots (the equation has no solutions). If the discriminant is zero, it means that there is only one real root (the equation has one solution). Therefore, if the discriminant is 64, it means that the function has two distinct real roots.

The graph of the function is a parabola that opens downward. The direction in which a parabola opens (upward or downward) is determined by the coefficient of the x^2 term (a). If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. In this case, the vertex of the parabola is in quadrant III.

36 is a multiple of two numbers added together without a common factor.

When a number is exactly divided by a divisor, that divisor is known as a factor of that number.

Alternatively, a factor of a number is an exact divisor of the provided number.

A number's factors are either less than or equal to the supplied number; they cannot be bigger. Every number is a factor of itself, and the common factor of all numbers is 1.

A number can be divided exactly by numerous divisors if it is a multiple of the divisor, therefore when we determine the factors of two or more numbers, we discover that some factors are common. As an illustration, the factors of 35 are 1, 5, 7, 35 while those of 45 are 1, 3, 5, 9, 15, 45. 1 and.

Hence, 36 is a multiple of two numbers added together without a common factor.

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The ordered pair for the given solution set should be (-1, 6) when the graph solution set for the given inequality function is involved.

What is inequality function?

Since an inequality is merely a particular kind of relation, we can graph it just like we would any other relation. When dealing with inequalities, the trick is to shade large portions of the graph rather than using lines to connect the dots. But you could use some cover.

The given inequality function be like

y > 1 ÷ 3x + 4

The ordered pair refer to the solution set that provided by plotting the graph of the inequality, that expressed the inequality where an equation, plotting the graph along with a solid line, and shading the sides should be above the line of the graph to show the greater than or equal to sign.

Hence, the ordered pair for the given solution set should be (-1,6).

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The solution to the system of equations is x = −7 and y = −1.

To solve the given system of equations using an inverse matrix, we can represent the system in matrix form, Ax=B, then find the inverse of matrix A to solve for 'x'.

Given matrix:

[tex]\left\{\begin{array}{ccc}x-6y=-1\\-2x+9y=5\end{array}\right[/tex]

[tex]\hrulefill[/tex]

First, we rewrite the system of equations in matrix for, Ax=B:

[tex]A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right], \ x = \left[\begin{array}{cc}x\\y\\\end{array}\right], \ B = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]

So, Ax=B can be written as:

[tex]\Longrightarrow \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right] \left[\begin{array}{cc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\left\begin{array}{ccc}\text{The inverse of a 2x2 matrix,} \ \left(\begin{array}{ccc}a&b\\c&d\end{array}\right), \ \text{is given by:}\\\\\\A^{-1}= \dfrac{1}{ad-bc}\left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\end{array}\right}[/tex]

Here,

[tex]\Longrightarrow A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right][/tex]

The determinant ∣A∣ is:

[tex]\Longrightarrow |A|=(1)(9)-(-6)(-2)=9-12\\\\\\\\\therefore |A|=-3[/tex]

Since the determinant is not zero, A has an inverse, which can be calculated as:

[tex]\Longrightarrow A^{-1}= \dfrac{1}{-3}\left(\begin{array}{ccc}9&6\\2&1\end{array}\right)\\\\\\\\\therefore A^{-1}=\left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)[/tex]

[tex]\hrulefill[/tex]

We can solve for 'x' using x=A⁻¹B:

[tex]\Longrightarrow x = \left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\left(\begin{array}{cc}-1\\5\\\end{array}\right)[/tex]

Upon multiplication, we get:

[tex]\Longrightarrow x = \left(\begin{array}{cc}(-3)(-1)+(-2)(5)\\(-2/3)(-1)+(-1/3)(5)\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}3-10\\2/3-5/3\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}-7\\-3/3\\\end{array}\right)\\\\\\\\\therefore \boxed{\boxed{x=\left(\begin{array}{cc}-7\\-1\\\end{array}\right)}}[/tex]

Thus, the solution to the system of equations is x = −7 and y = −1.