Colin's piano lesson is 45 minutes, or of an hour, long. If he practices 6 different songs and spends an equal amount of time on each song, what fraction of an hour does he spend practicing each song?​

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Answer:

Point A:  (2, 10)

Point B:  (-3, 0)

Point C:  (-5, -4)

Point D:  (-5, -32)

Step-by-step explanation:

Points A and B are the points of intersection between the two graphs.

Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:

\(\implies 2x+6=-2x^2+18\)

\(\implies 2x^2+2x-12=0\)

\(\implies 2(x^2+x-6)=0\)

\(\implies x^2+x-6=0\)

\(\implies x^2+3x-2x-6=0\)

\(\implies x(x+3)-2(x+3)=0\)

\(\implies (x-2)(x+3)=0\)

\(\implies x=2, -3\)

From inspection of the graph:

To find the y-values, substitute the found x-values into either of the equations:

\(\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}\)

\(\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}\)

Therefore, point A is (2, 10) and point B is (-3, 0).

If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

\(\textsf{Equation 1}: \quad y=2x+6\)

\(\textsf{Equation 2}: \quad y-28=-2x^2+18\)

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

\(\implies 2x+6-28=-2x^2+18\)

\(\implies 2x^2+2x-40=0\)

\(\implies 2(x^2+x-20)=0\)

\(\implies x^2+x-20=0\)

\(\implies x^2+5x-4x-20=0\)

\(\implies x(x+5)-4(x+5)=0\)

\(\implies (x-4)(x+5)=0\)

\(\implies x=4,-5\)

From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

\(\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}\)

\(\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}\)

Therefore, point C is (-5, -4) and point D is (-5, -32).

Answer:

a) A = (2, 10) and B = (-3, 0)

b) C = (-5, -4) and D = (-5, -32)

Explanation:

a) To determine the coordinates of A and B, find the intersection points of  the line "y = 2x + 6" and curve "y = -2x² + 18".

Solve the equation's simultaneously:

y = y

⇒ 2x + 6 =  -2x² + 18

⇒ 2x² + 2x + 6 - 18 = 0

⇒ 2x² + 2x - 12= 0

⇒ 2x² + 6x - 4x - 12 = 0

⇒ 2x(x + 3) - 4(x + 3) = 0

⇒ (2x - 4)(x + 3) = 0

⇒ 2x - 4 = 0, x + 3 = 0

⇒ x = 2, x = -3

Then find value of y at this x points,

at x = 2, y = 2(2) + 6 = 10

at x = -3, y = 2(-3) + 6 = 0

Intersection points: A(2, 10) and B(-3, 0)

b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.

\(2x + 6 = -2x^2 + 18 + 28\)

\(-2x^2 + 18 + 28-2x - 6 = 0\)

\(-2x^2-2x+40=0\)

\(-2x^2-10x+8x+40=0\)

\(-2(x+5)+8(x+5)=0\)

\((-2x+8)(x+5)=0\)

\(x = -5, 4\)

\(\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)\)

Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4

Find y value for Point D :  -2x² + 18 =  -2(-5)² + 18 = -32

\(\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)\)

\(\bf Step-by-step~explanation:\)

Kareem's statement: 4:1 is equal to 12:9. Let's see if this is correct.

\(\bf Step ~1:\)

We have to simplify the ratios. Since 4:1 is already simplified, we do not have to do anything with it. 12:9 could be simplified. To do so, we need to find the greatest common factor (GCF) of both numbers. The GCF of 12 and 9 is 3. Since 3 is the GCF for both numbers, we divide them by 3.

\(\bf 12 /3=4\\9/3=3\)

First number: 4

Second number: 3

Ratio: 4:3

\(\bf Step~2:\)

We compare the ratio 4:3 to 4:1. Since they have different values, they are not equivalent to each other.

\(\large\boxed{\bf Our~final~answer: ~Kareem~is~wrong.}\)

\(\bf {Explanation~in~Step~1}\)

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong

Correct question:

Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because

4 + 8 = 12 and 1 + 8 = 9. Is Kareem correct? Explain how you know

4 : 1 is in its simplest form already

12 : 9

= 12/9

= 4/3

= 4 : 3

Therefore,

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong based on his assumption that 4 + 8 = 12 and 1 + 8 = 9

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Answer:

-1

Step-by-step explanation:

the "slope" of a graph is rise / run

you divide the "rise" from one point on a graph to another  by the "run" from one point to another.

We can use any two points on a graph to find this value. (There are other ways to find slope, but this is the easiest method for find the slope of a graphed line)

We can see two points on the line already pointed out, but we can also look to see other points (that require less math)

[remember, points are written as (x,y) ]
We can see a point at (1,0) and another point at (0, 1)

the "rise" between two points is the difference in y-values.

0 - 1 = -1

{you can also look at the graph/count the boxes}

So, the rise between these two points is -1.

(really, it's a drop)

the "run" between these two points is the difference in x-values.

1 - 0 = 1

so, the run between these two points is 1.

Now, all that's left to do is divide the rise / run:

-1 / 1 = -1

So, the slope of this line is -1.

this can be summed up in the following formula:

\(m = \frac{y_{2} - y_{1}} {x_{2}-x_{1}}\)

where \(m\) is the slope of the graph,

\(x_{1}\) = x-value of first point on graph

\(y_{1}\) = y-value of first point on graph

\(x_{2}\) = x-value of second point on graph

\(y_{2}\) = y-value of second point on graph

the equation of a line

y = mx + b

incorporates the slope (as \(m\))

The probability that an adult resident has 3 or more vehicles 0.54.

The probability of an adult resident having 3 or more vehicles is the sum of the probabilities associated with owning 3, 4, or 5 or more vehicles:

P(3 or more vehicles) = P(3) + P(4) + P(5 or more)

P(3 or more vehicles) = 0.38 + 0.13 + 0.03

P(3 or more vehicles) = 0.54

Therefore, the probability that an adult resident has 3 or more vehicles is 0.54.

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Answer:

Step-by-step explanation:

1. x is inversely proportional to y

x=k/y

k is the constant of proportionality

x =60/y

2. x=60/y

x=60/12

x=5

Answer:

please give more information like what to find

3.5, -10.5

Step-by-step explanation:

Using conditional probability, it is found that there is a 0.00002 = 0.002% probability that an event that occurs in this region is that of an authorized user .

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

In this problem:

Probability of an event in this region:

Hence:

\(P(A) = 0.01\frac{1}{1000} + 0.5\frac{999}{1000} = \frac{0.01 + 0.5(999)}{1000} = \frac{499.51}{1000}\)

The probability of an event and an authorized user is:

\(P(A \cap B) = 0.01\frac{1}{1000} = \frac{0.01}{1000}\)

Hence, the conditional probability is:

\(P(B|A) = \frac{\frac{0.01}{1000}}{\frac{499.51}{1000}} = \frac{0.01}{499.51} = 0.00002\)

0.00002 = 0.002% probability that an event that occurs in this region is that of an authorized user .

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The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)  

When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials may be easily simplified with the use of factoring.

When a polynomial is factored, its factors are expressed as the polynomial's product. Finding the zeros of the polynomial expression or the values of the variables in the supplied expression are both made possible by factoring polynomials.

Here we have

24x⁶ - 1029y³  

Take 3 as common

=> 3(8x⁶ - 343y³)  

As we know 8 = 2³ and 343 = 7³

=> 3[(2x²)³ - (7y)³]  

From the algebraic identities

Take a = 2x² , b = 7y and apply above formula

=> 3[(2x² - 7x)((2x²)²+(2x²)(7y)+(7y)²)]  

=> 3 [ (2x² - 7x) (4x⁴ +14x²y+49y²)]  

Therefore,

(24x⁶ - 1029y³) = 3 (2x² - 7x) (4x⁴ +14x²y+49y²)  

Therefore,

The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)  

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Positive,

because 2*12 equals to 24, and 24 is positive!

The solutions to this system of conics is; x = 6 and y = -4

We are given the system of equations as;

(x - 1)² + (y + 4)² = 25    ------(eq 1)

(x - 1)²/25 + (y + 4)²/100 = 1  ------(eq 2)

From eq 1, we can make (x - 1)² the subject to get;

(x - 1)² = 25 - (y + 4)²  ----(eq 3)

Plug in eq 3 into eq 2 to get;

(25 - (y + 4)²)/25 + (y + 4)²/100 = 1

Multiply through by 100 to get;

4(25 - (y + 4)²) + (y + 4)² = 100

100 - 4(y + 4)² +  (y + 4)² = 100

Solving for y gives y = -4

Plug in -4 for y into eq 1 to get;

(x - 1)² + (-4 + 4)² = 25

√(x - 1)² = √25

x - 1 = 5

x = 6

Now, a conic section is defined as the curve which is the intersection of cone and plane. There are three primary conic sections namely parabola, hyperbola, and ellipse. Thus, the solutions are x = 6 and y = -4.

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Answer:

No, either convert pound to ounces or the other way around.

Step-by-step explanation:

Use 1 lb= 16 oz so 75 lb=16 x 75 =1200 oz ---> 1200 ounces per 1.5 years..

---> 1200 oz/1.5 years (1)

The second equation is 38.4 ounces per 0.75 years  , will be the same as 76.8 ounces per 1.5 years.---->76.8 oz / 1.5 years  (2)

So compare (1) and (2) are not equivalent....

The rates are not equivalent to each other..

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

Use 1 lb= 16 oz

Thus 75 lb=16 x 75 =1200 oz

Means 1200 ounces per 1.5 years..

Now 1200 oz/1.5 years ----- (1)

The second equation is 38.4 ounces per 0.75 years which will be the same as 76.8 ounces per 1.5 years.

76.8 oz / 1.5 years ----- (2)

So compare (1) and (2) are not equivalent to each other.

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Answer:

The n-th term of this sequence appears to be

3

n

−

1

,

n

≥

1

.

Step-by-step explanation:

These are powers of

3

ordered from

3

0

=

1

to

3

a

(for an integer

a

≥

1

). However, the first convenient value for

n

is

1

, not

0

(imagine saying the 0th term of a sequence). Because of that, since the first term is actually

3

0

, we need to start from the first term (

n

=

1

) being

3

1

−

1

. The next is

3

2

−

1

,

3

3

−

1

...

3

n

−

1

.

Determine the price of customer after discount.

Determine the interest paid by individual over 4 years.

The amount paid by individual at the end of 4 years is,

So after the discount the individual had to pay $816 and with no discount had to pay onle $800 after 4 years.

So individual must choose to pay off the price in 4 years without any discount and no interest.

Answer:

C, it is a one to one function

Step-by-step explanation:

A one to one function is when each y-value has its own x-value, which this graph does since negative numbers have negative numbers and positive numbers have positive numbers

Comment if you have any questions. Your welcome! :D

To determine whether the furnace will be adequate for a 1,400 square foot house with a 9-foot ceiling, we need to calculate the volume of the house and compare it to the volume the furnace is designed to heat.

The volume of the house can be found by multiplying the square footage by the ceiling height:

1,400 sq ft x 9 ft = 12,600 cubic feet

Since the furnace is designed to heat 10,000 cubic feet, and the house has a volume of 12,600 cubic feet, the furnace may not be adequate for heating the house. The furnace is not capable to heat the entire house.

The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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Answer:

see below

Step-by-step explanation:

center of circle = (2,-1)

r = 6 -2 = 4

We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

so the equation will be:

( x - 2 )^2 + ( y +1 )^2 =16

The amount of water left in the tub after 5 minutes is; 24 gallons

The given recursive formula is expressed as;

aₙ = aₙ ₋ ₁ - 12

We are told that a₀ represents the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled.

Thus, when n = 1, we have;

a₁ = a₁ ₋ ₁ - 12

a₁ = a₀ - 12

a₁ = 84 - 12

a₁ = 72

Then;

a₂ = a₁ - 12

a₂ = 72 - 12

a₂ = 60

It will seem that it follows a sequence pattern of;

aₙ = 84 - 12n

Thus;

a₅ = 84 - 12(5)

a₅ = 24 gallons

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Answer:

B. 75°

Step-by-step explanation:

The 2 lines are parallel, so corresponding angles theorem should prove that i is equal to 75°

Answer:

75 degrees

Step-by-step explanation:

ANSWER

B. Graph B

EXPLANATION

Graph B is discrete, because there are no values of the functions between each point, you can only know the value of the function for weekends 1, 2, 3, 4 and 5.

On the other hand, graph A is continuous, because there are values for each point on the graph - the points are all connected.

Answer:

False

Step-by-step explanation:

2 + 3x = 5

Put x as 1.1.

2 + 3(1.1) = 5

2 + 3.3 = 5

5.3 = 5

False.

Answer:

Solution,

X=1.1

\(2 + 3x = 5 \\ 2 + 3 \times 1.1 = 5 \\ 2 + 3.3 = 5 \\ 5.3 = 5 \: \: \\ hence \: it \: is \: false\)

Answer:

Well the answer would be 9.

Step-by-step explanation:

All you have to do is put 6 in the place of X. So the new equation would be 5x2+6-7, and all you do is solve that. So multiply 5 and 2 to get 10, than add 10 to 6 and get 16, 16 minus 7 to get your answer of 9.

Hope this is right, pls tell me and sorry its so late lol

Answer:

It's Angle ABC because an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle

Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Answer:

\(y = 4*x+3\)

Step-by-step explanation:

First pick any 2 set of points to find the slope. I chose (1,7) and (3,15)

The slope formula is shown below

\(m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

Now fill in the variables and solve

15 - 3 = 12

3 - 0 = 3

Divide

\(12/3 = 4\)

So the slope is 4

The y intercept is 3 since that is where x = 0

Now we can write the equation

\(y = 4*x+3\)

The given triangle is rotated about 180 degrees and as such, we can say that the triangle CBF is congruent to the triangle EDF.

From the attached image, we see that CB is parallel to ED. We also see that the transversal lines are  BD and CE.

The point E will become the image of point C by a rotation of 180° around the point F.

Now, the point D will be the image of point B by a rotation of 180° around the point F.

Rotation is a type of transformation and as such  ΔEDF will be the image of  ΔCBF.

Therefore we can conclude that ΔCBF ≅ ΔEDF

The second way to prove this congruency is as follows;

∠B = ∠D  (Due to the fact that alternate angles are congruent)

∠C = ∠E  (Due to the fact that alternate angles are congruent)

Now, since CB ≅ ED , then it means that ΔCBF ≅ ΔEDF by SAS congruency postulate

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The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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