How do you answer this?

Answer:

[tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]

Step-by-step explanation:

The straight line BD passes through points B(2a,2b) and D(c,0).

Therefore, the equation of the straight line BD will be given by  

[tex]\frac{y - 2b}{2b - 0} = \frac{x - 2a}{2a - c}[/tex]

⇒ [tex]y - 2b = \frac{2b}{2a - c}x - \frac{4ab}{2a - c}[/tex]

⇒ [tex]y = \frac{2b}{2a - c} x - \frac{4ab}{2a - c} + 2b[/tex]

⇒ [tex]y = \frac{2b}{2a - c} x + \frac{-4ab + 4ab - 2bc}{2a - c}[/tex]

⇒ [tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]

Therefore, third option is correct. (Answer)

We know that the equation of a straight line passing through the points ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by  

[tex]\frac{y - y_{1} }{y_{1} - y_{2}} = \frac{x - x_{1} }{x_{1} - x_{2}}[/tex]

Answer:

Step-by-step explanation:

       Area of a circular plot is [tex]9856\text{ }m^{2}[/tex].

The area of a circle with radius [tex]r[/tex] is given by [tex]\pi r^{2}[/tex]

       [tex]\pi r^{2}=9856\\r^{2}=9856\times\frac{7}{22}=3136\\r=56\text{ }m[/tex]

So, the radius of the circular plot is [tex]56\text{ }m[/tex].

       Cost of fencing the plot is [tex]32.50\frac{Rs}{m}[/tex].

   Total circumference of the circular plot is given by [tex]2\pi r[/tex]

Circumference = [tex]2\times\frac{22}{7}\times56=352\text{ }m[/tex]

Cost of fencing = [tex]352\text{ }m\times 32.50\frac{Rs}{m}=11440\text{ }Rs[/tex]

∴ Cost of fencing = Rs 11440

Answer:

82.8576

Step-by-step explanation:

P(a)

Explanation I just did it :)

For independent events A and B, the probability of both occurring P(A and B) is the product of their individual probabilities: C. P(A) * P(B).

Independent events are events in probability theory where the occurrence of one event does not affect the occurrence or likelihood of the other.

Let's use the definition of independent events to derive the formula for the probability of the intersection of two independent events.

If events A and B are independent, then the definition of independence is given by:

P(A and B) = P(A) * P(B)

This means that the probability of both events A and B occurring is the product of the individual probabilities of A and B.

So, if A and B are independent events, P(A and B) = P(A) * P(B). Therefore, the correct answer is C. P(A) * P(B).

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Answer:

Equation that represents the total cost is  y =  4 +  2 x

Step-by-step explanation:

Here,  x :  slices of pizza eaten at the dance.

y :  total cost paid in the school dance

Let a : Cost of each slice of pizza.

So, according to the question:

Entrance fee + cost 1 slice of pizza = $6

or, Entrance fee = $ 6 - Cost of 1 slice  .......  (1)

Similarly, Entrance fee + cost 3 slice of pizza = $10

or, Entrance fee = $ 10 - Cost of 3 slice ............ (2)

Comparing both equation , we get:

$ 6 - Cost of 1 slice = $ 10 - Cost of 3 slice

or, 6 - a  = 10 - 3 a

or, 2 a  = 4

⇒ a= 2, So the cost of each slice of pizza = $2

Putting the value of a in 1 we get

Entrance fee =  6 - $ 2 =$4

Now, the cost of x slice of pizza = x ( $2) = 2x

So, the total cost y for x slice of pizza = Entrance fee+ Cost of x  slices

or,  y = $ 4 +  2 x

Equation that represents the total cost is  y =  4 +  2 x

Final answer:

The equation that represents the total cost y after buying x slices of pizza is y = 2x + 4, which includes the cost of each slice of pizza ($2) and the entrance fee ($4).

Explanation:

To write an equation that represents the total cost y after buying x slices of pizza at the dance, you can use the information given to create two points: (1, $6) and (3, $10). From the first point, you know there is a fixed entrance fee plus the cost of one slice of pizza. By the time you purchase two more slices (for a total of three), the cost is $10. This scenario implies that each additional slice of pizza has a constant price.

With two points, you can find the slope of the line, which represents the price of each slice of pizza. The slope m is the change in cost divided by the change in the number of slices: m = ($10 - $6) / (3 - 1) = $4 / 2 = $2 per slice. The entrance fee is the y-intercept of the line, which is the initial cost without any pizza, and can be found by extending the line back to the y-axis. The total cost without any pizza is the cost after one slice minus the cost of that slice, which gives us $6 - $2 = $4.

The final equation becomes y = 2x + 4, where y represents the total cost and x represents the number of slices of pizza purchased.

Answer:

3(5) + 300 = 15 + 300 = 315

300(1.04)^5 = 300 * 1.21665 = 365

In 5 years, the second account is higher.

3(12) + 300 = 336

300(1.04)^12 = 300 * 1.601 = 480

In 12 years, the second account is higher

Answer:

-3 5/6 (-3.83333)

Step-by-step explanation:

(-1x3+2)/3+-(2x6+1)/6

-5/3+-13/6

-5x2/6+-13x1/6

-10/6+-13/6

(-10+-13)/6

-23/6

-(3x6+5)/6

=-3 5/6 or (-3.83333)

Answer:

it is letter B

The given quadrilateral is not a parallelogram, is convex, and is not a square.

The question asks for the statement that is true about the given quadrilateral with vertices A(4,9), B(2,5), C(8,2), and D(10,6). To determine the truth of statements, we need to consider the properties of the given quadrilateral.

One statement that is true is that it is not a parallelogram. This can be proven by showing that opposite sides are not parallel, as the slopes are not equal.

Another statement that is true is that it is a convex quadrilateral. A convex quadrilateral is one where all interior angles are less than 180 degrees. To prove this, we can calculate the angles and show that they are all less than 180 degrees.

Lastly, a true statement is that it is not a square. A square is a special type of parallelogram with 4 equal sides and 4 right angles. We can determine this by calculating the lengths of the sides and showing that they are not all equal.

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Answer:

64 nickels and 24 dimes are there in the piggy bank.

Step-by-step explanation:

There are  $5.60 in the piggy bank in nickels and dimes.

Let x number of nickels and y number of dimes are there.

Now, 1 nickel ≡ 0.05 dollars and 1 dime ≡ 0.1 dollars.

So, 0.05x + 0.1y = 5.6

⇒ 5x + 10y = 560

⇒ x + 2y = 112 ....... (1)

Again, from the condition given we can write that,

So, 3y - 8 = x ........ (2)

Now, solving (1) and (2) we get 3y - 8 + 2y = 112

⇒ 5y = 120

⇒ y = 24  

And from equation (2) we get x = 3y - 8 = 64.

So, there are 64 nickels and 24 dimes in the piggy bank. (Answer)

Answer:

 64 nickels and 24 dimes in the piggy bank.

Step-by-step explanation:

Answer:41

Step-by-step explanation:

Answer:

[tex]BC = 4.8[/tex] and [tex]B_{1}D_{1} = 6.25[/tex]

Step-by-step explanation:

The parallelograms ABCD and [tex]A_{1} B_{1} C_{1}D_{1}[/tex] are similar.

Now, AB = 8 (Given in the figure), so CD = 8.

Now, we can write, [tex]\frac{BC}{B_{1}C_{1}}  = \frac{CD}{C_{1}D_{1}}[/tex]

⇒ [tex]\frac{BC}{3} = \frac{8}{5}[/tex]

{Since, given that [tex]B_{1}C_{1} = 3[/tex] and [tex]C_{1}D_{1} = 5[/tex]}

⇒ [tex]BC = \frac{8 \times 3}{5} = 4.8[/tex] (Answer)

Again, we can write, [tex]\frac{BD}{B_{1}D_{1}}  = \frac{CD}{C_{1}D_{1}}[/tex]

⇒ [tex]\frac{10}{B_{1}D_{1}} = \frac{8}{5}[/tex] {Since, BD = 5 + 5 = 10}

⇒ [tex]B_{1}D_{1} = \frac{5 \times 10}{8} = 6.25[/tex] (Answer)

Answer:

(1,K) hope i could help

Step-by-step explanation:

Answer:

[tex](1,K)[/tex]

Step-by-step explanation:

According to the problem, the mixture must contain K ounces of oil for every gallon of gasoline. That is, each gallon of gasoline equals K ounces, this can be expressed as

[tex](1,K)[/tex]

Where [tex]x=1[/tex] expresses each gallon of gasoline and [tex]y=K[/tex] represents ounces of oil.

Therefore, the coordinate on the graph must represent [tex](1,K)[/tex], that is, K ounces of oil per gallon of gasoline.

Answer:

1.76666666666666666

Answer:

53/30=1.7666666...

Step-by-step explanation:

The right answer is Option B.

Step-by-step explanation:

A unit rate describes how many units of one type of quantity corresponds to one unit of other type of quantity.

A. Trevor spent $49 on 2 theater tickets.

2 theater tickets = $49

1 theater ticket = [tex]\frac{49}{2} = \$24.5[/tex]

B. Sally bought a pack of 5 shirts for $35.

5 shirts = $35

1 shirt = [tex]\frac{35}{5} = \$7\\[/tex]

C. Brandon bought 7 gallons of gas for $14.

7 gallons = $14

1 gallon = [tex]\frac{14}{7}=\$2[/tex]

D . Gina bought nail polish for $5 and a pack of gum for $2.

1 nail polish = $5

1 pack of gum =$2

The pack of 5 shirts for $35 has a unit rate of $7.

The right answer is Option B.

Keywords: unit rate, division

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Answer:

J would be the answer, my friend.

log2 (24/3) = log5 (x)

log(8)/log(2) = log(x)/log(5)

log(x) = [log(5)][3]

log(x) = log(5^3)

x = 5^3 = 125

Step-by-step explanation:

Answer:

x = 125

Step-by-step explanation:

[tex] \log_2 24 - \log_2 3 = \log_5 x [/tex]

Use the rule of subtracting logs:

[tex] \log_b x - \log_b y = \log_b \dfrac{x}{y} [/tex]

[tex] \log_2 \dfrac{24}{3} = \log_5 x [/tex]

[tex] \log_2 8 = \log_5 x [/tex]

[tex] 3 = \log_5 x [/tex]

Use the definition of log:

[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]

[tex] x = 5^3 [/tex]

[tex] x = 125 [/tex]

Answer:

y/x

Step-by-step explanation:

If y is directly proportional to x, then:

y = kx

k is the coefficient of proportionality, or the constant rate of change.  Solving for k:

k = y/x

Answer:

Increasing : [tex]-5<x<-1[/tex]  or [tex]-1<x<1[/tex]

Decreasing : [tex]-8<x<-5[/tex]  or [tex]4<x<7[/tex]

Neither : [tex]1<x<4[/tex]

Step-by-step explanation:

Increasing function : In this function, the y-value increases as the x-value increases.

From the given graph it is clear that the function is increasing on  

[tex]-5<x<-1[/tex]

[tex]-1<x<1[/tex]

Decreasing function : In this function, the y-value decreases as the x-value increases.

From the given graph it is clear that the function is decreasing on  

[tex]-8<x<-5[/tex]

[tex]4<x<7[/tex]

Neither increasing nor decreasing function : In this function, the y-value remains constant as the x-value increases.

From the given graph it is clear that the function is neither increasing nor decreasing on  

[tex]1<x<4[/tex]

To determine if a function is increasing, decreasing, or neither over intervals on a graph, analyze the direction of the graph. If the graph goes up, the function is increasing. If it goes down, the function is decreasing. If it remains flat, the function is neither increasing nor decreasing.

The question asks to determine if the function is increasing, decreasing, or neither over each interval on the given graph. To do this, we need to analyze the direction of the graph. If the graph goes up as we move from left to right, the function is increasing. If the graph goes down, the function is decreasing. If the graph remains flat, the function is neither increasing nor decreasing. Drag the intervals to the appropriate box based on these observations.

Answer:

-3°

Step-by-step explanation:

13°-16°=(-3°)

Answer:

15.43 pounds of meat in a day

Step-by-step explanation:

108 pounds per week,

1 week=7 days,

108/7=15.43

Answer:

15 remainder 3

Step-by-step explanation:

108÷7

7 because 1 week= 7 days

108÷7=

15 remainder 3

Answer: 6x2=y

Step-by-step explanation:

If Mitchell owns 6 pairs of hockey skates, then The equation for the number of hockey stakes can be written as, X - 12 = 0

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Mitchell owns 6 pairs of hockey skates,

The equation for number of hockey stakes  = ?

Suppose, the number of hockey stakes = X

According to given condition,

there are 6 pairs,

It is known that,

1 pair = 2 hockey stakes

So,

The equation is,

X = 2 x Number of pairs,

X = 2 x 6

X = 12

Hence, the equation is X - 12 = 0

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The right answer is Option B.

Step-by-step explanation:

Pieces of bread produced = 800

Pieces of bread sold = 750

Pieces left = Pieces produced - Pieces sold

Pieces left = 800 - 750 = 50

Percentage of bread left = [tex]\frac{Pieces\ left}{Pieces\ of\ bread\ produced}*100[/tex]

[tex]Percentage\ of\ pieces\ left=\frac{50}{800}*100\\Percentage\ of\ pieces\ left=\frac{5000}{800}\\Percentage\ of\ pieces\ left= 6.25\%\\[/tex]

Rounding off to nearest whole percent;

Percentage of pieces left= 6%

The right answer is Option B.

Keywords: percentage, subtraction

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Answer: 4

Step-by-step explanation:

(g*h)(5) = 4

Firstly, h(5) = 5 - 7 = -2

Then, evaluate g(-2) = (-2)^2 = 4

Answer:

The perimeter of the rectangle is 32 - 4y

Step-by-step explanation:

To find the perimeter, we will simply follow the steps below;

First write down the formula for finding the perimeter of a rectangle

The formula for finding perimeter in a rectangle is;

perimeter = 2l +2w

where l= length  of the rectangle  and   w is equal to width of the rectangle

From the question given, length =9 - 2y      and width =7

We can now proceed to insert the values into the formula;

perimeter = 2l +2w

                 =2(9-2y) + 2(7)

Then we will now simplify

perimeter  =2(9-2y) + 2(7)

                 =18 - 4y + 14

                = 18 + 14 - 4y

                 =32 - 4y

Therefore, the perimeter of the rectangle is 32 - 4y

The perimeter of the rectangle is 32-4y.

Step-by-step explanation:

Given information:

The length of the rectangle = 9-2y

The width of the rectangle = 7

Now

The perimeter (P) of the rectangle is :

[tex]P = 2( \text{Length} + \text{width})[/tex]

[tex]P= 2(9-2y+7)\\P=18-4y+14\\P=32-4y[/tex]

Hence, the perimeter of the rectangle is 32-4y.

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Those are the factors of 42 c:

(1, 42), (2, 21), (3, 14) and (6, 7).

Answer:

x^4 -x^3 -9x^2 -11x -4

Step-by-step explanation:

We can use the zero product property

(x-a)  (x-b) (x-c) (x-d)  where a b c d are the roots

(x- -1)(x- -1)(x- -1) ( x-4) since the root -1 is repeated 3 times and 4 is a root

(x+1)(x+1)(x+1) ( x-4)

Foil the first two terms  and the last two terms

(x^2 + 2x+1)( x^2 -3x-4)

Foil again

x^4 -3x^3 -4x^2 +2x^3 -6x^2 -8x +x^2 -3x-4

Combine like terms

x^4 -x^3 -9x^2 -11x -4

Answer:

Step-by-step explanation:

roots = -1, -1, -1, 4

(x + 1)(x + 1)(x + 1)(x - 4) = 0

(x^2 + 2x + 2)(x^2 - 3x - 4) = 0

x^2(x^2 - 3x - 4) + 2x(x^2 - 3x - 4) + 2(x^2 - 3x - 4) = 0

x^4 - 3x^3 - 4x^2 + 2x^3 - 6x^2 - 8x + 2x^2 - 6x - 8 = 0

x^4 - x^3 - 8x^2 - 14x - 8 = 0

Answer:

price before tip (b) = $26

Step-by-step explanation:

29.90 is INCLUDING tip, so the real bill, b, would be less.

Now, since 29.90 is including 15% tip, and we let the original bill be "b", we can say:

b INCREASED by 15% gives us 29.90

We need to come up with an equation and solve for b.

15% means 15/100 = 0.15

Now, we can write:

b + 15% of b = 29.90

or

b + 0.15b = 29.90

then

1.15b = 29.90

b = 29.90/1.15

b = 26

So, price before tip (b) = $26

Answer:

the answer is 26

Step-by-step explanation:

Answer:

35 hectometers

Step-by-step explanation:

1 kilometer=10 hectometers

3 1/2=7/2

7/2*10=35

Answer:

[tex]\large\boxed{3\dfrac{1}{2}\ kilometers=35\ hectometers}[/tex]

Step-by-step explanation:

[tex]PREFIXES\\\\mega\ (M)=10^6\\\\kilo\ (k)=10^3\\\\hecto\ (h)=10^2\\\\deko\ (da)=10\\\\decy\ (d)=10^{-1}=0.01\\\\centi\ (c)=10^{-2}=0.01\\\\mili\ (m)=10^{-3}=0.001\\\\mikro\ (\mu)=10^{-6}=0.000001[/tex]

[tex]3\dfrac{1}{2}=3.5\\\\1\ kilometers=10\ hectometers\ (1\ km=10\ hm)\\\\3\dfrac{1}{2}\ km=3.5\ km=3.5\cdot10\ hm=35\ hm[/tex]

Answer:

X would equal 15

Step-by-step explanation:

-1 × 27 = -27

-27 + 27 =0

18 + 27 = 45

3x ÷ 3 = x

45 ÷ 3 = 15

x = 15

Answer:

12 ≤ x - 7

Step-by-step explanation:

let "x" represent the number

The term decreased means subtraction.

The problem indicates that 12 cannot be greater than a number decreased by 7. Use ≤ which means less than or equal to.

≤ less than or equal to 12 means that 12 is the maximum value.