The play attendance decreased from 250 students to 195 students. What was the percent decreased

From the graph, we can see the line is passing through the points (-3,0) and (0,-3).

So the x-intercept of the graph is -3 and y-intercept of the graph is -3.

The slope of the line passing through (-3,0) and (0,-3) is

Hence slope of the line is m= - 1.

Now we know that equation of a straight line with slope m and intercept c is

Hence the equation is

Answer:

i) \( 3y^2 -4y +1=0\)

We can divide both sides of the equation by 3 and we got:

\( y^2 -\frac{4}{3}y +\frac{1}{3}=0\)

Now we can complete the square and we got:

\( (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0\)

\( (y- \frac{2}{3})^2 =\frac{1}{9}\)

We take square root on both sides and we got:

\( y-\frac{2}{3}= \pm \frac{1}{3}\)

And the solutions for y are:

\( y_1 = \frac{1}{3} +\frac{2}{3}=1\)

\( y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}\)

ii) \( y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}\)

And with \( a = 3, b=-4 and c =1\) we got:

\( y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}\)

And we got:

\( y_1 = 1 , y_2 =\frac{1}{3}\)

Step-by-step explanation:

Part i

For this case we have the following function given:

\( 3y^2 -4y +1=0\)

We can divide both sides of the equation by 3 and we got:

\( y^2 -\frac{4}{3}y +\frac{1}{3}=0\)

Now we can complete the square and we got:

\( (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0\)

\( (y- \frac{2}{3})^2 =\frac{1}{9}\)

We take square root on both sides and we got:

\( y-\frac{2}{3}= \pm \frac{1}{3}\)

And the solutions for y are:

\( y_1 = \frac{1}{3} +\frac{2}{3}=1\)

\( y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}\)

Part ii

We can use the quadratic formula:

\( y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}\)

And with \( a = 3, b=-4 and c =1\) we got:

\( y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}\)

And we got:

\( y_1 = 1 , y_2 =\frac{1}{3}\)

Answer:

820.341

Step-by-step explanation:

(8.2×10^2)+(3.41×10^-1)​=

(8.2×100)+(3.41×0.1)=

820+0.341=

820.341

Answer:820.341

Step-by-step explanation:

(8.2x10^2)+(3.41x10^-1)

(8.2x10x10)+(3.41 x 1/10)

(8.2x100)+(3.41x0.1)

820+0.341=820.341

Answer:

x = 27°

Step-by-step explanation:

Hello!

Complementary angles add up to 90°.

Since angles A and B are complementary, we can sum up the equations to 90° and solve for x.

The value of x is 27°.

Step-by-step explanation:

y=k/x

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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Weight of apple = 4.5 ounces

Total pieces = 4

Weight of 1 piece = 4.5 ÷ 4

= 1.125

•°• Each piece weighs 1.125 ounces

Hope it helps

Have a nice day

#BTS army

Answer:

(x)^2+ (y+2)^2 = 49

Step-by-step explanation:

The standard form of a circle is

(x-h)^2+ (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-0)^2+ (y--2)^2 = 7^2

(x)^2+ (y+2)^2 = 49

Answer:

Step-by-step explanation:

5,2

Answer:

3

Step-by-step explanation:

7 - 4 is 3

We have that y=121 and that x+y=180. Because this is an isosceles trapezoid. SO we get that

Answer:

the total surface area determined as all surfaces area.

and the lateral surface area determined as middle surface's area.

Answer:

lol

Step-by-step explanation:

Therefore, the solutions to the quadratic equation x² + 7x - 8 = 0 are -8 and 1. The answers are D and E.

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations. Equations can be solved by manipulating the expressions to find the value of the variables that satisfy the equation. Equations can be used to model real-world situations, and they are an important tool in many fields, including mathematics, physics, engineering, and economics.

Here,

To check which values are solutions to the quadratic equation, we can substitute each value into the equation and see if it equals zero.

Substituting -1 into the equation:

(-1)² + 7(-1) - 8 = 1 - 7 - 8 = -14, which is not equal to zero.

Substituting 2 into the equation:

2² + 7(2) - 8 = 4 + 14 - 8 = 10, which is not equal to zero.

Substituting -4 into the equation:

(-4)² + 7(-4) - 8 = 16 - 28 - 8 = -20, which is not equal to zero.

Substituting -8 into the equation:

(-8)² + 7(-8) - 8 = 64 - 56 - 8 = 0, which is equal to zero. Therefore, -8 is a solution to the equation.

Substituting 1 into the equation:

1² + 7(1) - 8 = 1 + 7 - 8 = 0, which is equal to zero. Therefore, 1 is a solution to the equation.

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Answer:

Step-by-step explanation: 36-9 equals 27. You can only fit 4 evenly so thats the answer

The maximum number of boxes that can be stacked in the space of 36 inches keeping 9 inches on the top empty is 4.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that the height of the space in which boxes are needed to be stored is 36 inches high. Also, the height of the box is 6 inches.

But a space of 9 inches must be left at the top. Therefore, the space left to keep the boxes is,

Space left to keep the boxes = 36 inches - 9 inches

                                                 = 27 inches

Now, the number of boxes that can be put in the leftover space is,

Number of boxes = 27 inches / 6 inches

                             = 4.5

Since a half box can be placed in the space, therefore, the number of boxes that can be in the space is 4.

Hence, the maximum number of boxes that can be stacked in the space of 36 inches keeping 9 inches on the top empty is 4.

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The expressions are simplified to give;

15xyz + 12

4ab + 10

Algebraic expressions are simply defined as mathematical expressions that are known to contain variables, constants, coefficient, factors and terms.

These algebraic expressions are also known to be made up of mathematical operations, such as;

From the information given, we have that;

13xyz +9 +2xyz + 3

Now, collect the like terms, we have;

13xyz + 2xyz + 9 + 3

Add the values

15xyz + 12

6ab + (-2ab) + 4 + 6​

expand the bracket and collect like terms

4ab + 10

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Answer:

In one month we have to pay an interest of $0.5.

Step-by-step explanation:

We are given that you borrow $60.00 at 10% interest and we have to find how much we have to pay in one month.

Let the Principal sum of money = P = $60

the rate of interest = R = 10%

Time period = T = \(\frac{1}{12}\)

Assuming the interest is simple interest, so the formula for simple interest is given by;

              Amount = Principal + Simple interest

                 A = P + ( \(\frac{\text{P}\times \text{R}\times \text{T}}{100}\) )

                 A = \(60 + \frac{60 \times 10 \times 1}{100 \times 12}\)

                 A = 60 + 0.5 = $60.5

So, in one month we have to pay an interest of $0.5.

Answer:

-3 or -$3.

Step-by-step explanation:First, the set of integer numbers is the set of all the whole numbers (negatives, zero, and positives).

We want to write a $3 loss, now, the most important part here is that we have a loss, so we must represent this with a negative number

is -3 or -$3 (if we want to also respect the units)

Answer: c

Step-by-step explanation:

Answer: 45 DVDs

Step-by-step explanation:

Assume that the number of DVDs owned by Manuel is x.

In comparison to Manuel therefore, the DVDs owned by Hakeem can be expressed as:

= 3/5 * x - 7

We know that Hakeem owns 20 DVDs so we can use this number to solve for x:

20 = 3/5x - 7

3/5x = 20 + 7

3/5x = 27

x = 27 ÷ 3/5

x = 27 * 5/3

x = 45 DVDs

The statement correctly describes the perpendicular bisector construction below The construction of JK to bisect GH: Option D is the correct answer

The term perpendicular bisector refers to the line that divides another line into two equal parts, making an angle of 90 degrees. The term is made up of two words, perpendicular and bisector.

Perpendicular refers to angle 90 degrees, while the bisector refers to dividing into two equal parts.

In the picture, the main line is GH while JK is the line constructed to bisect the main line

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Answer:

volume of tank is 157.5m

Step-by-step explanation:

that's too high

ANSWERS

a. True

b. False

c. True

d. False

EXPLANATION

a. Regions B and C are both rectangles with the same side lengths. Therefore, they are congruent rectangles, so the areas must be the same.

b. For this item we have to find the areas of region A and C.

Region A is a trapezoid. The area is:

The area of region C is:

Two times the area of region C is 96ft², so this statement is false.

c. In the previous item we found the area of regions A and C. From item a we know that the area of region C is the same area of region B. The area of the figure is:

This statement is true.

d. Since regions B and C have the same area, saying 'the sum of the areas of regions B and C' is the same as saying 'double the area of region C'. From item b, we know that the sum of areas B and C is 96ft², and area A is 84ft².

Area A is less than the sum of areas B and C. Therefore this statement is false.

Quadratic function whose graph has its vertex

at (−1, 2) and its y-intercept at y = 3 is f(x) = \((x+1)^{2}\) + 2

What do you mean by quadratic equation?

A quadratic equation in algebra is any equation that can be transformed in standard form like the following:

\(ax^{2} +bx+c\)

Where x stands for an unknown and a, b, and c are known numbers. The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient

It is given that graph of the quadratic funcion has vertex(-1,2) and y-intercept at y=3

Now, using formula, f(x) = a\((x-h)^{2}\) + k, where (h,k) is the vertex of the parabola.

Here, vertex of the quadratic function is (-1,2)

So, f(x) = a\((x+1)^2\) + 2

Now, we need to solve for a.

y-intercept is given as y=3, which means f(x)= 3 when x=0

Using this we get ,
f(0) = 3

a(1) + 2 = 3

a + 2 = 3

a = 3 - 2

a = 1

Quadratic function become:

f(x) = \((x+1)^{2}\) + 2

Therefore, quadratic function whose graph has its vertex

at (−1, 2) and its y-intercept at y = 3 is f(x) = \((x+1)^{2}\) + 2

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Answer:

Step-by-step explanation:

Because you already know what 1lb of flour is in the small bag you only have to find the price per pound in the 50lb bag so you would do $7/50 giving you $0.14 soo the Large bag would be cheaper

Answer:

Its D

Step-by-step explanation:

Its D because a, b,c are not actually answer there are what the variable are so the answer is D also tell me if you got it right.

Answer:

55 for number 3

hope it helps

The probability that a worker selected at random makes between $300 and $350 is 0.1359 Or 13.6%.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

Given, Weekly wages at a certain factory are normally distributed.

Mean(\(\overline{x}\)) = 400, S.D(\(\sigma\)) = 50.

Now, Since the wages are normally distributed we know,

\(z = \frac{x - \overline{x}}{\sigma}\).

Therefore,

z = (300 - 400)/50.

z = - 2.

And

z = (350 - 400)/2.

z = - 1.

Now, from the z-table,

P(z ≤ - 2) = 0.0228 and P(z ≤ - 1) = 0.1587.

Combining the two we have P( - 2 ≤ z ≤ - 1) =  0.1587 - 0.0228.

P( - 2 ≤ z ≤ - 1) = 0.1359.

As a result, the likelihood that a randomly chosen employee will earn between $300 and $350 is 0.1359, or 13.6%.

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The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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