7. Four-fifths of the senior class went to prom. If
324 seniors went to prom, how many are there
in the senior class?

The square root of a negative number is not a real number, this system of equations has no solution.

What is the system of equations?

A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

To solve for x and y, we can start by solving one of the equations for one of the variables. Let's solve the second equation for y:

2x + y = 5

y = 5 - 2x

Now we can substitute this expression for y in the first equation to get an equation in terms of x:

x² + 3x + (5 - 2x) = 0

x² + 3x + 5 - 2x = 0

x² - x + 5 = 0

We can then solve this equation for x using the quadratic formula:

x = (-3 ± √(9 - 20))/2

x = (-3 ± √(-11))/2

Hence, the square root of a negative number is not a real number, this system of equations has no solution.

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Answer:

A.86

is the answer will show how it's solved if necessary on comment.

hope it helps!!!

0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.

Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.

Let's understand what is positive real numbers.

That is all the real numbers that are greater than or equal to zero.

real numbers are numbers which include both rational and irrational numbers.

whole numbers are positive integers that mean only positive integers.

that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.

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The diagram that shows the rotation of rectangle ABCD by -90 degrees is; Option A

When we rotate positive 90 degrees, the rotation is said to be counterclockwise but when we rotate negative 90 degrees, the rotation is said to be clockwise.

Now, we want to find the rotation that correctly describes rotation of the rectangle ABCD by negative 90 degrees.

Thus, looking at the options, the only one that has the negative 90 degrees rotation that is clockwise will be option A because we see that when we rotate to the right which is clockwise, the first point is A which is exactly what is in option A.

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Answer:

whats the question?

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

9x^2-3x-10 = 0     Use quadratic Formula with a = 9   b = -3  and c = -10

to find the zeroes are   x = 1/6 ± sqrt (41) / 6

Answer:

see below

Step-by-step explanation:

A prime number is a whole number that cannot be exactly divided by another number other than itself and 1.

The two largest one digit prime numbers are 7 and 5. The product of them is 7×5=35.

The two largest two digit prime numbers are: 89 and 97.

89×97=8633

The length of the other leg is (c) √43

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

Hypotenuse = 7

One leg = √6

The length of the other leg can be calculated using

The length of the other leg = √(Hypotenuse^2 - One leg^2)

So, we have

The length of the other leg = √(7^2 - √6^2)

Evaluate

The length of the other leg = √43

Hence, the length is (c) √43

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Complete question

A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.

Average rate of growth over this period is 0.4%.

Average rate of growth over a period is given by:

A=P[tex]e^{rT}[/tex] where,

A- Population at time T

P- Initial population

r-average rate of growth

T-Time period

Now, P=250,000, A=310,000 and T=21 (2000-1980+1)

therefore, putting values in the equation, we get:

310,000=250,000[tex]e^{21r}[/tex]

⇒ [tex]e^{21r}[/tex] = 1.24

⇒ 21r = log(1.24)

⇒ r = 0.0044 or 0.4%.

so, the average rate of growth over this time period is 0.4%.

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Subtract 3

2y + 2xy – x + 4 from 9 - 7x + 3xy - 4

2y

Answer:

Step-by-step explanation:

The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:

h(0) = -5(0)² + 42(0) + 54

h(0) = 0 + 0 + 54

h(0) = 54

Therefore, the initial height of the rocket before it is launched is 54 meters.

Answer: 54 meters.

Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.

To confirm this, you can plug in t = 0 into the quadratic function to get:

h(0) = -5(0)² + 42(0) + 54 = 54 meters

This means that the initial height of the rocket before it is launched is 54 meters.

The amount of margarine needed in Kg for making biscuits is  0.6kg

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.

According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

The amount of margarine needed in Kg is calculated using proportions

If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require

0.225 l  = 0.15 kg

0.9 l = ?

cross multiplying

0.225 * ? = 0.9 * 0.15

? = 0.135 / 0.225

? = 0.6

Angela will require 0.6 kg of margarine

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Answer:

the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Step-by-step explanation:

To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).

Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.

We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.

We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:

y = -3/17 * x + (-3 3/4)

x = (y - (-3 3/4))/(-3/17)

Substituting the coordinates of the corner we found earlier, we get:

x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3

So, the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

The coordinates of Point E are (-4,2) and Point E is a reflection of point D across the X-axis.

Point E has the same y-coordinate as point D, which is 2. However, the x-coordinate of point E is the opposite of the x-coordinate of point D. The x-coordinate of point D is 4, so the x-coordinate of point E must be -4. Therefore, the coordinates of Point E are (-4,2).

As for the reflection, you can imagine a mirror placed on the x-axis (horizontally) and Point D and E being on the same side of that mirror.

Therefore, As Point D is reflected on the mirror, it will be flipped and the x-coordinate changes its sign and becomes -4. Therefore Point E is a reflection of point D across the X-axis.

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See full question below

Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x- coordinate of point D. Drag tiles to complete the statements. (4,2) (4,-2) (-4,2) (-4,-2) X-axis y-axis The coordinates of Point E are --- &Point E  is a reflection of point D across the ---

This mean there are infinite solutions.

Each side is equally satisfied in an endless solution. Infinite is a symbol for boundlessness or limitlessness. Typically, the sign "" is used to denote it.

Solving an equation, Henry gets to the last line of his work and is left with “3 = 3”.

Any value for the Variable would make the equation true, according to infinite solutions.

We can tell which instance it is by examining our findings. If both sides of the equal sign end up having the same word,

such as

3=3 or 3x=3x, then. Finite solutions exist.

This mean there are infinite solutions.

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The trigonometric ratio, cos E of the right triangle is 5 / 13.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;

Therefore,

cos E = adjacent / hypotenuse

Hence,

let's find the hypotenuse side using Pythagoras theorem,

24² + 10² = c²

c = √576 + 100

c = √676

c = 26

cos E = 10 / 26

Therefore,

cos E = 5 / 13

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The vertex of the function f(x) = 10.25 |x - 0.75| will be at (0.75, 0).

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The absolute function is given as,

f(x) = 10.25 |x - 0.75|

Compare the function f(x) with standard equation, then we have

h = 0.75

k = 0

The vertex of the capability f(x) = 10.25 |x - 0.75| will be at (0.75, 0).

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The decimal point is to be placed three places to the left.

What are decimal numbers?

When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.

Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.

If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.

Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.

The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.

The decimal point is to be placed three places to the left.

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the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

given expression p(x)= f(x)/1-f(x)

The derivative of the given expression will be

p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²

Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².

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The fractions 1/12 and 1/4 are equivalent to 2/6.

A fraction is a numeral that represents a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

Given that,

Two fractions are equivalent to 2/6.

There can be many fractions which are equal to 2/6.

Let one fraction is 1/12,

And other fraction is x,

So, according to given condition,

x + 1/12 = 2/6

x = 2/6 - 1/12

x = 3/12

x = 1/4

The required fractions are 1/12 and 1/4.

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Answer:

yx6-5= greater than or equal to 8

Step-by-step explanation:

math brain

The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]

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Answer: The answer is $s$ > 7, which represents the number of seconds that can pass for the temperature in the cryotherapy chamber to drop below -20°F.

Step-by-step explanation: The temperature in the chamber will drop below -20°F when it reaches -20°F + 2.5°F = -17.5°F.

The temperature in the chamber is currently 0°F, so we can represent this situation with the inequality 0 - (2.5 * $s$) < -17.5, where $s$ is the number of seconds that can pass.

We can simplify this inequality by multiplying both sides by -1 to get the following: 2.5 * $s$ > 17.5.

Dividing both sides by 2.5, we get the final inequality: $s$ > 7.

Therefore, the number of seconds $s$ that can pass for the temperature in the cryotherapy chamber to drop below -20°F is greater than 7 seconds.

The proof for the Base Angles Theorem is explained below:

A triangle's opposite angles are congruent if its two sides are congruent. We shall build the angle bisector through the vertex angle of an isosceles triangle in order to demonstrate the Base Angles Theorem. We created two congruent triangles by building the angle bisector, and then we utilized CPCTC to prove that the base angles are congruent. Base angles: The angles that include the base of an isosceles triangle are known as the "base angles."

Any triangle with at least two congruent sides is said to be isosceles. Legs are the isosceles triangle's congruent sides. The base is the other side. Base angles are the angles formed between the base and the legs.

Given: [tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

Prove: ∠M≅∠N

According to the figure,

Given,

[tex]\bar{ LM}[/tex]≅ [tex]\bar{LN}[/tex]

By the definition of mid-point,

O is the mid-point of [tex]\bar{MN}[/tex]

Now, by joining the two points determine and draw a line of [tex]\bar{LO}[/tex]

Now, Again by the definition of mid-point

[tex]\bar{MO}[/tex]≅[tex]\bar{NO}[/tex]

Now, by using reflexive property,

[tex]\bar{LO}[/tex]≅ [tex]\bar{LO}[/tex]

By SSS rule,

ΔLMO≅ΔLNO

By CPCTC rule,

∠M≅∠N

Hence proved.

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The probability that a person has colon cancer given that they have a positive test result is approximately 0.98. The answer lies in the range [0.95, 1.00].

Let's call the probability that a person has colon cancer given that they have a positive test result "p". We can use Bayes' Theorem to find this probability.

Bayes' Theorem is: p(A|B) = (p(B|A) * p(A)) / p(B)

In this case, A is the event that the person has colon cancer, and B is the event that the person has a positive test result.

We are given that:

p(B|A) = 1 (all people who have colon cancer will have a positive test result)

p(B|~A) = 0.02 (2% of people who do not have colon cancer will have a positive test result).

We are also given that p(A) = 2/102 (2 out of 102 people who undergo routine screening have colon cancer) and p(~A) = 100/102 (100 out of 102 people who undergo routine screening do not have colon cancer).

Substituting these values into Bayes' Theorem, we get:

p(A|B) = (1 * (2/102)) / (1 * (2/102) + 0.02 * (100/102))

Simplifying, we get:

p(A|B) = 0.98

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Answer: x = 3 and y = 4

Step-by-step explanation:

Step: Solve x + y= 7 for x:

x + y = 7

x + y + −y= 7+−y

x = −y + 7

Step: Substitute −y + 7forxinx+2y=11:

x + 2y = 11

−y + 7 + 2y = 11

y + 7 = 11

y + 7 + −7 = 11 + −7

y=4

Step: Substitute 4 for y in x = −y + 7:

x = −y + 7

x = −4 + 7

x = 3

Answer:

x = 3 and y = 4

Hope I did it right

The required original price of the coat is given as £95.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95

Hence, the cost of the coat before the sale is £95.

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