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Answer:

see explanation

Step-by-step explanation:

(1)

y = - x + 4 ( add x to both sides )

x + y = 4

with A = 1, B = 1, C = 4

(2)

y = 5x + 7 ( subtract y from both sides )

0 = 5x - y + 7 ( subtract 7 from both sides )

- 7 = 5x - y , that is

5x - y = - 7

with A = 5, B = - 1, C = - 7

----------------------------------------------------------

(1)

2x + y = 9 ( subtract 2x from both sides )

y = - 2x + 9

with m = - 2, c = 9

(2)

5x + 2y = 7 ( subtract 5x from both sides )

2y = - 5x + 7 ( divide terms by 2 )

y = - \(\frac{5}{2}\) x + \(\frac{7}{2}\)

with m = - \(\frac{5}{2}\) , c = \(\frac{7}{2}\)

The horizontal distance between the base of the ladder and the wall is 8.6 feet.

distance is the length between two points.

To calculate the horizontal distance between the ladder and the wall, we use the formula below.

Formula:

\(\sf cos \ \theta=\dfrac{adjacent(y)}{hypotenuse(h)}\)

Make y the subject of the equation

\(\sf h = \dfrac{y}{ cos\ \theta}\)........ Equation 2

Where:

From the question,

Given:

Substitute these values into equation 2

\(\sf y = \dfrac{24}{(cos \ 69^\circ)}\)

\(\sf y = \dfrac{24}{0.358}\)

\(\sf y =\bold{8.6 \ feet}\)

Hence, The horizontal distance between the base of the ladder and the wall is 8.6 feet.

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Answer:

\(3\)

Step-by-step explanation:

\( - 3( - 5x + 2) + x - 3 = 39\)

\(15x-6+x-3 = 39\)

\( 16x-9= 39\)

\( 16x= 39+9\)

\( 16x=48\)

\(x = 48-16\)

\(x = 3\)

Answer:

x = 3

Step-by-step explanation:

Given

- 3(- 5x + 2) + x - 3 = 39 ← distribute parenthesis and simplify left side

15x - 6 + x - 3 = 39

16x - 9 = 39 ( add 9 to both sides )

16x = 48 ( divide both sides by 16 )

x = 3

The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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Answer:

6/7

Step-by-step explanation:

First, cancel out 16 and 56 by a common factor of 8. The resulting expression is -2/5*-15/7. Then, simply 5 and 15 by a common factor of 5. Then, you will get: -2*(-3/7). The negatives cancel out, so the answer is 6/7.

a) The simplified expression to represent the number of sweets Jack has left after eating 2c sweets is: \(\displaystyle 9c-2c\).

b) To find how many sweets Jack has left if \(\displaystyle c=3\), we substitute \(\displaystyle c=3\) into the expression: \(\displaystyle 9(3)-2(3)=27-6=21\).

Therefore, if \(\displaystyle c=3\), Jack has 21 sweets left.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answers:

(a)  7c

(b)  21

============================

Explanation:

Start with 9c and subtract off 2c to get 9c-2c = 7c.

We can think of it like 9 candies - 2 candies = 7 candies. Replace each "candies" with "c" so things are shortened.

Afterward, plug in c = 3 to find that 7c = 7*3 = 21

Answer:

can u say what subject is that

(0, 1) is a local maxima and (π, −1) is a local minima of the given function.

The given function is f(x)=cos(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.

Amplitude: 1

Period: 2π

Phase Shift: None

Vertical Shift: None

The coordinates to plot the graph are (0, 1), (π/2, 0), (π, -1),....

To find the x-intercept, substitute in 0 for y and solve for x.

To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (π/2 +πn,0), for any integer n

y-intercept(s): (0,1)

Use the derivative to find the maximum and minimum.

(0, 1) is a local maxima and (π, −1) is a local minima

Therefore, (0, 1) is a local maxima and (π, −1) is a local minima of the given function.

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Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Finally, we have \(2\frac{11}{24}\) lbs of mini shrimps.

Given that;

A catering company needs 8.75 lbs of shrimp for a small party. they buy \(3\frac{2}{3}\) lbs of jumbo shrimps, \(2\frac{5}{8}\) lbs of medium-sized shrimps, and some mini-shrimps.

The total of 8.75th is changed as \(8\frac{3}{4}th\\\)

Sum of  \(3\frac{2}{3}\) +  \(2\frac{5}{8}\) this is bought by the company.

So, to purchase the remaining  \(8\frac{3}{4}th\\\) - \(3\frac{2}{3}\) - \(2\frac{5}{8}\)

We use a common denominator of 24 for the fraction parts.

Change \(8\frac{3}{4}\) as \(8\frac{18}{24}\)

Similarly, convert;

\(3\frac{2}{3}\) as \(3\frac{16}{24}\)

\(2\frac{5}{8}\) as \(2\frac{15}{24}\)

By solving all the above conversions, we get;

\(\frac{42-16-15}{24}\) = 11/24

Considering all the factors together we have \(2\frac{11}{24}\) lbs of mini shrimps.

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To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.

Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.

Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.

When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.

Hence the unit of analysis is objective of the section.

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Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.

Taking a look at the rectangle first, we can observe that it has the following area:

=> 120 square feet=  10 feet x 12 feet.

=> 40 square feet =  (1/2)(10 ft)(8 ft).

Consequently, the two triangles' combined area is:

=> 80 square feet =  2 x 40 square feet.

=> (12 square feet) = (1/2)(6 ft)(4 ft).

The total area of all the shapes is as follows:

=> 212 square feet=  120 square feet, 80 square feet, and 12 square feet.

=> 212 square feet of the wall are therefore covered by the design.

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Answer: the answer is 261 ^2 ft!

Step-by-step explanation:

Given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False

A local variable is a type of variable that we declare inside a block or a function, unlike the global variable. They can be used only by the statements that are inside the function or the block of the code. Local variables are not known to functions outside their own.

The variable declared is local within that function that is the declared variable is accessible inside that block itself, it cannot be accessible outside the given function.

Consider the following multiplication function:

ex - void multi()

{

int a = 10,  b = 2, c ;

c = a * b ;

cout << c ;

}

int main()

{

cout << "value for c is :"<< c ;

return 0;

}

Here inside the multi function variable a, b, c are declared and initialized inside the function.

Thus, a local variable is defined inside the body of the function and is not accessible outside of the function.

Therefore, given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False

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Answer:

x = 25.3

Step-by-step explanation:

83.49 = 3.3x

divide both sides by 3.3

x = 25.3

Answer:

x=1, y=1

Step-by-step explanation:

Sub y=2x-1 into 3x+8y=11

3x+8(2x-1)=11

3x+16x-8=11

19x=11+8

19x=19

x=1

Sub x=1 into y=2x-1

y=2(1)-1

y=2-1

y=1

The percentage increase from 5 laps of race on the first day to 9 laps after several weeks is 80%

The distance ran are given as:

Initial = 5 laps

Final= 9 laps

The percentage increase is calculated using:

Percentage = (Final - Initial)/Initial

So, we have:

Percentage = (9 - 5)/5

Evaluate

Percentage = 0.8

Express as percentage

Percentage = 80%

Hence, the percentage increase is 80%

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Answer:

imma celeb chek

Step-by-step explanation:

Part A: A reasonable domain to plot the growth function, considering the context, would be d ≥ 0, indicating that we are interested in studying the growth of the algae from the initial time onwards.

Part B: The y-intercept of the graph represents the initial radius of the algae when the study began, which is 11 mm.

Part C: The average rate of change of the function from d = 2 to d = 7 represents the average rate at which the radius of the algae is increasing per day over that time period.

Part A: To determine a reasonable domain to plot the growth function, we need to consider the context of the problem. In this case, the biologist is studying the growth of algae over time. The equation provided, \(f(d) = 11(1.01)^d\), represents the radius of the algae after d days.

Since time cannot be negative and the biologist concluded her study when the radius was approximately 11.79 mm, it implies that the radius cannot be negative as well.

Therefore, we can infer that the domain of the function should be limited to non-negative values of d.

Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0. Substituting d = 0 into the equation, we have \(f(0) = 11(1.01)^0 = 11(1) = 11.\)

Part C: To find the average rate of change of the function f(d) from d = 2 to d = 7, we need to calculate the slope of the secant line connecting the points (2, f(2)) and (7, f(7)).

Using the given equation, we can find the values of f(2) and f(7) as follows:

\(f(2) = 11(1.01)^2 \approx 11.2221 mm\\f(7) = 11(1.01)^7 \approx 11.6897 mm\)

The average rate of change (slope) is given by (f(7) - f(2))/(7 - 2) = (11.6897 - 11.2221)/(7 - 2) ≈ 0.0931 mm per day.

In this case, it indicates that, on average, the radius of the algae is increasing by approximately 0.0931 mm per day between days 2 and 7.

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Answer:

92

Step-by-step explanation:

Since 92 is the answer, we need to factor out 92

Ex: 1, 2, 4, 23, 46 and 92

1 x 92

4 x 23

Answer:

-2

Step-by-step explanation:

4 + (-6) = -2

Answer:

the answer is the third one k > - 5

Answer/Step-by-step explanation:

 Step 1: Simplify both sides of the inequality.

\(\frac{1}{4}k+\frac{-3}{4}>-2\)

Step 2: Add 3/4 to both sides.

\(\frac{1}{4}k+\frac{-3}{4}+\frac{3}{4}>-2+\frac{3}{4}\)

\(\frac{1}{4}k>\frac{-5}{4}\)

Step 3: Multiply both sides by 4.

\(4*\frac{1}{4}k>4*\frac{-5}{4}\)

K > -5

 So according to this the value of k has to be greater than -5

You can check your answer by substituting the values in for k.

You can use a calculator..

\(\frac{-10-3}{4} >-2\)  

\(\frac{-7-3}{4} >-2\)

\(\frac{-1-3}{4} >-2\)

\(\frac{0-3}{4} >-2\)

Solve these and you will get your 2nd answer.

[RevyBreeze]

Answer:

161453.307585

Step-by-step explanation:

139,594(1 + 0.021)^7

139,594(1.021)^7

139,594 x 1.1565920282

161453.307585

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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7 pints of white paint were used to paint her bedroom wall. This is a great way to ensure that the bedroom wall is painted to her desired color scheme with the right amount of blue and white paint.

The total amount of paint used is 9.5 pints.

One fourth of 9.5 pints is 2.375 pints of blue paint.

The remaining amount of paint is 9.5 - 2.375 = 7.125 pints of white paint.

Therefore, 7 pints of white paint were used to paint her bedroom wall.

Ivania used 9.5 pints of blue and white paint to paint her bedroom wall. One fourth of this amount was blue paint, meaning 2.375 pints of blue paint were used. This leaves the remaining amount of paint as 9.5 - 2.375 = 7.125 pints of white paint. Therefore, 7 pints of white paint were used to paint her bedroom wall. This means that the majority of the paint used was white paint, with only a quarter of the paint used being blue. This is a great way to ensure that the bedroom wall is painted to her desired color scheme with the right amount of blue and white paint.

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g sio2 is always 0.4 mg too high regardless of the weight of the sample taken for analysis. The relative error in parts per thousand would be 400.

This is because the relative error is calculated by taking the difference between the actual value and the measured value, and dividing this by the actual value.

In this case, the actual value is 0.4 mg and the measured value is

0.4 mg + (10% x 0.4 mg) = 0.44 mg. Thus the relative error is

(0.44 – 0.4)/0.4 = 0.1/0.4 = 0.25 = 400 parts per thousand.

The relative error in parts per thousand would be 400.

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The equation of the line is y = 2x + 8 that is parallel to the given line y = 2x + 2 and passes through the point (−3, 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a straight line is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are parallel if they have the same slope.

Let us assume that the line is parallel to y = 2x + 2 and passes through the point (−3, 2).

The slope of the line y = 2x + 2 is 2, Since it is parallel, the slope is also 2. hence:

y - y₁ = m(x - x₁)

y - 2 = 2(x - (-3))

y - 2 = 2(x + 3)

y = 2x + 8

The equation of the line is y = 2x + 8

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An equation of the line that is parallel to the given line and passes through the point (−3, 2) is: 4x + 3y = -6.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:

Points (x, y) = (3, -1)

Points (x, y) = (0, 3)

Substituting the given parameters into the formula, we have;

Slope, m = (3 + 1)/(0 - 3)

Slope, m = 4/-3

Slope, m = -4/3.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -4/3 = -4/3

Note: m represents the slope.

At point (-3, 2), an equation of the other line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 2 = -4/3(x - (-3))

y - 2 = -4/3(x + 3)

y - 2 = -4x/3 - 4

y - 2 = -4x/3 - 4 + 2

y = -4x/3 - 2

Multiplying all through by 3, we have:

3y = -4x - 6

Rearranging the equation, we have:

4x + 3y = -6

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The distance of the  point on the outer edge of the fan travel is found as 9,989,760 inches.

A circular ceiling fan rotates at a constant speed of 80 revolutions per minute. A point halfway between the center and the outer edge travels 97,968 inches in 15 minutes.

To find the distance a point on the outer edge travels in 30 minutes, we'll first calculate the radius of the fan.

Since the halfway point travels 97,968 inches in 15 minutes, it travels 97,968 / 15 = 6,531.2 inches per minute. This distance is equivalent to the halfway point's circumference, which is calculated as π * (0.5 * diameter). Thus, we have:

6,531.2 = π * (0.5 * diameter)

Diameter = (6,531.2) / (0.5 * π) = 4,158.4 / π ≈ 1,324 inches

Now that we have the diameter, we can find the outer edge's circumference: π * diameter = π * 1,324 ≈ 4,162.4 inches.

Since the fan rotates at 80 revolutions per minute, the outer edge point travels 4,162.4 * 80 = 332,992 inches per minute.

Over 30 minutes, the outer edge point travels 332,992 * 30 = 9,989,760 inches.

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Answer:

a. y= 1/3 x + 2

b. x= -6

c. y=2

Step-by-step explanation:

the points are (-3,1)

the gradient is 1/3 as it is perpendicular

1= 1/3 (-3) +c

1= -1 +c

c= 1+1

=2

So, y= 1 x + 2

3

b.

x-intercept is when y=0

so substituting 0 in the equation

here: 0=1/3x + 2

1/3 x = -2

x = -6

c.

y-intercept is when x=0

y=1/3 (0) +2

y=2

Answer:

10 I think-

Step-by-step explanation:

hope this helped :D

This may be right, this may be wrong

The probability that a randomly selected month's number of order is more than 150 is 0.13%

Given, shawn finds that the monthly number of take-out orders at a restaurant is normally distributed with mean 132 and standard deviation 6.

⇒ mean = 132

⇒ standard deviation = 6

Analysis:

Set the monthly number of take out order as x.

From the question, we know:

P(x > 150) = P(x-132/ > 150-132/6)

= P(x=132/6 > 3)

= 1 - P(x-132/6 ≤ 3)

≈ 1 - 0.9987 {standard normal distribution table}

≈ 0.0013

= 0.13%

Hence we get the probability as 0.13%.

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Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.