Find the value of this expression if x = 5.
x2 – 5

According to the information, the distance from your starting point to the library is 4 miles.

To calculate how far do you live from the library we have to assume that the distance from the starting point to the library is "x" miles.

According to the problem, when you are 75% of the way there, you realize you forgot a book. It means you have traveled 75% of the distance, which is 0.75x miles.

Now, you turn around and bike back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library.

From the starting point, you have traveled 0.75x miles to the point where you forgot the book, and then you traveled back 1/3 of 0.75x miles, which is (1/3)*0.75x = 0.25x miles.

Now you turn around again and bike 3.2 miles to the library. It means that the distance between the point where you realized you don't need the book and the library is 3.2 miles.

Therefore, the total distance from your starting point to the library is:

Simplifying the equation:

Thus, the distance from your starting point to the library is 4 miles.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Answer:

9 1/6

Step-by-step explanation:

multiplication of fractions

your 5 = 5/1

hence it will be 5/1 x 11/6 = 55/6

55 divided by 6 will be equal to 9 with one remainder

so your answer will be 9 1/6

Answer:

Y = 5.5x

The constant is 5.5

since no matter what y and x are there will always be a 5.5 difference

Also mark brainliest please

The required constant of proportionality is 5.5 in the given expression.

Given that,
The equation y = 5.5x represents a proportional relationship. What is the constant of proportionality is to be determined.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
The given proportion equation is,?
y = 5.5x
Where y is the dependent variable and x is the independent variable,
And 5.5 is contant.

Thus, the required constant of proportionality is 5.5 in the given expression.

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Answer:

Step-by-step explanation:

(18 - 6)/(4-2)= 12/2= 6 slope

y - 6 = 6(x - 2)

y - 6 = 6x - 12

y = 6x  - 6

y int= (0, -6)

The paint should be used is Cloudy Sunrise.

As a fraction of 100, a percentage is a number or ratio. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no associated unit of measurement.

Light-at-Dawn: A 1-gallon can normally costs $24, however it is now on sale for 25% less than that amount. This kind of paint needs two coats.

Cloudy Sunrise: A gallon-sized can costs $28. Only one coat of this kind of paint is necessary.

350 square feet will be covered by each gallon at a time.

The price of 1 gallon of light at dawn is 24 - 25/100 * 24 = 18.

1 gallon of clouded sunrise color costs 28 dollars.

It appears overcast. Prior to accounting for the number of square feet that each hue may cover, sunrise color is more expensive.

350 square feet are claimed to be covered by both cans.

if everything else remains the same,.

Dawn color lighting would cost:

18 / 350, or.0514285714, per square foot.

However, the light at dawn color needs two coats.

The total cost per square foot for the light at dawn color would be

2 * 0.0514285714 = 0.1028571429.

The price of a cloudy sunrise is 28/350 = 0.08 per square foot.

This represents the total cost per square foot for cloudy sunrise color since it only needs one coat.

It looks that the total cost of cloudy sunrise color is less expensive than the total cost of light at dawn color, assuming that the second coat of paint uses the same amount of paint as the first coat.

Hence, The paint should be used is Cloudy Sunrise

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As a result, the following parametric equations describe the motion of the heat-seeking particle: x = a - 2t and y = b - 4t

As per the question given,

To find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field T(x,y) = 100 - x^(2) - 2y^(2), we need to use the gradient vector of T(x,y).

The gradient of T(x,y) is given by:

∇T(x,y) = (-2x, -4y)

The heat-seeking particle moves in the direction of maximum increase of temperature, so it moves in the direction of the gradient vector, that is, (-2x, -4y).

To find the path of the particle, we need to integrate the gradient vector starting at point P = (a,b), where a and b are the coordinates of the point on the metal plate where the particle is placed.

So the path of the heat-seeking particle is given by the following parametric equations:

x = a - 2t

y = b - 4t

where t is the parameter that represents time.

These equations represent a straight line in the direction of the gradient vector of T(x,y). The particle moves from point P in the direction of the gradient vector, with a speed proportional to the magnitude of the gradient vector.

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Answer:

A. Eva

Step-by-step explanation:

Given that

The entire school, 250 students, went to the soap box derby.2 vans went to soap box derby and each van held 6 students.

To find the total number of students from the Math Club who went to the soap box derby, we need to add the number of students in each van, the number of times equal to the number of vans.

i.e. by adding 6 (i.e. number of students in each van) 2 (number of vans )number of times, we can get the number of students from Math Club who went to the soap box derby.

Number of Math Club students who went to the soap box derby = 6 + 6 = 12

OR

Simply, multiply number of students in each van with the number of vans .

6 \(\times\) 2 = 12

Therefore, Eva is correct about the calculations.

The double integral for this problem has the result given as follows:

\(\int_{0}^4 \int_0^1 \frac{4x}{1 + xy} dy dx = 20\ln{(5)} - 16\)

Considering the variable y as the inner variable, the double integral is defined as follows:

\(\int_{0}^4 \int_0^1 \frac{4x}{1 + xy} dy dx\)

We start calculating the inner integral, as follows:

\(I = \int_0^1 \frac{4x}{1 + xy} dy\)

Using substitution, we have that:

u = 1 + xy

du = x dy.

dy = du/x

Hence:

\(I = \int \frac{4x}{u} \times \frac{du}{x}\)

\(I = 4\int \frac{1}{u} du\)

I = 4 ln(u).

Returning to x and y, we have that:

I = 4 ln(1 + xy), from y = 0 to y = 1.

Applying the Fundamental Theorem of Calculus for the definite integral, we have that:

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

I = 4ln(1 + x).

Then the outer integral is given as follows:

\(O = \int_{0}^4 4 \ln{(1 + x)} dx\)

Hence:

O = 4[ln(1 + x) + xln(1 + x) - 1 - x], from x = 0 to x = 4.

Applying the Fundamental Theorem again, now for the variable x, we have that:

O = 4[ln(5) + 4ln(5) - 1 - 4] - 4[ln(1) + 0ln(1) - 1 - 0]

O = 4[5ln(5) - 5] + 4

O = 20ln(5) - 20 + 4

O = 20ln(5) - 16.

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Answer: 4.330747

Step-by-step explanation: Hoped this helped:))

Answer:

4.330747

Step-by-step explanation:

Answer:

Mandatory, prohibition, warning, danger, fire, emergency information, and limitation are the seven types of safety signage.

Step-by-step explanation:

Answer:

$9 per week

Step-by-step explanation:

36/4 = 9

Answer:

Step-by-step explanation:

The equation is poorly written and I cannot unfortunately solve it.

Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:

Time = (100 x (Amount - Principal)) / (Principal x Rate)

In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:

Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years

Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.

Step-by-step explanation:

So, Gina's farm produced approximately 471.8 tons of sweet potatoes this year. Rounded to the nearest whole number, this is 472 tons.

When we talk about an increase, we are referring to a change in quantity or value that is greater than the original amount. In other words, an increase means that something has gotten bigger, larger, or more than it was before.

Given by the question.

To find out how much sweet potatoes Gina's farm produced this year, we need to add 40% of last year's production to the amount produced last year:

40% of 337 tons = 0.4 x 337 = 134.8 tons

Adding this to last year's production gives:

337 + 134.8 = 471.8 tons

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Answer:

11/48 = 0.02083

I'm pretty sure-

Answer:

A = number of adult tickets

S = number of student tickets

1033 = total tickets sold

A + S = 1033

5A = money collected for adult tickets

S = money collected for student tickets

2265 = total money collected

5A + S = 2265

two equations and two unknowns:

5A + S = 2265

A + S = 1033

subtract 2nd equation from 1st and solve for A:

4A = 1232

A = 308

Plug in value for A in 1st equation and solve for S:

A + S = 1033

308 + S = 1033

S = 725

It will take 1 hour 40 minutes to fill the swimming pool using four large and four small pumps.

In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

Let R and r the rate of work of the large and the small pumps respectively

4(2R+ r) = 1

4(R+ 3r) = 1

T(4R+ 4r) = 1

Solve for R and r the system of first two equations then substitute in the third and solve for T to find the time.

T = 5/3 hours = 1 hour 40 minutes

It will take 1 hours 40 minutes to 4 large and 4 small pumps to fill the swimming pool.

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Felipe is a software salesman. His base salary is $2400, and he makes an additional $50 for every copy of History is Fun he sells. His total pay if he sells 21 copies of History is Fun is 3450

An employee's basic salary is the amount they are paid before any other remuneration, such as investments, fees, overtime pay, or bonuses, is added to or subtracted from it. A base pay is a set sum of money that a company gives to a worker in exchange for the labor hours that are put in.

The needed equation  relating P to N is   P =  $2400 + 50 N

His total pay if he sells 21 copies of History is Fun is 3450.

Given that,

The base salary (P) = $2400

The earning on per copy sold (N)= $ 50

Now, here his earnings per copy sold = $50

So, the total earnings after selling N copies  

= N ( earning after 1 copy)

=  N ( $50)  = 50 N

Therefore,

Total earnings = Base salary + Money earned after selling N copies.

Thus, P =  $2400 + 50 N

So, the needed equation relating P to N is

P =  $2400 + 50 N

Now, in second case: N = 21

So, P = 2400 +  50 N = 2400 + 50 (21)  

or, P =  2400 + 1050

or, P =  3450

Hence, his total pay if he sells 21 copies of History is Fun is 3450

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let h=-12, k=-11 then

(x-h)^2 + (y-k)^2= r^2

(x+12)^2 + (y+11)^2 = 7^2

x^2 + 24x + 144 + y^2 + 22y + 121 = 49

x^2 + y^2 + 24x + 22y + 144+121-49= 0

x^2 + y^2 + 24x + 22y + 216 = 0 is the required eq

Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

79/9 or 8.4 or 8 4/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

5)

y= 3x - 5  m = 3   b = -5

y = -x -1    m = -1   b = -1

6)

y= x+3   m = 1    b = 3

y= -2x -3   m = -2  b = -3

Answer:

5.

y = 3x - 5  m = 3   b = -5

y = -x -1    m = -1  b = -1

6.

y = x+3   m = 1    b = 3

y = -2x -3   m = -2  b = -3

Answer: 37.9 degrees

Step-by-step explanation:

We can use tangent to solve this, since it's clearly not a 30-60-90 triangle:

tanY = sqrt(23)/sqrt(38)

tanY = 0.778

Y = tan^-1(0.778) = 37.9 degrees. Hope this helps!

Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Check the picture below.

\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

Make sure your calculator is in Degree mode.

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Explanation:

x = number of pounds of coffee

1 pound costs 8.32 dollars

Multiply both quantities by x to show that x pounds cost 8.32x dollars.

Subtract this amount from the $90 and 90-8.32x represents how much is left on the card, which we're told is $65.04

Therefore, the equation to solve is 90-8.32x = 65.04

Solving said equation leads us to...

90-8.32x = 65.04

-8.32x = 65.04-90

-8.32x = -24.96

x = -24.96/(-8.32)

x = 3

Lena bought 3 pounds of coffee

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

Check:

1 pound = $8.32

3 pounds = 8.32*3 = 24.96 dollars

90 - 24.96 = 65.04 which matches what we're told she had left on the card. The answer is confirmed.

Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)