5,649 rounded to the nearest: 10 =

Answer:

Y = -X - 7

Step-by-step explanation:

y-y1 =m(x-x1)

y-(-2)= -1(x-(-5)

y+2 = -1(x+5)

Solve for y

subtract 2 from both sides

y=-x-5-2

Y = -x-7

Answer:

-2

Step-by-step explanation:

9 - [4^2 - (3 + 2)]

PEDMAS says parentheses first

Work from the inside out

9 - [4^2 - (5)]

9 - [16-5]

9 - [11]

Subtract

9-11

-2

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Answer:

\(\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1\)

Step-by-step explanation:

Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:

\(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\)

Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).

Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0

To find b we use the equation of the focus which is:

\(c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}\)

Substituting the values of a, b, h and k:

\(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1\)

Answer:

1/4.

Step-by-step explanation:

2^-2 = 1/2^2

= 1/4.

Answer:

2) 43

4) 65

Step-by-step explanation:

The first and third quartile of the data can be found by calculating the median of the first and second halves of the data.  For example, the first quartile of the data can be calculated thus:

40,41,43,50,56

41,43,50

43

and the third quartile thus:

62,63,65,78,97

63,65,78

65

Hope it helps <3

Answer:

A) 43

B) 65

Step-by-step explanation:

A) First Quartile = \((N+1)\frac{1}{4}\)

Where N is the number of observations

=> 1st Quartile = (11+1)(1/4)

=> 1st Quartile = (12)(1/4)

=> 1st Quartile = 3rd number

B) Third Quartile = \((N+1)\frac{3}{4}\)

=> 3rd Quartile = (11+1)(3/4)

=> 3rd Quartile = (12)(3/4)

=> 3rd Quartile = 3*3

=> 3rd Quatile = 9th number

Answer:

-9x(5j) + -9x(k)

Step-by-step explanation:

distribute -9x by multiplying it with the different numbers in the parenthesis

To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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Answer:

\(x = -5\)

Step-by-step explanation:

\(5(2) - 3x = 25\\10 - 3x = 25\\-15 = 3x\\-5 = x\)

Step-by-step explanation:

The solution is shown in the image above

Answer: 8 = 23 (-8)4 = (23)4 = 212

1/(2048x)

Step-by-step explanation:Negative number raised to an even power is positive

For example let's look at (-7)6 , where (-7) , a negative number, is raised to 6 , an even exponent :

(-7)6 can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)6 can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 76 which is positive.

We proved that (-7)6 is equal to (7)6 which is a positive number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

Dividing exponential expressions :  x3 divided by x4 = x(3 - 4) = x(-1) = 1/x1 = 1/x

Final result :

1/2048x

im in middle school

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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Answer:

k = -17 + 4x

Step-by-step explanation:

Simplifying

4x + -1k = 17

Reorder the terms:

-1k + 4x = 17

Solving

-1k + 4x = 17

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-4x' to each side of the equation.

-1k + 4x + -4x = 17 + -4x

Combine like terms: 4x + -4x = 0

-1k + 0 = 17 + -4x

-1k = 17 + -4x

Divide each side by '-1'.

k = -17 + 4x

Answer:

The amount of salt in the tank at any moment \(t\) is

           \(f(t)=-\frac {4\times 10^6}{(200+t)^2}+200+t\)

The concentration of salt in the tank when it is at the point of overflowing is \(0.968\).

The theoretical limiting concentration of an infinite tank is \(1\) lb per gallon.

Step-by-step explanation:

Let \(f(t)\) be the amount of salt in the tank at any time \(t.\)

Then, its time rate of change, \(f'(t)\),  by (balance law).

Since three gallons of salt water runs in the tank per minute, containing \(1\)lb of salt, the salt rate is

                               \(3.1=3\)

The amount of water in the tank at any time \(t\) is.

                           \(200+(3-2)t=200+t,\)

Now, the outflow is \(2\) gal of the solution in a minute. That is \(\frac 2{200+t}\) of the total solution content in the tank, hence \(\frac 2{200+t}\) of the salt salt content \(f(t)\), that is \(\frac{2f(t)}{200+t}\).

Initially, the tank contains \(100\) lb of salt,

Therefore we obtain the initial condition   \(f(0)=100\)

Thus, the model is

                       \(f'(t)=3-\frac{2f(t)}{200+t}, f(0)=100\)

                \(\Rightarrow f'(t)+\frac{2}{200+t}f(t)=3, f(0)=100\)

                      \(p(t)=\frac{2}{200+t} \;\;\text{and} \;\;q(t)=3\)   Linear ODE.

 so, an integrating factor is

                 \(e^{\int p dt}=e^{2\int \frac{dt}{200+t}=e^{\ln(200+t)^2}=(200+t)^2\)

and the general solution is

               \(f(t)(200+t)^2=\int q(200+t)^2 dt+c\)

            \(\Rightarrow f(t)=\frac 1{(200+t)^2}\int 3(200+t)^2 dt+c\)

           \(\Rightarrow f(t)=\frac c{(200+t)^2}+200+t\)

Now using the initial condition and find the value of \(c\).

   \(100=f(0)=\frac c{(200+0)^2}+200+0\Rightarrow -100=\frac c{200^2}\)

                                                  \(\Rightarrow c=-4000000=-4\times 10^6\)

            \(\Rightarrow f(t)=-\frac {4\times 10^6}{(200+t)^2}+200+t\)

is the amount of salt in the tank at any moment \(t.\)

Initially, the tank contains \(200\) gal of water and the capacity of the tank is \(500\) gal. This means that there is enough place for

                                 \(500-200=300\) gal

of water in the tank at the beginning. As concluded previously, we have one new gal in the tank at every minute. hence the tank will be full in \(30\)min.

Therefore, we need to calculate \(f(300)\) to find the amount of salt any time prior to the moment when the solution begins to overflow.

       \(f(300)=-\frac{4\times 10^6}{(200+300)^2}+200+300=-16+500=484\)

To find the concentration of salt at that moment, divide the amount of salt with the amount of water in the tank at that moment, which is \(500\)L.

               \(\text{concentration at t}=300=\frac{484}{500}=0.968\)

If the tank had an infinite capacity, then the concentration would be

              \(\lim\limits_{t \to \infty} \frac{f(t)}{200+t}= \lim\limits_{t \to \infty}\left(\frac{\frac{3\cdot 10^6}{(200+t)^2}+(200+t)}{200+t}\right)\)

                              \(= \lim\limits_{t \to \infty} \left(\frac{4\cdot 10^6}{(200+t)^3}+1\right)\)

                               \(=1\)

Hence, the theoretical limiting concentration of an infinite tank is \(1\) lb per gallon.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. The variable is 28 square feet with x = 150 and A = (4)(7).

A variable is anything that can take on any one of a number of values, such as a quantity, a sign for a variable, or an element of a scientific experiment that is susceptible to change.

Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye colour, and vehicle type.

A variable is a value that can be altered depending on the mathematical issue. Numerous mathematical expressions and equations use the generic letters x, y, and z.

1)

\($$\begin{aligned}& \frac{6}{100}=\frac{9}{x} \\& \frac{6 x}{6}=\frac{900}{6} \\& x=\frac{300}{2}\end{aligned}$$\)=150.

2)

\($A=(4)(7)$\)

\($A=28$\) thirty feet

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The length of wire is 82.78 foot.

After guiding wire,

It form a right angle triangle which have

One angle is of 65 degree

perpendicular = 75 foot

And we have to find hypotenuse of the triangle which is length of wire.

Since we know that,

The trigonometric ratio sin is the ratio of opposite side of angle and

hypotenuse.

Therefore,

⇒ Sin65 = 75/hypotenuse

⇒ 0.906 = 75/hypotenuse

⇒  hypotenuse = 82.7 foot

Since hypotenuse of triangle represents  length of wire

So, required length of wire is 82.7 foot.

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Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

Amount earned annually = 24,895

since 12 months are in 1 year'

Amount earned per month = annualy amount earned/12

Amount earned per month = 24,895/12

Amount earned per month = 2074.58

Hence the amount he will earned per month if he is paid a minimum is 2074.58

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Answer:

Step-by-step explanation:

Substituting y = 4x+1 into 2y = -x-1 gives the equation

2(4x+1) = -x-1

Solve the equation:

8x+2 = -x-1

9x = -3

x = -⅓

Substituting y = 4x+1 into 2y = -x-1 will produce the equation 2(4x+1) = -x-1

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. Based on the degree, there are four different main types of equations. Equations that are linear, quadratic, cubic, and polynomial

Given,  the equation y = 4x + 1 and another equation 2y = -x – 1.

Substituting equation 1 into equation 2 we will get

2(4x+1) = -x-1

Solve the equation:

8x+2 = -x-1

9x = -3

x = -⅓

Therefore, The equation 2(4x+1) = -x-1 is created when y = 4x+1 is substituted into 2y = -x-1.

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Answer:

3 7/12

Step-by-step explanation:

Write out the volume of a cylinder shown below

Formula

Hence the volume of the figure = 628.4mi³

Step-by-step explanation:

\(y - y_1 = m.(x - x_1)\)

\(y - 4 = \frac{1}{4} (x - ( - 1))\)

\(y = \frac{1}{4} x + \frac{1}{4} + 4\)

\(y = \frac{1}{4} x + 4 \frac{1}{4} \: \: or \: \: y = \frac{1}{4} x + \frac{17}{4} \)

This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.

A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.

Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.

by the question.

let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:

\(f(x) = (1.20x) + 2\)

In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.

We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:

\(g(x) = 1.20x\)

\(h(x) = x + 2\)

Using function composition, we can write the function for the worker's new hourly wage as:

\(f(x) = h(g(x)) = h(1.20x) = 1.20x + 2\)

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Answer:

460 miles

Step-by-step explanation:

Since it is a ratio problem, you see that the prius drives 70 miles on 2 gallons of gas which gives you 70:2 or 70/2.

You also set up the other ratio as a fraction with the unknown value as x --> x/13.

now, you cross multiply

70/2=x/13

70*13=910

910/2=460

460 miles

Answer:

455 miles

Step-by-step explanation:

Distance Prius can travel with one gallon of gas:

70/2

= 35 miles

Distance Prius can travel with 13 gallons of gas:

35*13

= 455 miles

Hope this helped!

The measure of the length EF of the triangle is; 21

We are given the the triangle BCD and we are told that;

E is the midpoint of BD.

F is the midpoint of CD

Now, since we have those midpoints, it means that by the concept of similar triangles, that;

DF/DC = EF/BC

Since F is the midpoint of DC, then it means that;

2DF = DC

We are given;

EF = 43 - 4x, and BC = 32 - 2x

Thus, we now have;

DF/(2DF) = (43 - 4x)/(32 - 2x)

1/2 = (43 - 4x)/(32 - 2x)

Cross multiply to get;

32 - 2x = 43 - 4x

4x - 2x = 43 - 32

2x = 11

x = 11/2

x = 5.5

Thus;

EF = 43 - 4(5.5)

EF = 43 - 22

EF = 21

Thus, we conclude that the side length EF is 21.

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