3) Si x = – 2, que vaut 3 + 5x ?

Answer: yea

Step-by-step explanation:

Answer: 5

Step-by-step explanation: f(3) = 2x - 1

substitute the x with 3. 2(3)-1

6-1

5

Answer:

The answer is 5, hope you like!

Answer:

380g

Step-by-step explanation:

hope this answer will help u

The weight of basic kit is 73.33 g and weight of Designer kit 146.68 g.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let the weight of basic kit be x and weight of designer kit be y.

The weight of 2 basic kites and 2 designer kites are 400g.

and, the weight of 4 basic kites and 1 designer kites are 440g.

So, the system of equation is

2x + 2y = 400.............(1)

4x + y = 440

y = 440 - 4x.............(2)

Solving equation (1) and (2), we get

2x + 2(440 - 4x) = 400

2x + 880 - 8x = 400

-6x = -440

x = 73.33

and, y= 440 - 4(73.33)

y = 146.68

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Using a system of equations, the number of hours the artisan worked overtime, y, is 25 hours.

A system of equations is two or more equations solved concurrently.

A system of equations is called simultaneous equations because they are solved at the same time.

The normal hourly rate = sh. 30

The overtime hourly rate = sh. 50

The total hours worked  for a week = 65 hours

The total remuneration for the week = sh. 2,450

Let the normal hours = x

Let the overtime hours = y

x + y = 65 Equation 1

30x + 50y = 2,450 Equation 2

Multiply Equation 1 by 30:

30x + 30y = 1,950 Equation 3

Subtract Equation 3 from Equation 2:

30x + 50y = 2,450

-

30x + 30y = 1,950

20y = 500

y = 25 hours

x = 40 hours

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Answer:

The true statements are the 1st, 2nd, and 4th statement.

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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The length of Ward Island on the map is 8.3 inches, which corresponds to the actual length of 1,660 yards. (option c).

The problem states that on the map, 1/4 inch represents 50 yards. This means that if you measure 1/4 inch on the map, it corresponds to a distance of 50 yards in real life. To find the length of Ward Island on the map, we need to figure out how many 1/4 inches correspond to the actual length of the island.

The problem tells us that the actual length of Ward Island is about 1,660 yards. To find the length on the map, we need to set up a proportion. A proportion is an equation that states that two ratios are equal. In this case, we can set up a proportion using the ratio of inches on the map to yards in real life.

Let x be the length of Ward Island on the map in inches. Then we can write:

1/4 inch / 50 yards = x inches / 1660 yards

To solve for x, we can cross-multiply and simplify:

1/4 inch * 1660 yards = 50 yards * x inches

415 inches = 50 yards * x inches

x inches = 415 inches / 50

x inches = 8.3 inches

The correct answer choice is (C) 8.3 in.

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Answer:

12 m

Step-by-step explanation:

1200 mm = 1.2 m

Step-by-step explanation:

no

10 times smaller

1,200 mm = 1.2 m

29 Nickels

15 Dimes

Hope this is helpful!

The total earning of the Brent for watch group of 7 preschool children is $28.75.

For the given question;

Let 'x' be the number of hours Brent watched the preschool children.

The rate of one hour is $7.25.

The number of hours from 9:00 am to noon is 3 hours.

Let 'y' be the number of children.

The price per child is $1.00.

Thus, the formation of linear equation will be;

= 7.25x + 1.00y

For x = 3 hours and y = 7 child.

= 7.25×3 + 1.00×7

= 21.75 + 7

= 28.75

Thus, the total earnings of the Brent for today is $28.75.

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Given he paid $950 for each credit hour of classes.

If he teaches a total of 51 credit hours.

For 1 credit hour he takes $950. for 51 credit hours, he will take

Thus, the total money for 51 credit hours will be $48,450.

To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.

Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.

Step 1: Determine the step size, h.

Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.

Step 2: Calculate the approximations within each subinterval.

Using Simpson's rule, the integral within each subinterval is given by:

∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]

where x₀, x₁, and x₂ are the data points within each subinterval.

For the first subinterval [2, 2.2]:

∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]

≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]

For the second subinterval [2.2, 2.4]:

∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]

≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]

Step 3: Sum up the approximations.

To obtain the approximation of the total integral, we sum up the approximations within each subinterval.

Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)

Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.

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Answer:

14.500

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    (2)/(5)*(g-7)-(3)=0

Step by step solution :

STEP

1

:

           2

Simplify   —

           5

Equation at the end of step

1

:

  2              

 (— • (g - 7)) -  3  = 0

  5              

STEP

2

:

Equation at the end of step 2

 2 • (g - 7)    

 ——————————— -  3  = 0

      5        

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

        3     3 • 5

   3 =  —  =  —————

        1       5  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 • (g-7) - (3 • 5)     2g - 29

———————————————————  =  ———————

         5                 5  

Equation at the end of step

3

:

 2g - 29

 ———————  = 0

    5  

STEP

4

:

When a fraction equals zero

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 2g-29

 ————— • 5 = 0 • 5

   5  

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  2g-29  = 0

Solving a Single Variable Equation:

4.2      Solve  :    2g-29 = 0

Add  29  to both sides of the equation :

                     2g = 29

Divide both sides of the equation by 2:

                    g = 29/2 = 14.500

One solution was found :

g = 29/2 = 14.500

Answer:

g=29/2

Step-by-step explanation:

2/5(g-7)=3

Distribute:

2/5g - 14/5 = 3

        + 14/5  +14/5

2/5g=29/5 Divide:

29/5 x 5/2 = 29/2

g=29/2 - Improper fraction

As a mixed number it is \(14 \frac{1}{2}\)

Hope this helps :)

The cosine of the angle between the given planes x+2y−2z=2 and the plane 4y−5x+3z=−2 is -0.123 (approx).

Given planes are:x + 2y - 2z = 24y - 5x + 3z = -2

We need to find the cosine of the angle between the given planes.

So, let's find the normal vectors of the planes.

Normal vector to the first plane is <1, 2, -2>

Normal vector to the second plane is <-5, 4, 3>

Now, the cosine of the angle between the planes is given by:

cos(θ) = (normal vector of plane 1 . normal vector of plane 2) / (magnitude of normal vector of plane 1 .

magnitude of normal vector of plane 2)cos(θ) = ((1)(-5) + (2)(4) + (-2)(3)) / (sqrt(1² + 2² + (-2)²) . sqrt((-5)² + 4² + 3²))cos(θ) = -3 / (3√3 . √50)cos(θ) = -0.123

It can also be expressed as:

cos(θ) = cos(pi - θ)So, θ = pi - cos⁻¹(-0.123)θ = 3.208 rad or 184.16 degrees

Therefore, the cosine of the angle between the given planes is -0.123 (approx).

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The cosine of the angle between the two planes is -3 / (15 * sqrt(2)).

To find the cosine of the angle between two planes, we need to find the normal vectors of both planes and then use the dot product formula.

First, let's find the normal vector of the first plane, x + 2y - 2z = 2. To do this, we take the coefficients of x, y, and z, which are 1, 2, and -2 respectively. So the normal vector of the first plane is (1, 2, -2).

Now, let's find the normal vector of the second plane, 4y - 5x + 3z = -2. Taking the coefficients of x, y, and z, we get -5, 4, and 3 respectively. Therefore, the normal vector of the second plane is (-5, 4, 3).

Next, we calculate the dot product of the two normal vectors:
(1, 2, -2) · (-5, 4, 3) = (1)(-5) + (2)(4) + (-2)(3) = -5 + 8 - 6 = -3.

The magnitude of the dot product gives us the product of the magnitudes of the two vectors multiplied by the cosine of the angle between them. In this case, the dot product is -3.

Finally, to find the cosine of the angle, we divide the dot product by the product of the magnitudes of the two vectors:
cosθ = -3 / (|(1, 2, -2)| * |(-5, 4, 3)|).

To compute the magnitudes of the vectors:
|(1, 2, -2)| = sqrt(1^2 + 2^2 + (-2)^2) = sqrt(1 + 4 + 4) = sqrt(9) = 3,
|(-5, 4, 3)| = sqrt((-5)^2 + 4^2 + 3^2) = sqrt(25 + 16 + 9) = sqrt(50) = 5 * sqrt(2).

Substituting the values:
cosθ = -3 / (3 * 5 * sqrt(2)) = -3 / (15 * sqrt(2)).

Therefore, the cosine of the angle between the two planes is -3 / (15 * sqrt(2)).

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Answer:

The concept of "difference of squares" is a special case in factoring where you have a quadratic expression that can be written as the difference of two perfect squares. Specifically, it takes the form of (a^2 - b^2), where 'a' and 'b' represent any real numbers or algebraic expressions.

Let's consider an example to help explain this concept. Suppose we have the expression x^2 - 9. Notice that x^2 is a perfect square because it can be written as (x * x). Similarly, 9 is a perfect square because it can be written as (3 * 3). So, we can rewrite the expression as (x^2 - 3^2), where '3' represents the square root of 9.

Now, according to the special case rule for difference of squares, we can factor this expression by recognizing that it is the difference between two perfect squares. The rule states that (a^2 - b^2) can be factored as (a + b) * (a - b).

Applying this rule to our example, we can factor x^2 - 9 as follows:

x^2 - 9 = (x + 3) * (x - 3).

Here, (x + 3) represents the sum of the square root of x^2 and the square root of 9, while (x - 3) represents the difference between them.

To summarize, the concept of difference of squares refers to a special case in factoring where a quadratic expression can be expressed as the difference between two perfect squares. By applying the special case rule (a^2 - b^2) = (a + b) * (a - b), we can factor such expressions easily.

Step-by-step explanation:

The difference of squares is a special case in factoring quadratic expressions, where we subtract the square of one term from the square of another term. The special case rule for factoring a difference of squares is (a²- b²) = (a + b)(a - b). An example is given to illustrate the process of factoring a difference of squares.

The concept of difference of squares is a special case in factoring where a quadratic expression is a result of subtracting the square of one term from the square of another term. It can be expressed in the form (a² - b²), where 'a' and 'b' are algebraic terms. To factor a difference of squares, we use the special case rule: (a² - b²) = (a + b)(a - b).

For example, let's consider the expression x² - 4. In this case, 'a' is x and 'b' is 2. We apply the special case rule: (x² - 4) = (x + 2)(x - 2). This means that the quadratic expression x² - 4 can be factored as the product of (x + 2) and (x - 2).

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Answer:

Variable = x

Coefficient = 2

Constant = 7

A variable is an unknown that holds an unknown value.

A coefficient is a number that multiplies something.

A constant is a fixed number.

Hope This Helps :)

Answer:

d. 0.771.

Step-by-step explanation:

This probability is equal to the area other than the green triangle divided by the total area of backyard.

Total area = 120^2 = 14400

Area of green triangle = 1/2 * 120 * 55 = 3300

So area of the part of yard not covered by the triangle = 14400 - 3300

and the required probability =  (14400 - 3300) / 14400

= 0.771.

Answer:

d. 0.771

Step-by-step explanation:

What is probability?

Probability is the likelihood of the occurrence of something.

In simpler terms we can say probability = # of favorable outcomes / total # of outcomes.

Understanding the question

Here we have a square and a triangle inside of the square and we want to find the probability that a tennis ball thrown inside of the square will not land inside of the triangle.

So we have # of favorable outcomes as the area of the outside of the triangle but inside of the square ( so area of square - area of triangle ) and we have total # of outcomes as the total area of the square including the triangle

Finding the areas

Area of square

Area of square = (side length)²

the square shown has a given side length of 120ft

So area = 120² = 120 × 120 = 14400

Area of triangle

Area of a triangle = (base length × height) / 2

Here the base length is shared with the side length of the square menaing the base length of the triangle = 120 and the given height of the triangle is 55 feet

So area would = ( 120 × 55 ) / 2 = 3300

Finding the probability

Again we want to find the probability that a ball thrown in the square will not land in the triangle

This can be calculated using the probability formula we created earlier

probability = ( area of square - area of triangle ) / area of square

we have area of square = 14400 and area of triangle = 3300

so probability = (14400 - 3300) / 14400

==> subtract 3300 from 14400

probability = 11100 / 14400 = 0.771 ( rounded )

And we are done!

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Answer:

whats the equation?

Step-by-step explanation:

Answer:

3913

Step-by-step explanation:

Step:1 setup

set up your multiplication problem like this

   91

  43

X_______

Step:2 Multiply 1 x 3=3 Put 3 below the line and 0 as a reminder on top:

0

91

43

x_______

            3

Step 3:Multiply

3 x 9 = 27. Take 27 and add 0 from the previous step to get 27 Enter 27 the bottom:

91

43

X

----------

     273

step 4:Add 0 Enter a 0 at the bottom right as a place holder,because you now move over one digit:

91

43

X

_______

273

+       0

Step 5: Multiply

4 x 1 = 4. Put 4 below the line and 0 as a reminder on top:

0

91

43

x

________

          273

+            40

Step 6:Multiply

4 x 9 = 36 and add 0 from the previous step to get 36. Enter 36 at the bottom:

91

43

x

__________

             273

+          3640

Step 7: Add to get answer

Add up the bottom two numbers (273 + 3640 = 3913 to get the answer:

91

x   43

_________

            273

+          3640

____________

=  3913

Answer:

27 years old

Step-by-step explanation:

Let Alvin's age be x and Elga's age is y:

y - x = 15

x + y = 27

2y = 42 (use elimination method)

y = 21

x = 6 (plug it back into either equation)

Therefore Alvin is 6 and Elga is 27

In a 8.5 x 10⁻⁴ M solution, the percentage of dissociation would be > 4.6%. This is because the concentration of the weak acid is lower, and weak acids tend to dissociate more in dilute solutions.

To answer this question, we can use the relationship between the concentration of the weak acid, its dissociation constant (Ka), and the percentage of dissociation. Since we don't know the Ka of the acid, we cannot directly calculate the percentage of dissociation in the 8.5 x 10^-4 M solution.

However, we can make an assumption that the weak acid behaves similarly in both solutions, since the concentration difference is only by a factor of 10. This means that the percentage of dissociation in the 8.5 x 10^-4 M solution should be similar to that in the 8.5 x 10^-3 M solution.

Therefore, the answer is: the same.

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Answer:

The answer is true.

Step-by-step explanation:

Because we are working on negative integers and if a negative number is leaning more to the right on a number line it is bigger.

The return value of the function call round(3.14159, 3) is c. 3.14. The round function rounds the first argument (3.14159) to the number of decimal places specified in the second argument (3). In this case, it rounds to 3.14.

The function call in your question is round(3.14159, 3). The "round" function takes two arguments: the number to be rounded and the number of decimal places to round to. In this case, the number to be rounded is 3.14159 and the desired decimal places are 3.

The return value is the result of the rounding operation. In this case, rounding 3.14159 to 3 decimal places gives us 3.142.

So, the correct answer is:

b. 3.142

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Answer:

149.49° (nearest hundredth)

Step-by-step explanation:

To calculate the direction of the plane's resultant vector, we can draw a vector diagram (see attachment).

Since the two vectors form a right angle, we can use the tangent trigonometric ratio.

\(\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$ \tan x=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $x$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}\)

The resultant vector is in quadrant II, since the plane is travelling north (positive y-direction) and then west (negative x-direction).

As the direction of a resultant vector is measured in an anticlockwise direction from the positive x-axis, we need to add 90° to the angle found using the tan ratio.

The angle between the y-axis and the resultant vector can be found using tan x = 767 / 452. Therefore, the expression for the direction of the resultant vector θ is:

\(\theta=90^{\circ}+\arctan \left(\dfrac{767}{452}\right)\)

\(\theta=90^{\circ}+59.4887724...^{\circ}\)

\(\theta=149.49^{\circ}\; \sf (nearest\;hundredth)\)

Therefore, the direction of the plane's resultant vector is approximately 149.49° (measured anticlockwise from the positive x-axis).

This can also be expressed as N 59.49° W.

Answer:

7.5 ,9.1 ans. hhfjvfbhhvvnjgvjki