The equation y = 4x + 3 models the data below.
x 12 3 4 5 6 78
y 8 13 16 21 26 29 33. 37
a. Calculate the residuals and use the points (x, residual) to make a scatter
plot.
b. Complete the statement below to explain why the model is or is not a good
fit.
The points
So, the equation y = 4x +3
a good fit.
5
2
4-
-2
44
-5-
Point
1
Undo
2
3
Redo
7
x Reset
8
9 10

Using Squeeze theorem, the limit of the function is 0

The Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.

We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).

We can see that

(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)

As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.

Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.

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Answer:

B

Step-by-step explanation:

A quadratic function is a polynomial function which has a degree of 2, and is generally expressed in standard form: [tex]ax^2+bx+c\text{ where }a\ne 0[/tex]. The degree of a polynomial function can be determined by looking at which term has the largest exponent.

By looking at both options, B would be the correct option as it is a polynomial function with degree 2, while option A is a polynomial function with degree 1, also known as a linear equation.

By solving a linear equation we will see that the polygon has 19 sides.

Remember that for a polygon of n sides, the sum of the interior angles is equal to:

(n - 2)*180°

Here we also know that 3 angles are:

136°, 138°, and 146°

And the rest of the angles (n - 3) angles are of 165° each.

Then the sum of the interior angles gives:

136° + 138° + 146° + (n - 3)*165°

And that must be equal to the expression above, so we can write the linear equation:

136° + 138° + 146° + (n - 3)*165°  = (n - 2)*180°

420° + n*165° - 495° = n*180° - 360°

n*165° - 75° = n*180° - 360°

360° - 75° = n*180 - n*165

285° = n*15°

285°/15° = n

19 = n

That is the solution.

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For the local salesman to have a monthly income of $3,000, using mathematical operations, he would need to sell $20,045 worth.

The sales revenue that the local salesman should generate to reach his monthly income target is determined by working backward with the mathematical operations of subtraction, division, multiplication, and addition.

Firstly, the base salary is deducted from the expected monthly earnings to obtain the amount of the sales commission.

The sales commission is equated to its commission percentage through division and multiplication operations.

The result is added to $500 to arrive at the expected sales revenue.

The monthly base salary = $850

Commission = 11% on sales above $500

Needed monthly income = $3,000

Sales commission = $2,150 ($3,000 - $850)

11% = $2,150

100% = $19,545 ($2,150/11% x 100%)

$19,545 = Sales above $500

Total target sales = $20,045 ($19,545 + $500)

Thus, if the salesman expects a monthly income of $3,000, he must generate monthly sales revenue of at least $20,045.

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Answer:

60% of the total calories is from fat

Step-by-step explanation:

We already have our first value 180 and the second value 108. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1Y =

108

180

By multiplying both numerator and denominator by 100 we will get:

STEP 2Y =

108

180

×

100

100

=

60

100

STEP 3Y = 60

Answer:

Step-by-step explanation:

Answer:

y = -x - 3

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given that the point (-8,5) lies on the line and the slope of the line is m=-1, we can use the point-slope form of a linear equation to write the equation of the line.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

So substituting the given point (-8,5) and slope m=-1 into the point-slope form, we get:

y - 5 = -1(x + 8)

Simplifying, we get:

y = -x - 3

This equation is the slope-intercept form of the line that passes through the point (-8,5) and has a slope of -1.

The age of the older brother is 13

From the information given, let their ages by x and y

This is represented as;

x + y = 22

(x - 6) (y -6) = 21

From equation (1), make x, the subject of formula

x = 22 - y   (3)

Substitute equation (3) in equation (2), we get;

(22 - y- 6)(y - 6) = 21

expand the brackets

(16 - y)(y-6) = 21

16y - 96 - y² +6y = 21

collect iike terms

-y² + 22y - 96 - 21 = 0

subtract like terms

-y² + 22y - 117 = 0

y²- 22y + 117 = 0

Find the pairs factors of 117 and substitute the values

y² - 13y - 9y + 117 = 0

(y² - 22y) - (9y + 117) = 0

factorize

y(y - 22) - 9(y - 22) = 0

Then y = 9 and y = 22

The older brothers age = x = 22 - y = 22- 9 = 13

Hence, the value is 13

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The complete question:

The sum of the ages of two brothers is 22 years. Six years ago, the product of their ages was 21 years. What is the age of the elder brother?

Answer:

The equation that this graph corresponds to is y -3/4x + 8

Step-by-step explanation:

The answer choice you chose is correct.

Answer:  True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.

Step-by-step explanation:

Answer:

  -0.155

Step-by-step explanation:

You want the slope of Bob's descent when he descends 3200 feet in a horizontal distance of 3.9 miles.

To find the slope of Bob Dean's descent, we can use the formula:

  slope = (change in elevation) / (change in horizontal distance)

In this case, the change in elevation is 3200 feet and the change in horizontal distance is 3.9 miles.

  slope = -3200 feet / (3.9 miles)

To convert the horizontal distance to feet, we multiply by 5280 (the number of feet in a mile)

  slope = -3200 feet / (3.9 * 5280 feet)

  slope = -3200 / 20,592

  slope ≈ -0.1554

The slope of Bob Dean's descent is about -0.155.

__

Additional comment

As a percent grade, this is a 15.5% grade, very steep. He will need to check his brakes before he starts down.

Therefore , to calculate the  average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.

The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.

Here,

Total cost is equal to total fixed cost plus total variable cost, or TC.

In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.

AVC is now equal to VC divided by Q.

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Answer:

Step-by-step explanation:

You want to use the graph to evaluate the compositions ...

where f(x) = x² -2x -3, and g(x) = x -2.

To find the value of a graphed function, locate the function argument on the x-axis and find the point of intersection of that vertical line with the graph. The y-coordinate of that point is the function value.

Here, we're asked to read the graph to find f(1), use that value to find g(f(1)), then use that value to find f(g(f(1))). This last value is f(-6), which is off the top of the graph. We need to use the equation to find the value:

  f(x) = (x -2)x -3

  f(-6) = (-6 -2)(-6) -3 = 48 -3 = 45

The value of f(g(f(1))) is 45. The equation must be used for this.

Reading the graph for g(0), we find the value to be -2. Then f(-2) is 5, and g(5) is 3.

The value of g(f(g(0))) is 3.

__

Additional comment

A suitable calculator or spreadsheet can evaluate these expressions for you.

Answer:

total probability (1,1),(1,2),(1,3)(1,4) (1,5)(1,6)

 (2,1) (2,2) (2,3) (2,4) (2,5)(2,6)

(3,1)(3,2)3,3 3,4) (3,5) (3,6)

(4,1) (4,2)(4,3)(4,4)(4,5)(4,6)

(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)

(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

3/36=1/12

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The number of tickets that Sam can buy, given the amount he has to spend and the price of admission, is 36 tickets.

The rate of change is $ 0.75 per attraction.

The table on the number of tickets and total cost is:

Number of tickets                 1                        5                 10               15

Total cost                          $ 10. 75             $ 13.75       $17.50        $ 21. 25

The number of tickets that Sam can buy when he has $ 37 is:

= (Amount to spend - Cost of admission ) / Cost per ticket

= ( 37 - 10 ) / 0.75

= 36 tickets

The rate of change is therefore the $ 0.75 charged per ticket per event.

The number of tickets for $ 10. 75 is:

= ( Total cost - Cost of admission ) / cost per ticket

= ( 10. 75 - 10 ) / 0.75

= 1 ticket

The cost of 5 tickets :

= ( Number of tickets x cost per ticket) + cost of admission

= (5 x 0. 75 ) + 10

= $ 13. 75

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To answer this, you get to pick any x-value and then solve for y OR you can pick any y-value and solve for x.

For this one, let's pick x = 3.  We'll then substitute 3 in for x in the equation:

       - (3) + 2y = 7

and then solve for x:

       -3 + 2y = 7

Add 3 to both sides:
              2y = 10

Divide by 2 on both sides:
                y = 5

This shows that (3,5) is a solution for the equation.

Again, you could pick any x-value and solve for y OR pick any y-value and solve for x.  There are an infinite number of solutions.

A coefficient is a number that is multiplied by a function or an expression.

A coefficient is a multiplier to a function or an expression.

For example, in a polynomial function, the coefficients are the terms that multiply the powers of x.

Taking the standard quadratic function as follows:

y = ax² + bx + c.

The coefficients are a, b and c.

Considering this concept, the blanks are completed on the answer at the beginning.

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The required system of equation has no solution.

The more physical interpretation of the idea of two linear equations having a linear equation is that it will always have a singular solution regardless of whether the lines are parallel or coinciding.

We have,

4x + 10y = 57---------------(1)

2x + 5y = 38

Multiply 2

4x + 10y = 76----------(2)

So, above equation (1) and (2) has no solution.as values of x and y are not same for both the equation.

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The measure of side KL from triangle KLM is 22 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle HIJ is similar to triangle KLM.

From the similar triangles,

JH/MK =HI/KL

31/13.9 =49/KL

31KL=49×13.9

31KL=681.1

KL=681.1/31

KL=21.97

KL≈22

Therefore, the measure of side KL is 22 units.

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19.63

Step-by-step explanation: area of circle=pi*r^2

3.14*2.5^2

3.14*6.25

=19.625 rounded to nearest tenth is 19.63

For the graph of the function F(x), when x goes from 0 to 1, F(x) is a negative number with large absolute value. Option D is correct.

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.

When the value of x goes from 0 to 1 the function shifts and the value is decreased gradually, thus giving F(x) as negative number with a large absolute value.

Hence, option D is the correct answer.

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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The graphs of the functions f(x) and g(x) are attached with the answer.

       [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given are the functions f(x) and g(x).

The given functions are -

f(x) = [tex]$100(\frac{3}{5})^{x}[/tex]

g(x) = [tex]$100(\frac{2}{5})^{x}[/tex]

Refer to the graphs of the function f(x) and g(x).

Therefore, the graphs of the functions f(x) and g(x) are attached with the answer.

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Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...

Step-by-step explanation:

How I've been today? Quite magnificent. Thank thou for your generosity.

The given system of equations has infinitely many solutions. Option A is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
- 6x - 2y = 10 - - - -1

y = - 3x - 5  - - - -2

From equation 1
-6x - 2y = 10
Reform the equation,
-2y = 6x + 10

Divide the above equation by -2,
y = -3x - 5

Since the above equation is equivalent to equation 2, therefore the system of equations has infinitely many solutions.

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The trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given triangle WVX, WV=24, WX=51 and VX=45

We know that, sinθ = Perpendicular/Hypotenuse and cosθ = Base/Hypotenuse

Here, sin X= 24/51

sin X= 8/17

cos W= 24/51

cos W= 8/17

Therefore, the trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.

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