Write an equation in point-slope form of the line having the given slope that contains the given point. y= 3 4 ,(5 1 3 ,2 7 8 )

Elvira spend $83 on the fifth order to keep the average within her budget.

What is Average mean?

The average mean of numbers is calculated by dividing the sum of all numbers by the total number of terms.

Given that;

Elvira finds that she has order veggie burgers four times and paid $78, $72, $87, and $90 on the orders.

And, To stay within budget, she needs to be sure her average order of veggie burgers is not more than $82.

Now, Let the fifth order to keep the average within her budget = $x

Then, By the definition of average mean we get;

= 78 + 72 + 87 + 90 + x / 5 = 82

= 327 + x = 82 × 5

= 327 + x = 410

= x = 410 - 327

= x = 83

Thus, Elvira spend $83 on the fifth order to keep the average within her budget.

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The rate of mr Rodriguez to complete 1 job is 1/3 while that of his assistant is 1/4.5.

So if mr Rodriguez works for 1 hour, the job left would be 2/3 of the job. So the total time needed by assistant is:

(2/3) / (1/4.5) = 3 hours

Answer:

3 hours

Answer:

Option: b is the answer.

( f(x)=(x-a)^2(x-b)^4 )

Step-by-step explanation:

Clearly from the graph of the function we could see that zero is not a root of the polynomial function hence option (a) ( f(x)=x(x-a)^3(x-b)^3 ) and option (c) (  f(x)=x(x-a)^6(x-b)^2 )are discarded.

Now we will check for option (b) and option (d)

As the graph touches the x-axis at two point i.e. a and b that means that both the roots of the polynomial equation are of even degree.

Hence, the correct option is:

option: b ( f(x)=(x-a)^2(x-b)^4 ).

It can be deduced that the option that represents the graph is B. f(x)=(x-a)²(x-b)⁴

From the graph, a and b be real numbers where a=b=0. In this case, zero is not a root of the polynomial function

When the graph touches the x-axis at two point l, it implies that means that both the roots of the polynomial equation are of even degree.

In conclusion, the correct option is B.

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width=m

length=5m

Area= l x w

Area=5m x m

Area=5m^2

(^ the exponent or power)

bottom left,

 since the lines are parallel with each other there is no solution

Final answer:

The length of the room is calculated by dividing the area of 271.25 square feet by its width of 15.5 feet, resulting in a length of 17.5 feet.

Explanation:

To find the length of the room given its area and width, we will divide the area by the width. The formula for finding the area of a rectangle is Area = length × width. So, to find the length, we can rearrange this formula as length = Area ÷ width, which means dividing the given area by the width.

We know the area of the room is 271.25 square feet and the width is 15.5 feet. So the calculation for the length will be:

Length = 271.25 sq ft ÷ 15.5 ft

Length = 17.5 ft

Therefore, the length of the room is 17.5 feet.

The two lines 4x + 5y = 10 and 5x - 4y = 28 are perpendicular to each other as they have slopes that are negative reciprocals of each other.

The slope is generally defined as the rate of change of the y-axis with respect to the x-axis.

We know we can determine if two lines are parallel or perpendicular to each other by their slope.

If they are parallel they will have the same slope and if they are perpendicular they will have slopes that are negative reciprocals of each other.

Given are two lines 4x + 5y = 10 and 5x - 4y = 28.

We know the equation of a line is y = mx + b.

∴ 4x + 5y = 10 can be written as 5y = -4x + 10 Or y = -(4/5)x + 5/2.

And 5x - 4y = 28 can be written as -4y = -5x + 28 Or y = (5/4)x - 7.

Thus we can conclude that these two lines are perpendicular to each other as (-4/5) is the negative reciprocal of (5/4).

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Answer:

Diameter= 6 inches

Step-by-step explanation:

Answer:

C. 18,22

Step-by-step explanation:

To determine the fraction of area of triangle XYZ that is occupied by triangle PQR on a square grid, we can compare their linear dimensions and use the fact that area is proportional to the square of these dimensions, or we can approximate the area through summation of small rectangular areas on the grid. Alternatively, vector methods such as the cross product can provide precise area calculations for triangles with known vertices.

Finding the Area of Triangles on a Square Grid

To find what fraction of the area of triangle XYZ is the area of triangle PQR, we follow several steps. First, we can draw both triangles on a square grid and establish their respective areas. If we assume that XYZ is the larger triangle and PQR is the smaller one, we can use the fact that area scales in proportion to the square of the linear dimensions. This means, if the linear dimensions of PQR are half that of XYZ, the area of PQR would be one-fourth that of XYZ. In mathematical terms, if the side length of XYZ is scaled by a factor of 's', the area is scaled by s².

Another method to approximate the area of irregular shapes like these triangles, as mentioned in a reference, is by dividing the shape into smaller, manageable rectangular areas whose sum approximates the total area. Counting the smallest square units within the grid and making rough estimates of the fractional squares can yield the area as well.

To demonstrate the calculation of the area of a triangle through vector methods, one can use the cross product of two vectors defined by the triangle's vertices. Given vertices A(1,2,3), B(2,4,5), and C(1,-8,0), their position vectors can be used to compute the cross product, and the magnitude of this cross product gives twice the area of the triangle ABC. This is a more advanced method and offers a precise way to calculate the area without relying on the grid.

the correct graph is bottom left

 the one that the 2 lines cross each other

When no bags of sand are bought, you can buy 15 bags of mulch with $105.

To find the number of bags of mulch that can be bought with $105 when no bags of sand are bought, we need to substitute x = 0 into the equation 3x+7y = 105. This will allow us to solve for y.

Since x = 0, the equation becomes:

3(0) + 7y = 105

0 + 7y = 105

7y = 105

Dividing both sides by 7, we get:

y = 15

Therefore, when no bags of sand are bought, you can buy 15 bags of mulch with $105.

Answer:

The answer would be (D) 77 coins :)

Step-by-step explanation: