Please help me answer this question.

Photography World has a portrait special. A three-pose portrait package has a sitting fee of $35, and a six-pose package has a s

ki77a [65]

We know that a three-pose portrait package has a sitting fee of $35 and <span> a six-pose package has a sitting fee of $60. The total amount they collect is $690.

</span> $\text{Therefore, the equation can be}$ $35x + 60y = 690$

6 0

3 years ago

The points in the table lie on a line. Find the slope of the line.

Rina8888 [55]

5/2 or 2.5
Hope this helps!

6 0

2 years ago

What is the average rate of change for ƒ(x) = −2x + 70 over the interval 2 ≤ x ≤ 6?

Anvisha [2.4K]

Answer:

The average rate of change is -2

Step-by-step explanation:

we know that

To find out the average rate of change, we divide the change in the output value by the change in the input value.

In a linear function the average rate of change is a constant and is equal to the slope of the function

The linear function in slope intercept form is equal to

$f(x)=mx+b$

where

m is the slope or unit rate of the linear function

b is the y-intercept or initial value of the linear function

In this problem we have

$f(x)=-2x+70$

so

$m=-2\\b=70$

therefore

The average rate of change is -2

4 0

3 years ago

Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i

sp2606 [1]

i. The Lagrangian is

$L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)$

with critical points whenever

$L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4$

$L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_\lambda=4x^2+y^2-9=0$

If $x=0$ , then $L_\lambda=0\implies y=\pm3$ .
If $y=0$ , then $L_\lambda=0\implies x=\pm\dfrac32$ .
Either value of $\lambda$ found above requires that either $x=0$ or $y=0$ , so we get the same critical points as in the previous two cases.

We have $f(0,-3)=9$ , $f(0,3)=9$ , $f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25$ , and $f\left(\dfrac32,0\right)=\dfrac{729}4$ , so $f$ has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

$L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)$

with critical points whenever

$L_x=2\lambda x=0\implies x=0$ (because we assume $\lambda\neq0$ )

$L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda$

$L_\lambda=x^2+y^2+z^2-36=0$

If $x=y=0$ , then $L_\lambda=0\implies z=\pm6$ .
If $\lambda=-1$ , then $z=-5$ , and with $x=0$ we have $L_\lambda=0\implies y=\pm\sqrt{11}$ .

We have $f(0,0,-6)=60$ , $f(0,0,6)=-60$ , $f(0,-\sqrt{11},-5)=61$ , and $f(0,\sqrt{11},-5)=61$ . So $f$ has a maximum value of 61 and a minimum value of -60.

5 0

2 years ago

The following dot plot shows the number of players at each table in Bill's Bingo Hall. Each dot represents a different table.

SVEN [57.7K]

The lowest number of people at a table is 0.

<h3>What is the lowest number of people at a table?</h3>

A dot plot is a graph that is used to represent the frequency of a data set. The dots in a dot plot represent the frequency of a number. The greater the height of a number, the higher its frequency. A dot plot is also known as a strip plot or a dot chart.

Looking at the dot plot, it can be seen that there are two dots above 2. This means that at two tables there was no one there.

To learn more about dot plots, please check: brainly.com/question/22746300

#SPJ1

5 0

1 year ago