AB is a straight line work out the size of angle X

On a coordinate plane, 2 exponential fuctions are shown. Function f (x) decreases from quadrant 2 into quadrant 1 and approaches

Gala2k [10]

Answer:

$g(x)=6(3)^x$

Step-by-step explanation:

We are given that

$f(x)=6(\frac{1}{3})^x$

Function f decreases from quadrant 2 to quadrant 1 and approaches y=0

It cut the y- axis at (0,6) and passing through the point (1,2).

Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.

It passing through the point (-1,2) and cut the y-axis at point (0,6).

Reflection across y- axis:

Rule of transformation is given by

$(x,y)\rightarrow (-x,y)$

Using the rule then we get

$g(x)=6(\frac{1}{3})^{-x}=6(3)^x$

By using

$x^{-a}=\frac{1}{x^a}$

Substitute x=-1

$g(-1)=6\times (\frac{1}{3})=2$

Substitute x=0

$g(0)=6$

Therefore, $g(x)=6(3)^x$ is true.

8 0

2 years ago

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Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

zalisa [80]

General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

Statement 1: "The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

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Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

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Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

$178=x^2+3x-y\\ \\ -6=4x-3y$

8 0

2 years ago

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A local Dominos sold a total of 1600 small pizzas ($9) and pasta dinners ($13) during the Super Bowl. How many of each did Domin

vitfil [10]

S=small pizzas
p=pasta dinners

s+p=1600

9s+13p=15600
multiply first equaiton by -9 and add to the second one

-9s-9p=-14400
9s+13p=15600 +
0s+4p=1200

4p=1200
divide by 4
p=300

sub back

s+p=1600
s+300=1600
minus 300 both sides
s=1300

1300 small pizzas
300 pasta dinners

5 0

2 years ago

The manager of a shopping mall distributed a customer-satisfaction survey by handing it to people as they came through one of th

Nina [5.8K]

Answer:

No. The results of the survey cannot be generalized to the population of all customers of the shopping mall.

Step-by-step explanation:

Survey results are biased, because data is collected from customers who came trough one specific door of the mall.

Some of the customers may be using some other door where satisfaction survey is not given to these people while passing the door.

Therefore survey results does not reflect thoughts of the population of all customers.

4 0

2 years ago

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A farmer has 5 cartons of eggs for sale. Each carton contains 12 eggs.

MariettaO [177]

Answer:

10 eggs

Step-by-step explanation:

5 cartons multiplied by 12 eggs each equals 60 eggs in total.

Therefore 5/6 would be equal to 50/60 since we multiply the denominator and numerator by 10

As a result 10 of the eggs are not brown

4 0

2 years ago