The 6 elephants at the zoo have a combined weight of 11,894 pounds. About how much does each elephant weigh?

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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What’s the domain and range? An airplane travels at 565 mph.

viktelen [127]

Answer:

Domain:

The domain of this can be any value between 0 to 565 miles per hour

Range:

The reasonable range can be the distance traveled which can be from 0 to 13,560 miles (no plane travel is longer than 24 hours, we assume).

Step-by-step explanation:

Domain is the input, set of x values for the function.

Range is the output, set of y values for the function.

This isn't a function essentially, but it is given that an Airplane travels at 565 miles per hour.

We can say that the domain will be the speed of the airplane and the range would be the distance it travels.

Domain:

The domain of this can be any value between 0 to 565 miles per hour

Range:

The reasonable range can be the distance traveled which can be from 0 to (565*24=13,560 miles) 13,560 miles (no plane travel is longer than 24 hours, we assume).

4 0

2 years ago

During geometry class, students are told that ΔTSR ≅ ΔUSV. Marcus states that ΔTSR is mapped to ΔUSV by performing a rotation ab

Paha777 [63]

Answer: Both students are correct.

Explanation:

In rotation a shape is rotated about a fixed point and it does not affect its measurements. it only changes its position.

Now, When Marcus rotated the $\triangle TSR$ about point S then this process did not affect its shape and size this is why he got the $\triangle USV$ which is congruent to the $\triangle TSR$ .

In reflection, when a shape reflected across a line then its all points get reflected across this line. But it also does not affect the measurement of the shape.

So, when Sam mapped $\triangle USV$ by the reflection of $\triangle TSR$ then the measurement of the $\triangle USV$ did not change. And, he also got the congruent triangle.

Thus, we can say that, Both Marcus and Sam are right.

7 1

2 years ago

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James multiplies 38 by 55. He finds three of the four partial products: 40, 150, and

jeka94

Answer:

He is missing 1500, the final solution would be 2090

Step-by-step explanation:

5 times 8 equals 40

5 times 30 equals 150

50 times 8 equals 400

50 times 30 equals 1500

40+150+400+1500= 2090

6 0

2 years ago

The number of ducks to geese in Miller's Pond last year was 2:3. This year the ratio of ducks to geese is 5:9. The number of gee

My name is Ann [436]

No decreased-

Set up equaivalent ratioo. It started out 2 duck to every 3 geese, continue the pattern and see for a change

ducks 2 4 6
geese 3 6 9

but now its 5 ; 9 instead of 6 to 9, therefore the number of ducks decreased

4 0

2 years ago