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4 years ago

6

The points (3, 2) and ( -2, -3) are solutions to a system of two linear equations. What must be true about the two linear equati

ons?

1 answer:

Gala2k [10]4 years ago

6 0

Answer:

The two linear equations are the same line

Step-by-step explanation:

two different linear equations can only possibly intersect at one point. once the two lines intersect, they cannot curve back to intersect once again.

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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

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

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

------

<u>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"</u>

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

------

<u>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."</u>

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

------

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

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

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

4 years ago

Read 2 more answers

what is the mistake in this problem and why is it wrong? 15+(√9•7)÷13 = 15+(3•7)÷3 = 15+(21)÷3 = 36+3 =12

Serggg [28]

[Edit:}

Okay! So after you have 15+(21)÷3, you have to remember PEMDAS.

PEMDAS is the order in which you solve equations.

1. Parentheses: you solve everything in the parentheses first, all while following the rules of PEMDAS

2. Exponents: after you solve the things in the parentheses, you do the exponents.

3. Then you do Multiplication or Division, solving in the order from left to right.

4. After, you do Addition or Subtraction, solving in the order from left to right.

So using PEMDAS, we'll solve 15+(21)÷3.

We do division before addition, so 21/3 is 7.

Then you add 15 to 7 and get 22 as your final answer.

Hope this helps!

7 0

3 years ago

Find the numbers b such that the average value of f(x) = 7 + 10x − 9x2 on the interval [0, b] is equal to 8.

barxatty [35]

Answer:

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

Step-by-step explanation:

The mean value of function within a given interval is given by the following integral:

$\bar f = \frac{1}{b-a}\cdot \int\limits^b_a {f(x)} \, dx$

If $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ , $a = 0$ , $b = b$ and $\bar f = 8$ , then:

$\frac{1}{b}\cdot \int\limits^b_0 {7+10\cdot x -9\cdot x^{2}} \, dx = 8$

$\frac{7}{b}\int\limits^b_0 \, dx + \frac{10}{b} \int\limits^b_0 {x}\, dx - \frac{9}{b} \int\limits^b_0 {x^{2}}\, dx = 8$

$\left(\frac{7}{b} \right)\cdot b + \left(\frac{10}{b} \right)\cdot \left(\frac{b^{2}}{2} \right)-\left(\frac{9}{b} \right)\cdot \left(\frac{b^{3}}{3} \right) = 8$

$7 + 5\cdot b - 3\cdot b^{2} = 8$

$3\cdot b^{2}-5\cdot b +1 = 0$

The roots of this polynomial are determined by the Quadratic Formula:

$b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

7 0

3 years ago

What is the number of roots for polynomial function of f(x) = (x^2 + 6)^2

Lena [83]

Answer:

x=±√6i

Step-by-step explanation:

$(x^{2} +6)^{2} =0$

$x^{2}+6=0$

$x^{2} =-6$

x=±√6i

5 0

3 years ago

Really never learned this

kykrilka [37]

The perimeter of a two-dimensional figure is always the sum of its sides.

The exercise mat has a perimeter (P) of <u>36 feet</u>. ...

Let length be <em>L</em>, and width be <em>W</em>.

P = 36

L = 2w

P=2(l+w)=2·(12+6)=36

L = 12 feet

W = 6 feet

8 0

3 years ago