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2 years ago

After ace is dilated by a factor of 5, it has an area of 100 square inches. What was its area before dilation?

Mathematics

1 answer:

velikii [3]2 years ago

5 0

Answer:

The area of the dilated square is 196

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Can someone help me with this, please? No links or false answers, please

VARVARA [1.3K]

The exact value is found by making use of order of operations. The

functions can be resolved using the characteristics of quadratic functions.

Correct responses:

$\displaystyle 1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7} =\frac{9}{14}$

x = -4, y = 12

When P = 1, V = 6

$\displaystyle x = -3 \ or \ x = \frac{1}{2}$

$\displaystyle i. \hspace{0.1 cm} \underline{ f(x) = 2 \cdot \left(x - 1.25 \right)^2 + 4.875 }$

ii. The function has a minimum point

iii. The value of x at the minimum point, is 1.25

iv. The equation of the axis of symmetry is x = 1.25

<h3>Methods by which the above responses are found</h3>

First part:

The given expression, $\displaystyle \mathbf{ 1\frac{4}{7} \div \frac{2}{3} -1\frac{5}{7}}$ , can be simplified using the algorithm for arithmetic operations as follows;

$\displaystyle 1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7} = \frac{11}{7} \div \frac{2}{3} - \frac{12}{7} = \frac{11}{7} \times \frac{3}{2} - \frac{12}{7} = \frac{33 - 24}{14} =\underline{\frac{9}{14}}$

Second part:

y = 8 - x

2·x² + x·y = -16

Therefore;

2·x² + x·(8 - x) = -16

2·x² + 8·x - x² + 16 = 0

x² + 8·x + 16 = 0

(x + 4)·(x + 4) = 0

x = -4

y = 8 - (-4) = 12

y = 12

Third part:

(i) P varies inversely as the square of V

Therefore;

$\displaystyle P \propto \mathbf{\frac{1}{V^2}}$

$\displaystyle P = \frac{K}{V^2}$

V = 3, when P = 4

Therefore;

$\displaystyle 4 = \frac{K}{3^2}$

K = 3² × 4 = 36

$\displaystyle V = \sqrt{\frac{K}{P}$

When P = 1, we have;

$\displaystyle V =\sqrt{ \frac{36}{1} } = 6$

When P = 1, V = 6

Fourth Part:

Required:

Solving for x in the equation; 2·x² + 5·x - 3 = 0

Solution:

The equation can be simplified by rewriting the equation as follows;

2·x² + 5·x - 3 = 2·x² + 6·x - x - 3 = 0

2·x·(x + 3) - (x + 3) = 0

(x + 3)·(2·x - 1) = 0

$\displaystyle \underline{x = -3 \ or\ x = \frac{1}{2}}$

Fifth part:

The given function is; f(x) = 2·x² - 5·x + 8

i. Required; To write the function in the form a·(x + b)² + c

The vertex form of a quadratic equation is f(x) = a·(x - h)² + k, which is similar to the required form

Where;

(h, k) = The coordinate of the vertex

Therefore, the coordinates of the vertex of the quadratic equation is (b, c)

The x-coordinate of the vertex of a quadratic equation f(x) = a·x² + b·x + c, is given as follows;

$\displaystyle h = \mathbf{ \frac{-b}{2 \cdot a}}$

Therefore, for the given equation, we have;

$\displaystyle h = \frac{-(-5)}{2 \times 2} = \mathbf{ \frac{5}{4}} = 1.25$

Therefore, at the vertex, we have;

$k = \displaystyle f\left(1.25\right) = 2 \times \left(1.25\right)^2 - 5 \times 1.25 + 8 = \frac{39}{8} = 4.875$

a = The leading coefficient = 2

b = -h

c = k

Which gives;

$\displaystyle f(x) \ in \ the \ form \ a \cdot (x + b)^2 + c \ is \ f(x) = 2 \cdot \left(x + \left(-1.25 \right) \right)^2 +4.875$

Therefore;

$\displaystyle \underline{ f(x) = 2 \cdot \left(x -1.25\right)^2 + 4.875}$

ii. The coefficient of the quadratic function is 2 which is positive, therefore;

The function has a minimum point.

iii. The value of x for which the minimum value occurs is -b = h which is therefore;

The x-coordinate of the vertex = h = -b = 1.25

iv. The axis of symmetry is the vertical line that passes through the vertex.

Therefore;

The axis of symmetry is the line x = 1.25.

Learn more about quadratic functions here:

brainly.com/question/11631534

6 0

1 year ago

Read 2 more answers

What is the solution to this system of equations? x-2y=15 2x + 4y=-18

jeyben [28]

Answer:

x = 3; y = -6

Step-by-step explanation:

x - 2y = 15

2x + 4y = -18

Multiply both sides of the first equation by 2. Write the second equation below it, and add the two equations.

2x - 4y = 30

(+) 2x + 4y = -18

---------------------------

4x = 12

4x/4 = 12/4

x = 3

Now we substitute 3 for x in the first equation and solve for y.

x - 2y = 15

3 - 2y = 15

-2y = 12

y = -6

Answer: x = 3; y = -6

4 0

2 years ago

Can someone please explain to me how I'm supposed to solve 2x+y=12? Like step by step solving?

Ne4ueva [31]

Well, first put the function in slop-intercept form (y = mx + b). 2x + y = 12, y - 2x = 12 - 2x, y = -2x + 12. So y = -2x + 12 is the slope-intercept form. Then graph the function to solve for all possible solutions to the function. In y = mx + b, m is the slope and b is the y intercept. In y = -2x + 12, m equals -2, so the slope is -2, and b equals 12, so 12 is the y intercept. Make a point on the y intercept at y = 12. The slope is -2, or -2/1. The graph will be sloping downward. From the point at y = 12, move down two units and to the right one unit and make another point. Then from this new point move down two units and to the right one unit and make another point, and so on. Then to extend the graph in the other direction, start at the point y = 12 and move two units up and one unit to the right and make a point there. Then from this new point move two units up and one unit to the right and make another point there, and so on.

3 0

2 years ago

What is the answer plz help :/

Svetradugi [14.3K]

The answer is b)tens
when you have a division problem you nearly always go to the second (in this case tens) place.

7 0

2 years ago

Read 2 more answers

Which expression shows another way to write 36+16? 4(9)+4 4(9+4) 6(6+8) (6+4)(6+4)

allsm [11]

Answer:

36+16= 52

4(9)+4= 40, which does not equal 52.

4(9+4) = 52.

6(6+8) = 84, which does not equal 52.

(6+4)(6+4) = 100, which does not equal 52.

So, 4(9+4) is correct.

Let me know if this helps!

4 0

2 years ago