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anygoal [31]
3 years ago
15

What is the distance between points A = ( 1 , 4 ) and C = ( − 3 , 3.5 ) ?

Mathematics
1 answer:
tino4ka555 [31]3 years ago
3 0

Answer:

4.03units

Step-by-step explanation:

Distance between A and C=√(1--3)²+(4-3.5)²

=√(4)²+(.5)²

=√16+.25

=4.03units

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What is the end behavior of the graph of
lutik1710 [3]

The end behavior of the graph of f(x) = -0.25x2 - 2x + 1 is that A) As x increases, f(x) increases. As x decreases, f(x) decreases.

<h3>What is the end behavior about?</h3>

The end behavior of a function f tells us that the way that the graph function behaves at the "ends" of the x-axis.

Note that the end behavior of a function tells the trend of the graph and in this graph, f(x) -----> +∞ as x----> -∞  (as the value of x decreases the value of f(x) increases) and  f(x) -----> -∞ as x----> +∞ (as the value of x increases the value of f(x) decreases).

Therefore, The end behavior of the graph of f(x) = -0.25x2 - 2x + 1 is that A) As x increases, f(x) increases. As x decreases, f(x) decreases.

See full question below

What is the end behavior of the graph of f(x) = -0.25x2 - 2x + 1?

A) As x increases, f(x) increases. As x decreases, f(x) decreases.

B) As x increases, f(x) decreases. As x decreases, f(x) decreases.

C) As x increases, f(x) increases. As x decreases, f(x) increases.

D) As x increases, f(x) decreases. As x decreases, f(x) increases

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5 0
2 years ago
What would y=x^2 +x+ 2 be in vertex form
balu736 [363]

Answer:

y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

Step-by-step explanation:

y =  {x}^{2}  + x + 2

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

y = a(x - h)^{2}  + k

The following equation above is the vertex form of Quadratic Function.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Formula</u>

h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{4a}

We substitute the value of these terms from the standard form.

y = a {x}^{2}  + bx + c

h =  -  \frac{1}{2(1)}  \\ h =  -  \frac{ 1}{2}

Our h is - 1/2

k =  \frac{4(1)(2) - ( {1})^{2} }{4(1)}  \\ k =  \frac{8 - 1}{4}  \\ k =  \frac{7}{4}

Our k is 7/4.

<u>Vertex</u><u> </u><u>—</u><u> </u><u>Calculus</u>

We can use differential or derivative to find the vertex as well.

f(x) = a {x}^{n}

Therefore our derivative of f(x) —

f'(x) = n \times a {x}^{n - 1}

From the standard form of the given equation.

y =  {x}^{2}  +  x + 2

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times  {x}^{1 - 1} ) + 0

Any constants that are differentiated will automatically become 0.

f'(x) = 2 {x}+ 1

Then we substitute f'(x) = 0

0 =2x + 1 \\ 2x + 1 = 0 \\ 2x =  - 1 \\x =  -  \frac{1}{2}

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

y =  {x}^{2}  + x + 2

y = ( -  \frac{1}{2} )^{2}  + ( -  \frac{1}{2} ) + 2 \\ y =  \frac{1}{4}  -  \frac{1}{2}  + 2 \\ y =  \frac{1}{4}  -  \frac{2}{4}  +  \frac{8}{4}  \\ y =  \frac{7}{4}

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

y = a {(x - h)}^{2}  + k \\ y = (x - ( -  \frac{1}{2} ))^{2}  +  \frac{7}{4}  \\ y = (x +  \frac{1}{2} )^{2}  +  \frac{7}{4}

7 0
3 years ago
Reflect (7, 3) in (a) the x-axis and (b) the y-axis
Kisachek [45]

Answer:

In x-axis: (7,-3), In y-axis: (-7,3)

Step-by-step explanation:

The rule of the reflection of a point across the x-axis is as shown:

The reflection of the point (x,y) across the x-axis is given by (x,-y).

The point given to us is (7,3), when reflected across the x-axis we get:

(x,-y)=(7,-3)

Now, when a point (x,y) is reflected across the y-axis we get the point (-x,y).

So when the point (7,3) is reflected across the y-axis we get: (-x,y)=(-7,3).

3 0
3 years ago
The area of triangle scarf is 21 square inches.
Scrat [10]

the base of the scarf is 7

Step-by-step explanation:

B=2(A/H)

B=2×21÷6=7

2×21=42

42÷6=7

5 0
2 years ago
Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about th
Svetradugi [14.3K]

The conclusion about the functions is they have the same y-intercept.

<h3>How to make conclusion about the functions?</h3>

The complete question is added as an attachment

The function is given as:

f(x) = (x + 4)^2

From the attached graph, the graph has a y-intercept at:

y = 16

This can be represented as:

(0, 16)

Next, we set x = 0 in f(x) = (x + 4)^2

f(0) = (0 + 4)^2

Evaluate

f(0) = 16

This means that the y-intercept of f(x) = (x + 4)^2 is (0, 16)

So, the functions have the same y-intercept

Hence, the conclusion about the functions is they have the same y-intercept.

Read more about y-intercept at

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3 0
1 year ago
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