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An equation that describes the graph is [tex]y=-x^{2} +1[/tex]

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

"It is a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. "

For given question,

The graph describes the parabola.

The parabola opens downward, so the equation of the parabola would be,

[tex]y=-x^{2}[/tex]

We know that, for a function f(x) is transformed to f(x) + c if c > 0 then the graph of the function moves up by c units.

if c < 0 then the graph of the function moves down by c units.

As the graph of the parabola moves down by 1 unit, the equation of the parabola would be,

[tex]y=-x^2+1[/tex]

Therefore, the equation that describes the graph is [tex]y=-x^{2} +1[/tex]

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The answer is Option C) 7th graders in her school.

In order to ascertain the suitability of a candidate for any popular position, his popularity can be assessed by taking a survey of the concerned sample.

Answer:

She should ask the 7th graders in  the school

Step-by-step explanation:

Because their opinion is important in electing the president.

To solve this, we need to use our trignometric functions;

   ⇒ look at the diagram attached

Let's examine what the problem wants:

Let's examine what the problem gives us:

Let's solve:

   [tex]sin(45)=\frac{5}{x} \\5=x*sin(45)\\x = \frac{5}{sin(45)} \\x=7.07[/tex]

Answer: 7.1 (rounded to nearest tenth)

Hope that helps!

Answer:

[tex]5\sqrt2[/tex]

Step-by-step explanation:

This is a 45-45-90 triangle so we can find all the side lengths easily.

The ratio between the base and the hypotenuse of a 45-45-90 triangle is [tex]1:\sqrt2[/tex], which means for this triangle it would be [tex]5:5\sqrt2[/tex]. This means the length of the hypotenuse is [tex]5\sqrt2\\[/tex], which is [tex]x[/tex], which is the answer.

Answer:

34.48cm²

Step-by-step explanation:

Assuming the shaded area doesn't contain the triangle:

area of triangle = bh/2

area of triangle = 4(2)/2

area = 4

area of circle = πr²

area = π3.5²

area = 38.48

area of shaded = 38.48 - 4

area = 34.48cm²

[tex]y= 6x -4~~~~~~...(i)\\\\y = 5x -3~~~~~~...(ii)\\\\\text{From (i) and (ii):}\\\\~~~~~6x -4 = 5x -3\\\\\implies 6x -5x = -3 + 4\\\\\implies x = 1\\\\\text{Substitute x = 1 in equation (i):}\\\\y = 6(1) -4 = 2\\\\\text{Hence,}~ (x,y) = (1,2)[/tex]

Answer:

16 cm²/m²

Step-by-step explanation:

The formula to find the area of a triangle is:

 Area of the triangle = [tex]\frac{1}{2}[/tex] × base × height

Where base = 8 and height = 4

 So, the area of the triangle =  [tex]\frac{1}{2}[/tex] × 8  × 4 = 16 cm²/m²

Answer:

equivalent. not equivalent. not equivalent

Step-by-step explanation:

Answer:

7.070 to the nearest thousandth

Step-by-step explanation:

You could use a calculator or do it manually using long division:

61)431 .2500(7.0695 <---------Quotient

    427

        425

         367

           580

           549

              310

               305

Step-by-step explanation:

[tex] \sin {}^{2} ( - 300) \cos {}^{2} (120) + \cos {}^{2} ( - 240) \sin {}^{2} (390) = \frac{1}{4} [/tex]

[tex] \sin {}^{2} (60) \cos {}^{2} ( {}^{} 120) + \cos {}^{2} (120) \sin {}^{2} (30) [/tex]

[tex] \frac{3}{4} \frac{1}{4} + \frac{1}{4} \frac{1}{4} [/tex]

[tex] \frac{3}{16} + \frac{1}{16} = \frac{4}{16} = \frac{1}{4} [/tex]

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.

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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The  statement that best  describes the relationship between lines s and t is: Lines s and t are parallel.

Parallel lines can be defined as those lines that are equal to one another but does not intersect one another.

For Lines s and t to be parallel lines this means that lines s ant t are cut by transversal. Hence, transversal intersect lines s and t to make it parallels lines.

Therefore Lines s and t are parallel.

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Answer: Your answer is going to be 32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

1/8 is nothing but 0.125

4/.125 = 32

.125 goes into four 32 times.

The solutions are where the red and blue lines cross each other.

Answer would be D. X ≅ 1 and x ≅ 4.2

Answer:

0-4

derivate first

function is missing

substitute the value of X

Answer:

y= -1/2x+5

Step-by-step explanation:

Answer:

[tex]y=-\frac{1}{2}x+2[/tex]

Step-by-step explanation:

The equation for slope-intercept form is [tex]y=mx+b[/tex].

First, we find b by looking at where the line passes through where [tex]x=0[/tex]. We can see that it is 2, so in our equation for slope-intercept form [tex]b=2[/tex].

Next, we find the slope or m. Find the slope by taking two points and plugging them into this expression [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]. To demonstrate, I will choose points (0,2) and (2,1), however, any pair of points will give you the same answer. When we plug in these points, we should get the expression [tex]\frac{0-2}{2-1}[/tex]. By solving this, we get -1/2. Therefore, in our equation for slope-intercept form, [tex]m=-\frac{1}{2}[/tex].

By putting the information we have about m and b together, we get the equation [tex]y=-\frac{1}{2}x+2[/tex].

Answer:

x=36

Step-by-step explanation:

2x+2x+70+78+68=360

4x+216=360

4x=360-216

4x=144

x=144/4=36

Answer:

Step-by-step explanation:

perp. -4

y - 2 = -4(x - 0)

y - 2 = -4x + 0

y = -4x + 2

Answer:

The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.

They are the three x-intercepts, the maximum point, and the minimum point. All of these are on your unit circle. The values of sin x correspond to the y-values, so those key points are (angle, y-value) or (0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0).

Since the values on both sides are different, hence the set of equations has no solution

System of equation are made of two equations with unknown variables. Given the following equations

y = 6x + 9

y = 6x + 2

Equate

6x + 9 = 6x + 2

Collect the like terms

6x - 6x = 2 - 9

0x = -7

Since the values on both sides are different, hence the set of equations has no solution

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Answer:

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

3/4 x 2/4 = 6/24

6/24 simplified is 1/4

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Answer:

6/12 or 1/2

Step-by-step explanation:

Start by multiplying the numerators

3 x 2 = 6

Then multiply the denominators

4 x 3 = 12

Then you get your answer of 6/12

But if you want it simplified then divide both the denominator and numerator by 6 and you will get your final answer of

1/2

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Answer:

Table C

Step-by-step explanation:

The input value in Table C gives a different value in the output.

Step-by-step explanation:

650065 = (a² + 1)(c² + 1)

and

650065 = (ac - 1)² + (a + c)² = the sum of 2 squared numbers (ac - 1)² and (a + c)².

we see that 5 and 13 and therefore 5×13=65 are all factor of 650065. and then 650065/65 = 10001.

and we know that 65 = (64 + 1) = (8² + 1)

and 10001 = (10000 + 1) = (100² + 1)

so, a = 8, c = 100

that means the 2 squared numbers summing up to 650065 are

(ac - 1)² = (8×100 - 1)² = 799² = 638,401

(a + c)² = (8 + 100)² = 108² = 11,664

650,065 = 638,401 + 11,664 = 799² + 108²

Answer:

1.5:1

Step-by-step explanation:

the original answer is 12:8, so you have to simplify it down. you can get it down to 3:2 with whole numbers, but to get it down to a ratio with one, you'll have to divide each number by 2 because the bottom number is 2, so the final answer would be 1.5:1

Answer:

B.   The maximum occurs at the function's x-intercept.

Step-by-step explanation:

Given table:

[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & -5 & -4 & -3 & -2 & -1 & 0\\\cline{1-7} g(x) & -1 & 0 & -1 & -4 & -9 & -16\\\cline{1-7}\end{array}[/tex]

From inspection of the table, we can see that:

This indicates symmetry.  

The line of symmetry is the mid-point between the two x-values.

Therefore, the line of symmetry is x = -4

The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0).  As the function decreases as x → 0, the vertex is a maximum.

As the y-value of the vertex is 0, the maximum occurs at the function's x-intercept.

Answer:

B

Step-by-step explanation:

Finding the line of symmetry :

⇒ Two x-values have the same y-coordinate → (-5) and (-3)

⇒ This means the symmetry is exhibited and it lies between these 2 x-values

⇒ Line of symmetry : x = -4

=============================================================

Now, on plotting these points on a graph we see that this graph has a negative coefficient.

⇒ This means this graph will have a maximum point as the vertex

⇒ The vertex lies on the line of symmetry, hence the vertex (according to the graph and table) is (-4, 0)

Hence, we can say that the maximum occurs at the function's x-intercept.

Answer:

x^2-1^2

Step-by-step explanation:

formula:

(a-b)(a+b)=a^2-b^2

Answer:

The answer is 97

Step-by-step explanation:

According to PEMDAS, we will solve the multiplication first. 2 × 42 is 84. Next, we will add or subtract from left to right. 9 + 84 + 6 – 2 is 97, the answer to our problem.

9 + 2 × 42 + 6 - 2

Multiply 2 and 42 to get 84.

9 + 84 + 6 - 2

Add 9 and 84 to get 93.

93 + 6 - 2

Add 93 and 6 to get 99.

99 - 2

Subtract 2 from 99 to get 97.

97 ===> Answer

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