Which equation best fits the graphed data?
6+
4+
2+
+X
-6
-4
- 2
2
6
N
-2+
.
.
-4
-6+

The shape of the graph of quadratic functions is the shape of a parabola.

The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;

Reasons:

The given function is; f(x) = 2·(x + 4)² - 3

The function is given in the vertex form; f(x) = a·(x - h)² + k

Therefore, the vertex, (h, k) = (-4, -3)

Step (a);

The vertex can be plotted on the graph

Step (b);

Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²

From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and  up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)

Step (c);

To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)

Step (d);

A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;

(-4 + 3, -3 + (2 × 3²)) = (-1, 15)

Step (e);

The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4

The line x = -4 can be drawn on the graph next

Step (f);

The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;

(-3, -1) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-5, -1)

(-2, 5) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 5)

(-1, 15) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 15)

Step (g);

The parabola that is U shaped can be drawn from the points plotted in the steps above.

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Answer:

The expression is d(45) + 25 = c

Step-by-step explanation:

The expression is d(45) + 25 = c. Let's test it out to see if it is correct. We will test it out by substituting d and c.

Day 1:

Day 2:

Day 3:

Day 4:

Therefore, the expression is d(45) + 25 = c.

Hoped this helped.

Based on the definition of an isosceles triangle, the measure of angle L is: 43°

Recall:

Given that KL ≅ MK in △KLM, it means △KLM is an isosceles triangle.

If m∠M = 43°, therefore, m∠M = m∠L (equal angles directly opposite KL and MK).

This implies that: m∠L = 43°

In summary, based on the definition of an isosceles triangle, the measure of angle L is: 43°

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Answer:

[tex]\huge{\mathfrak{Solution}}[/tex]

[tex]\huge{\bold{ \frac{ {y}^{2} }{36} - \frac{ {x}^{2} }{121} = 1 }}[/tex]

[tex]\huge{\bold{ \frac{(y - k) {}^{2} }{ {a}^{2} } - \frac{(x - h) {}^{2} }{ {b}^{2} } = 1 \: is \: the \: standard \: equation \: with \: center \: (h ,k),semi-axis \: a \: and \: semi-conjugate \: -axis \: b.}}[/tex]

[tex]\huge\boxed{\mathfrak{We \: get,}}[/tex]

[tex](h,k) = (0,0),a = 6,b = 11[/tex]

[tex]For \: hyperbola \: assymtoms \: are \: y = + \frac{a}{b} (x - h) + k[/tex]

[tex]Therefore,y = \frac{6}{11} (x - 0) + 0,y = - \frac{6}{11} (x - 0) + 0[/tex]

[tex]\large\boxed{\bold{y = \frac{6x}{11},y = - \frac{6x}{11} . }}[/tex]

If y²/36 - x²/121 = 1, the asymptotes are y = (36/121) x and y = -(36/121) x.

To find the equations for the asymptotes of the hyperbola represented by the equation y²/36 - x²/121 = 1, we can compare it with the standard form of a hyperbola:

(y - k)² / a² - (x - h)² / b² = 1

where (h, k) represents the center of the hyperbola.

In the given equation, we have y²/36 - x²/121 = 1. To put it in standard form, we need to divide both sides by 1 (which is essentially dividing by 1 on the right side):

y²/36 - x²/121 = 1 / 1

Now, we can see that a² = 36 and b² = 121.

To find the equations of the asymptotes, we use the center (h, k) and the values of a and b. The asymptotes of a hyperbola have equations of the form:

y = k ± (a/b)(x - h)

In this case, the center (h, k) is (0, 0), a² = 36, and b² = 121:

The equations for the asymptotes are:

y = 0 ± (36/121) x

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Answer:

 1-2y+y^2

Step-by-step explanation:

(1–y)^2

(1-y) * (1-y)

FOIL

first: 1*1 =1

outer: 1*-y = -y

inner: -y *1 = -y

last: -y*-y = y^2

Add together: 1+-y-y+y^2  

Final answer1-2y+y^2

Credit:

wegnerkolmp2741o

He solved it earlier.

Answer:

90lbs

Step-by-step explanation:

If Tim weights 90lbs, his brother must weigh 130lbs which add to make 220lbs

Answer:

>

Step-by-step explanation:

> means greater than and because 79 is greater than -5, the correct sign you would use will be >

79 > -5

Answer:

d=100t or d=300t depending on how much the truck travels for an hour because no image was provided i dont know

Step-by-step explanation:

Answer:

8x-29y Sorry if wrong!

Step-by-step explanation:

You have to distribute first and then combine like terms.

Answer:

8x-29y

Step-by-step explanation:

You have to distribute first and then combine like terms.

And that is where you get your answer.

Hope this helps.

Answer:

Distance (d) = 15

Step-by-step explanation:

The given requires the distance between the point of origin, (0, 0), and (-12, 9). We can use the following distance formula for this problem:

[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(x_2-x_1)^2\:+\:(y_2-y_1)^2}}[/tex]

Let (x₁, y₁) = (0, 0)

     (x₂, y₂) = (-12, 9)

Substitute these values into the distance formula.

[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(x_2-x_1)^2\:+\:(y_2-y_1)^2}}[/tex]

[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(-12\:-\:0)^2\:+\:(9-0)^2}}[/tex]

Perform the required subtraction within each parenthesis:

[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(-12)^2\:+\:(9)^2}}[/tex]

Next, take the squared values of -12 and 9 under the radical:

[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{144\:+\:81}}[/tex]

Add 144 and 81:

[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{225}}[/tex]

Distance (d) = 15

Therefore, the distance between the point of origin and (-12, 9) is 15.

Answer:

C

Step-by-step explanation:

C is the only graph that passes the vertical line test.

Answer:

c

Step-by-step explanation:

The line doesn't cross eachother

Answer:

v=32

Step-by-step explanation:

23-15=8x4=32

32/4+15=23

Answer:

1x+-8(-4)=b

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

1/5 x 21 = 21/5

Answer: 90%

135/150 * 100

45*2

90

Answer:

10

Step-by-step explanation:

Answer:

A rational number is a number that doesn't terminate or repeat

a non rational number is a number that terminates or repeats

so she basicelly got mixed up

Hope This Helps!!!

The ratio of the height of the triangle to the side of the square (B) 1 : 2

The area of a triangle is (1/2)×base×height.

The area of a square is (side)².

Given, The area of a square is four times the area of a triangle.

∴ (side)² = 4{(1/2)×base×height}.

The base of the triangle and the side of the square are equal let this be 'a'.

∴ a² = 4(1/2)×a×height.

a = 2×height.

a = 2h.

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Answer:

y=(5/3)x + 5

Step-by-step explanation:

Every line is in the form: y = ax+b. If some points are on this line, they satisfy this equation. So we can write:

-5 = a(-6) + b

0 = a(-3) + b

It's a system of equations. We can solve them by subtracting the second equation from the first:

-5-0 = -6a - (-3a) + b - b

That becomes:

-5 = -3a

Therefore:

a = 5/3

Now we plug this value in the second equation of the system, and find the value of b:

0 = 5/3*(-3) +b

b=5

The final line equation will be: y=(5/3)x + 5

y = [tex]\frac{5}{3}[/tex]x + 5

First, find the slope. The formula to find slope can be defined as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

Given points (-6, -5) and (-3, 0), we can substitute those values in and find that the slope for this line will be [tex]\frac{5}{3}[/tex].

Using slope-intercept form, our equation so far is y = [tex]\frac{5}{3}[/tex]x + b. To find b, we substitute the coordinates of any point and solve. Doing so gets us a value of 5 for b.

Therefore, our final answer is y = [tex]\frac{5}{3}[/tex]x + 5.

Answer:

yes, this line will pass through the point of origin

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sam's car is 1 ft in front of the start line and its speed is 13.5 ft/s.

The distance after x seconds is:

Alice's car the speed 12 ft/s and after 3 seconds is 40 ft in front of the start line.

The distance after x seconds is:

After 15 seconds the distance from the start line is:

As we see Sam is further from the start line than Alice

Answer:

-127 is colder

Step-by-step explanation:

-54 is closer to 0 than -127 so -127 is colder

They are both negatives BUT! -127 is greater than -54 and the 0 is the begginging of frezing point

Answer:

I think you might be able to work with this: 0.15 * x - x + x * 0.06

Step-by-step explanation:

The item's cost is X.

So he has a coupon for 15%, so the cost of the item times 0.15 = how much he's getting as a discount, for example: A toy robot costs 13.46, Jenny has a coupon for 25% off, to find out how much she paid, multiply 0.25 by 13.46 which equals about 3.37, so 13.46 - 3.37 = 10.09

So 0.15 (the coupon price) * x (the item's original price) - x (the items orignal price) + x * 0.06 (the sales tax)

Comment if you need any help T^T

Answer:

5

Step-by-step explanation:

5 =5 +5+5=5+5

She needs 1 box of strawberries

She needs 2 cups of strawberries total

Answer:

B) x^3-x^2-8x-2

Step-by-step explanation:

Expand the equation of g(x) to standard form

f(x) = x^3-4x+2

g(x) = x^2-4x+4

Subtract like terms in the equation and solve for the answer.

f(x) - g(x) = x^3-x^2-4x-4x+2-4

x^3-x^2-8x-2