which graph corresponds with the equation [tex]f(x)=\frac{1}{2 } (x+1)^{2} +2[/tex]

Answer:

b

Step-by-step explanation:

its correct

Step-by-step explanation:

a)

y = 2x³ + 4x

a polynomial of 3rd degree cannot have an axis of symmetry.

it can only have a point of symmetry, like in this case.

(0, 0) is the point of symmetry, because due to the fact there is no squared term, any negative x values create exactly the same values (in absolute values) as their positive counterparts - just negative.

the vertex of a polynomial of 3rd degree is the point where the function changes directions.

that point for x³ is the origin, as it is for x. the factors only stretch the graph, but the vertex stays the same.

only if we had a term like (x+a)³ in the polynomial, this would shift the vertex.

so, the point of symmetry and the vertex are the same :

(0, 0).

b)

y = -x² + 4x - 5

the vertex form of a quadratic function is

f(x) = a(x − h)² + k

with (h, k) is the vertex.

x = h is the axis of symmetry.

we use "complete the square" to get it into that form.

-x² + 4x - 5 = -(x² - 4x + 5) = -(x - 2)² - 1

therefore,

y = -(x - 2)² - 1

h = 2, k = -1

the vertex is (2, -1)

the axis of symmetry is x = 2

Answer: it would be y/2 if im not mistaken.

Step-by-step explanation: because with x+3/3 the 3 on the top is canceled out leaving x/3 so it would be the same with y+2/2.  I hope im right and that this helps. If not i am sorry.

Answer: 48 cm^2

Step-by-step explanation:

The equation for the area of a triangle is 1/2(base*height). Plug in the numbers to get an equation of 1/2(8*12). 8*12 = 96. Now divide by 2. 96/2 = 48.

Answer:

48 cm^2

Step-by-step explanation:

a triangle area is hb/2

so 8*12=96

96/2=48 therefore 48 is the answer.

Answer:

The slope is 4/3

Step-by-step explanation:

The solution is in the image

53= 29t < 343

Step-by-step explanation:

Answer:

53 = 343t-29

Step-by-step explanation:

53 is equal to (53 =)

t times 343 (343t)

29 less than the quantity (-29)

Good luck! :)

Answer:

  85.2 m²

Step-by-step explanation:

Perhaps one of the easiest ways to decompose this composite figure is to consider it as a rectangle with a triangle removed from it.

__

The vertical dimension of the missing triangle is 8-4 = 4 m. The horizontal dimension of the missing triangle is 11.4 -8.4 = 3 m. The overall rectangle, including the missing triangle, is 11.4 m wide and 8 m high.

The area of the figure is ...

  area = rectangle area - triangle area

  = (11.4 m)(8 m) -1/2(4 m)(3 m) = 91.2 m² -6 m² = 85.2 m²

The area of the shape is 85.2 square meters.

_____

Additional comment

The area of a rectangle is the product of its length and width:

  A = LW

The area of a triangle is half the product of its base and height:

  A = 1/2bh

Answer:

55

Step-by-step explanation:

we can get the answer by putting it in the calculator

Answer:

Dimensions of tank:

⇒ Volume of each tank = width × length × height

                                       = 8.75 × 8.75 × 23

                                       = 1760.9375 in³

Given:

mass = density × volume

⇒ mass of hot coffee = 5.8 oz/in³ × 1760.9375 in³

                                     = 10213.44 oz (nearest hundredth)

⇒ mass of cold coffee = 3.5 oz/in³ × 1760.9375 in³

                                      = 6163.28 oz (nearest hundredth)

Convert the masses of the tanks from ounces to pounds

1 lb = 16 oz

⇒ mass of hot coffee tank = 10213.44 ÷ 16

                                            = 638.34 lb (nearest hundredth)

⇒ mass of cold coffee tank = 6163.28 ÷ 16

                                             = 385.21 lb (nearest hundredth)

If the table can hold a maximum of 800 lb:

hot coffee:  800 lb ÷ 638.34 lb = 1.25 (nearest hundredth)

cold coffee:  800 lb ÷ 385.21  lb = 2.08 (nearest hundredth)

Therefore, either:

can be placed on a table which can support a maximum weight of 800 lb

The rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]

The formula of the sequence is given as:

an = 9(0.4)^n

The above means that:

The sum Sn is then represented as:

[tex]S_n =\frac{a(1 - r^n )}{1 - r}[/tex]

So, we have:

[tex]S_n =\frac{9 * (1 - r^n )}{1 - 0.4}[/tex]

Evaluate the difference and divide

[tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]

Hence, the rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]

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Answer:

In standard form: (x+2)² + (y-4)² = 98

Use the distance formula to find radius:

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

where (x1, y1), (x2, y1) are points

[tex]\rightarrow \sf d = \sqrt{(-2 - 5)^2 + (4-(-3))^2}[/tex]

[tex]\rightarrow \sf d = \sqrt{(-7)^2 + (7)^2}[/tex]

[tex]\rightarrow \sf d = 7\sqrt{2}[/tex]

Equation of circle:

Using it's concept, it is found that the theoretical probability of Scott rolling a 3 if his number cube is fair is of [tex]\frac{1}{6}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For a theoretical probability, these number of outcomes are taken before any experiment.

In this problem, there are six numbers, one of which is three, hence the probability is given by:

[tex]p = \frac{1}{6}[/tex].

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Answer:

  π = C/(2r)

Step-by-step explanation:

The equation that relates the circumference of a circle to the radius is ...

  C = 2πr

__

We can divide both sides of the equation by 2r to get an expression for π.

  [tex]C=2\pi r\\\\\dfrac{C}{2r}=\dfrac{2\pi r}{2r}\\\\\boxed{\pi=\dfrac{C}{2r}}[/tex]

Answer:

25%???

Step-by-step explanation:

I think

The answer would be 115

Step-by-step explanation:

Answer:

9-1=8

Step-by-step explanation:

he started with 9 but at the end of the day he had 8. meaning he ate 1 peice

The solution to the question is arrived at using the knowledge of mathematical models.

A mathematical model is a linguistic and mathematical concepts-based description of a system.

The appropriate model for the given data is:

Because there are discrepancies and no direct equation that can complete all of these points, a Least Square Regression Line is the best option for resolving this problem.

They could be outliers, so we need use a calculator to create a regression line to find the residual value.

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Answer:

8 hits

Step-by-step explanation:

The ratio is :

Now, we have 18 times at bat.

Multiply both sides of the ratio with 2 :

Harry should make 8 hits in 18 times at bat.

Answer:

answers

Step-by-step explanation:

125000 Submit Answer.

Answer:

12763

Step-by-step explanation:

Based on the given conditions, formulate: 

10000 x ( 5%+1)⁵

Evaluate the equation/expression: 12762.81563

Find the closest integer: 12763

Answer:

636/928 = 137/200

0.685

68.5%

Step-by-step explanation:

Answer:

7.92 cm²

Step-by-step explanation:

Area of Trapezium :

Answer:

for $5 plan if he rents 47 dvd it will pay 47% as one DVS cost 1 $ .

Step-by-step explanation:

3 yards 5 feet 6 inches X 7 is 33.833333 yards. The correct option is K- none of these.

First step

One yard is 36 inches hence:

3 yards 6 inches=(36 inches×3)+6 inches

3 yards 6 inches=108 inches+6 inches

3 yards 6 inches=114 inches

Second step

5 Feet to inches=5 ft×12

5 feet to inches=60 inches

Third step

Yards=[(114 inches+60 inches)×7]/ 36 inches

Yards=(174 inches×7)/ 36 inches

Yards=1,218 /36 inches

Yards=33.833333

Therefore the correct option is K- none of these.

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In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

In the first triangle, we need to use trigonometric ratio to find the missing side in the triangle

Data;

To find the adjacent side, we need to use cosine rule on this problem.

[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]

The adjacent side is equal to 8 units

In the second triangle, we also need to use trigonometric ratio, but let's write down our data

We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.

[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]

The adjacent side is equal to 8.660, let's find the opposite side using sine rule

[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]

And lastly, the value of the other angle is

[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]

From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively

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Answer:

[tex]8[/tex].

Step-by-step explanation:

Notice that in equation for the total dollar amount collected ([tex]12+ 1.75\, n[/tex]), every additional bottle sold at the new price brings in [tex]1.75[/tex] dollars:

[tex]\begin{aligned}& 12 + 1.75\, n && \text{$n$ bottles at new price} \\ -\; & 12 + 1.75\, (n+1) && \text{$(n+1)$ bottles at new price} \\ =\; & 1.75\end{aligned}[/tex].

Therefore, the per-bottle price after the [tex]\$0.25[/tex] price increase would be [tex]\$1.75[/tex]. The per-bottle price before the price increase would be [tex]\$1.75 - \$0.25 = \$1.50[/tex].

Also notice that when [tex]n = 0[/tex], the total amount collected was [tex]t = 12 + 1.75\, n = 12[/tex]. In other words, the total amount collected was [tex]\$12[/tex] before any bottle was sold at the new price.

Thus, the vendor had collected [tex]\$12\![/tex] by selling at the initial price of [tex]\$1.50[/tex] per bottle. The number of bottles sold at that price would be:

[tex]\begin{aligned}\frac{12}{1.50} = 8\end{aligned}[/tex].

The slope of the line is 2 and y-intercept is -20 and the linear equation can be framed as y = 2x—20 option first is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Taking two points to find the slope of the line:

(0, -20) and (5, -10)

[tex]\rm m =\dfrac{-10+20}{5-0}[/tex]

m = 2

The straight line equation:

y = mx + c

y = 2x + c

Plug (0, -20)

-20 = c

Thus, the slope of the line is 2 and y-intercept is -20 and the linear equation can be framed as y = 2x—20 option first is correct.

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Answer:

45 m2

Step-by-step explanation:

It was the only reasonable answer lol

9x5=45

Work Shown:

A = pi*r^2

A = 3.14*(4.25)^2

A = 56.71625

A = 56.72