Some ocean plants grow 6 cm every 2 years.
Select the graph with a slope that best
represents this rate?

Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

Question 14

You can check using the distributive and commutative properties that all of these are equivalent to 6x+3.

Question 15

(7+5)p - p = 12p - p = 11p

Question 16

7 + 5(p-p) = 7 + 5(0) = 7

Question 17

No parentheses are needed.

Answer:

C= 200 + 50h

Step-by-step explanation:

Let us represent

Cost to hire movers = C

Number of hour = h

We are told in the question that:

The cost to hire movers is $200 plus $50 each for each hour they work.

Hence ,our linear equation =

C = $200 + $50 × h

C = 200 + 50h

Answer:

stocks, bonds, mutual funds, and collectables

Step-by-step explanation:

Answer:

not sure but 4 quarts i think

Answer:

4 quarts is greater because it is equal to 16 cups

Answer:

4

Step-by-step explanation:

The greatest common factor of [tex]4d+12e[/tex] is [tex]4[/tex].

[tex]4(d+3e)[/tex]

Answer: Pythagorean theroem

Step-by-step explanation:

The easiest method to use in terms of a missing side as long as you know at least two other variables whether its another side or angle

Answer:

10

I took the quiz ;)

Answer:

10

Step-by-step explanation:

First we need to find A and B

A(-7;-6)

B(1;0)

Given:

Principal value = 2,00,000

Rate of interest = 20% p.a. compounded quarterly.

To find:

The compound interest and the amount after one year.​

Solution:

Formula for amount is:

[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]

Where, P is principal, r is the rate of interest in decimal, n is the number of times interest compounded in an year and t is the number of years.

The interest is compounded quarterly. So, the value of n is 4.

Putting [tex]P=200000,\ r=0.2,\ n=4,\ t=1[/tex] in the above formula.

[tex]A=200000\left(1+\dfrac{0.2}{4}\right)^{4(1)}[/tex]

[tex]A=200000\left(1+0.05\right)^{4}[/tex]

[tex]A=200000\left(1.05\right)^{4}[/tex]

[tex]A=200000(1.21550625)[/tex]

[tex]A=243101.25[/tex]

Therefore, the amount after one year is 2,43,101.25.

We know that the compound interest is the difference between amount and principal value. So,

[tex]C.I.=A-P[/tex]

[tex]C.I.=2,43,101.25-2,00,000[/tex]

[tex]C.I.=43,101.25[/tex]

Therefore, the amount is 2,43,101.25 and the compound interest is 43,101.25.

Answer:

C 50 mi

Step-by-step explanation:

You have to use the Pythagorean theorem:

14²+48²

196 + 2304

2500

Now you make the square root of 2500 and found the result: 50 mi

x = 24

Step-by-step explanation:

First, find the length RT. Note that we can use the definition of sine 60:

sin 60° = (12√3)/RT

Solving for RT,

RT = (12√3)/sin60° , sin 60 = (√3)/2

= 24

Since ∆QRT is a 45°-90°-45° triangle, that means that

x = RT = 24

Answer:It would be 30!

Step-by-step explanation:

You need to line them all up in order and then see the one that sticks out from all of the others. All the other numbers are in the 40s and 50s and this one is 30.

Answer:

(6,-11)

Step-by-step explanation:

Answer:

B. 1,130.4 cm³

Step-by-step explanation:

The formula for volume of a cylinder: πr²h (π x radius x radius x height).

(3.14 is the substitute for pi).

According to the word problem, the radius is 6.

And the height is how high a shape is; the height is 10.

Now we have our whole equation.

πr²h (π x radius x radius x height)

π · 6²· 10 (3.14 · 6 · 6 · 10)

π · 6²· 10 (3.14 · 6 · 6 · 10) = 1,130.4

Therefore, 1,130.4 cm³ is the volume of this cylinder.

Answer:

Step-by-step explanation:

volume = length x width x height

                 ————————————-

                                   3

Answer:

0,37

Step-by-step explanation:

Answer:

D.36cm

Step-by-step explanation:

If the top rectangle have 6 cm, it means 6×16=108 ft

If the two rectangles are the same, it means that the bottom rectangle have also 108 ft, so:

108÷3= 36 cm

Answer:

It would be D.

Step-by-step explanation:

After graphing, option D best correlates to the red triangles (patient B).

Answer:

24.77

Step-by-step explanation:

The final without coupons is 31.52, but because you use 4.75 in coupons and 2.00 in manufacturer's rebate, it drops down to 24.77.

Hope this helps!

Answer:

B = 49.1°

C = 93.9°

c = 77.9

Step-by-step explanation:

Given:

a = 47, b = 59, and A = 37°

Required:

B, C, and c

Solution:

✔️To find B, apply the law of sines:

[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]

Plug in the values

[tex] \frac{sin(37)}{47} = \frac{sin(B)}{59} [/tex]

Cross multiply

[tex] 47*sin(B) = sin(37)*59 [/tex]

Divide both sides by 47

[tex] \frac{47*sin(B)}{47} = \frac{sin(37)*59}{47} [/tex]

[tex] sin(B) = 0.7555 [/tex]

[tex] B = sin^{-1}(0.7555) [/tex]

[tex] B = sin^{-1}(0.7555) [/tex]

B = 49.0690779° ≈ 49.1° (nearest tenth)

✔️C = 180° - (A + B) (sum of triangle)

C = 180° - (37° + 49.1°)

C = 93.9°

✔️To find c, apply the law of sines:

[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]

Plug in the values

[tex] \frac{sin(49.1)}{59} = \frac{sin(93.9)}{c} [/tex]

Cross multiply

[tex] c*sin(49.1) = sin(93.9)*59 [/tex]

Divide both sides by sin(49.1)

[tex] c = \frac{sin(93.9)*59}{sin(49.1)} [/tex]

c = 77.8766982

c ≈ 77.9 (nearest tenth)

Answer:

$350

Step-by-step explanation:

[tex]\frac{250}{y} :\frac{5}{7}[/tex]

y · 5 = 250 · 7

5y = 1750

5y ÷ 5 = 1750 ÷ 5

y = 350

Answer:

$350

Step-by-step explanation:

5 is to 250 as 7 is to 'x'

5/250 = 7/x

cross-multiply:

5x = 1750

x = 350

Answer:

10 2/4

Step-by-step explanation:

Answer:

look at the picture i sent

Answer:

24/60 or 0.4

Step-by-step explanation:

3/4×2/5=6/20

4/3×6/20=24/60

24/60

The no. of unique card combinations we can create is 59280

What is permutation and combination?

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.

There are 52 cards in a deck in which, there are 12 face cards and 40 numbered cards.

So, by using fundamental principle of counting=40x39x38                                                      =59280

Therefore, the no. of unique card combinations we can create is 59280

Learn more about Permutation and combination,

https://brainly.com/question/1216161

#SPJ2

Answer:

90

Step-by-step explanation:

Answer:

its 75 or A.

Step-by-step explanation:

Answer:

[tex]\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)[/tex]

Step-by-step explanation:

[tex]f\left(x\right)\:=\:2x^2\:+\:16x\:-\:9[/tex]

- Given

[tex]\mathrm{X\:Intercepts}:\:\left(\frac{-8+\sqrt{82}}{2},\:0\right),\:\left(-\frac{8+\sqrt{82}}{2},\:0\right)[/tex]

By definition of zeros of  a function,  the zeros of the quadratic function f(x) = 2x² + 16x – 9 are [tex]x1=-4+\frac{\sqrt{82}}{2}[/tex] and [tex]x2=-4-\frac{\sqrt{82}}{2}[/tex] .

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In a quadratic function that has the form:

f(x)= ax² + bx + c

the zeros or roots are calculated by:

[tex]x1,x2=\frac{-b+-\sqrt{b^{2}-4ab } }{2a}[/tex]

The quadratic function is f(x) = 2x² + 16x – 9

Being:

the zeros or roots are calculated as:

[tex]x1=\frac{-16+\sqrt{16^{2}-4x2x(-9) } }{2x2}[/tex]

[tex]x1=\frac{-16+\sqrt{256 +72 } }{4}[/tex]

[tex]x1=\frac{-16+\sqrt{328} }{4}[/tex]

[tex]x1=\frac{-16+\sqrt{4x82} }{4}[/tex]

[tex]x1=\frac{-16+2\sqrt{82} }{4}[/tex]

[tex]x1=\frac{-16}{4}+\frac{2\sqrt{82}}{4}[/tex]

[tex]x1=-4+\frac{\sqrt{82}}{2}[/tex]

and

[tex]x2=\frac{-16-\sqrt{16^{2}-4x2x(-9) } }{2x2}[/tex]

[tex]x2=\frac{-16-\sqrt{256 +72 } }{4}[/tex]

[tex]x2=\frac{-16-\sqrt{328} }{4}[/tex]

[tex]x2=\frac{-16-\sqrt{4x82} }{4}[/tex]

[tex]x2=\frac{-16-2\sqrt{82} }{4}[/tex]

[tex]x2=\frac{-16}{4}-\frac{2\sqrt{82}}{4}[/tex]

[tex]x2=-4-\frac{\sqrt{82}}{2}[/tex]

Finally, the zeros of the quadratic function f(x) = 2x² + 16x – 9 are [tex]x1=-4+\frac{\sqrt{82}}{2}[/tex] and [tex]x2=-4-\frac{\sqrt{82}}{2}[/tex] .

Learn more about the zeros of a quadratic function:

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