What is the equation of the parabola shown with its directrix on this graph?

Answer:

it already is rounded up to the nearest hundredth

Step-by-step explanation:

Answer:

Using the concepts of Number System, we find that the sum of the largest and the smallest of the given four numbers is 4.29.

Step-by-step explanation:

The given set of numbers is 3.09, 3.9, 0.39 and 0.399.

The given numbers are related to each other as:

3.9 > 3.09 > 0.399 > 0.39

3.9 is greater than 3.09 as

3.9 > 3.09

3 + 0.9 > 3 + 0.09

0.9 > 0.09

90 > 9

0.399 is greater than 0.39 as

0.399 > 0.39

399 > 390

Now, the smallest number in the series is 0.39 and the largest number in the series is 3.9.

The sum of the largest and the smallest of the given four numbers is:

3.9 + 0.39

4.29

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Answer:

a=9

b=-6

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:\dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{4 + \sqrt{45} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{4}{6} + \cfrac{ \sqrt{45} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{3 \times 3 \times 5} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ 3\sqrt{5} }{6} [/tex]

[tex]\qquad \tt \rightarrow \: \dfrac{2}{3} + \cfrac{ \sqrt{5} }{2} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

60

Step-by-step explanation:

Total degree of triangle interior angles is 180

So x+2x+3x=180

6x=180

x=30

Measurement of angle C is 2x which is 60 degree

Answer:

Let consider the following linear equation systems by using the known points and second-grade polynomial:

(-1, 7)

a + b + c = 7a+b+c=7

(5, 7)

25\cdot a + 5\cdot b + c = 725⋅a+5⋅b+c=7

(6,10)

36\cdot a + 6 \cdot b + c = 1036⋅a+6⋅b+c=10

After some algebraic manipulation, the values for the polynomial coefficients are found:

a = \frac{3}{5}a= 53 , b = -\frac{18}{5}b=− 518

, c = 10c=10

The polynomial is:

y = \frac{3}{5}\cdot x^{2} - \frac{18}{5}\cdot x+10y= 53

⋅

Step-by-step explanation:

For complete solution see the above attachment!

Answer: -4

Step-by-step explanation: Notice that the increments in the graph do not go in 1's, but in 2's. Meaning the first line is 2, and second line is 4, and in the middle is 3. Be careful.

The range is where the line on the graph hits the y-axis (horizontal line, or line going up). The only possible place the line hits the y-axis is at -4. No other y-value. Thus, the range of the function is -4.

Answer:

2.5 gallons of the 20% solution must be replaced by the 36% solution.

Step-by-step explanation:

[tex].12(20 - x) + .36x = 20(.15)[/tex]

[tex]2.4 - .12x + .36x = 3[/tex]

[tex]2.4 - .24x = 3[/tex]

[tex] - .24x = - .6[/tex]

[tex].24x = .6[/tex]

[tex]x = 2.5[/tex]

Answer:

Answer x=2/3, -1
Option B

Step-by-step explanation:

Answer:

B) x =( 2/3, -1)

Step-by-step explanation:

Equation:

[tex]6x {}^{2} + 2x = 4[/tex]

Solution:

We know that,

[tex] \rm \: Quadratic \: formula (x)=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

According to the problem,

Plugging them on the formulae,we obtain,

Choice B is accurate.

Answer:

-1/2

Step-by-step explanation:

Answer:x is -1

Step-by-step explanation:

la componente "cubica" será aquella que tenga un exponente igual a 3.

Un polinomio tiene la forma general:

[tex]p(x) = a_n*x^n + ... + a_1*x^1 + a_0[/tex]

Donde todos los exponentes de x son numeros naturales.

Particularmente, la componente "cubica" será aquella que tenga un exponente igual a 3.

Entonces, por ejemplo, en:

[tex]p(x) = 4*x^5 + 2*x^4 + 5*x^3[/tex]

La parte cubica será:

[tex]5*x^3[/tex]

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Answer:

x=1/3

Step-by-step explanation:

first multiply both bracket to together and then you get, 9x=3

x=1/3, then sub in to other equation and get the rest answer.

hope it helpful

Step-by-step explanation:

since we are using Pythagoras

c² = a² + b²

with c being the Hypotenuse (the baseline opposite of the 90° angle),

you want to get the expression

y² = 3² + 3²

so, you pick the ² and put it next to the y left of the "=" sign.

and to the right of the "=" sign you put 3, ², +, 3, ²

Fatoumata's salary after 3 years will be $58,000.

Fatoumata's salary after tt years will be $43,000 + (5,000tt).

The linear equation that can be used to determine Fatoumata's salary after the passage of time is:

Initial salary + (yearly increase x number of years)

$43,000 + 5000t

$43,000 + 5000(3) =  $58,000.

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Hello! I hope you are having a nice day. My name is Galaxy and I will be helping you with this problem. We can solve this problem in 2 steps, respectively Theory and Solving.

I'll go ahead and start with the Theory.

Before we attempt to solve the problem mathematically, we must first figure out how we're going to solve this problem.  

We know that we have a line and a point, we can start by graphing the equation and point that we've received.

Now that we have our points plotted and our equations graphed, we can start to see that something odd is happening, the given point is on the line itself.

We can check this by inputting the points into our equation:

[tex](-4)+2(-3)=-10?\\(-4)+(-6)=-10?\\-10=-10[/tex]

This proves that our point is on the line that we were given.

According to the basic rules of Euclidean Geometry, we know that parallel lines can never intersect each other and due to this there cannot be any solution to this problem.

Any other line using this point would intersect the given line, and due to this, this problem has no real solutions.

* The only line that can use these points and graph is the line provided, and that cannot work due to the lines intersecting at an infinite number of points.

Cheers,
Galaxy.

Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.

In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:

A = ½ × d₁ × d₂

Where:

Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.

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Answer: [tex]f(x)=-\frac{1}{2}x+1[/tex]

Step-by-step explanation:

The slope is [tex]\frac{-1-1}{4-0}=-\frac{1}{2}[/tex], which matches the second option.

Linear function that is represented by the graph is f(x)= -1/2 x+1.

Here, we have,

From the graph,

y - intercept of the linear function is 1 , i.e. c = 1

and there are two points on the line (-4, 3), (4, -1)

We can get the equation of line by applying slope-intercept formula,

Slope of the line,

m = y₂ -y₁ / x₂-x₁

so, we get,

m = -1 -3 / 4 + 4

   = -4/8

   = -1/2

Now applying slope-intercept formula,

y = mx+c

Putting the values,

=> y = -1/2 x + 1

=>f(x) = -1/2 x + 1.

Therefore, linear function that is represented by the graph is

f(x) = -1/2 x + 1.

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Answer:

Step-by-step explanation:

Expanding the right-hand side,

[tex](a-b)(a^{2}+ab+b^{2})=a^{3}+a^{2}b+ab^{2}-a^{2}b-ab^{2}-b^{3}=a^{3}-b^{3}[/tex]

Thus, the identity is true.

The angle of depression from the top of the lighthouse to the sinking boat is 6.9°.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

From ΔABC it is obtained that;

Height of lighthouse, AC = 25 meters

Distance of boat from the lighthouse, BC = 204 meters

The angle of depression from the top of the lighthouse to the sinking boat is;

[tex]\rm tan \theta = \frac{P}{B} \\\\ \rm tan \theta = \frac{AC}{BC} \\\\ tan \theta = \frac{25}{204} \\\\ \theta = tan^{-1}(0.12)\\\\ \theta = 6.9 ^0[/tex]

Hence, the angle of depression from the top of the lighthouse to the sinking boat is 6.9°

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The difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

The given polynomials are [tex](1.3t^{3}+0.4t^{2} -24t )[/tex] and [tex]0.6t^{2} +8-18t[/tex].

We need to find the additive inverse of the polynomial being subtracted.

In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This number is also known as the opposite, sign change, and negation.

Now, [tex](1.3t^{3}+0.4t^{2} -24t )-(0.6t^{2} +8-18t)[/tex]

[tex]=1.3t^{3}+0.4t^{2}-0.6t^{2}-24t+18t-8[/tex]

[tex]=1.3t^{3}-0.2t^{2}-6t-8[/tex]

The additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

Therefore, the difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

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Answer:

A ≈ 22.2 ft²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{50}{360}[/tex]

   = π × 7.13² × [tex]\frac{5}{36}[/tex]

    = 50.8369π × [tex]\frac{5}{36}[/tex]

    ≈ 22.2 ft² ( to the nearest tenth )

Answer:

Add all of the sides up:

x^2 + y + 6x + 2y + y^2 + 6x + 2y + y^2 + 4x^2

= 5x^2 + 12x + 2y^2 + 5y

Answer:

The sum of the other two numbers is 120.

Step-by-step explanation:

To find an average, you add all the numbers involved and divide it by the amount of numbers involved. in this case,

(x+y+z) ÷ 3 =50

x=30

Divide both sides by three to remove the denominator.

(30+y+z)÷ 3 (*3) = 50(*3)

(30+y+z)=150

Subtract 30 from both sides.

(30+y+z)-30= 150-30

y+z=120

a straight line make an angle of 180° ,

so 115+y=180

y=65°

for the top part of the triangle it makes an angle of 360° , so 304+y=360

y=56

sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .

so

65+56+y= 180

121+y=180

y=59( the angle next to X)

X+59=180( together they make an angle of 180)

x=121°

Hope it helps

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Answer:

  b, c

Step-by-step explanation:

A function is continuous if its graph can be drawn without lifting the pencil. It is decreasing wherever its slope is negative.

__

A graph of the function is attached. It has a "jump" discontinuity at x=0, so is not a continuous function.

The value of f(0) is 2, so the y-intercept is 2.

The given function is defined for all values of x, so its domain is all real numbers.

The function is decreasing for values of x > 0, so does not approach positive infinity for large positive x.

The function has a stationary point at x=0, so is not decreasing over its entire domain.

_____

Additional comment

The function is decreasing everywhere except at x=0. The point (0, 2) is the vertex of the quadratic portion of the function, so a tangent is horizontal there. At such horizontal tangent points, a function is neither increasing nor decreasing. It is tempting to ignore this exception, because the function is decreasing everywhere else.

Answer:

(-2,-9)

(-1,8)

(0,-5)

(1,0)

(2,7)

Step-by-step explanation:

The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.

It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Triangle ABC ~ EDC

Angle ACD = Angle BCE = 90 degree  (vertically opposite angle)

Angle ACB = Angle DCE = 90 degree  (vertically opposite angle)

BE ║ AD

Angle EBC = Angle CDA = 40 degree  (alternative angles)

Triangle ABC ~ Triangle EDC

Angle ABC = Angle CDE

Angle BAC = Angle DEC

∴ AB ║ DE

Triangle ACD ~ Triangle ECB

Angle EBC = Angle CDA and

Angle BEC = Angle CAD

∴ Triangle ACD ~ Triangle ECB

Angle A + Angle E = 180 degree

∠x + 50 + 50 + ∠x = 180

∠x = 40

Angle CAD = 40 degree

We know,

Angle A = Angle E = Angle B = Angle D = 90 degree

So ABCD is a square

AB = ED = 12

AD = AB  = BE = ED = 12

Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.

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Answer:

[tex]a_{n} =18-8n\\a_{8} =18-8(8)=-46[/tex]

Answer:

-46

Step-by-step explanation:

(hello, I just answered your previous question--some stuff will sound similar because we are applying the same concept :)  )

We know that the nth term of the sequence is 18 - 8n

the "nth" term of a sequence means that you can plug in the term place to get the term value (ex. if the nth term is n + 2, we can plug any term in {let's say, the eighth term, 8 + 2 = 10 ; to get our term's value}  )

  18 - 8n is sequence

  18 - 8(8) is 8th term

  18 - 64 is 8th term

 -46 is the 8th term

hope this helps!! :)

The cost to buy 18 notebooks and 12 desktop computers will be $8100.

The cost to buy n notebooks and d desktop computers will be 300n + 225d

The cost of a given material is the amount attached and to be paid for getting that material.

From the given information:

The cost to buy 18 notebooks and 12 desktop computers will be:

= 300(18) + 225(12)

= 5400 + 2700

= $8100

The cost to buy n notebooks and d desktop computers will be:

= 300(n) + 225(d)

= 300n + 225d

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