A parabola can be drawn given a focus of (3,9) and a directrix of y = -5.
Write the equation of the parabola in any form.

Answer: If a1 = 16 and a2 = -8, then we can write a recursive formula for the nth term of the sequence as follows:

an = a(n-1)/2

This formula states that the nth term of the sequence is equal to the previous term (n-1) divided by 2. For example, if n = 3, then a3 = a(3-1)/2 = a2/-8/2 = 4.

We can also write this formula in terms of the initial values of the sequence as follows:

a(n) = (-1)^(n-1) * 8

This formula states that the nth term of the sequence is equal to (-1) raised to the power of (n-1), multiplied by 8. This formula will always give the correct value for the nth term of the sequence, regardless of the initial values of the sequence.

When we say, "a system of linear equations works" it means that the linear equations share one or more ordered pairs (x,y) when graphed.

In many practical applications in daily life, linear equations are a crucial tool in science. They enable scientists to, among other things, make predictions, compute rates, and characterize relationships between two variables in the physical world. In order to see trends, linear equations are often graphed.

Slope intercept form, direct variation, point slope form and standard form are four types of linear functions.

When we have a system of linear equations and when we solve them simultaneously we get one or more ordered pair depending upon the variable in system.

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The category of the expression x⁴ + 2x³ - x² + 7x + 11  is not quintic binomial

From the question, we have the following expression that can be used in our computation:

x^4+2x^3-x^2+7x+11

Rewrite this expression properly

So, we have the following representation

x⁴ + 2x³ - x² + 7x + 11

The degree of the above polynomial is 4

As a general rule, a quintic binomial is any polynomial that has a degree of 5

A degree of 5 and a degree of 4 are not the same

Hence, the expression is not a quintic binomial

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A line's angle of slope between two points is (5, -4)

A line's angle of slope between two points is given as follows:

m = y2-y1/x2 - x1

A line passing through a given point and having the following equation:

y - y₁ = m(x - x₁)

Line A:

m = -1 - 5 /3- (-1) = -6 /4 = -3/2

y - 5 = -3 / 2(x +1)

y = -3/2 (x + 1) + 5.

Line B:

m = -1-2/6-7  = -3 / -1 = 3

y - 2 = 3 (x - 7)

y = 3(x -7) + 2.

Point of intersection denotes identical x and y coordinates.

So:

3(x - 7)+ 2 = -3/2 (x + 1 ) +5

3x - 21 + 2 = -3/2x - 3/2 +5

3x - 19 = -3/2x + 7/2

6x - 38 = 3x +7

6x + 3x = 7 + 38

9x =45

x = 5

y = 3(5 - 7) + 2 = 3(-2) + 2 = -4.

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Option A and D are appropriate.

There is just one correct answer to some equations. There is only one value for the variable in these equations that causes the equation to be true. If you solve an equation and the result is a variable equal to a number, the problem has just one solution.

To date,

1) x has just one solution since -5x + 12 = 5x -5

-5x -5x = -5 -12

-10x = -17

x = 1.7

2) -5x+12=-5x-12 -5x + 5x = -12-12

0x (not possible)

3) -5x+12=5x+12 -5x + 5x = +12-12

0x ( not possible)

4) The equation -5x+12=-12x-12

-5x + 12x = -12 -12

7x = -24

x = -24/7, indicating that x has just one solution.

Option A and D thus have a single solution.

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Answer:

Step-by-step explanation:

4y=3x+7

divide both sides by 4

y= 0.75x+1.75

or in fraction

y=3/4x+7/4

The slope of the line y = 14x – 1 is 14.

To find the slope of a line, we need to know two points on the line. We can choose any two points, as long as they are not the same. For example, we can choose the points (0, -1) and (1, 13):

y = 14x – 1

y = 14(0) – 1 = -1 when x = 0

y = 14(1) – 1 = 13 when x = 1

The slope of the line is the change in y divided by the change in x between these two points. In this case, the change in y is 13 – (-1) = 14, and the change in x is 1 – 0 = 1. Therefore, the slope of the line is 14/1 = 14.

We can also write the slope as a simplified fraction. In this case, 14 is already a simplified fraction, so we don't need to simplify further. Therefore, the slope of the line y = 14x – 1 is 14.

The inequality on the graph is a linear inequality, and it can be written as:

y > 2x - 4

On the graph, we can see a linear inequality, we can see a dashed line with a positive slope, and the shaded area is above that line, so the inequality is of the form:

y > line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

We can find two points on the graph, we can see that the line passes through (0, -4) and (2, 0), then the y-intercept is -4 and the slope is:

a = (0 + 4)/(2 - 0) = 2

y = 2x - 4

then the inequality is:

y > 2x - 4

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Answer: 3353

Let's solve this equation:

[(3)(3)+(4)(4)]2+[(8)(3)+(7)(4)]2+(2)(3)(4)

=(9+(4)(4))2+((8)(3)+(7)(4))2+(2)(3)(4)

=(9+16)2+((8)(3)+(7)(4))2+(2)(3)(4)

=252+((8)(3)+(7)(4))2+(2)(3)(4)

=625+((8)(3)+(7)(4))2+(2)(3)(4)

=625+(24+(7)(4))2+(2)(3)(4)

=625+(24+28)2+(2)(3)(4)

=625+522+(2)(3)(4)

=625+2704+(2)(3)(4)

=3329+(2)(3)(4)

=3329+(6)(4)

=3329+24

=3353

Hope this helps!!

Answer: 732.76

Step-by-step explanation: 28 x 26.17 = 732.76, and if by units you mean decimals, then its 732

The angles which makes 45° and 90° in square are shown below.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

ABCD is a square,

The angles which are 45°,

∠ CAD, ∠ CAB, ∠ DBA, ∠ DBC, ∠ ACB, ∠ ACD, ∠ BDA, ∠ BDC

The angle which are 90°,

∠ DAB, ∠ ABC, ∠ BCD,  ∠ ADC

And central angles also make 90°,

∠ AEB, ∠ BEC, ∠ CED, ∠ DEA

In square there is no angle that neither makes 45° nor 90°.

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Angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and

∠ABC = ∠AED = 90° respectively.

Square is a polygon which has 4 sides. All four sides of square are equal length and perpendicular to each other that means the angle between two adjacent side is 90°.

Given that ABCD is a square surface. And diagonal of square creates two isosceles triangles.

So the ∠ABC = ∠BCD = ∠CDA = DAB = 90°

Here, BD and AC are two diagonals of a square ABCD and E is the intersection point of diagonals.

Diagonals cut each other perpendicular.

So, ∠AED = 90°  and ∠EAD = ∠EDA = 45°

Now to find ∠BAC;

we have ∠ABC = 90° so from the property of isosceles triangle

∠BAC = ∠BCA = 45°

In isosceles triangle BCD,

∠BCD = 90° and ∠DBC = ∠BDC = 45°

Therefore, the angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and ∠ABC = ∠AED = 90° respectively.

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Answer:

11c-63ab

Step-by-step explanation:

8c +b+3c-9a6b

( b n 6b are common)

8c + 3c-9a7b

(8c and 3c are also common)

11c-9a7b

11c-63ab

The correct equation is [tex]P = 2.5w[/tex] .

The average cost is the ratio of the total of cost of all the products to the total number of products.

The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

An equation says that two things are equal. It will have an equals sign "=" .

A 12-ounce box of cereal costs $4.80.

The price be 'P' and weight be 'w'.

$4.80 is the price of box with weight 12-ounce

i.e. 4.80P = 12w

Divide both side by 4.80

[tex]\frac{4.80P}{4.80} = \frac{12w}{4.80}[/tex]

[tex]P = 2.5w[/tex]

Therefore, the correct equation is [tex]P = 2.5w[/tex] .

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Answer:

m= -1

Step-by-step explanation:

An equation is a formula that expresses the equality of  expressions, with the aid of using connecting them with the equals signal =. The value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x is x = 1.

The required details for equation in given paragraph

The word equation and its cognates in different languages can also additionally have subtly extraordinary meanings; for example, in French an equation is described as containing one or more variables, whilst in English, any well-shaped formula which includes expressions associated with an equals signal is an equation. Solving an equation containing variables includes figuring out which values of the variables make the equality true. The variables for which the equation must be solved also are called unknowns, and the values of the unknowns that fulfill the equality are called solutions of the equation.

To find the value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x, we need to first get all of the terms with x on the same side of the equation.

We can start by moving the 3 1/3 to the right side of the equation by subtracting it from both sides:

8/3x + 1/3x - 3 1/3 = 7/3x - 3 1/3

Next, we can combine the coefficients of x on the left side of the equation:

(8/3 + 1/3) x = (7/3 - 3 1/3)

4/3 x = 4/3

Finally, we can divide both sides of the equation by 4/3 to find the value of x:

(4/3) x / (4/3) = (4/3) / (4/3)

x = 1

Therefore, The value of x in the equation 8/3x + 1/3x = 3 1/3 + 7/3x is x = 1.

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Answer:

Step-by-step explanation:

8/3x+1/3x=3 1/3+ 7/3x

find value of x

8/3x + 1/3x = 3 1/3 + 7/3x

3x = 7/3x + 10/3

2/3x = 10/3

---------------------------

8/3 x 5 + 1/3 x 5 = 3 1/3 + 7/3 x 5

15 = 15

the answer is good

Answer:

13.0434782609%

Step-by-step explanation:

200000 - 230000

-----------

230000

x 100% = 13.0434782609% - 100 = 86.9565217

86.9565217 x 230,000 = 200,000

For both the experienced bricklayer and her apprentice working together it will take 2 hours to complete the work.

This is type of combined rate or time and work problem. Here, the experienced bricklayer takes 3 hours and apprentice take 6 hours to complete the job. So the experienced bricklayer completes 1/3rd of work in an hour and her apprentice completes 1/6th of work in an hour.        

Let us consider they would take x hours to complete the work together. The work done is the summation of product of time taken by each person to do the work and the rate of work done by each person.

x (1/3 + 1/6) = 1

x = 1/(1/3 + 1/6)

=18/9

=2

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According to Hooke's law, a material's strain will increase in direct proportion to its applied stress up to its elastic limit. When elastic materials are stretched, atoms and molecules deform up to a point of stress, after which they return to their original shape.

Hooke's law only approximates in first-order linear terms how springs and other elastic bodies actually react to applied forces. Since no material can be stretched or squeezed beyond a given size without permanently deforming or changing its condition, it must inevitably fail once the forces reach a certain threshold.

Many substances will diverge from Hooke's law clearly before they reach such elastic limits.

On the other hand, as long as the forces and deformations are small enough, Hooke's law provides a close approximation for the majority of solid bodies. Since it is the basis of many fields including seismology, molecular mechanics, and acoustics,

Hooke's law is widely applied in all branches of science and engineering. It.

Hence, a material's strain will increase in direct proportion to its applied stress up to its elastic limit. When elastic materials are stretched, atoms and molecules deform up to a point of stress, after which they return to their original shape.

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Answer:

£990

Step-by-step explanation:

£11000 * 2.25% * 4 = £990

Safety net policies like food assistance, housing assistance, and family tax credits keep millions of Americans from poverty each year and reduce hardship for millions more.

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Answer:

-19

Step-by-step explanation:

Use a calculator

Answer:

X <-2 or X > 5

Step-by-step explanation:

According to the angle of incidence, the angle of reflection will also be 36°

Angle of incidence:

In math it means the angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence.

Given,

Here we need to find the If light strikes a plate mirror at a 36° angle of incidence, then what would you expect the resulting angle of reflection to be.

Here we know that, the incident ray, the reflected ray and the normal ray at the point of incidence all lies in the same plane.

Then the angle of incidence is equal to the angle of reflection

And it can be written as,

=> Angle of incidence = angle of reflection

As per the 2nd law given above, we say that if a light ray incident at 45°, then the reflected angle will also be 45°

Here we know that the value of,

=> Angle of incidence = 36°

Therefore, the Angle of reflection = 36°

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The graph of the quartic function f(x) = -x⁴ + 1 is attached below with points at (-1 ,0), (0, 1) and (1, 0)

Quartic polynomials are continuous curves like the cubic polynomials. This means that you can draw the graph of the quartic without lifting your pencil from the page. There are no holes or jumps in the curve but, unlike the cubic graph, a graph of the quartic looks like a W or an M.

The general form of quartics of this form is y = a(x − h)⁴ + k The turning point is at (h, k). When sketching quartic graphs of the form y = a(x − h)⁴ + k, first identify the turning point. To add further detail to the graph, the x-axis and y-axis intercepts are found.

In this function given;

f(x) = -x⁴ + 1

This quartic function has points at (-1 ,0), (0, 1) and (1, 0)

Kindly find the attached graph below

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The required measures of the angle are given as,
∠JKL = 72°      ∠MLK = 108°      ∠JMK = 36°
∠MJL = 54°       ∠KNL = 90°

Given that.
The measure of the rhombus is given, we have to determine the measure of the angles,

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as angle.

Here,
∠JKL= 2 × ∠JKM  = 72°
∠MLK = 180 - 2 × ∠JKM =  108°
∠JMK = ∠JKM = 36°
∠MJL = ∠MLK/2 =  54°
The diagonal of the rhombus bisect each other at an angle of 90°
So,
∠KNL = 90°

Thus, all the measure of the angles is shown above.

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Answer:

840000 K's

Step-by-step explanation:

Since 5T = 1000K then T = 1000K/5 which is T = 200K. Multiply both sides by 4200 so you can find how many K's needed for 4200T's.

[tex]\displaystyle{4200T=200K\cdot 4200}\\\\\displaystyle{4200T=200K\cdot 4200}\\\\\displaystyle{4200T=840000K}[/tex]

Therefore, you need 840000 K's for 4200T's.

Answer:

840 000 K

Step-by-step explanation:

 5 T = 1000k

4200 T = ? K

⇒4200 × 1000 ÷ 5

⇒840 000 K answer.

hope that helps...

Answer:

A.) [tex]\frac{1}{5^6}[/tex]

Step-by-step explanation:

To simplify [tex](5^2)^3[/tex], use the exponent rule that states [tex](a^m)^n=a^{mn}[/tex]

So,

[tex](5^2)^3=5^{2*3}=5^6[/tex]

Use the same exponent rule to begin simplifying [tex](5^4)^{-3}[/tex]:

[tex](5^4)^{-3}=5^{4*(-3)}=5^{-12}[/tex]

To further simplify [tex]5^{-12}[/tex], use the exponent rule that states [tex]a^{-m}=\frac{1}{a^m}[/tex]

So,

[tex]5^{-12}=\frac{1}{5^{12}}[/tex]

Then multiply the two new expressions as indicated in the original problem:

[tex](5^6)(\frac{1}{5^{12}})=\frac{5^6}{5^12}=\frac{1}{5^6}[/tex]

Alternatively, you could use the exponent rule that states [tex]a^m*a^n=a^{m+n}[/tex]

where

[tex]a^m=5^6\\a^n=5^{-12}[/tex]

So,

[tex](5^6)(5^{-12})=5^{6+(-12)}=5^{-6}=\frac{1}{5^6}[/tex]

Answer:

12x -7

Step-by-step explanation:

Answer:

Equal to.

Step-by-step explanation:

there's 1000 ML in one L

so .25 x 1000 =

2500

which would mean they're equal

Answer:

[tex]\frac{25}{144}[/tex] ft

Step-by-step explanation:

We can find the area by multiplying 2 sides together

Multiply [tex]\frac{5}{12}[/tex]  × [tex]\frac{5}{12}[/tex] to find the area

[tex]\frac{5}{12}[/tex] × [tex]\frac{5}{12}[/tex] = [tex]\frac{25}{144}[/tex]

The area of the coaster would be [tex]\frac{25}{144}[/tex] ft