Determine the equation, in both factored and standard forms of the following parabola

Answer:

this is just a system of equations

x+y=4

2x+3y=12

x=-y+4

plug in

2(-y+4)+3y=12

-2y+8+3y=12

y+8=12

y=4

plug in

x+4=4

x=0

(0,4)

Hope This Helps!!!

Answer:

(0,4)

Step-by-step explanation:

find x by subtracting y from both sides

Answer:

d

Step-by-step explanation:

becoz u already answered it lloll

The difference between causation and correlation is that, Causation is characterized by cause-and-effect while correlation establishes a probable relationship.

While Causation is characterized by a situation in which an action certainly causes an outcome and hence, is described as a cause-and-effect relationship, Correlation on the other hand only establishes a relationship between the two events and doesn't necessarily ascertain the occurrence of the other event .

An example of two variables which may be correlated is; the height and weight of an individual in which case it is generally perceived that taller people are heavier.

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FALSE

Exponential growth is a pattern of data that shows sharper increases over time. In finance, compounding creates exponential returns. Savings accounts with a compounding interest rate can show exponential growth.

One of the best examples of exponential growth is observed in bacteria. It takes bacteria roughly an hour to reproduce through prokaryotic fission. If we placed 100 bacteria in an environment and recorded the population size each hour, we would observe exponential growth

First, population size is influenced by the per capita population growth rate, which is the rate at which the population size changes per individual in the population. This growth rate is determined by the birth, death, emigration, and migration rates in the population.

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Exponential growth depends on the per capita growth rate (rmax) of a population gradually increasing over time.

The given statement is false.

Exponential growth is a continuous boom or lower in a populace in which the price of change is proportional to the range of people at any given time.

It is growth that maintains acceleration with time and is a J-shaped curve. The intrinsic price of an increase in a populace is calculated by including the dying rate and the birth price.

Divide both sides by N and you get the growth rate per number of individuals ("per capita"): Because r = rmax [1-(N/K)] in the logistic model, we can substitute r: Thus, r equals the per capita growth rate.

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A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The numbers that are located below -3.5 on a vertical number line are (-∞,-3.5).

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The numbers that are located below -3.5 on a vertical number line are all the numbers that are less than -3.5. The numbers that are located below -3.5 on a vertical number line are (-∞,-3.5).

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Let us first define what any of these terms mean.

The mean is found by adding all the numbers in the set, and dividing the sum by how many numbers are found in the set.

> Given set {5, 12, 6, 3, 8, 16, 8, 6}, the sum of the numbers is 5 + 12 + 6 + 3 + 8 + 16 + 8 + 6 = 64. 64 ÷ 2 = 32. Thus, the mean is 32.

The median is found by finding the number in the middle of the set, and dividing it by 2. This is easy in odd numbers as there is only one number in the middle that is the same amount of numbers left and right proportionally. However, in even numbers, there are two middles to be proportional. If it as an even number, then add the 2 middles together, and divide by 2.

> Given set {5, 12, 6, 3, 8, 16, 8, 6}, this set has an even number of numbers in the set. Thus, the middles are 3 and 8. 3 + 8 = 11, and 11 ÷ 2 = 5.5. Thus, the median is 5.5.

The mode is the number that most frequently appears in the set. In this case, we have 2 frequent numbers. That is 6 and 8. They both appear 2 times separately. Thus, 6 and 8 are the modes of this set.

The range is the difference (i.e subtraction) between the largest number on the set and the smallest number on the set.

> Given set {5, 12, 6, 3, 8, 16, 8, 6}, the range is 16-3 or 13. Thus, the range is 13.

Now that we have the definitions, we can compute the other set very easily.

> Given set {2, 7, 4, 11, 12, 4, 6}, the mean is 18.

> Given set {2, 7, 4, 11, 12, 4, 6}, the median is 5.5.

> Given set {2, 7, 4, 11, 12, 4, 6}, the mode is 4.

> Given set {2, 7, 4, 11, 12, 4, 6}, the range is 10.

Hope it helped!

Answer:

-4 and -5

Step-by-step explanation:

is what i got from what i did

The parabola intersects x axis between -5 & -4 .

∴ The vertex of a parabola is located at (1.-7)

∵the parabola is symmetric  about the x = 1.

∴ The parabola intersects the axis between 6 & 7 .

            6 - 1 = 5               7 - 1 = 6

           1 - 5 = 4                 1 - 6 = 5

Therefore, the parabola intersects x axis between -5 & -4 .

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Answer:

35= 8x + 3

35 - 3 = 8x

32 = 8x

32/8= 8x/8

x = 4

Answer:

1. can't answer, can only approximate

2. when f(x) = 2, x = -1

Step-by-step explanation:

We can't evaluate f(2)  because we don't have f(x), if we did, we would plug in 2 for x.

On the other hand, solve f(x) = 2 asks for what x is equal to when f(x) = 2, f(x) is just the value on the y axis in relationship with x (in short terms, the value on the y axis).

So looking at the graph, we cam see that when x = -1, f(x) = 2.

The total average credit card debt for  a U.S household will be $9292.

We are given that an expression which gives an approximate value of the total average credit card debt in a U.S. household (in dollars )t years after 1995

We have to find the total average credit card debt will be in the year 2004.

Number of years =2004-1995=9

t=9 years

Substitute the value of t in the given expression

Then , total average credit card debt in a U.S household will be in the year

Debt(t)=418t+5530

Debt(9)=418 * 9+5530= $9292  in 2004

Hence, in the year 2004, the total average credit card debt for  a U.S household will be $9292.

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Answer:

Step-by-step explanation:

Most of the questions can be answered by comparing the given equation to vertex form.

The vertex form of the equation for a parabola is ...

  y = a(x -h)² +k

where 'a' is a vertical scale factor, and (h, k) is the vertex. The sign of 'a' determines whether the parabola opens upward or downward.

When we compare the given equation to the vertex form, we can easily see the values of 'a' and (h, k).

  y = -2(x -5)² +3 . . . . . . . given equation

  y = a(x -h)² +k . . . . . . . vertex form

The parameters are ...

  a = -2, (h, k) = (5, 3)

We notice ...

The axis of symmetry is the vertical line through the vertex. It has the equation ...

  x = h

  x = 5 . . . . equation of the axis of symmetry

The sign of 'a' is negative. This means that large x-values will result in large negative y-values. The parabola opens downward.

When the curve opens downward, it means the vertex is the highest point on the curve. The maximum is the y-value of the vertex: k. There is no minimum.

The maximum is y = 3.

The y-intercept is where the graph crosses the y-axis. It can be found by setting x=0, and computing the value of y:

  y = -2(0 -5)² +3

  y = -2(25) +3 = -50 +3

  y = -47 . . . . the y-intercept.

The ordered pair for the point there is (0, -47).

__

We show the graph so you can see how these features relate to the shape of the graph and points on it.

The fully factorized version of  -x-5 is [tex]-1 \times (x+5)[/tex].

What is Factorization?

Usually, factorization or factoring means writing a number (or another mathematical object) as a product of minor or more uncomplicated objects of the same kind.

Given -x-5 is a linear expression.

For factorizing, first, make the coefficient of x positive. For this take -1 common.

⇒ -x-5 = [tex]-1\times(x+5)[/tex]

Now take the greatest common divisor (gcd) of absolute values of coefficients in x+5.

⇒ gcd(1,5) = 1.

Now take gcd 1 common in the expression.

⇒ [tex]-1\times1\times(x+5)[/tex]

⇒ [tex]-1\times(x+5)[/tex].

∴ The fully factorized version of -x-5 is [tex]-1\times(x+5)[/tex].

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Answer:

B = 87

Step-by-step explanation:

The Attached Pic includes Sine Law which can be used in any Triangle

So for our Question

we have A=33 , a=6 , b=11

by Applying Sine Law

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

Then

[tex]sin(B)=\frac{b*sin(A)}{a} =\frac{11sin(33)}{6}=0.9985\\ B=sin^{-1}( 0.9985)=87[/tex]

Answer:

24/5

Step-by-step explanation:

5x : 9

(8 : 3)×3

5x : 9

24 : 9

5x = 24

x = 24/5 = 4/4/5

Hello!

5x : 9 = 8 : 3

5x × 3 = 8 × 9

15x = 72

5x = 24

x = 24/5

x = 4.8

∴ The value of x is 4.8.

The first three values of g² + 3 are 3, 4, 7. The correct option is the first option 3, 4, 7

From the question, we are to determine the first three possible values of g² + 3

From the given information,

g stands for a whole number

∴ The first three values of g are 0, 1, 2

When g = 0

g² + 3 becomes

0² + 3

= 0 + 3

= 3

When g = 1

g² + 3 becomes

1² + 3

= 1 + 3

= 4

When g = 2

g² + 3 becomes

2² + 3

= 4 + 3

= 7

Hence, the first three values of g² + 3 are 3, 4, 7. The correct option is the first option 3, 4, 7.

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Answer: D

Step-by-step explanation:

[tex]V=\frac{1}{3}\pi r^{2} h[/tex] is the general formula for the volume of a cone with radius r and height h.

Substituting in s for both r and h, [tex]V=\frac{1}{3}\pi s^{3}[/tex].

Answer:

16yd²

Step-by-step explanation:

We only want to focus on the rectangles with carrots. Draw a line down the middle of the shape, giving you 2 recntangles for carrots. Let's start with the big one on the right.

It has a length of 2 and a height of 7. So the area is 14 square yards

The second rectangle

It has a height of 1 yard and a length of 2 yards so an area of 2 square yards.

Finally, 14 + 2 = 16yd²

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \: \sin {}^{4} ( \alpha) + 2 \sin {}^{2} ( \alpha) \cos {}^{2} ( \alpha) + { \cos {}^{4} ( \alpha) }^{} [/tex]

[tex] \qquad❖ \: \sf \:( \sin {}^{2} ( \alpha) ) {}^{2} + 2( \sin {}^{2} ( \alpha))( \cos {}^{2} ( \alpha)) + {( \cos {}^{2} ( \alpha)) }^{} [/tex]

( use identity a² + 2ab + b² = (a + b)² )

[tex] \qquad❖ \: \sf \:( {\sin {}^{2}( { \alpha}) + \cos {}^{2} ( \alpha)) }^{2} [/tex]

( sin² x + cos ² x = 1 )

[tex] \qquad❖ \: \sf \: {1}^{2} [/tex]

[tex] \qquad❖ \: \sf \: {1}^{} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Value of that expression is 1

Answer:

Step-by-step explanation:

a = 12 mi

b ≈ 14.0 mi

c = 7 mi

m∠A ≈ 59.0 °

m∠B ≈ 91°

m∠C ≈ 30.0 °

The lengths of the triangle are:

a = 12 mi

b ≈ 14.0 mi

c = 7 mi

And the angles of the triangle are :

m∠A ≈ 59.0°

m∠B ≈ 91°

m∠C ≈ 30.0°

What are the angles in a triangle?

Every triangle has interior angles that total 180.

Angles in a triangle are the total (sum) of the angles at each of its three vertices.

Given, in a triangle ∠B is = 91°

length of c = 7 mi

              a = 12 mi

We need to find the missing angles and side length of b.

⇒ b² = a² ₊ c² ₋ 2accosB

⇒ b/sinB = a/sinA = c/sinC

b² = 12² ₊ 7² ₋ 2(12)(7)cos91°

b² = 144 ₊ 49 ₋ 2(84)cos91°

b² = 193 ₋ 168 cos 91°

b² = 195.856

b=√195.856

b = 14.0 mi

⇒14.0/sin91° = 12/sinA

⇒ sinA = 12sin91°/14.0

sin A = 0.857

A = arcsin(0.857)

A = 59.0°

∴ C = 180° ₋ (sum of two angles in a triangle)

C = 180 ₋ (91° ₊ 59°)

C = 180 ₋ 150°

C = 30°

Hence we get the angles in the triangle as m∠A = 59.0°, m∠B = 91° and  m∠C = 30°

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Answer:

for st1: It's Given

For St2: Definition

For St3: Dividing BE as BF and FE or You can write From Figure:

For St4: You can write From st3

for st5: From St 4

For St7 : They are congruent by SSS axiom

Answer:

30

Step-by-step explanation:

3mn=3x5x2=30

The confidence interval which shows 90% confidence level for the mean and assumed standard deviation is (2.94 meals, 3.0565 meals).

Given standard deviation=1.4. Sample size =1271, mean=3.

We have to find the confidence interval for 90% confidence level.

We have to find out α level that is the subtraction of 1 by the confidence interval divided by 2.

α=(1-0.90)/2

=0.05

Now we have to find z in the z table as such z has a p value of 1-α so it is z with p value of 1-0.05=0.95

Z=1.44 from z table.

Now find M as such that

M=z* st/[tex]\sqrt{n}[/tex]

where st is standard deviation ,n is sample size.

M=1.44*1.4/[tex]\sqrt{1271}[/tex]

=1.44*1.4/35.65

=2.016/35.65

=0.0565

Lower end= mean -M

=3-0.0565

=2.94

Upper end=Mean+ M

=3+0.0565

=3.0565

Hence the confidence interval showing 90% confidence level is (2.94,3.0565).

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Answer:

10

Step-by-step explanation:

proportion

35 ÷ 7 = 5

2 x 5 = 10

[tex]f(x) = 5x {}^{3} - 2x \\ g(x) = 3x {}^{3} [/tex]

[tex] \frac{f(x)}{g(x)} = \frac{5x {}^{3} - 2x }{3x {}^{3} } = \frac{x(5x {}^{2} - 2)}{3x {}^{3} } = \frac{5x {}^{2} - 2}{3x^2} [/tex]

[tex]f(g(x)) = 5( 3x {}^{3} ) {}^{3 } - 2(3x {}^{3} ) \\ f(g(x)) = 135x {}^{9} - 6x {}^{3} [/tex]

[tex]g(f(x)) = 3(5x {}^{3} - 2x) {}^{3} \\ g(f(x)) = 3(125x {}^{9} - 150x {}^{7} + 60x {}^{5} - 8x {}^{3} ) \\ g(f(x) )= 375x {}^{9} - 450x {}^{7} + 180x {}^{5} - 24x {}^{3} [/tex]

Answer: -1/2

Step-by-step explanation:

Use double-angle identities:

cos(2θ)=cos^2θ−sin2^θ

cos(2θ)=1−2sin^2θ

cos(2θ)=2cos^2θ−1

sin(x)=1/2

cos(2x)=1−2sin^2x=1−2(1/4)=1/2

cos(4x)=2cos2^(2x)−1=2(1/4)−1=-1/2

Answer: cos4x=-1/2 if sinx=1/2.

Step-by-step explanation:

[tex]sinx=\frac{1}{2}\\ x=\frac{\pi }{6} .\\4x=4*\frac{\pi }{6}=\frac{2\pi }{3}.\\ cos4x=cos\frac{2\pi }{3}=-\frac{1}{2} .[/tex]

Bobby will have $557 in his account after 4 years.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account.

Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Simple interest = (principal amount×Rate of interest×time-period)/100

The principal amount deposited was $500.

The rate of interest given by the bank is 2.85%.

The duration of deposit is 4 years.

Simple interest = (500×2.85×4)/100

                         = 57

Simple interest given by the bank after 4 years is $57.

The total sum of money Bobby will have in his bank is $500 + $57 = $557.

Therefore, after 4 years Bobby will have $557 in his account.

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The distance Tim drives is 300 kilometers


Average speed= 80 km

Time= 3 hours 45 minutes (15/4 hours)

Distance= Average speed/time

= 80 × 15/4

= 1200/4

= 300 kilometers

Hence the distance Tim drives is 300 kilometres

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The height of the cone is 24 cm.

The distance along the curved surface, measured from the edge at the top to a point on the circumference of the circle at the base, is known as the slant height of an object (such as a cone or pyramid). In other words, the slant height, represented either as s or l, is the shortest distance that may be traveled along the surface of the solid.

Slant height(l)=26cm

Radius(r)=10cm

It is known that, [tex]l^{2}=r^{2}+h^{2}[/tex]

Here, h is the height of the cone.

On substituting the values,

[tex]26^{2}= 10^{2}+h^{2}[/tex]

[tex]\\676=100+h^{2}\\[/tex]

[tex]h^{2}=676-100\\[/tex]

[tex]h^{2}=576\\[/tex]

[tex]h=\sqrt{576}\\[/tex]

h=24

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