What is the equation of this graph?

What Is The Equation Of This Graph?

Answers

Answer 1

The equation of the parabola given in the graph is:

(x - 5)² = -8(y + 4).

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

a(y - k) = (x - h)²

In which a = 4p is the leading coefficient.

In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:

a(y + 4) = (x - 5)²

The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:

a = 4p = 4(-2) = -8

Hence the equation is:

(x - 5)² = -8(y + 4).

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Related Questions

WILL MARK U BRAINLIEST THANK U

Answers

Based on the radius of the being 4 units and the area of the equilateral triangle, the area of the shaded area is 32.85 units².

What is the area of the shaded area?

First, find the area of the triangle.

The center of a triangle divides the median into a 2:1 ratio which means that the radius can be found as:

Radius = 1/3 x Area of Equilateral triangle

4 = 1/3 x (√3/ 2)a

a can be worked out to be:

= 8√3

The area of the triangle is:

= (√3 / 4) x a²

=  (√3 / 4) x (8√3 )²

= 83.14 units ²

The area of the circle is:

= π x radius²

= 22/7 x 4 x 4

= 50.29 units²

The area of the shaded area is therefore:

= 83.14 - 50.29

= 32.85 units²

In conclusion, the area of the shaded area is 32.85 units².

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Solve the system of equations for x. The value of x is ____. 3x + 4y = −16 x = 4y

Answers

Taking into account the definition of a system of linear equations, the value of x is -4.

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

This case

In this case, the system of equations to be solved is

[tex]\left \{ {{3x+4y=-16} \atop {x=4y}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

3×4y +4y= -16

Solving:

12y +4y= -16

16y= -16

y= (-16)÷ 16

y= -1

Remembering that x=4y, then x= 4×(-1)= -4.

Finally, the value of x is -4.

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Anais bought yards of ribbon. she had feet inches of ribbon left after trimming some curtains. how many inches of ribbon did anais use to trim the curtains?

Answers

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.

What is Unit Conversion?

Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion. The units are expressed using scientific notation and converted into numerical values as per the quantities.

Anais bought 2 1/2 yards of ribbon.

And she had 2 feet 8 inches left after trimming some curtains.

The first thing to do is to convert all units to inches;

From standard conversion rate.

1 yard  = 36 inches

As such  2 1/2 yards of ribbon in inches will be:

= 2 1/2 × 36 inches

= 5/2 × 36 inches

= 5 × 18 inches

= 90 inches of ribbon bought.

Similarly, since 1 foot  = 12 inches.

The amount of curtains left after trimming is:

= ( ( 2 × 12 ) + 8 )inches

= (24 + 8) inches

= 32 inches

If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.

It implies that the number of inches of ribbon that Anais used is:

= 90 inches - 32 inches

= 58 inches

Therefore, we can conclude that Anais used 58 inches of ribbon.

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The complete question is-

Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

Anais used _____ inches of ribbon.

What is the value of y¹ when y = 5 and x - 10?​

Answers

Answer:

5

Step-by-step explanation:

y^1 = 5^1 (y = 5)

Anything raised to the power of 1 is just itself.

So, 5^1 = 5

[tex]\frac{12}{20}=[/tex] ____% = ____ hundredths

Answers

The equivalent numbers of 12/20 are 60% and 0.60

How to convert the fraction?

The fraction expression is given as:

12/20

Multiply the fraction expression by 100%

So, the expression becomes

12/20 * 100%

Evaluate the product

60%

Express as fraction, again

60/100

Evaluate the quotient

0.60

Hence, the equivalent numbers of 12/20 are 60% and 0.60

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a homeowner has budgeted $10,000 for some home remodeling. a contractor has told him the labor and the cost of materials will be about the same amount. the homeowner wants to have about $3,000 left over for furnishings. how much will the homeowner be able to spend on labor and on materials?

Answers

Answer:

$3,500 labor and $3,500 materials

Step-by-step explanation:

furnishings + labor + materials = 10,000

furnishings = 3000

3000 + labor + materials = 10,000

labor = materials

3000 + labor + labor = 10,000

2(labor) = 7,000

labor = 7,000/2

labor = 3,500

labor = materials = 3,500

The following lines are ______

4x + 2y = 10 y = -2x + 15

Answers

Answer:

Parallel

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + 2y = 10 ( subtract 4x from both sides )

2y = - 4x + 10 ( divide through by 2 )

y = - 2x + 5 ← in slope- intercept form

with slope m = - 2

and

y = - 2x + 15 ← is in slope- intercept form

with slope m = - 2

• parallel lines have equal slopes

then the 2 lines are parallel

Answer:

Parallel

Step-by-step explanation:

They have the same slope, but different y intercepts.

4x + 2y = 10  Subtract 4x from both sides

2y = -4x +10  Now divide both sides by 2

y = -2x + 5  Compare to y = -2x + 15.  Both equations have the same slope or steepness, but they do not cross the y axis at the same place.  The first equation given crosses the y axis at 5 and the second equation crosses the y axis at 15

In the figure below, what is the length of BC?
A) 12
B) 13
C) 17
D) 18
E) 22

Answers

B is the answer

i simplified the theorem, but i hope this makes sense!

Answer:

B

Step-by-step explanation:

A(n) _____is a type of group design in which the species of animals within the study constitutes one of the independent variables.

Answers

A  comparative design is a type of group design in which the species of animals within the study constitutes one of the independent variables.

A group of animals, plants, or other living things that all have similar traits and are categorized as one species are considered to be living organisms. All humans are one species, for instance.

It is essential for both biologists and the general public to comprehend what species are and how to recognize them. As species disappear, biological variety is lost, and the only way to influence the social, political, and economic factors that influence conservation efforts is to understand the nature of species.

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What are the lengths of A ⁢ D ¯ , D ⁢ B ¯ , A ⁢ E ¯ , and E ⁢ C ¯ ? Measure and record them.

Answers

For this exercise, you could get the following lengths by using a scale (ruler):

AD = 7.5 units. DB = 18.5 units. AE = 7.01 units. EC = 17.28 units.

What is a line segment?

A line segment can be defined as the part of a line in a geometric figure such as a triangle, that is bounded by two (2) distinct points and it typically has a fixed length.

In Geometry, a line segment can be measured by using the following measuring instruments:

A scale (ruler)A divider

In this scenario, you're required to determine the lengths of the given line segments. However, the geometric figure wasn't included and as such an accurate answer can't provided.

For instance, you could get the following lengths by using a scale (ruler):

AD = 7.5 units. DB = 18.5 units. AE = 7.01 units. EC = 17.28 units.

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16. The average age of a group of 8 people is 22. After the oldest person leaves the room the average age decreases to 20. How old was the person who left the room? (A) 15 (B) 16 (C) 24 (D) 36​

Answers

The age of the oldest person that leaves the room is 36 years

How to calculate the average of a data?

The average of a data is defined as the ratio of the sum of the data to the sample size. Mathematically;

Average = sum/sample size

If the average age of a group of 8 people is 22. then;

22 = Xn/8

Xn = 22 * 8

Xn = 176

If after the oldest person leaves the room the average age decreases to 20, hence;

20 = H/7

H = 140

Xn  = H + x

176 = 140 + x

x = 176 - 140

x = 36

Hence the age of the oldest person that leaves the room is 36 years

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Round 51.6172 to the
thousandths place.

Answers

Answer:

51.617

Step-by-step explanation:

tythe answer is 51.617 hope it helps

Explanation: The thousandths place is 51.6172 (Underlined is the thousandths) and since 2 is closest to zero we get an answer of 51.617.

Answer: 51.617

:)

Please solve quickly

Answers

The degenerate conic that is formed when a double cone is sliced at the ap-ex by a plane parallel to the base of the cone is a Point.

What degenerate conic is formed?

When a plane that is parallel to the base of a double cone is used to slice the ap-ex, the conic section formed is a circle.

Circles lead to a Point degenerate conic being formed because a single point will be formed on the double cone that separates the shape.

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Determine the most probable next term in each list of numbers.

Answers

Answer:

23. 216
24. 56

25. 52

for 26, 27 i'll try to calculate the answer, sorry

Pick the correct answer
Help me please thanks so much

Answers

Answer:

E

Step-by-step explanation:

line I slopes downwards from left to right and has a negative slope.

line K is a horizontal line and has a slope of zero

line J slopes upwards from left to right and has a positive slope

slopes from least to greatest are therefore I, K, J

Volume=
Help asap!! Pleaseee thanks so much

Answers

The volume of the right prism is 1280 cm³

Volume of a right prism

The volume of a right prism is calculated using the formula

Volume = length × width × height

Where

height = 20cm

width = 8cm

length = 8cm

Substitute into the formula

Volume = 20 × 8 × 8

Volume = 1280 cm³

Thus, the volume of the right prism is 1280 cm³

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An amusement park rounds its total attendance for last year to 120,000 people.
Which could have been the attendance at the amusement park if it was rounded to the nearest ten thousand?
Choose 1 answer:
A
126,458


B
116,390

(Choice C)

125,007

Answers

Answer:

B

Step-by-step explanation:

B Rounded to nearest ten thousand

The attendance that aligns with rounding to 120,000 is B) 116,390.

To determine the possible attendance at the amusement park if it was rounded to the nearest ten thousand, we need to consider the rounding process.

When rounding to the nearest ten thousand, we look at the digit in the ten thousand place. If this digit is 5 or greater, we round up to the next ten thousand. If it is less than 5, we round down to the previous ten thousand.

In this case, the attendance was rounded to 120,000. To round to the nearest ten thousand, we look at the digit in the ten thousand place, which is 2. Since 2 is less than 5, we round down.

Therefore, the attendance at the amusement park could have been rounded to 120,000 people if it was rounded to the nearest ten thousand.

Among the given options, the attendance that aligns with rounding to 120,000 is B) 116,390.

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Qusai made a scaled copy of the following trapezoid. he used a scale factor less than 111. what could be the length of the longer base of the scaled copy of the trapezoid?

Answers

The length of the longer base of the trapezoid could be 0.75 units, [tex]\frac{7}{3}[/tex] units, 4 units.

What is a trapezoid?

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

Given: The original length of trapezoid= 6 units

The scale factor of less than 1

So, compare the given lengths with the trapezoid longer base length,

0.75 units<6 units

[tex]\frac{7}{3}[/tex] units<6 units

8.75 units< 6 units

But, 12 units> 6 units

Therefore, the length of the longer base can be 0.75, [tex]\frac{7}{3}[/tex], 4 units.

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The complete question is:

“ Qusai made a scaled copy of the following trapezoid. He used a scale factor less than 1.What could be the length of the longer base of the scaled copy of the trapezoid?

Choose 3 answers:

Which has no real roots?

Answers

Answer:

[tex] \sqrt[4]{ - 8} [/tex]

Explanation:

The input of a radical should be strictly positive or equal to zero when the nth root is even.

Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
The second plan has an initial fee of $53 and costs an additional $0.10 per mile driven. For what amount of driving do the two plans cost the same?What is the cost when the two plans cost the same?

Answers

Answer:

100 miles

Cost = $63

Step-by-step explanation:

Let us assume that the distance driven for both plans when they both equal in cost is X miles

Plan 1

Cost = 48  + 0.15X

Plan2

Cost = 53 + 0.1X

If they are both equal then

48 + 0.15X = 53 + 0.10X

Collecting like terms

0.15X - 0.10X = 53 - 48

0.05X = 5

X 5/0.05 = 100 miles

Plan 1 Cost = 48 + 0.15(100) = 48 + 15 = $63

Plan 2 Cost = 53 + 0.1(100) = 53 + 20 = $63

15 points please help me ASAP

Answers

The distance between the means is equal to 4. The mean absolute deviation (MAD) for player A is equal to 2.The mean absolute deviation (MAD) for player B is equal to 2.Distance between the means = two (2) times the MAD.There is some overlap and the distance between the means is between 1 times the MAD and 5 times the MAD.

What is a number line?

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

What is a line plot?

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

What is a mean?

A mean is also referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both players A and B is given by:

Distance = Mean of player B - Mean of player A

Distance = 10 - 6

Distance = 4.

The mean absolute deviation (MAD) for player A is given by:

MAD A = 1/11[2(3 - 6) + 2(4 - 6) + (5 - 6) + (6 - 6) + (7 - 6) + 2(8 - 6) + 2(9 - 6)]

MAD A = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]

MAD A = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]

MAD A = 1/11 × [22]

MAD A = 22/11

MAD A = 2.

Also, the mean absolute deviation (MAD) for player B is given by:

MAD B = 1/11[2(7 - 10) + 2(8 - 10) + (9 - 10) + (10 - 10) + (11 - 10) + 2(12 - 10) + 2(13 - 10)]

MAD B = 1/11[2(3) + 2(2) + (1) + (0) + (1) + 2(2) + 2(3)]

MAD B = 1/11[6 + 4 + 1 + 0 + 1 + 4 + 6]

MAD B = 1/11 × [22]

MAD B = 22/11

MAD B = 2.

Therefore, distance between the means = two (2) times the MAD.

Distance = Means × MAD

4 = 2 × 2.

In conclusion, we can infer and logically deduce that there is some overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

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Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 595, α=0. 05, n=17

Answers

Answer: Yes, the correlation coefficient is statistically significant

The correlation coefficient describes how one variable actions when it comes to every other. A high-quality correlation shows that the 2 circulate within the identical path, with a +1.zero correlation once they move in tandem. A poor correlation coefficient tells you that they as a substitute flow in opposite directions. A correlation of 0 shows no correlation in any respect.

where ρ corresponds to the population correlation.

The sample size is n = 17,

so then the number of degrees of freedom is df = n-2 = 17-2 = 15

The corresponding critical correlation value re for a significance level of a 0.05, for a two-tailed test is た= 0.482

Observe that in this case,

              the null hypothesis H0 : ρ-0 is rejected

                             if |r> re 0.482.

Based on the sample correlation provided, we have that lrl = 0.595 >=0.482,                            

which is concluded that the null hypothesis is rejected.

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A 3D electron microscope magnifies objects 1 000 000 times. A water molecule has a diameter of
[tex]2 \times {10}^{ - 10} [/tex]
m.

How large will it appear in the microscope?
give your answer in milimetres.






Answers

The diameter of the water molecule is  2 * 10^-4 m or 0.2 mm.

What is a microscope?

The term microscope refers to a device that is capable of increasing the size of an object. If the object is quite large, then it can be seen with the unaided eye.

Microscopes are very important in the sphere of scientific research as it was very instrumental in the study of cells and in the process of examination of other samples. There are several kinds of microscopes hay could be used for several purposes such as;

Electron microscopeCompound microscopeScanning electron microscope Light microscope etc.

Each of these microscopes have a unique instance in which they could be utilized.

Given that the diameter of water is about 2 * 10^-10 m,  a magnification by   1 000 000 times gives a diameter of 2 * 10^-4 m or 0.2 mm.

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The numbers 1, 2, 3, 4, 5, 6, 7, and 8 are arranged to form four two-digit numbers. What is the largest amount of primes that could possibly be among these four numbers?

Answers

Answer:  3 primes

==========================================================

Reason:

The only even prime number is 2. The other primes are odd.

The list of the first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

A prime is any number that has factors of 1 and itself, and nothing else.

For instance, 13 is prime because 1 and 13 are the only factors.

-----------

As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).

So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.

So we reduce the list of choices to 1, 3, 7, 9 for the units digit.

Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.

-----------

Let's try to build some primes.

Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.

On the other hand, 31 is prime since only 1 and 31 are factors.

The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.

Cross 1 and 4 off the list.

The next odd number is 3 which is our units digit. The value 23 is prime.

So far we have 41 and 23 as our two primes.

Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.

The number 67 is prime for similar reasoning mentioned earlier.

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

We have these primes: 41, 23, 67

The next number either 58 or 85 isn't prime

This is one way to show an example of why we're only able to get 3 primes out of this.

Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4? f(n 1) = f(n) 99.4, n ≥ 1 f(n 1) = f(n) – 99.4, n ≥ 1 f(n 1) = 99.4f(n), n ≥ 1 f(n 1) = –99.4f(n), n ≥ 1

Answers

The recursive formula for the given sequence is [tex]f(n+1)=f(n)-99.4[/tex]

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula [tex]a_n = a_{n-1} + d[/tex]. [tex]a_n = a_{n-1}r[/tex] is the recursive formula for a geometric sequence.

We are given a sequence as:

99.4,0,-99.4,-198.8, and so on

We can see that the sequence is constantly getting decreased by -99.4

i.e. f(1)=99.4

Then, f(2)=f(1)-99.4

               =99.4-99.4

               =0

f(3)=f(2)-99.4

   =0-99.4

   =-99.4

Therefore, the recursive formula of the given series is [tex]f(n+1)=f(n)-99.4[/tex]

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The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes. What does the slope of the linear equation that models the data indicate?

Answers

The slope of this linear equation that models the data indicate: B. the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute.

What is a linear function?

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

What is a slope?

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

How to calculate the slope of a line?

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (5 - 5.5)/(10 - 5)

Slope = -0.5/5

Slope = -0.1.

In conclusion, we can infer and logically deduce that the slope of this linear equation that models the data indicate the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute.

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Is the given point interior, exterior, or on the circle (x 2)2 (y - 3)2 = 81? p(8, 4) click on the graphic to choose the correct answer.

Answers

From the equation we see that the center of the circle is at (-2,3) and the radius is 9.

So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...

d^2=(8--2)^2+(4-3)^2  and d^2=r^2=81 so

81=10^2+1^2

81=101  which is not true...

So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.  

Thus the point lies outside or on the exterior of the circle...

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what is a real world example of a rational function, and how could you graph it and put it in a table?

Answers

A real world example is when a patient is injected with medicine until the concentration of the medicine in the blood is at its ideal level. Here is how you would graph it. In a table it would be on the left side, 123456, and on the right side, 1, 0.5, 0.25, 0.2, 0.15, 0.1

Solve for x. You must show all of your work to receive credit.

Answers

Step-by-step explanation:

the inner WU arc angle is 23x - 5.

the outer WU arc angle is 37x + 5.

together they must be 360°, as this is the full circle.

so, we have

360 = 23x - 5 + 37x + 5 = 60x

x = 6

therefore, the angle at V is

V = 5x + 17 = 5×6 + 17 = 30 + 17 = 47°

inner WU arc angle = 23x - 5 = 133°

outer WU arc angle = 37x + 5 = 227°

this also fits with

V = (outer arc angle - inner arc angle)/2 =

= (227 - 133)/2 = 94/2 = 47°

Which statements describe the function ? check all that apply. f(x) has one real zero because it crosses the x-axis once. f(x) has two real zeros because it crosses the x-axis twice. f(x) has real zeros at 1 and –1. f(x) has a real zero at 2.5. f(x) has x-intercepts at (1, 0) and (–1, 0). f(x) crosses the x-axis when x = 1 and x = –1. f(x) has an x-intercept at (2.5, 0).

Answers

Statements that describe the given function are:

(A) f(x) has one real zero because it crosses the x-axis once.(D) f(x) has a real zero at 2.5.(G) f(x) has an x-intercept at (2.5, 0).

What is a function?A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

To find the statements that describe the given function:

The following function can be reorganized: [tex]f(x)=\frac{2*x-5}{2*(x-1)*(x+1)}[/tex]There is one real zero (numerator) in the function (x-intercept), which is x = 2.5. Besides, x = 1 and x = -1 are poles (denominator), that is, x-values so that function is undefined.

Lastly, the correct answers are:

(A) f(x) has one real zero because it crosses the x-axis once.(D) f(x) has a real zero at 2.5.(G) f(x) has an x-intercept at (2.5, 0).

Therefore, statements that describe the given function are:

(A) f(x) has one real zero because it crosses the x-axis once.(D) f(x) has a real zero at 2.5.(G) f(x) has an x-intercept at (2.5, 0).

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The complete question is given below:

Which statements describe the function f(x)=2x-5/2(x^2-1)? Check all that apply.

(A) f(x) has one real zero because it crosses the x-axis once.

(B) f(x) has two real zeros because it crosses the x-axis twice.

(C) f(x) has real zeros at 1 and –1.

(D) f(x) has a real zero at 2.5.

(E) f(x) has x-intercepts at (1, 0) and (–1, 0).

(F) f(x) crosses the x-axis when x = 1 and x = –1.

(G) f(x) has an x-intercept at (2.5, 0).

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