What are the foci of the graph y2 – 25x2 = 25?

Answer:

C

Step-by-step explanation:

To evaluate f(g(7)), substitute x = 7 into g(x), then substitute the result into f(x)

g(7) = (2 × 7) - 5 = 14 - 5 = 9, then

f(9) = 3(9)² - 4 = 243 - 4 = 239 → C

Option C is correct.

Given functions are, [tex]f(x)=3x^{2} -4,g(x)=2x-5[/tex]

We have to find  [tex]f(g(7))[/tex].

             [tex]g(7)=2*7-5=14-5=9[/tex]

So that,  [tex]f(g(7))=f(9)[/tex]

           [tex]f(9)=3*(9)^{2}-4\\ \\f(9)=243-4=239\\\\f(g(7))=f(9)=239[/tex]

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Answer:

C

Step-by-step explanation:

Since the angles at the centre subtended by the congruent arcs WX and YZ

Then ∠YOZ = ∠WOX = 103° → C

The measure of the angle YOZ is b°.  Option c is correct.

In a circle arc WX and YZ are congruent. Than angle YOZ is to be determine.

Arc is defined as the circular curve or part of circle. Arc = angle * radius.

Here, arc WX = arc YZ
If arc is equal in a circle than angle sub tainted by this arc to center are also equal.
angle YOZ = angle WOX = 103°

Thus, the measure of the angle YOZ is 103°.

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Step-by-step explanation:

Use Pythagorean theorem:

c² = a² + b²

Here, c = 42 and a = 31.

42² = 31² + b²

b = √803

b ≈ 28.3

[tex]\text{Hey there!}[/tex]

[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]

[tex]\text{Percentages (\%) usually run out of 100}[/tex]

[tex]\text{First, put the numbers set to multiply from each other.}[/tex]

[tex]\text{7\%}\times\text{14.50}[/tex]

[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]

[tex]\dfrac{7\%}{100}[/tex]

[tex]\dfrac{7\%}{100}=0.07[/tex]

[tex]\text{Next, solve for your answer.}[/tex]

[tex]\text{0.07}\times\text{14.50 = ?}[/tex]

[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]

[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]x^{5}[/tex]

Step-by-step explanation:

We simply add the exponents together. This depicts the exponent product rule, which states that when multiplying together two values with the same base (x) but different exponents, we can solve the answer by adding together the exponents with the base staying the same.

Explanation / Proof:

[tex]2^{2} * 2^{3} = 4 * 8 = 32\\\\2^{2} * 2^{3} = 2^{5} = 2*2*2*2*2 = 32[/tex]

As you can see, adding together the exponents will give the same answer. Therefore, the answer is [tex]x^{5}[/tex].

Answer:

y = 4.125x + 496.25

Step-by-step explanation:

Set the data up as points. Then deal with the points.

Givens

(30,620)

(70,785)

y2 = 785

y1 = 620

x2 = 70

x1 = 30

Formula

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

Solution

Slope = (785 - 620)/(70 - 30)

Slope = 165 / 40

Slope = 4.125

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

Now you need the y intercept. Either one of the two given points will give you that.

y = 620

x = 30

m = 4.125

y = mx + b

620 = 4.125*30 + b

620 = 123.75 + b

620 - 123.75 + b

b = 496.25

the linear function that describes the relationship between study hours and exam scores is:

y = 4.125x + 496.25

To find a linear function that fits the data provided, we'll use the points (30, 620) and (70, 785), which represent the number of hours spent studying and the corresponding exam scores. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

First, we calculate the slope (m):

m = (y2 - y1) / (x2 - x1) = (785 - 620) / (70 - 30) = 165 / 40 = 4.125

Next, we use one of the points to solve for b (y-intercept). Let's use the point (30, 620):

620 = 4.125(30) + b

b = 620 - (4.125 × 30) = 620 - 123.75 = 496.25

So the linear function that describes the relationship between study hours and exam scores is:

y = 4.125x + 496.25

Answer:

5

Step-by-step explanation:

1. Find the Mean

(2+8+10+16)/4=9

2.For each number, subtract the Mean and square the result.

(2-9)^2=49

(8-9)^2=1

(10-9)^2=1

(16-9)^2=49

3. Find the Mean of those squared differences.

(49+1+1+49)/4=25

4.Take the square root of that and this is what you want.

square root of 25 = 5

If the value of the mean is 9. Then the mean absolute deviation will be 4.

It is the average distance between each data point and the mean.

The MAD is given as

[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]

The data set is given below.

2,8,10,16

Then the mean will be

μ = (2 + 8 + 10 + 16) / 4

μ = 36 / 4

μ = 9

Then the mean absolute deviation will be

MAD = (|2 - 9| + |8 - 9| + |10 - 9| + |16 - 9|) / 4

MAD = (7 + 1 + 1 + 7) / 4

MAD = 16 / 4

MAD = 4

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Answer:

Option B is correct.

Step-by-step explanation:

4x+3y-z= -6     eq(1)

6x-y+3z= 12     eq(2)

8x+2y+4z=6    eq(3)

We need to solve these equations and find the value of x, y and z.

Multiply equation 2 with 3 and then add equation 1 and 2

18x -3y +9z = 36

4x +3y -z = -6

_____________

22x + 8z = 30    eq(3)

Multiply equation 2 with 2 and add with equation 3

12x -2y + 6z = 24

8x +2y +4z = 6

____________

20x + 10 z = 30  eq(4)

Multiply equation 3 with 10 and equation 4 with 8 and then subtract

220x + 80z = 300

160x + 80z = 240

-        -            -

_________________

60x = 60

x= 60/60

x= 1

Putting value of x in equation 3

22x + 8z = 30

22(1) + 8z = 30

8z = 30 - 22

8z = 8

z = 8/8

z=1

Putting value of x and z in equation 1

4(1)+3y-(1)=-6

4 + 3y -1 = -6

3 + 3y = -6

3y = -6 -3

3y = -9

y = -3

so, Option B x=1, y=3 and z=1 is correct

Answer:

b

Step-by-step explanation:

Answer:

The resulting equation is

x^2/4+16x^2/9=1

Step-by-step explanation:

The given equations are:

3y=12x   eq(1)

x^2/4+y^2/9=1    eq(2)

We need to isolate variable y in equation 1

Divide both sides of the equation with 3

3y/3 = 12x/3

y = 4x

Now, substitute the value of y=4x in second equation

x^2/4+y^2/9=1

x^2/4 + (4x)^2/9 = 1

The resulting equation is

x^2/4+16x^2/9=1

Answer:

[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]

Step-by-step explanation:

Given system of equations,

[tex]3y=12x-----(1)[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{9}=1----(2)[/tex]

As per statement,

Isolating the variable y in the first equation,

[tex]y=\frac{12}{3}x=4[/tex]

Now, substituting into the second equation,

[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]

Which is the resulting equation,

Simplifying the equation,

[tex]\frac{x^2}{4}+\frac{16x^2}{9}=1[/tex]

[tex]\frac{9x^2+64x^2}{36}=1[/tex]

[tex]73x^2=36[/tex]

Answer:

m=4

Step-by-step explanation:

3-(-1)/-1-(-2)=3+1/-1+2=4/1

Answer:

4

Step-by-step explanation:

Slope formula:

     ↓

[tex]\frac{\huge Y_2-Y_1}{\huge X_2-X_1}=\frac{Rise}{run}[/tex]

[tex]Y_2=(-1)\\Y_1=3\\X_2=(-2)\\X_1=(-1)\\[/tex]

[tex]\frac{(-1)-3}{(-2)-(-1)}=\frac{-4}{-1}=4[/tex]

Therefore, the slope is 4.

4 is the correct answer.

I hope this helps you, and have a wonderful day!

Answer:

n² + 3

Step-by-step explanation:

It's a quadratic sequence, so it follows the form:

y = ax² + bx + c

We're given five points that satisfy the equation.  (1, 4), (2, 7), (3, 12), (4, 19), and (5, 28).  Picking any three points, we can form a system of equations.

If we pick (1, 4), (2, 7), and (4, 19):

4 = a(1)² + b(1) + c

7 = a(2)² + b(2) + c

19 = a(4)² + b(4) + c

4 = a + b + c

7 = 4a + 2b + c

19 = 16a + 4b + c

Through substitution, elimination, or trial and error, we can find a = 1, b = 0, and c = 3.

y = x² + 3

So the nth term of the sequence is n² + 3.

Answer:

a(n) = a(n-1) + (2n - 1)

Step-by-step explanation:

Start by analyzing the pattern:

7 is 3 more than 4;

12 is 5 more than 7;

19 is 7 more than 12, and so on.  

Each step is an odd number and is 2 greater than the previous step.

a(2) = 7 = 4 + step = 4 + 3 = 7

a(3) = 12 = 7 + step = 7 + 5 = 12

a(4) =                      12 + 7  = 19

a(5) =                       19 + 9 = 28

and so on.  

Looking at a(2), we see that the step is 2+1, or 3;

Looking at a(3), we see that the step is 2(3) - 1, or 5;

Looking at a(4), we see that the step is 2(4) - 1, or 7; and so on.

Looking at a(n), we see that the step is 2n - 1.

Thus, a(n) = a(n-1) + (2n - 1)

Answer:(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)

Step-by-step explanation:

We can rewrite left side into right side form

(x^2+y^2)^2=(x^2+y^2)(x^2+y^2)

we can expand it

(x^2+y^2)^2=x^4+x^2y^2+x^2y^2+y^4

(x^2+y^2)^2=x^4+y^4+2x^2y^2

we can add and subtract 2x^2y^2

(x^2+y^2)^2=x^4+y^4+2x^2y^2+2x^2y^2-2x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+2x^2y^2+2x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+4x^2y^2

(x^2+y^2)^2=x^4-2x^2y^2+y^4+(2xy)^2

(x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2

The Pythagorean triple generator typically involves an algebraic formula where variables m and n are used to generate the sides of a right triangle such that a^2 + b^2 = c^2, with a common formula being a = m^2 - n^2, b = 2mn, and c = m^2 + n^2 for positive integers m and n.

The form of the Pythagorean triple generator refers to a set of algebraic formulas that produce Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the condition of the Pythagorean theorem (a^2 + b^2 = c^2) for a right triangle.

One well-known formula to generate these triples is given by:

where m and n are positive integers with m > n. This formula will produce a Pythagorean triple as long as m and n are coprime and not both odd. It's important to note that not all Pythagorean triples can be generated by this formula, but it is a very common method of finding such triples.

Answer: 45°

Step-by-step explanation:

Because AB and CD are parallel, angle x must be congruent with its corresponding angle.

See the attached picture:

Answer:

12 days

Step-by-step explanation:

Sally has  pet snail that fell into a well.

Depth of the well = 16 feet

Snail climbs up 5 feet but each night it slides back down 4 feet.

So the snail climbs up per day = 5 feet - 4 feet = 1 feet.

Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet

Remaining distance to cover by the snail = 16 - 11 = 5 feet

Number of days to cover remaining 5 feet to reach the top of the well = 1 day

Therefore, snail will take 12 days to reach the top of the well.

Final answer:

The snail climbs up 5 feet and slides back 4 feet each day in a 16-foot deep well. With a net gain of 1 foot per day, the snail will escape on the 16th day after reaching the top without sliding back.

Explanation:

Sally's pet snail finds itself in a classic mathematical problem often associated with algebra and arithmetic sequences. The snail is attempting to escape a 16-foot deep well by climbing up 5 feet during the day and sliding back 4 feet each night. To determine how many days it will take for the snail to get out, we need to calculate the net progress made by the snail each day and then examine how this applies on the final day of the snail's ascent.

Each day, the snail makes a net gain of 1 foot (5 feet up during the day minus 4 feet down at night). After 15 days, the snail would have climbed 15 feet during the day. On the 16th day, the snail climbs up 5 feet and reaches the top of the well, coming out without sliding back down since it already reached the goal during daylight. Therefore, it will take the snail a total of 16 days to escape the well.

Answer:

D

Step-by-step explanation:

The first and last sequence have a common difference in them. The first having d = 4 and the second having d = 7.

The second and third have a common ratio instead and are geometric sequences. The second has r = 2, and the third having r = (-3)

Answer:

The fourth graph shows and exponential growth function.

Step-by-step explanation:

The last graph shows the value increasing by a large amount.

An exponential function can represent growth or decay.

The graph represents an exponential growth function is graph (d)

An exponential function is represented as:

[tex]y = ab^x[/tex]

Where:

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

From the diagrams, only the last graph represent an exponential growth function.

Hence, the graph represents an exponential growth function is graph (d)

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Answer:

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Step-by-step explanation:

If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by:  8.25 - 0.25X.

If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by:  9.75 - 0.75X.

If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:

Equation: 8.25 - 0.25X = 9.75 - 0.75X

Step 1: -1.50 - 0.25X = - 0.75X

Step 2: -1.50 = - 0.50X

Step 3: x=3

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Answer: Option B

From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.

Step-by-step explanation:

To solve this problem, let's consider the initial equation that Jorge had.

[tex]8.25-0.25x=9.75-0.75x[/tex]

Subtract 9.75 on both sides of equality

[tex]8.25-9.75-0.25x=9.75-9.75-0.75x[/tex]

[tex]-1.50-0.25x=-0.75x[/tex]

Add 0.25x on both sides of equality

[tex]-1.50-0.25x+0.25x=-0.75x+0.25x[/tex]

[tex]-1.50=-0.50x[/tex]

[tex]x=3[/tex]

You can see then that Jorge's error was adding [tex]-0.75x + 0.25x[/tex]

When this sum is correctly done, the result is [tex]-0.50x[/tex]

The answer is the option B.

Answer:

1. 50 cm

2. 550 mm

3. 5000 mm

4. 5000 cm

5. 5000 m

Step-by-step explanation:

We can convert all the measures in same unit to arrange them one by one.

5000 cm:

As there are 10 millimeters in 1 cm,

5000 cm = 5000*10mm

=> 50000 mm

5000 meters:

As there are 100 cms in one meter

5000 m = 5000*100 cm

=> 500000 cm

Now to convert in millimeter

500000*10= 5000000 mm

50 cm:

50*10 = 500 mm

Then there is 550 mm and 5000 mm

So, the order from least to greatest is:

1. 500 mm which is equivalent of 50 cm

2. 550 mm

3. 5000 mm

4. 50000 mm which was equivalent of 5000 cm

5. 5000000 mm which was equivalent of 5000 m ..

Final answer:

To compare the given measurements, we converted each one to millimeters (mm) using a conversion table, then arranged them in ascending order: 50 cm (500 mm), 550 mm, 5,000 mm, 5,000 cm (50,000 mm), and 5,000 m (50,000,000 mm).

Explanation:

To determine which of the given measures is the smallest and which is the largest, we need to convert each measure to the same unit for comparison. Using the ratio conversion table, we will convert all measures to millimeters (mm).

Now we arrange the measures in order from least to greatest:

Answer:

-3

Step-by-step explanation:

Answer:

The slope of the line is [tex]m=-3[/tex]

Step-by-step explanation:

For a linear equation of the form

[tex]y = mx + b[/tex]

the slope of the line is the constant m

in this case we have the equation

[tex]y + 1 = -3x[/tex]

Solving for y we have:

[tex]y = -3x -1[/tex]

Then [tex]m = -3[/tex]

The slope of the line is -3

Answer:

(x−8)2+C−64(x-8)2+C-64

Replace x with the binomial a - 2.

f(a - 2) = [3(a - 2) + 5]/(a- 2)

f(a - 2) = [3a - 6 + 5]/(a - 2)

f(a - 2) = [3a - 1]/(a - 2)

f(a - 2) = (3a - 1)/(a - 2)

Done.

Answer:

-a (14 +a) =0

Step-by-step explanation:

-14a-a^2=0

Factor out  -a

-a (14 +a) =0

Using the zero product property

-a =0   14+a =0

a =0   a = -14

Answer:

5

Step-by-step explanation:

When you given input of "x" into a floor function  y = ⌊x⌋ , it gives as output the "greatest integer less than or equal to x"

For example, if we were to given 1.4 as the input for floor function, it will return the greatest integer that is less than or equal to 1.4, so it would be 1.

So, if we put 5.7 into this function, the floor function would give "5" as the output.

Thus value of y would be 5

Answer:

5

Step-by-step explanation:

Answer:

dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]

Step-by-step explanation:

* Lets revise some rules for the derivative

- The derivative of ㏑(f(x)) = 1/f(x) × f'(x)

- The derivative of u/v = (vu'-uv')/v²

- The derivative of the constant is 0

* Lets solve the problem

∵ y = ㏑[(4x³ - 7)/(3x^5 + 1)]

- Let u = 4x³ - 7 and v = 3x^5 + 1

∵ u = 4x³ - 7

∴ u' = 4(3)x^(3-1) - 0 = 12x²

∵ v = 3x^5 + 1

∴ v' = 3(5)x^(5-1) + 0 = 15x^4

∵ The derivative of u/v = (vu' - uv')/v²

∴ The derivative of u/v = [tex]\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)^{2}}[/tex]

∵ The derivative of ㏑(f(x)) = 1/f(x) × f'(x)

∴ dy/dx = [tex]\frac{1}{\frac{(4x^{3}-7)}{(3x^{5}+1)}}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4}}{(3x^{5}+1)^{2}}][/tex]

- Simplify by cancel bracket (3x^5 + 1)from the 1st fraction with the

 same bracket in the 2nd fraction

∴ dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad ~\hspace{10em}slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=4[x-(-2)]\implies y-1=4(x+2) \\\\\\ y-1 = 4x+8\implies y=4x+9[/tex]

Answer for A. (-8,-2)

answer for B. (4,-7)

Approximately 18.42% of the beef production annually worldwide comes from the U.S.

In the U.S., 12.0 million metric tons of beef are produced annually, while worldwide beef production is 65.1 million metric tons.

To find the percentage of beef produced in the U.S. compared to worldwide production, you can divide the U.S. beef production by the worldwide beef production and multiply by 100.

Percentage = ( U.S. beef production / Worldwide beef production ) x 100 = ( 12.0 million / 65.1 million ) x 100 = 18.42%.

Therefore, approximately 18.42% of the beef produced annually in the world is from the U.S.

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Answer:

The length of the missing side of the triangle is represented by the equation:

  (6a + 2b - 5) - (2a - 3b) - (a - 3)

= 6a + 2b - 5 - 2a + 3b - a + 3

= 3a + 5b - 2