For the system shown below, what are the coordinates of the solution that lies in quadrant 1?
Write your answer in the form (a,b) without using spaces.

[tex]3y^2-5x^2=7\\3y^2-x^2=23[/tex]

Answer:

[tex]f(x)=(x-2)^{\frac{1}{3}}-2[/tex] ⇒ answer B

Step-by-step explanation:

* Lets revise some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ f(x) = x^1/3

- f(x) shifted 2 units to the right

∴ f(x) = (x - 2)^1/3

- f(x) shifted 2 units down

∴ f(x) = (x - 2)^1/3 - 2

* [tex]f(x)=(x - 2)^{\frac{1}{3}}-2[/tex]

Answer:

The correct inequality for the given graph is x + 3y < -3 ⇒ 1st answer

Step-by-step explanation:

* Lets study the graph

- The angle between the positive part of x-axis and the line is obtuse,

 that means the slope of the line is negative value

- The shaded part is under the line, that means the solutions of the

 inequality are under the line , so the sign of the inequality is <

- The y-intercept is < -1 ⇒ (the value of y when x = 0)

* Now lets check the answers to find the correct answer

- At first we will choose the answer with sign <

∴ The answers are x + 3y < -3 OR x - 3y < -1

- At second lets check the y-intercept (put x = 0)

- Substitute x by 0 in the two answer to choose the right one

∵ x = 0

∴ 0 + 3y < -3 ⇒ ÷ 3 both sides

∴ y < -1

* OR

∵ x = 0

∴ 0 - 3y < -1 ⇒ ÷ -3 both sides

∴ y > 1/3 ⇒ because we divide the inequality by negative number

  we must reverse the sign of inequality

∵ the y-intercept is < -1

∴The first equation is right

* To be sure check the slope of each line

∵ y < mx + c, where m is the slope of the line

- Put each inequality in this form

∵ x + 3y < -3 ⇒ subtract x from both sides

∴ 3y < -3 - x ⇒ ÷ 3

∴ y < -1 - x/3

∴ m = -1/3 ⇒ the slope is negative

* OR

∵ x - 3y < -1 ⇒ subtract x from both sides

∴ -3y < -1 - x ⇒ ÷ -3

∴ y > 1/3 + x/3

∴ m = 1/3 ⇒ the slope is positive

∵ The slope of the line is negative

∴ The correct inequality for the given graph is x + 3y < -3

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° × (n - 2) ← n is the number of sides

Here n = 8 ( octagon ), hence

sum = 180° × 6 = 1080°

let the measure of 1 congruent angle be x

Then sum the 8 angles and equate to 1080

100 + 120 + 140 + 5x = 1080

360 + 5x = 1080 ( subtract 360 from both sides )

5x = 720 ( divide both sides by 5 )

x = 144

Thus each of the 5 congruent angles is 144°

Final answer:

To calculate the original loan amount for Scott, who paid $750 in interest at a 3% rate, we use the formula for simple interest and determine that the original loan amount was $25,000.

Explanation:

If Scott pays $750 in interest at a rate of 3%, to find out the original amount of the loan, we can use the formula I = PRT, where I stands for interest, P is the principal amount (the original loan amount), R is the rate of interest, and T is the time in years. Since Scott already knows the interest and the rate, we can rearrange this formula to solve for P:  P = I / (RT).

In this case, we assume the time T to be 1 year, since no specific time was given. The calculation would be:

P = $750 / (0.03 * 1)

P = $750 / 0.03

P = $25,000

So, the original loan amount Scott must have taken out is $25,000.

Answer

workbook =x

1/4   3/5

x    5/5 (1 hour)

then x=(5/5 * 1/4):3/5

x= 5/20 * 5/3  

x=1/4 *5/3

x= 5/12

The value of [p] at equilibrium is equivalent to 43.12.

At equilibrium, the demand is equal to supply. Mathematically, we can write -

D{x} = S(x)

Given is are the demand and supply equations.

We have the demand and supply equations as -

D{p} = (-5/8)p + 35

S{p} = (6/5)p - 44

Now, at equilibrium, we can write -

D{p} = S{p}

(-5/8)p + 35 = (6/5)p - 44

(6/5)p + (5/8)p = 35 + 44

p{(48 + 25)/40} = 79

p(73/40) = 79

p = (79 x 40)/73

p = 43.12

Therefore, the value of [p] at equilibrium is equivalent to 43.12.

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Answer:

the answer would be like finding the point and then doing the math

after the math u will find you answer on the am going to say either C or D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

If g(x) is a transformation of f(x), then we can consider function f(x) as parent function.

So, to get the graph of the function g(x), we have to translate the graph of the function f(x) 8 units up.

This translation will give us the function

[tex]g(x)=f(x)+9\\ \\g(x)=\dfrac{1}{4}\cdot 3^x-6+8\\ \\g(x)=\dfrac{1}{4}\cdot 3^x+2[/tex]

Answer:

37.8

Step-by-step explanation:

Length = radius * Θ

L=7*5.4

L=37.8

If wrong don't report, just notify me so I can edit.

Have a great day!

The length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm is 37.8 cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

The arc subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm.

As we know, the relationship between radius of the circle, central angle, and arc length is:

s = rθ

r = 7 cm

θ = 5.4 radians.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

s = 7×5.4

s = 37.8 cm

Thus, the length, to 1 decimal place, of the arc that subtends an angle of 5.4 radians at the center of a circle with a radius of 7 cm is 37.8 cm.

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Answer:

  11 m by 18 m

Step-by-step explanation:

The area is the product of two adjacent sides of a rectangle. The perimeter is twice the sum of two adjacent sides, so that sum is (58 m)/2 = 29 m.

We want to find two factors of 198 that sum to 29.

  198 = 1·198 = 2·99 = 3·66 = 6·33 = 9·22 = 11·18

Of these factor pairs, only the last one has a sum of 29.

The dimensions of the pool are 11 meter by 18 meters.

Answer:

There's a lot of them.

There are many different ways to calculate [tex]\pi[/tex]. The ones used by computers to generate tons of digits are usually infinite series.

The series that has been prominent in recent records for the most digits of pi is the Chudnovsky algorithm.

The algorithm is this:

[tex]\frac{1}{\pi}=12\sum_{k=0}^{\infty}\frac{\left(6k\right)!\left(545140134k+13591409\right)}{\left(3k\right)!\left(k!\right)^3\left(640320\right)^{3k+\frac{3}{2}}}[/tex]

For faster performance, it can be simplified to this:

[tex]\frac{426880\sqrt{10005}}{\pi}=12\sum_{k=0}^{\infty}\frac{\left(6k\right)!\left(545140134k+13591409\right)}{\left(3k\right)!\left(k!\right)^3\left(-262537412640768000\right)^k}[/tex]

Other algorithms have been used, but right now this is the one that is being used to set the recent records.

There are also some approximations that are used because they are very easy to calculate.

first, [tex]\frac{22}{7}[/tex] can be used to calculate a fairly accurate pi, but a better rational approximation is [tex]\frac{355}{113}[/tex] This fraction is actually accurate to 6 digits and it is the best approximation of [tex]\pi[/tex] in simplest form and with a denominator below 30,000.

There are several other approximations and if you want to learn more I would recommend looking at the Wikipedia page which has tons of algorithms for pi.

Answer:

24 pieces

Step-by-step explanation:

Divide:

 6 sandwiches

---------------------------- = 24 pieces

1/4 sandwich/piece

Answer:

Option C (x < -5/4)

Step-by-step explanation:

((2 - 5x)/(-3)) + 4 < -x.

Take LCM on LHS:

(2 - 5x - 12)/(-3) < -x.

Multiplying -3 on both sides (this will also flip the inequality):

-5x - 10 > 3x.

Adding 10 on both sides and subtracting -3x on both sides:

-8x > 10.

Dividing -8 on both sides (this will also flip the inequality):

x < -5/4.

Therefore, Option C is the correct answer!!!

Answer:

240

Step-by-step explanation:

Volume of the cylinder

= π(4)²(10)

= 160π in³

Volume of the cone

= 1/3 π(1)²(2)

= 2/3 π in³

Number of cones

= 160π ÷ 2/3 π

= 240

By calculating the volumes of both the original cylinder and one of the cones, we can determine that 80 solid right circular cones can be formed from the melted cylinder.

The question involves calculating the number of solid right circular cones that can be formed from melting and recasting a solid metal cylinder with given dimensions. First, we need to calculate the volume of the original cylinder and then the volume of one of the right circular cones, followed by dividing the volume of the cylinder by the volume of a cone to determine how many cones can be formed.

Step 1: Calculate the Volume of the Cylinder

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height (altitude). For the cylinder with a 4-inch radius and 10-inch altitude, the volume is V = π(4²)(10) = 160π cubic inches.

Step 2: Calculate the Volume of a Cone

The formula for the volume of a cone is V = ⅓πr²h, where r is the radius and h is the height. For a cone with a 1-inch radius and 2-inch altitude, the volume is V = ⅓π(1²)(2) = ⅓π cubic inches.

Step 3: Determine the Number of Cones Formed

To find the number of cones that can be formed, divide the volume of the cylinder by the volume of a cone: Number of cones = (160π) / (⅓π) = 80. Therefore, 80 solid right circular cones can be formed from the melted cylinder.

Answer:

6:45

Step-by-step explain if she has to leave 45 minutes before you take away 45 from 7:30 giving you the time she would have to leave

Answer: [tex]ln-10[/tex] is the length of Santa Monica and [tex]ln>10[/tex]

Step-by-step explanation:

Let the length of Nina Pinta be ''ln'

According to question, we have given that

the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta.

and 10 ft shorter than that of Nina Pinta is expressed as [tex]ln-10[/tex]

So, the length of Santa Monica be 'ln'-10'

Restriction on ln is that ln>10.

As Length of Santa Monica cannot be negative or equal to zero.

so, [tex]ln>10[/tex]

Hence, [tex]ln-10[/tex] is the length of Santa Monica and [tex]ln>10[/tex]

The speed of the Santa Monica, given the hull length of Nina Pinta as 'ln' and that Santa Monica is 10 ft lesser in hull length, can be represented by 1.34 * sqrt(ln - 10). The restriction on this is that ln must be greater than 10 ft.

The hull length of the Santa Monica is defined as ln - 10, where ln is the hull length of the Nina Pinta. The hull speed of the Santa Monica, according to the hull speed formula, is calculated as 1.34 times the square root of the hull length. Therefore, the hull speed of the Santa Monica in terms of the hull length of the Nina Pinta, ln, can be represented by the expression 1.34 * sqrt(ln - 10) where sqrt stands for 'square root'.

The restriction on the domain is that ln must be greater than 10 as the hull length cannot be negative.

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Answer:

Option C. x = 12

Step-by-step explanation:

we have that

Traingles MOP and MNQ are similar

therefore

The ratio of its corresponding sides is proportional

[tex]\frac{MO}{MN}=\frac{MP}{MQ}[/tex]

substitute the values

[tex]\frac{21+7}{21}=\frac{36+x}{36}[/tex]

[tex]28*36=21*(36+x)\\ \\1,008=756+21x\\ \\21x=252\\ \\x=12\ units[/tex]

I took the test, (for this particular graph) it was -1.5.

Answer:

The correct option is 1.

Step-by-step explanation:

The formula for residual value is

[tex]\text{Residual Value = Observed Value - Estimated value}[/tex]

In the given graph points represents the observed value and the line represents the expected or estimated value.

From the given graph it is clear that the observed value at x=5 is 5.5 and the estimated value at x=5 is 7.

[tex]\text{Residual Value}=5.5-7[/tex]

[tex]\text{Residual Value}=-1.5[/tex]

The residual value is -1.5, therefore the correct option is 1.

Answer:

10,995.6 ft^3.

2300.3 gallons.

(both to the nearest tenth).

Step-by-step explanation:

Area of the surface of the river =  area of the  outer circle - area of the inner circle.

Radius of the outer circle  = 30 *3 = 90 feet.

So the surface area of the river = π(90)^2 - π(85)^2

= 875π ft^2

Also the volume of the river = surface area * depth = 875π*4 = 3500π ft^3

= 10,995.6 ft^3.

Number of gallons of water it will hold = 10,995.6 /  4.78

= 2300.3 gallons.

Answer:

I believe it is C

Hope This Helps!     Have A Nice Day!!

Answer:

its

B.The graph of W(x) is 7 units to the right of the graph of f(x)

Divide 50 by 2 so 25 then divide that by 2 so 12.5 =x

The equation 2x² = 50 has two solutions, x = 5 and x = -5.

The equation 2x² = 50 can be solved algebraically by dividing both sides by 2 and then taking the square root of both sides. This gives us two solutions, x = 5 and x = -5.

Another way to solve this equation is to factor the left side. We can see that 2x² = 2(x²). We can also factor x² as (x)(x). This gives us the following equation:

2(x)(x) = 50

Dividing both sides by 2, we get:

(x)(x) = 25

Taking the square root of both sides, we get:

x = ±5

Therefore, the two solutions to the equation 2x² = 50 are x = 5 and x = -5.

We can check our answer by substituting x = 5 and x = -5 back into the original equation.

2(5)² = 50

2(25) = 50

50 = 50

This is true.

2(-5)² = 50

2(25) = 50

50 = 50

This is also true.

Therefore, our solutions are correct.

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Beep bop I’m a beginner and need this

Hshaks jdlsmavsusksns those were so that you would reach the answer minimum of 20 characters

Answer:

c

Step-by-step explanation:

Answer:

I believe it would be 42.25?  or 42 and 1/4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given a function of a parabola (quadratic) in the form f(x) = x^2, we have a translated function as:

g(x) = a(x-b)^2

Where

The function given is p(x) = 3(x-8)^2

So it means that it is a vertical stretch with a factor 3 and the graph is shifted horizontally 8 units right

the correct answer is B

The matrix

[tex]A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}[/tex]

has eigenvalues [tex]\lambda[/tex] such that

[tex]\det(A-\lambda I)=\begin{vmatrix}\cos\theta-\lambda&-\sin\theta\\\sin\theta&\cos\theta-\lambda\end{vmatrix}=0[/tex]

[tex](\cos\theta-\lambda)^2+\sin^2\theta=0[/tex]

[tex](\cos\theta-\lambda)^2=-\sin^2\theta[/tex]

[tex]\cos\theta-\lambda=\pm\sqrt{-\sin^2\theta}[/tex]

[tex]\lambda=\cos\theta\pm\sqrt{-\sin^2\theta}[/tex]

[tex]\sin^2\theta\ge0[/tex] for all values of [tex]\theta[/tex], so we need to have [tex]\sin\theta=0[/tex] in order for [tex]\lambda[/tex] to be real-valued. This happens for

[tex]\sin\theta=0\implies\theta=n\pi[/tex]

where [tex]n[/tex] is any integer, and over the given interval we have [tex]\theta=0[/tex] and [tex]\theta=\pi[/tex].

The matrix a will always have real eigenvalues for any value of θ.

To find the values of the angle θ for which the matrix a has real eigenvalues, we need to determine when the determinant of the matrix is greater than or equal to 0. The matrix a can be written as:

a = cos(θ) -sin(θ)

sin(θ) cos(θ)

To calculate the determinant, we use the formula det(a) = cos(θ) * cos(θ) - (-sin(θ)) * sin(θ) = cos²(θ) + sin²(θ) = 1. Since the determinant is always 1, the matrix a will always have real eigenvalues for any value of θ.

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Answer:

B. 13.26

Step-by-step explanation:

To go from the Degree-Minute-Second (DMS) system to a numeric one, we simply use this formula:

numeric = d + (min/60) + (sec/3600)

Where you take the degree number as is (13 in our case), then you divide the number of minutes by 60 (15 in our case) and the number of seconds by 3600 (36 in our case) and you add everything together.

So, if we plug in our numbers, we have

numeric = 13 + (15/60) + (36/3600)

numeric = 13 + 0.25 + 0.01

numeric = 13.26

For this case we have by definition that the volume of the pyramid is given by:

[tex]V = \frac {A_ {b} * h} {3}[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

We have, according to the figure shown:

[tex]A_ {b} = 8 ^ 2 = 64 \ units ^ 2\\h = 6 \ units[/tex]

Then, replacing:

[tex]V = \frac {64 * 6} {3}\\V = \frac {384} {3}\\V = 128 \ units ^ 3[/tex]

Answer:

Option D

Answer:

The correct answer is option D.  128 units²

Step-by-step explanation:

Formula:-

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

To find the volume of pyramid

Here base side = 8 units and h = 6 units

Volume = (a²h)/3

 = (8² * 6)/3 = 8100/3 = 2700  units²

Therefore the correct answer is option D.  128 units²

Answer:

36

Step-by-step explanation:

The 5 part of the ratio represents 60 girls.

Divide 60 by 5 to find the value of one part of the ratio

60 ÷ 5 = 12 ← value of 1 part of the ratio

The 3 part of the ratio represents the number of boys, hence

3 × 12 = 36 ← number of boys

Answer:

[tex]37.76\ g[/tex]

Step-by-step explanation:

we know that

The density is equal to divide the mass by the volume

[tex]D=m/V[/tex]

Solve for the mass

[tex]m=D*V[/tex]

Find the volume of the cube

The volume of the cube is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=4\ cm[/tex]

substitute

[tex]V=4^{3}[/tex]

[tex]V=64\ cm^{3}[/tex]

Find the mass

[tex]m=0.59*64=37.76\ g[/tex]

Answer:

Let's suppose the distance between gold town and silver town is 9 kilometers.

The first trip takes 9 km / 6 km / hour = 1.5 hours

The return trip takes 9 / 9 km / hour = 1 hour

TOTAL TRIP = 18 kilometers in 2.5 hours

= 18 / 2.5 = 7.2 hours

Answer is c

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

the formula is 2π rh +2πr^2

you put the values in

2π (6*15) +2π(6)^2

then you solve

180π+ 72π= 252π

For this case we have that by definition, the surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

A: It's the radio

h: It is the height of the cylinder

We have to:

[tex]r = 6 \ units\\h = 15 \ units[/tex]

Substituting:

[tex]SA = 2 \pi * 6 * 15 + 2 \pi * (6) ^ 2\\SA = 2 \pi * 6 * 15 + 2 \pi * (6) ^ 2\\SA = 180 \pi + 72 \pi\\SA = 252 \pi \ units ^ 2[/tex]

Answer:

Option A