A carton of 6 eggs costs $1.44. At that rate, how much would a carton of 12 eggs cost?

Answer:

elimination

Step-by-step explanation:

multiply 2nd eqn by 2 and take eqn 1 - eqn 2 and you'll get rid of x term, leaving only the y term and a constant, where you can then easily solve for y and sub to get x

Topic: simultaneous eqn

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Answer:

15/64

Step-by-step explanation:

First make 1 3/5 into a improper fraction, or a fraction greater than one.

1 3/5 -> 8/5

Next, do the reciprocal of 8/5 which is 5/8 and multiply 5/8 by 3/8 to get 15/64.

Answer:

A)Jo arrived at the destination and prepared to return.

B)8km/h

Step-by-step explanation:

divide 30 by 3.75 which will give you 8km/h.

Hope this helps.

1. The terminal point P(x, y) determined by a real number t is given. So, the answer is sin t = 3/5, cos t = 4/5, and tan t = 3/4.

We need to first determine the values of x and y in order to find sin t, cos t, and tan t. We are given the point P(x, y) = (4/5, 3/5), which is centered on the unit circle.

We can use the Pythagorean theorem to find the value of the radius r of the unit circle:

r = √(x² + y²)

= √(4/5)² + (3/5)²)

= √(16/25 + 9/25)

r = √(25/25)

r = 1

So the point P lies on the unit circle, and its coordinates satisfy x = 4/5 and y = 3/5.

Now, we can use the definitions of sin t, cos t, and tan t to find their values:

sin t = y/r = (3/5) / 1 = 3/5

cos t = x/r = (4/5) / 1 = 4/5

tan t = y/x = (3/5) / (4/5) = 3/4

Therefore, sin t = 3/5, cos t = 4/5, and tan t = 3/4.

2. The terminal point P(x, y) determined by a real number t is given. So, the answer is sin t = (√15)/8, cos t = -7/8, and tan t = -(√15)/7

We need to first determine the values of x and y in order to find sin t, cos t, and tan t. The point P(x, y) = (-7/8, (√15/8) on the unit circle centered at the origin is provided to us.

We can use the Pythagorean theorem to find the value of the radius r of the unit circle:

r = √(x² + y²)

= √(-7/8)² + (√15)/8)²

= √(49/64 + 15/64)

r = √(64/64) = 1

r = 1

So the point P lies on the unit circle, and its coordinates satisfy x = -7/8 and y = √15/8.

Now, we can use the definitions of sin t, cos t, and tan t to find their values:

sin t = y/r = (√15)/8) / 1 = √15/8

cos t = x/r = (-7/8) / 1 = -7/8

tan t = y/x = (√15)/8) / (-7/8) = -(√15)/7

Therefore, sin t = (√15)/8, cos t = -7/8, and tan t = -(√15)/7.

3. The values of the trigonometric functions of t from the given information. tan t= (-5/12) cos t > 0. So, the answer is sin t = 12/13 , cos t = -5/13

We know that tan t = (-5/12) cos t > 0. We know that t must be in the second quadrant since tan t is negative in the second and fourth quadrants and cos t is negative in the second and third quadrants. Cosine is negative in the second quadrant, while sine is positive. The Pythagorean identity may be used to calculate the value of sin t:

sin² t + cos² t = 1

sin² t + (-5/12)² sin² t = 1

(1 + 25/144) sin² t = 1

169/144 sin² t = 1

sin² t = 144/169

sin t = √(144/169) = 12/13

Now, we can find the cos t:

cos t = -√(1 - sin² t)

= -√(1 - (144/169))

cos t= -5/13

Therefore, sin t = 12/13 , cos t = -5/13

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Answer:

6.7234724... ; ✓7

Step-by-step explanation:

In the most simplest of terms, we can explain irrational numbers as numbers which cannot be expressed as a ratio of two integers usually because they cannot give an exact value when evaluated.

Using the values given :

6.7234724... - - >This is an irrational number because the '...' depicts that the values are unending and as such an exact expression in the form of a ratio (p/q) cannot be determined.

315, 26, 17, 8 - - - > Is a rational number, it could be express in ratio form as : 315/1. 315 is an integer and all integers are rational.

-0.25 - - > it could be expressed as - 1 /4. Hence it is a rational number.

✓7 - irrational as the simplification gives : 2.6457513...

Two single receptacles can be installed in a two-gang box made up of two single-gang boxes ganged together.

A two gang-box is a square electrical box, also called a double-gang box, houses two devices. The two gang-box have a combination switch/outlet or a pair of switches/outlets inside that can control two lighting circuits.

A two-gang box made up of two single-gang boxes which are ganged together can install two single receptacles- receptacles refer to the openings in the gang box into which electronics can be plugged.

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Answer:

The angle measures of  ABC and the other triangles are the same measures, and the side lengths in ABC and the other triangles are the same lengths when ABC coincides with them. It appears that angle measures and side lengths are both preserved when  ABC is rotated.

Step-by-step explanation:

The equation of each quadratic function in vertex form are as follows;

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

y = a(x - h)² + k

Where:

Part 1.

With vertex (1, -5) and point (3, -1), the quadratic function is given by;

-1 = a(3 - 1)² - 5

4a = 4

a = 1

y = (x - 1)² - 5

Part 2.

With vertex (2, 3) and point (1, 2), the quadratic function is given by;

2 = a(1 - 2)² + 3

-a = 3 - 2

a = -1

y = -(x - 2)² + 3

Part 3.

With vertex (-2, 1) and point (0, 0), the quadratic function is given by;

0 = a(0 + 2)² + 1

4a = -1

a = -1/4

y = -1/4(x + 2)² + 1

Part 4.

With vertex (-4, -1) and point (-3, -2), the quadratic function is given by;

-2 = a(-3 + 4)² - 1

-a = -1 + 2

a = -1

y = -(x + 4)² - 1

Part 5.

With vertex (-5, -1) and point (-3, 3), the quadratic function is given by;

3 = a(-3 + 5)² - 1

-4a = -1 - 3

a = 1

y = (x + 5)² - 1

Part 6.

With vertex (2, 4) and point (0, 2), the quadratic function is given by;

2 = a(0 - 2)² + 4

-4a = 4 - 2

a = -1/2

y = -1/2(x - 2)² + 4

Part 7.

With vertex (-3, 0) and point (0, 3), the quadratic function is given by;

3 = a(0 + 3)² + 0

-9a = 0 - 3

a = 1/3

y = 1/3(x + 3)² + 0

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Answer: lineales

Step-by-step explanation:

Hay una tasa constante de aumento.

The relation displayed in the table is

The relation in the table is compared by identifying how a coordinate point are expressed as ordered pair and how they are expressed as a table

For instance, say (b, c) is represented in a table as

x    y

a    b

Using this instance and writing out the values in the table we have

(3, 3), (-1, 1), (2, -2), and (-3, 2)

This is similar to option B making option B the appropriate option

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Answer:

D

Step-by-step explanation:

So sorry for the late response I didn't even see this but it is D

rate of change is the same as slope and in the equation you can see the slope is 3 but in the table it is a little more tricky to find

we use the formula y2-y1/x2-x1 for this

7-2/4-3

5/1

5

so the slope or rate of change is 5

This is possible if the first twin was born just before midnight and the second twin was born just after midnight, on different calendar days.

For the most part, twins and multiples share the same birthday. However, depending on the time of day the babies are born and how long the timespan is between each baby's birth, twins can be born on different days.

Twins are defined as two offspring born together, but that doesn't necessarily mean they are born on the same date. Multiples are generally born only a few minutes apart. If delivered by cesarian section, the interval between births is usually only a minute, maybe two.

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Answer:

Picture so I can solve it

Using the definition of big o notation, t(n) = 32 * 4^n is O(f(n)) = 5^n with c = 26 and n0 = 1.

The definition of Big O notation states that a function t(n) is said to be O(f(n)) if there exist positive constants c and n0 such that |t(n)| <= c * |f(n)| for all n >= n0. In other words, t(n) grows no faster than f(n) as n becomes large.

To find the constants c and n0 that show that t(n) = 32 * 4^n is O(f(n)) = 5^n, we need to find a value of c and an n0 such that:

|32 * 4^n| <= c * |5^n|

for all n >= n0.

Let's start by finding a value for c that works for n = 1. We have:

|32 * 4^1| = 128 <= c * |5^1| = 5c

So, c >= 128 / 5 = 25.6.

Now let's try c = 26. We have:

|32 * 4^n| <= 26 * |5^n|

for all n >= 1.

Since 26 * |5^n| is an increasing function as n increases, we can conclude that:

t(n) = 32 * 4^n is O(f(n)) = 5^n

with c = 26 and n0 = 1.

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Answer:

15.9% (nearest tenth)

Step-by-step explanation:

\(X \sim \sf N(\mu, \sigma^2)\)

Given:

\(X \sim \sf N(7.8, 0.3^2)\)

Using a calculator:

\(\implies \textsf{P}(X < \sf 7.5)=0.1586552539=15.9\%\:(nearest\:tenth)\)

Converting to z-value:

\(\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \dfrac{X-\mu}{\sigma}=Z, \quad \textsf{where }\: Z \sim \textsf{N}(0,1)\)

\(\implies \textsf{P}(X < 7.5)=\textsf{P}\left(Z < \dfrac{7.5-7.8}{0.3}\right)=\textsf{P}(Z < -1)\)

\(\implies \textsf{P}(Z < \sf-1)=0.1586552539=15.9\%\:(nearest\:tenth)\)

Answer:

u +v = < 7,9 >

Step-by-step explanation:

You are given u = <9,4> and v = <-2,5>. You are asked to find u+v. all you need to do is to add them with their respective position. u+v = <9-2, 4+5>, u+v = <7,9>. This is the correct answer.

Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

Answer:

might be 50 b cause 50+55is 105 which is the are outside the triangle

Step-by-step explanation:

hi

Answer:

To solve this problem, you can write a simple equation:

55+x=105

This equation works, thanks to the exterior angle theorem.

Solving for x, we see that it is equal to 50 degrees.

Let me know if this helps

The height of a Doric column that has a base diameter of 555 feet is 666 feet greater than the height of a Doric column that has a base diameter of 222 feet.

Given that the line in the xyxyx, y-plane above represents the relationship between the height h(x)h(x)h, (, x, ), in feet, and the base diameter xxx, in feet, for cylindrical Doric columns in ancient Greek architecture.

The question is asking us to find the difference between the height of a Doric column that has a base diameter of 555 feet than the height of a Doric column that has a base diameter of 222 feet.

Let's solve the problem.

:Let the height of a Doric column with base diameter 222 feet be y1 and the height of a Doric column with base diameter 555 feet be y2.

Given equation of the line in the xy-plane as,  y=2x+7

From the above equation, we have  

y1=2(222)+7  y1=451 feet (approximately)

y2=2(555)+7  y2=1117 feet (approximately)

The height of the Doric column with a base diameter of 555 feet is 1117 feet and the height of the Doric column with a base diameter of 222 feet is 451 feet. So, the difference in their heights is 1117 - 451 = 666 feet.

Thus, the height of a Doric column that has a base diameter of 555 feet is 666 feet greater than the height of a Doric column that has a base diameter of 222 feet.

The height of a Doric column with a base diameter of 555 feet is 666 feet greater than the height of a Doric column with a base diameter of 222 feet. Using the equation of the line in the xy-plane y=2x+7, we have calculated the height of a Doric column with base diameter 222 feet as 451 feet (approximately) and the height of a Doric column with base diameter 555 feet as 1117 feet (approximately). So, the difference in their heights is 1117 - 451 = 666 feet.

Therefore, the height of a Doric column that has a base diameter of 555 feet is 666 feet greater than the height of a Doric column that has a base diameter of 222 feet.

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Answer:

The speed of Sara is 78.4 km/h.

Step- by-step explanation:

Manuel and Sara travel a certain distance, and the times they use are in the ratio 21/15. Manuel's speed is 56km / h. What is Sara's speed?

Let the distance is d.

speed of Manuel = 56 km/h

time taken by Manuel = 21 t

time taken by Sara =  15 t

Let the speed of Sara is v.

Distance = speed x time

For Manuel:

d = 56 x 21 t ..... (1)

For Sara:

d = v x 15 t ..... (2)

From (1) and (2)

56 x 21 t = v x 15 t

v = 78.4 km/h

Answer:

I can't see the pictures clearly but its between Option A and Option C

Step-by-step explanation:

\(\frac{y^{2}-y^{1} }{x^{2}-x^{1} }=\frac{60-20}{42-14}=\frac{40}{28}=\frac{20}{14}=\frac{10}{7}\)

Slope = \(\frac{10}{7}\)

\(y-y_{1}=m(x-x_{1} ) \\\\y-20=\frac{10}{7}(x-14)\\\\y-20=\frac{10}{7}x-20\\\\y=\frac{10}{7} x\)

y-intercept = origin (0, 0)

Answer:

123

Step-by-step explanation:

thank you know what the plan

The work done by vector field F on the particle moving along curve C is 11.

To compute the work done by vector field F on a particle moving along curve C, we can use the line integral. The line integral of a vector field F along a curve C is given by:

∫ F · dr

where F is the vector field and dr is the differential displacement along the curve.

Given:

Curve C: r(t) = (1 + 3sin(t))i + (1 + 4sin²(t))j + (1 + 4sin³(t))k, 0 ≤ t ≤ π/2

Vector Field F: F(x, y, z) = xi + yj + zk

To compute the line integral, we need to parameterize the curve C. We can use the given parameterization r(t) to obtain the differential displacement vector field dr.

dr = (dx/dt)dt i + (dy/dt)dt j + (dz/dt)dt k

Let's calculate the line integral step-by-step:

Calculate the differential displacement vector dr:

dx/dt = 3cos(t)

dy/dt = 8sin(t)cos(t)

dz/dt = 12sin²(t)cos(t)

dr = (3cos(t))dt i + (8sin(t)cos(t))dt j + (12sin²(t)cos(t))dt k

Compute F · dr:

F · dr = (xi + yj + zk) · ((3cos(t))dt i + (8sin(t)cos(t))dt j + (12sin²(t)cos(t))dt k)

= 3cos(t)dt + 8sin(t)cos(t)dt + 12sin²(t)cos(t)dt

= (3cos(t) + 8sin(t)cos(t) + 12sin²(t)cos(t))dt

Integrate F · dr along the curve C with respect to t from 0 to π/2:

∫ F · dr = ∫[0 to π/2] (3cos(t) + 8sin(t)cos(t) + 12sin²(t)cos(t))dt

To evaluate this integral, we can split it into three separate integrals:

I₁ = ∫[0 to π/2] 3cos(t) dt

I₂ = ∫[0 to π/2] 8sin(t)cos(t) dt

I₃ = ∫[0 to π/2] 12sin²(t)cos(t) dt

Let's calculate each integral:

I₁ = ∫[0 to π/2] 3cos(t) dt

= [3sin(t)] from 0 to π/2

= 3sin(π/2) - 3sin(0)

= 3 - 0 = 3

I₂ = ∫[0 to π/2] 8sin(t)cos(t) dt

= [4sin²(t)] from 0 to π/2

= 4sin²(π/2) - 4sin²(0)

= 4 - 0

= 4

I₃ = ∫[0 to π/2] 12sin²(t)cos(t) dt

= [4sin³(t)] from 0 to π/2

= 4sin³(π/2) - 4sin³(0)

= 4 - 0

= 4

Now, we can find the total line integral:

∫ F · dr = I₁ + I₂ + I₃

= 3 + 4 + 4

= 11

Therefore, the work done by vector field F on the particle moving along curve C is 11.

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Incomplete question:

If C is the curve given by r (t) = (1 + 3 sin t) i + (1+4 sin² t) j + (1+4 sin³ t) k, 0 ≤t ≤ π/2 and F is the radial vector field F(x, y, z) = xi+yj+zk, compute the work done by F on a particle moving along C.

Answer:

  use similar triangles

Step-by-step explanation:

The Basic Proportionality Theorem states that a line parallel to the base of a triangle divides the sides proportionally.

To prove it, use the relations related to angles at a transversal of parallel lines to show the triangles are similar. Similar triangles have corresponding sides that are proportional.

Answer: 140,000

............................

C. True, because to use the Law of Sines, at least two sides must be known.

The Law of Sines is a trigonometric rule that relates the sides and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

To use the Law of Sines, at least two sides and the angle opposite one of them (or two angles and one side) must be known.

Therefore, the statement "The Law of Sines can be used to solve triangles where three sides are known" is false, as it is not necessary to use the Law of Sines to solve a triangle where all three sides are known.

In summary, the correct answer is C. True, because to use the Law of Sines, at least two sides must be known.

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Answer:

5

Step-by-step explanation:

as x goes up one y goes up 5

slope is change in y over changes in x

5/1=5

The equation of the circle graphed below is (x - 1)² + (y - 1)² = 4.

To determine the equation of a circle, we need to know the coordinates of its center and the radius. The general equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

where (x,y) are the coordinates of any point on the circle. The equation shows that the distance between any point (x,y) on the circle and the center (h,k) is always equal to the radius r.

To determine the equation of the circle graphed below, we need to identify the coordinates of its center and the radius. One way to do this is to use the distance formula between two points. We can choose any two points on the circle and use their coordinates to find the distance between them, which is equal to the diameter of the circle. Then, we can divide the diameter by 2 to find the radius.

To find the radius, we can choose any point on the circle and use the distance formula to find the distance between that point and the center. We can use the point (5,1), which is on the right side of the circle. The distance between (5,1) and (1,1) is 4 units, which means that the radius is 2 units.

Substituting the values of (h,k) and r in the general equation of the circle, we get:

(x - 1)² + (y - 1)² = 4

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