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A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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F(x,y) · r(x,y) = 4(yi - xj) · (xi + yj)= 4xy - 4xy = 0

The two vectors are perpendicular to each other, and the length of F(x,y) is 4, as desired.

A two-dimensional vector field is a vector field in which each point in the plane is associated with a vector.

It is represented by a pair of functions (P, Q), each of which maps (x, y) to a real number, and the vector field itself is written as F = P i + Q j. Let's write a formula for a two-dimensional vector field that has all vectors of length 4 and is perpendicular to the position vector at that point

The formula for a two-dimensional vector field that has all vectors of length 4 and is perpendicular to the position vector at that point is given by:

F(x,y) = 4(yi - xj)

Here, the position vector at any point (x, y) in the plane is given by r(x,y) = xi + yj, and its magnitude is

|r(x,y)| = √(x² + y²).

To see that F(x,y) is perpendicular to r(x,y), take their dot product:

F(x,y) · r(x,y) = 4(yi - xj) · (xi + yj)= 4xy - 4xy = 0

Thus, the two vectors are perpendicular to each other, and the length of F(x,y) is 4, as desired.

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The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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Answer:

3 upon 2. that's the answer ..

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

Answer:

Step-by-step explanation:

The application of algebraic equations is important in solving this question.

The equation that could be used to determine how much each bottle cost is: 18.76 = 3 + 8x.

The cost of each bottle of juice =  x

The total cost before tax = C = $18.76

The cost of a bag of chips = $3

The equation is written as :

c = $3 + 8 * x

c = 3 + 8x

18.76 = 3 + 8x

Solving for the cost of each bottle of juice =

18.76 = 3 + 8x

Subtract 3 from both sides

18.76 - 3 = 3 - 3 + 8x

15.76 = 8x

Divide both sides by 8

15.76/8 = 8x/8

x = $1.97

The cost of each bottle of juice is $1.97.

Therefore, the equation that could be used to determine how each bottle cost is: 18.76 = 3 + 8x.

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Answer:

sorry i cant find anything for u

Step-by-step explanation:

Answer:

a)

Step-by-step explanation:

Answer:

Acute

Step-by-step explanation:

The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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Answer:

350 customers

Step-by-step explanation:

Since this is a ratio question and we only have variable that we need to solve (total people that entered last week), Then we can use the Rule of Three to solve this problem. We do this by multiplying the diagonal values of the following model and dividing by the third value in order to find the variable, like so...

18% of customers  <====>  63 customers

100% of customers  <====>  x customers

(100 * 63) / 18 = x

6,300 / 18 = x

350 = x

Finally, we can see that a total of 350 customers entered the store last week.

About 92 days are taken for 90 % of the material to decay.

The mass of radioisotopes (\(m\)), measured in milligrams, decreases exponentially in time (\(t\)), measured in days. The model that represents such decrease is described below:

\(m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }\) (1)

Where:

In addition, the time constant is defined in terms of half-life (\(t_{1/2}\)), in days:

\(\tau = \frac{t_{1/2}}{\ln 2}\) (2)

If we know that \(m_{o} = 85\,mg\), \(t_{1/2} = 27.7\,d\) and \(m(t) = 8.5\,mg\), then the time required for decaying is:

\(\tau = \frac{t_{1/2}}{\ln 2}\)

\(\tau = \frac{27.7\,d}{\ln 2}\)

\(\tau \approx 39.963\,d\)

\(t = -\tau \cdot \ln \frac{m(t)}{m_{o}}\)

\(t = -(39.963\,d)\cdot \ln \frac{8.5\,mg}{85\,mg}\)

\(t\approx 92.018\,d\)

About 92 days are taken for 90 % of the material to decay.

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Answer:

6n+12z

Step-by-step explanation:

then we got this bc we do like terms so 6n from 2 x3n then 12z bc 2x6

Answer:

a = 17 sqrt(2)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite / hypotenuse

sin 45 = 17/a

Multiply each side by a

a sin 45 = 17

Divide each side by sin 45

a = 17 / sin 45

a = 17 / ( 1 / sqrt(2))

a = 17 sqrt(2)

Answer:

I think it's D:)

Step-by-step explanation:

Answer: -4

Step-by-step explanation:

the slope is -4 because when x goes down by 2, y goes down by -8, so the y intercept is -4 because when x=-1 y=0 so if you go down 4 and over 1, you get the point x=0 and y=-4

Answer:

Choice a :  x= 102 degrees because 180°- (63°+39° ) = 78° and 180° - 78° = 102°

Step-by-step explanation:

Two angles are given as  63° and 39°

To find the third angle we subtract the other two angles from 180°

180°- 63°-39° gives 78°as the third inner angle .

The third angle and the outer angle x lie on the straight line making a total of 180°.

To find x we again subtract the inner angle 78° from 180°.

This gives the value of x to be 102°

180°- 78°=102°

Choice a is the best option.

Answer:

Step-by-step explanation:

Answer:

i think that it is. C.

i think it will help

The largest population to which the results can be generalized is in option C i.e. All student-athletes at the college.

Population: A population can be described as a complete group with at least one characteristic in common and a sample of the population can be used to get the features of the population.

We were told that a random sample of 50 student-athletes from all the student-athletes at a college, even though the population can be used to have an idea about how the consumption of beetroot juice enhances exercise performance, and it can not be used to get the results that can be generalized as more than 50 students-athletes is required which is chosen randomly.

All the other options are wrong because of this reason.

Therefore, option C is correct.

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Answer:

see explanation

Step-by-step explanation:

In a parallelogram the opposite angles are congruent , then

2p - 50 = p + 10 ( subtract p from both sides )

p - 50 = 10 ( add 50 to both sides )

p = 60

Then

∠ E = ∠ I = p + 10 = 60 + 10 = 70°

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

consecutive angles sum to 180° , so

∠ L = ∠ K = 180° - 70° = 110°

Answer:

win the lotto

Step-by-step explanation:

Answer:

i d k

Step-by-step explanation:

Answer:

Step 1: Identify the coordinates of each of the vertices of the triangle.

Step 2: Translate each point by adding the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. For these translations, add a negative number if the horizontal translation is to the left or if the vertical translation is downward.

Step 3: Plot the three translated points and draw the triangle by connecting each pair of points with a straight line.

Step-by-step explanation:

Triangle: A triangle is a three-sided geometric figure made by connecting each pair of points in a set of three with straight lines. The points that define a triangle are known as vertices

Answer:

x = 4y

Step-by-step explanation:

Answer:

4 is the answer. Hope it helps you.

Answer:

D. 491.52

Step-by-step explanation:

the vertex, focus, and directrix of the given parabola are given by:
Vertex: (h, k) = (- 2, - 3)

Focus: (h - a, k) = (- 2 - 3/4, - 3)

= (- 11/4, - 3)

Directrix: x = - 5/4.

The equation of the given parabola is y² + 6y + 3x + 3 = 0. We are to find the vertex, focus, and directrix of the parabola.

We can rewrite the given equation in the form: y² + 6y = - 3x - 3 + 0y + 0y²

Completing the square on the left side, we get:

(y + 3)²

= - 3x - 3 + 9

= - 3(x + 2)

This is in the standard form (y - k)² = 4a(x - h), where (h, k) is the vertex. Comparing this with the standard form, we have: h = - 2,

k = - 3.

So, the vertex of the parabola is V(- 2, - 3).Since the parabola opens left, the focus is located a units to the left of the vertex,

where a = 1/4|4a|

= 3/4

The focus is F(- 2 - 3/4, - 3) = F(- 11/4, - 3).

The directrix is a line perpendicular to the axis of symmetry and is a distance of a units from the vertex.

Therefore, the directrix is the line x = - 2 + 3/4

= - 5/4.

Therefore, the vertex, focus, and directrix of the given parabola are given by:

Vertex: (h, k) = (- 2, - 3)

Focus: (h - a, k) = (- 2 - 3/4, - 3)

= (- 11/4, - 3)

Directrix: x = - 5/4.

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