solve using elimination

9x-3y=24
7x-3y=20

The area of the small triangle is equal to 25 ft².

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

In Mathematics and Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:

(Scale factor of dimensions)² = Scale factor of area

Therefore, the area of the small triangle can be calculated as follows;

Area of small triangle = (12/28)² × 135

Area of small triangle = 24.80 ≈ 25 ft².

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If each bag of chips costs $1 less than a granola bar, and jack buys 2 more items than jane buys, Jack buys 15 bags of chips

Let's assume that Jack buys x bags of chips and Jane buys y granola bars. We know that they each spend $24 on snacks, so we can set up the following equation:

x*(price of one bag of chips) + y*(price of one granola bar) = $24

We also know that each bag of chips costs $1 less than a granola bar, so we can write:

(price of one bag of chips) = (price of one granola bar) - $1

Substituting this into the first equation, we get:

x*((price of one granola bar) - $1) + y*(price of one granola bar) = $24

Expanding and simplifying, we get:

x*(price of one granola bar) + y*(price of one granola bar) - x = $24

We also know that Jack buys 2 more items than Jane, so we can write:

x = y + 2

Substituting this into the previous equation, we get:

(y + 2)(price of one granola bar) + y(price of one granola bar) - (y + 2) = $24

Simplifying, we get:

2*(price of one granola bar) + y = $26

We can now solve for y:

(price of one granola bar) = ($26 - y)/2

Substituting this back into the equation for x, we get:

x = y + 2

x = (26 - y)/2 + 2

Simplifying, we get:

x = (28 - y)/2

We know that x and y must be whole numbers, so we can test different values of y until we find one that makes x a whole number. Starting with y = 2, we get:

(price of one granola bar) = ($26 - 2)/2 = $12

2*(price of one granola bar) + y = $26

2*($12) + 2 = $26

Therefore, Jack buys 15 bags of chips (x = (28 - y)/2 = (28 - 2)/2 = 15) and Jane buys 13 granola bars (y = 2).

In summary, Jack and Jane each spend $24 on snacks. Jack buys bags of chips and Jane buys granola bars. Each bag of chips costs $1 less than a granola bar, and Jack buys 2 more items than Jane buys. We can solve for the number of bags of chips Jack buys by setting up and solving equations based on these facts. We find that Jack buys 15 bags of chips.

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Step-by-step explanation:

When x = 0    y = 20      Plug in:

20 = 20 b^0  

20 = 20      true , but we didn't find 'b'

when x = 1   y = 10        Plug in:  

10 = 20 * b^1

10 = 20 b

b = 1/2

The dilated points are:

G' = (1, 1)

H' = (1, 3)

J' = (4, 1)

Option C is the correct answer.

We have,

To dilate with a scale factor of 1/3, we need to multiply the coordinates of each point by 1/3.

The new coordinates of G will be:

x-coordinate: 3 × 1/3 = 1

y-coordinate: 3 × 1/3 = 1

So, the new coordinates of G are (1, 1).

The new coordinates of H will be:

x-coordinate: 3 × 1/3 = 1

y-coordinate: 9 × 1/3 = 3

So, the new coordinates of H are (1, 3).

The new coordinates of J will be:

x-coordinate: 12 × 1/3 = 4

y-coordinate: 3 × 1/3 = 1

So, the new coordinates of J are (4, 1).

Therefore,

The dilated points are:

G' = (1, 1)

H' = (1, 3)

J' = (4, 1)

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The area of the parallelogram in the figure is given as follows:

A = 39.96 in².

The area of a parallelogram is given by the multiplication of the base of the parallelogram by the height of the parallelogram, that is:

A = bh.

The parameters for this problem are given as follows:

h = 3.7 in, b = 10.8 in.

Multiplying the base of the parallelogram by the height of the parallelogram, the area is given as follows:

A = 10.8 x 3.7

A = 39.96 in².

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The inequality for the shaded region shown in the figure is; y ≥  x^2 - 1

We can see that the shaded region seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)

Then:

y ≥ ax^2 + bx + c

where ax^2 + bx + c is the general quadratic equation.

Now to find the equation for the parabola:

f(x) = ax^2 + bx + c

We also can see that the vertex of the parabola is at the point (0, -1)

This means

f(0) = -1 = a0^2 + b0 + c

     -1 = c

c = -1

Then:

f(x) = ax^2 + bx - 1

Now we can see at the graph again, to see that the zeros of the parabola are at +1 and -1

Which means that:

f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1

f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1

Then we have two equations:

a + b - 1 = 0

a - b - 1 = 0

b = 0

these equations become:

a - 1 = 0

a - 1 = 0

Then solving for a, a = 1

Then the quadratic equation is:

f(x) = 1*x^2 + 0*x - 1

f(x) = x^2 - 1

And the inequality is y ≥  x^2 - 1

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Using similar side theorem and taking the ratios of similar sides, the value of AD is 3.6 units

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

In this problem, we can use the similar side theorem by taking ratios of similar sides.

4.5 / 5 = AD / 4

Cross multiply both sides

AD = (4.5 * 4) / 5

AD = 18/5

AD = 3.6

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Answer:

Yes, 86.76 is a rational number. A rational number is any number that can be expressed as a ratio of two integers (where the denominator is not zero).

86.76 can be expressed as the ratio of two integers: 8676/100, which can be simplified to 2169/25. Since 2169 and 25 are both integers, and the denominator is not zero, 86.76 is a rational number.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A rational number is any number that can be expressed as the ratio of two integers (i.e., a fraction where the numerator and denominator are both integers).

In this case, we can express 86.76 repeating as the fraction:

8676/100 = 8676 ÷ 100

Simplifying this fraction, we get:

8676/100 = 8676 ÷ 4 ÷ 25 = 2169/25

Since 2169 and 25 are both integers, we have expressed 86.76 repeating as a ratio of two integers, and therefore it is a rational number.

The Rutherford model of the atom is known to be a term that is also seen as planetary model. It was said to have been proposed by Ernest Rutherford in 1911. It was a vital improvement over previous models, but it had some few limitations.

Below are some advantages and disadvantages of the Rutherford model:

In terms of Advantages:

In terms of Disadvantages:

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See text below

advantages and disadvantages of the rutherford model of the atom

The requried measure of the hypotenuse of the given right triangle is 37.

The hypotenuse of the right angle triangle can be evaluated by Pythagoras' theorem, which states that the sum of squares of the legs of a right triangle is equal to the square of the third side.

Hypotensue² =  12²+35²
Hypotensue = √1369 = 37

Thus, the requried measure of the hypotenuse of the given right triangle is 37.

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Answer:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * base area * height

where "base area" is the area of the base of the pyramid.

In this case, the base of the pyramid has a length of 9 meters and a width of 7 meters, so its area is:

base area = length * width = 9 m * 7 m = 63 m^2

The height of the pyramid is 13 meters.

Now we can calculate the volume:

V = (1/3) * base area * height

= (1/3) * 63 m^2 * 13 m

= 273 m^3

Therefore, the volume of the pyramid is 273 cubic meters.

The population will exceed 7569 at moments beyond 7.4 years hence from 8 years (to the nearest years)​

Exponential function is a function of the form f(x) = a e^(kt)

Considering the given problem,

the initial value = a

the base factor = k

the exponents in time = t

Information given in the problem are

solving for the time wen the population will exceed 7569

7569 = 1600 x e(0.21 * t)

7569 / 1600 = e(0.21 * t)

take ㏑ of both sides

㏑ (7569 / 1600) = ㏑ e(0.21 * t)

㏑ (7569 / 1600) = 0.21t

t = ㏑ (7569 / 1600) / 0.21

t = 7.40

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Answer:  Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘

Step-by-step explanation:

Answer:

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

To find the sum of the interior angles of a 16-sided polygon, you can use the formula:

In our case, n = 16.

Substitute the value of n into the formula:

The matching choice is D.

Step-by-step explanation:

Circumference of a circle is found by:

Circ = pi * d

      = pi * 9.7 cm = 30.5 cm

Answer: 2.333  

Step-by-step explanation:

Since 3 feet equal 1 yard, we can divide 7 feet by 3 to get the equivalent distance in yards:

7 feet ÷ 3 feet/yard = 2.333 yards (rounded to 3 decimal places)

Therefore, 7 feet is equivalent to approximately 2.333 yards.

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The normal to the parabola[tex]z = x^2 + y^2[/tex] at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20).

To find the normal to the paraboloid[tex]z = x^2 + y^2[/tex] at points (3, 3, 18), we first need to find the slope of the surface at that point. The gradient vector is given by

[tex]∇f(x,y,z) = < 2x, 2y, -1 >[/tex]

So the gradient vector at points (3, 3, 18) is

∇f(3, 3, 18) = <6, 6, -1>

This gradient vector is orthogonal to the plane tangent to the surface at the point (3, 3, 18). So the surface normal at this point is parallel to the gradient vector and can be expressed as

x = 3 + 6t

y = 3 + 6t

z = 18 - t

To discover where this line converges the parabola once more, we ought to substitute the x, y, and z equations into the parabola's condition. 

[tex]z = x^2 + y^2[/tex]

So it looks like this:

[tex]18 - t = (3 + 6t)^2 + (3 + 6t)^2[/tex]

[tex]18 - t = 18t^2 + 36t + 18[/tex]

[tex]0 = 18t^2 + 37t[/tex]

t=0 or t=-37/18

The value t = 0 corresponds to the starting point (3, 3, 18), so we are interested in the second value t = -37/18. Substituting this value into the normal equation gives:

x = 3 + 6(-37/18) = -1/3

y = 3 + 6(-37/18) = -1/3

z=18-(-37/18)=360/18=20

therefore, the normal to the parabola [tex]z = x^2 + y^2[/tex] at the point (3, 3, 18) intersects the parabola again at the point (-1/3, -1/3, 20). 

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The equation about the conic is r = 6/(4|sinθ| - 3cosθ).

We have,

Since the focus is at the pole, the conic is a polar equation with the form

r = e d / (1 - e cosθ), where d is the distance from the pole to the directrix and e is the eccentricity.

In this case,

e = 3/4 and the directrix is r sinθ = -2.

We can rewrite the equation of the directrix in Cartesian coordinates as

y = -2/sinθ.

Now we can use the formula for the distance from a point (x, y) to a line Ax + By + C = 0, which is:

d = |Ax + By + C| / sqrt(A^2 + B^2)

In our case,

The equation of the directrix is y + 2/sinθ = 0, which we can rewrite as

y = -2/sinθ.

The coefficients of x and y are both 0 and the constant term is 2/sinθ, so

A = 0, B = 1, and C = -2/sinθ.

Substituting into the formula.

d = |-2/sinθ| / √(0² + 1²)

d = 2/|sinθ|

Now we can write the equation of the conic as:

r = e d / (1 - e cosθ) = (3/4) (2/|sinθ|) / (1 - (3/4) cosθ)

Simplifying.

r = 6/(4|sinθ| - 3cosθ)

This is the polar equation of the conic with focus at the pole and directrix r sinθ = -2, and eccentricity e = 3/4.

Thus,

The equation about the conic is r = 6/(4|sinθ| - 3cosθ).

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Answer:

  14 inches

Step-by-step explanation:

You want the diameter of a circle that has a circumference of 43.96 inches.

The equation for the circumference of a circle is ...

  C = πd

Then the diameter is ...

  d = C/π

  d = (43.96 in)/3.14 = 14 in

The circle's diameter is 14 inches.

<95141404393>

When analyzing a resultant vector, the equation to find the magnitude of the vector is the Pythagorean theorem. This equation states that the magnitude of the resultant vector is equal to the square root of the sum of the squares of its components.

To find the direction of the resultant vector, the trigonometric function of inverse tangent or arctan can be used. This involves taking the inverse tangent of the vertical component divided by the horizontal component, which gives the angle of the vector with respect to the positive x-axis.

Alternatively, the direction can also be found using the trigonometric functions of sine and cosine by dividing the vertical and horizontal components of the vector by its magnitude.

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a) The variables are the variable unit cost of candles and the fixed cost of shipping.

b) The information given in the question include the total costs for 4 candles and 12 candles, including their shipping costs.

c) An equation representing the situation is given as

d) Allie can get 18 candles for $60.

An equation is a mathematical statement showing that two or more algebraic expressions are equal or equivalent.

Algebraic expressions combine variables, values, constants, and numbers without the equal symbol (=), but they use the mathematical operands.

The total cost for ordering 4 candles = $35

The total cost for ordering 12 candles = $49

The difference = 8 candles = $14

Unit cost of candles = $1.75 ($14 ÷ 8)

Shipping (fixed) cost for the first order = $28 ($35 - $1.75 x 4)

Shipping (fixed) cost for the second order = $28 ($49 - $1.75 x 12)

For ordering candles for $60, the number of candles Allie can get = 18 ($60 - $28) ÷ $1.75

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Starting with the given equation:

4x² - 30 = 34

Adding 30 to both sides:

4x² = 64

Dividing both sides by 4:

x² = 16

Taking the square root of both sides:

x = ±4

Therefore, the solutions to the equation are x = 4 and x = -4.

Checking each option:

A. x = -√√8 is not a solution.

B. x = 4 is a solution.

C. x = -8 is not a solution.

D. x = √√√8 is not a solution.

E. x = -4 is a solution.

F. x = 8 is not a solution.

Therefore, the solutions to the equation are x = 4 and x = -4, which are options B and E.

If the water were redistributed equally among the 4 glasses, the fractional part of each glass that would be filled include the following: K. 31/80.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (1/4 + 1/2 + 4/5) ÷ 4

Fraction = 31/20 ÷ 4

Next, we would multiply the fraction 31/20 by the reciprocal of 4 as follows;

Fraction = 31/20 × 1/4

Fraction = 31/80

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

After discount the cost is $53.6 and  the processing fee is $5.36

The discount reduces the price of the shoes by 20%, which means Evan only has to pay 80% of the original price.

To find the price after the discount

we multiply the original price by 0.8:

Price after discount = 0.8 × $67 = $53.60

Next, the website applies a 10% processing fee to this discounted price. To find the processing fee, we can multiply the discounted price by 0.1:

Processing fee = 0.1 × $53.60

= $5.36

Hence, the processing fee is $5.36 and after discount the cost is $53.6

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Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

For a sample of room temperature during winter, an upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees is equals to the 0.25.

For a sample of temperature during winter, Average temperature of room

= 70 degree

Standard deviations = 2 degrees

We have to determine upper bound of the probability that the temperature in your room deviates from the mean by at least 4 degrees. According to chebyehev's theorem, [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex].

here , σ = 2 , μ = 70, kσ = 4

=> k = 2

So, the required upper bound of probability is [tex]P( | X - μ |≥ k σ ) ≤ \frac{ 1 }{k²} [/tex]

≤ [tex]\frac{ 1 }{2²} [/tex]

≤ [tex]\frac{ 1 }{4} [/tex]

= 0.25

Hence, required upper bound value is 0.25.

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Step-by-step explanation:

First, use law of SINES to find QS :

11.7 / sin 28  = QS / sin95

      shows QS = 24.83 cm

Now use law of COSINES to find QR

QR^2 = 10.2^2 + 24.83^2 - 2 ( 10.2)(24.83) cos ( 110)

   shows QR = 29.9 cm

Independent events- events that do not affect each other's probability of occurring. Dependent events- events where the occurrence of one event affects the probability of the other event happening. Mutually exclusive events- events that cannot occur at the same time. Exhaustive events- events that cover all possible outcomes.


1. Independent events: Independent events are events in which the occurrence of one event does not affect the probability of the occurrence of another event. In other words, the outcome of one event has no impact on the outcome of the other event.

2. Dependent events: Dependent events are events in which the occurrence of one event does affect the probability of the occurrence of another event. The outcome of one event is influenced by the outcome of the other event.

3. Mutually exclusive events: Mutually exclusive events are events that cannot occur at the same time. The occurrence of one event means the other event cannot occur. For example, flipping a coin and getting both heads and tails at the same time is a mutually exclusive event, as it is impossible for both to happen simultaneously.

4. Exhaustive events: Exhaustive events are a set of events that include all possible outcomes in a given situation. They are complete and cover every possibility, leaving no room for additional outcomes. For example, when flipping a coin, the set of exhaustive events includes both heads and tails, as there are no other possible outcomes.

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Answer:

The formula for ordinary interest is:

I = P * r * t

where:

I = the interest

P = the principal

r = the interest rate per year

t = the time in years

In this case, the principal is $12,500, the interest rate is 4%, and the time is 292/360 years (since there are 360 days in a year according to the problem statement). Therefore, we have:

t = 292/360 = 0.811111111

I = 12500 * 0.04 * 0.811111111 = 405.5555555

To find the maturity value, we add the interest to the principal:

M = P + I = 12500 + 405.5555555 = 12905.56

Therefore, the maturity value of the promissory note is $12,905.56 rounded to the nearest cent.

The probability that Tally is on the red team would be 1/4

Probability means a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Tally's teacher divides her class of 16 students into 4 equally sized teams: red team, yellow team, green team and the blue team.

Therefore, the probability that Tally is on the red team will be;

P(E) = Number of favorable outcomes / total number of outcomes

P(E) = Number of teams / total number of students

P(E) = 4/16

P(E) = 1/4

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Using A linear equation, It ia found that:

• The equation is: L = 56 + 3d

Where D is representing the number of day crew has worked and L presenting the total length of the road. So let's solve this.

Step by step Explanation:

= L = 56 + 3d

= L = 56 + 3(36)

= L = 54 + 108

= L = 162