If the sides of a rectangle are in the ratio 3:4 and the length of the diagonal is 10 cm, find the length of the sides

The equation of the line parallel to the graph of y = (-1/2)x - 1 and containing the point (-4, 5) is y = (-1/2)x + 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the graph

y = (-1/2)x - 1

The equation of a line parallel to the graph of y = (-1/2)x - 1 will have the same slope as the given line, which is -1/2.

Now. using the point-slope form, we can find the equation of the line that passes through the point (-4, 5) with slope -1/2:

y - y1 = m(x - x1)

y - 5 = (-1/2)(x - (-4))

y - 5 = (-1/2)x - 2

y = (-1/2)x + 3

Therefore, the equation of the parallel line is y = (-1/2)x + 3.

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Answer:

Inga can use the following steps to solve the quadratic equation 2x^2 + 12x - 3 = 0:

Therefore, the steps that Inga could use to solve the quadratic equation are:

2(x^2 + 6x + 9) = -3 + 2(9) (Option 1)

2(x^2 + 6x) = 3 (Option 2)

x + 3 = ±√(27/2) (Option 3)

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The calculated value of x in the right triangle is 6

from the question, we have the following parameters that can be used in our computation:

The right triangle

Where we have

x/6 = 6/x

To solve this equation, we can use the property of cross-multiplication.

So for the equation x/6 = 6/x, we can cross-multiply as follows:

x/6 = 6/x

x * x = 6 * 6

x^2 = 36

To solve for x, we need to take the square root of both sides of the equation:

√(x^2) = √36

x = 6

The value of x is 6

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The height of the antenna is approximately 17 meters.

To solve for the height of the antenna, we need to use trigonometry. Let's call the height of the antenna "h".

First, we need to find the distance from point A to point B. We can use the angle of elevation from her eyes to the roof (17°) and the horizontal distance from the building (29m) to find the height of the building.

tan(17°) = height of building / 29m

height of building = 29m * tan(17°)

height of building = 8.20m

Now we can use the height of the building and the angle of elevation from her eyes to the top of the antenna (31°) to find the distance from point A to point B.

tan(31°) = h / 29m + 8.20m

h = (29m + 8.20m) * tan(31°)

h = 15.51m

Finally, we need to add the height of Bilquis' eyes to the height of the antenna to find the total height.

total height = h + 1.51m

total height = 17.02m

Therefore, the height of the antenna is approximately 17 meters.

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If the photo’s current height is 314 inches, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.

To calculate the enlarged height, you need to find out the percentage increase in height from the current height to the desired height.

The desired height is 234 inches, which is 234/314 = 0.744 or 74.4% of the current height.

To find the actual enlarged height, you need to increase the current height by 74.4%.

Enlarged height = current height + (current height x percentage increase)
Enlarged height = 314 + (314 x 0.744)
Enlarged height = 314 + 233.616
Enlarged height = 547.616

Therefore, the enlarged height should be approximately 547.6 inches (rounded to one decimal place), which is 80.0% larger than the current height.

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2x+14=30

2x =30-14

2x=16

x =8

Answer:

8

Step-by-step explanation:

Twice means 2 so twice a number,n, means 2 times n thus 2n

sum means add so, 2n + 14

"is" means equal so 2n + 14 = 30

Solve for n:

2n=16

N=8

Answer:

Locker and Phone number

Step-by-step explanation:

Gym student grouped together with no thought doesnt matter, lunch menu doesn't need order, and a classroom seating chart doesn't really matter

To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:

7² + 2² = x²

Simplifying this equation, we get:

49 + 4 = x²

53 = x²

To find the value of x, we need to take the square root of both sides:

√53 = x

So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.

In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.

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Approximately 21.3 percent of the total items sold were baseball items.

Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:

300 - 5 = 295

We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:

0.20 * 295 = 59

Therefore, the total number of baseball and football items sold is:

59 + 5 = 64

The percentage of total items sold that were baseball items is:

(64 / 300) * 100% = 21.3%

Therefore, approximately 21.3 percent of the total items sold were baseball items.

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Answer:

  C = (-1, -2)

  D = (2, 0)

Step-by-step explanation:

You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).

The diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:

  E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC

  C = 2E -A = 2(0, 2) -(1, 6)

  C = (-1, -2)

and

  D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern

  D = (2, 0)

The surface area of the triangular prism is

The surface area of the triangular prism is

= area of the two side rectangles + area of the base rectangles + area of the 2 triangles

= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24

= 2160 + 1296 + 1296

= 5752 square millimeters

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Answer: f(t) = 2.4t - 500

Step-by-step explanation:

So first of all, we need how much she actually profits from each taco. She charges $3.25 per taco, but we cannot forget that it is not free to make a taco in the first place. It costs her $0.85 to make a taco. This means we have to subtract the 85 cents from the 3 dollars 25 cents, which means it ends up being $2.40, or as the answer choices have it, 2.4.

So now we know what the number of tacos is being multiplied by: 2.4.

2.4t is now the profit per taco multiplied by the number of tacos.

But we're not quite done yet.

She has a fixed expense of $500 a month, which means this has to be subtracted from her taco profits to find her true profit.

Putting all of this together, we get f(t)=2.4t - 500.

(t)= (profit per taco)(amount of tacos sold) - (fixed expenses)

The price that maximizes revenue for the given monthly price-demand equation with price range between $100 and $500 is $220.

(b) The maximum revenue from selling microwaves can be found by multiplying the price that maximizes revenue by the corresponding quantity of microwaves sold. Using the price-demand equation p(x) = 280 - 0.4x, we can find the quantity that corresponds to the price that maximizes revenue as follows:p(x) = 280 - 0.4x220 = 280 - 0.4x0.4x = 60x = 150Therefore, the quantity that corresponds to the price that maximizes revenue is x = 150. The maximum revenue can be found by multiplying the price and quantity:Revenue = Price * QuantityRevenue = $220 * 150Revenue = $33,000Therefore, the maximum revenue from selling microwaves is $33,000.

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The perimeter of Rebakh's new mural is 9 meters.

Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.

So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.

Therefore, the perimeter of Rebakh's new mural is 9 meters.

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The absolute maximum value of f(x) on the interval [-2,3] is 201 and occurs at x = -2, and the absolute minimum value of f(x) on the interval [-2,3] is -79 and occurs at x = 2.

To find the absolute maximum and absolute minimum values of f(x) on the interval [-2,3], we need to first find the critical points of the function and evaluate the function at these points as well as at the endpoints of the interval.

To find the critical points, we need to find where the derivative of the function equals zero or does not exist. Taking the derivative of f(x), we get:

f'(x) = 12x^3 - 12x^2 - 24x

Setting this equal to zero and factoring out 12x, we get:

12x(x^2 - x - 2) = 0

Using the quadratic formula to solve for x^2 - x - 2 = 0, we get:

x = -1, 0, 2

These are our critical points.

Now we evaluate f(x) at the critical points and the endpoints of the interval:

f(-2) = 201
f(-1) = 6
f(0) = 1
f(2) = -79
f(3) = 16

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A, c, D

Step-by-step explanation:

A) we can sample these 7th graders as we are looking to study 7th graders.

b) The first 20 students could be from any grade and so this option wouldn't work.

c) Involves 7th graders.

d) involves 7th graders

E) The students could be any grade level on the debate team so, this option wouldn't work.

To test whether shoes cost less on average at Payless than at Famous Footwear, we can conduct a two-sample t-test for the difference in means.

The null hypothesis is that there is no difference in the mean prices between the two stores, and the alternative hypothesis is that the mean price at Payless is less than the mean price at Famous Footwear.

We can calculate the t-statistic using the formula:

t = [tex](x1 - x2 - 0) / sqrt(s1^2/n1 + s2^2/n2)[/tex]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the values given in the table, we get:

t =[tex](21.39 - 45.66 - 0) / sqrt((7.47^2/30) + (16.54^2/30))[/tex] = -10.78

The degrees of freedom for this test is (30-1) + (30-1) = 58.

Using a t-table or calculator, we find the p-value to be very small, much less than 0.05.

Therefore, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 significance level that shoes cost less on average at Payless than at Famous Footwear.

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3.75 kg of meat will cost 712.50, The correct answer is option (c).To determine how much 3.75 kg of meat will cost at ?190.00 per kilogram, you'll need to perform a multiplication using the given weight and price per kilogram, we need to :

1. Identify the weight of the meat: 3.75 kg.
2. Identify the cost per kilogram: ?190.00.
3. Multiply the weight (3.75 kg) by the cost per kilogram (?190.00).

3.75 kg × ?190.00/kg = 712.50
So, 3.75 kg of meat will cost ?712.50, which corresponds to option (c) in your list of possible answers. Remember to always check your calculations and units when solving problems like this to ensure accuracy.

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The critical points of f(x) are x = -3 and x = 4.

Derivative of 4y = sin(cos(8x)):
We can find the derivative of the given function using the chain rule of differentiation. Let u = cos(8x), then we have:
y = sin(u)
dy/du = cos(u) (derivative of sin(u))
du/dx = -8sin(8x) (derivative of cos(8x) using chain rule)
dy/dx = dy/du * du/dx = cos(cos(8x)) * (-8sin(8x))
Therefore, the derivative of 4y = sin(cos(8x)) is:
dy/dx = -32sin(8x)cos(cos(8x))
Critical points of f(x) = x√(x+6):
To find the critical points of f(x), we need to find where the derivative of the function is equal to zero or undefined.
f(x) = x√(x+6)
f'(x) = (√(x+6) + x/2√(x+6))
To find the critical points, we need to set f'(x) equal to zero and solve for x:
(√(x+6) + x/2√(x+6)) = 0
Multiplying both sides by 2√(x+6), we get:
2x + 6 = -x√(x+6)
Squaring both sides, we get:
4[tex]x^2[/tex] + 24x + 36 = [tex]x^3[/tex] + 6[tex]x^2[/tex]
Rearranging, we get:
[tex]x^3[/tex] + [tex]2x^2[/tex] - 24x - 36 = 0
We can solve this cubic equation using numerical methods or by factoring.

By testing values, we can see that x = -3 is a root of the equation. Dividing the equation by (x+3), we get:
[tex]x^2[/tex]- x - 12 = 0
This quadratic equation can be factored as (x-4)(x+3) = 0.
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The mean number of people in passenger cars on the highway is 1.7 (approximately 2).

The mean of a probability distribution function is also known as Expectation of the probability distribution function.

The mean number of people in passenger cars (or expectation of number of people in passenger cars ) on the highway can be denoted as E(x) where x is the number of people in passenger cars on the highway.

Thus E(x) can be calculated as,

E(x) = ∑ [tex]x_{i} p_{i}[/tex] ∀ i= 1,2,3,4,5

where, [tex]p_{i}[/tex] is the probability of number of people in passenger cars on the highway

⇒ E(x) = (1)(0.56) + (2)(0.28) + (3)(0.08) + (4)(0.06) + (5)(0.02)

⇒ E(x) = 1.7

Hence the mean number of people in passenger cars on the highway is 1.7, which is less than 2.

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The correct answer is C.

The cost of membership is fixed at $50 per year, and the cost of purchasing games is $60 each. If you purchase up to 6 games a year, the cost of each purchase will be $60, and the total cost of membership and games will be $50 + ($60 x number of games purchased).

The function that relates the number of games purchased to the total cost is:

Total cost = 50 + 60(number of games purchased)

Now, let's consider the options provided:

A. Domain: All real numbers

Range: All real numbers

This is not a valid option since the domain and range are not restricted to the given context.

B. Domain: {50, 110, 170, 230, 280, 340}

Range: {0, 1, 2, 3, 4, 5, 6}

This option does not represent the relationship between the number of games purchased and the total cost correctly.

C. Domain: {0, 1, 2, 3, 4, 5, 6}

Range: {50, 110, 170, 230, 290, 350, 410}

This option correctly represents the relationship between the number of games purchased and the total cost. The domain represents the number of games purchased (up to 6), and the range represents the total cost (membership fee + cost of games).

D. Domain: {0, 1, 2, 3, 4, 5, 6}

Range: {60, 160, 210, 270, 320, 380}

This option represents the cost of games purchased only, and does not include the cost of membership.

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Answer:  B   g(x)=1/4f(x)    odd

Step-by-step explanation:

First Page:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Second Page:

Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).

lets test for even:  does f(x)=f(-x)   =>    f(1)=f(-1)  no   -2[tex]\neq[/tex]2

see image for plotted points

lets test for odd:  does f(x)= -f(-x)   =>    f(1) = -f(-1)  yes  -2 = -2

Answer:

[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\textsf{B)} \quad \textsf{odd}[/tex]

Step-by-step explanation:

Functions f(x) and g(x) are exponential functions.

From inspection of the given points on both graphs:

When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):

[tex]g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\hrulefill[/tex]

And even function is symmetric about the y-axis:

According to the table, f(3) = -4 and f(-3) = 4.

Therefore, as f(x) ≠ f(-x), the function is not even.

An odd function is symmetric about the origin:

According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.

Therefore, as f(-3) = -f(3), the function is odd.

[tex]\hrulefill[/tex]

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The exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].

To write an exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416), follow these steps:

1. Use the point (0, 13) to determine the value of a. Since the x-coordinate is 0, we have y = a * b⁰, which simplifies to y = a. Therefore, a = 13.

2. Use the point (5, 416) to determine the value of b. Plug in the values for x and y, as well as the value of a we just found: 416 = 13 * b⁵.

3. Solve for b: b⁵ = 416 / 13 = 32. Taking the fifth root of both sides, we get b = 2.

So, the exponential function in the form y = [tex]ab^x[/tex] that goes through the points (0, 13) and (5, 416) is y = 13 * [tex]2^x[/tex].

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Answer:

Step-by-step explanation:

First, let's simplify the numerator:

3^6 - 3^8 = 729 - 6561 = -5832

Now, let's simplify the denominator:

9^4 - 9^2 = 6561 - 81 = 6480

So, the expression simplifies to:

(-5832) / 6480 = -0.9

Answer: No they are not

Step-by-step explanation:

Distribute the 4 from the left equation into the parenthesis.

you would get 20k - 12

that is not equivalent to 14k - 8

Answer:

[tex]\overset{\frown}{BX}=\angle BCX=2\angle BNX[/tex]

Step-by-step explanation:

A chord is a straight line joining two points on the circle.

Therefore, the chords in the given diagram are BN and XN.

An inscribed angle is the angle formed (vertex) when two chords meet at one point on a circle.

Therefore, the inscribed angle in the given diagram is BNX.

An intercepted arc is the arc that is between the endpoints of the chords that form the inscribed angle.

Therefore, the intercepted arc in the given diagram is BX.

The radius is a straight line joining the center to a point on the circle.

Therefore, the radii in the given diagram are CB and CX.

The central angle of a circle is the angle formed at its center by two radii.

Therefore, the central angle in the given diagram is BCX.

[tex]\hrulefill[/tex]

The measure of the central angle of a circle is equal to the measure of the corresponding intercepted arc. Therefore:

    [tex]\angle BCX=\overset{\frown}{BX}[/tex]

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:

    [tex]\angle BNX=\dfrac{1}{2}\overset{\frown}{BX}[/tex]

So the relationship between the arc BX, the central angle BCX and the inscribed angle BNX is that both the arc and central angle are equal to twice the inscribed angle:

[tex]\overset{\frown}{BX}=\angle BCX=2\angle BNX[/tex]

Check the picture below.

Answer:

AEC is similar to BDC in terms of the type of triangle

That's all I can really say

I hope this helps :)