The diagram shows a line with intercepts 3 and 9 and one of many rectangles which can be inscribed under this line and within the first quadrant.
a. Write an equation for the line.
b. Determine if the rectangle can have x = 4 and y = 2 as its dimensions.
c. Find x and y if the rectangle is a square.
d. Write an expression for A, the area of the rectangle, using x as the only variable.
e. Find x if the area of the rectangle is 6.
f. Which x gives the rectangle its largest area?

To model the pressure function in the pipe that oscillates between 40 and 280 ten times an hour, we can use a sine function. The formula is P = f(t) = 120 sin(π/3 t) + 160.

The pressure in the pipe oscillates between 40 and 280 ten times an hour, this is a trigonometric function scenario. Assuming the oscillation is sinusoidal, we can use a sine function to model the pressure in the pipe. The oscillation's period is 6 minutes because the pressure changes happen 10 times per hour. Thus, the function modelling this pressure will be of the form

P = a sin(b(t - c)) + d.

Given that the middle value of the pressure (between the max of 280 and the minimum of 40) is 160, this makes

'd' = 160.

The amplitude 'a' is half the total swing of the pressure which is 120.

To find 'b', we use the fact that the period of a sinusoid in this form is (2π/b).

As our period is 6 minutes, that makes 'b' = π/3.

The pressure is at a minima at t=0 so the phase shift 'c' = 0

Hence the formula P = f(t) = 120 sin(π/3 t) + 160.

https://brainly.com/question/4116396

#SPJ11

The correct answer is:

$38.75

Explanation:

35 feet of trim at $1.75 per foot would give us a cost of

35(1.75) = 61.25.

Paying with a $100 bill, he would receive

100-61.25 = $38.75 in change.

The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.

To find the diameter, circumference, and area of the circle watered by the lawn sprinkler, we can use the formulas:

1. **Diameter [tex](\(d\)) = \(2 \times \text{radius}\)[/tex]

2. **Circumference [tex](\(C\)) = \(2 \times \pi \times \text{radius}\)[/tex]

3. **Area [tex](\(A\)) = \(\pi \times \text{radius}^2\)[/tex]

Given:

Radius[tex](\(r\)) = 40 feet[/tex]

1. Diameter:

[tex]\[d = 2 \times r\]\[d = 2 \times 40 \text{ feet}\]\[d = 80 \text{ feet}\][/tex]

2. Circumference:

[tex]\[C = 2 \times \pi \times r\]\[C = 2 \times \pi \times 40 \text{ feet}\]\[C \approx 2 \times 3.14159 \times 40 \text{ feet}\]\[C \approx 251.327 \text{ feet}\][/tex]

3. Area:

[tex]\[A = \pi \times r^2\]\[A = 3.14159 \times 40^2 \text{ square feet}\]\[A = 3.14159 \times 1600 \text{ square feet}\]\[A \approx 5026.548 \text{ square feet}\][/tex]

Answer:

The approximate diameter of the circle is 80 feet, the circumference is approximately 251.327 feet, and the area is approximately 5026.548 square feet.

Answer:

$144

Step-by-step explanation:

Just did test

The expression given to us is:

[tex] 9m^2-\frac{6}{5}m+c [/tex]

If the above expression is a perfect square then the middle term will have to be 2 times the square root of the first term times the square root of the last term. Thus:

[tex] -\frac{6}{5}m=2\times 3m\times \sqrt{c} [/tex]

[tex] \therefore \sqrt{c}=-\frac{1}{5} [/tex]

Thus, [tex] c=\frac{1}{25} [/tex]

Thus, for 9m^2-(6/5)m+c to be a perfect square, the value of c must be equal to [tex] \frac{1}{25} [/tex] or 1/25

Final answer:

The probability of drawing two green marbles consecutively without replacement from a basket of 4 green marbles and 8 blue marbles is 0.1, or 10%.

Explanation:

The question involves calculating the probability of drawing two green marbles in succession without replacement from a basket containing 4 green marbles and 8 blue marbles. For the first draw, the probability of drawing a green marble is 4 out of 12, which reduces to 1/3 or about 0.3333. Once that marble is drawn, there are 3 green marbles left and 7 blue marbles, making a total of 10.

Therefore, the probability of drawing another green marble is 3 out of 10, or 0.3. To find the probability of both events happening consecutively, we multiply the two individual probabilities: (1/3) * (3/10) = 1/10 or 0.1. Hence, the probability that both marbles will be green is 0.1, or 10%.

Answer:

A rotation

Explanation:

A reflection across the y-axis would map trapezoid 1 to trapezoid 8.

A horizontal translation would also map trapezoid 1 to trapezoid 8.

However, a rotation would map trapezoid 1 to trapezoid 7; it would not map it to trapezoid 8.

Answer: The answer is (c) rotation.

Step-by-step explanation: We are given a figure where 8 trapezoid are drawn on the coordinate plane. We are to select from the given option the transformation that will not map trapezoid 1 to trapezoid 8.

We can easily check that by reflecting and translating that both these transformations will definitely map trapezoid 1 to trapezoid 8.

Only the rotation will not work here. If we rotate trapezoid 1 by 180° taking origin as the centre of rotation, the the image will be opposite of trapezoid 8. Therefore, rotation will not map trapezoid 1 to trapezoid 8.

Thus, (c) is the correct option.

Answer:

x = 8.4 cm

Step-by-step explanation:

Here we have to use the tan ratio to find the value of x.

tan = opposite/adjacent

tan 35 = x/12

Multiplying both sides by 12, we get

x = 12 tan 35               [tan 35 = 0.7]

x = 12*0.7

x = 8.4

Therefore, the value of x = 8.4 cm

Hope this will helpful.

Thank you.

Answer:

true

Step-by-step explanation:

In this problem, you are asked to compute for the value of y when x = 21. The function shows how the value of y changes with the given value of x.

Y = 2/3x + 20

Y = 2/3 (21) + 20

Y = 14 + 20

Y = 34

Answer:

5

Step-by-step explanation:

just trust me

Answer:

hudadagra what does a say im sorry for putting this in answer but it wont let me comment.

Step-by-step explanation:

i cant see the pic

Answer:

Midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:

1+2i

Step-by-step explanation:

The midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:

[tex]\dfrac{6-2i-4+6i}{2} \\\\=\dfrac{2+4i}{2}\\ \\=1+2i[/tex]

Hence, midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:

1+2i

Answer:  2 + 4 i

Step-by-step explanation:

Hi, to solve this we have to apply the next expression:

(a1 +a2)/ 2 + (b1 +b2 )/2 i=

Where a is the real part, and b is the imaginary part (with i)

For example, for our case:

6 -2i , 6 is the real part (2) and -2 is the imaginary part (b)

Replacing with the values given

(6 -4) /2+ (-2 +6) /2 i = 2 + 4 i

Feel free to ask for more if needed or if you did not understand something.

The equation y - 5x = -9 defines a line that none of the given points (1,5), (2,10), (3,7), and (4,14) lie on, as substituting their x-values in the equation doesn't yield the corresponding y-values.

The question involves identifying points on a line described by the equation y - 5x = -9. To verify which points belong to this line, we can substitute the x-values of the given points into the equation and see if the resulting y-values match those in the points. We solve for y in the equation to get y as a function of x (dependence of y on x): y = 5x - 9.

Now, let's examine the points (1,5), (2,10), (3,7), and (4,14) to see if they satisfy this equation:

None of these points lie on the line defined by y = 5x - 9. For a point to be on the line, plugging its x-coordinate into the equation must result in its corresponding y-coordinate.

To simplify the given rational expression, we factor both the numerator and the denominator, cancel out the common factor, and express the result as (n^2 - 6) / (n^2 - 2), with restrictions on n that it can't equate to the square roots of 5 or 2.

The question involves simplifying the rational expression n^4 - 11n^2 + 30 divided by n^4 - 7n^2 + 10, and stating any restrictions on the variable. To simplify this, we first factor both the numerator and the denominator.

Numerator: (n^2 - 5)(n^2 - 6)
Denominator: (n^2 - 5)(n^2 - 2)

After factoring, we can cancel out the common factor (n^2 - 5) from both the numerator and the denominator. This leaves us with (n^2 - 6) / (n^2 - 2).

However, we must state the restrictions on the variable n. The original denominator cannot be equal to zero, thus n^2 cannot be equal to 5 or 2, leading to restrictions of n != sqrt(5) and n != sqrt(2).

Answer:

Step-by-step explanation:

We plot the points on a graph with months on x-axis and Revenue/expenses on y-axis.

A straight line shows the decrease in expenses and another line showing increase in revenue.

The point of intersection shows the common point where the revenue and expenses become equal. This point of intersection we get at 6.5 months as shown in the graph attached.

Answer:

Week 7

Step-by-step explanation:

You can solve this problem by graphing the revenue and the expenses and it's asking on which week the lines intersect.

(1) The measure of angle B is [tex]140^o.[/tex]

(2) The measure of angle A is [tex]65^o.[/tex]

(3) The measure of angle C is [tex]80.5^o.[/tex]

(1) The quadrilateral [tex]\(ABCD\)[/tex] is inscribed in a circle. For any quadrilateral inscribed in a circle, the opposite angles are supplementary (i.e., their sum is [tex]\(180^\circ\)).[/tex]

In the first image:

[tex]- \( \angle DAB = x^\circ \)\\ - \( \angle DCB = (4x - 20)^\circ \)[/tex]

Since these two angles are opposite angles of the inscribed quadrilateral, we have:

[tex]\[ x + (4x - 20) = 180 \][/tex]

Solving for [tex]\(x\):[/tex]

[tex]\[ 5x - 20 = 180 \][/tex]

[tex]\[ 5x = 200 \][/tex]

[tex]\[ x = 40 \][/tex]

Therefore, [tex]\( \angle B = (4x - 20) = 4(40) - 20 = 160 - 20 = 140^\circ \).[/tex]

(2) In the second image:

[tex]- \( \angle ADC = x^\circ \)\\ - \( \angle ABC = 148^\circ \)[/tex]

These are opposite angles of the inscribed quadrilateral. Thus:

[tex]\[ x + 148 = 180 \][/tex]

Solving for [tex]\(x\):[/tex]

[tex]\[ x = 180 - 148 = 32 \][/tex]

Therefore, [tex]\( \angle A = (2x + 1) = 2(32) + 1 = 64 + 1 = 65^\circ \).[/tex]

(3) In the third image:

[tex]- \( \angle DAB = (x + 15)^\circ \)\\ - \( \angle DCB = (x + 10)^\circ \)\\ - \( \angle BCD = (x + 24)^\circ \)[/tex]

Using the property that opposite angles are supplementary:

Opposite angles are [tex]\( (x + 15) \)[/tex] and [tex]\( (x + 24) \),[/tex] thus:

[tex]\[ (x + 15) + (x + 24) = 180 \][/tex]

Solving for [tex]\(x\):[/tex]

[tex]\[ 2x + 39 = 180 \][/tex]

[tex]\[ 2x = 141 \][/tex]

[tex]\[ x = 70.5 \][/tex]

Therefore, the measure of angle C is [tex]\( (x + 10) = 70.5 + 10 = 80.5^\circ \).[/tex]

Final answer:

The solutions to the equation 2sin^2x = sinx in the interval [0, 2π) are x = 0, π, π/6, 5π/6 and x = π/6, 5π/6.

Explanation:

The given equation is: 2sin^2x = sinx.

To solve this equation, we can first factor out sinx:

sinx(2sinx - 1) = 0.

Setting each factor equal to zero, we get two equations:

Solving for x, we find: