Suppose that the functions q and r are defined as follows

Answer:

4x + y = 2

Step-by-step explanation:

y + 2 = - 4(x - 1) ← distribute parenthesis by - 4

y + 2 = - 4x + 4 ( add 4x to both sides )

4x + y + 2 = 4 ( subtract 2 from both sides )

4x + y = 2 ← in standard form

(a) The height after t years is given by

h(t) = 0.6t² + 3t + 11

(b) The shrubs are 38 centimetres tall when they are sold.

The growth rate of the shrubs during the first year of growth can be determined by setting t = 1 in the given differential equation dh/dt = 1.2t + 3. This gives us dh/dt = 1.2(1) + 3 = 4.2 centimeters per year.

Therefore, during the first year of growth, the shrubs will grow at a rate of 4.2 centimeters per year. This rate of growth is expected to increase as the shrubs age and reach the end of the 5-year growth period before they are sold by the nursery.

(a) To find the height after t years, we integrate the growth rate function with respect to t:

∫dh/dt dt = ∫(1.2t + 3) dt

h(t) = 0.6t² + 3t + 11

(b) The shrubs are sold after 5 years, so we plug in t = 5 into the function we found in part (a):

h(5) = 0.6(5)² + 3(5) + 11

= 38 cm

Therefore, the shrubs are 38 centimetres tall when they are sold.

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Answer:

Step-by-step explanation:

38.06

The statement that describes the point of intersection on the graph is  Calvin will plant lily bulbs and iris bulbs. Option C

The point of intersection on the graph represents the values of x and y where both conditions are satisfied.

In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.

So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".

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Answer: X= -66

Step-by-step explanation:

If m angle UYV=56

Then WYX= -x-10=56

then X=-66

Answer:

11/3

Step-by-step explanation:

-4(r-2/3)+4<-8

-4r+8/3+4<-8

8/3+4<-8+4r

8/3+4+8<4r

44/3<4r

44/12=r

11/3=r

Answer:

There are approximately 38 cows in the herd.

Step-by-step explanation:

In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.

Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).

[tex]100\%-16\% = 84\%[/tex]

We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.

[tex]32 \text{ cows} = 84\% \cdot x[/tex]

Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.

[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]

[tex]x \approx 38 \text{ cows}[/tex]

So, there are approximately 38 cows in the herd.

Answer:

To perform a dilation with a scale factor of 2 centered at the origin, we need to multiply each coordinate of the original points A and B by the scale factor of 2.

The coordinates of point A after dilation are:

A′(2 * 3, 2 * 7) = A′(6, 14)

Similarly, the coordinates of point B after dilation are:

B′(2 * 4, 2 * 9) = B′(8, 18)

So, the endpoints of the dilated line segment are A′(6, 14) and B′(8, 18).

Answer:

its c

Step-by-step explanation:

133 days saw either rain or high winds.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Example: If an experiment has 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event will be as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

P(r) = 66 days

P(w) = 98 days

P(both) = 31 days

P(r or w) = P(r) + P(w) - P(both)

P(r or w) = 66 + 98 - 31

P(r or w) = 133 days

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The exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

What is meant by tangent?

A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.

Given function is f(x)=4-2secx

We can write it as

y=4-2secx

The slope of the tangent to this curve is:

[tex]\frac{dy}{dx} =-2secx*tanx[/tex]

Given that the tangent is horizontal, which means that the slope is zero.

-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].

So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].

When x=0 ⇒ y=4-2sec0

⇒y=2

When x=π ⇒ y=4-2secπ

y=6

When x=-π⇒ y=4-2sec(-π)

y=6

Therefore the exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

The graph is attached below.

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Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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The first equation is:

(5 1/5)^5 = 25x

To solve for x, we need to simplify the left side of the equation first.

(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776

So,

7776 = 25x

Therefore,

x = 7776/25 = 311.04

For the second equation:

If (8 1/3)^2 = 4x, then x =

We need to simplify the left side of the equation first.

(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81

So,

81 = 4x

Therefore,

x = 81/4 = 20.25

So the values of x that make each sentence true are 311.04 and 20.25, respectively.

Answer:

3/50

Step-by-step explanation:

3 g, 5 r, 2 o

3 + 5 + 2 = 10

Orange = 2 jelly beans

Probability of selecting an orange jelly bean: 2/10 or 1/5

If you put the jelly bean back in, there is still 10 jelly beans.

Green = 3 jelly beans

Probability of selecting a green jelly bean: 3/10\

Multiply the probabilities:

1/5 x 3/10

= 3/50

Step-by-step explanation:

we all know that development is positive change in society and fidelity is a process of fertilization of human in society that explain us development and fertilization are the process of positive changes in our environment and province

Using matrix inversion, the value of x and y are 1.104 and 39.704 respectively

The system of equations can be written in matrix form as:

|  -650    1 |   | x |   |  175    |

|  120     1 |   | y |   |  25,080 |

To solve for x and y, we can use matrix inversion to get:

| x |   |  -650    1 |^-1   |  175    |

| y | = |  120     1 |     |  25,080 |

Using matrix inversion, we get:

| x |   |  -0.00016  0.00875 |   |  175    |    | 1.104 |

| y | = |  0.00476   0.00004 |   |  25,080 | =  | 39.704 |

Therefore, the solution to the system of equations is x = 1.104 and y = 39.704.

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Answer:

Step-by-step explanation:

4.

first, you broke the 2 eggs, and then cooked the eggs. after cooking them, you ate the two eggs that you cracked and cooked.

Answer:

[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]

Step-by-step explanation:

Let the unknown fraction be x

We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9

First convert 5 3/8 to an improper fraction for easier calculation

[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]

Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]

Subtract  [tex]\dfrac{7}{9}[/tex]  on both sides to isolate x:

[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

To compute the right side

The inverse function f-¹(x) as required to be determined from the given function; f(x) = (x-7)³ is; f¯¹(x) = ³√x + 7.

It follows from the task content that the inverse function of the given function; f(x) = (x-7)³ is to be determined.

Therefore, let f(x) = y; so that we have;

y = (x - 7)³

make x the subject so that we have;

³√y = x - 7

x = ³√y + 7

By switching the variables; we have;

y = ³√x + 7

Therefore, the required inverse function; f-¹ as required is; f¯¹(x) = ³√x + 7.

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An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73

The formula for finding the equation of a circle is expressed as:

(x-a)^2 + (y - b)^2 = r^2

Determine the value of r^2 using the distance between two points

r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9

r^2 = 73

Given the centre (a, b) as (-3, 2), the equatio of the circle will be;

(x-(-3))^2 + (y - 2)^2 = 73

(x+3))^2 + (y - 2)^2 = 73

Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73

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PLEASE GIVE BRAINLIEST!
thank you and have a good day :)

Answer:

20

Step-by-step explanation:

1/5(3+2+5)^2

3+2+5 = 10

10^2 = 100

100/5 = 20

The area of the running track, given the parallel sections and the semicircle sections, is https://brainly.com/question/30584763

To find the area of the running track, you first need to find the area of the whole shape and then the area of just the inner section.

Area of whole shape :

= Area of both semicircles + Area of the rectangle

= ( π x 46. 41 ²) + ( 85 x ( 46. 41 x 2 ))

= 14, 659.06 m ²

Then, find the area of the inner section :

=  ( π x 36. 41 ²) + ( 85 x ( 36. 41 x 2 ))

= 10, 356. 45 m ²

The area of the running track is :

= 14, 659.06 - 10, 356. 45

= 4, 302. 61 m ²

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Answer:

see image

Step-by-step explanation:

First of all, the problem might be that we need to set this up differently than how it is written.

"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:

THAT - THIS



Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.

Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.

1/5 - 2/5 is -1/5.

And -1/4 - 1/4 is -2/4, which is -1/2.

see image.

Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.

Using sine law and cosine law, s is 13.6 units and T is 37.7 degrees while U is 59.3 degrees

The Law of Cosines, also known as the Cosine Formula, is a fundamental mathematical relationship between the sides and angles of a triangle. It states that the dot product of two sides of a triangle is equal to the product of the third side and the cosine of the angle between the two sides.

The general form of the Law of Cosines is:

C^2 = A^2 + B^2 - 2ABcos(C)

where C is the angle between sides A and B, and A, B, and C are the lengths of the sides of the triangle. The formula can be rearranged to solve for any one of the sides or angles given the other two.

In this problem, we can easily solve for s.

s² = 8² + 12² - 2(8)(12)cos83

s² = 184.601

s = √184.601

s = 13.6 units

The value of angle T is calculated using sine law;

13.6 / sin 83 = 8 / sin T

sin T = 8(sin 83) / 13.6

sin T = 0.58385

T = sin⁻¹(0.58385)

T = 37.7°

Using sum of angle in a triangle;

T + S + U = 180°

83 + 37.7 + U = 180

U = 180 - 120.7

U = 59.3°

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Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.

The equation for the vertical movement of an object will be:

H(t) = -16*t^2 + v0*t + h0

Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height,  55ft.

Then the height equation is:

H(t) = -16*t^2 + 85*t + 55

The object will hit the ground when the height is equal to zero, then we need to solve:

-16*t^2 + 85*t + 55 = 0

Using the quadratic formula we will get:

[tex]t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}[/tex]

We only care for the positive solution, which is:

t = (-85 - 103.7)/-32 = 5.9

So it will take 5.9 seconds for the object to hit the ground.

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Answer:

[tex]\textsf{C.} \quad \sin x[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]

Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:

[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]

Therefore:

[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]

Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:

[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]

[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]

Cancel the common factor cos²x:

[tex]=\dfrac{\sin^2x}{\sin x}[/tex]

Simplify:

[tex]= \sin x[/tex]

Therefore:

[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]

In the xy-plane, the point (2,10) lies on the graph of the function f(x) = 2x^2 + bx - 8.  The value of b is 4.

What is linear equation?

A linear equation is an equation that describes a straight line in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope of a line is the measure of how steeply the line rises or falls, and the y-intercept is the point at which the line crosses the y-axis.

In a two-dimensional coordinate system, a linear equation represents a straight line that can be graphed by plotting pairs of x and y values that satisfy the equation. The line passes through all points that satisfy the equation and no others.

We can find the value of b by using the point-slope form of a linear equation, which states that the equation of a line with slope m that passes through the point (x1, y1) is given by y - y1 = m(x - x1).

In this case, the slope of the line is equal to 4x, and the point (x1, y1) is (2, 10), so we have:

y - 10 = 4x * (x - 2)

Expanding the right-hand side, we get:

y - 10 = 4x^2 - 8x

Matching this equation with the given function f(x) = 2x^2 + bx - 8, we see that b = 4.

So the value of b is 4.

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Velocity of rock when it hits the ground is -22.9955152 ft/s

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

Its position function is s(t) = –25t² + 1.86t

When it reaches back ground s(t) = 25 m/s

Substituting

               s(t) = –25t² + 1.86t = 25

Using the quadratic formula (-b±√b²-4ac)/2a

(-1.86 ±√1.86-4*25*-25)2*25

(-1.86 ±√1.7298+625)50

(-1.86 ±√626.7298)/50

(-1.86÷25)50

(-1.86+25)50 or( -1.86 -25)50

48.14/50 = 0.9628

This figure is taken because its positive

Time = 0.9628 seconds

Now we need to find velocity when it reaches ground, that is velocity after 0.9628 seconds.

Differentiating s(t) equation

   Substituting t = 0.9628 seconds

               v(t) = –25(0.9628)² + 1.86(0.9628)

v(t) = -23.174596 + 0.1790808

Velocity of rock when it hits the ground is -22.9955152 ft/s

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Based on the given information,

only one triangle is possible.

The correct option is C.

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Given:

The angle measure of B = π/6 = 30°.

a = 20, and b = 10

That means,

m∠A = 2∠B = 2 x 30 = 60°.

Now, there is only one possibility of a triangle, and that triangle is 30-60-90 triangle.

Hence, only one triangle is possible.

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Answer:

To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:

b_n = b_1 + (n-1)d

where d is the common difference. In this case, d = -3.

So, we can plug in the values for b_1 and d to find b_n:

b_n = 8 + (n-1)(-3)

b_n = 8 - 3(n-1)

Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:

b_14 = 8 - 3(14-1)

b_14 = 8 - 3(13)

b_14 = 8 - 39

b_14 = -31

So, the value of b_14 is -31, and the answer is (1) 14.