An archer shoots an arrow up towards a target located on a hill, which is shown by the graph
G16,43)
Which set of equations best models the point of intersection of the arrow and the target?
Oy=0.002x² +0.15x + 2 and y=x
Oy=-0.002x²+0.15x+2 and y=-x
Oy=0.002x²+0.15x + 2 and y=0,2x
Oy=-0.002x² +0.15x+2 and y = 0.2x

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

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Answer:

x-5

Step-by-step explanation:

since we don't know bob's age, x will represent it. we know that heather is 5 years YOUNGER than bob.

x (bob's age) - 5 (because that's how many years heather is younger than bob is)

hope this helps :D

Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.

To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.

The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.

Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).

Plugging these values into the formula, we get:

A = £3700(1 + 0.004167/12)^(12*2.917)

A ≈ £3947.46

The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.

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Answer:

The system of equations has one solution at (-4, 4).

Step-by-step explanation:

We are given the system of equations:

\(\displaystyle\left \{ {{5x+9y=16} \atop {x+2y=4}} \right.\)

We can use elimination to solve this system. We need to multiply the second equation by -5 so we can cancel out our x-terms.

\(-5\times(x+2y=4) \rightarrow -5x - 10y = -20\)

Therefore, our system now becomes:

\(\displaystyle\left \{ {{5x+9y=16} \atop {-5x-10y=-20}} \right.\)

Now, we can add these two equations together and solve for y.

\(\displaystyle(5x + 9y) + (-5x - 10y) = 0 - y\\\\16 + (-20) = -4\\\\-y = -4\\\\\frac{-y}{-1}=\frac{-4}{-1}\\\\y = 4\)

Now, we can substitute our value for y into one of the equations and solve for x.

\(x+2(4)=4\\\\x + 8 = 4\\\\x = -4\)

Therefore, our final solution is (-4, 4).

As per the random sampling, the marginal relative frequency for action movies is 44%.

The term sampling refers the process of selecting the group that you will actually collect data from in your research.

Here we have given that  a relative frequency table that shows the percentage of comedy lovers that prefer each location and the percentage of drama lovers that prefer each location.

And we need to find the marginal relative frequency of action movies.

While we looking into the given question, we have identified that the joint relative frequency for 8th graders who like comedy movies is 16%. And the half of the 7th graders prefer action movies.

Based on these facts the resulting frequency is 44%.

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9514 1404 393

Answer:

  p > 3

Step-by-step explanation:

  3p -4 -8p < -19 . . . . . . given

  -5p -4 < - 19 . . . . . . . . collect terms

  -5p < -15 . . . . . . . . . . . add 4

  p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)

The components of the force exerted on the plate at C are 1080N in the x direction and 1060N in the y direction.

The forces exerted on the plate at C can be determined using the equations of equilibrium. According to the equation of equilibrium, the sum of the forces in the x and y direction must be equal to zero. Therefore, we can calculate the x and y components of the force as follows:

Fx = 0 = Tcos(theta) – Fc

Fy = 0 = Tsin(theta) – Fb

Where T is the tension in the cable AC, theta is the angle of the cable AC, Fc is the force in the x direction, and Fb is the force in the y direction.

Using the given information, we can solve for Fc and Fb as follows:

Fc = Tcos(theta) = 2140N * cos(60°) = 1080N

Fb = Tsin(theta) = 2140N * sin(60°) = 1060N

Therefore, the components of the force exerted on the plate at C are 1080N in the x direction and 1060N in the y direction.

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Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

The answer is A

Hope this helps!

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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There 4 crust types, 2 sauces types, and 3 topping types. That is a total of 24 combinations. The answer is

(T, R, M), (T, R, O), (T, R, G), (T, W, M), (T, W, O), (T, W, G)

(H, R, M), (H, R, O), (H, R, G), (H, W, M), (H, W, O), (H, W, G)

(D, R, M), (D, R, O), (D, R, G), (D, W, M), (D, W, O), (D, W, G)

(S, R, M), (S, R, O), (S, R, G), (S, W, M), (S, W, O), (S, W, G)

Answer: 4y3(1x1 - 12)

3x4y3 – 48y3

4y3(1x1 - 12)

Answer:

Width = 17 feet, Length = 22 feet

Step-by-step explanation:

Let the width, w, be x

Therefore, length, L = x + 5

Perimeter = 78

p = 2(L+b)

78 = 2(x + x+5)

Adding the variables,

78 = 2( 2x + 5)

Dividing both sides by two,

39 = 2x + 5

Subtracting two from both sides,

34 = 2x

Dividing by two on both sides,

17 = x

Therefore, the width = x = 17 feet, and the length = x + 5 = 17 + 5 = 22 feet.

Hope you understood

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The value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

using the trigonometric ratio of tan 45°

{recall that tan 45° = 1}

tan 45° = QR/RT {opposite/adjacent}

tan 45° = x/2√3

x = tan 45 × 2√3 {cross multiplication}

x = 1 × 2√3

x = 2√3

Therefore, the value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.

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Answer:

134.04

Step-by-step explanation:

Answer:

Step-by-step explanation:

to get the area of the given figure,

we need to split it in to two (see attached)

then area of a rectangle = length x width

A1 = 15 cm x 4 cm = 60 cm²

A2 = 5 cm x 4 cm = 20 cm²

Area = A1 + A2

        = 60 + 20

        = 80 cm²

Area in this figure will be 80cm².

The area of the rectangle can be calculated by the product of length and breadth of the rectangle.

A=l*b

where l is length and b is the breadth.

So according to asked question in the drawn figure,

connect the point B and G.

now this figure will give two rectangle i.e. ABGH and CDEF

Rectangle ABGH has length l=5cm

breadth b=4cm

area of the rectangle ABGH= length * breadth=l*b=5*4=20cm²

Now CF=CB+BG+GF=5+5+5=15

Rectangle CDEF has length l=CF=15cm

breadth b=4cm

area of the rectangle ABGH= length * breadth=l*b=15*4=60cm²

Area of the figure= area of the rectangle ABGH+area of the rectangle CDEF

=20cm²+60cm²

=80cm²

Therefore area in this figure will be 80cm².

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Answer:

A

Step-by-step explanation:

Slope = (change in y)/ (change in x)

          = (-1 - 4)/ (8 - 3)

          = -5/5

          = -1

Answer:

Step-by-step explanation:

3/5 - 2/5 = (3-2)/5 = 1/5

7/10 - 3/10 = (7-3)/10 = 4/10 = 2/5

Answer:

0

Step-by-step explanation: 2x+8=2x+6 --> 8=6

8 cant be equal to 6 so this equation is wrong and has no solution.

Answer:

Absolute maximum of 1 at x = pi/4 ; \((\frac{\pi}{4}, \ 1)\)

Absolute minimum of -1 at x = 5pi/4 ; \((\frac{5\pi}{4} , \ -1)\)

Local maximum of √2/2 at x = 0 ; \((0, \ \frac{\sqrt{2} }{2} )\)

Local minimum of 0 at x = 7pi/4 ; \((\frac{7\pi}{4}, \ 0)\)

No critical points that are not stationary points.

Step-by-step explanation:

\(f(x)=sin(x+\frac{\pi}{4} ), \ 0 \leq x\leq \frac{7 \pi}{4}\)

Let's start by taking the derivative of the function.

Use the power rule and the chain rule to take the derivative of f(x).

The derivative of sin(x) is cos(x), so we can write this as:

Now, we can apply the power rule to x + pi/4.

Now that we have the first derivative of \(f(x)=sin(x+\frac{\pi}{4})\), let's set the first derivative to 0 to find the critical points of this function.

Take the inverse cosine of both sides of the equation.

Inverse cosine and cosine cancel out, leaving us with x + pi/4. The inverse cosine of 0 is equal to 90 degrees, which is the same as pi/2.

Solve for x to find the critical points of f(x). Subtract pi/4 from both sides of the equation, and move x to the left using the symmetric property of equality.

Since we are given the domain of the function, let's use the period of sin to find our other critical point: 5pi/4. This is equivalent to pi/4. Therefore, our critical points are:

Since this is a sine graph, we don't need to create a sign chart to check if the critical values are, in fact, extreme values since there are many absolute maximums and absolute minimums on the sine graph.

There will always be either an absolute maximum or an absolute minimum at the critical values where the first derivative is equal to 0, because this is where the sine graph curves and forms these.

Therefore, we can plug the critical values into the original function f(x) in order to find the value at which these extreme values occur. We also need to plug in the endpoints of the function, which are the domain restrictions.

Let's plug in the critical point values and endpoint values into the function f(x) to find where the extreme values occur on the graph of this function.

There is a maximum value of 1 at x = pi/4.

There is a minimum value of -1 at x = 5pi/4.

There is a maximum value of √2/2 at x = 0.

There is a minimum value of 0 at x = 7pi/4.

We need to first compare the critical point values and then compare the endpoint values to determine whether they are maximum or minimums.

A critical point is called a stationary point if f'(x) = 0.

Since f'(x) is zero at both of the critical points, there are no critical points that are not stationary points.  

Answer:

\(x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} \)

Answer:

r = 5 units

Step-by-step explanation:

Given:

Angle subtended at the centre (∅) in radians = 2π/3

Arc length (S) = 10π/3

radius (r) = ?

Required:

Radius (r)

Solution:

Formula for arc length given the central angle in radians is:

S = r∅

Make e the subject of the formula by dividing both sides by ∅

S/∅ = r∅/∅

r = S/∅

Plug in the values

r = (10π/3) / (2π/3)

Change the operation sign to multiplication and turn the fraction by your right upside down

r = 10π/3 × 3/2π

r = (10π × 3)/(3 × 2π)

Cross out terms that can divided each other

r = 5

The amount of sandwich they eat altogether is 2/3

A fraction can be defined as the part of a whole number, a whole number, a whole element.

The different types of fractions are listed as;

From the information given, we have that;

Angie ate 1 / 3 of the sandwich

Kim ate another 1 / 3 of the sandwich

To determine the total amount, we have;

1/3 + 1/3

add the values

1 + 1/3

add the values, we get;

2/3

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The complete question:

Angie and Kim are sharing a large sub sandwich. Angie ate 1 / 3 of the sandwich, and Kim ate another 1 / 3 of the sandwich. Please work out in detail.

Answer:

377 is answer

Step-by-step explanation:

12.33-25 +6

396-25+6

377

Answer:

35.66

Step-by-step explanation:

Don't work with the mean given at first

1. Multiply the mean of class A by the number of students in class A

35 times 15=525

2. Multiply the mean of class B by the number of pupils in class B

36 times 29=1044

3. Add the answers you got

1044+525

4.Add the pupils of both classes

29+15=44

5.Then divide the total grades and pupils

1569/44 =35.659

6 Then round off

=35.66

(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.

(10) The slope of a line parallel to this line, y = 10 -8x is -8.

The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.

Question 9.

f(x) = 0.75x + 6

where;

The slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3

Question 10.

For the equation of another line, y = 10 - 8x

The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;

y = 10 - 8x

where;

slope of a line parallel to the line = -8

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