5 Bob is 5 years younger than twice Mark's age. Bob is 31. How old is Mark?​

Answer:consumer surplus

Step-by-step explanation:

Answer:

Its B consumer

Step-by-step explanation:

Answer:

(4,5)

Step-by-step explanation:

Answer:

The area of the Plexiglas is given by the formula for the area of a rectangle, which is A = L * W, where L is the length and W is the width of the rectangle. In this case, the width is 5 centimeters shorter than the length, so we can represent it as W = L - 5. Substituting this expression for the width into the formula for the area, we get:

A = L * (L - 5)

This expression represents the area of the Plexiglas in terms of its length.

Answer:

25,000 rent for 5 months

Step-by-step explanation:

The annual rent of a room in KTM is rs 60,000. Find the rent of 5 months.

60,000 / 12 = 5,000 rent per month

5,000 * 5 = 25,000 rent for 5 months

Answer:25,000 rent for 5 months

Step-by-step explanation:

The annual rent of a room in KTM is rs 60,000. Find the rent of 5 months.

60,000 / 12 = 5,000 rent per month

5,000 * 5 = 25,000 rent for 5 months

Step-by-step explanation:

Therefore , the required inequality expression is 4.50x+1.75y ≤50

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

One cupcake costs $4.50,

So, “x” cupcakes cost = 4.50x.

One brownie cost $1.75,

so “y” brownies cost = 1.75y.

thus, the total 4.50x+1.75y  must be less or equal to $50.

Therefore , the required inequality expression is 4.50x+1.75y ≤50

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The number of terms in the algebraic expression is 3 terms.

An algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

Coefficient refees to a constant by which an algebraic term is multiplied.

Constant is a quantity that remains at a fixed value throughout a given discussion.

x + 3 + 7x

Thr terms are;

x;

3;

7x

Therefore, the algebraic expression has Coefficient, constant, and like terms.

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Answer:

18x24=432 so basically 432 should go to the carpenters

Answer:

D) [tex]\frac{\sqrt{14}}{7}[/tex]

Step-by-step explanation:

[tex]\sqrt{\frac{2}{7}}=\frac{\sqrt{2}}{\sqrt{7}}=\frac{\sqrt{14}}{7}[/tex]

Answer:

the answer for slope is -1

In the pair of numbers 64,4 and 16,2 the first number is a multiple of the second number.

A multiple in math are the numbers you get when you multiply a certain number by an integer.

Check whether the first number is a multiple of the second number

A) In the pair 64,4

64=16×4, yes 64 is multiple of 4

B) In the pair 29,3

Here, 29 is prime number

No, 29 is not a multiple of 3

C) In the pair 16,2

16=8×2, yes 16 is multiple of 2

D) In the pair 42,8

Here, 42=2×3×7 and 8=2×2×2

No, 42 is not multiple of 8

E) In the pair 31,7

Here, 31 is prime number

No, 31 is not a multiple of 7

Therefore, in the pair of 64,4 and 16,2 the first number is a multiple of the second number.

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Answer:

90

Step-by-step explanation:

Let's call the initial distance from the jet to the airport $x$. We are told that $x = 5$ miles.

Let's call the initial ground distance from the projection of the jet onto the ground to the airport $y$. We are told that $y = 4$ miles.

Let's call the rate at which the distance from the jet to the airport is increasing $v_x$. We are told that $v_x = 180$ miles/hour.

Let's call the rate at which the ground distance from the projection of the jet to the ground to the airport is increasing $v_y$. We are told that $v_y = 150$ miles/hour.

We want to find the vertical speed of the jet at this moment in time. Let's call this quantity $v_z$.

Since the jet is flying in the eastward direction, we can use the Pythagorean theorem to relate the three sides of the right triangle formed by the jet, the projection of the jet onto the ground, and the airport. Specifically, we have

$$x^2 = y^2 + z^2$$

where $z$ is the vertical distance from the jet to the ground (i.e., the height of the jet above the ground).

Since the distance from the jet to the airport and the ground distance from the projection of the jet to the airport are both increasing, we can take the derivative of both sides of the equation above to find the rate of change of $z$ with respect to time. This gives us

$$2x \frac{dx}{dt} = 2y \frac{dy}{dt} + 2z \frac{dz}{dt}$$

where $t$ is time.

We are given the values of $x$, $y$, $v_x$, and $v_y$, so we can plug these values into the equation above to solve for $v_z$. This gives us

$$2 \cdot 5 \cdot 180 = 2 \cdot 4 \cdot 150 + 2z \frac{dz}{dt}$$

Solving for $\frac{dz}{dt}$, we get

$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2z}$$

We are told that $z = x - y$, so we can plug this into the equation above to find $\frac{dz}{dt}$. This gives us

$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2(x-y)}$$

Substituting the values of the known quantities, we get

$$\frac{dz}{dt} = \frac{2 \cdot 5 \cdot 180 - 2 \cdot 4 \cdot 150}{2(5-4)} = \frac{180}{2} = 90$$

Therefore, the vertical speed of the jet at this moment in time is $v_z = 90$ miles/hour.

The vertical speed of the jet is approximately 300 miles/hour.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is traveling along a route.

Let's call the distance from the jet to the airport "d" and the height of the jet "h". Then we have two related rates:

d is increasing at a rate of 180 miles/hour.

The horizontal distance is increasing at a rate of 150 miles/hour.

Using the Pythagorean theorem, we can relate these two distances:

d² = h² + 4²

Taking the derivative of both sides with respect to time, we get:

2d(dd/dt) = 2h(dh/dt)

Simplifying, we get:

dd/dt = (h/d)(dh/dt)

We're looking for the vertical speed of the jet, which is dh/dt. We can solve for this by plugging in the given values:

d = 5 miles

dd/dt = 180 miles/hour

h² + 4² = 5² (from the Pythagorean theorem)

dh/dt = ?

Solving for h, we get:

h² = 5² - 4² = 9

h = 3 miles

Now we can plug in all the values and solve for dh/dt:

dh/dt = (dd/dt)(d/h) = (180 miles/hour)(5 miles/3 miles) ≈ 300 miles/hour

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The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)

An expression in maths, a statement involving at least two different numbers (known or unknown) and at least one operation.

Given an expression, -3x²-24x-36;

Factorizing, we get,

-3x²-24x-36 = -3(x²+8x+12)

= -3(x²+6x+2x+12)

= -3[x(x+6)+2(x+6)]

= -3(x+6)(x+2)

Hence, The expression equivalent to the expression -3x²-24x-36 is -3(x+6)(x+2)

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Answer:

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

Given expression:

Simplify it in below steps:

Answer:

4+(8×3x)+(8×(-2))-7x

4+24x-16-7x

4-16+24x-7x

-12+17x

or 17x-12

Answer: c

Step-by-step explanation:

A function cannot have repeated X value in a set

Perpendicular lines intersect at 90° - definition of perpendicular.

Here is the two column proof:

     Statement                                        Reason                                              

The equation of the line perpendicular to the line y = 2x and is passes through (10,2) is given by  y = (-1/2)x + 7.

As given in the question,

Equation of the line is given by :

y = 2x

Point (x₁ , y₁ ) = (10, 2) through which line passes .

Slope intercept form is given by :

y = mx + c

'm' is the slope of the line.

slope of the line y = 2x is equal to  'm₁' = 2

let 'm₂' be the slope of the line perpendicular to the given line y = 2x.

Relation between the slopes of two perpendicular lines is given by :

m₁ × m₂ = -1

⇒2 × m₂ = -1

Divide both the side by 2 we get,

⇒m₂ = -1/2

Equation of the required line is:

(x₁ , y₁ ) = (10, 2)

y - y₁ = m₂ ( x - x₁ )

⇒ y - 2 = (-1/2) ( x - 10 )

⇒ y =(-1/2)x + 7

Therefore, the equation of the line perpendicular to the given line y =2x  is given by  y = (-1/ 2)x + 7 .

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Answer:

Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Here are 4 options available to choose from:

1) 45 = 3² x 5 (multiply the sum of 3 times 3 by 5)

2) (3 x 8 )+ (24 x 2) - 3 (multiply 8 times 3 and then 24 times 2 add expressions together then subtract 3 from sum of expressions)

3)  (9 x 9)- 36 = 45 (multiply 9 times 9 and subtract 36 from 81)

4) [tex]6^{2}[/tex] -9 (multiply 6 times 6 and subtract 9 from 36)

(Hope this helped you )

The volume of water in Tank C is 12800 ml.

Given that the group of students brought two tanks of water to clean the classroom.Tank A held 5,511 ml of water and Tank B held 7,275 ml of water and the water from both tanks was poured into Tank C which was empty.

It should be noted that the volume on tank C will be the addition of A and B volume. This will be calculated thus:

= Volume of A + Volume of B

= 5511 ml + 7275 ml

= 12786 ml

= 12800 ml to nearest hundred.

The volume is 12800 ml.

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Answer:

- 7/9

Step-by-step explanation:

Answer:

When x has a value of 0, the equation -2x+3y=18 becomes 0+3y=18. Solving for y, we find that y=6.

When y has a value of 0, the equation -2x+3y=18 becomes -2x+0=18. Solving for x, we find that x=-9.

These solutions are called the x-intercept and the y-intercept, respectively, when they are graphed as part of the line -2x+3y=18. The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. In this case, the x-intercept is (-9,0) and the y-intercept is (0,6). These points can be used to graph the line and to understand its slope and direction.

Step-by-step explanation:

Answer: 6, -9, ?

Step-by-step explanation:

When x has a value of zero:

-2x + 3y = 18

Substitute 0 into the value of x:

-2(0) + 3y = 18

We know that anything multiplied by 0 will always be zero, so you get:

3y = 18

Therefore, after dividing both sides by 3 to get y on its own, you get:

y = 6

When y has a value of zero:

-2x + 3y = 18

Substitute 0 into the value of y:

-2x + 3(0) = 18

We know that anything multiplied by 0 will always be zero, so you get:

-2x = 18

To get a positive number from a negative number x needs to be a negative number. Remember - and - makes +.

x = -9

Unfortunately, I am unable to answer the final part of the question, but hopefully what I've already written will spark a memory of something you learnt in class :)

Hoped this helped!

Answer:

224

Step-by-step explanation:

28x8=224

Answer: 224 flowers

Step-by-step explanation:

8*28=224

Barry will post all of his parcels separately at £17.84

The information in the table have the amount to post certain weights of the parcel. This will be used to ascertain how much to send Barry's parcel

Barry's parcel will contains (starting from the least)

weight of parcel                    cost of posting as from the table

less than 1 kg (1kg to 5kg)      £2.04

0.245 kg (1kg to 5kg)             £2.04

2.7 kg (1kg to 5kg)                  £2.04

4.16 kg (1kg to 5kg)                £2.04

27.3 kg (More than 20kg)      £9.68

addition of the costs

= £2.04 * 4 + £9.68

= £17.84

hence the cost of sending the five parcels is £17.84

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Answer: y=7/4x-2

Step-by-step explanation:

I find the slope first, using 5--2/4-0. This is 7/4. I then plug it into point-slope form, which is y--2=7/4(x-0). Simplifying get y=7/4x-2.

Answer:

Step-by-step explanation:

The 25° angle the light ray makes with the normal, B which is the angle of incidence, according to the laws of reflection, indicates that the angle of reflection, which is the angle the reflected ray makes with the normal, C, is 25°

The laws of reflection states that (1) The angle of incidence and the angle of reflection have the same value (2) The incident ray, the reflected ray and the normal are coplanar (3) The refracted ray is on the opposite side of the normal with regards to the incident ray.

The law of reflection states that the angle the in of reflection and the angle of incidence are equal; [tex]\theta_i = \theta_r[/tex]

The angle the incident ray makes with the normal of the plain mirror and the angle the reflected ray makes with the normal are the same.

The angle the incident ray in the diagram of the question makes with the normal line segment, B = 25°

The angle the reflected ray makes with the normal line segment = C

Therefore, according the to the laws of reflection, we get;

Angle B = Angle C

Angle B = 25°

Therefore;

Angle C = Angle B = 25° (symmetric property)

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Answer:

[tex]90^{\circ}[/tex]

Step-by-step explanation:

A right angle measures [tex]90^{\circ}[/tex].

The linear approximation found to estimate ln(0.97) is 9.1%.

The definition of a linear approximation of a function is simply utilising a line to approximate the value of the function at a point. We recall the idea of the tangent line as soon as we see a curve (of a function) and a point on it. The value of the function at any point that is very close to the provided point can be roughly determined using the equation of the tangent line if the equation of the tangent line is found at the supplied point.

The given function is f(x) = ln(x).

We start by finding the equation of the tangent line at x=1 to the graph of y=lnx.

f(1)=ln(1)=0

We know the derivative of f(x) will be f'(x)=1/x

f'(1)=1/1=1

Therefore, the equation of the tangent is:y−y1=m(x−x1)

y−0=1(x−1)

y=x−1

An approximation for ln(1.19) would be y=1.19−1=0.19

The actual value, obtained using a calculator, would be 0.174. This means the percent error is (0.19−0.174)/0.174 ×100

= 9.1%

Therefore, the linear approximation found to estimate ln(0.97) is 9.1%.

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-12 will be the term for y

Let us suppose that x= 0

then we will get

3y + 4 = x

and then it will be

3y+ 4 = 0

Now, we will move 4 to the right hand side and it being positive this side will become negative on right hand side

3y= -4

now,

3y = 1/4

y = 1/[4*3]

y=1/12

y= - 12

Hence the answer will be y= -12

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