A builder wants to build a sump to store water in an apartment. The volume of the
rectangular sump will be modelled by V(x) = x3 + x2 - 4x - 4.
He planned in such a way that its length and breadth are (x + 1) and (x - 2) respectively.
How much he has to dig?
(a) (x + 1]
(b) (x - 2)
(c) (x-3)
(d) (x + 2)
(ii) If x = 4 meter, what is the storage capacity (in litres) of this sump?
(iii) A ladder is kept a point halfway from the base as shown in the figure. It just touches
the top of the sump. Find the length of the ladder, assuming x-42 (correct to 1 dp)​

Answer:

a)

The function that represents the value of the account at any time, t

[tex]\:\:A=Pe^{rt}[/tex]

b)

The total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 5,500.00 at a rate of 3.75% per year  compounded continuously  over 6 years is $ 6,887.77.

Step-by-step explanation:

a. Write the function that represents the value of the account at any time, t.

The function that represents the value of the account at any time, t

[tex]\:\:A=Pe^{rt}[/tex]

where

A represents the Future Value

P represents the Principle (Initial Value)

r represents the Interest rate

t represents the time

b) What will the value be after 6 years?

Given

The principal amount  P = $5500

Annual Rate r = 3.75% = 3.75/100 = 0.0375

Time Period  t  = 6 years

To Determine:

The total amount A = ?

Using the formula

[tex]\:\:A=Pe^{rt}[/tex]

substituting the values

[tex]A\:=\:5500\left(2.71828\right)^{\left(0.0375\right)\left(6\right)}[/tex]

[tex]A=5500\cdot \:2.71828^{0.225}[/tex]

[tex]A = $ 6,887.77[/tex] $

Therefore, the total amount accrued, principal plus interest,  from compound interest on an original principal of  $ 5,500.00 at a rate of 3.75% per year  compounded continuously  over 6 years is $ 6,887.77.

Answer:

the quotient of -30/6 and 30/ -6 are same ie. -5, because if the numerator or denominator is negative the quotient will be negative.

hope it helps!

Answer:

tell me the choices so i can help you............

Answer:

x=3.6

Step-by-step explanation:

multiply 4 by 9 and then divide by 10

Answer:

x/4=9/10

x*10=9*4

x=(9*4)/10

X=3.6

Answer:

dude what type of question is this

Answer:

-40

Step-by-step explanation:

An integer is any whole number, positive or negative. However, an integer cannot be a fraction. Since you have just spent $40, you have lost that amount, therefore making your number negative or -40.

Answer 40 - 20

Step-by-step explanation:

20 is he number

Answer: For #6, domain is {-3≤x<4}, range is {-3<y≤-1}

Step-by-step explanation: For #6 domain, the leftmost point on the graph is -3, with a closed circle. This means that x is greater than or equal to -3 (-3≤x). The rightmost point is 4, with an open circle, meaning that x is less than 4 (x<4). Put them together in the standard format, and you get {-3≤x<4}. Same principle for range; lowest point is -3, with an open circle (-3<y), and highest point is -1, with a closed circle (x≤-1). Result is {-3<y≤-1}.

I'm not sure whether you are a beginner at this or if it's just this one that you're stuck on, I hope my answer was sufficient.

Answer:

c

Step-by-stepexplanation:

Answer:

i believe the answer is a

i'm not sure...........

hope its right

:)

Given:

x, y and z are integers.

To prove:

If [tex]3x-y+5z[/tex] is even, then at least one of x, y or z is even.

Solution:

We know that,

Product of two odd integers is always odd.          ...(i)

Difference of two odd integers is always even.          ...(ii)

Sum of an even integer and an odd integer is odd.      ...(iii)

Let as assume x, y and z all are odd, then [tex]3x-y+5z[/tex] is even.

[tex]3x[/tex] is always odd.          [Using (i)]

[tex]5z[/tex] is always odd.          [Using (i)]

[tex]3x-y[/tex] is always even.       [Using (ii)]

[tex](3x-y)+5z[/tex] is always odd.       [Using (iii)]

[tex]3x-y+5z[/tex] is always odd.

So, out assumption is incorrect.

Thus, at least one of x, y or z is even.

Hence proved.

Answer:

m%(n)

Step-by-step explanation:

whenever the word "of" comes up in a math problem, it's going to mean to multiply.  This case is no exception.

m% of n = m%(n)

n=number

m=the percent number

Ex: m=25

n=315

plug the values into m%(n)

25%(315)

There are two different forms you can do to solve this expression.

fraction: 25/100(315)=7875/100=78.75

the reason why it would be 25/100 hundred is because, %=per cent.  Cent=100 and per would mean you would have to divide.

decimal: 0.25(315)=78.75

if 25% is 25/100 that means that 25 would be in the hundreths place in a decimal(0.ab)

9514 1404 393

Answer:

Step-by-step explanation:

For dilations about the origin, such as these, the scale factor is always the ratio of any image point coordinate* to the corresponding preimage point coordinate. If the scale factor is k, the transformation can be written as ...

  (x, y) ⇒ (kx, ky)

__

  S(9,12) ⇒ S'(6, 8) . . . . scale factor is 6/9 = 2/3; relation is (x, y) ⇒ (2/3x, 2/3y)

  U(8, 18) ⇒ U'(4, 9) . . . scale factor is 4/8 = 1/2; relation is (x, y) ⇒ (1/2x, 1/2y)

  I(0,8) ⇒ I'(0, 7) . . . scale factor is 7/8; relation is (x, y) ⇒ (7/8x, 7/8y)

  X(16, 8) ⇒ X'(4, 2) . . . scale factor is 2/8 = 1/4; relation is (x, y) ⇒ (1/4x, 1/4y)

_____

* The origin is the one invariant point in a dilation, so the chosen coordinate cannot be zero.

Answer:

slope = - [tex]\frac{7}{6}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, 8) and (x₂, y₂ ) = (4, - 6) ← 2 ordered pairs from the table

m = [tex]\frac{-6-8}{4+8}[/tex] = [tex]\frac{-14}{12}[/tex] = - [tex]\frac{7}{6}[/tex]

Answer:

9000000

Step-by-step explanation:

Complete Question

Mr. Nguyen bought a package of 3 chicken legs and a package of 7 chicken wings. Ms. Dawes bought a package of 3 chicken legs and a package of 6 chicken wings. Mr. Nguyen bought 45 ounces of chicken. Ms. Dawes bought 42 ounces of chicken. How much did each chicken leg and each chicken wing weigh?​

Answer:

Weight of Chicken leg = x = 8 ounces

Weight of Chicken wing = y = 3 ounces

Step-by-step explanation:

Let us represent

Weight of Chicken leg = x

Weight of Chicken wing = y

Mr. Nguyen bought a package of 3 chicken legs and a package of 7 chicken wings.Mr. Nguyen bought 45 ounces of chicken.

3x + 7y = 45 ounces.... Equation 1

Ms. Dawes bought a package of 3 chicken legs and a package of 6 chicken wings. Ms. Dawes bought 42 ounces of chicken.

3x + 6y = 42 ounces... Equation 2

Combining both Equations together we solve by Elimination method

3x + 7y = 45.... Equation 1

3x + 6y = 42... Equation 2

We eliminate x by subtracting Equation 2 from Equation 1

Hence:

y = 3 ounces

Solving for x

3x + 6y = 42 ounces... Equation 2

3x +6(3) = 42 ounces

3x + 18 = 42 ounces

3x =( 42 - 18) ounces

3x = 24 ounces

x = 24 ounces/3

x = 8 ounces

Hence:

Weight of Chicken leg = x = 8 ounces

Weight of Chicken wing = y = 3 ounces

Answer:

chicken leg- 8 oz

chicken wing- 3 oz

Step-by-step explanation:

Answer: X is 0.4

Explanation: I typed 5/2 x a bunch of random numbers and decimals on a calculator until I tried 0.4 and when I typed 5/2 x 0.4 on the calculator it said 5/2 x 0.4 = 1.

Answer:

3

Step-by-step explanation:

"Find a number which, when added to 3, yields 7"

may be written as:

3 + ? = 7, 3 + n = 7, 3 + x = 1

and so on, where the symbols ?, n, and x represent the number we want to find. We call such shorthand versions of stated problems equations, or symbolic sentences. Equations such as x + 3 = 7 are first-degree equations, since the variable has an exponent of 1. The terms to the left of an equals sign make up the left-hand member of the equation; those to the right make up the right-hand member. Thus, in the equation x + 3 = 7, the left-hand member is x + 3 and the right-hand member is 7.

SOLVING EQUATIONS

Equations may be true or false, just as word sentences may be true or false. The equation:

3 + x = 7

will be false if any number except 4 is substituted for the variable. The value of the variable for which the equation is true (4 in this example) is called the solution of the equation. We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result.

Example 1 Determine if the value 3 is a solution of the equation

4x - 2 = 3x + 1

Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member.

4(3) - 2 = 3(3) + 1

12 - 2 = 9 + 1

10 = 10

Ans. 3 is a solution.

Answer:

x = 8

y = -11

Step-by-step explanation:

In this question, we have to find out the value of "x" and "y".

Solve:

Lets solve for y first.

-2(3x + 4y = -20)

6x + 5y = -7

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

-6x - 8y = 40

6x + 5y = -7

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

-3y = 33

Divide both sides by -3

y = -11

We now know what the value of "y" is, now we must find the value of x. To do this, we would plug -11 to "y" in one of our equations.

Solve for x:

3x + 4y = -20

3x + 4(-11) = -20

3x - 44 = -20

Add 44 to both sides.

3x = 24

Divide both sides by 3

x = 8

Now we know that our answer are:

x = 8

y = -11

Answer:

root4 by 2

Step-by-step explanation:

multiply the whole no with root5-root3 up and down also

Answer:

yes

Step-by-step explanation:

Answer:

I'm confused

Step-by-step explanation:

Answer:

6h=

Step-by-step explanation:

You have to combine the terms the way they are supposed to be

Answer:

(-5/2,5)

I hope it will be useful.

The coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now the given coordinates are,

(-4,10) and (2,-10)

Thus, we have,

x₁  = -4

y₁ = 10

x₂ = 2

y₂ = -10

Given ratio, m₁ : m₂ = 1 : 3

⇒ m₁ =  1; m₂ =  3

Let (x,y) be the coordinates of the point on the directed line segment from (-4,10) to (2,-10) that partitions the segment into a ratio of 1 to 3.

Since the section formula is given as,

So, x = (m₁x₁ + m₂x₂) / (m₁ + m₂)  

y =  (m₁y₁ + m₂y₂) / (m₁ + m₂)  

Put the values,

x = [1(-4) + 3*2)] / (1 + 3) = (-4+6) / 4 = 2/4

⇒ x = 1/2

Similarly y = [1(10) + 3*(-10)] / (1 + 3) = (10-30) / 4 = -20/4

⇒ y = -5

So, the required coordinates are (1/2, -5)

Thus, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).

To learn more about line segment :

brainly.com/question/12774890

#SPJ2

Answer:

35%

Step-by-step explanation:

40%+25%=65%

100%-65%=35%

Answer:

(f - g)(x) = x² - 3x - 70

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² - 2x - 63

g(x) = x + 7

(f - g)(x) is f(x) - g(x)

Step 2: Find (f - g)(x)

Answer:

The rule of dilation is [tex]P'(x,y) = 3\cdot P(x,y)[/tex].

The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.

Step-by-step explanation:

From Linear Algebra, we define the dilation by the following definition:

[tex]P'(x,y) = O(x,y) + k\cdot[P(x,y)-O(x,y)][/tex] (1)

Where:

[tex]O(x,y)[/tex] - Center of dilation, dimensionless.

[tex]k[/tex] - Scale factor, dimensionless.

[tex]P(x,y)[/tex] - Original point, dimensionless.

[tex]P'(x,y)[/tex] - Dilated point, dimensionless.

If we know that [tex]O(x,y) = (0,0)[/tex], [tex]k = 3[/tex], [tex]A(x,y) = (-7,-6)[/tex], [tex]B(x,y) = (-5,-2)[/tex] and [tex]C(x,y) =(-1,-5)[/tex], then dilated points of triangle ABC are, respectively:

[tex]A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)][/tex] (2)

[tex]A'(x,y) = (0,0) + 3\cdot [(-7,-6)-(0,0)][/tex]

[tex]A'(x,y) = (-21, -18)[/tex]

[tex]B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)][/tex] (3)

[tex]B'(x,y) = (0,0) + 3\cdot [(-5,-2)-(0,0)][/tex]

[tex]B'(x,y) = (-15,-10)[/tex]

[tex]C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)][/tex] (4)

[tex]C'(x,y) = (0,0) +3\cdot [(-1,-5)-(0,0)][/tex]

[tex]C'(x,y) = (-3,-15)[/tex]

The rule of dilation is:

[tex]P'(x,y) = 3\cdot P(x,y)[/tex] (5)

The vertices of the dilated triangle are [tex]A'(x,y) = (-21, -18)[/tex], [tex]B'(x,y) = (-15,-10)[/tex] and [tex]C'(x,y) = (-3,-15)[/tex], respectively.

Every line from the tangent to the centre is 90°. This is said in the circle theorems.

So angle OBC and ODC are 90°.

angle O is twice the size of angle F. This is another circle theorem.

Therefore angle O is 152°.

The quadrilateral of ODBC would equal to 360°. Which means 90° + 90° + 152° = 332°

360° - 332° = 28°.

The answer is 28°

Answer:

∠BCD = 28°

Step-by-step explanation:

arc BD = 2 x inscribed angle ∠BFD = 2 x 76 = 152

arc BFE = 360 - arc BD = 360 - 152 = 208

tangent-tangent angle ∠BCD = (arc BFE - arc BD)/2 = (208 - 152)/2 = 28

Given:

The graph of a function.

To find:

The zeros of this function on the graph.

Solution:

We know that, zeros are the values at which the values of the function is 0. It means, the points where the graph of function intersect the x-axis are know as zeros of the function.

From the given graph it is clear that, the graph intersect the x-axis at two points.

Therefore, the marked points on the below graph are the zeros of the function.

Answer:

A does

Step-by-step explanation:

5+3+10+6=24x56310B=A+B=A

Answer:

Step-by-step explanation:

[tex] \frac{16 {x}^{2} {y}^{2} }{4xy} [/tex]

[tex]4 {x}^{2 - 1} {y}^{2 - 1} [/tex]

[tex]4xy[/tex]

Answer:

0

Step-by-step explanation:

Answer:

0

Step-by-step explanation: