MATHEMATICS HIGH SCHOOL

The value of X and Y vary directly, and when X= 4 Y equals -10. Find the value of Y when X equals 10.

Answers

Answer 1

Answer:

y = - 25

since x varies directly with y then we can express the relationship as

x = ky ← k is the constant of variation

to find k use the given condition y = - 10 when x = 4

k = $(x)/(y)$ = $(4)/(-10)$ = - $(2)/(5)$

hence x = - $(2)/(5)$ y

when x = 10

10 = - $(2)/(5)$ y

multiply both sides by - 5 and divide both sides by 2 )

- 50 = 2y ⇒ y = - 25

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Whats the answer to this in the picture?
2/3(3x-15y)+(9-11x)

Answers

$(2)/(3) (3x-15y)+(9y-11x)$

$= 2(x-5y)+(9y-11x)$

$= 2x-10y+9y-11x$

$=-9x-y$

A) -9x - y

3 * (2/3) = 2
-15 * (2/3) = -10

(2x - 10y) + (9y - 11x)

Combine like terms:
9y - 10y = -1y (or -y)
-11x + 2x = -9x
A) -9x - y

How do you write(−∞,8),(10,∞),as an inequality? A. x < 8 or x > 10
B. x < 10 or x > 8
C. x < 8 and x > 10
D. x < 10 and x > 8

Answers

Answer:

The answer is the option A

$x< 8$ or $x>10$

Step-by-step explanation:

we know that

The interval -----> (-∞,8)

Is all real numbers less than $8$

$x<8$

The interval -----> (10,∞)

Is all real numbers greater than $10$

$x>10$

The expression (-∞,8) U (10,∞) represent the inequality

$x< 8$ or $x>10$

see the attached figure to better understand the problem

(−∞,8),(10,∞) is equal to x < 8 οr x > 10

Alexa drew a retangle with an area of 36 square centimeters. The rectangle she drew has the smallest perimeter possible for this area. What is the lenght and width of the rectangle she drew.

Answers

The length is 6 cm and width is 6 cm.

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

The Formula for Area of rectangle

= length x width

We have Alexa drew a rectangle with an area of 36 square centimeters.

and, Perimeter P = 2L + 2W

P = 2(36/W) + 2W

P = (72/W) + 2W

-72/W² + 2 = 0

-72/W² = -2

W² = 36

W = 6 cm

and, Length = 36/6 = 6 cm

Learn more about Area here:

brainly.com/question/27683633

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length=6
width=6
20 charr

A cell phone company charges $40 per month for unlimited calling, and $0.20 per text message sent. If t represents the number of text messages Roxy sent last month, which expression represents the cost of her bill last month before any taxes or additional fees?

Answers

We know that 40$ is a constant and the number of texts sent (t) will change the price therefire we can plug it in the basic linear equation (p being the total price): p= 0.2t + 40

Answer:

40+0.2t

Step-by-step explanation:

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square feet per second, at which the area is changing when AC = 3 is?

Answers

Answer: $-(7)/(4) \quad \text{ft}^(2)/\sec$

Step-by-step explanation:

Since ABC is a right triangle, at any moment it holds that

$5^2=(AC)^2+(BC)^2$

Moreover, the area A of the triangle is given by

$A= (1)/(2)(AC)(BC)$

and we know that the rate of change of the length (AC) is

constant decreasing 2, which may be written using the Leibniz

notation as

$(d(AC))/(dt)=-2$ .

Using the chain rule and the product rule for derivation, the two

first equations tell us

that

$0 = 2 (d(AC))/(dt)(AC) + 2 (d(BC))/(dt)(BC)$

and

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot (AC)\right)$

Moreover, using the first of the last two equations we get

$(AC)(d(AC))/(dt) = -(BC)(d(BC))/(dt) \Rightarrow\n\n\n(AC)(-2) = -(BC) (d(BC))/(dt) \quad \Rightarrow \quad (d(BC))/(dt)=2 ((AC))/((BC))$

Now, when (AC)=3, we have that

$25=(AC)^2 + (BC)^2 \quad \Rightarrow 25 = 9 + (BC)^2\n \n\Rightarrow \quad 16=(BC)^2 \quad \Rightarrow (BC)=4$

and

$(d(BC))/(dt) = 2 ((AC))/((BC))=2 (3)/(4)=(3)/(2)$ .

Hence, at this moment the rate of change of the area of the triangle is

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot(AC) \right)=(1)/(2)\left( -2 \cdot 4 + (3)/(2)\cdot 3\right ) = -(7)/(4)$

okay
we have the rate of change of AC = d(AC)/dt = -2
the rate of change od BC = d(BC)/dt
area = (1/2) *AC) (BC)
taking differential on both sides we ge
d(A)/dt = 1/2){ (BC) d(AC)/dt + (AC) d(BC)/dt)}....(1)
again
when AC= 3
applying pythagorous thm
we get
(5)^2 =(3)^2 +(BC)^2
hence we get BC = 4
now we need to find d(BC)/dt
we have
(5)^2 = (AC)^2 +(BC)^2
taking differenial
0=2(AC) d(AC/dt) +2BC d(BC)/dt
that is
d(BC)/dt = -(3) *(-2)/4 ..(at AC =3)
hence
d(BC)/dt = 3/2
substituting these values in equation (1)
d(A)/dt = (1/2) {4 * -2 + 3 *3/2}

which gives
d(A)/dt = -7/4

The rate, in square feet per second, at which the area is changing when AC = 3 is -7/4 ft/sec.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

Joe works on an assembly line that fills boxes with various toy trinkets. Every sixth box gets a red ball and every eighth box gets a blue whistle. How often does a box get both a red ball and a blue whistle?

Answers

So we know that every 6th box gets a red ball and every 8th box gets a whistle, so now multiply 6, 8 until you get the same numberf EX: 6x1=6 8x1=8 and so on

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