Solve the system by substitution. Check your solution.
a minus 1.2 b = negative 3. 0.2 b + 0.6 a = 12
a.
(15, 15)
c.
(13, 12)
b.
(10, 12)
d.
(7, 9)



Please select the best answer from the choices provided


A
B
C
D

Answer:

Hi,

Step-by-step explanation:

PR²=PQ²+QR²-2*PQ*QR*cos(51°)

=15²+12²-2*15*12*cos(51°)

=142,444659....

PR=11.9350...

PQ²=QR²+PR²-2*QR*PR*cos(R)

cos(R)=(12²+142.444...-15²)/(2*12*11.9350...)=0,21451112....

angle R=77,61315...°≈77.6°

angle P=180°-51°-77.6°≈51,4°

a) The compound interest equation is [tex]C = 4250 \cdot 0.9675^{t}[/tex].

b) There is an approximate loss of $ 987.16.

c) The stock will take approximately 12.979 to decrease by half.

Compound interest model represents the gain of a deposit as a function of the number of periods and initial amount. The model is represented below:

[tex]C = C_{o}\cdot (1+r)^{t}[/tex]     (1)

Where:

Capital decreases in time when interest rate is a negative number. The equation that models the situation is [tex]C = 4250 \cdot 0.9675^{t}[/tex] and the current capital after eight years is:

C = 4250 · 0.9675⁸

C = 3262.84

That represents an approximate loss of $ 987.16.

And the number of periods required to decrease the capital by half is:

[tex]2125 = 4250 \cdot 0.9675^{t}[/tex]

[tex]0.5 = 0.9675^{t}[/tex]

㏒ 0.5 = t · log 0.9675

t ≈ 20.979

The stock will take approximately 12.979 to decrease by half.

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Answer:

infinite number of solutions

Step-by-step explanation:

x + y = 1 → (1)

3y = - 3x + 3 ( add 3x to both sides )

3x + 3y = 3 ( divide through by 3 )

x + y = 1 → (2)

since the 2 equations are the same, this indicates the system has an infinite number of solutions

Answer:

x=30

Step-by-step explanation:

You have to use intercept theorem, also known as Thales's theorem to slvoe this.

it would be 45 minutes

Answer:

4/13 is the answer

total = 4+3+5+1= 13

let a be the event of getting red marbles= total is 4

probability=4/13

Answer: [tex]18^{\circ}[/tex]

Step-by-step explanation:

In triangle RUV, angle RUV is a right angle (and thus measures 90 degrees), and angle RVU measures 72 degrees.

Since angles in a triangle add to 180 degrees, angle VRU measures

Answer:

[tex]\frac{3}{22}[/tex]

Step-by-step explanation:

the bar above 36 means that the digits 36 are being repeated

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.13636.. ( multiply both sides by 10 and 1000 )

10x = 1.3636... (1)

1000x = 136.3636... (2)

subtract (1) from (2) thus eliminating the repeating digits

990x = 135 ( divide both sides by 990 )

x = [tex]\frac{135}{990}[/tex] = [tex]\frac{3}{22}[/tex] ← in simplest form

The 5th term of the sequence is 27.98

The given parameters are:

The nth term of a geometric sequence is calculated using:

[tex]T_n = ar^{n-1[/tex]

So, we have:

[tex]T_5 = 1 * 2.3^{5-1[/tex]

Evaluate the difference

[tex]T_5 = 1 * 2.3^4[/tex]

Evaluate the product

[tex]T_5 = 27.98[/tex]

Hence, the 5th term of the sequence is 27.98

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Answer:

give clear image is next question

Step-by-step explanation:

i will give you the answer

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Given that;

To determine how long it take to fill the dam, we say;

Time need = Amount of water needed ÷ Pump rate

T = A ÷ r

T = 30000 litres ÷ 75 litres/minute

T = 400 minutes

Note that; 60min = 1hrs

Hence,

T = 6hours 40minutes

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

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Answer: x = 13

Step-by-step explanation: First, we simplify the equation to get 4x + 7 = 5x - 6. Then, from there, we subtract 7 on both sides to get 4x = 5x - 13. Then we subtract 5x from both sides, which would give us -x = -13. Finally, we can divide both sides by -1 (because remember, x = 1) to get that x = 13. Hope this helps!

Solve for t in terms of y :

[tex]y = t - 2 \implies t = y + 2[/tex]

Substitute this into the parametric equation for x :

[tex]x = (3t + 2)^2 \implies x = (3(y + 2) + 2)^2 \implies \boxed{x = (3y+8)^2}[/tex]

Answer:

200 KM/H

Step-by-step explanation:

A plane has a speed of 840 km/h in still air. It can travel 3120 km with the wind in the same time it would take to travel 1920 km against the wind. Find the speed of the wind.

let x=speed of wind

(840+x)=speed of plane with wind

(840-x)=speed of plane against wind

Travel time = distance/speed (same with and against the wind)

3120/(840+x)=1920/(840-x)

cross-multiply

3120*840-3120x=1920*840+1920x

3120*840-1920*840=1920x+3120x

5040x=1008000

x=200 km/hr

answer

Speed of wind=200 km/hr

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression

An extraneous solution is a solution that in obtained after completely solving an equation but it does not  work in the original given equation.

You should must check for an extraneous solution when  the variable appears both inside and outside the absolute value expression (Option D).

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Answer:

24.19

Step-by-step explanation:

[tex] \tan(x) = \frac{6.2}{13.8} \\ x = { \tan}^{1} \frac{6.2}{13.8} \\ x = 24.19320899[/tex]

or the value of x can be 24.20

Step-by-step explanation:

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in

Answer:

 x = -1

y = 4

Step-by-step explanation:

Solving system of linear equations by elimination method.

    8x +  3y = 4 ---------------(I)

    2x  + y = 2 --------------(II)

Multiply the second equation by (-3) and then add them.Thus y will be eliminated and we will obtain the value of 'x'.

       (I)                8x  +  3y = 4

     (II)*(-3)         -6x - 3y = -6   {Now add}

                           2x         = -2

                                     x = -2/2

                           [tex]\sf \boxed{\bf x = -1}[/tex]

Plugin x = (-1) in any one of the equations. Here I have chosen equation (II)

2*(-1) + y = 2

    -2 + y  = 2

           y = 2 + 2

            [tex]\sf \boxed{\bf y = 4}[/tex]

Answer:

5;   2n + 5 ≤ 15

6;   n/5 ≤ 15

7;   5n ≥ 15

Step-by-step explanation:

"a number" means a variable denoted "n"

"product" means to multiply

"quotient" means to divide

"The sum" means to add

"is at least" means greater than or equal to or  ≥

"is no greater than" means less than or equal to or ≤

"Is at most" means less than or equal to or ≤

The expression that is equivalent to √10 / (4√8) is given as √5 / 8

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

√10 / (4√8)

Simplifying:

= √10 / (4√(4 * 2))

= √10 / (8√2)

= √5 / 8

The expression that is equivalent to √10 / (4√8) is given as √5 / 8

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The statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.

Since the height of the plane is a function given by a parabola, we need to know the equation of a parabola in vertex form

The equation of a parabola with vertex (h,k) is given by y = a(x - h) + k

Since the height (in feet) of the airplane as a function of time (in seconds after the timer was started) is given by the equation h(t) = −(t − 12) + 81

So, the statement which is true is the airplane reaches its maximum height of 81 feet in 12 seconds.

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Answer:

14.5 Meters

Step-by-step explanation:

1 centimeter= 0.01 Meters

1450 cm x 0.01 =14.5

b²-4ac is the discriminant (D)!

you use it when you have a second degree function and want to find the x. If:

D<0 -> no x that we can find

D=0 -> 1 answer for x

D>0 -> 2 answers for x

when your D is = or > 0 then you use these formulas to find the x:

x1= (-b-VD)/2a

x2= (-b+VD)/2a

example1:

f(x)=2x²+3x+4=0

D= b²-4ac

= 3²-4×2×4

=9- 32

=-23

-> no answers for x

example2:

f(x)=2x²+5x+2=0

D= 4²-4×2×2

= 25-16

=9

x1= (-b-VD)/2a

= (-5-3)/4

= -8/4

=-2

x2= (-b+VD)/2a

= (-5+3)/4

=-2/4

=-1/2

Answer:

0.17 (rounded)

Step-by-step explanation:

There's only one way a 1 can appear on a number cube out of 6 possible sides. Thus, the theoretical probability of the number cube showing a 1 is 1/6, or 0.17 rounded.

Answer:

Step-by-step explanation:

Comment

It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.

The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.

Answer

product

12

The equation of the translation is y = sin(x - π/4)

The equation is given as:

y = sin(x)

The rule of translation to the right is:

(x,y) => (x - h,y)

This gives

(x,y) => (x - π/4,y)

So, we have:

y = sin(x - π/4)

Hence, the equation of the translation is y = sin(x - π/4)

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Answer:

Option A

Step-by-step explanation:

Remember the things.

In Q1

in Q2

in Q3

in Q4

Answer:

A. The x-coordinate is positive and the y-coordinate is positive.

Step-by-step explanation:

The Cartesian plane is divided into four regions by the x-axis and y-axis.

These regions are called "quadrants".

Quadrant I is the top right region, where x and y coordinates of points are positive.

From here, move in a counterclockwise direction.  

Therefore, Quadrant II is the top left region, where the x-coordinate is negative and the y-coordinate is positive.

Quadrant I → (x, y)

Quadrant II → (-x, y)

Quadrant III → (-x, -y)

Quadrant IV → (x, -y)

The perimeter and area of the equilateral, isosceles and right angled triangle are  16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.

Note that:

The perimeter of an Equilateral triangle is expressed as P = 3a

The area of an Equilateral triangle is expressed as A = ((√3)/4)a²

Where a is the dimension of the side.

The perimeter of an Isosceles triangle is expressed as P = 2a + b

The area of an Isosceles triangle is expressed as A = (ah)/2

Where b is the slant height, a is the dimension of the base and h is the height.

The perimeter of a Right angled triangle is expressed as P = a + b + c

The area of a Right angled triangle is expressed as A = (ab)/2

Where a and b is the dimension of the two sides other than the hypotenuse and c is the hypotenuse.

For the Equilateral triangle.

Given that;

Perimeter P = 3a

P = 3 × 5.4mm

P = 16.2mm

Area A = ((√3)/4)(5.4mm)²

A = ((√3)/4)( 29.16mm² )

A = 12.6mm²

The Perimeter and Area of the Equilateral triangle are 16.2mm 12.6mm² respectively.

For the Isosceles triangle.

Given that;

Perimeter P = 2a + b

P = 2(b) + a

P = 2(5.9in) + 3.4in

P = 11.8in + 3.4in

P = 15.2in

The height h is the imaginary line drawn upward from the center of a.

First, we calculate the height using Pythagorean theorem

x² = y² + z²

Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h

(5.9in)² = (1.7in)² + h²

34.81in² = 2.89in² + h²

h² = 34.81in² - 2.89in²

h² = 31.92in²

h = √31.92in²

h = 5.65in

Now, the area will be;

A = (ah)/2

A = (3.4in × 5.65in )/2

A = 19.21in²/2

A = 9.61in²

The Perimeter and Area of the Isosceles triangle are 15.2in and 9.61in² respectively.

For the Right angled triangle.

Given that;

Perimeter P = a + b + c

P = 8.2yds + 4.1yds + 9.17yds

P = 21.47yds

Area A = (ab)/2

A = ( 8.2yds × 4.1yds)/2

A = ( 33.62yds²)/2

A = 16.81yds²

The Perimeter and Area of the Right angled triangle are 21.47yds and 16.81yds² respectively.

Therefore, the perimeter and area of the equilateral, isosceles and right angled triangle are  16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.

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