Solve the equation below for x. cx - 4 = 7

A)

Replace the letters in the given equation with the corresponding values given in the problem:

A = 10,000 x 2.718^(0.05 x 2)

A = 11,051.59 , rounded to nearest dollar = $11,052

B)20,000 = 10000 x 2.718^(0.05 x t)

Divide both sides by 10,000:

2 = 2.718^(0.05 x t)

Apply exponent rules:

0.05tln(2.718) = 2

Solve for t:

t = ln(2) / 0.05ln(2.718)

t = 13.86 years, rounded to nearest year = 14 years.

Answer:

Step-by-step explanation:

Using [tex]A=Pe^{rt[/tex] as instructed, our equation looks like this:

[tex]A=10,000e^{(.05)(2)}[/tex] which simplifies a bit to

[tex]A=10,000e^{.1[/tex] which simplifies a bit more to

A = 10,000(1.10517) so

A = 11,051.71  Easy. Now onto the second part: solving for the number of years it takes for the investment to double. Setting A equal to 20,000 since 20,000 is 10,000 doubled:

[tex]20,000=10,000e^{.05t[/tex]  Begin by dividing both sides by 10,000 to get

[tex]2=e^{.05t[/tex] and take the natural log of both sides to get that exponent down out front, keeping in mind that the natural log will "undo" the e, leaving us with:

ln(2) = .05t and

t = 14 years (that's 13.8 rounded up to the nearest year)

Answer:

The first one

Step-by-step explanation:

The product[tex]-4.\left[\begin{array}{c}8&-1&-5&9\end{array}\right][/tex] is equal to[tex].\left[\begin{array}{c}-32&4&20&-36\end{array}\right][/tex]. Option A is correct.

We have to find the product of[tex]-4.\left[\begin{array}{c}8&-1&-5&9\end{array}\right][/tex].

To do this we need to multiply -4 with each element in the matrix.

-4×8 = -32

-4×-1 =4

-4×-5=20

-4×9=-36

Now the matrix becomes [tex].\left[\begin{array}{c}-32&4&20&-36\end{array}\right][/tex].

Hence, the product[tex]-4.\left[\begin{array}{c}8&-1&-5&9\end{array}\right][/tex] is equal to[tex].\left[\begin{array}{c}-32&4&20&-36\end{array}\right][/tex]. Option A is correct.

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Answer:

-6xy²

Step-by-step explanation:

xy² - 2xy² - 5y²x

use commutative property to reorder terms

xy² - 2xy² -5xy²

combine like terms

- xy² - 5xy²

- 6xy²

Answer:

The original price is $90.

Step-by-step explanation:

100% - 40% = 60%

[tex]\frac{54}{y} :\frac{60}{100}[/tex]

y × 60 = 54 × 100

60y = 5400

60y ÷ 60 = 5400 ÷ 60

y = 90

Answer:

90

Step-by-step explanation:

If the discount is 40%, we are still paying 100-40% or 60 %

original price * 60% = sale price

original price * .6 = 54

Divide each side by .6

original price = 54/.6

original price =90

Answer:

y = 1/2x - 6

Step-by-step explanation:

y2 - y1 / x2 - x1

-3 - (-5) / 6 - 2

2/4

= 1/2

y = 1/2x + b

-3 = 1/2(6) + b

-3 = 3 + b

-6 = b

Answer:

V = 378y³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Geometry

Volume of a Rectangular Prism: V = lwh

Step-by-step explanation:

Step 1: Define

Identify variables

l = 9y

w = 7y

h = 6y

Step 2: Find Volume

___________________________________

[tex]\quad\quad\quad\quad \boxed{\tt{v = lwh}}[/tex]

[tex]\quad\quad\quad\quad\tt{length (l)= 9y}[/tex]

[tex]\quad\quad\quad\quad\tt{width(w)= 7y}[/tex]

[tex]\quad\quad\quad\quad\tt{height(h)= 6y}[/tex]

[tex]\quad\quad\quad\quad\tt{v = lwh}[/tex]

[tex]\quad\quad\quad\quad\tt{v = (9y)(7y)(6y)}[/tex]

[tex]\quad\quad\quad\quad\tt{v = (9y)(42 {y}^{2}) }[/tex]

[tex]\quad\quad\quad\quad \underline{\tt{v = 378 {y}^{3} }}[/tex]

[tex]\quad\quad\quad\quad \underline { \boxed{\tt{ \color{magenta}v = 378 {y}^{3} }}}[/tex]

___________________________________

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✍︎ C.Rose❀

Answer:

1. x=3/2-y-3z/2

2.x=-y/2-17/3

3.x=3-5y/2-z/2

Step-by-step explanation:

i gusse

Let a,b,c,d and e are five numbers

mean = (a +b+ c+ d+e)/5 = 30

⇒ (a +b+ c+ d+e) = 150_______(1)

now, Let the number excluded be a

then, new mean =  (b+ c+ d+e)/4 = 28

⇒ (b+ c+ d+e)= 112

putting this value in (1),

⇒a + 112 = 150

⇒a = 150 -112 = 38

excluded number = 38

Answer:

D) X >= to -1

Step-by-step explanation:

Since the dot on -1 is filled in, -1 is included. The arrow points to the right, implying that X is greater than or equal to -1.

It's D)

Because the full circle means "equal to" and it's going towards the right which means it will be greater.

Answer:

P = 2x +2y + 14

Step-by-step explanation:

The perimeter of the rectangle is 2x + 2y + 14.

The perimeter of an object is calculated by adding the sides length of the objects.

Given that, the length and width of a rectangle is x+8 and y-1, we need to find the perimeter,

P = 2(length + width)

P = 2(x+8+y-1)

P = 2(x+y+7)

P = 2x+2y+14

Hence, the perimeter of the rectangle is 2x + 2y + 14.

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Answer:

.............soooooooooooooooerrrrrrrrrrrrryyyyyyyyyyyyyyy.......... iiiiiiiii........ doooooooonnnnnnnnntttttttt......... kkkknnnnnooooowwww

Answer:

lol i genuinely dunno

Step-by-step explanation:

like B'(4,8) or something

which expression is equivalent to 6-(-8)

Given:

A cube has square sides with area [tex]x^2+24x+144[/tex].

To find:

The expression that represents the surface area of the cube.

Solution:

It is given that,

The area of each side of cube = [tex]x^2+24x+144[/tex]

Number of sides of a cube = 6

Total surface area of the cube is the product of number of sides of the cube and the area of each side. So, the total surface area of the cube is

[tex]SA=6(x^2+24x+144)[/tex]

[tex]SA=6(x^2)+6(24x)+6(144)[/tex]

[tex]SA=6x^2+144x+864[/tex]

Therefore, the expression that represents the surface area of the cube is [tex]6x^2+144x+864[/tex].

your ans is here........

Answer:

The output of (-6,0) is (-9,4)

Step-by-step explanation:

Given

[tex](x,y) \to (x -3,y+4)[/tex] --- rule

Required

The output of [tex](-6,0)[/tex]

[tex](-6,0)[/tex] implies that:

[tex](x,y) = (-6,0)[/tex]

So, we have:

[tex](x,y) \to (x -3,y+4)[/tex]

[tex](-6,0) \to (-6 -3,0+4)[/tex]

[tex](-6,0) \to (-9,4)[/tex]

The output of (-6,0) is (-9,4)

Answer:

i. y = 4

ii. p = 45

iii. m = 5

Step-by-step explanation:

(a) In triangle PQR, PQ = QR. So that,

Perimeter = PQ + PR + QR

40 = (2y + 3) + (5y - 2) + (2y + 3)

    = 2y + 3 + 5y - 2 + 2y + 3

40 = 9y + 4

40 - 4 = 9y

36 = 9y

y = [tex]\frac{36}{9}[/tex]

y = 4

(b) The age of Rahim's father is p years. Since he is 29 years older than Rahim, we have;

p = 16 + 29

p = 45

Rahim's father is 45 years old.

(c) Cost of a chair = RM 5.90

Cost of m chairs = RM 5.90 x m

                           = RM 5.90m

Amount paid = RM 50 - RM 20.50

                      = RM 29.50

Thus,

RM 5.90m = RM 29.50

5.90m = 29.50

m = [tex]\frac{29.50}{5.90}[/tex]

   = 5

m = 5

The number of units of chairs bought is 5.

Answer:

Solution

Height is not an example of a continuous variable.

D) The number of cheeseburgers sold yesterday at a drive-thru is not an example of continuous data.

Here, we have,

Continuous data refers to numerical data that can take on any value within a certain range or interval. It typically involves measurements or quantities that can be expressed as real numbers.

A) The time it takes to cut the grass can be measured in minutes or seconds, and it can take on any value within a range. This is an example of continuous data.

B) The lifetime (in hours) of a flashlight battery is a continuous variable. It can take on any value within a range, such as 5.3 hours, 10.7 hours, or any decimal or fractional value.

C) The weights of dogs in an animal shelter can be measured in pounds or kilograms and can take on any value within a range. This is also an example of continuous data.

D) The number of cheeseburgers sold yesterday at a drive-thru is a discrete variable. It represents a count or a whole number, such as 50 cheeseburgers, 100 cheeseburgers, etc. Discrete data involves distinct values and is not continuous.

Therefore, option D is not an example of continuous data.

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Answer:

Step-by-step explanation:

Surface area:

Volume:

Answer:

> V = 217.68 cm³

> S = 227.14 cm²

Step-by-step explanation:

We are required to find the surface area and the volume of the given figure . This question is from Combination of solids . As we can see that this figure is made up of a cuboid and cylinder.

Firstly let's find out the volume .

> V = V_( cuboid) + V_(cylinder)

> V = 9cm × 4cm × 5cm + π × ( 2cm)²× 3cm

> V = 180 cm³ + 3.14 × 4cm² × 3cm

> V = 180 cm³ + 37.68 cm³

> V = 217.68 cm³

Lets find the surface area :-

> S = S_( cuboid) + S_( cylinder) - πr²

> S = 2( 9×4 + 4× 5 + 5×9) cm² + 2×π×2cm × 3cm - 3.14 × (2cm)²

> S = 239.7 cm² - 12.56 cm²

> S = 227.14 cm²

Note :-

Answer:

36000cm

V= Length×Width×height

Answer:

[tex]36000 cm^{3} [/tex]

Step-by-step explanation:

Rectangular Tank is,

[tex]100cm = long[/tex]

[tex]30cm = wide[/tex]

[tex]12cm = height[/tex]

Let's Solve now

[tex]v = l \times w \times h \\ \: = 100cm \times 30cm \times 12cm \\ = 36000 {cm}^{3} [/tex]

Answer:

x = 60

Step-by-step explanation:

t = [tex]\frac{k}{x}[/tex]

15 = k/68

k=1020

~~~~~~~~~~~

17 = 1020/x

x = 1020/17

x = 60

The speed of car must be 60mile/hour, so that the trip will complete in 17 hours.

The rate of change of position of an object in any direction is called speed.

[tex]speed = \frac{distance}{time}[/tex]

According to the given question

At a speed of 68 miles per hour, the trip will be complete in 15 hours.

⇒ Total distance covered in 15 hours = 68 × 15 = 1,020 miles  

( because, distance = speed × time)

Therefore, the speed of car to complete the trip in 17 hours

= [tex]\frac{1020}{17} =60miles/hr[/tex]

Hence, the speed of car must be 60mile/hour, so that the trip will complete in 17 hours.

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Answer:

[tex]y = \sqrt{900 - x^2[/tex]

Step-by-step explanation:

Given

From the complete question, we have:

[tex]r=30[/tex] --- radius

Required

Expression for the height of the roller coaster

We have:

[tex]x^2 + y^2 = r^2[/tex] --- equation of circle

Substitute 30 for r

[tex]x^2 + y^2 = 30^2[/tex]

[tex]x^2 + y^2 = 900[/tex]

Since the roller coaster is half of the circle, the height is defined by y.

So: make y the subject

[tex]y^2 = 900 - x^2[/tex]

Take square roots

[tex]y = \sqrt{900 - x^2[/tex]

Hence, the height is:

[tex]\sqrt{900 - x^2[/tex]

Answer:

yes it is correct

Step-by-step explanation:

option 1  

Answer:

Your answer is correct! 9:1

Step-by-step explanation:

Old Area = side x side

? = 2 x 2

     4cm

New Area-

Step 1: Triple the sides

2 x 3 = ?

    6cm

Step 2: Find the area

6 x 6 = ?

  36cm

The ratio of the new area to the old area is:

                     36 : 4

But wait! You can simply it!

36 / 4 = 9

4 / 4 = 1

So the new ratio would be:

                     9 : 1

Hope this helps!

Good Luck!

:)

Answer:

option E, C

Step-by-step explanation:

From the graph we will find the equation of g(x).

g(x) is a parabola with vertex ( h, k) = ( 0, 9)

Standard equation of parabola is ,  y = a (x - h)² + k

                                                     y = a (x - 0)² + 9

                                                     y = ax² + 9 ----------  ( 1 )

Now we have to find a .

To find a we will take another point through which the parabola passes .

Let it be ( 3, 0).

Substitute ( 3 , 0 ) in  ( 1 ) =>  0 = a (3 )² + 9

                                     => - 9 = 9a

                                     => a = - 1

Substitute a = - 1 in ( 1 ) => y = -1 x² + 9

                                  => y = - x² + 9

Therefore , g(x) = -x² + 9

Now using the table we will find h(x)

 [tex]h(x) = 4^{x}[/tex]

So g(x) = -x² + 9 and [tex]h(x) = 4^{x}[/tex]

Option A : both function increases on ( 0, ∞ ) - False

               [tex]\lim_{x \to \infty} g(x) = \lim_{x \to \infty} -x^2 + 9[/tex]

                                  [tex]= - \lim_{x\to \infty} x^2 + \lim_{x \to \infty} 9\\\\= - \infty + 9\\\\=- \infty[/tex]

g(x) decreases on ( 0 , ∞)

             [tex]\lim_{x\to \infty} h(x) = \lim_{x \to \infty} 4^{x}[/tex]

                                [tex]= \infty[/tex]

h(x) increases on ( 0, ∞)

option B : g(x) increasing on (- ∞, 0) - False

      g(x) = -x² + 9

       g( -2 ) = - (-2)² + 9

                 = - 4 + 9 = 5

       g ( -5) = - ( -5)² + 9

                =  - 25 + 9 = - 14

   As the value of x moves towards - ∞ , g(x) moves towards - ∞

   Therefore g(x) decreases on  (- ∞, 0)

Option C: y intercept of g(x) is greater than h(x) - True

         y intercept of g(x) = ( 0 , 9 )

         y intercept of h(x)  = ( 0 , 1 )

Option D : h(x) is a linear function - False

Option E : g(2) < h(2) - True

        g(x) =  -x² + 9

        g(2) = -(2)² + 9 = - 4 + 9 = 5

        h(x) = 4ˣ          

        h(2) = 4² = 16      

Answer:

1: 98

2: 82

3: 98

4: 82

Step-by-step explanation:

So 2 is 82deg then the opposite is also 82 so 4 is 82deg

Then 82+82 = 164deg, and we remain with 360deg-164deg which is = 196.

Since the other two angles will be equal (they are opposite each other) we can decide 196/2 = 98

So 3 and 1 are 98deg

Answer:

Step

<2 and <4 are vertically opposite. They are equal

<2 = 82               Given

<4 =  82              Vertically opposite to a given

<3 = 180 - 82       <3 and <4 are supplementary. They are on the same straight line.

<3 = 98

<1 = 98                 Vertically opposite  angles are equal.

Answer:

10

Step-by-step explanation:

[tex]\sqrt{36 + 64}[/tex]

[tex]\sqrt{100}[/tex]

10

is it like this pls don't mind how I snap it