you plan to take $450 U.S on a trip to South Africa. How many rands is this if one U.S dollar equals 3.70 rands ?

822 rands
1,216 rands
1,665 rands
8,222 rands

Answer:

The graph is attached below

Step-by-step explanation:

y – 1 = 2(x – 2)

y-1 = 2x - 4

add 1 on both sides

y = 2x - 3

To graph the given equation we make a table

Plug in some number for x and find out the value of y

x      y = 2x-3

-1       2(-1)-3= -5

0        2(0) -3= -3

1          2(1) -2= -1

The point to get the graph of the given equation is

(-1,-5)   (0,-3) (1,-1)

The graph is attached below

Answer:

The answer is the first graph or graph A.

BTW this is just the short answer...

Its quicker.      :-)

When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.

To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.

Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.

Final answer:

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

Explanation:

To find the interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

Using the given information, we can plug in the values and solve for r:

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

The interest rate, for continuous compounding, is approximately 5.775%.

To find the interest rate for continuous compounding, we can use the formula for compound interest:

[tex]\[ A = P \times e^{rt} \][/tex]

Where:

- [tex]\( A \)[/tex] is the final amount of money,

- [tex]\( P \)[/tex] is the principal amount (initial investment),

- [tex]\( r \)[/tex] is the interest rate (annual rate in decimal),

- [tex]\( t \)[/tex] is the time the money is invested for (in years),

- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.

Given:

- [tex]\( P = $750 \)[/tex],

- [tex]\( A = $1500 \)[/tex],

- [tex]\( t = 12 \)[/tex] years.

We need to solve for [tex]\( r \)[/tex], the interest rate.

**Substitute the Given Values into the Formulaa :

[tex]\[ 1500 = 750 \times e^{12r} \][/tex]

**Divide Both Sides by 750**:

[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]

[tex]\[ 2 = e^{12r} \][/tex]

**Take the Natural Logarithm of Both Sides**:

[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]

[tex]\[ \ln(2) = 12r \ln(e) \][/tex]

[tex]\[ \ln(2) = 12r \][/tex]

**Solve for [tex]\( r \)[/tex]**:

[tex]\[ r = \frac{\ln(2)}{12} \][/tex]

[tex]\[ r = \frac{0.693}{12} \][/tex]

[tex]\[ r = 0.05775 \][/tex]

**Convert the Interest Rate to a Percentage**:

[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]

[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]

So, the interest rate is approximately 5.775%.

The solution is c = 14

How many extraneous solutions are there? zero

Answer:

Option A is correct

equation [tex]2(x+14)=42[/tex] could be used.

Step-by-step explanation:

Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.

Perimeter(P)of a rectangle in inches is given by:

[tex]P= (2l+w)[/tex] ; where [tex]l[/tex]  is the length of the rectangle and w is the width of the rectangle.

Substitute the value of  P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;

[tex]42 = 2 \cdot (14+x)[/tex]

Divide by 2 on both sides  we get;

[tex]21 = 14+x[/tex]

On simplify, we get;

x = 21-14 = 7 inches

therefore, the width of the rectangle is, x = 7 inches

Check :

Substitute the value of x =7 in option A.

[tex]2(x+14) =42[/tex]

[tex]2(7+14)=42[/tex]

[tex]2\cdot 21 =42[/tex]

42 = 42      

Hence, the only equation that could be used to find the width, x is,  [tex]2(x + 14) = 42[/tex]

We have to find the value of 'x' in [tex] \sin (x+22)^{\circ}=\cos (2x-7)^{\circ} [/tex]

By using the complementary angle formula which states:

[tex] \cos (90-\Theta )=\sin \Theta [/tex]

Now,

[tex] \cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ} [/tex]

Therefore, we get

[tex] 90-(x+22)= (2x-7) [/tex]

[tex] 90-x-22= (2x-7) [/tex]

[tex] 68=3x -7 [/tex]

[tex] 75=3x [/tex]

[tex] x=25^{\circ} [/tex]

Answer:

Lets go by a step-by-step process.

Step-by-step explanation:

\cos (90-\Theta )=\sin \Theta  

Now,

\cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}

Now we have...

 90-(x+22)= (2x-7)

90-x-22= (2x-7)

68=3x -7

75=3x

x=25^{\circ}

Answer:

  3x⁵ + 7x² -9x⁴

Step-by-step explanation:

In the order given, the polynomials have degrees 3, 2, 5, 4. The one of degree 5 is "quintic." That one also happens to be a trinomial. It is ...

  3x⁵ + 7x² -9x⁴

Fifteen is a factor of the number because both 3 and 5 are prime factors and this can be determined by using the arithmetic operations.

Given :

Number -- [tex]2^3\times 3^2\times 5[/tex]

The following steps can be used in order to determine the correct statement:

Step 1 - Write the given number.

[tex]2^3\times 3^2\times 5[/tex]

Step 2 - Simplify the above expression.

[tex]= 8\times 9 \times 5[/tex]

Step 3 - Multiply 8 by 9 in the above expression.

[tex]= 72\times 5[/tex]

Step 4 - Multiply 72 by 5 in the above expression.

= 360

Step 5 - 15 is a factor of 360.

Therefore, the correct option is 1).

For more information, refer to the link given below:

https://brainly.com/question/10454590

Answer: [tex]80.47\ m^2 [/tex]

Step-by-step explanation:

The area of a sector is given by :-

[tex]\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}[/tex]

Given :Central angle = [tex]\theta=\frac{\pi}{3}[/tex]

radius = 12.4 m

Then,

[tex]\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2 [/tex]

Answer:

1. 49

2. 169

3. 81

4. 100

5. 441

6. 36

Step-by-step explanation:

1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]

= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]

= 7×7 = 49

2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]

= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]

= 169

3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]

= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]

= 81

4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]

= 10²

= 100

5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]

= 21²

= 441

6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]

= 6²

= 36                                        

Answer:

Yes, because the center is on the x-axis.

Step-by-step explanation:

First, write the equation in standard form by completing the square.

x2 - 4x + y2 = -3

x2 - 4x + 4 + y2 = -3 + 4

(x - 2)2 + y2 = 1

The circle is centered at (2, 0) with a radius of 1. Since the circle is centered on the x-axis, it intersects the x-axis two times, at (3, 0) and (1, 0).

Answer:

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Step-by-step explanation:

Given the diameter of circle 60 cm

we have to find the area of circle

Diameter=60 cm

Radius=30 cm

[tex]\text{Area of circle=}\pi r^2[/tex]

[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Option A is correct

The acronym CPCTC stands for "  Corresponding  parts of congruent triangles are congruent. "

CPCTC--

It is a rule which states that if any of the two triangles are congruent by any of the congruency such  as ASA, RHS , SAS or SS then the remaining sides and the remaining angles which were not covered in the congruency  are also congruent.

       Also, the acronym is:

     Corresponding parts of congruent triangles are congruent.