Answer:
Step-by-step explanation:
We'll first find out how long it takes for the account to have 2500 in it, then we'll add a year (we'll check ourselves anyway, just to be sure!) This is an exponential growth problem of the form
[tex]A(t)=P(1+r)^t[/tex] since the compounding is only done once a year. Filling in:
[tex]2500=2000(1.02)^t[/tex] Begin by dividing both sides by 2000 to get
[tex]1.25=(1.02)^t[/tex] In order to get that t down from its current position in the equation, we will take the natural log of both sides. This allows us to pull the t down and put it out front like this:
ln(1.25) = t ln(1.02) Now divid both sides by ln(1.02) and you will see that
t = 11 years. At 11 years (rounded), the account will have
[tex]A(t)=2000(1.02)^{11}[/tex] = 2486.75 and after 12 years:
[tex]A(t)=2000(1.02)^{12[/tex] = 2536.48
t = 12 works!
The minimum number of complete years it would take the investment to increase to $2500 is 12 years.
Definition of compound interestCompound interest is when both the principal and the interest earned increases in value at the interest rate per period.
Formula for determining the number of yearsNumber of years = In(FV / PV) ÷ r
FV = future value PV = present value r = interest rate
In(2500 / 2000) ÷ 0.02
In (1.25) ÷ 0.02
= 11.2 years
= 12 years
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What is the slope of the line that passes through the points (-3,5) and (6,-1)?
Answer:
C.
[tex]slope = \frac{( - 1 - 5)}{6 - ( - 3)} \\ = \frac{ - 6}{9} \\ = - \frac{2}{ 3} [/tex]
HELPPPPPP PLEASEEE!!
Answer:
the trend is increasing
Step-by-step explanation:
Se tienen 25 billetes de 5 y de 20 lempiras con un monto de 350 lempiras cuantos billetes de 5 lempiras se tienen y de 20 lempiras
Answer:
El número de facturas
5 lempiras = 10 billetes
20 lempiras = 15 billetes
Step-by-step explanation:
Vamos a representar
El número de facturas de
5 lempiras = x
20 lempiras = y
Nuestro sistema de ecuaciones se da como:
x + y = 25 ..... Ecuación 1
x = 25 - y
5 × x + 20 × y = 350
5x + 20y = 350 .... Ecuación 2
Sustituiríamos x por 25 - y en la ecuación 2
5 (25 - años) + 20y = 350
125 - 5 años + 20 años = 350
125 + 15 años = 350
15 años = 350 - 125
15 años = 225
y = 225/15
y = 15
Resolviendo para x
x = 25 - y
x = 25 - 15
x = 10
Por lo tanto, el número de facturas
5 lempiras = 10 billetes
20 lempiras = 15 billetes
Perform the indicated subtraction. -5 - (-6)=
Answer:
1
Step-by-step explanation:
Answer:
-5 - (-6)= 1
Step-by-step explanation:
hope this is what you're asking for
find the area of the figure below
A.288.62
B.266.22
C.186.66
D.236.6
Answer:
A. 288.62
Step-by-step explanation:
Area of two triangles = 15.3 * 10.4 = 159.12
Area rectangle = hypotenuse triangle * 7
hypotenuse = √108.16 + 234.09
Hypotenuse = 18.5
Area rectangle = 18.5 * 7 = 129.5
129.5 + 159.12 = 288.62
Answer = A. 288.62
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Write x^2 + 4x +5 in the form of (x + a)^2 + b where a and b are integers
Answer:
[tex](x+2)^2 + 1 \ , \ where \ a = 2 \ , \ b = 1[/tex]
Step-by-step explanation:
[tex](x + 2)^2 = x^2 + 4x + 4\\\\(x+2)^2 + 1 = x^2 + 4x + 5[/tex]
[tex]Therefore,[/tex]
[tex]x^2 + 4x + 5 = (x+2)^2 + 1[/tex]
CSC(4x) - cot(4x)
CSC(4x) + cot(4x) =
A. tan(2x)
B. cot(4x)
C.tan^2(2x)
D. tan^2 (4x)
Answer:
c. tan^2(2x)
Step-by-step explanation:
The required simplified expression is given as tan²(2x). Option c is correct.
[CSC(4x) - cot(4x) ] / [CSC(4x) + cot(4x) to be simplified.
What is simplification?The process in mathematics to operate and interpret the function to make the function simple or more understandable called simplifying and the process is called simplification.
[tex]= [csc(4x) - cot(4x)] / [csc(4x) + cot(4x)] \\= [1/sin4x - cos4x/sin4x] / [1/sin4x + cos4x/sin4x]\\= [(1-cos4x)/sin4x] / [(1+cos4x) /sin4x] - - - - (1)[/tex]
Here,
[tex]1 - cos4x = 2sin^24x[/tex]
[tex]sin4x = 2sin2xcos2x,\\ 1+cos4x = 2cos^22x[/tex]
now put the value in equation 1
[tex]= [(2sin^22x)/2sin2xcos2x] / [(2cos^22x) /2sin2xcos2x] \\= [(sin2x)/cos2x] / [(cos2x) /sin2x] \\=tan2x/cot2x\\=tan^22x[/tex]
Thus, the required simplified expression is given as tan²(2x). Option c is correct.
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Which linear inequality is represented by the graph?
y<3x+2
y>3x+2
y<1/3x+2
y>1/3x+2
Answer:
Y < 3x+2
Step-by-step explanation:
Alright so if you ever get stuck on something like this, Go on demos and put in (0,2) and then add in (-3,-7) and then add in the other answers to see if they match.
So your answer is:
y>3x+2
In RST, RS = 8 and ST = 10. Which one of the following cannot be true?
RT cannot equal 18 because then A + B would be equal to C which and then the sides cannot touch.
-4x4+1.5-2.5-2x4-6.5
Answer:
0.5
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I have this math problem and it is: an equation in function from that reflects f(x)=3x over the line y=0.
Answer:
[tex]g(x) = -3x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 3x[/tex]
Required
Reflect over [tex]y = 0[/tex]
This means that we reflect over the x-axis
And the rule of reflection is:
[tex](x,y) \to (x,-y)[/tex]
Hence:
[tex]f(x) = 3x[/tex]
Will become:
[tex]g(x) = -f(x)[/tex]
So, we have:
[tex]g(x) = -3x[/tex]
PLEASE HELP ASAP ITS URGENT
Step-by-step explanation:
the answer is in the image above
if -4/3y is = -3/4 then y =
Answer:
y = 9/16
Step-by-step explanation:
-4/2y = -3/4
y = -3/4 x -3/4
= 9/16
How many possible outcomes are in spinning a spinner divided into red, yellow, orange, purple, blue, and pink?
SOMEONE ANSWER PLS
Answer:
Possible outcomes = 6
Step-by-step explanation:
Since the spinner is divided into red, yellow, orange, purple, blue and pink
Total of 6 colors.
The image of ADEF is ADE'F'. Under which transformation will the triangles not be congruent?
O a reflection through the origin
O a reflection over the line y = x
O a dilation with a scale factor of 1 centered at (2,3)
a dilation with a scale factor of centered at the origin
Answer:
there is no image go see here
PLEASE HELP! SEE PHOTO FOR QUESTION
Answer:
A
Step-by-step explanation:
Intercepts are basically points where if one of the coordinates is a number above 0, the other one HAS TO BE 0
Since there are three points where there are x-intercepts (since the y is 0), there will be three x-intercepts.
Since there is only one point where there are y-intercepts (since the x is 0), there will be only one y-intercept.
The intercepts don't give an exact answer so you would have to estimate where they are on the graph. For example, the y-intercept is between 20-30 and is leaning more towards 30, so you would think it's around 27-29 (And if you look at option A, you can see that it's (0,28))
You got the answer wrong because for one of the x-intercepts, you said that it was negative when it was actually positive. (I believe it was the (2.3,0) one.)
SU is a midsegment of △QRT. If QR=v–66 and SU=v–76, what is the value of v?
Answer:
v=56
Step-by-step explanation:
su is half qr, 2(v-66)=v-76, simplifies to v=56
Can someone help me with this question pls :)
What is the value of x in degrees? (picture above)
the length are all same so i guess it must be 48°
Which of the following figures have an area greater than 40 square centimeters?
Select ALL that apply.
A. A triangle that has a base of 8 cm and height of 9 cm
B. A square that has a side length of 7 cm
C. A rectangle that has a base of 14 cm and height of 3 cm
D. A parallelogram that has a base of 5 cm and a height of 6 cm
B AND C
Step-by-step explanation:
B
AREA OF SQUARE =L²
= 7²
= 49cm²
C..
area of a rectangle Base × height
= 14 × 3
= 42cm²
Square root of negative 8
Answer:
the square root of negative 8 is 64
Answer:
Square root of -8 will be 2.28i
Step-by-step explanation:
Given :
[tex]\sqrt{-8} \\[/tex]
=2.82i
1. You win a prize and are offered two choices. Which of the choices could be represented by a linear equation?
Choice A: $100 on January 1, $200 on February 1, $400 on March 1, $800 on April 1, and so on, with the amount doubling each month,
Choice B: $50 the first month, $100 the second month, $150 the third month, and so on, with $50 added each month,
ONeither is linear
O Choice A
O Choice B
Not enough information is given
Answer:
Coice a
Step-by-step explanation:
O Choice A could be represented by a linear equation,
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Choice A: $100 on January 1, $200 on February 1, $400 on March 1, $800 on April 1, and so on, with the amount doubling each month,
Choice B: $50 the first month, $100 the second month, $150 the third month, and so on, with $50 added each month,
we have to find, Which of the choices could be represented by a linear equation,
we know that,
O Choice A could be represented by a linear equation,
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Zack has 2 feet of basla wood. He needs twice that amounts to finish his project. The cost is $0.05 per inch how much will the balsa wood cost
Answer:
$2.40
Step-by-step explanation:
Zack needs a total of 4 feet of balsa wood which costs $0.05 per inch.
Note that 4 feet = 48 inches.
The overall cost will be ($0.05/in)(48 in) = $2.40
Given that sin(Θ)=1/2 and Θ is in quadrant II, which of the following would be the value of cos(Θ)?
a. 1/2
b. -1/√3
c. √3/2
d. -√3/2
e. 2
i think it should be e but not shure
Raul is flying a kite at the end of a string that is 200 feet long. Raul is holding the string 5 feet off the ground at the angle to the horizontal of 25. How high is the kite off the ground?
Answer:
Kite is 89.52 ft off the ground
Step-by-step explanation:
We are told that the string is 200 ft long.
That the string is 5 ft off the ground at an angle of 25° to the horizontal.
I have drawn a triangle to depict this illustration with x being the height of the kite from the end of the string.
Also, I have depicted the ground level which is 5 ft below the end of the string.
From the triangle, we can calculate the height of the kite above the end of the string using pythagoras theorem.
x/200 = sin 25
x = 200 sin 25
x = 200 × 0.4226
x = 84.52 ft
Now, the bottom of the kite is 5 ft off the ground as depicted in the attachment.
Thus, height of kite above the ground = 84.52 + 5 = 89.52 ft
Write the equation of a circle that has a radius of 1/2 and a center at (1, -1),
O (x - 1)^2 + (y - 1)^2 - 1/2
O (x - 1)^2 + (y +1)^2 - 1/4
O (x+1)^2 - (y + 1)^2 - 1/4
O (x + 1)^2 + (y - 1)^2 = 1/2
Answer:
[tex](x-1)^2+(y+1)^2=\frac{1}{4}[/tex]
Step-by-step explanation:
The equation of a circle with center [tex](h,k)[/tex] and radius [tex]r[/tex] is given by [tex](x-h)^2+(y-k)^2=r^2[/tex].
What we're given:
[tex]r[/tex] of 1/2Center at (1, -1)Substituting given values, we get:
[tex](x-1)^2+(y-(-1))^2=\frac{1}{2}^2,\\\boxed{(x-1)^2+(y+1)^2=1/4}[/tex]
HELP ME NOW OOR NO DINO COOKIES snsndndnd
Answer:
it is because the volume of the box is 200in^2
30 dollars
Step-by-step explanation:
which method should be used for x? 2.5x=5.7
Answer:
2.28
Step-by-step explanation:
2.5x = 5.7
Divide both sides by 2.5 to isolate the x variable.
x = 2.28
i’m not sure what the last one is .. can u help pls
Answer:
136
Step-by-step explanation:
180 - <BAC
10. Which is the best approximation for Pi? A 14/7 B 44/14 C 14/3 D 3/14
Answer:
I think its D 3/14
Step-by-step explanation:
Pi is 3.141592654
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