Answer:
d = [tex]\sqrt{65}[/tex]
Step-by-step explanation:
The distance between two points is found by
d = [tex]\sqrt{( x2-x1)^2 + ( y2-y1)^2}[/tex] where (x1,y1) and (x2,y2) are the two points
d = [tex]\sqrt{(-2 - -1)^2+(-6 - -14)^2 }[/tex]
d =[tex]\sqrt{( -2+1)^2 + (-6+14)^2}\\[/tex]
d = [tex]\sqrt{(-1)^2 +( 8)^2 }[/tex]
d = [tex]\sqrt{1+64}[/tex]
d = [tex]\sqrt{65}[/tex]
find the length of the semi-major axis of the ellipse x^2/49+y^2/36=1
The length of the semi-major axis of the ellipse is 7.
What is the semi-major axis of an ellipse?
The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.
The general equation of an ellipse is :
⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis
x²/49+y²/36=1
x²/(7²)+y²/(6²)=1
x²/a²+y²/b²=1
a=7
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Katrina has the option of an 8-year nonsubsidized student loan of $29,000 at an annual interest rate of 2.5% or an 8-year subsidized loan of $29,000 at an annual interest rate of 4.5%. Determine for which loan Katrina will pay less interest over the term of the loan if she starts making payments 2 years after obtaining the loan. (Assume Katrina makes monthly payments for each loan. Round your answers to the nearest cent, as appropriate.) The total interest paid on the nonsubsidized loan is $
Katrina would pay less amount of interest on the nonsubsidized student loan
The total interest paid on the nonsubsidized loan is $3,860.80
What is monthly compounding?
Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.
In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.
In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:
FV=PV*(1+r/n)^(n*t)
FV=balance after 2 years=unknown
PV=loan amount
r=annual interest rate
n=number of times interest is compounded annually=12
t=number of years before repayments commence=2
Non-subsidized loan:
FV=$29,000*(1+2.5%/12)^(12*2)
FV=$30,485.28
Subsidized loan:
FV=$29,000*(1+4.5%/12)^(12*2)
FV=$31,725.71
Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly payments would occur at the end of each month:
PV=PMT*(1-(1+r)^-N/r
PV=balance of loan after 2 years
PMT=monthly payment=unknown
r=monthly interest rate=annual interest rate/12
N=number of monthly payments in 6 years=12*6=72
Non-subsidized loan:
$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)
PMT=$456.40
total monthly payments=$456.40*72
total monthly payments=$32,860.80
Interest= total monthly payments-loan
interest=$32,860.80-$29,000
interest=$3,860.80
Subsidized loan:
$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)
PMT=$503.61
total monthly payments=$503.61 *72
total monthly payments=$36,259.92
Interest= total monthly payments-loan
interest=$36,259.92 -$29,000
interest=$7,259.92
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1.
Find a polynomial f(x) of degree 3 that has the following zeros.
4, 0, -7
Leave your answer in factored form.
Answer:
x³+3x²-28x
Step-by-step explanation:
(x-4)(x-0)(x+7)
(x-4)(x)(x+7)
(x-4)(x+7)=(x²+3x-28)
(x²+3x-28)(x)=x³+3x²-28x
A rectangle has a width w that is 5units longer than its lenght/. Which equation expresses the rectangle's area, A?
Area equals Length times Width.
since the width of this equation is 5 units Longer then its Length
W = L + 5
To put this area in a equation we could say
L(L+5)=A
Simplify the equation, L^2 + 5L = A.
A TV has a listed price of $540.99 before tax. If the sales tax rate is 9.75% , find the total cost of the TV with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
■ Sales tax: $52.75
■ Cost/Price before ST: $540.99
■ Total Cost/Price including ST: $593.74
Step-by-step explanation:
540.99 x 0.0975
= 52.75
Total
= 540.99+52.75
=593.74
Cross Multiply With Fractional Ratios.
5 (1/2)
=
8 x
cross multiply to find the awnser
Answer:
5/16
Step-by-step explanation:
assuming you mean 5(1/2) = 8x
5(1/2) is the same as 5/2
so, 5/2 = 8x
5 = 16x
x= 5/16
Please help me with this question <3 ASAP!
Answer:
54°
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so;
[tex]9x+9=8x+14 \\ \\ x=5 \\ \\ m\angle S=9(5)+9=54^{\circ}[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Angle S = 54°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
In a Parallelogram, opposite angles are equal, so we infer that :
[tex] \qquad❖ \: \sf \:9x + 9 = 8x + 14 [/tex]
[tex] \qquad❖ \: \sf \:9x - 8x = 14 - 9[/tex]
[tex] \qquad❖ \: \sf \:x = 5 \degree[/tex]
Next,
Measure of Angle S is :
[tex] \qquad❖ \: \sf \:9x + 9[/tex]
[tex] \qquad❖ \: \sf \:9(5) + 9[/tex]
[tex] \qquad❖ \: \sf \:45 + 9[/tex]
[tex] \qquad❖ \: \sf \:54 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Angle S = 54°what base could be written in the blank to make the exponential function model 15% decay ? y= (___) ^t\12
The base of the exponential function model in order to get 15% decay should be 0.85
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
The first step would be figuring out the function's base.
The function's form should be, [tex]y=a*b^{t}[/tex]
Here,
'a' denotes the starting value.
'b' denotes the decrease rate.
't' denotes time.
According to the question, the exponential function model is,
[tex]y=b^{\frac{t}{12} }[/tex]
In order to get a 15% decay,
The base of the function should be (100-15)/100 = 0.85
Thus, Base of function(b) = 0.85
The exponential function model is written as:
[tex]y=0.85^{t/12}[/tex]
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giving brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The given focal points and the lengths of the minor and major axis of 16 and 20 gives the equation of the ellipse as the option;
[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
Which method can be used to obtain the ellipse?The equation of an ellipse is presented as follows;
[tex] \mathbf{ \frac{(x - h)^{2}}{ {a}^{2} } + \frac{(y - k)^{2}}{ {b}^{2} } } = 1 [/tex]
Where;
(x, y) = Coordinates of the center of the ellipse
a = Semi major axis
b = Semi minor axis
Length of minor axis = 16 units
Length of major axis = 20 units
By observation of the coordinates of the focal point, we have;
y-value of the center of the ellipse, k = 2
x-value of the center, h = (-9 + (3 - (-9))/2 = -3
The equation of the ellipse is therefore;
[tex] \frac{(x - ( - 3))^{2}}{ {10}^{2} } + \frac{(y - 2)^{2}}{ {8}^{2} } = 1 [/tex]
[tex] \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
The equation that represents the ellipse is the option;
[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
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P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
¿Cuál es el volumen remanente entre una caja cúbica vacía y una pelota?
En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.
Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:
Cubo
V = l³
V = (4 cm)³
V = 64 cm³
Esfera
V' = (4π / 3) · R³
V' = (4π / 3) · (2 cm)³
V' ≈ 33.5103 cm³
Segundo, determinamos la diferencia de volumen entre los dos elementos:
V'' = V - V'
V'' = 64 cm³ - 33.5103 cm³
V'' = 30.4897 cm³
El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
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There are 2,900 students at our school. If 51% of them are female, how many female students are there at our school?
Answer:
Step-by-step explanation:
1479
6) Evaluate 4x if x = -1/4
Answer: -1
Step-by-step explanation:
Evaluate 4x if x = -1/4
4(-1/4) = -1
Answer: -1
Step-by-step explanation:
4x and x = -1/4
plug x into the expression
[tex]4(-\frac{1}{4} )[/tex]
simplifies to:
[tex]-\frac{4}{4}[/tex]
4 divided by 4 is just 1, but it is negative so your final answer is
-1
Is the answer true or false?
The formula =MID("ABCDEFGHI",3,4) would yield the result
If the formula, =MID("ABCDEFGHI",3,4) is used, the result yielded would be CDEF.
What would =MID("ABCDEFGHI",3,4) yield?When using the =MID function on a spreadsheet, the number after the text in the formula would show the position of the text from the left that the function would begin to count from.
The text in the third position from the left as shown in ABCDEFGHI is C so we need to start counting from letter C.
The second number in the function would then show the number of texts that needs to be counted and selected from the row of letters. That number is 4.
So from the letter C, you'll count 4 letters including the letter C itself.
The result you get would therefore be C, D, E, F which are the four letters from C.
In conclusion, the formula =MID("ABCDEFGHI",3,4) would yield the result, "C, D, E, F,."
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Someone please help me with this!!!
Answer:
279/1640
Step-by-step explanation:
The relations between the various trig functions can be used to find the necessary function values.
Other trig functionsSolving for cos(θ), we have ...
41 cos(θ) = 9
cos(θ) = 9/41 . . . . . divide by 41
The Pythagorean relation tells you ...
sin²(θ) +cos²(θ) = 1 ⇒ sin(θ) = √(1 -cos²(θ))
sin(θ) = √(1 -(9/41)²) = (√(41² -9²))/41 = 40/41
The tangent relation is ...
tan(θ) = sin(θ)/cos(θ) = (40/41)/(9/41) = 40/9
Expression value
The value of the given expression is ...
(sin(θ) -cos(θ))/tan(θ) = (40/41 -9/41)/(40/9) = (31/41)(9/40) = 279/1640
__
Additional comment
This can also be figured by a suitable calculator or spreadsheet. Output formatted as a fraction is often an option. Here, the result is rational.
PLEASE HELP!!
Select all the correct answers.
Consider the graph of the function f (x) = 2³.
y
-5 -4
Fm.
-~
-5
4
3-
2
-1-
-2-
-3-
-4-
-5-
O
N.
2
Which statements describe key features of function gif g (z) = f(x + 2)?
horizontal asymptote of y = 2
3 4 5
Oy-intercept at (0,4)
O y-intercept at (0, 1)
O horizontal asymptote of y = 0
O domain of (-∞0 < x < ∞0}
[tex]f(x) = 2 {}^{x} \\ g(x) = f(x + 2) = 2 {}^{x + 2} \\ g(x) = 2 {}^{x + 2} =2 {}^{x} .2 {}^{2} = 4.2 {}^{x} [/tex]
[tex]a.b {}^{x} = > horizontal \: asymp \: y = 0[/tex]
[tex]4.2 {}^{0} = 4 = > vertical \: int \: (0,4)[/tex]
[tex]a.b {}^{x} = > x ∈ \: ] -∞ , ∞ [[/tex]
Answer: Options:2 4 5The horizontal asymptote of the function f ( x ) = 2ˣ is y = 0 and the y-intercept is ( 0 , 4 )
What are Asymptotes?An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required
There are 3 types of asymptotes
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero
Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b
Given data ,
Let the function be denoted as f ( x )
Now , the value of f ( x ) is
f ( x ) = 2ˣ be equation (1)
The y-intercept of the function is when x = 0
So , when x = 0
f ( 0 ) = 2⁰
f ( 0 ) = 1
So , the y-intercept of the function is at ( 0 , 4 )
And , when the function f ( x ) is tending to zero , the horizontal asymptote is y = 0
Therefore , the horizontal asymptote is y = 0
The domain of the exponential function is { -∞ < x < ∞ }
Hence , the horizontal asymptote of the function f ( x ) = 2ˣ is y = 0
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The spread of a disease can be modeled as N = 250√ where N is
the number of infected people, and t is time (in days).
How long will it take until the number of infected people reaches
2,500?
The spread of the disease will take a time 100 days to reach 2,500 infected people.
How to find the number of infected people at a certain time
In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)
2,500 = 250 · √t
√t = 2,500 / 250
√t = 10
t = 10²
t = 100
The spread of the disease will take a time 100 days to reach 2,500 infected people.
Remark
The statement is poorly formatted and presents typing mistakes, correct form is shown below:
The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?
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Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
What is this expression in simplified form 5/2 times 9/6? A.90 B.90/3 C.45/2 D. 45/3
5√2 · 9√6
Simplify.
5 × 9 √ 2 x 6 ⇒ Multiply 2 × 6.
5 × 9 √12
Simplify √12 to 2√3.
5 × 9 × 2√3 ⇔ Multiply
90√3
Therefore, the correct alternative is option "B".
The simplified form of the given expression is 90√3. Therefore, the correct answer is option B.
The given expression is 5√2·9√6.
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Here, 5×9×√2×√6
= 45√12
= 45√4×3
= 90√3
Therefore, the correct answer is option B.
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Is 3 1/4 a rational or irrational number?
Answer:
It is a rational number.
Step-by-step explanation:
A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.
Hi :)
Below is the difference between rational & irrational numbers
______________RATIONALA number that can be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] form, where [tex]\large\boldsymbol{q\ne0}[/tex]Evidently,
An irrational number is a number that cannot be expressed in [tex]\sf{\dfrac{p}{q}}[/tex] formLet's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]
Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.
Thus
[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
How can you make a 95% confidence interval smaller without changing the confidence level?
Step-by-step explanation:
1. Lower the confidence level.
2. Use a one-sided confidence interval. ...
3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...
4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...
PLEASE MARK ME AS BRAINLIST
Answer:
Increase the sample size.
Usually, the more observations that you have, the narrower the interval around the sample statistic is.
Suppose that you repeated questions 5 and 6 using two line segments of your choice. The line segments could be any length and in any
orientation as long as the midpoints were marked correctly and coincided with each other. Would you reach the same conclusion that you
reached in question 7? How does your conclusion relate to the diagonals of a parallelogram?
A line segment can be defined as the part of a line in a geometric figure such as a parallelogram, that is bounded by two (2) distinct points and it typically has a fixed length.
In Geometry, a line segment can be measured by using the following measuring instruments:
A scale (ruler).A divider.What is a parallelogram?A parallelogram refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
Based on the previous experiment conducted in question 5, 6 and 7, we can logically conclude that the opposite sides of quadrilateral ABCD have the same (equal) slopes, which implies that the opposite sides are parallel. Hence, quadrilateral ABCD is simply a parallelogram by definition.
In this context, yes I would you reach the same conclusion that I reached in question 7 because the line segments that I drew represent the diagonals of a parallelogram.
Therefore, if the point of intersection of the diagonals divide each diagonal in half, then, the quadrilateral belonging to these diagonals forms a parallelogram.
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Any help with this greatly appreciated.
Put the equation in standard linear form.
[tex]x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}[/tex]
Find the integrating factor.
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5[/tex]
Multiply both sides by [tex]\mu[/tex].
[tex](t+5) x'(t) + x(t) = 5(t+5)e^{5t}[/tex]
Now the left side the derivative of a product,
[tex]\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}[/tex]
Integrate both sides.
[tex](t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt[/tex]
On the right side, integrate by parts.
[tex](t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C[/tex]
Solve for [tex]x(t)[/tex].
[tex]\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}[/tex]
I'm trying to figure this out for extra credit but I don't know what to do can someone step by step take me through it with the answer?
Answer:
2800
Step-by-step explanation:
The choice at any node (except the edges) is to go right or go down.
A to BTo get from A to B requires a total of 4 choices to go down, and 4 choices to go right. Those can occur in any order. Locating the "right" choices in the list of "all" choices is effectively choosing 4 of 8. The number of ways those choices can be made is ...
C(8, 4) = 8!/(4!(8-4)!) = 8·7·6·5/(4·3·2) = 70
B to CSimilarly a total of 2 choices must be made, 1 of which is a "right" choice. The number of ways those can be ordered is ...
C(2, 1) = 2 . . . . . . . that is: (right, down) or (down, right)
C to DA total of 6 choices must be made, of which 3 are "right." The number of possible orderings is ...
C(6, 3) = 6·5·4/(3·2·1) = 20
Total pathsEach set of choices is independent of the others, so the total possible number is the product of the numbers of choices on the subpaths:
total paths = (70)(2)(20) = 2800
There are 2800 possible paths from A to D.
Find the measure of XY
Answer:
18
Step-by-step explanation:
For this problem, you have to look at the ratios of the corresponding sides.
Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18
The manger of a company planned to distribute a $50 bouns to each employee from the company fund, but the fund contained $5 less than what was needed. Instead, the manger gave each employee a $45 bouns and kept the remaing $95 in the company fund. How much money was in the company fund before any bonuses were paid?
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Let y represent the total company fund and x represent the number of staffs.
From the first statement:
y - 50x = -5 (1)
Also:
y - 45x = 95 (2)
From equation 1 and 2:
x = 20, y = 995
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
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−5y2−3y−2, when y=2.
y=2
-5(2)²-3(2)-2
-5(4)-3(2)-2
-20-6-2
=12
(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball x) and the number of minutes he
plays volleyball (y) every day. (5 points)
Part B: How much time doos Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball (or 25 minutes
longer than he plays volleyball? Explain your reasoning. (2 points)
A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 729 cubic feet. The concrete for the base cost $8 per square foot, The material for the roof costs $3 Per square foot, and the material for the sides costs $5.50 Per square foot. Find the dimensions of the most economical shed.
The dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height if the storage shed is to be built in the shape of a box with a square base.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A storage shed is to be built in the shape of a box with a square base.
It is to have a volume of 729 cubic feet.
Let x be the length of the base
Let y be the height of the box.
V = 729 cubic feet
The base is square:
l = w = x
V = x²y
y = 729/x²
Cost of the base = $8x²
Cost of the roof = 3x²
Cost of the sides = 4(5.50)xy
= 22xy
Total cost
C= 8x² + 3x² + 22xy
C = 11x² + 22x(729/x²)
C = 11x² + 16038/x
Find the first derivative:
dC/dx = 22x - 16038/x²
Equate; dC/dx = 0
22x - 16038/x² = 0
22x = 16038/x²
22x³ =16038
x³ = 729
x = 9
y = 729/(9)² = 9
Length of base = 9 ft
Width of base = 9 ft
Height of box = 9 ft
Thus, the dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height.
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If my savings of $x grows 10% each year. How much will I have in: 5 years
Answer:
See below
Step-by-step explanation:
Assuming the interest is compounded annually
x * (1 + .10)^5 = 1.61051 x
your final amount will be 1.61051 times bigger than the initial deposit
