Answer:
[tex]-6.5x+11[/tex]
Step-by-step explanation:
Expand The Brackets:
[tex]x-1+12-7.5x[/tex]
[tex]=x+(-1)+12+(-7.5x)[/tex]
Combine Like Terms:
[tex]=x+(-1)+12+(-7.5x)[/tex]
[tex]=(x+-7.5x)+(-1+12)[/tex]
Answer:
[tex]-6.5x+11[/tex]
I Hope This Helps
4. Three weeks later, you find a scooter on sale for $399.99, which reflects a discount rate of 30%.
What percentage of the original price is $399.99? Show the proportion to solve the equation.
What was the original price? (Hint, you will need to perform subtraction, similar to the
example).
Answer:
70%
$571.41
Step-by-step explanation:
100% means 1, or a whole thing.
Since the discount is 30% of the original price, and the original price is 100% of the original price, then
100% - 30% = 70%
With a 30% discount, you actually pay 70% of the original price.
$399.99 is 70% of the original price.
399.99 / 70% = x / 100%
70x = 100 × 399.99
x = 571.41
The original price was $571.41.
find the slope of the line on the graph write your answer as a whole number or a fraction not a mixed number or decimal
Answer: 3/4
Step-by-step explanation:
Expand and simplify: (6a+2)(6a-5)-(7a-1)(a-2)
Answer:
29a² - 3a - 12
Step-by-step explanation:
Given expression:
(6a+2)(6a-5)-(7a-1)(a-2)
Solution:
Apply distributive property.
[tex] \rm=(6a)(6a)+(6a)(-5)+(2)(6a)+(2)(-5)-7a^2+15a-2[/tex]
[tex] \rm= 36a {}^{2} - 30a + 12a - 10 - 7a {}^{2} + 15a - 2[/tex]
Combine like terms:
[tex] \rm=(36a {}^{2} - 7a {}^{2} )+( - 30a+12a+15a)+( - 10 - 2)[/tex]
[tex] = \boxed{ \rm \: 29a {}^{2} - 3a - 12}[/tex]
Done!
F(x)=x^2.what is g(x) ?
Answer:
Option C. [tex]g(x)=(\frac{1}{3}x)^2[/tex]
Step-by-step explanation:
Stretch transformations of functionsIn which direction is the transformation happening?Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.
Transformations on the outside
Ex. [tex]g(x)=(x^2)-3[/tex] is subtracting 3 outside, so its transformation is vertical.
Transformations on the inside
Ex. [tex]g(x)=(x-7)^2[/tex] is subtracting 7 inside, so its transformation is horizontal.
Stretch/compression transformationsFor any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.
Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.
For example, [tex]\$10*2 = \$20[/tex], but [tex]\$10*\frac{1}{2} = \$5[/tex]
For transformations, this intuition needs a small modification:
Operations outside: transformations happen "normally" as you would expect.Operations inside: transformations happen "backwards" from the natural way one might expect.Multiplying on the outside
When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.
Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).
Multiplying outside by [tex]\frac{1}{2}[/tex] , things get smaller (compress) vertically down to [tex]\frac{1}{2}[/tex] as much as (50% of) normal (toward a height of zero).
"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).
Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.
Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".
Putting 3 into the "f" function, f(3)=9. Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.
Multiplying on the inside
When multiplying inside, transformations happen horizontally, and inside things happen "backwards".
So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).
If multiplying by a number less than one (but positive), like [tex]\frac{1}{3}[/tex] , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of [tex]\frac{1}{3}[/tex]) as much as normal.
Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.
How far has the function been stretched out horizontally?Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).
Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away. Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.
Answer C multiplies inside by [tex]\frac{1}{3}[/tex], so it actually makes things 3 times bigger horizontally.
The correct answer is option C.
Verifying algebraicallyTo verify, from (3,1), put 3 into the option C g(x) -- it gives "1" as an output.
[tex]g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\[/tex]
An alternative solutionThis function could have been compressed vertically to obtain the red graph.
Note that f(3)=9.
The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function. We could compress the "f" vertically by 1/9th to transform the blue function into the red function.
Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.
Thus, an alternative answer to transform f(x) to g(x) is [tex]g(x)=\frac{1}{9}(x^2)[/tex]
Two last things:
Simplifying this function we just obtained we get [tex]g(x)=\frac{1}{9}x^2[/tex]
Returning to the function that we chose for our answer in option C, [tex]g(x)=(\frac{1}{3}x)^2[/tex]
[tex]g(x)=(\frac{1}{3}x)(\frac{1}{3}x)[/tex]
[tex]g(x)=\frac{1}{9}x^2[/tex]
Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.
3x² - 2x + 1 = [?]
x=4
Answer:
3(4)² - 2(4) + 1 = 48 - 8 +1 = 41
x = 4
[tex] {3x}^{2} - 2x + 1 \\ \\ 3 \times {4}^{2} - 2 \times 4 + 1 \\ \\ 3 \times 16 -8 + 1 \\ \\ 48 - 8 + 1 \\ \\ 41.[/tex]
help fast please
i have no idea what to do in math so i need help
Answer:
see the attachment photo!
Use the rational zeroes theorem to state all the possible zeroes of the following polynomial:
f (x) = 3x^(6) + 4x^(3) - 2x^(2) + 4
Answer:
All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are ±1 , ±2 , ±4 , ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex] , ±[tex]\frac{4}{3}[/tex] by using rational zeroes theorem.
Step-by-step explanation:
Rational zeroes theorem gives the possible roots of polynomial f(x) by taking ratio of p and q where p is a factor of constant term and q is a factor of the leading coefficient.
The polynomial f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex]
Find all factors (p) of the constant term.
Here we are looking for the factors of 4, which are:
±1 , ±2 and ±4
Now find all factors (q) of the coefficient of the leading term
we are looking for the factors of 3, which are:
±1 and ±3
List all possible combinations of ± [tex]\frac{p}{q}[/tex] as the possible zeros of the polynomial.
Thus, we have ±1 , ±2 , ±4 , ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex] , ±[tex]\frac{4}{3}[/tex] as the possible zeros of the polynomial
Simplify the list to remove and repeated elements.
All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are ±1 , ±2 , ±4 , ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex] , ±[tex]\frac{4}{3}[/tex]
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by what percent will the fraction change if its numerator decreased by 20 and its denominator is decreased by 60
I consider the original fraction: x/y.
If the numerator "x" increases by 20%, it can be interpreted in this way:
"x" represents 100% (the unit) and when increasing by 20% we have that the value of "x" becomes 120%
120% of "x" is [tex]\bf{\frac{120*x}{100}=1,2x }[/tex]
This is what we have left in the numerator.
By the same reasoning, in the denominator "y" remains:
100% - 40% = 60% of "and"
60% of "y" is...[tex]\bf{\frac{60*y}{100}=0.6 y }[/tex]
The new fraction is: 1,2x / 1,6y.
...simplifying by dividing top and bottom by 0.6,... 2x / y
To find out the percentage by which the original fraction has changed, we first find the relationship or ratio between the original fraction and the new fraction with the fraction quotient:
[tex]\bf{\dfrac{\frac{2x}{y} }{\frac{x}{y} }=\frac{2xy}{xy}=2 }[/tex]
... that is to say that the new fraction has doubled in relation to the original.
Therefore, the percentage of variation per increase is 100%.
Pisces04What is the product? Assume x≥0.
(√3x + √5)√15x+2√30)
A. 3x√√5 +3√165x+10√√6
B. 3x√5+6√10x +5√3x +10√6
C. 3x√√5+10√6
D. 6√3x+10√6
The product of (√3x + √5)(√15x+2√30) assuming x ≥ 0 is 3√5x² + 6√10x + 5√3x + 10√6
What is the product of the expression?It follows from the task content that the expression given whose product is to be evaluated is;
(√3x + √5)(√15x+2√30)
Hence, by multiplying the terms with each other accordingly; we have;
= (√45x² + 2√90x + √75x + 2√150)
= 3√5x² + 2√90x + √75x + 2√150
= 3√5x² + 2×3√10x + √75x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 10√6
= 3√5x² + 6√10x + 5√3x + 10√6
Ultimately, the product of the expression is; 3√5x² + 6√10x + 5√3x + 10√6
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A company pays $20 per hour for up to 7 hours of work, and $30 per hour for
overtime hours (hours beyond 7). If x is the total hours worked, and more
than 7 hours have been worked, what is the expression for just the overtime
hours worked?
Answer:
Step-by-step explanation:
current total of hours work earnings (7hrs): $140
total earnings: $980 per week
49 hours work per week (no overtime)
immagine you're working another 4 hours for overtime payment everyday:
current total of hours work earnings (11hrs): $280 including 4 hours overtime ($120)
total working hours: 77 hours per week
total earnings: $1,960 per week
A linear function on a coordinate plane passes through (minus 2, 3), (minus 1, 0), (0, minus 3), and (1, minus 6)
Which equation describes the line graphed above?
A.
B.
C.
D.
The equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The options are missing.
The options are:
A) y = 3x - 3
B) y = -3x + 3
C) y = 3x + 3
D) y = -3x - 3
From the points [tex]\left(-2,3\right)[/tex] and [tex]\left(-1,0\right)[/tex]:
[tex]\rm y\ =\ \dfrac{3}{-1+2}\left(x+1\right)[/tex]
y = 3(x + 1)
y = 3x + 3
Thus, the equation of line is y = 3x + 3 that passes throgh the provided points option (C) y = 3x + 3 is correct.
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What is the value of x?
The value of x in the segment is 3
How to determine the value of x?Using the secant and segment theorem, we have:
x * (x + 21) = (x + 1) * (x + 1 + 14)
Evaluate the sum
x * (x + 21) = (x + 1) * (x + 15)
Expand
x^2 + 21x = x^2 + 15x + x + 15
Subtract x^2 from both sides
21x = 15x + x + 15
Evaluate the like terms
5x = 15
Divide both sides by 5
x = 3
Hence, the value of x is 3
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Which best describes the range of the function #(x) = 2(3)x? O y>0 O y≥0 O y = 2 O y≥2
Answer:
The range of the function f(x) : is y > 0.
The correct option is (A)
Step-by-step explanation:
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
Please help!
38 [tex]\frac{22}{75}[/tex] + 3 [tex]\frac{11}{15}[/tex] = ?
The value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]
How to add the fractions?The summation expression is given as:
[tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex]
Rewrite as:
[tex]38 + 3 + \frac{22}{75} + \frac{11}{15}[/tex]
Evaluate the sum and take LCM
[tex]41 + \frac{22 + 5 * 11}{75}[/tex]
Evaluate the sum
[tex]41 + \frac{77}{75}[/tex]
Express as mixed number
[tex]41 + 1\frac{2}{75}[/tex]
Add
[tex]42\frac{2}{75}[/tex]
Hence, the value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]
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What is the value of log5^125?
Step-by-step explanation:
I'm going to assume you mean
[tex]log(5^{125})[/tex] which can be rewritten as [tex]125 log(5)[/tex] since if you start with [tex]log(a) = x = > 10^x=a\\(10^x)^c=a^c\\c *log(a^c)[/tex]since when you do (10^x)^c you're just multiplying the exponent which is represented by the x but is equal to the log you just multiply the log which is why you can bring it in front.
You can then approximate the value of log(5) using a calculator and multiply by 125 to get around 87.371
Mario was riding a bicycle with wheels 26 inches in diameter. During one minute of Mario’s ride, the wheels made exactly 200 revolutions. At what average speed, in feet per second, was Mario riding during that minute?
The correct answer is A.
Step - by - step answer:
Mario will travel a distance equal to 1 circumference of the wheel for each complete revolution of the wheel.
Circumference of Mario's wheel, C = πD, where D is the diameter of the circle.
Hence, C = 26π inches
Speed = Distance / Time
Distance for 200 revolutions in ft = 26π x 200 x 1/12
Time in sec = 60
So, speed = (26π x 200)/(12 x 60)
= 65π/9
=22.69 is the average speed.
P.s: Answer is copied from https://www.myactguide.com/math/mario-was-riding-a-bicycle-with-wheels-26-inches-in-diameter
Where r is the radius of the cylinder and h is the height of the cylinder. Find the surface area when r is 3 inches and h
is 5 inches.
A. 48 in²
B. 80% in²
c. 112 in²
D. 50% in²
Answer:
48π
Step-by-step explanation:
→ State the formula for the surface area of a a cylinder
2π × r × h + 2π × r²
→ Substitute in the numbers
2π × 3 × 5 + 2π × 3²
→ Simplify
48π
Solve the problem.
The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is
198 feet, what are the room's dimensions?
Answer:
width is 30, and the length 69.
Step-by-step explanation:
In order to do this, we need to do ALGOOBRAA
lets say x is equal to the width of the room
then, that means the length is (9+2x) Sooooo,
198=2x+2(9+2x)
Using the distributive property, we know that
2(9+2x)=18+4x
If you dont know what that is, then go search it up :/
so,
198=2x+18+4x
198=6x+18
180=6x
30=x
BAM
Now, we know that the width is 30, bro.
That means the length is 60+9, Which is 69.
Therefore, the width is 30, and the length 69.
Sry if im wrong btw.
The width of rectangle is 30, and the length is 69.
What is Rectangle?
A rectangle is a quadrilateral. The opposite sides of a rectangle are equal and parallel to each other. The interior angle of a rectangle at each vertex is 90°. The sum of all interior angles is 360°. The diagonals bisect each other.
Here, lets say x is equal to the width of the room
then, that means the length is (9+2x) So,
198 = 2x+2(9+2x)
Using the distributive property, we know that
2(9+2x)=18+4x
If you don't know what that is, then go search it up :/
so,
198 = 2x+18+4x
198=6x+18
180=6x
30=x
Now, we know that the width is 30,
That means the length is 60+9, Which is 69.
Thus, the width of rectangle is 30, and the length is 69.
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Out of 220 racers who started the marathon, 203 completed the race, 12 gave up, and 5 were disqualified. What percentage did not complete the marathon?
A surgery has a success rate of 75%. Suppose that the surgery is performed on 4 patients. What is the probability that the surgery is successful on exactly 3 patients?
0.21094 is the probability that the surgery is successful on exactly 3 patients.
What is probability?
It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
According to the given question,
Let Y = The number of patients who respond yes: [tex]Y - Bin (n,p)[/tex]
Given , [tex]n = 4 , p = 0.75 , q = 1 - p = 0.25[/tex]
[tex]P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094\\\\[/tex]
The probability that the surgery is successful on exactly 3 patients is 0.21094
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how is -x^6+7x^5 considered a sixth degree binomial?
Answer:
Polynomial, 6. Constant. The highest value of the exponent in the expression is known as the Degree of Polynomial. The degree of a polynomial is the largest exponent. It is also known as an order of the polynomial. While finding the degree of the polynomial, the polynomial powers of the variables should be either in ascending or descending order.
Step-by-step explanation:
A term is defined as a part of an equation separated by a +/- operation. Because there is a + operation separating two terms (-x^6 and 7x^5), the expression is a binomial, meaning the expression has two terms.
The highest exponent or degree, present in the expression is to the power of 6. Therefore, the expression is in the sixth degree.
Taken together, the expression is a sixth-degree binomial.
Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±10)
Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
Given, that a hyperbola centred at the origin has vertices at (0, ±9) and foci at (0, ±10).
What is hyperbola?In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The formula for a hyperbola centred at the origin is [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]
Where (h, k) is the center = (0, 0)
Distance from centre to vertices a = 9 ⇒ a² = 81
Distance from centre to vertices which is given from the foci c = 10
⇒ c² = 100
Using the Pythagorean formula, c²= a²+ b²
Substituting the values 100 = 81 + b²
So we get, b²= 100 - 81 = 19
Substituting the values in the standard form [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
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At the end of 2 years, P dollars invested at an interest rate r compounded annually increases to an amount, A dollars, given by the following formula. Upper A equals Upper P (1 plus r )squared Find the interest rate if $32 increased to $50 in 2 years. Write your answer as a percent.
The interest rate will be equal to 24% in 2 years.
What is compound interest?Compound interest is the interest levied on the interest. The formula for the calculation of compound interest is given as:-
Given that:-
Find the interest rate if $32 increased to $50 in 2 years.The interest rate will be calculated by using the following formula:-
[tex]A = P[1+\dfrac{r}{n}]^{nt}[/tex]
[tex]50=32[1+\dfrac{r}{1}]^{2}[/tex]
[tex]\dfrac{50}{32}=(1+r)^2[/tex]
1.56 = ( 1 + r )²
√1.56 = ( 1 + r )
r = 1.24 - 1
r = 0.24
r = 24%
Therefore interest rate will be equal to 24% in 2 years.
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Which expression can be used to convert 80 US to Australian dollars?
Answer:
0.9668 USD
Step-by-step explanation:
1 USD=1.0343 AUD 1AUD=0.9668 USD.
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2x+4+5x+25=4x-32+2x-4
7x+29=6x-36
7x-6X=-36-29
X=-65
Answer:
x = -65
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Distribute:
2(x + 2): 2x + 4
5(x + 5): 5x + 25
=
4(x - 8): 4x - 32
2(x - 2): 2x - 4
Combine like terms:
(2x + 4) + (5x + 25) = (4x - 32) + (2x - 4)
5x + 2x: 7x = 4x + 2x: 6x
4 + 25 = 29 = -32 - 4: -36
7x + 29 = 6x - 36
Now we want to separate like terms,
subtract 29 from both sides
subtract 6x from both sides
7x + 29 - 29 - 6x = 6x - 29 - 6x- 36
7x - 6x = - 29 - 36
x = -65
Which of the following is the graph of y = log3 x - 1
The options are not mentioned , but the correct graph is plotted and attached with the answer.
What is a function ?A function is a mathematical statement that relates a dependent variable with an independent variable .
It is given to find among the options which is the correct graph for
y = log₃ (x-1)
The options are not mentioned , but the correct graph is plotted and attached with the answer.
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what is the fourth term in the binomial expansion (a+b)^6)
Answer:
[tex]20a^3b^3[/tex]
Step-by-step explanation:
Binomial Series
[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Therefore, the fourth term in the binomial expansion (a + b)⁶ is:
[tex]\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3[/tex]
[tex]\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3[/tex]
[tex]\implies \dfrac{6!}{3!3!}a^{3}b^3[/tex]
[tex]\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3[/tex]
[tex]\implies \left(\dfrac{120}{6}\right)a^{3}b^3[/tex]
[tex]\implies 20a^3b^3[/tex]
Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?
D: [–1, 5]; R: [–7, 5]
D: [–5, 7]; R: [–5, 1]
D: [–5, 1]; R: [–5, 7]
D: [–7, 5]; R: [–1, 5]
The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have an ellipse equation:
[tex]\rm x^{2}+4y^{2}-2x+16y-19=0[/tex]
We can write the above equation as:
[tex]\rm \dfrac{\left(x-1\right)^{2}}{36}+\dfrac{\left(y+2\right)^{2}}{9}=1[/tex]
The domain will be:
D: [–5, 7]
The range will be:
R: [–5, 1]
Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]
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Find the monthly house payment necessary to amortize the following loan. In order to purchase a home, a family borrows $110,000 at 2.9% for 30 yrs. What is their monthly payment? Round the answer to the nearest cent.
The monthly payment for purchasing the home will be $457.85.
What is a monthly payment?The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.
Then the formula of monthly payment (MP) will be
[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]
In order to purchase a home, a family borrows $110,000 at 2.9% for 30 years.
We have
P = $110,000
r = 0.029 / 12 = 0.0024
n = 30 × 12 = 360
Then the monthly payment will be
[tex]\rm MP = 110,000\times \dfrac{0.0024(1+0.0024)^{360}}{(1+0.0024)^{360} - 1}\\\\[/tex]
On further solving, we have
MP = 110000 × 0.0024 × 1.723
MP = $ 457.85
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You deposit $400 in an account earning 2% interest compounded annually. How much will you have in the account in 20 years?
Answer:
Approximately $594.38
Step-by-step explanation:
Use the formula: y = a(1 + r)^t
a is the initial amount
r is the percent of interest in decimal form
t is the time in years
y is the money after t years
Substitute the values given in the problem into the equation:
400(1+0.02)^20
Use a calculator or solve manually
Around 594.38
