the straight line l has equation x-y =3
the curve c has equation 3x^2 -y^2+xy=9
l and c intersect at the points p and q
find the coordinates of the midpoint of pq
Answers
Answer: The Midpoint of P and Q are (-0.5, -3.5)
Step-by-step explanation: To find the coordinates of the intersection points of the line and the curve, we can substitute the equation of the line into the equation of the curve and solve for x and y.
From the equation of the line: x - y = 3, we can see that y = x - 3
Substituting this into the equation of the curve:
3x^2 - (x-3)^2 + x(x-3) = 9
Now we can simplify and group
3x^2 - x^2 + 6x - 9 + x^2 - 3x = 9
3x^2 + 3x - 9 = 9
3x^2 + 3x = 18
3x(x+1) = 18
x(x+1) = 6
We can see that x = 2 and x = -3 are the solutions.
Substituting the x value back into the original equation of the line to find the y coordinate:
x = 2 => y = 2 - 3 => y = -1
x = -3 => y = -3 - 3 => y = -6
So the intersection points are (2,-1) and (-3,-6)
To find the midpoint of these two points, we take the average of their x and y coordinates:
x = (2 + -3) / 2 = -0.5
y = (-1 + -6) / 2 = -3.5
so the midpoint of the two intersection points is (-0.5, -3.5)
Answer:
Point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].
Step-by-step explanation:
Given the equations [tex]x-y=3[/tex] and [tex]3x^{2} -y^{2} +xy=9[/tex] . Find where they intersect and find the midpoint, [tex](p,q)[/tex], of the two intersection points. To find find points of intersection, you can either set up these equations as a system and solve algebraically or you can use a graphing calculator to graph the functions and see where they cross.
I will set up these equations as a system of equations,
[tex]\left \{ {{x-y=3} \atop {3x^{2} -y^{2} +xy=9}} \right.[/tex]
I will solve the top equation for [tex]x[/tex], and substitute it into the bottom.
[tex]x-y=3 = > x=3+y[/tex]
Now substitute [tex]x=3+y[/tex] for x into the bottom equation. Solve for y,
=> [tex]3x^{2} -y^{2} +xy=9[/tex]
=>[tex]3(3+y)^{2} -y^{2} +(3+y)y=9[/tex]
=> [tex]3(y^{2}+6y+9) -y^{2} +y^{2}+3y =9[/tex]
=>[tex]3y^{2}+18y+27 -y^{2} +y^{2}+3y =9[/tex]
=> [tex]3y^{2}+18y+27+3y =9[/tex]
=> [tex]3y^{2}+21y+27 =9[/tex]
=>[tex]\frac{3y^{2}+21y+27 =9}{3}[/tex]
=>[tex]y^{2}+7y+9 =3[/tex]
=>[tex]y^{2}+7y+6 =0[/tex]
=> [tex](y+1)(y+6)=0[/tex]
=>[tex]y=-1[/tex] or [tex]y=-6[/tex]
Now plug these values for [tex]y[/tex] into [tex]x=3+y[/tex].
When y=-1:
[tex]x=3+(-1)[/tex]
=> [tex]x=2[/tex]
When y=-6:
[tex]x=3+(-6)[/tex]
=> [tex]x=-3[/tex]
The solution to the system (points of intersection) is [tex](-3,-6)[/tex] and [tex](2,-1)[/tex]. I also attached a graph of the intersection points.
Now to find the midpoint of the two intersection points, [tex]midpoint=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
[tex](x_{1},y_{1}) = > (-3,-6)[/tex]
[tex](x_{2},y_{2}) = > (2,-1)[/tex]
=>[tex]midpoint=(\frac{-3+2}{2} ,\frac{-6+(-1)}{2} )[/tex]
=>[tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex]
Thus, the point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].
Related Questions
What is the value of Y enter your answer in the box
Answers
Answer: y = 40
Step-by-step explanation:
we know 5x=40 so the 2 bottom angles combined are 80
so you have 2y+20=100
2y=80
y=40
which value of w makes the equation true
2w+4=28
Answers
Answer:
12
Step-by-step explanation:
2w + 4 = 28
2w = 24
w = 12
w = 12.
Step-by-step explanation:1. Write the expression.[tex]2w+4=28[/tex]
2. Subtract 4 from both sides of the equation.[tex]2w+4-4=28-4\\ \\2w=24[/tex]
3. Divide by 2 in both sides of the equation.[tex]\frac{2w}{2} =\frac{24}{2} \\ \\w=12[/tex]
4. Verify your answer.To verify the answer, write the original expresion and substitute variable "w" by the calculated value (12). If the calculations equal the same number of both sides of the equal sign (=) then the answer is correct.
[tex]2(12)+4=28\\ \\24+4=28\\ \\28=28[/tex]
The same number appears on both sides of the equal sign. Hence, the answer is correct!
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what is the inverse f(x)=3x^3-4
Answers
Answer:
f^-1(x) = [tex]\sqrt[3]{(x + 4)/3}[/tex]
Step-by-step explanation:
y = 3x^3 - 4 ==> solve for x
y + 4 = 3x^3 ==> isolate x by adding 4 on both sides
(y + 4)/3 = x^3 ==> divide 3 into both sides
x = [tex]\sqrt[3]{(y + 4)/3}[/tex] ==> isolate x by taking the cube root on both sides
y = [tex]\sqrt[3]{(x + 4)/3}[/tex] ==> switch both x and y
f^-1(x) = [tex]\sqrt[3]{(x + 4)/3}[/tex]
Which of the following correctly uses exponents to write "6factors of 2
Answers
The mathematical expression which correctly uses exponents to write "6 factors of 2" include the following: B. 2⁶
What is an exponent?In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as bⁿ.
What are factors?In Mathematics, factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors simply refers to numbers which can be multiplied together to get another number.
Next, we would translate the word statement into an algebraic expression as follows;
6 factors of 2 = 2 × 2 × 2 × 2 × 2 × 2
6 factors of 2 = 2⁽¹ ⁺ ¹ ⁺ ¹ ⁺ ¹ ⁺ ¹ ⁺ ¹⁾
6 factors of 2 = 2⁶
In this context, we can reasonably infer and logically deduce that "6 factors of 2" can be correctly written by using an exponent as 2⁶.
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Complete Question:
Which of the following correctly uses exponents to write "6 factors of 2"? A. 6² B.2⁶ C. 6 ∙ 2 D. 12
through (2,4) parrallel to y=3x+
Answers
The slope y is 3x - 10.When the line to be examined's slope is known, and the provided point also serves as the y intercept.
The slope intercept form of a line's equation can be found by using this method?When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.
According to question:-
In the equation of a line's slope-intercept form, y = mx + b, we get y = 3x + 2, m1 = m2 gives us y = 3x +2, and m = 3 gives us the point (2 -4) where x = 2 and y = -4.
4 6 + b deducts 6 from both sides.
-10 = b, b = -10
After all, y = 3x - 10.
The complete question is,
y=3x+2 via (2,-4) parallel to
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what is the value of 5 to the six power
Answers
Answer:
15,625
Step-by-step explanation:
5 to the 6 power = 5 × 5 × 5 × 5 × 5 × 5 = 15,625
Substitution Property of Equality
y=-5 and 7x + y =11
Answers
Answer:
x=2.28
Step-by-step explanation:
7x +y=11 we substitute y by ( -5)
7x +(-5)=11 (+)×(-)= --
7x-5=11
7x=11+5 when we move -5 to the opposite it become +5
7x =16
x=16 ÷7
x=2.28
Find a formula for R n for the function f ( x ) = ( 3 x ) 2 on [ − 1 , 5 ] in terms of n .
Answers
The formula for Rn for the given function is[tex]\int\limits^5_{-1} {9x^2} \, dx =\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)[/tex]. And the area is 378 units².
The approximate area under the graph of a function f(x) throughout the range [a, b] can be calculated using a Riemann sum. Then, the formula to determine the length of each subinterval is given by [tex]\Delta x=\frac{b-a}{n}[/tex].
Substituting the given interval in the above formula, we get,
[tex]\begin{aligned}\Delta x &=\frac{5+1}{n}\\&=\frac{6}{n}\end{aligned}[/tex]
Now, the sample point [tex]x_i[/tex] is given as
[tex]\begin{aligned}x_i&=a+i\Delta x\\&=-1+i\left(\frac{6}{n}\right)\\&=\frac{6i}{n}-1\end{aligned}[/tex]
The formula for Rₙ is calculated as follows,
[tex]\begin{aligned}R_n&=\sum_{i=1}^{n}f(x_i)\Delta x\\&=\sum_{i=1}^{n}9\left(-1+\frac{6i}{n}\right)^2\frac{6}{n}\\&=\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)\end{aligned}[/tex]
Then, the area under the curve is computed as follows,
[tex]\begin{aligned}\int\limits^{5}_{-1} {9x^2} \, dx&= \lim_{n \to \infty} \sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)\\&=\lim_{n \to \infty}\left( \sum_{i=1}^{n}\frac{54}{n}-\sum_{i=1}^{n}\frac{648i}{n^2}+\sum_{i=1}^{n}\frac{1944i^2}{n^3}\right)\\&=\lim_{n \to \infty}\left(\frac{54}{n}\sum_{i=1}^{n}(1)-\frac{648}{n^2}\sum_{i=1}^{n}(i)+\frac{1944}{n^3}\sum_{i=1}^{n}(i^2)\right)\end{aligned}[/tex]
Solving this we get,
[tex]\begin{aligned}\int\limits^5_{-1} {9x^2} \, dx &=\lim_{n \to \infty}\left(\frac{54}{n}(n)-\frac{648}{n^2}\left(\frac{n(n+1)}{2}\right)+\frac{1944}{n^3}\left(\frac{n(n+1)(2n+1)}{6}\right)\right)\\&=\lim_{n \to \infty}\left(54-\frac{324(n+1)}{n}+\frac{324(n+1)(2n+1)}{n^2}\right)\\&=\lim_{n \to \infty}\left(54-324\left(1+\frac{1}{n}\right)+324\left(2+\frac{1}{n}+\frac{2}{n}+\frac{1}{n^2}\right)\right)\end{aligned}[/tex]
As the value of n tends to ∞, then 1/n is zero. Substituting these n values, we get,
[tex]\begin{aligned}\int\limits^5_{-1} {9x^2} \, dx&=54 -324+324(2+0)\\&=\mathrm{378\;units^2} \end{aligned}[/tex]
The required answers are [tex]\int\limits^5_{-1} {9x^2} \, dx =\sum_{i=1}^{n}\frac{54}{n}\left(1-\frac{12i}{n}+\frac{36i^2}{n^2}\right)[/tex] and 378 units².
The complete question is -
Find a formula for Rₙ for the function f (x) = (3x)² on [− 1, 5] in terms of n. Compute the area under the graph as a limit.
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Indicate in standard form the equation of the line given the following information: The line that contains the point Q(1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3) Enter your answer into the blank equation box.
Answers
The equation of the parallel line will be y = (2/3)x - 8/3.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation of the line is given below.
y - 4 = 2/3 (x - 3)
The equation of the line that is parallel to the given line will be written as,
y = (2/3)x + c
The equation of the line that passes through (1, -2), then we have
- 2= (2/3)(1) + c
- 2 = 2 /3 + c
c = - 8 / 3
Then the equation of the parallel line will be y = (2/3)x - 8/3.
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Submarine A is 1200 feet underwater and has descended at a constant rate of 12 feet per minute. Submarine B is 1100 feet underwater but descends at a constant rate of 16 feet per minute. When will the two submarines be at the same depth?
Answers
The time when the two submarines will be at the same depth is 25 minutes.
How to calculate the value?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, Submarine A is 1200 feet underwater and has descended at a constant rate of 12 feet per minute. Submarine B is 1100 feet underwater but descends at a constant rate of 16 feet per minute
The equation will be:
1200 - 12m = 1100 - 16m
Collect the like terms
16m - 12m = 1200 - 1100
4m = 100
Divide
m = 100 / 4
= 25 minutes
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help. i don’t understand this
Answers
Answer:
the answer is 1
Step-by-step explanation:
b(n) = -4 so b(n) is 2-4 then n is -1
b(n) = -2
n = -1
Answer:
Step-by-step explanation:
b(n) = -4 -2(n -1)
Find the 12th term in the sequence.
Put 12 where n is and evaluate.
The 12th term of the sequence is -2052.
simplify
[2/11]^3 ÷ [4/22]^6
Answers
Answer:
(2/11)^3/(4/22)^6
= (2/11)^3/(2/11) ^6
=1/(2/11)^3
=(11/2)^3
Evaluate each geometric series described.
17) -2-4-8-16..., n=9
B) -1022
D) 2
A) -975
C) -947
Answers
The geometric series of the pattern is -512 for n = 9: -2, -4, 8-16,. is a geometric progression and .
What is the geometric series ?In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).
is a geometric progression and r= 2.
is a geometric progression ai —2 and r= 2.
= —512
The place w Formulas are employed.
In this instance, we have and n=9. These values are added to the formula above to get the following results:
an
9—1
-2. (256)
= —512
The initial terms in this series are:
8, -16...
The total number of terms in a geometric sequence makes up a geometric series. Using the initial term and the common ratio r, it is possible to determine the nth partial sum of a geometric series as follows: .
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2 divided by 3xy raised to power 2 when x = negative 1 divided by 3, and y = one half
Answers
The value for expression 2/3xy² when x = -1/3 and y = 1/2 is 8.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is 2/3xy².
The value of x is given as x = -1/3.
The value of y is given as y = 1/2.
To find the value of the expression, substitute the value of x and y in the expression -
= 2/3xy²
Expand using the power rule -
= [2/(3 × (-1/3) × (1/2)²)]
Use the arithmetic operation of multiplication -
= [2/(3 × (-1/3) × (1/4)]
= [-2/(-3/12)]
= -2/(-1/4)
The denominator will reciprocate -
= -2 × -4
= 8
Therefore, the final value is obtained as 8.
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The inequality 2c−3<9 represents the amount of money a student can spend on c candy bars. Select the values that best complete the sentence. The solution to the inequality is , and it represents that the student can buy a maximum of whole candy bars.
Answers
The number of candy bars that the student can buy is given by the inequality c < 6 which means less than 6.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
The inequality represents the amount of money a student can spend on c candy bars.
2c - 3 < 9
2c < 9 + 3
2c < 12
c < 6
This means,
c is less than 6.
Thus,
The number of candy bars that the student can buy is less than 6.
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4. If we want to find the volume of the ice cream shown below, we will need to find the volumes of which 3D solids? (Mark all that apply)
A Sphere/Hemisphere
B Prism
C Cylinder
D Pyramid
E Cone
F Cube
Answers
Answer:
A, E
Step-by-step explanation:
The lower part, the cone, is shaped like a cone.
The upper part, the ice cream, is shaped like a hemisphere.
Answer: A, E
If triangle ABC has the following measurements, find the measure of side c:
a = 17
b=23
C = 76°
O a
Ob
Od
37.56
7.69
31.74
25.08
Answers
If triangle ABC has the following measurements, than the measure of side c is 25.08
What is triangle ?
A triangle in which it contains three sides and three angles and the sum of three angles be 180 degrees.
Given ,
a = 17
b = 23
C = 76 degrees.
So,
we know that,
c = [tex]\sqrt{a^{2}+b^{2}-2abcosc }[/tex]
c = [tex]\sqrt{17^{2} + 23^{2} - 2*17*23*cos76 }[/tex]
c = [tex]\sqrt{289 + 529 - 884*cos76}[/tex]
c = [tex]\sqrt{818-189}[/tex]
c = [tex]\sqrt{629}[/tex]
c = 25.08
hence , If triangle ABC has the following measurements, than the measure of side c is 25.08
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Find the area of the rectangle.
The area of the rectangle is
(3x-4) yards
(Simplify your answer.)
(3x+4) yards
Answers
The area of rectangle with length 3x + 2 and width 3x - 4 is 9x² - 6x - 8.
What is the area of rectangle?Once the length and width of a rectangle are known, the area is calculated. The area of a rectangle can be calculated by multiplying its length and width.
Here given that,
The rectangle's length is (3x + 2) units.
The width of the rectangle is (3x - 4).
We must determine the area of a rectangle.
Now,
Since the area of a rectangle equals length x width .
As a result, the area of a rectangle equals,
A = (3x + 2) (3x - 4)
By simplifying the expression we get,
= (3x)(3x) + (3x)(-4) + 2(3x) + 2(-4)
= 9x² - 12x + 6x - 8
= 9x² - 6x - 8
Therefore the area of rectangle will be 9x² - 6x - 8.
The complete question:
"The length of a rectangle is 3x + 2 and the width is 3x – 4. What is the area of the rectangle in terms of x?"
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15. A savings account earns interest. The account initially had $1,500 deposited in it. The worth of the account
after t-years can be calculated using the formula:
A(t)=1500e^0.3r
Answers
So, on solving the question we can say that the linear equation A(t)=1500e^0.3r = A(t) = 1232
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
A(t)=1500e^0.3r
the linear equation
A(t) = 1232
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4) Match the polynomial with its factored form.
a. (a - b)(a - b)
b. (a + b)(a - b)
c. (a+b) (a²-ab+6²)
d. (a-b) (a² + ab +6²)
e. (a + b)(a + b)
a³ - 6³
a³ + b³
a²-6²
a² + 2ab + b²
a² - 2ab + b²
Answers
Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.
what is polynomial ?The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials are mathematical expressions made up of variables (also known as indeterminates) and coefficients. A mathematical expression known as a polynomial is made up of two or more algebraic terms that are added, subtracted, or multiplied (never divided!). In polynomial expressions, which often also have at least one variable, constants and positive exponents are frequently utilized. The equation x2 4x + 7 denotes a polynomial.
given
a) (a - b)(a - b) = a² - 2ab + b²
b. (a + b)(a - b) = a²-6²
c. (a+b) (a²-ab+6²) = a³ - 6³
d. (a-b) (a² + ab +6²) = a³ - 6³
e. (a + b)(a + b) = a² + 2ab + b²
Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.
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The complete question is :- Match the following polynomial by its factored form .
a. (a - b)(a - b)
b. (a + b)(a - b)
c. (a+b) (a²-ab+6²)
d. (a-b) (a² + ab +6²)
e. (a + b)(a + b)
Write a system of linear inequalities represented by the graph.
Answers
Linear inequality represented by the graph is y > x/3
along with linear equations: y = x/3 and y = (x/3) - 2
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The first line passes through
(0, 0) and (3, 1)
The slope of line is m = 1-0/3-0 = 1/3
y intercept = 0
So the equation of line is y = x/3
As the shading is outside so y > x/3
Now let us find for second line
(-3, -3) and (3, -1)
slope m' = -1 - -3/3 - - 3 = 2/6 = 1/3
Now y intercept
-2 = m(0) + c
c = - 2
So equation is y = x/3 - 2
Hence, linear inequality y > x/3 and linear equations: y = x/3, y = x/3 - 2 represent the graph.
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For f(x), the transformation of the function is stated in the first column. Determine the type of transformation
Answers
The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.
What is functions ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
transformation of functions
f(x) - f(x) -2
translate 2 units down
f(x) - f(x - 2)
translate 2 units right
f(x) - f(x) + 2
translate 2 units up
The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.
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I need to show my work help me out
Answers
The distance of the flag pole from the end of the shadow is 23.32 feet.
How to find the side of a right triangle?A 20 foot flag pole is casting a shadow that is 12 feet long. Therefore, the distance of the top of the flag pole to the tip of the shadow can be calculated as follows:
The situation forms a right angle triangle.
Hence, using Pythagoras's theorem, we can find the distance.
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the legsTherefore,
20² + 12² = c²
400 + 144 = c²
c = √544
c = 23.3238075794
Therefore,
distance of the flag pole to the end of the shadow = 23.32 feet
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If there are 10 decimeters in a meter, explain why there are not 10 cubic decimeters in a cubic meter.
Choose the correct answer below.
OA. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter squared. This means
that there are 10² cubic decimeters in a cubic meter.
OB. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means
that there are 10 cubic decimeters in a cubic meter.
OC. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter squared. This means
1
that there are cubic decimeters in a cubic meter.
10²
OD. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means
that there are
1
cubic decimeters in a cubic meter.
10
Answers
Answer:
B. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means that there are 10³ cubic decimeters in a cubic meter.
Step-by-step explanation:
When we cube a number, we multiply the number by itself twice.
Therefore a cubic meter is:
m × m × m = m³To calculate the number of cubic decimeters in a cubic meter, we need to cube the number of decimeters in a meter.
Given there are 10 decimeters in a meter, then there are 10³ cubic decimeters in a cubic meter:
10 × 10 × 10 = 10³What is the interest earned in a savings account after 12 months on a balance of $5000 if the interest rate is 1% APY compounded yearly?
Answers
The interest earned in savings is given by the equation I = $ 50
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the interest be represented as I
Now , the amount invested A = $ 5000
The number of months = 12 months = 1 year
The rate of interest = 1 %
The interest I = A - P = P ( 1 + r/n )ⁿᵇ - P
So , the compound interest I = 5000 ( 1 + 1/100 )¹ - 5000
On simplifying the equation , we get
The compound interest I = 5000 ( 1 + 0.01 ) - 5000
The compound interest I = 5000 ( 1.01 ) - 5000
The compound interest I = 5050 - 5000
The compound interest I = $ 50
Hence, the interest is $ 50
To learn more about compound interest click :
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The number line represents the solution to which inequality?
Answers
Answer: Choice G [tex]3\text{x} \le 21[/tex]
======================================================
Reason:
The inequality for choice G solves to the following shown below.
[tex]3\text{x} \le 21\\\\3\text{x}/3 \le 21/3\\\\\text{x} \le 7\\\\[/tex]
In the second step, I divided both sides by 3 to undo the multiplication going on when saying "3x".
Once we arrive at [tex]\text{x} \le 7[/tex], the graph will have a closed endpoint at 7 and shading to the left. This is to visually describe all values of x that are 7 or smaller. The endpoint is included as part of the solution set.
This shows why choice G is the answer.
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Something like choice F has the inequality [tex]\text{x}-2 \le 9[/tex] solve to [tex]\text{x} \le 11[/tex] after adding 2 to both sides. The graph of [tex]\text{x} \le 11[/tex] involves a closed endpoint at 11 and shading to the left, which doesn't match the given number line graph. This allows us to rule out choice F.
Choices H and J are ruled out for similar reasoning.
What are the solutions of x² - 5x+7=0?
Answers
Answer:
x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2
Step-by-step explanation:
Solve for x:
x^2 - 5 x + 7 = 0
Subtract 7 from both sides:
x^2 - 5 x = -7
Add 25/4 to both sides:
x^2 - 5 x + 25/4 = -3/4
Write the left hand side as a square:
(x - 5/2)^2 = -3/4
Take the square root of both sides:
x - 5/2 = (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2
Add 5/2 to both sides:
x = 5/2 + (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2
Add 5/2 to both sides:
Answer: x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2
the table and the scatter plot the total earning y(in dollars) of a food server who works x hours
Answers
Answer is B
y=16.9x+0.7
To Calculate line of best fit you can simply input the values into the stats function on your calculator and using the "Reg" function to get your values of the standard equation form of your line of best fit which is y=bx+a
b=16.9
a=0.7
Please guys i need help 80 points for this
Answers
Answer:
mario
Step-by-step explanation:
Consider a segment with endpoints S(-7,-6) and T(2,4). what is the length?
Answers
Answer:
Below
Step-by-step explanation:
Use the distance formula ( a modification of Pythagorean theorem)
d^2 = ( x1-x2)^2 + (y1-y2)^2
d^2 = (-7-2)^2 + (-6-4)^2
d = sqrt (181) =~ 13.454