The equation of the line with slope -2 and passing through the point (3,-2) is y+2x-4=0.
What is the equation of a line with a given slope and a point?The point-slope formula is used to find the equation of the line passing through a point (a,b) and having a slope of m.
A straight line equation of the form (y-b) = m(x-a), where m is the slope of the line and (a,b) are the coordinates of a given point on the line, is the standard form given for the point-slope form of the line.
A point (3,-2) and a slope -2 are given.
Use the standard Point-slope form of the line to find the equation of the line.
(y-b) = m(x-a)
Put the given values in the Point-slope equation.
y-(-2)=-2(x-3)
Simplify the equation to get the equation of the line.
y+2=-2x+6
y+2x-4=0
So, the equation of the line is y+2x-4=0.
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If f(x) = 2x +1 and g(x) = -x2,
The value of (f·g)(x) from the given function is -2x³ - x².
The given functions are f(x) = 2x +1 and g(x) = -x².
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here,
(f·g)(x) = f(x) × g(x)
= (2x +1) × (-x²)
= 2x × (-x²) + 1 × (-x²)
= -2x³ - x²
Therefore, the value of (f·g)(x) from the given function is -2x³ - x².
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"Your question is incomplete, probably the complete question/missing part is:"
If f(x) = 2x +1 and g(x) = -x², then find (f·g)(x).
6) What is the length of side x?
The given triangle is a right angled triangle. Therefore, by Pythagoras theoram,
[tex]\text{hypo}^2=base^2+altitude^2[/tex]From the figure,
[tex]\begin{gathered} x^2=2^2+5^2 \\ x^2=29 \\ x=\sqrt[]{29} \end{gathered}[/tex]Hence, Option D is the right answer.
Taylor works on an art project that uses rectangular pieces of paper the first rectangle has length 3/8 inches in width 3 in.
Find the indicated value. (Round your answer to eight decimal places.) 26!
The factorial expression 26! has a value of 4.032914600e+26
How to evaluate the expression?The expression is given as
26!
The above expression is a factorial expression
And the factorial of a number n where n >= 0 and n is not a decimal number is calculated using
n! = n x (n - 1) x (n - 2) x ..... x 1
This means that
n = 26
So, we have
26! = 26 x 25 x 24 x 23 x ..... x 1
Evaluate the products
26! = 4.0329146e+26
Approximate
26! = 4.032914600e+26
Hence, the value of the expression is 4.032914600e+26
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systems of equations
The solution to the system of equations in problem 13 is (0, -4).
The solution to the system of equations in problem 14 is (-6, -1).
In problem 13, the system of equations is:-5x-5y = 20x+6y = -24Simplify the first equation.x + y = -4x = -4-ySubstitute this value into the second equation.-4-y + 6y = -245y = -20y = -4x = -4-yx = -4-(-4)x = 0In problem 14, the system of equations is:-7x+12y = 30-3x+6y = 12Simplify the second equation.x-2y = -4x = 2y-4Substitute this value into the first equation.-7(2y-4)+12y = 30-14y + 28 + 12y = 30-2y = 2y = -1x = 2y-4x = 2(-1)-4x = -2-4x = -6To learn more about equations, visit :
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Please help me. I know I’m solving for the principal but need help with the steps
Given: The information below
[tex]\begin{gathered} time(t)=5\text{years} \\ rate(r)=4\%=0.04 \\ Interest(I)=40 \end{gathered}[/tex]To Determine: How much Austine invested
Solution
Please note that the amount invested is the Principal
The formula combining principal, rate, time and interest for simple interest is
[tex]I=\text{Prt}[/tex]Make P the subject of the formula
[tex]P=\frac{I}{rt}[/tex]Substitute for I, r and t given into the formula as shown below
[tex]\begin{gathered} P=\frac{40}{0.04\times5} \\ P=\frac{40}{0.2} \\ P=200 \end{gathered}[/tex]Hence, the amount invested by Austine is $200
please show me how to graph 4x + 5y = -40
Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph. Therefore, the graph for the given equation is plotted below.
The given equation is 4x + 5y = -40.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Put x=0, 1, 2, 3, 4, 5,.....in the given equation and solve for y
When x=0, 4(0)+5y=-40
⇒ 5y=-40
⇒ y=-8
When x=1, 4(1)+5y=-40
⇒ 5y=-44
⇒ y=-8.8
When x=2, 4(2)+5y=-40
⇒ 5y=-48
⇒ y=-9.6
Plot the points (0, -8), (1, -8.8) and (2, -9.6) on the graph
Therefore, the graph for the given equation is plotted below.
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Find the value of x. Then find the measure of each labeled angle.
x= ____° (Simplify your answer.)
13x°= _____° (Simplify your answer.)
7x°= ____° (Simplify your answer.)
Answer:
13x + 7x = 180 (corresponding angles, sum of adjacent angles on a straight line=180)
20x = 180
x = 9
Substitute x into angle measures to find values.
13x° = 13(9)
= 117°
7x° = 7(9)
= 63°
Use the factor theorem to find all real zeroes for the given polynomial function and one factor Enter your answer as a comma separated list
Given:
[tex]2x^3+5x^2-4x-10[/tex](2x+5) is one of the factor.
[tex]\begin{gathered} 2x^3+5x^2-4x-10=(2x+5)(2x^2-4) \\ =2(2x+5)(x^2-2) \end{gathered}[/tex]By taking the factors equal to zero then we get the values of x.
Therefore, the zeros of the polynomial are
[tex]-\frac{5}{2},\sqrt[]{2},-\sqrt[]{2}[/tex]Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1, 5), (2, 3). You must set up a system of three equations to get credit for this question.
The equation of the parabola for the given points is y = -3x² + 7x + 1
Equation of the parabola
The standard form of the equation of a parabola is expressed as
y = f(x) = ax² + bx + c
where a, b, and c are constants and a ≠ 0.
Given,
Here we have the points (0, 1), (1, 5), (2, 3).
Now, we have to find the equation of the parabola.
Here we are given three coordinates (0, 1), (1, 5), and (2, 3) which lie on the parabola and which means that it satisfies the parabolic equation.
In order to find the values of a, b and c we need to formulate three equations using the three given points.
Since for the three unknowns a, b, and c, we will require three equations.
For that we have to take the Point (0,1) i.e. x = 0 and y = 1
Substituting the values of x and y in the standard parabola equation, then we get,
1 = a(0)² + b(0) + c
1 = 0 + 0 + c
c = 1 -------------------(1)
Next, we have to take the Point (1, 5) i.e. x = 1 and y = 5
Substituting the values of x and y in the standard parabola equation, then we get,
5 = a(1)² + b(1) + c
5 = a + b + c
It can be written as,
a + b + c = 5 -----------------------------(2)
Finally, we have to take the Point (2, 3) i.e. x = 2 and y = 3
Substituting the values of x and y in the standard parabola equation, then we get,
3 = a(2)² + b(2) + c
3 = 4a + 2b + c
It can be written as,
4a + 2b + c = 3 -----------------------------(2)
Apply the value of c as 1 in equation (2), then we get,
a + b + 1 = 5
a + b = 4 ---------------------(4)
Similarly, apply the value of c on the equation (3), then we get,
4a + 2b + 1 = 3
4a + 2b = 2
Divide the equation by 2 on both sides, then we get,
2a + b = 1 --------------------(5)
Subtract equation (5) from equation (4),
(2a - a) +(b - b) = 1 - 4
a = -3
Apply the value of a in the equation (4) to get the value of b,
(-3) + b = 4
b = 7
Therefore, the equation of the parabola is
y = -3x² + 7x + 1
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Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser. Kevin has p people sponsoring him, MIka has one more than Kevin, and Cheryl has one more than MIka. Write and solve and equation to find the number of people sponsoring each person
The equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser.
Consider that Kevin has p people sponsoring him, Mika has one more than Kevin, and Cheryl has one more than Mika.
Kevin = p
MIka = m
Cheryl = c
Then m = 1 + p
c = 1 + m
Or
m = c - 1
Now solve both equation;
m = 1 + p = c - 1
p = c - 1 -1
p = c + 2
p = m -1
p = c + 2
Then m - 1 = c + 2
m = c + 3
Hence, the equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
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The weights of four puppies are shown in pounds. 9.5, 9 3/8, 9.125, 9 3/4 Which list shows these weights in order from greatest to least?
The data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.
What is Descending order?Any data, including numbers, alphabets, amounts, lengths, etc., are arranged in descending order from highest to lowest.
In other terms, anything is considered to be in descending order when it is arranged from a higher value to a lower value. It is possible to arrange numbers in descending order, including whole numbers, natural numbers, integers, fractions, and decimals.
For example 7, 3, 9, 2 in decreasing order, for instance. Starting with the biggest number, we'll work our way down to the lesser ones one at a time. When these numbers are listed in descending sequence, they are written as 9, 7, 3, and then 2.
Given data:
9.5, 9 3/8, 9.125, 9 3/4
Now, simplifying the mixed fraction as
9 3/8
=75/8
= 9.375
9 3/4
=39/4
= 9.75
Thus, we have the data in decimal form
9.5, 9.375, 9.125, 9.75
Hence, the data from greatest to least is 9 3/4 > 9.5> 9 3/8> 9.125.
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find the domain of (x). express your answer in interval notation.
so the domain is
[tex](0,\propto)[/tex]simplify 5/7 x + 2/7 y − 2 − 1/7 x + 7
The simplification of the given expression would be; 4x/7 + 2y /7 + 5.
What is a simplification of an expression?Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
We have been given an expression as 5/7 x + 2/7 y − 2 − 1/7 x + 7
Thus,
5/7 x + 2/7 y − 2 − 1/7 x + 7
Combine the like terms first;
5/7 x − 1/7 x + 2/7 y − 2+ 7
Then solve the like terms;
(5 -1)x/7 + 2y /7 + 5
4x/7 + 2y /7 + 5
Therefore, the simplification of the given expression would be; 4x/7 + 2y /7 + 5.
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The cost for Albert to play 2 games of laser tag is $18. Based on this relationship, which equation can be used to determine the total cost, y, in dollars, for Albert to play any number of games, x, of laser tag?
The equation that can be used to determine the total cost, y, in dollars for Albert to play any number of games, x, is Y = 18x/2 or 9x.
What is an equation?An equation is a mathematical statement expressing the equality that two values or expressions share.
Equations are generally represented using the equation sign (=).
The cost of 2 games of laser tag = $18
The cost of 1 game of laser tag = $9 ($18/2)
The cost of x laser tag games = $9x or 18x/2
Thus, we can represent the equation of the total cost as y = 9x.
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5. Refer to Table 1. Suppose the government imposes a price ceiling of $5 on this market. What will be the size of
the shortage in this market?
0 units
2 units
8 units
10 units
There is no shortage of units in this market with a $5 price ceiling and the size of shortage is 0 units.
In mathematics, what is a data table?Tables are a good way to organize data by using rows and columns. Tables are a versatile organizational tool that can be used to communicate information on their own or in conjunction with another type of data representation (like a graph).Given: On this market, the government imposes a $5 price ceiling.
We need to find the size of the shortage in this market.
From the given table, we can see that the quantity demanded for $5 price ceiling is 4 units and the quantity supplied is 8 units.
So, the demand is satisfied and an extra 4 units are also provided.
Therefore, there is no shortage of units in this market a $5 price ceiling and the size of shortage = 0 units.
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factor out 28p^5q^3+24p^3
Answer: 4p^3(7p^2q^3+6
Step-by-step explanation: Im pretty sure.
Identify two segments that are marked congruent to each other on the diagrambelow. (Diagram is not to scale.)
Step 1:
What are congruences?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Step 2:
JH is congruent to HI
Final answer
JH is congruent to HI
What is variable rate of change
Answer:
It is a rate of change that is not the same at all points - in time or space.
Step-by-step explanation:
Suppose that R and S are points on the number line.
If RS 6 and R lies at -18, where could S be located?
==========================================================
Explanation:
Draw a vertical number line. Plot point R at -18 which is 18 units below 0.
Then move up 6 units to arrive at -12 which is one potential location of point S. The distance from R = -18 to R = -12 is RS = 6 units.
Now go back to point R = -18. This time move down 6 units to arrive at -24 as the other possible location of S.
See the diagram below.
Quadrilateral ARMY is rotated 90° about the origin.
Draw the image of this rotation.
A 3,3
Y 5,1
M 7,5
R 5,7
The quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5).
What do math quadrilaterals mean?
A polygon called a quadrilateral has four sides, four angles, and four vertices. Quadrilateral is a derivative of the Latin words quadri, which means four, and latus, which means side. A quadrilateral is shown in the above image as an example. quadrilateral pieces.If a point (x, y) is rotated 90 degrees counterclockwise with respect to the origin, the rotational rule is:
(x, y) → (-y, x) (-y, x)
Consequently, the image point's coordinates following rotation will be (-y, x).
According to this rule, the quadrilateral's image points will be A(3, 3) A'(-3, 3) R(5, 7) R'(-7, 5) M(7, 5) M'(-5, 7) Y(5, 1) Y' (-1, 5)
We may obtain the graph of the picture quadrilateral A'R'M'Y' by graphing the image points.
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3 sailboats to 5 fan boatsHow many fan boats if therewere 54 sailboats?
we can use cross multiplication
[tex]\begin{gathered} 3\text{sail}\longrightarrow5\text{fan} \\ 54\text{sail}\longrightarrow\text{xfan} \end{gathered}[/tex]where x is the number of fan boats
[tex]\begin{gathered} x=\frac{54\times5}{3} \\ \\ x=90 \end{gathered}[/tex]the number of fan boats to 54 sailboats is 90
Rosa uses 1/2 of a cup of vinegar in her salad dressing recipe. How
much vinegar would Rosa use to make 1/3 of a recipe?
Answer:
1/6
Step-by-step explanation:
1/2 1/3
lcd(least common denomitator)=6
there fore it is 1/6
You borrow $90,000 for college at an APR of 6.25%. You plan to elect 25-year repayment. How much more must you repay in total if your loan is unsubsidized, as opposed to being subsidized?
The amount which needs to be replayed if the loan is unsubsidized, as opposed to being subsidized is $59,295.86.
The monthly payment amount formula on a loan of P at rate r for t years is A = P(r ÷ 12) ÷ (1 -[tex]\frac{(1 +r)}{12} ^{-12t}[/tex])
For the normal compensation plan, T = 25. The P = $90,000 and r = 0.625, so the formula is,
A = $90,000(0.625 ÷ 12) ÷ (1 - (1 +[tex](\frac{1 +0.625}{12} )^{(-300)}[/tex])
A = $90,000(0.625) ÷ (1 - [tex](1.135)^{(-300)}[/tex])
A = $90,000(0.625) ÷ (1.832)
A = $(90,000 × 0.625) ÷ (1.832)
A = $30704.14
Payments under the extended repayment plan last for 25 years. The amount which needs to be replayed is $90,000 - $30704.14 = $59,295.86.
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how do you write 4.501795324E^-6 in simpler form
Answer: you cant but here are some ways to practice:)
Find the greatest common divisor of both the numerator and the denominator. This can be done either with prime factor trees or another method.
Divide both the numerator and the denominator with the greatest common divisor.
The result is a simplified fraction. hope this helps and sorry.
I only need the answer
THANK YOU!!
Cartesian coordinates are- 4.2426
The horizontal component of the Cartesian coordinate system is denoted by the letter x, whereas the vertical component is denoted by the letter y. In this coordinate system, equations for lines will need to include both the x and y variables.
Given
(r,θ) = (6,π/4)
x= r cosθ =6 x cos(π/4)
= 6√2 = 3√2
≈ 4.2426
y= r sinθ = 6 x sin(π/4)
= 6√2 = 3√2
≈ 4.2426
Hence the answer is 4.2426
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Mr. Stern owns an apartment building with 60 suites. He can rent all the suites if he charges a monthly rent of $200 per suite. At a higher rent, some suites will remain vacant. On the average, for each increase of $5, one suite remains vacant with no possibility of renting it. Determine the functional relationship between the total monthly revenue and the number of vacant units. What monthly rent will maximize the total revenue? What is the monthly revenue?
If Mr. Stern charges a monthly rent of $200, we still can rent all suites. An average increase of $5 in the monthly rent imply in the addition of one suite vacant.
Therefore, the total monthly revenue r in function of the number of vacant units v can be writen in the form:
[tex]\begin{gathered} r=(200+5v)\cdot(60-v) \\ r=-5v^2+100v+1200 \\ 0\leq v\leq60 \end{gathered}[/tex]The monthly rent m is given by:
[tex]m=200+5v[/tex]The value of v that maximize the total revenue r is the one found in the vertex of the parabola that represents r:
[tex]v_{\max }=-\frac{100}{2\cdot(-5)}=10[/tex]Therefore, the monthly rent that maximize the total revenue is m = 200 + 5*10 = $700
The monthly revenue with this monthly rent is:
[tex]r=-5\cdot10^2+100\cdot10+1200=\text{ \$1700}[/tex]
32
3 ÷ (z -
5
2
-)=2=÷(z+
3
2
+
3
Step-by-step explanation:
Consider the Cartesian equation,
2
x+3
=
4
y−5
=
2
z+6
Now,
a
=−3
i
+5
j
−6
k
b
=2
i
+4
j
+2
k
Vector equation,
r
=
a
+λ.
b
=−3
i
+5
j
−6
k
+λ(2
i
+4
j
+2
k
)
This is the required equation
px+5=7x–q please help me
Answer:
Step-by-step explanation:
Simplifying
px + 5 = -4x + q
Reorder the terms:
5 + px = -4x + q
Reorder the terms:
5 + px = q + -4x
Solving
5 + px = q + -4x
Solving for variable 'p'.
Move all terms containing p to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + px = q + -5 + -4x
Combine like terms: 5 + -5 = 0
0 + px = q + -5 + -4x
px = q + -5 + -4x
Reorder the terms:
px = -5 + q + -4x
Divide each side by 'x'.
p = -5x-1 + qx-1 + -4
Simplifying
p = -5x-1 + qx-1 + -4
Reorder the terms:
p = -4 + qx-1 + -5x-1
The two ways we can measure the SPREAD of a distribution:a. mean and quartilesb. median and standard deviationc. mean and mediand.quartiles and standard deviation
In statistics, there are ways of analyzing data and these include measures of "central tendency" and "measures of dispersion."
This question is focused on "measures of dispersion," that is, an analysis of how well the data set is being spread away from the centre. The centre is most commonly denoted as the mean (average), and the SPREAD is an analysis of how farther away the observed data is from the centre.
The Mean, Median and Mode are basically measures of "central tendency" and therefore, options A, B and C do not measure the SPREAD of a distribution.
The Quartiles and Standard deviation actually measure how well (either very close or very far) the data set move away from the distribution.
The Quartiles basically examine the data set from all four quarters of the entire set, the 1st, 2nd, 3rd and 4th quarters. This measure of spread measures how well the data is from the distribution depending on which quartile it falls. The Standard deviation measures how far the mean deviates (or drifts away) from the data set.
The correct answer therefore is option D.