Answer: y=2x+8
Step-by-step explanation:
you take the reverse of the slope being 2 including the negative.
Lee Holmes deposited $17,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $42,000 at 9% interest compounded semiannually.
At the end of 6 years, what is the balance in Lee’s account? (Use the Table provided.)
The balance in Lee's account at the end of 6 years is $384,830.53.
What is the balance?The first step is to determine the future value of the initial amount deposited in the savings account.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate = 9% / 2 = 4.50%m = number of compoundingN = number of yearsBalance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42
The total value of the account after $42,000 is deposited is:
$42,000 + $22,138.42 = $64,138.42
The future value of $64,138.42 at the end of 6 years is:
Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53
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12) m/GOP = 80°, m/ROP
and m/ROG= 32x + 4. Find x.
R
Q
= 3 +59x,
G
The angular value of x is 3° as per the given the given information in the question.
What is meant by an angle?An angle in Euclidean geometry is the figure produced by two rays, called the sides of the angle, that have a common termination, called the vertex of the angle. Angles formed by two rays lie in the plane containing the rays. Angles are also generated by the intersection of two planes. These are referred to as dihedral angles. Two intersecting curves can also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Given,
m ∠GQP=80
m ∠RQP=3+59x
m ∠RQG=32x+4
From the figure,
m ∠RQG+ m ∠GQP= m ∠RQP
32x+4+80°=3+59x
27x=81°
x=3°
Therefore, the value of x=3°
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consider the ellipse given by x^2+xy+2y^2=7. Find the y-coordinate(s) of all points where the ellipse has a vertical tangent line.
The ellipse given by x^2+xy+2y^2=7. The y-coordinate(s) of all points are -11.3, 11.2, -5.665, 5.585 where the ellipse has a vertical tangent line.
Define differentiation.Differentiation is the process of determining a function's derivative. Differentiating algebraic functions, trigonometric functions, and exponential functions are the three fundamental derivatives.
Given,
Ellipse given,
x²+ xy + y ² = 7
Differentiating:
dy/dx
x²+ xy + y² = 7
d/dx(x² + xy + y²) = d/dx(7)
2x + 1y + x dy/dx + 2y dy/dx = 0
dy/dx = 2x + y/ x + 2y
dy/dx = 0
2x + y = 0
x + 2y = 0
Now, we have 2 equations,
x² + xy + y² = 0
y = -2x
Solving equations by substitution method,
x² + x(-2x) + (-2x)² = 7
x² - 2x² + 4x² = 7
3x² = 7
x = ±√21/3
Using y = -2x
Points are:
( -2√21/3 , √21/3) and (2√21/3 , -√21/3)
±√21/3 = ±1.528
x² + xy + y² = 7 [-11.3, 11.2, -5.665, 5.585]}
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Solve the following simultaneous equations using substitution
Answer:
the answer is 18 lol....
(−3,y) and (x,2).
y=−2x+2
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Complete the table below.
x y
row 1−3 Answer
row 2 Answer
2
The value of x in the second ordered pair is - 0.5 or - 1/2 and that of y in the first ordered pair is 8.
The given ordered pair is (-3,y) and (x,2)
the equation y=-2x+2
In the first step we put the value of x as -3 as given in (-3,y) in the equation y=-2x+2, we get
y=-2(-3)+2
⇒y=6+2
⇒y=8
So the value of y is 8 then the ordered pair will be (-3,8).
Again, in the second step, we put the value of y as 2 as given in (x,2) in the equation y=-2x+2, and we get
2=-2x+2
⇒2x=2-2
⇒2x=0
⇒x=0
So the value of x is 0, and the ordered pair will be (0,2).
The table:
# Value of x Value of y 1 -3 8 2 0 2I have provided a photo of the table:
Order these numbers from least to greatest.
2.9042, 2.9, 4.419, 2.94
Help pls I will give brainliest!!
Answer:
C. -16
Step-by-step explanation:
Hope this helps you! :))
16
Step-by-step explanation:
the answer is c
just took a test and I got it right
Select all of the descriptions which describe a transformation of the graph of f(x) = x that could result in the graph of g(x) = 7x.
A: The graph is translated 7 units to the right.
B: The graph is rotated about (0, 0), becoming steeper.
C: The graph is reflected across the x−axis.
D: The graph is vertically shrunk.
E: The graph is translated 7 units up.
F: The graph is vertically stretched.
Answer:
A,C,D
Step-by-step explanation:
The perimeter of a triangle is 42 feet. One side of the triangle is one foot longer than the second side. The third side is five feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)
Answer:
12 ft, 13 ft , 17 ft
Step-by-step explanation:
let x be the length of the second side , then
one side is x + 1
third side is x + 5
the perimeter P is the sum of the 3 sides, then
P = x + x + 1 + x + 5 ← collect like terms
P = 3x + 6
given P = 42 , then equating gives
3x + 6 = 42 ( subtract 6 from both sides )
3x = 36 ( divide both sides by 3 )
x = 12
x + 1 = 12 + 1 = 13
x + 5 = 12 + 5 = 17
the 3 sides are 12 ft, 13 ft , 17 ft
Which ordered pair is a solution of the equation? 2 x + 4 y = 6 x − y 2x+4y=6x−y
The solution to the equation given as 2x + 4y = 6x − y has the ordered pair of (3, 4)
How to determine the ordered pair of the solution?From the question, we have the following equation that can be used in our computation:
2x+4y=6x−y
Solving further, we need to collect the like terms
So, the equation becomes
2x - 6x = -4y - y
Next, we evaluate the like terms in the above equation
So, we have the following representation
-4x = -3y
Divide both sides by -3
The equation becomes
x = 3/4y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x = 3/4 * 4
Evaluate the products
x = 3
So, we have
x = 3 and y = 4
Express as ordered pairs
(x, y) = (3, 4)
Hence, the ordered pair of the solution is (3, 4)
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Use the definition of exponents as repeated multiplication to simplify. Enter only the simplified expression (2/3)^2
The expression (2/3)² when simplified by repeated multiplication is 4/9
How to evaluate the expression?From the question. the expression is given as
(2/3)²
We start by rewriting the expression using repeated multiplication
This in other words means that:
We rewrite the (2/3)² as repeated multiplication
To do this, we apply the exponent rule of indices
This rule states that:
a^m = a * a * a .... in m places
So, we have
(2/3)² = (2/3) x (2/3)
Evaluate the products
(2/3)² = 4/9
Hence, the equivalent expression is 4/9
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Evaluate the given function for f (2).
The value of f(2) is 2.
What is graph function?
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.
All y-coordinates of the graph function are an output of the graph function.
All x-coordinates of the graph function are an input of the graph function.
f(2) is an output of the function.
Here find the y-coordinates of the point on the graph when the value of x is 2.
(2,3) is a point on the graph.
Thus f(2) = 3
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Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a
brief evaluation of your work.
Activity
In the first Lesson Activity, you derived an equation to model a car wash. The equation is y = 5x - 75. In this activity, you will graph this equation.
Question 1
Is it possible to graph the line that represents this equation by using two points found in the previous Lesson Activity, (15, 0) and (0, -75)? Explain
your answer.
Yes, the graph goes through those two points.
What is Graph?
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Explanation for the answer:
The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.
You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.
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Rationalize the denominator 1/ square root of 2
Answer:
Multiply and divide by √2 . You'll get √22
Step-by-step explanation:
If a truck weighs 20% more than a car, then the truck's weight is % of the car's weight.
Describe the graph of g?
The given points gives us a line with constant slope of -2.
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
The points are in the form of ( x, y) , where y= g(x)
Plot these points on the graph and join the points through a line.
Refer to the attachment for the graph.
The slope is constant.
consider any 2 points:
(x,y) = (0,7)
(m,n) =(2,3)
Slope = change in y values/ change in x values
= (7-3)/(0-2) = 4/-2 = -2
The given points gives us a line with constant slope of -2.
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A home developer is planning to build h houses with identical floor plans. Each house will have 3 smaller bedrooms that each require 150 square feet of carpet and 1 larger bedroom that requires 270 square feet of carpet.
The required expression is 3h(150) + h(270) which is the correct answer would be an option (D).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Since each house will have 3 smaller bedrooms that required 150 square feet of carpet
⇒ 3 × 150
Each house will have 1 larger bedroom that requires 270 square feet of carpet.
⇒ 270
So, (3 × 150 + 270) × h
⇒ 3h(150) + h(270)
Thus, The required expression is 3h(150) + h(270).
Hence, the correct answer would be an option (D).
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The question seems to be incomplete the completed part has been attached below
JMP made a profit of $85,000 last year. If the profit margin increased by 20% this year what is the amount of profit made by JMP
The amount of profit made by JMP is 102000.
Given,
In the question;
JMP made a profit of $85,000 last year.
If the profit margin increased by 20% this year.
To find the amount of profit made by JMP.
Now, According to the question:
Based on the given condition:
Formulate:
= 85000 x (20% + 1)
Calculate;
85000 x (0.2 + 1)
Calculate the sum or difference
85000 x 1.2
= 102000
Hence, The amount of profit made by JMP is 102000.
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Use the formula F = mg-3t²
m = 4, g = 6 and t = 2
1. What is the result if you divide -12x8y8 by 3x4y ²?
O A. 4x4yê
O B. 4x²y
O C.-4x²yA
O D. -4x^y6
Please look at photo, it didn’t type correctly.
Consider the equation and the following ordered pairs: (−3,y) and (x,2).
y=−3x−1
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Complete the table below.
x y
row 1−3 Answer
row 2 Answer
2
The missing values of the ordered pairs using the given equation are:
x = -1; y = 8
The computed table is:
x | y
-3 8
-1, 2
How to Complete a table Using Equation?To complete a table of values, we can plug in the known value of each of the ordered pairs that are represented in a table into the given equation that models the relationship, then find the value of the missing variable.
The equation that represents the relationship between x and y is given as y = -3x - 1.
Find the value y in the ordered pair (-3, y) by substituting x = -3 into y = -3x - 1:
y = -3(-3) - 1 = 8
y = 8
Find the value x in the ordered pair (x, 2) by substituting y = 2 into y = -3x - 1:
2 = -3x - 1
Add 1 to both sides
3 = -3x
Divide both sides by -3
x = 3/-3
x = -1
The ordered pairs with the missing values are: (-3, 8) and (-1, 2).
The table would be computed as:
x | y
-3 8
-1, 2
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What is the equation of the line shown in the graph? Drag and drop the expressions to write the equation of the line in slope-intercept form. Giving Brainlist
y =_+_
Answer:
Step-by-step explanation:
IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = % c) In a sample of 600 people, how many people would have an IQ less than 110? people d) In a sample of 600 people, how many people would have an IQ greater than 140? people
Write the equation of a line, in slope-intercept form, that is perpendicular to y = - 1/3 x + 4 and passes through the point (-2-5)
The equation of the line perpendicular to the given line is, y = 3x + 1.
What is slope of the line?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.
Consider, the given equation of line
[tex]y = -\frac{1}{3}x+4[/tex]
We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.
Here, the point is (-2, 5).
First to find the slope of the line.
Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.
Here, the slope of given line is, -1/3.
So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]
Therefore, the slope of the line is 3.
Now to find the equation of the line.
Consider, the point - slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]
⇒
[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]
Hence, the equation of line in slope - intercept form, is y = 3x + 1.
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(x2 + 3x –9) ÷ (x – 2).
Answer:
Step-by-step explanation:
Point KK is located at (-2,-5)(−2,−5) on the coordinate plane. Point KK is reflected over the yy-axis to create point K'K ′ . Point K'K ′ is then reflected over the xx-axis to create point K''K ′′ . What ordered pair describes the location of K''?K ′′ ?
The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5).
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
The given point K(-2,-5)
If we reflect a point(x,y) along the y-axis then the coordinate after reflection converts as K'(-x,y)
The reflection of K(-2,-5) along the y-axis will be K'(2,5).
Hence "The sign of coordinate of x of a point after the reflection along the y-axis will be interchanged thus the coordinate of K'(2,5)".
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What is 1+1? is it 11-de-7 or 2
Answer:
2
Step-by-step explanation:
This is because yes. If you add 1 and 1 (use your fingers) and count the two, you simply get 2.
Ingia went to the farmers market to get ingredients. Determine the price per item of each vegetable.
4.1 6 onions for $1.80
12 mushrooms for $3 4.3 5 peppers for $5.50
4.2
The expression on the left side of an equation is shown below.
3(x+1)+9-
k
If the equation has no solution, which expression can be written in the box on the other side of the equation?
Q3(x+4)
O 2(x+6)+x
O 4(x-3)-x
O 3(x+1)+9x
Answer:
3x + 12
Step-by-step explanation:
3(x+1)+9
= 3x + 3 + 9
= 3x + 12
Find the values of P and Q in the arithmetic progression: -12, P, Q, 18.
The value of P=2 and Q=8 as in AP, The difference in two terms is equal between all the terms.
What is Arithmetic Progression?A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. Sn = n/2[2a + (n 1) d] is the formula to determine the sum of an arithmetic progression. where an is the first term in the arithmetic progression, n is the total number of terms, and d is the common difference. If there is always the same difference between any two consecutive terms in a series of numbers, that progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series.
Here,
18--12=30/3=10
P=-12+10
=-2
Q=-2+10
=8
P=2 and Q=8 as in AP, the difference between the two terms is equal for all terms.
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