The equation of the line that passes through the point (6,-5) and has a slope of -1/6 is y = (-1/6)x - 4.
We know that, the slope intercept form of a line is given by:-
y = mx + c
Where,
m represents the slope of the line,
c represents the y -intercept and,
(x,y) represent the coordinates of each of the ordered pairs in the line
Hence, we can write,
m = -1/6
One of the ordered pairs, (x,y) is (6,-5).
Hence, we can write,
-5 = (-1/6)*6 + c
-5 = -1 + c
c = -5 + 1
c = - 4
Hence, the equation of the line is given by:-
y = (-1/6)x - 4
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Classify the following functions as growth or decay: f(x) = 10 (6/7)^x, g(x)= 1/3e^x, h(x)=5e^-x, k(x)= -10(6/7)^x
It is known that any exponential function with the form f(x)=a^x is an increasing function while a function of the form g(x)=a^(-x) is a decreasing function.
Furthermore, it a function h(x) is increasing, then the function -h(x) is decreasing. By analogy, if a function k(x) is decreasing, then -k(x) is increasing.
Now let's analyze the functions from the problem.
[tex]\text{ Let }f(x)=10\cdot(\frac{6}{7})^x[/tex]Since (6/7)^x is increasing and the multiplying factor of 10 is positive, then the function f(x) is also increasing.
Use these rules to find whether each function is increasing or decreasing.
Remember that increasing functions are used to represent growth while decreasing functions are used to represent decay.
What is a different common Denominator you could use in problem 2
Answer:
what is the problem ???
Step-by-step explanation:
Provide the correct reason for the statement in line 1. (please help)
Answer:
d) given
Step-by-step explanation:
nothing has been done yet, the statement is given as stated above the statement
a student has 200 Naira if someone gives her 160 Naira how much will she have if someone gives her x Naira how much would she have
Answer:
360 naira hope it will be helpful
Step-by-step explanation:
hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?
The height of balloon is 1.99 miles above the ground.
What is angle of depression ?In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.
Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.
We can state the following if the angle of this milepost's depression is 24 degrees:
Tan(24)=[tex]\frac{h}{b}[/tex]
b = [tex]\frac{h}{tan(24)}[/tex]
We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.
tan(20)=[tex]\frac{h}{b+1}[/tex]
b +1 = [tex]\frac{h}{tan(20)}[/tex]
Therefore, substituting equation 1
[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]
1 = [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]
1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )
h = 1.99 miles
Consequently, the height of balloon is 1.99 miles above the ground.
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Through how many radians does the minute hand of a clock rotate from12:40 PM to 1:10 PM?o10- 10The minute hand rotates through radians.(Simplify your answer. Type an exact answer in terms of Use integers orfractions for any numbers in the expression)-10
As you can see in the given figure the minute hand of a clock rotate from 12:40 to 1:10 formig a straigth angle.
A straight angle in radians is π radians.
Then, the minute hand rotates π radiansA teacher is organizing binders for her students. She has 54 pieces of lined paper, 36 pieces of grid paper, and 72 dividers. What is the greatest number of identical binders that she can make? Please help!
Using the highest common factor, the greatest number of identical binders that the teacher can make is 18.
What is the highest common factor?The highest common factor or multiple of the given numbers is the highest number that can divide them without a remainder.
We know that 2, 9, and 18 can divide 54, 36, and 72 without leaving a remainder.
We can see that the highest common factor is 18.
When we divide 54 by 18, the quotient is 3. If you divide 36 by 18, the quotient is 2. When you divide 72 by 18, the result is 4.
The number of lined paper = 54 pieces
The number of grid paper = 36 pieces
The number of dividers = 72 dividers
The common factors of 54, 36, and 72 are 2, 9, and 18.
The highest common factor of 54, 36, and 72 is 18.
Thus, 18 binders containing 3 pieces of lined paper, 2 pieces of grid paper, and 4 dividers can be made from the collection, using their HCF.
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The graph of a linear function is given below.What is the zero of the function ?A. -3B. -3/2C. -2/3D. -2
Using the graph, we can deduce the following:
• x-intercept: x = -2
,• y-intercept: y = -3
Let's determine the zero of the function.
The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.
The zero of a function is the point the line crosses the x-axis.
From the graph the x-intercept is at x = -2.
Therefore, the zero of the function is:
x = -2
ANSWER:
D. -2
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)
If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.
Maximum heightGiven equation:
y = 88t - 16t²
Maximum height dy/dt = 0
88-32t = 0
32t = 88
t = 88/32sec
t = 2.75sec
Hence,
Maximum height attained by the ball :
Maximum height attained by the ball = 88(2.75)-16(2.75)²
Maximum height attained by the ball = 242 - 121
Maximum height attained by the ball = 121 feet
Therefore the maximum height is 121 feet.
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12. The perimeter of a triangle with sides 5x-1, 5x-1, 2.2x +10, and the perimeter of a square with a side length of 6.5x -11.8 are the same. What is the value of x?
The value of x is 4.
The perimeter of any shape is the sum of lengths of all its sides.
We are provided with the sides of triangle i.e., 5x-1, 5x-1 and 2.2x +10.
So, The perimeter of a triangle = sum of length of all three sides = (5x-1) + (5x-1) + (2.2x +10)
The perimeter of a triangle = 12.2x + 8 equation 1
Also, we are provided with the side of square i.e., 6.5x -11.8.
The perimeter of a square = 4 (side) = 4 (6.5x - 11.8)
The perimeter of a square = 26x - 47.2 equation 2
As per question,
Perimeter of a triangle = Perimeter of a square
12.2x + 8 = 26x - 47.2
13.8x = 55.2
x = 4
So we can write, the value of x is 4.
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1. Write the regression2.r =3. what does the r mean?I predict there will be a [blank] relationship between [blank] and [blank] I think it’s because [blank] and I’m gonna send a photo about my graphing points
First of all, we have to find the mean of x values.
According to the given graph, the x values are: 0, 1, 2, 2, 3, 3, 4, 5, 6, 7.
So, the mean is
[tex]\bar{x}=\frac{0+1+2+2+3+3+4+5+6+7}{10}=\frac{33}{10}=3.3[/tex]The mean of x values is 3.3.
The y values are: 2, 2, 3, 4, 4, 4, 5, 6, 8, 9.
The mean would be
[tex]\bar{y}=\frac{2+2+3+4+4+4+5+6+8+9}{10}=\frac{44}{10}=4.4[/tex]The mean of y values is 4.4.
Now, we find the standard deviation for x values and y values.
[tex]undefined[/tex]Sarah enrolled $10,000 worth of debt with National Debt Relief. We negotiated with the creditors and reduced the debt by 50%. Sarah’s fee for our services was 25% of the enrolled debt ($10,000). How much did Sarah end up saving after reducing her debt and paying us our fee?*
Answer:
7500$
Step-by-step explanation:
The equation for the line that has a slope of -3/8 and passes through (0, 10) is: y = -3/8x + 10 : y = 3/8 x - 10
The standard form of expression equation of a straight line is;
[tex]y\text{ = mx+c}[/tex]where;
m is the slope
c is the intercept
Given
slope m = -3/8
Next is for us to get the y- intercept of the line. This is done by subtituting the slope and the point (0,10) given into the equation y = mx+c and calculating c as shown;
[tex]\begin{gathered} y\text{ = mx+c} \\ 10\text{ = -3/8(0)+c} \\ 10\text{ = 0+c} \\ c\text{ = 10} \end{gathered}[/tex]Next is to get the equation of the line by substituting m = -3.8 and c= 10 into the standard form of the equation as shown;
[tex]\begin{gathered} y\text{ = mx+c} \\ y\text{ = -}\frac{3}{8}x+10 \end{gathered}[/tex]Hence the first option is correct
How many months does it take $428 to double at a simple interest rate of 12%
When $428 doubles, it means that the
y= −2x+8
x-intercept:
Enter as a coordinate: such as
(a,b)
y
-intercept:
Enter as a coordinate: such as
(a,b)
For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)
In this question, we have been given an equation y = -2x + 8
We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)
To find the x-intercept we need to substitute y = 0 in the above equation.
0 = -2x + 8
2x = 8
x = 4
So, the x-intercept is (4, 0)
To find the y-intercept we need to substitute x = 0 in the above equation.
y = -2(0) + 8
y = 0 + 8
y = 8
So, the y-intercept is (0, 8)
Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)
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Scott is a software salesman. His base salary is $2500, and he makes an additional $80 for every copy of English is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 28 copies of English is Fun.
SOLUTION
Given the question in the question tab, the following are the solution steps to get the equation
Step 1: Represent the statement using mathematical notation
Base salary is $2500 (Base salary is constant since it does not change)
P represent his total pay (in dollars)
N represent the number of copies of English is Fun he sells
price made per copy of the product is $80
The equation relating P to N will be written as:
[tex]P=2500+80N[/tex]Part B: Using this equation in step 1 above to find his total pay if he sells 28 copies of English is Fun
[tex]\begin{gathered} P=2500+80N \\ N=28 \\ P=2500+80(28) \\ P=2500+2240 \\ P=\text{\$}4740 \end{gathered}[/tex]Hence, his total pay if he sells 28 copies of English is Fun is $4740
Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y=-1/6x+3
The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.
How to rewrite equation in standard form?The standard form for linear equations in two variables is Ax + By = C.
where
A , B and C are constantx and y are the independent and dependent variables respectivelyTherefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .
y = - 1 / 6 x + 3
multiply the equation by 6 to eliminate the fraction
6y = 6(- 1 / 6 x) + 6(3)
Therefore,
6y = - x + 18
x + 6y = 18
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Solve the given equation or inequality graphically. State your answers rounded to two decimals. (a) x3 + 5x2 = −x2 + 5x + 3
The solutions of the equation x³ + 5x² = - x² + 5x + 3 when solved graphically is x = - 0.41, 1.09.
Draw a graph for each side, or component, of the equation and check to see where the curves intersect or are equal, to solve an equation graphically. The answers to the equation are the x values of these places.
Consider the equation,
x³ + 5x² = - x² + 5x + 3
Solving Equations Graphically:
The solution(s) of the equation f(x) = g(x) are the values of x where the graphs of f and g intersect.
Therefore,
f(x) = x³ + 5x² and g(x) = - x² + 5x + 3
By graphing the function we find the intersection of the two functions.
Hence, the graphs intersect each other at ( - 0.411, 0.776) and ( 1.092, 7.268).
Therefor,e the solution of the equation x³ + 5x² = - x² + 5x + 3 is x = - 0.41 and x = 1.09.
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Can you check work please?
When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.
[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]
[tex]3-\sqrt{x} 5[/tex]
The value of the expression given as 3 - √x⁵ is 3 - x^2√x
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
3 - √x⁵
Express 5 as the sum of 4 and 1
So, we have the following equation
3 - √x⁵ = 3 - √x^(4 + 1)
Apply the law of indices to expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √(x^4 * x)
Next, we expand the equation
So, we have the following equation
3 - √x⁵ = 3 - √x^4 * √x
Evaluate the square root of x^4
So, we have the following equation
3 - √x⁵ = 3 - x^2 * √x
Evaluate the product
So, we have the following equation
3 - √x⁵ = 3 - x^2√x
Hence, the value of the expression is 3 - x^2√x
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7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.
We can use the following formula:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]So:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]Answer:
0.3%
Find the equation for the circle with a diameter whose endpoints are (5,5) and (3,−5).
The equation of the circle in standard form whose center is at (h, k) = (4, 0) is (x - 4)² + y² = 26.
How to derive the standard equation of the circle based on the coordinates of diameter endpoints
In this question we find the coordinates of the endpoints of the diameter of the circle, then, the center of the circle is the midpoint of the line segment. The center of the circle is found by midpoint formula:
(h, k) = 0.5 · (5, 5) + 0.5 · (3, - 5)
(h, k) = (4, 0)
And the radius of the circle is determined by Pythagorean theorem:
r = √[(4 - 5)² + (0 - 5)²]
r = √[(- 1)² + (- 5)²]
r = √26
Then, the equation of the circle in standard form is describe below:
(x - h)² + (y - k)² = r²
If we know that (h, k) = (4, 0) and r = √26, then the equation of the circle is:
(x - 4)² + y² = 26
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Solve the equation for x.
6(x + 3) - 8 = 4x + 2(4 + x)
Hello! So...
We are given the following to solve:
Solve for x.
[tex]6(x+3)-8=4x+2(4+x)[/tex]
_______________________________________________________
1. Expand both sides of the equation.
[tex]6(x+3)-8=6x+10[/tex]
[tex]4x+2(4+x)=6x+8[/tex]
[tex]6x+10=6x+8[/tex]
______________________________
2. Subtract 10 from both sides.
[tex]6x+10-10=6x+8-10[/tex]
_______________________________
3. Simplify.
[tex]6x=6x - 2[/tex]
_______________________________
4. Subtract 6x from both sides.
[tex]6x-6x=6x-2-6x[/tex]
_______________________________
5. Simplify.
[tex]0=-2[/tex]
^Notice, the sides are not equal in the solution. This being said, there would be no solution.
___________________________________________________
Hope this helps! If you need anything else, feel free to comment below. Thanks and good luck!
Fill in the blanks below with the correct units.(a) The school bus had a mass of about 9000 ?(b) Last week, Ravi drove about 13?to visit his uncle.(c) Goran added 5 ?e of cream to his coffee.
The first unit is kilograms because the bus is really heavy.
The second is kilometers because meters are too small.
The third one is milliliters because liters are too much for ice cream.
i need help the problem is
solve for y
2x+y=3
Answer:
y = 3 - 2x
Step-by-step explanation:
Subtract 2x from both sides of the equation.
Answer:
y = x or 1x
Step-by-step explanation:
x as a variable can also be expressed as 1x.
so we can say that 2x + 1x
because x & y are two different type of variables. you think of y as a question mark ( ? ).
Now the new equation is
y = ?
so 1x + ? = 3
because x is the same thing as a 1x you can say that 2x + 1x = 3
Please help me I was sick today and missed out on class and I don’t understand this question
Answer: 72 i think
Step-by-step explanation:
Horatio left a campsite, hiking at a rate of 1 mile per hour. Ivan left 3 hours later, hiking at a rate of 2 miles per hour. How long will it take Ivan to catch up to Horatio?
Ivan will catch up to Horatio in 3 hours .
In the question ,
it is given that
speed of Horatio is 1 miles per hour
speed of Ivan is 2 miles per hour .
and Ivan leaves 3 hours late than Horatio .
Let "t" be the time ( in hours ) taken for Ivan to meet Horatio ,
So, the distance covered by Ivan will be 2*t .
Since Horatio left 3 hours before so the time taken for Horatio to meet Ivan is (t+3).
So, the distance covered by Horatio will be 1*(t+3) .
The distance covered for Horatio and Ivan will be equal ,
which means
2*t = 1*(t+3)
2t = t + 3
2t - t = 3
t = 3
Therefore , Ivan will catch up to Horatio in 3 hours .
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the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?
Answer:
The new price of the article is $270
Step-by-step explanation:
270-240/240
x 100% = 12.5%
12.5x240/100
= 30
find all real and complex zeros for f(x)=x^3-x^2+3x-3
The real and complex zeros for the function given as .f(x) = x³ - x² + 3x - 3 are x = 1 and x = ±i√3, respectively
How to determine the zeros of the function?The equation of the function is given as
f(x) = x³ - x² + 3x - 3
Group the terms of the function in two's
So, we have the equation
f(x) = (x³ - x²) + (3x - 3)
Factor each group in the function
f(x) = x²(x - 1) + 3(x - 1)
Factor out x - 1
f(x) = (x² + 3)(x - 1)
Set to 0
(x² + 3)(x - 1) = 0
This gives
x² = - 3 and x = 1
Evaluate the roots
x = ±i√3 and x = 1
Hence, the zeros of the equation are x = ±i√3 and x = 1
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find the answer to this problem (15/16) - ( -3/16)
A. 3/4
B. -3/4
C. -1 1/8
D. 1 1/8