coordinates of the new station= (5,98/4)
When two lines intersect at a point then the angle between them can be expressed in terms of their slopes and is given by the following formula:
tan θ = |
|where
are the slopes of the line AB and CD respectively.
If
is positive then the angle between the lines is acute. If
is negative then the angle between the lines is obtuse.
Slope of Vertical Lines
Vertical lines have no slope, as they do not have any steepness. Or it can be said, we cannot define the steepness of vertical lines.
A vertical line will have no values for x-coordinates. So, as per the formula of slope of the line,
Slope, m = (y2 – y1)/(x2 – x1)
But for vertical lines, x2 = x1 = 0
Therefore,
m = (y2 – y1)/0 = undefined
In the same way, the slope of horizontal line is equal to 0, since the y-coordinates are zero.
m = 0/(x2 – x1) = 0 [for horizontal line]
Positive and Negative Slope
If the value of slope of a line is positive, it shows that line goes up as we move along or the rise over run is positive.
If the value of slope is negative, then the line goes done in the graph as we move along the x-axis.
Let R,Q,T be the points that divide the line into 3:4 equal parts
Let the Q = (x,y)
R(1, 2) and T(8, 23) ,
x = m1x1+m2x2/m1+m2
y = m1y1+m2y2/m1+m2
X= 3.1+4.8/7
x= 3+32/7
x=35/7
x=5
y=2.3+23.4/3+4
y= 6+92/4
y=98/4
y= 24.5
(x,y) = (5,98/4)
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helo asapp THANK YOUUU
Answer:
(-2 , 0)
Step-by-step explanation:
The solution to this system of equations is the x and y values where the two lines cross. That is where x is -2 and y is 0. You can check/verify by putting these x and y values into the original equations.
Find the coordinates of the midpoint of a segment with the given endpoints
(-4, -7), (12, -6)
ASAP. Please help me with 63 please. I will give an Brainly and bunch of extra points to whoever answers it right please.
i believe this is correct hope it helps
one-half the product of x and
y
Answer: x*y/2
Step-by-step explanation:
x*y is the product of x and y.
1/2 * x* y is half the product of x and y.
Answer: x*y/2
What inequality is represented by the number line graph?
Answer:
An open circle indicates "less than" or "greater than," while a closed circle indicates "greater than or equal to" or "less than or equal to". This number line includes values that are less than or greater than or equal to .
Step-by-step explanation:
Which means it would be B. Or D.
what is 4 less than 1
Answer:
±3
Step-by-step explanation:
4 - 1 = 3
1 - 4 = -3
Either way you subtract them, the answer is still 3, whether negative or positive.
(01.05 LC)
Which of the following is an equivalent form of the compound inequality -22 > -5x - 7≥-33?
O-5x-7<-22 and -5x - 72 -33
O-5x-7-22 and -5x - 72-33
O-5x > -22 and -7 ≥-33
O-5x-7<-22 and -5x - 7 ≤-33
The equivalent form of the compound inequality -22 > -5x - 7≥-33 is -22 > -5x - 7 and -5x - 7≥-33
Inequality:
A mathematical phrase in which the sides are not equal is referred to as being inequal. In essence, a comparison of any two values reveals the existence of an inequality when one of the values is less than, larger than, or equal to the value on the opposite side of the equation.
Given inequality is -22 > -5x - 7≥-33
The equivalent inequality is -22 > -5x - 7 and -5x - 7≥-33
Therefore,The equivalent form of the compound inequality -22 > -5x - 7≥-33 is -22 > -5x - 7 and -5x - 7≥-33.
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f(x) = -x + 7
g(x) = x² - 4x + 4
Find: (gof)(x)
Answer:
[tex](g \circ f)(x) = x^2-10x+25[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=-x+7\\g(x)=x^2-4x+4 \end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The composite function (g o f)(x) means to substitute the function f(x) in place of the x in function g(x).
[tex]\begin{aligned} \implies (g \circ f)(x) & = g\left[f(x)\right]\\& = g(-x+7)\\& = (-x+7)^2-4(-x+7)+4\\& = (-x+7)(-x+7)+4x-28+4\\& = x^2-14x+49+4x-28+4\\& = x^2-14x+4x+49-28+4\\& = x^2-10x+25\end{aligned}[/tex]
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Answer:
x² - 10x + 25
Step-by-step explanation:
The given information is,
→ f(x) = -x + 7
→ g(x) = x² - 4x + 4
The equation we form is,
→ (gof)(x)
→ g[f(x)]
→ f(x)² - 4f(x) + 4
Let's solve the problem,
→ f(x)² - 4f(x) + 4
→ (-x + 7)² - 4(-x + 7) + 4
→ x² - 14x + 49 + 4x - 28 + 4
→ x² - 10x + 25
Hence, answer is x² - 10x + 25.
The value of a piece of factory equipment was $20,000 when it was purchased. During each 1 -year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period. Which of the following statements identifies the most appropriate type of function to model this scenario and provides a reason to support its appropriateness?
A- A linear function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was $10 less than its value 1 year before.
B- A linear function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was $2,000 less than its value 1 year before.
C- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.1 times its value 1 year before.
D- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.
The correct option for the function in this problem is:
D- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, during each 1 -year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period, hence r = 0.1 and the equation is:
[tex]A(t) = A(0)(1 - 0.1)^t[/tex]
[tex]A(t) = A(0)(0.9)^t[/tex]
Which means that option D is correct.
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The elevation of a sunken ship is $-120$ feet. You are in a submarine at
an elevation that is $\frac{5}{8}$
of the ship’s elevation. What is your elevation?
The supplied statement indicates that the angle of elevation will be = -75 feet.
What is angle of elevation?The term angle of elevation refers to the angle between the horizontal and an object. The line of sight of an observer would be over the horizontal. The term angle of depression refers to the angle between the horizontal and an item. The line of sight of an observer would fall below the horizontal.
In arithmetic, how do you find elevation?"rise over run" is an easy-to-remember equation for calculating a change in elevation as a decimal, which means the rise (the change in vertical distance) divided by that of the run (the change in horizontal distance). As an example, suppose the increase is two and the run is six. So you'd multiply 2 by 6 (or 2/6) to get.
According to the given information:Given The elevation of a sunken ship = 120 feet
the elevation of a submarine = 5/8
So,
Your elevation will be given by employing the MULTIPLICATION OPERATION.
(5/8) x -120 feet
= -75 feet
The supplied statement indicates that the angle of elevation will be = -75 feet.
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What is 3 x
3,280
328
32.80
3x (10) + 2x (100) + 8x (1.000)
0.328
written in standard form?
Answer:
I have no clue
hector paid $56 for 7 books what is the unit rate
What is five half’s multiplied by three twentieths?
Answer:3/8
Step-by-step explanation: ok so go to calculator soup and go to calculators then go fractions it's the first one then click on a thing that says fractions then type in problem and show answer hope this helps and remember your awesome and have great day and the name is kirsten michelle baker.
3. Omar runs around the edge of a circular park 6 times every morning. The park has an area of .02 square miles. How far does Omar run each morning?
Omar runs 0.9577 miles each morning .
Circumference of circle or perimeter of the circle is that the measure of the boundary of the circle whereas the world of circle defines the region occupied by it which is given by A = πr² where "r" is the radius of the circle.If we tend to open a circle and create a line out of it, then its length is that the circumference which is given by C = 2πr where "r" is the radius of the circle.It's typically measured in units, like cm or unit m.It is given that area of the circular park is .02 square miles .
Using area formula , we get
0.02 = πr²
0.02 = 3.14r²
0.0063 = r²
0.079 = r
Omar run each morning = 6 × Circumference of circle
= 6 × 2πr
= 12 × 0.079
= 0.9577 miles
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1. State the operation used to solve the following
equation.
x-7 = 15
Answer: Addition
Step-by-step explanation:
x-7 = 15
x-7+7 = 15+7 ==> Addition
x=15+7
x=22
Make a reasonable conjecture for the next term in the sequence.
1 4 9 16 25
Answer:
36
Step-by-step explanation:
Each time it goes up it adds the next highest odd number.
1
+3
4
+5
9
+7
16
+9
25
And so we can reasonably assume that the next number in the sequence will be the previous number (25) plus the next highest odd number (11). This means that the next number in the sequence is most likely 36.
Answer:
Ans is 36 ...
Step-by-step explanation:
Well,
lets add these number with odd number
1
3+1=4
5 + 4= 9
7+ 9= 16
9 + 16=25
11 + 25 = 36.........
Hope you will get it.
Use the figure below to list the slopes m₁, m₂, m3, and m4 in order of decreasing size.
In decreasing size, the slopes of the linear functions are given as follows:
m4, m3, m2, m1.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Regarding the slope, we have that:
Increasing lines have positive slopes.Decreasing lines have negative slopes.Hence, for the lines in this graph:
m4 and m3 are positive.m2 and m1 are negative.Then, we consider the intensity of growth/decay.
The pink line increases faster than the green line, meaning that it has a greater slope, that is, m4 > m3.The red line falls faster than the blue line, meaning that it's slope has a greater absolute value, but is less than m2, as they are negative, hence m2 > m1.Thus the list is given by:
m4, m3, m2, m1.
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f has a range of (-infinaty, 7),
and a graph that is symmetric
about the line x = 3, and has a
Y-intercept of 4
Answer:
[tex]f(x)=-|x-3|+7[/tex]
Step-by-step explanation:
The parent function of an absolute function is the modulus function:
[tex]f(x)=|x|[/tex]
Graph of Modulus function:
(see 2nd attachment)
[tex]f(x)=|x|=\begin{cases} \textsf{\:\:\:$x$, \quad if $x\geq 0$}\\\textsf{$-x$, \quad if $ x < 0$} \end{cases}[/tex]
Its vertex is at the origin (0, 0).
Its line of symmetry is x = 0.
It opens upwards.
Given information:
Range: (-∞, 7)Axis of symmetry: x = 3y-intercept: (0, 4)The axis of symmetry is the x-value of the vertex of an absolute function.
The y-value of the range is the y-value of the vertex of an absolute function.
Therefore, the vertex of the absolute function f(x) is (3, 7).
Graphing
Plot the vertex at (3, 7) and the y-intercept at (0, 4).As the function f(x) has a range of (-∞, 7), it opens downwards. Draw a straight line through the y-intercept that terminates at the vertex.Draw a line that is symmetrical to this line.To find the equation of the absolute function, work out the series of transformations that take the parent function to the given function.
As the function f(x) has a range of (-∞, 7), it opens downwards. Therefore, the parent function has been reflected in the x-axis:
[tex]\implies -f(x)=-|x|[/tex]
As the function f(x) is symmetric about the line x=3, the parent function has been translated 3 units to the right:
[tex]\implies -f(x-3)=-|x-3|[/tex]
Finally, as the highest y-value of the function is y = 7, the y-value of its vertex is y = 7. Therefore, the parent function has been translated 7 units up:
[tex]\implies -f(x-3)+7=-|x-3|+7[/tex]
Therefore, the equation of the absolute function with the given parameters is:
[tex]f(x)=-|x-3|+7[/tex]
The function f(x) = + 9-3 is one-to-one and therefore invertible. Determine f1. Graph both f
and f-1, along with the identity function f(x) = x.
Answer: I hope this helps.
Step-by-step explanation:
will give Brainly please help I don’t understand look at the picture
The G.P.A of the student with the given grades is 2.7875
How to compute the GPA of a Student?We are told that the grades that the student had are as follows;
2.8 in a 5 credit math's course
2.4 in a 3 credit music course
3.1 in a 5 credit chemistry course
2.9 in a 5 credit journalism course
Thus, the G.P.A can be calculated as;
[(2.8 * 5) + (2.4 * 3) + (3.1 * 5) + (2.9 * 5)]/(5 + 3 + 5 + 5)
= (14 + 7.2 + 15.5 + 7.9)/16
= 44.6/16
= 2.7875
Thus, we conclude that the G.P.A of the student with the given grades is 2.7875
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What is the following product?
47 47 47.47
The product of the given equation for the fourth root is 7.
What is defined as the 4th root?The 4th root of an amount is the number that, when multiplied four times by itself, yields the original number.
In other words, the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root of the square root. In addition, the fourth root is demonstrates the idea by multiplying the radical by 4, i.e. 4√.A number that is a square root of 4 has a result of 4 when multiplied by itself. There are two numbers which will work: 2×2=4 and −2×−2=4 which means that the numbers 2 and 2 are square roots of 4.For, the given question;
= ⁴√7 × ⁴√7 × ⁴√7 × ⁴√7
This equation can be written as;
=(⁴√7)⁴
Further writing the fourth root in terms of fraction;
= (7)∧(1/4)×4
Both power will cancel each other.
= 7
Therefore, the product of the fourth root is found as 7.
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The correct question is-
What is the following product?
⁴√7 × ⁴√7 × ⁴√7 × ⁴√7
A partir del siguiente plano se harán dos maquetas de una sala de concertos: para construir la primera, cada dimensión se dividira entre 24, y para la segunda, entre 5.6
Reverse the roles of the variables by solving for the indicated variable. Solve for t: w = uv + t
The subject of the function is t = w - v
How to solve the function?It should be noted that the function that's given is illustrated as:
w = uv + t
Subtract uv from both sides.
w - uv = uv + t - uv.
w - uv = t
Therefore, it can be seen that the subject of the function is t = w - v
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suppose that a box contains 6 cameras and that 4 of them are defective
The random variable x, which represents the number of defective cameras in the sample, is x = 0, 1, 2
What is random variable?A random variable is a variable with an unknown value or a function that gives values to each outcome of an experiment. A random variable might be discrete (with discrete values) or continuous (with continuous values) (any value in a continuous range).
According to the given data:The box contains two malfunctioning cameras.
The random variable, x, represents the sample space for the number of malfunctioning cameras that can be chosen;
The outcomes are:
Both cameras are faulty; x = 2
One is flawed, one is not; x = 1
Both cameras are in good working order; x = 0
This defines that the random variable , x = 0, 1, 2
The random variable x, which represents the number of defective cameras in the sample, is x = 0, 1, 2
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I understand that the question you are looking for is:
Suppose that a box contains 6 cameras and that 4 of them are defective. a sample of 2 cameras is selected at random. define the random variable x as the number of defective cameras in the sample. ( round to two decimal places when needed.)
point A bisects LS BC. If LS BA=6x-3 and LS AC= 3x+7. Solve for X. PLS ANSWER QUICKLY!!!
Based on the bisection of line BC by point A, the value of x is 10/3
How to determine the value of x?The given parameters are:
Point A bisects BCBA = 6x - 3 AC= 3x + 7Because the point A bisects BC, then
BA = AC
Substitute the known values in the above equation
So, we have
6x - 3 = 3x + 7
Collect the like terms
6x - 3x = 3 + 7
Evaluate the like terms
3x = 10
Divide both sides of the equation by 3
x = 10/3
Hence, based on the bisection of line BC by point A, the value of x is 10/3
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Sherry will mail a square
photo to her grandma.
The area of the photo is
about 71.4 square inches.
All of Sherry's envelopes
are perfect squares.
What's the length of one
side of the smallest
envelope she can use?
Answer:
Take the root
Step-by-step explanation:
Area of the square equal
[tex] {x}^{2} [/tex]
Then the side length of the pictures equal
[tex] \sqrt{71.4 } [/tex]
The result will be 8.44
augustin and edson are going to a baseball game to get to the stadium they travel east on the highway at 120km/hr for 30 minutes then they turn onto the stadium parkway and travel south at 60km/hr for 10 minutes assume their starting point is at the origin what is the position of the stadium
The position of the stadium, given the data is 60 Km east and 10 Km south
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
With above formula, we can determine the position of the stadium. Details below
How to determine the distance travelled in 30 minutesTime = 30 minutes = 30 / 60 = 1/2 hourSpeed = 120 Km/hDistance =?Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 120 × 1/2
Distance = 60 Km east
How to determine the distance travelled in 10 minutesTime = 10 minutes = 10 / 60 = 1/6 hourSpeed = 60 Km/hDistance =?Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 60 × 1/6
Distance = 10 Km south
Thus, we can conclude that the position of the stadium is 60 Km east and 10 Km south
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14. Find a counterexample for each of the following: a. If n is a natural number, then(n+5)/5 -n-1. b. If n is a natural number, then (n + 4)² = n² + 4².
n = 1 is a counterexample for both the given equations.
Here, we are given two equations, let us look at them one by one-
a. (n + 5) / 5 = n + 1
let us take n = 1
the, (1 + 5) / 5 = 1 + 1
6/ 5 = 2
This equation does not hold as 6/5 ≠ 2. Thus, n = 1 doesn't satisfy the given equation and hence is a counterexample.
b. (n + 4)² = n² + 4²
Let us take n = 1
(1 + 4)² = 1² + 4²
5² = 1 + 16
25 = 17
Again, this equation does not hold as 25 ≠ 17. Thus, n = 1 doesn't satisfy the given equation and hence is a counterexample.
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write an equation in slope intercept form for this line
Answer:
Step-by-step explanation:
P=2(x+y) Solve for y
[tex] \bf \implies \: y \: = \frac{1}{2} p - x[/tex]
Step-by-step explanation:Let's solve for yp = 2(x + y)p = 2x + 2yp - 2x = 2y2y = p - 2x[tex] \bf \frac{ \cancel{2}y}{ \cancel{2}} = \frac{p \: - \: 2x}{2} [/tex][tex]y = \frac{p}{2} - \frac{ \cancel{2}x}{ \cancel{2} }[/tex][tex] \boxed{y = \frac{1}{2}p - x} \: \bf \mathfrak {ans}[/tex]