The average temperature range in Newport, Oregon is between 45 and 65 degrees.
The average yearly temperature T in degrees for Newport, Oregon is given by: |T−55|≤10. This means that the temperature T is within 10 degrees of 55 degrees. To find the average temperature range, we consider the range between 55+10 = 65 degrees and 55-10 = 45 degrees.
Therefore, the average temperature range in Newport, Oregon is 45 to 65 degrees.
What is the graph of the system? y ≤ -x – 1 y ≥ 2x + 4
See the attached graph
Step-by-step explanation:The comparison operator includes "or equal to" in each case, so the graph of the boundary line is solid. Each bounary line can be graphed in the usual way. Considering the y-intercept and slope is often easiest when the equations are presented in this form:
y = -x -1y = 2x +4Since the solution space includes y-values less than those in the first line, the graph is shaded below that line.
Since the solution space includes y-values greater than those in the second line, the graph is shaded above that line.
Where the graph is doubly-shaded is the solution space for the system of equations.
the sum of three number 20. the sum of twice the first number, and 5 times the third number is 71. the difference between 4 times the first number and the scond number is 27. find the three numbers. Helllp
1. Describe how factoring a quadratic expression ax2 + bx + c, where a ≠ 1, is different from factoring x2 + bx + c.
2. Two students factored 2x2 + 6x – 20. Keiko said that the factorization was (2x – 4)(x + 5). Ray gave the factorization as (x – 2)(2x + 10). Confirm that both of these factorizations are correct. Then explain why they are not complete.
3. Explain the relationship between the factors of a quadratic expression, the roots of the related quadratic equation, and the x-intercepts of the graph of the related function.
Answer:
1. Dividing the expressions [tex]ax^2+bx+c[/tex] by a is a different step.
2. Yes, both of these factorization are correct. They are not complete because they can be factored further.
3. The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.
Step-by-step explanation:
1.
To factorize the quadratic expressions [tex]ax^2+bx+c[/tex] first we divide it by a. Then we factorize it same as [tex]x^2+bx+c[/tex].
It means all the steps of factoring a quadratic expressions [tex]ax^2+bx+c[/tex] and [tex]x^2+bx+c[/tex] are same except the first step, i.e., divide the expressions [tex]ax^2+bx+c[/tex] by a.
2.
The given quadratic expression is
[tex]P(x)=2x^2+6x-20[/tex]
[tex](2x-4)(x+5)=2x(x+5)-4(x+5)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)[/tex]
[tex](x-2)(2x+10)=x(2x+10)-2(2x+10)\Rightarrow 2x^2+10x-4x-20=2x^2+6x-20=P(x)[/tex]
The product of factors is equal to the given expression. It means both of these factorization are correct.
They are not complete because they can be factored further.
[tex](2x-4)(x+5)=2(x-2)(x+5)[/tex]
[tex](x-2)(2x+10)=(x-2)2(x+5)[/tex]
3.
If the factored form of a quadratic expression is defined as
[tex](x-a)(x-b)[/tex]
Then the related quadratic equation is
[tex](x-a)(x-b)=0[/tex]
[tex]x=a,b[/tex]
The roots of the quadratic equation are a and b.
The related function is
[tex]f(x)=(x-a)(x-b)[/tex]
The x-intercepts of the function are a and b because at x=a and x=b the value of function is 0.
The roots of the related quadratic equation are the x-intercepts of of the related function and factors of the expression are difference of x and roots of the related quadratic equation.
It should be noted that in order to factorize the quadratic expression, one will have to divide it by a.
FactorizationThe factorization of the quadratic expression ax² + bx + c is different from factoring x² + bx + c as one has to first divide it by a.
Secondly, the factorization by the students isn't complete because they can be factored further.
Lastly, the relationship between the factors of a quadratic expression, the roots of the related quadratic equation is that the roots are the x-intercept of the related function.
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the length of a rectangular floor is 5 feet less than twice it's width. the area of the floor is 150 square feet. what is the width of the room?
There are 147 peaple attending a diner party if each table can seat 7 peaple how many tables are needed for the dinner party?
Solve for "W"
-1 > 2W + 7
-1>2W+7
-8>2w
w = -8/2 = -4
w>-4
Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.
Final answer:
The question asks for the original vector function given its derivative and an initial condition. Through integration and applying the initial condition, the vector function is found to be r(t) = t⁵i + t⁶j + (t²/2 + 1/2)k.
Explanation:
The question involves finding the vector function r(t) given its derivative r'(t) = 5t⁴i + 6t⁵j + t k and an initial condition r(1) = i + j. To find r(t), integrate each component of r'(t) with respect to t. The integration results in:
The i component: ∫5t4 dt = t⁵/1 + C₁The j component: ∫6t5 dt = t⁶/1 + C₂The k component: ∫t dt = t²/2 + C₃Therefore, r(t) = (t⁵/1 + C₁)i + (t⁶/1 + C₂)j + (t²/2 + C₃)k. Substituting t = 1 and using the initial condition r(1) = i + j to find the constants C₁, C₂, and C₃, we get:
C₁ = 0C₂ = 0C₃ = 1/2Finally, r(t) = t⁵i + t⁶j + (t²/2 +1/2) k.
The function [tex]\( r(t) \)[/tex] is:
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]
[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]
To find [tex]\( r(t) \) given \( r'(t) \) and \( r(1) \)[/tex], we need to integrate[tex]\( r'(t) \)[/tex]with respect to ( t ) and then use the given initial condition ( r(1) ) to determine the constant of integration.
Given:
[tex]\[ r'(t) = 5t^4i + 6t^5j + tk \][/tex]
[tex]\[ r(1) = i + j \][/tex]
First, let's integrate [tex]\( r'(t) \)[/tex] with respect to [tex]\( t \)[/tex] to find [tex]\( r(t) \)[/tex]:
[tex]\[ r(t) = \int 5t^4i \, dt + \int 6t^5j \, dt + \int tk \, dt \][/tex]
[tex]\[ r(t) = \frac{5}{5}t^5i + \frac{6}{6}t^6j + \frac{1}{2}t^2k + C \][/tex]
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k + C \][/tex]
Now, we apply the initial condition [tex]\( r(1) = i + j \)[/tex]:
[tex]\[ r(1) = (1)^5i + (1)^6j + \frac{1}{2}(1)^2k + C = i + j \][/tex]
[tex]\[ i + j + \frac{1}{2}k + C = i + j \][/tex]
Comparing the coefficients of [tex]\( i \), \( j \), and \( k \)[/tex], we get:
Coefficient of [tex]\( i \): \( 1 = 1 \)[/tex] (matches)
Coefficient of [tex]\( j \): \( 1 = 1 \)[/tex] (matches)
Coefficient of [tex]\( k \): \( \frac{1}{2} = 0 \)[/tex] (doesn't match)
So, to make the coefficients match, [tex]\( C = -\frac{1}{2} \)[/tex].
Therefore, the function [tex]\( r(t) \)[/tex] is:
[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]
[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]
Jeanie has $500 to spend on dance lessons there's $50 one time registration fee and the lessons cost 35 each how many lessons can Jeanie take
What is the simplified form of 14x^5y^9 divided by 2xy^3
a.Find the perimeter of the triangle.
b.Find the area of the triangle.
c. If tile cost $6 per square centimeter, how much will it cost to tile the triangle?
There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
Answer:
It represents a linear function because there is a constant rate of change.
Step-by-step explanation:
Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.
Here, number of hours represents input value and minutes represents the output value,
Now, By the given table,
The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),
Also,
[tex]\frac{120-60}{2-1}=\frac{180-120}{3-2}=\frac{240-180}{4-3}=\frac{300-240}{5-4}=60[/tex]
⇒ The rate of change output value with respect to input value remains constant,
Hence, It represents a linear function because there is a constant rate of change.
What is the sum of two and two
The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the left three units and up two units.
The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the left three units and up two units.
Explanation:To vertically compress the parent function f(x) = 5x by a factor of one-half, we multiply the function by the compression factor, which is 1/2. So the compressed function is f(x) = (1/2)(5x) = 2.5x.
To shift the function to the left three units, we subtract the shift amount from the x-variable. So the shifted function is f(x + 3) = 2.5(x + 3) = 2.5x + 7.5.
To shift the function up two units, we add the shift amount to the y-variable. So the final transformed function is f(x + 3) + 2 = 2.5x + 7.5 + 2 = 2.5x + 9.5.
In triangle ABC angle c is a right angle find the value of the trig function indicated. find sec A if c=25, a=7
The value of trigonometric function sec A is,
⇒ sec A = 25/24
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In triangle ABC angle c is a right angle.
And, c = 25, a = 7
Now, We can draw the tringle ABC.
And, Find the value of side b by using Pythagoras theorem as;
⇒ c² = a² + b²
⇒ 25² = 7² + b²
⇒ 625 = 49 + b²
⇒ b² = 625 - 49
⇒ b = 24
We know that;
⇒ sec A = Hypotenuse / adjacent
Hence, We get;
⇒ sec A = Hypotenuse / adjacent
⇒ sec A = 25 / 24
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URGENT!!!
Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive bird nests in the trees. The height of the camera above the water can be modeled by the equation
y = -16t^2 + 400, where t represents the seconds after the camera is dropped. How long will it take (in seconds) before Kay sees the splash from the camera hitting the water.
The given equation in this case is:
y = -16 t^2 + 400
We can see that the slope of the equation is negative (-16) which means that the position of Kay is on the positive y-axis , while the bottom of the river is in the origin. This is supported by taking t = 0, the initial y becomes y = 400. Therefore the position of Kay now is at (0, 400).
So to find for the time when the camera hits the water, then y must be zero (t, 0) so we have to find for t in this case.
When y = 0
0 = -16 t^2 + 400
16 t^2 = 400
t^2 = 25
t = 5 s
Therefore it takes 5 seconds for the camera to hit the water and for Kay to see a splash.
Answer:
5 seconds
Step-by-step explanation:
Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive bird nests in the trees. The height of the camera above the water can be modeled by the equation
y = -16t^2 + 400, where t represents the seconds after the camera is dropped.
When splash from the hits the water then the height becomes 0
height is y so we replace y with 0 and solve for t
0 = -16t^2 + 400
Subtract 400 on both sides
-400 = -16t^2
Divide by 16 on both sides
25= t^2
take square root on both sides
t= 5
It takes 5 seconds
12 pounds of apples. Each pounds costs $3. If she gives the cashier two $20 bills, how much change should she receive.
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight? If muscle weight is 90 pounds, how much does the person weigh?
six times the difference between a number and 4 equals the product of the number and -2. find the number.
I just want maybe a reteach for this.
*Solving problems with unknown numbers*
Prove that if a and b are two matrices such that a+b and a*b are both defined, then a and b are square matrices
Which factor do 64x^2+48x+9 and 64x^2 - 9 have in common?
There are 6 students in a small class. To make a team, the names of 2 of them will be drawn from a hat. How many different teams of 2 students are possible?
Evaluate the line integral for x^2yds where c is the top hal fo the circle x62 _y^2 = 9
The school choir has 84 members. The ratio of girls to boys in the color is 3: 4. How many members are girls?
show steps !
For which function is f(x) not equal to f-1(x)?
A- f(x)=2-x
B-f(x)=2/x
C=f(x)=-x
D=f(x)=2x
Answer:
[tex]f(x)= 2x[/tex]
Step-by-step explanation:
For which function is f(x) not equal to f^-1(x)
LEts check with each function, we find out inverse for each option
[tex]f(x)= 2-x[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]y= 2-x[/tex]
[tex]x= 2-y[/tex], Add y on both sides
[tex]x+y= 2[/tex], Subtract x from both sides
[tex]y= 2-x[/tex], Inverse is equal to f(x)
[tex]-f(x)= \frac{2}{x}[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]-y= \frac{2}{x}[/tex]
[tex]-x= \frac{2}{y}[/tex], cross multiply it
[tex]-xy = 2[/tex], divide by x on both sides
[tex]-y= \frac{2}{x}[/tex], Inverse is equal to f(x)
[tex]f(x)= -x[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]y= -x[/tex]
[tex]x=-y[/tex], Add y on both sides
[tex]x+y= 0[/tex], Subtract x from both sides
[tex]y=-x[/tex], Inverse is equal to f(x)
[tex]f(x)= 2x[/tex]
Replace f(x) by y, then switch the variables and solve for y
[tex]y= 2x[/tex]
[tex]x= 2y[/tex], divide by 2 on both sides
[tex]\frac{x}{2}=y[/tex], Inverse is not equal to f(x)
4% of what number is 6
4% = 0.04
divide 6 by 0.04 = 150
6 is 4% of 150
double check 150*0.04 = 6
Polk elementary school has three classes for each grade level kindergarten through fifth grade if there is an average of 27 students per class about how many students attend Polk school
Write the given system without the use of matrices. d/dt (x y z) =( 1 −1 6 3 −8 1 −2 7 5) (x y z) + (1 2 2)
The waitress and hostess at a restaurant share the tips at the end of every shift. Between the two of them, they earn an average of $75 in tips. The waitress take $55 and the hostess takes $20. If they continue to earn money at this rate, how much will the waitress receive if they earn $300 at the end of their next shift?
thy get 55/75 and you want to know x/300
55/75 x X/300
cross multiply 55 x 300 = 16500
divide that by 75
16500/75 = 220
x = 220
they will get $220
Jan needed to empty 18 gallons of water from a tub into jugs that hold 0.5 gallons of water. How many jugs did Jan need?
divide 18 by 0.5
18/0.5 = 36
36 jugs are needed
How to find two fractions between 1/2 and 1/3