Step-by-step explanation:
all real numbers greater than our equal to -1.
as the parabola function is y = something in x², the parabola opens up either up or down.
if the function would have been x = something in y², the parabola would open left or right.
but our parabola here opens therefore up and down.
the vertex is therefore the maximum or minimum of the parabola. y does not get larger or smaller than the y value of the vertex.
as we see that the curve goes through points with y value 0 (which is clearly larger than -1), it means the vertex is a minimum, and the parabola opens up.
therefore the answer at the beginning. any y value of the function can only be greater than or equal to -1.
13. What value of b would make the function f (x)- Ibal stretch horizontally by a
factor of 4 and reflect across the y-axis?
Answer:
give me those points boy=o >:)
Step-by-step explanation:
While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function
f
(
x
)
=
b
x
by a constant
|
a
|
>
0
. For example, if we begin by graphing the parent function
f
(
x
)
=
2
x
, we can then graph the stretch, using
a
=
3
, to get
g
(
x
)
=
3
(
2
)
x
and the compression, using
a
=
1
3
, to get
h
(
x
)
=
1
3
(
2
)
x
.
Aviva's pay stub shows gross earnings of $662.30 for a week. Her regular rate of pay is $10.80 per hour for a 35 hour week and overtime is paid time and a half regular pay. How many Hours did she work
Number of hours Aviva's work for gross earnings of $662.30 for a week with regular rate of $10.80 per hour for 35 hour week and 1.5 of regular pay for overtime is 52.6hours.
Given,
Gross earning for week=$662.30
Regular rate per hour for 35hour week=$10.80
Overtime rate=1.5×(10.80)
For 'h' number of hours
(10.80×35)+(10.80×1.5) h=$662.30
⇒378 +16.20h=662.30
⇒h=284.30/16.20
⇒h≈17.6hours
Number of hours Aviva's work=35 +17.6
=52.6hours
Therefore, number of hours Aviva's work for gross earnings of $662.30 for a week with regular rate of pay $10.80 per hour for a 35 hour week and 1.5 of regular pay for overtime is 52.6hours.
Learn more about number here
brainly.com/question/17429689
#SPJ1
Question
The value of y varies directly as a, and y = 2 when x = 8. Find the equation represents this relationship.
Optionally you can replace 0.25 with the fraction 1/4
===================================================
Explanation:
The variable y varies directly with x, which means we have the template of y = kx for some constant k.
Plug in x = 8 and y = 2. Then solve for k
y = kx
2 = k*8
8k = 2
k = 2/8
k = 1/4
k = 0.25
Therefore, we go from y = kx to y = 0.25x
-------------
Check:
Plugging in x = 8 should get us to y = 2
y = 0.25x
y = 0.25*8
y = 2
The answer is confirmed.
(a) Write a formula for the distance between the points (x,y) and (4,6)
(b) If the distance
between above points is 9 units, write an equation.
Whats (500 x 2) divided by 2?
Answer:
500
Step-by-step explanation:
500*2=1000
1000/2=500
Solve the nonlinear inequality. Expr
x³-9x>0
(-3,0) U (3,00)
Graph the solution set.
How would I graph this on a number line ?
Answer:
x∈(-3;0)∪(3;+∞).
Step-by-step explanation:
1) if to solve the inequality x³-9x>0, then
x(x-3)(x+3)>0, and solution is
x∈(-3;0)∪(3;+∝).
2) the graph is provided in the attachment (it is marked with red colour).
explain how to write 50,000 using exponents
Explanation:
Place the decimal point between the first two digits to get 5.0
Then we must move the decimal point 4 spots to the right to get back to 50,000
So that's where the "4" comes in with the 10^4
This means 50,000 = 5 * 10^4 which is in scientific notation.
The answer in scientific notation is 5 times 10^4
The exponent of four tells you to multiply 10 by itself 4 times.
10 x 10 = 100 x 10 = 1000 x 10 = 10000
And 10000 times 5 is equal to 50,000.
Is (0, 3) a solution to the equation y=x+3? (1 point)
O yes
Ono
Answer: Yes, it is.
Step-by-step explanation:
given: x is 0 and y is 3. Plug in the equation and solve
y=x+3
3=0+3
3=3
Yes, it is a solution
4.
Juan was competing in a 1000 meter
race. He had to pull out of the race after
running 3/4 of it. How many meters did
he run?
Answer:14
Step-by-step explanation:
Step-by-step explanation:
B is the midpoint of AC, in other words it is the halfway point.
So A to B should be equal to B to C
Our expression is:
2x + 9 = 37
Subtract 9
2x = 28
Divide by 2
x = 14
Answer:
750
Step-by-step explanation:
3/4 is 75%
Juan did 75% of the 1000 meters meaning he did 750
To get the answer u just do (3/4)*1000 and you get 750
2/3x=6
a. x=9
b. x=4
c. x=18
d. x=12
option (a) x = 9
Step-by-step explanation:
2/3x = 6
2x = 18
x = 18/2
x = 9.
Find the solutions to x² = 28.
A. x=+7√2
OB. x=+2√/14
OC. x=+14√2
X
OD. x=+2√7
X
Answer:
x=+2√7
Step-by-step explanation:
Juan and Mahdi are to run a race, but Juan can run 18 meters per second, whereas Mahdi can run 6 meters per second. If Mahdi has a 228 -meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? Round your answer to the nearest whole number.
Answer:
19 seconds
Step-by-step explanation:
You want to know the time it takes for Juan, running 18 m/s, to overtake Mahdi, running 6 m/s, if Mahdi has a 228 meter head start.
Closing timeThe time to close the gap between the runners will be ...
time = distance/speed
time = (228 m)/(difference in speeds) = (228 m)/(18 m/s -6 m/s)
time = (228 m)/(12 m/s) = (228/12) s = 19 s
It will take Juan 19 seconds to catch Mahdi.
__
Additional comment
The fastest human runner will not exceed 12.3 meters per second, especially over a 300+ meter distance.
In general, a
person is 1% shorter in the evening than in the
morning. Use your height to write a conditional
that uses this fact.
The conditional statement is that; If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.
How to write conditional statements?
First, we will calculate how much is one percent of your height and then subtract that percentage from the total height to get your" height in the evening".
For example:
If my height is 1.64 m, then;
0.01 * 1.64 m = 0.0164 m
Step 2 is;
1.64m - 0.0164m = 1.62326 m
Now, using these height, let's write a conditional that uses the described fact:
Conditional:
If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.
Read more about Conditional Statement at; https://brainly.com/question/11073037
#SPJ1
List 5 questions you would ask if your conducting a parent teacher conference ik its not math but i need help i will mark brainlest
Describe the features of a Cartesian Plane in terms of its axes, the direction of the axes and its centre.
Answer:
A Cartesian Plane is a plane in Geometry which is an flat surface of infinite size. It has two number lines that intersect at right angles at their zeros. One number line is horizontal, and the other number line is vertical. The point of intersection is the zero of each line. In the horizontal line, the numbers increase to the right. In the vertical line, the numbers increase up. The horizontal line is called the x axis. The vertical line is called the y axis. The center of the Cartesian Plane is the intersection of the two axes, the two number lines, and is called the origin. Points on the Cartesian Plane are described with two numbers in parentheses separated by a comma. The position of the point in the Cartesian Plane is given by the first number, called the x-coordinate, telling us the number of units to the right (positive) or left (negative) of the origin and by the second number, called the y-coordinate, telling us the number of units up (positive) or down (negative) from the origin.
SOLVE. y''+3y'+2y=4e^x cos3x
Solve the homogeneous equation
[tex]y'' + 3y' + 2y = 0[/tex]
Its characteristic equation is
[tex]r^2 + 3r + 2 = (r + 1) (r + 2) = 0[/tex]
with roots at [tex]r=-1[/tex] and [tex]r=-2[/tex], hence the characteristic solution is
[tex]y_c = C_1 e^{-x} + C_2 e^{-2x}[/tex]
For the nonhomogeneous equation, I'll use variation of parameters. We're looking for a solution of the form
[tex]y = u_1 y_1 + u_2 y_2[/tex]
to the equation
[tex]y'' + a(x) y'' + b(x) y = f(x)[/tex]
such that
[tex]\displaystyle u_1 = - \int \frac{y_2f(x)}{W(y_1,y_2)} \, dx[/tex]
[tex]\displaystyle u_2 = \int \frac{y_1 f(x)}{W(y_1,y_2)} \, dx[/tex]
The Wronskian [tex]W(y_1,y_2)[/tex] of the two fundamental solutions [tex]y_1=e^{-x}[/tex] and [tex]y_2=e^{-2x}[/tex] is
[tex]W(y_1,y_2) = \begin{vmatrix} y_1 & y_2 \\ {y_1}' & {y_2}' \end{vmatrix} = -e^{-3x}[/tex]
Then we have
[tex]\displaystyle u_1 = - \int \frac{e^{-2x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = 4 \int e^{2x} \cos(3x) \, dx[/tex]
[tex]\displaystyle u_2 = \int \frac{e^{-x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = -4 \int e^{3x} \cos(3x) \, dx[/tex]
Recall Euler's identity,
[tex]e^{(a+bi)t} = e^{at} (\cos(bt) + i \sin(bt))[/tex]
Then we have the general antiderivative
[tex]\displaystyle \int e^{(a+bi)t} \, dt = \frac1{a+bi} e^{(a+bi)t} + C = \frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C[/tex]
Taking the real parts of both sides, we have
[tex]\displaystyle \mathrm{Re}\left\{\int e^{(a+bi)t} \, dt \right\} = \mathrm{Re}\left\{\frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C\right\} \\\\ \int\,\mathrm{Re}\left\{e^{(a+bi)t}\right\} \, dt = \frac{e^{at}}{a^2+b^2} \mathrm{Re}\left\{(a-bi)(\cos(bt) + i \sin(bt))\right\} + C \\\\ \int e^{at} \cos(bt) \, dt = \frac{e^{at}}{a^2+b^2} (a\cos(bt)+b\sin(bt)) + C[/tex]
so that
[tex]\displaystyle u_1 = 4 \int e^{2x} \cos(3x) \, dx = \frac{4e^{2x}}{13} (2\cos(3x) + 3 \sin(3x))[/tex]
and
[tex]\displaystyle u_2 = -4 \int e^{3x} \cos(3x) \, dx = -\frac{2e^{3x}}3 (\cos(3x) + \sin(3x))[/tex]
We've found
[tex]y = u_1 y_1 + u_2 y_2[/tex]
[tex]\displaystyle y = \frac{4e^x}{13} (2\cos(3x) + 3 \sin(3x)) - \frac{2e^x}3 (\cos(3x) + \sin(3x))[/tex]
[tex]\displaystyle y = \frac2{39} e^x (5\sin(3x) - \cos(3x))[/tex]
Then the general solution to the differential equation is
[tex]\boxed{y(x) = C_1 e^{-x} + C_2 e^{-2x} + \frac2{39} e^x (5\sin(3x) - \cos(3x))}[/tex]
(100 points!) What is the slope-intercept form for the following equation?
x + 5y = 12
Questions:
x= 5y + 12
y= -1/5x + 12/5
x + 5y = 12x
5y= −x + 12
Answer:
the slope intercept form is 5y= -x+12
Divide the following and then check by multiplying.
48,845
405
Answer:
The given Divisor = 405 and Dividend = 48849
The Quotient is 120 and the Remainder is 249
Hope it helps you
1/2(x+4)=1/2x+1 is there a solution
the points on the table are in a line what is the slope
Answer:
the slope of the table is -0.857
Acme Movers charges $105 plus $40 per hour to move household goods across town. Hank's Movers charges $55 per
Khour. For what lengths of time does it cost less to hire Hank's Movers?
It costs less to hire Hank's Movers for times less than
hours.
Incom
It costs less to hire Hank's Movers for times less than 7 hours.
What time would it cost less to hire Hank Movers?
The equation that can be used to represent the cost of hiring Acme movers is: $105 + $40t
The equation that can be used to represent the cost of hiring Hank's Movers : $55t
Where : t represent number of hours
The inequality sign that would be used is < less than or equal to
$55t < $105 + $40t
Combine similar terms
$55t - $40t < $105
$15t < $105
t < 105 / 15
t < 7 hours
To learn more about inequality, please check: https://brainly.com/question/5031619
#SPJ1
Three friends want to buy a DVD that costs $17.49, including tax. The friends agree to pay an equal amount. Each friend will pay??
help meee!!!!
Answer:
5.83
Step-by-step explanation:
You just divide the total amount by 3
Answer:
Each will pay $5.83
Step-by-step explanation:
Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 71 and a standard deviation of 5. Find the percent of juniors whose score is at least 71. % of juniors scored at least 71.
The percent of juniors whose score is at least 71 % is 69.15 %.
We are given that:
Test of the students are normally distributed.
Mean = μ = 71
Standard deviation = σ = 5
We need to find the percent of juniors whose score is at least 71 %.
Now, we know that:
z = ( x - μ) / σ
z = 100 - 71 / 5
z = 29 / 5
z = 5.8
So, percentage = 69.15 %
Therefore, we get that, the percent of juniors whose score is at least 71 % is 69.15 %.
Learn more about percent here:
https://brainly.com/question/843074
#SPJ9
Erica is participating in a road race. The first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25∘ north of east. The road then turns due north for another 6.0 mi to the finish line.
In miles, what is the straight-line distance from the starting point to the end of the race?
The distance between the starting point(initial) and the ending point(last) is known as displacement is 9.46miles.
What is displacement?
Displacement is defined as the change in position of an object. It's a vector volume and has a direction and magnitude. It's represented as an arrow that points from the starting position to the final position. For illustration- If an object moves from A position to B, also the object's position changes. Distance is a scalar volume that refers to" how important ground an object has covered" during its stir. Displacement is a vector volume that refers to" how far out of place an object is" it's the object's overall change in position. Displacement is a defense medium that involves an individual transferring negative heartstrings from one person or thing to another.In the first(1st) part of the race displacement of Erica is
d1 = 5.2 miles at 25(twenty-five) deg North of East
x(ax) and y-component of 1st(first) part of the race will be:
d1 = 5.2*cos 25(twenty five) deg i + 5.2*sin 25(twenty five) deg j
d1 = (4.71 i + 2.20 j) miles (this id d1)
In the second(2nd) part of the race
d2 = 6(six) miles towards north,
So
d2 = (6 j) miles (this is d2)
Now net(accurate) displacement of Erica will be, Using Vector addition(summation):
d = d1(4.71 i + 2.20 j) + d2(6j)
d = (4.71 i + 2.20 j) +(sum) (6 j)
d = 4.71 i +(sum) 8.20 j
So Magnitude of net(accurate) displacement will be:
|d| = [tex]\sqrt{4.71^2+8.20^2}[/tex]
|d| = 9.46 miles(nine.four-six) = distance between starting(initial) point and ending point
Learn more about displacement here: https://brainly.com/question/14422259
#SPJ9
In Ms. Block's class 8 students share a box of cherries equally. Each of them receives 9 cherries. There are
then 6 cherries left over. How many cherries were there altogether in the box?
Answer: 78
Step-by-step explanation:
first, you multiply 8 by 9 then you get 72, and then you can add the leftover cherries with 72 so 72 + 6 = 78
Answer:
Step-by-step explanation:
78
Describe the end behavior of each polynomial.
(a) The leading coefficient is positive and the degree is odd, so:
As x approaches infinity, y approaches infinity.As x approaches negative infinity, y approaches negative infinity.(b) The leading coefficient is negative and the degree is even, so:
As x approaches infinity, y approaches negative infinity.As x approaches negative infinity, y approaches negative infinity.A business has a budget of $720 to spend on their marketing campaign. Each month, x, the business spends $40 on different advertisements. The amount of money remaining in the budget
for marketing can be modeled by the function Mx)=-40x+720. Based on the graph of the linear function M(x) and the context of the problem, what is the domain?
O [10, 18]
O [10, 720]
0 [10, 8]
O [R]
A reasonable domain for this function is [0, 18)
Domain of a functionThe domain of a function is a value of the independent variable of the function for which it exists.
Given the equation below:
M(x)= -40x+720
Since the function represents the The amount of money remaining in the budget for marketing then the function f(x) must be greater than zero;
−40x + 720 > 0
-40x> -720
x < 720/40
x < 18
This shows that a reasonable domain for this function is [0, 18)
Learn more on domain of a function here: https://brainly.com/question/26098895
#SPJ1
i need some help please help
3x + 1<10
The value of x from the inequality is x < 3
What is an inequality?An inequality is defined as a statement of an order relationship between two numbers or algebraic expressions.
Given the inequality;
3x + 1 < 10
To determine the solution, we take the followings steps;
collect like terms
3x < 10 - 1
Find the difference between the terms
3x < 9
Make 'x' the subject of formula
x < 9/ 3
x < 3
Thus, the value of x from the inequality is x < 3
Learn more about inequalities here:
https://brainly.com/question/25275758
#SPJ1
A line passes through the point point (-6, -5) and has a slope of - 4/3. Write an equation in slope-intercept firm for this line.
The equation in slope-intercept firm for this line is y = -4/3x - 13
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the linear equation?The given parameters are
Slope, m = -4/3
Point (x1, y1) = (-6, -5)
The linear equation is calculated as
y = m(x - x1) + y1
So, we have
y = -4/3(x + 6) - 5
Open the bracket
y = -4/3x - 8 - 5
Evaluate the difference
y = -4/3x - 13
Hence, the equation in slope-intercept firm for this line is y = -4/3x - 13
Read more about linear equations at
https://brainly.com/question/14323743
#SPJ1
find the area of 8in 5in 4in 4in 10in 6in
By decomposing the figure into simpler ones, we conclude that the area of the irregular figure is 108 square inches.
How to find the area of the irregular figure?
Here we have an irregular figure that can be decomposed into 3 simpler figures, these are:
A rectangle of 6 inches by 8 inches (the top one).A rectangle of 10 inches by 4 inches (the one in the middle).A rectangle of 5 inches by 4 inches (the one at the right).Remember that the area of a rectangle is the product between the two dimensions, so the areas of these 3 rectangles are:
a = 6in*8in = 48in^2
a' = 10in*4in = 40in^2
a'' = 5in*4in = 20in^2
Adding these areas we get:
48in^2 + 40in^2 + 20in^2 = 108 in^2
The area of the irregular figure is 108 square inches.
If you want to learn more about areas:
https://brainly.com/question/24487155
#SPJ1
