Answer:
3x²
Step-by-step explanation:
3x²
They would all reduce to 1, 2x^4, and -4x
Quadratic below
2^2−7−4
Vertex -
Y-Intercept -
X-Intercept -
Answer:
The y-intercept is y = -4.
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
Step-by-step explanation:
Quadratic equation:
Has the following format:
[tex]y = ax^2 + bx + c[/tex]
The y-intercept is c.
Finding the x-intercepts:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
In this question:
The quadratic equation is [tex]2x^2 - 7x - 4[/tex], which has [tex]a = 2, b = -7, c = -4[/tex]. This means that the y-intercept is y = -4.
x-intercepts:
[tex]\Delta = (-7)^2-4(2)(-4) = 81[/tex]
[tex]x_{1} = \frac{-(-7) + \sqrt{81}}{2*2} = 4[/tex]
[tex]x_{2} = \frac{-(-7) - \sqrt{81}}{2*2} = -\frac{1}{2}[/tex]
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
Vertex:
[tex]x_{v} = -\frac{(-7)}{2*2} = \frac{7}{4}[/tex]
[tex]y_{v} = -\frac{81}{4(2)} = -\frac{81}{8}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
A flashlight flashes every 45 seconds. After 10 ½ minutes, how many times does the light flash?
Answer:
14
Step-by-step explanation:
Answer:
14 flashes.
Step-by-step explanation:
1 minute = 60 seconds
x minutes = 45 seconds.
1/x = 60/45 Cross multiply
60x = 45 Divide by 60
x = 45/60
x = .75
10 1/2 minutes = 10.5 minutes.
x flashes / 10.5 minutes = 1 flash / 0.75 minutes Multiply by 10.5
x = 10.5/0.75
x = 14
plz answer these questions without putting links and files
what is 3/4 multiplied by 1/2 then add 3/4
what is 1 and 1/8 multiplied by 1/2 then add 3/4
Answer:
11/8 and 21/16
Step-by-step explanation:
3 x 1 = 3
4 x 2= 8
3/8+3/4(convert to eighth's)
3/8+6/8=11/8
1 1/8 = 9/8
9 x 1 = 9
8 x 2 = 16
9/16+3/4(convert to sixteenth's)
9/16+12/16
21/16
---
hope it helps
=3/4 × 1/2 + 3/4
=3/8 + 3/4
=9/8
2nd questions ans
=1×1/2 + 3/4
=1/2 + 3/4
=5/4
the suppliment angle of 3 by 4 of 160 ° is
How to find the perimeter of a rectangle ,when given the area of the rectangle?
Answer:
120 m
Step-by-step explanation:
Width - x
Length - 5x
x*5x = 500m²
5x² = 500 m²
x²= 500 ÷ 5
x²= 100
x = root 100
x = 10
Therefore width = 10
length 5*10 = 50
Perimeter = 2(l+w)
= 2(10 + 50)
=2*60
=120
Determine the amplitude of the trigonometric function: *attached image*
Answer:
[tex]\displaystyle 2[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = -2cos\:(\frac{\pi}{3}x - \frac{2}{3}\pi) + \frac{1}{2}} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow \frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{2} \hookrightarrow \frac{\frac{2}{3}\pi}{\frac{\pi}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6} \hookrightarrow \frac{2}{\frac{\pi}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle \boxed{y = -2sin\:(\frac{\pi}{3}x - \frac{\pi}{6}) + \frac{1}{2}} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow \frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{1}{2}} \hookrightarrow \frac{\frac{\pi}{6}}{\frac{\pi}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{6} \hookrightarrow \frac{2}{\frac{\pi}{3}}\pi \\ Amplitude \hookrightarrow 2[/tex]
As you can see, the right-centred photograph displays the trigonometric graph of [tex]\displaystyle y = -2cos\:\frac{\pi}{3}x + \frac{1}{2},[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will horisontally shift and map the graph onto the sine graph [photograph farthest to the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so be very careful with your calculations. So, between the two photographs, we can tell that the cosine graph [centre right photograph] is shifted [tex]\displaystyle 2\:units[/tex]to the left, which means that in order to match the sine graph [photograph farthest to the left], we need to shift the graph FORWARD [tex]\displaystyle 2\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you get [tex]\displaystyle \boxed{2} = \frac{\frac{2}{3}\pi}{\frac{\pi}{3}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = -2cos\:(\frac{\pi}{3}x - \frac{2}{3}\pi) + \frac{1}{2}.[/tex]Intermediate, we have two sine graphs to deal with [centre left photograph and the photograph farthest to the left]. The left-centred photograph displays the trigonometric graph of [tex]\displaystyle y = -2sin\:\frac{\pi}{3}x + \frac{1}{2}.[/tex]So, just like before, we need to figure out the appropriate C-term that will horisontally shift the graph back into position ["position", meaning shifting this sine graph back in plase (matching the sine graph in the photograph on the left)]. So, between the two photographs, we can tell that the left-centred sine graph is shifted [tex]\displaystyle \frac{1}{2}\:unit[/tex]to the left, which means that in order to match the leftward sine graph, we need to shift the graph FORWARD [tex]\displaystyle \frac{1}{2}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you get [tex]\displaystyle \boxed{\frac{1}{2}} = \frac{\frac{\pi}{6}}{\frac{\pi}{3}}.[/tex]So, when shifted back into original position, the sine graph is [tex]\displaystyle y = -2sin\:(\frac{\pi}{3}x - \frac{\pi}{6}) + \frac{1}{2}.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-2\frac{1}{2}, \frac{1}{2}],[/tex]from there to [tex]\displaystyle [3\frac{1}{2}, \frac{1}{2}],[/tex]they are obviously [tex]\displaystyle 6\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 6.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, and to be certain, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = \frac{1}{2},[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. Now... the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
What is the slope of line a?
Given:
The graph of a line a.
To find:
The slope of the line a.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given graph it is clear that the line a passes through the points (-1,1) and (0,-2). So, the slope of the line a is:
[tex]m=\dfrac{-2-1}{0-(-1)}[/tex]
[tex]m=\dfrac{-3}{1}[/tex]
[tex]m=-3[/tex]
The slope of the line a is -3. Therefore, the correct option is C.
x=21 is a solution to the inequality26≤ 2 + x
true or false
Answer:
FalseStep-by-step explanation:
Isolate by the x from one side of the equation.
First, you have to switch sides.
[tex]\sf{2+x\geq 26}[/tex]
Then, subtract by the 2 from both sides.
[tex]\sf{2+x-2\geq 26-2}[/tex]
Solve.
Subtract.
[tex]26-2=24[/tex]
[tex]\large\boxed{x\geq 24}[/tex]
The answer should be false.
Solve the system of equations.
{y=30x+10y=5x2−25
I need major help!!! Please!!!!
If y varies directly as x and y = 24 when
x= 16, what is y when x = 50?
Answer:
[tex]y = 75[/tex]
Step-by-step explanation:
Given
[tex]y\ \alpha\ \ x[/tex]
[tex]y=24; x =16[/tex]
Required
Find y when [tex]x = 50[/tex]
We have:
[tex]y\ \alpha\ \ x[/tex]
Express as equation
[tex]y = kx[/tex]
Solve for k
[tex]k = \frac{y}{x}[/tex]
When [tex]y=24; x =16[/tex]
[tex]k = \frac{24}{16}[/tex]
[tex]k = \frac{3}{2}[/tex]
When [tex]x = 50[/tex], we have:
[tex]y = kx[/tex]
[tex]y = \frac{3}{2} * 50[/tex]
[tex]y = 75[/tex]
What is the period of the parent cosine function, y=cos(x)? degrees
What is the period of the cosine function shown in the graph? degrees
Answer: first 360 second 1080 third horizontal stretch
Step-by-step explanation:
The period of this parent cosine function [y=cos(x)] is equal to 360 degrees.
What is the period of a cosine function?The period of a cosine function can be defined as the overall length of the interval of values on the x-axis over which a graph lies and it's repeated. Mathematically, the period of this parent cosine function [y=cos(x)] is given by:
T = 2π/A
Where:
A is the coefficient of the x.When A = 1, we have:
T = 2π/1 = 360 degrees.
For the graphed function, the period of this cosine function is given by:
T = 6π
T = 6 × 360
T = 1080 degrees.
Read more on cosine function here: https://brainly.com/question/4599903
Mandy is shopping for plates. She is trying to decide between the three packages below. If Mandy is looking for the best deal for each individual plate, which package should she buy
Answer:
Package 3
Step-by-step explanation:
Package 1,
No. of plates = 5
Cost = $38.75
Cost of 1 plate = [tex]\dfrac{38.75}{5}=\$7.75[/tex]
Package 2,
No. of plates = 8
Cost = $58
Cost of 1 plate = [tex]\dfrac{58}{8}=\$7.25[/tex]
Package 3,
No. of plates = 14
Cost = $94.5
Cost of 1 plate = [tex]\dfrac{94.5}{14}=\$6.75[/tex]
The cost of 1 plate in package 3 is the least. It means she should buy package 3.
help I want to understand how to do this
9514 1404 393
Answer:
arc RS = 100°RS is a minor arcarc ST = 80°Step-by-step explanation:
The measure of an arc of a circle is the same as the measure of the central angle it subtends. That is, arc RS has the same measure as central angle RPS, which is marked as 100°.
Of course, the total of all central angles, hence all arcs, of a circle is 360°. A diameter of a circle cuts the circle in half, so each semicircle has a central angle measure and arc measure of 180°.
Any arc that is more than a semicircle is called a "major" arc. If it is less than a semicircle, it is a "minor" arc. Arcs RS and ST are minor arcs.
As always in geometry, the whole is the sum of the parts, so arcs RS and ST are supplementary. They total the measure of semicircle RST, which is 180°. Then ST = 180° -RS = 180° -100° = 80°.
__
Additional comment
Usually, an arc identified only by its end points is a minor arc. If the major arc is intended, then it will either be described as "major arc RS" or a point on the major arc will be given, as "arc RTS". The measure of arc RTS is 280°.
johns rent is $1,355. what is his standardized z-score
Answer:
His standardized z-score is [tex]Z = \frac{1355 - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean price of rents and [tex]\sigma[/tex] is the standard deviation for price of rents.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Johns rent is $1,355.
This means that [tex]X = 1355[/tex]
What is his standardized z-score
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1355 - \mu}{\sigma}[/tex]
His standardized z-score is [tex]Z = \frac{1355 - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean price of rents and [tex]\sigma[/tex] is the standard deviation for price of rents.
Click on the measure of angle s.
38°
) 152
142
38
52
Answer:
here,
38+X=180 (being straight line)
or,X=180-38
therefore, X=142 ans,,,
A billboard is 5.0 m by 2.5 m. A scale diagram of the billboard is 0.25 m by
0.125 m.
a.
1:
Calculate the scale.
b. Calculate the scale factor (k).
c.
Is this a reduction or enlargement? Justify your thinking.
Pls help
Answer:
A the answer is a because i was just working on that rn
Step-by-step explanation:
PLEASE HELP ASAP
Mr. Green has a class of 15 students. He can spend $20 on each student to buy math supplies for the year. He first buys all of his students calculators, which
costs a total of $144.75. After buying the calculators, how much does he have left to spend on each student?
Answer:
10.35
Step-by-step explanation:
He has $300 (15x$20). He spends 144.75. He has 155.25 in total. That leaves 10.35 (155.25/15) to spend on each student.
Factor 3x2 + 42x + 147 completely.
A) 3(x + 1)(x + 49)
B) (3x + 21)(x + 7)
C) 3(x + 7)2
D) (3x + 7)2
Ben rented a car. It cost $30.00 plus $0.25 per mile. If Ben paid $85.00 for the car rental, how many miles did he drive the car? Write an equation and then use your equation to find your answer.
Answer:
220 miles
Step-by-step explanation:
85-30=55
55/.25=220
220 = miles
Answer:
Equation:
30 + 0.25x = 85
Work:
30 + 0.25x = 85
85 - 30 = 55
55 / 0.25 = 220
Final answer:
200 miles
Step-by-step explanation:
Hope this helped and have a nice day!!!
please help i dont get it
Which team has the shortest player? Explain.
Which team has the tallest player? Explain.
Which box plot has the greater IQR? Explain.
Ms.A thinks that the 25% of the NY Knicks are at least 74 inches tall. Do you agree or disagree?
Explain using mathematical reasoning.
Ms.T rann thinks that 1the NY Knicks has a larger spread than Liverpool. Do you agree or disagree? Explain using mathematical reasoning.
Answer:
1. the team of Liverpool FC has the shortest player because the minimum is 64.
2. ny Knicks has the tallest player with a height of 84.
3. the NY Knicks box has the largest IQR because 82 - 74 = 8.
MS. A is wrong bc the 75% of players are taller than 74 inches.
Step-by-step explanation:
Fun Fact that has nothing to do with this:
The Beatles meet in Liverpool.
I need the answer pls I really neeed it
In how many ways can the letters A, C, E, G, K, S be arranged
Answer:720
Step-by-step explanation:Now let's imagine we are filling them with letters. There are six places we can put the first letter, so after we've placed one letter, we have six different outcomes.
There are then five remaining gaps for the second letter, so we have 5*6=30 different outcomes after two letters.
There are four spaces for the third letter, three for the fourth letter, two for the fifth letter and finally we have to put the sixth letter in the remaining gap.
So we end up with 6*5*4*3*2*1=720 ways to arrange six different letters.
This is called the factorial function, and is denoted by an exclamation mark. The factorial function is defined as the number of ways to arrange n different options and is calculated as n! = 1*2*3*…*(n-1)*n, with a extra bit that 0!=1 as there is one way to arrange a set of 0 objects (this comes into play later in statistics).
Which of the following would be in the solution set for x < 4
Group of answer choices
4
-4
4.2
4.002
Answer:
- 4
Step-by-step explanation:
The set of all possible value that would make the above statement true must be less than 4.
Therefore the only option we have is -4
Nigel, Gina, and Kamal bought dog supplies.
Each person spent between $15 and $20.
Nigel bought 4 items.
Gina bought 5 items.
Kamal bought 2 items.
The prices of the items are given below. Drag items to each box to show what each person could have bought.
PLEASE HELP I BEG YOU
Answer:
5 items: 1 dog bone, 3 water bowls, 1 collar
4 Items: 3 Water bowls, 1 Box Of Dog Food
2 items: 1 box of dog food, 1 collar
Whats the Diameter? I really need help understanding this
Answer:
1.8 in.
Step-by-step explanation:
Hi there!
1) Determine the radius of the base
[tex]V=\frac{1}{3} \pi r^2h[/tex] where r is the radius of the base and h is the height of the cone
Plug in the known values (h=4.2, V=3.6)
[tex]3.6=\frac{1}{3} \pi r^2(4.2)[/tex]
Isolate r; divide both sides by 4.2
[tex]\frac{3.6}{4.2} =\frac{1}{3} \pi r^2\\\frac{6}{7} =\frac{1}{3} \pi r^2[/tex]
Multiply both sides by 3
[tex]\frac{6}{7}*3 =\pi r^2\\\frac{18}{7}=\pi r^2[/tex]
Divide both sides by π
[tex]\frac{18}{7\pi }=r^2[/tex]
Take the square root of both sides
[tex]\sqrt{\frac{18}{7\pi }} =r[/tex]
2) Determine the diameter
Now that we have the radius, to find the diameter, multiply r by 2:
[tex]d=\sqrt{\frac{18}{7\pi }}*2\\d=1.8[/tex]
Therefore, the diameter is 1.8 in. when rounded to the nearest tenth.
I hope this helps!
Answer:
1.8 in
Step-by-step explanation:
we know the equation for the volume of a cone is pi*r^2 h/3=3.6
pi r^2 *4.2=10.8
solve for r
r is about 0.9 so diameter is 1.8 in
Plz help me well mark brainliest if correct.............
Answer:
Yup, 11 is the answer. because 4 -15 is 11.
I would greatly appreciate if you could solve this 4 me. Thank you!
Answer:
B would be your Answer
Step-by-step explanation:
There are three 2s, one 2 1/4, three 2 1/2, two 2 3/4, and one 3 (which is all displayed on B).
Hope this helped :)
28518
43600
兄YTON
g3627
What is X + 9 < 5 =
Answer:
x<-4
Step-by-step explanation:
x+9<5
-9 -9
x<-4
1. subtract the 9 on both sides to have x alone
The volume of the cylinder is 13,665.28 cm³ and the height is 17 cm what is the radius
Answer:
V = π²h
r = √V/πh
r = √13,665.28cm³/(3.14)(17cm)
r =√13,665.28/53.38 cm
r = √256 cm
r = 16 cm