Answer:
[tex]a_{n}[/tex] = n + 3Step-by-step explanation:
Each number increases by 3. Therefore, n+3.
Topic: The Quadratic Formula
Progress:
The movement of the progress bar may be uneven becouse questions can be worth more or less (including zero) depending
your answer
Match each equation on the left with the number and type of its solutions on the right.
x + 3x – 4= 0
two complex (nonreal) solutions
x2 + 3x + 4 = 0
two real solutions
4x² + 1 = 4x
one real solution
Clear
Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your
the target before Feleasing. The target will highlight or the cursor will change. Need help? Watch this vide
Answer:
Step-by-step explanation:
The quadratic formula for a equation of form
ax²+bx + c = 0 is
[tex]x= \frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]
For the first equation,
x²+3x-4=0,
we can match that up with the form
ax²+bx + c = 0
to get that
ax² = x²
divide both sides by x²
a=1
3x = bx
divide both sides by x
3 = b
-4 = c
. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.
Plugging our values into the equation, we get
[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1[/tex]
as our possible solutions
Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.
Next, we have
x²+3x+4=0
Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus
[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\[/tex]
Because √-7 is not a real number, this has no real solutions. However,
(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions
Finally, for
4x² + 1= 4x,
we can start by subtracting 4x from both sides to maintain the desired form, resulting in
4x²-4x+1=0
Then, a=4, b=-4, and c=1, making our equation
[tex]x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2[/tex]
Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution
Is it true that every whole number is a solution of x > 0? Use complete sentences to explain your reasoning.
Whole numbers are natural numbers, and natural numbers do not include negatives, decimals, fractions, or roots, so all whole numbers can indeed satisfy the inequality.
Instructions: Determine if the two triangles in
the image are congruent. If they are, state how
you know by identifying the postulate.
th
The 2 triangles are congruent
solve the inequality
Answer:
D
Step-by-step explanation:
-13.4 => 6.7+4.3+w
-13.4-6.7-4.3 => w
-24.4 => w
10) Find three numbers whose product is -72. You may use integers from -10 to 10. Give two
examples
Answer:
Step-by-step explanation:
-8 * 9 * 1
If you are going to get - 72, you need to have an odd number of minus signs.
4 * 3 * - 6
You must be careful of the limits. You can't use something like 36 * 2 * 1 because the numbers don't fall within +/- 10
You could use 6*6*-2
Lauren bought 15 rainbow and balloon stickers for her little sister. The rainbow stickers cost 3 cents apiece and the balloon stickers cost 6 cents apiece. If Lauren spent exactly 81 cents, how many of each type of sticker did she buy?
Answer:
3 rainbow stickers and 12 balloon stickers
Step-by-step explanation:
Let x = rainbow count
Let y = balloon count
x + y = 15
x = 15 - y
3x + 6y = 81
3(15 - y) + 6y = 81
45 - 3y + 6y = 81
3y = 36
y = 12
x = 15 - 12
x = 3
find x in the following
Answer:
i. ans in picture
ii. ans in picture
iii. ans in picture
iv. 19
v. 38
Step-by-step explanation:
i. working in picture
ii. working in picture
iii. working in picture
iv.
180-90=90
90=2x+7+45=2x+52
2x=90-52=38
x=19
v.
angle COD=3x+10
180-3x+10-2x
180+10=2x+3x
190=5x
x=38
Answer:
x = 123- 56=67x= 17x=125x=19x= 20Step-by-step explanation:
Apply the following triangle laws:
The sum of the angles of a triangle will always be 180 degrees.
Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answer:
450 people
Step-by-step explanation:
The number of people running a race this year will be 450.
What is an expression?
Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that last year, Rob set up the Road Runner Race for his school. The race was 1,200 meters long and 188 people signed up to run the race. 38 people did not show up to run. This year, there will be 3 times as many runners as last year.
The number of people running a race this year:-
Number = ( 188 - 38 ) x 3
Number = 150 x 3
Number = 450
Therefore, the number of people running a race this year will be 450.
To know more about an expression follow
https://brainly.com/question/22880916
#SPJ2
A ball thrown upwards hits a roof and returns back to the ground.
The upward movement is modeled by a function [tex]s=-t^2+3t+4[/tex]
s= −(t^2)+3t+4
and the downward movement is modeled by [tex]s=-t^2+3t+4[/tex]
s= −2(t^2)+t+7, where s is the distance (in metres) from the ground and t is the time in seconds.
Find the height of the roof from the ground.
Answer: 6 m
A ball thrown upwards from the altitude 4 m,
hits a roof and returns back to the ground.
upward movement: s= −t²+3t+4
downward movement: s=-2t²+t+7
Step-by-step explanation:
Let's calculate the intersection:
[tex]- t^2+3t+4 =-2t^2+t+7\\\\t^2+2t-3=0\\\\t^2+3t-t-3=0\\\\t(t+3)-(t+3)=0\\\\(t+3)(t-1)=0\\\\t=-3 \ (exclude)\ or\ t=1\\\\if\ t=1 \ then\ s=-1^2+3*1+4=6\\\\height\ is\ 6\ m.\\[/tex]
Sorry, i have forgotten the picture.
What is force? How is it measured? Write any two effects of force
Answer: Please refer to:
- A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. ... Forces only exist as a result of an interaction.
- Force is a vector quantity, with both direction and magnitude. It is defined as Mass x Acceleration = Force.
+ The SI unit of force is the newton (N); defined as the unit of force which would give to a mass of one kilogram an acceleration of 1 meter per second squared.
- two effects of force:
+ It can change the state of movement of the body on which force is applied, i.e. it can move a stationary object or stop a moving object.
+ It can change the shape and size of an object.
Step-by-step explanation:
I'm not sure but hope it helps.
A model rocket is launched with an intitial upupward velocity of 202 ft/s. The rocket’s height h (in feet) after seconds is given by the following.
H=202t-16t^2
Given that the height of a object thrown within a gravitational field is given as a quadratic equation in time, t, the time at which the object is at a specified height can be found by the quadratic formula
The values of, t, for which the height of the rocket is 82 feet are;
t = 12.21 seconds or t = 0.42 seconds
Question: Parts of the question that appear missing but can be found online are (i) To find the values of the time, t, when the rocket's height is 82 feet and round answers to the nearest hundredth
The known parameters of the rocket are;
The initial upward velocity of the rocket, v = 202 ft./s
The given function representing the height, h, (in feet) after t seconds is presented as follows;
H = 202·t - 16·t²
The unknown;
The time for which the height of the rocket is 82 feet
Method;
Substitute H = 82 feet in the height function equation and solve for t as follows;
When H = 82, we get;
82 = 202·t - 16·t²
Therefore;
16·t² - 202·t + 82 = 0
Dividing the above equation by 2 gives;
(16·t² - 202·t + 82)/2 = 0/2
8·t² - 101·t + 41 = 0
By using the quadratic formula, we get;
[tex]\mathbf{t = \dfrac{101 \pm \sqrt{(-101)^2 - 4 \times 8 \times 41} }{2 \times 8} = \dfrac{101 \pm \sqrt{8889} }{16}}[/tex]
Therefore, the values of t given by rounding off to the nearest hundredth are;
t = 12.21 or t = 0.42
The values of the time, t, at which the height of the rocket is 82 feet are t = 12.21 seconds or t = 0.42 seconds
Learn more about equation models of height as a function of time here;
https://brainly.com/question/84352
4)
Write an inequality for the graph below. If necessary, use
<= for < or >= for .
9514 1404 393
Answer:
y < -1/4x -1
Step-by-step explanation:
The boundary line appears to go through the points (-4, 0) and (0, -1). This tells you it has a "rise" of -1 for a "run" of 4. The slope is ...
m = rise/run = -1/4
The y-intercept (b) is the point where the y-axis is crossed. The slope-intercept equation of the boundary line is ...
y = mx + b
y = -1/4x -1
__
The boundary line is dashed, so is not included in the solution set. The shading is below the line, so all y-values less than (but not equal to) the boundary line are in the solution set:
y < -1/4x -1
Select the statement that correctly compares two numbers. (GIVING BRAINLIEST)
4.13 = 4.130
5.16 < 5.06
6.28 < 6.08
7.09 > 7.19
Answer:
4.13=4.130
If there is a 0 at the end of a decimal then you can drop it.
The statement that correctly compares two numbers is 4.13 = 4.130. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
From the given options the correct expression which represents equality will be 4.13 = 4.130. The value of both the numbers is the same. There is not any significance of 0 at the end of the expression.
Therefore, the statement that correctly compares two numbers is 4.13 = 4.130. The correct option is A.
To know more about an expression follow
https://brainly.com/question/28040125
#SPJ2
14
11. The number of kilograms of corn needed
to feed 5000 chickens is 30 less than twice
the number of kilograms needed to feed
2800 chickens. How many kilograms of
corn are needed to feed 2800 chickens?
(A) 70
(B) 110
(C) 140
(D) 190
(E) 250
Answer:
x = 2515
Step-by-step explanation:
5000 = 2x - 30
2800 = x
have a great day! I hope this helps!140 kilograms of corn is needed to feed 2800 chickens.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the number of kilograms of corn needed to feed 5000 chickens is 30 less than twice the number of kilograms needed to feed 2800 chickens.
Assume that [x] kilograms of corn is needed to feed 2800 chickens.
for 2800 chickens → [x] Kg of corn is needed
for 1 chicken → [x/2800] Kg of corn is needed.
So, we can write -
5000 × [x/2800] = 2x - 30
50x/28 = 2x - 30
50x = 28(2x - 30)
50x = 56x - 28 x 30
50x - 56x = - 840
- 6x = - 840
6x = 840
x = 140
Therefore, 140 kilograms of corn is needed to feed 2800 chickens.
To solve more questions on Equation Modelling, visit the link below -
brainly.com/question/14441381
#SPJ2
answer no explantion pls i need asap
Answer:
Below.
Step-by-step explanation:
Area = 5(x + 3)
= 5x + 15
Perimeter = 2(x + 3) + 2(5)
= 2x + 6 + 10
= 2x + 16.
I need the answer explained
Answer:
Question cannot nicely
Jimmy measured to find the total number of square inches that covered the top of a rectangular table.
Which was Jimmy measuring?
0
A. area
B. circumference
C. distance
D. perimeter
E. volume
Answer: it is a
Step-by-step explanation:
If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown
Review the experimental question and hypothesis. Which statement best explains why the hypothesis is testable?
Question:
How does the amount of water individuals drink everyday affect the number of facial blemishes they receive every month?
Hypothesis:
If the amount of water people drink everyday affects the concentration of certain hormones in their blood, then increasing the amount of water consumed daily will decrease the number of facial blemishes they receive each month.
The hypothesis includes an explanation and makes a prediction.
The hypothesis is written using an "If …, then …" format.
The hypothesis includes both an independent variable and a dependent variable.
The hypothesis can be used to accurately explain observable facts.
Answer:
Step-by-step explanation:
I think the answer should be that there is an if -- then way the statement is worded. Quite often if then statements are used in this kind of experiment. Beyond that I can't make any comment. I don't know that it truly is testable, but it sounds like it should be.
Answer:
The hypothesis includes an explanation and makes a prediction.
Step-by-step explanation: I took the quiz on primavera and got that answer
10. (30-i)-(18+6i)+30i
Answer:
[tex]12+23i[/tex]
Step-by-step explanation:
[tex](30−i)−(18+6i)+30i[/tex]
[tex]30−i−18−6i+30i[/tex]
[tex]12−i−6i+30i[/tex]
[tex]12−7i+30i[/tex]
[tex]12+23i[/tex]
Hope it is helpful....- -
X+y=3 and x+y=-2 find the value of x and y
Answer:
no solutions.
Step-by-step explanation:
the given lines are parallel, then they can not have intersection points.
Yemi earns 8000naira a month and Bisi earns 6000naira a month. Find the ratio between their income.
Answer:
8:6
or
4:3
Step-by-step explanation:
Can you help me? Please
9514 1404 393
Answer:
a.
Step-by-step explanation:
For an even-index radical, ...
[tex]\sqrt[n]{x^n}=|x|\qquad\text{n even}[/tex]
This lets us simplify the given expression as follows:
[tex]\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}[/tex]
fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50 how many miles was the trip to the airport
the trip to the airport was 6.25 miles.
Simplify:-
(2x) ×(2x)-3×(2x)4
Answer:
[tex]2x \times 2x - 3 \times 2x \times 4 \\ = 4 {x}^{2} - 24x \\ = 4( {x}^{2} - 6) \\thank \: you [/tex]
40pts and a brainliest to the person who answers this question with detailed explanations and steps to solve shown.
Find y. Give your answer in the simplest form.
Answer:
y = 7 sqrt(2)
Step-by-step explanation:
Since this is a triangle, we can use trig functions
sin theta = opp/ hyp
sin 45 = 7/y
y sin 45 = 7
y = 7/ sin 45
y = 7 / (1/sqrt(2) )
y = 7 sqrt(2)
Answer:
the answer is y = 7 sqrt (2)
Step-by-step explanation:
[tex]\sf{}[/tex]
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
One meter is about 39.36 inches. How many inches are in 100 meters?
Step-by-step explanation:
When I was a kid, the inch was a different length than the inch of today. Back then, there were approximately 39.36 inches in one meter. I had no trouble memorizing that number and still use it today, even though the number today is actually 39.37 inches (plus a tiny amount extra).
Today, the inch is defined to be exactly 2.54 centimeters long, so if we want to know exactly how many inches are in the meter, we would divide the number of centimeters in one meter by the number of centimeters in one inch.
[math]\frac{100\,cm\,per\,meter}{2.54\,cm\,per\,inch}\,=\,\frac{100}{2.54}[/math] inches per meter
My Windows calculator says that this is equal to:
39.37007874015748031496062992126…
I recommend memorizing the number 39.37.
As long as you memorize the fact that there are 2.54 centimeters in one inch, you can always use your calculator to get the approximate number of inches in one meter.
Addendum:
The old Mendenhall inch (1893) was exactly 39.37 inches per meter. The international inch, 0.0254 m, gives 39.37 and a bit. Total change is 2 parts per million.
Answer:
3936 inches
Step-by-step explanation:
39.36 x 100 since each meter is 39.36 inches
charles is 22 years older than his sister danielle. in 10 years he will be twice as old as danielle. how old is each of them now?
9514 1404 393
Answer:
Charles: 34Danielle: 12Step-by-step explanation:
If Charles is 22 years older, he will be double Danielle's age when she is 22. If that is 10 years from now, Danielle is 12 and Charles is 34.
Solve 6y - 9 + 2y - 5 = -8 y + 17 + 4y
Please Mark my answer brilliant
Evaluate the expression when x=6 and y=-3.
-x+7y
Answer:
-27
Step-by-step explanation:
Let x = 6 and y = -3
[tex]-(6)+7(-3)\\-6-21\\-27[/tex]
