Answers
Answer:
Part (a)
Given quadratic: [tex]y=x^2+2x-8[/tex]
Factored form
To factor, find two numbers that multiply to -8 and sum to 2: 4 and -2
Rewrite the middle term of the quadratic as the sum of these number:
[tex]\implies y=x^2+4x-2x-8[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies y=x(x+4)-2(x+4)[/tex]
Factor out the common term [tex](x+4)[/tex]:
[tex]\implies y=(x-2)(x+4)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies (x-2)(x+4)=0[/tex]
[tex]\implies (x-2)=0\implies x=2[/tex]
[tex]\implies (x+4)=0\implies x=-4[/tex]
Therefore, the zeros are 2 and -4
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-4+2}{2}=-1[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]y=(-1)^2+2(-1)-8=-9[/tex]
Therefore, the vertex is (1, -9)
------------------------------------------------------------------------------------------------
Part (b)
Given quadratic: [tex]y=-x^2-9x-14[/tex]
Factored form
To factor, first factor out -1:
[tex]y=-(x^2+9x+14)[/tex]
Now find two numbers that multiply to 14 and sum to 9: 7 and 2
Rewrite the middle term of the quadratic as the sum of these number:
[tex]y=-(x^2+2x+7x+14)[/tex]
Factorize the first two terms and the last two terms separately:
[tex]y=-(x(x+2)+7(x+2))[/tex]
Factor out the common term [tex](x+2)[/tex]:
[tex]y=-(x+7)(x+2)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies -(x+7)(x+2)=0[/tex]
[tex]\implies -(x+7)=0 \implies x=-7[/tex]
[tex]\implies (x+2)=0 \implies x=-2[/tex]
Therefore, the zeros are -7 and -2
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-7+(-2)}{2}=-4.5[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]y=-(-4.5)^2-9(-4.5)-14=6.25[/tex]
Therefore, the vertex is (-4.5, 6.25)
Related Questions
How would I be able to solve all of these?
Answers
Answer:
I'm suggesting that you should read your books!!!
You should be more thoughtful...
Answer:
Part A) x = 6, 13, 22, 33
Part B)
Part ASome examples of perfect squares are 9, 16, 25, and 36. They are the squares of 3, 4, 5, and 6. To generate these values, add x to 3 and plug these numbers into an equation:
√(x + 3) = 3
√(6 + 3) = √9
x = 6
√(x + 3) = 4
√(13 + 3) = √16
x = 13
√(x + 3) = 5
√(22 + 3) = √25
x = 22
√(x + 3) = 6
√(33 + 3) = √36
x = 33
Part B
1. (6, 3)
2. (13, 4)
3. (22, 5)
4. (33, 6)
I hope this helps!
A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?
Answers
Answer:
See below ↓↓
Step-by-step explanation:
Finding the radius
C = 2πr25 = 2 x 3.14 x rr = 25 / 6.28r = 3.98 cm ≅ 4 cmSurface Area
4πr²4 x 3.14 x 4 x 43.14 x 64200.96201 cm²Volume
4/3πr³ = 4πr² x r/3201 x 4/367 x 4268 cm³Anyone can help me with this? Kinda confusing. Thank you!
Answers
Answer:
14
Step-by-step explanation:
you can do 9 x 14 and get 126
Decide whether it would be more convenient to solve the system of equations by substitution or elimination.
{−2x/3−15y=−6, 10x−6y=−4
Select the correct answer below:
elimination
substitution
Answers
Answer:
I would use elimination in this scenario. Because in both equations there is a coefficient on both variables, it would be difficult to isolate one variable and would leave the equation as a fraction. Instead, use elimination. Multiply the first equation by -15, which changes it to 10x + 225y = -90, and then subtract the second equation, thus cancelling out the 10x's and letting you solve for Y. Hope this helps!
Marlo uses 252 lb of gravel to cover a garden plot of 36 ft2.
Answers
Answer: 7lb
Step-by-step explanation:
The amount of gravel required cover each square feet of the garden obtained by dividing the total amount of gravel used and the total area of the garden is 7 lb
Total area of garden = 36 ft²
Total amount of gravel used = 252 lb
The amount of gravel used to cover each ft² of the garden can be calculated thus :
(Total amount of gravel used) ÷ (Total area of garden)
252 ÷ 36 = 7 lb
Therefore, the amount of gravel required to cover each square feet of the garden is 7 lb
Answer:
See below
Step-by-step explanation:
D o you want pounds / sq foot ?
252 lbs / 36 ft^2 = 7 pounds per square foot
Write an equation in slope-intercept form of the line that passes through ( 7,2 ) ( 2,12 )
Answers
Answer:
y = -2x + 16
Step-by-step explanation:
Slope-intercept form is:
y = mx + bWhere m = slope
b = y-intercept
To find the slope of the line containing (7,2) and (2,12), we have to find the slope, m.
m = (y2 - y1)/ (x2 - x1)= (12 - 2)/(2 - 7) = 10/-5 = -2Now, to find the y-intercept (b), insert m = -2 into the equation and one of the given points:
y = -2x + blet's use point (7,2) to find b:
2 = -2(7) + b2 = -14 + bb = 16Now, we can find the equation of this line:
y = -2x + 16Answer:
y=-2x+16
Step-by-step explanation:
First we should find the slope.
We can use the formula (y2-y1)/(x2-x1)
(12-2)/(2-7)=10/-5=-2
So, the slope is -2.
From there, we can plug in one of the points into the standard slope-intercept equation, y=mx+b, along with the slope we already found
y=-2x+b
12=-2(2)+b
12=-4+b
b=16
So, the slope-intercept equation is y=-2x+16
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Answers
Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
Martinez and grouse swimming pool is finally finished and all this left to do is fill it with water. Martinez family decides to fill their pool using their garden hose to save money even though they know it will take a really long time the swimming pool is 10 m long and 5 m wide and Martinez family wants to the water to be 2 m deep water from the garden holes flows at a rate of 2500 l or 2.5 m³ per hour how long will it take to fill the pool
Answers
Answer:
the answer ia true
Step-by-step explanation:
hope this helps
Which set of angle measures could be the interior angles of a triangle?
Answers
Answer:
the three angles inside a triangle need to add up to 180 degrees
Step-by-step explanation:
In Houston, 9 bats ate 50 grams of insects in one night. At this rate, how many grams of insects could 81 bats eat in one night?
Answers
Answer:
Step-by-step explanation:
Remark
Using Algebra, this is a proportion question. A proportion is 2 equal ratios
If the of the 2 ratio parts are known, it is possible to solve for the 4th one.
Formula
9_bats/50_grams::81_bats/x grams insects
Solution
Put the three knowns in and solve for the 4th which is not known
9 bats/ 50 insects = 81 bats /x insects. Cross multiply
9 * x = 50 * 81 Combine
9x = 4050 Divide by 9
9x/9 = 4050/9
Answer: x = 450 grams
I need help with this one
which of the following ordered pairs (x y) satisfies the system of inequalities above
Answers
Just put the options in the inequalities and check if they are true or not :
A ) ( - 1 , 0 )
[tex]2x + y \leqslant 3[/tex]
[tex]2( - 1) + 0 \leqslant 3[/tex]
[tex] - 2 \leqslant 3 \: \: \: kinda \: true[/tex]
And
[tex]x - y < - 3[/tex]
[tex] - 1 - 0 < - 3[/tex]
[tex] - 1 < - 3 \: \: \: false[/tex]
Thus A is wrong
_____________________________________________
B ) ( - 1 , - 1 )
[tex]2( - 1) + ( - 1) \leqslant 3[/tex]
[tex] - 2 - 1 \leqslant 3[/tex]
[tex] - 3 \leqslant 3 \: \: kinda \: true[/tex]
And
[tex] - 1 - ( - 1) < - 3[/tex]
[tex] - 1 + 1< - 3[/tex]
[tex]0 < - 3 \: \: \: false[/tex]
Thus B is wrong
_____________________________________________
C ) ( - 2 , 4 )
[tex]2( - 2) + 4 \leqslant 3[/tex]
[tex] - 4 + 4 \leqslant 3[/tex]
[tex]0 \leqslant 3 \: \: kinda \: true[/tex]
And
[tex] - 2 - 4 < - 3[/tex]
[tex] - 6 < - 3 \: \: \: true[/tex]
Thus C is the correct option
_____________________________________________
U can do D urself ...
Have a great day ♡
Use the proof above to answer the question: What reason can be used to prove that the triangles are congruent?
A. AAS B. ASA C. AAA D. SAS E. SSS
Answers
Answer:
E. SSS
Step-by-step explanation:
AB=BC (Given)
AD=CD (Midpoint)
BD=BD (common)
Therefore answer is : SSS
What is the area of the figure?
A. 18 yd
B. 54 yd
C. 72 yd
D. 90 yd
Answers
I solved by multiplying 9 x 5 and 3 x 9 and adding them.
Hope this helps
In analysis of variance, then the term factor refers to_______
a) a dependent variable
b) a treatment total
c) an independent variable (or quasi-independent) variable
d) a treatment mean
Answers
!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I believe it would be 9.
Step-by-step explanation:
Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9
A sample of 36 people yielded the information about their health insurance in the table to the right.
Two people who provided information for the table were selected at random, without replacement. Find the probability that neither had traditional insurance.
Answers
The probability that neither of the two people selected have traditional insurance is 0.33.
What is the probability that neither had traditional insurance?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that neither of the two people selected have traditional insurance = (number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed x [(number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed - 1]
21/36 x 20/35 = 0.33
Please find attached the table. To learn more about probability, please check: https://brainly.com/question/13234031
Find x in each triangle
Answers
Answer:
Applying Pythagoras we get x= 9
Answer:
using the relation,
h²=p²+b²:
15²=x²+12²
x=(225-144)^0.5
x=9
therefore x equal 9 meter.
I don't know how to do this (don't mind the 21)
Answers
Answer:
The definition of alternate interior angles is that those two angles are the same.
Therefore because they are the same you can set them equal to eachother
3x + 24 = 78 is true
3x = 54
x = 18
Just know the definitions, for instance 3 and 4 are the same, 2 and 5 are the same, 1 and 6 are the same
A demolition crew can do a job in 10 days. Another demolition crew can do the same job in 15 days. How many days would it take the two crews to do the job if they work together?
Answers
Answer:
6 days
Step-by-step explanation:
In one day, one demolition crew:
One day = [tex]\frac{1}{10} x[/tex] with x = the entire job
Other demolition crew:
One day = [tex]\frac{1}{15} x[/tex]
Together, they do it in [tex]\frac{1}{10}x\\[/tex] + [tex]\frac{1}{15}x[/tex] = [tex]\frac{3}{30}x + \frac{2}{30}x = \frac{5}{30}x[/tex] [tex]= \frac{1}{6}x[/tex] in one day
So [tex]\frac{1}{6}x[/tex] x 6 = x
so it takes 6 days to complete the work together.
For what value of k will the relation R = {(2k+1, 3), (3k−2, −6)} not be a function?
Answers
For the relation to not to be a function we need the same value of x in (x,y) that gives off different values (y).
2k+1= 3k-22k-3k = -2-1-k = -3k = 3Now plugging in the value of k,
(2 x 3+1 ,3) =( 7,3)(3 x 3-2,-6) = (7,-6)hence , the relation won't be function if k would be equal to 3
The value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.
What is a function?In general terms, a function is a mathematical rule or relationship that maps one set of values (the input or domain) to another set of values (the output or range). In other words, it's a specific process that takes some input and produces a corresponding output.
For the given relation R to be a function, each input in the domain should have exactly one corresponding output in the range.
We can determine whether the relation R is a function by checking if both ordered pairs have the same first coordinate. If they do, then the relation is not a function.
Let's equate the first coordinate of the ordered pairs:
2k+1 = 3k-2
Solving for k, we get:
k = 3
If we substitute k = 3 into the relation, we get:
R = {(2(3)+1, 3), (3(3)−2, −6)}
R = {(7, 3), (7, -6)}
Since both ordered pairs have the same first coordinate of 7, the relation R is not a function.
Therefore, the value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.
To know more about function follow
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Two rooms in a tiny house share a wall.
Answers
Answer:
54 + 42 = 6 (9 + 7)
Sorry if this answer is not correct, if it is or is not, please tell me in the comments!
Step-by-step explanation:
The equation already gives the 7 in the parenthesis, so we know that 7 x 6 = 42.
The 6 will be on the outside of the equation since we will be using Distributive Property to multiply the 6 and 7.
Since we already know the 6 is on the outside, your new equation is:
6 x (what number) = 54
54 divided by 6 = 9
There are 110 calories per 28.4 grams of Cereal X. Find how many calories are in 39.76 grams of this cereal
Answers
Step-by-step explanation:
28.4 g there are 110 calories
1 g there are 110/28.4 = 3.87 calories
39.76 g there are 3.87 × 39.76 = 153.87
Krystal was given $3000 when she turned 2 years old. Her parents invested at a 2% interest rate compounded annually. No deposits or withdrawals were made. Determine how much money Krystal had in the account when she turned 18.
Answers
Answer:
4131.38
Step-by-step explanation:
Since it's compounded annually, and no time needs to be converted, we can use the formula [tex]y=Pe^r^t[/tex], where P is the starting amount, e is Euler's number, r is the rate in decimals, and t is time. The first task would be to find the t. The question set us a timeframe of 2 to 18, so 18-2=16, therefore our t is 16. Plugin the known into the formula and calculate:
[tex]y=3000e^0^.^0^2^*^1^6\\y=3000*e^0^.^3^2\\y=4131.38[/tex]
Given the function f(x) = 4 - 2x, find f(3r - 1).
Answers
Answer:
6 - 6r
Step-by-step explanation:
we just plug in 3r - 1 instead of x
f(3r - 1) = 4 - 2(3r - 1)
= 4 - 6r + 2
= 6 - 6r
- If the difference of 15 and a number is 5, what is the number?
Answers
Answer:
The difference of 15 and a number is 5 indeed 10 to be 15
Answer:
10
Step-by-step explanation:
A spinner is divided into 12 identical sectors and labeled 1 through 12.
How many spins are expected for a multiple of 5 to be spun 8 times?
Select from the drop-down menu to correctly complete the sentence.
The spinner is expected to have to spin approximately
times for a multiple of 5 has been spun 8 times.
Answers
Answer: The awnser is 48
Step-by-step explanation: I took the quiz
6.03 Quiz: Use Theoretical Probability to Predict
It is expected to take 48 spins for a multiple of 5 to be spun 8 times.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Since there are 12 sectors, the probability of landing on a multiple of 5 is 2/12 or 1/6.
The probability of not landing on a multiple of 5 is 5/6.
We can use the geometric distribution formula to find the expected number of spins:
E(X) = 1/p, where p is the probability of success.
As per the question, the probability of success is 1/6.
Therefore, E(X) = 1/(1/6) = 6.
We need to spin a multiple of 5 8 times, so we multiply the expected number of spins by 8:
6 x 8 = 48.
Therefore, we can expect to spin a multiple of 5-8 times after 48 spins.
Learn more about the probability here:
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(02.01 LC) Which of the following tables represents a function?
Answers
Answer:
the answer is the third one
Step-by-step explanation:
because in a function the x value has to be unique.
Answer:
c (third one)
Step-by-step explanation:
Please help me with these 2 questions, I don’t really need explanations I just need straight forward answers ! The questions are linked below. 50 points
Answers
Answer:
1. The value of 5 is fifty thousand
2. The value of 6 is six thousand
Step-by-step explanation:
1. 8.156 million - 8,156,000
2. 6,521
^ 6000
If f(x) -
X-3
and g(x) = 5x - 4, what is the domain of (f•g)(x)?
Answers
Plot 1 goes from 0 to 8. There are 2 images above 5, 2 above 6, 4 above 7, and 5 above 8. Plot 2 goes from 0 to 8. there are 5 images above 1, 2 images above 2, 4 images above 3, 3 images above 4, 1 image above 5, 1 image above 6, and 1 image above 8.
Use visual clues to decide which plot has the highest measure. No calculations should be necessary, although you may use them to verify your answers.
Highest mean:
✔ Plot 1
Highest median:
✔ Plot 1
Highest range:
✔ Plot 2
Highest interquartile ranges:
✔ Plot 2
Answers
Answer: the answer is 45
Step-by-step Step-by-step explanation:
so it says a pilot goes from 0 to 8 and then two images above so you add to to eat and then you add 5 to 2:30 for me to 522 the artistic 24 + 27 + 5 then you answer 8 + 2028 and then you add 5 + 1 + 2 + 2 + 4 + 3 + 3 + 4 + 1 + 5 + 16 + 18 and you get 45
Answer:
A, A, B, B
Step-by-step explanation: