Answers
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+3}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{3}{2(-1)}~~,~~8-\cfrac{3^2}{4(-1)} \right)\implies \left( \cfrac{3}{2}~~,~~ 8+\cfrac{9}{4}\right)\implies \left( \cfrac{3}{2}~~,~~ \cfrac{41}{4}\right)[/tex]
now, for the solutions, or namely the x-intercepts, we simply set y = 0 and solve for "x", now this one doesn't factor into integers nicely, so we'll need to use the quadratic formula to get them.
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+3}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x=\cfrac{ - 3 \pm \sqrt { 3^2 -4(-1)(8)}}{2(-1)}\implies x = \cfrac{-3\pm\sqrt{9+32}}{-2}\implies x = \cfrac{3\mp\sqrt{41}}{2}[/tex]
[tex]x = \begin{cases} \cfrac{3-\sqrt{41}}{2}\\[2em] \cfrac{3+\sqrt{41}}{2} \end{cases}\qquad \leftarrow \qquad na mely\textit{ solutions or zeros or x-intercepts}[/tex]
Related Questions
Find one value of x for F(x)=-4
Answers
F(x) = -4 means y = -4. That means whatever the x is, the answer is going to be -4.
Does each pair of expressions form an equation when joined with an equals sign?
Select Yes or No for each pair of expressions.
Expressions
(1/3) ² +1 and 2 - 8/9
(1+ 1/5)^2 and 2
16/25
Answers
Equations are expressions with equal values
(1/3) ² +1 and 2 - 8/9 form an equation when joined together with an equals sign(1+ 1/5)^2 and 2 16/25 do not form an equation when joined together with an equals sign(a) (1/3) ² +1 and 2 - 8/9
Rewrite as:
[tex]\mathbf{(1/3)\² +1 = 2 - 8/9}[/tex]
Evaluate the exponent
[tex]\mathbf{1/9 +1 = 2 - 8/9}[/tex]
Take LCM
[tex]\mathbf{1\frac 19 = \frac{18- 8}{9}}[/tex]
[tex]\mathbf{1\frac 19 = \frac{10}{9}}[/tex]
Simplify
[tex]\mathbf{1\frac 19 = 1\frac{1}{9}}[/tex]
Hence, (1/3) ² +1 and 2 - 8/9 form an equation when joined together with an equals sign
(b) (1+ 1/5)^2 and 2 16/25
Rewrite as:
[tex]\mathbf{(1+ 1/5)^2 =2\frac{ 16}{25}}[/tex]
Take LCM
[tex]\mathbf{(\frac{5 + 1}{5})^2 =2\frac{ 16}{25}}[/tex]
[tex]\mathbf{(\frac{6}{5})^2 =2\frac{ 16}{25}}[/tex]
[tex]\mathbf{\frac{36}{25} =2\frac{ 16}{25}}[/tex]
Rewrite as:
[tex]\mathbf{1\frac{9}{25} =2\frac{ 16}{25}}[/tex]
Hence, (1+ 1/5)^2 and 2 16/25 do not form an equation when joined together with an equals sign
Read more about equations at:
https://brainly.com/question/13636476
Answer:
(1/3)^2 + 1 and 2 - 8/9 : Yes
(1 + 1/5)^2 and 2 - 16/25 : No
Kaylee needed to fold 586 paper notices for a fundraiser. The notices would be mailed in 22 days. Which expression gives the best estimate of the number of notices she must fold each day to meet her goal?
A.
500
÷
20
B.
500
÷
30
C.
600
÷
20
D.
600
÷
30
Answers
Answer: C
Step-by-step explanation: Round to the nearest 100
A driver travels 120 miles, stops, and then travels ¼ of the distance she has already driven. After stopping again, the driver travels ⅔ of the distance she has already traveled. Now, the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. How many miles does the driver still have to travel?
Answers
Answer:
75 miles
Step-by-step explanation:
We know that she has driven 120 miles before the first stop.
Then she drives for 1/4 of the the distance she has already driven (120 miles). One fourth of 120 is 30.
So now, she's driven for 120 + 30 miles, or 150 miles.
She drives for another 2/3 of the distance she's traveled (150 miles). Two thirds of 150 is 100.
So now, she's driven for 150 + 100 miles, or 250 miles.
What we need to find out now is how much of the trip has she traveled.
We know that the entire distance she has driven is 55 miles more than 1 ⅔ of the remaining trip. So, in other words, the distance she has traveled minus 55 is equal to 1 2/3 of the trip.
To put this in an equation:
250 - 55 = 1 2/3t
t = the whole trip
Now, we solve for t.
250 - 55 = 195
1 2/3 = 5/3
so, 195 = 5/3t
t = 325
We subtract what she has already driven to the total to get the remaining distance.
325 - 250 = 75
Which relation has a domain of (2, 4) and a rang of (2, 8)
A (2, 4) (2,8)
B (2, 2) (2,8) (4,2)
C{(2,4)(8,2)(8,4)}
D{(2,2)(2,4)(4,2)(8,8)}
Answers
Range: y values
The relation would need to have (2, y) and (4, y). And also (x, 2) and (x, 8)
See which ones match
Solution: B
Solve the given equations. PLEASE show your work. Choose if the equation has infinite many solutions or no solution. It can have a solution
-2(x + 4) + 9x = 4 - 7x
Answers
Segments KN and LM are transversals. What is true about the measure of angle N?
Answers
Answer:
It is congruent to M
Step-by-step explanation:
pls help its an image scroll down
Answers
Answer:
D. y = 3x + 9
Step-by-step explanation:
Use the point-slope formula to find the equation in slope-intercept form.
[tex]y-y_1=m(x-x_1)\\\\y-33=3(x-8)\\\\y-33=3x-24\\\\y=3x+9[/tex]
√12 - 1 √3=?
is correct the answer is 1/√3
THANK YOU
Answers
Answer:
[tex]\huge\boxed{\text{Is inorrect. Correct answer is:}}\\\boxed{\dfrac{6-\sqrt3}{3}\neq\dfrac{1}{\sqrt3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt{12}-1}{\sqrt3}=\dfrac{\sqrt{12}}{\sqrt3}-\dfrac{1}{\sqrt3}=\sqrt{\dfrac{12}{3}}-\dfrac{1}{\sqrt3}=\sqrt4-\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=2-\dfrac{\sqrt3}{3}\\\\=\dfrac{6}{3}-\dfrac{\sqrt3}{3}=\dfrac{6-\sqrt3}{3}\neq\dfrac{1}{\sqrt3}\\\\\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{\sqrt3}{3}[/tex]
Henry steps onto an elevator at the first floor. He goes up to the 9th floor and then comes down 2 floors. He then goes up 4 floors and down 6 floors. What floor is Henry on?
Answers
Answer:
He is on the 5th floor
Step-by-step explanation:
9 - 2 = 7
7 + 4 = 11
11 - 6 = 5
Answer:
he goes 1 +9=10
10-2=8
8+4=12
12-6=6
so he is ont the sixth floor
Explain what a graph for Jed’s test scores {61%, 65%, 73%, and 79%} would look like if it was not misleading. Make sure it is different than Jed’s graph – that some may say is misleading.
Answers
Answer:
61
^
^
^ 65 73
^ 79 ^ ^
^ ^ ^ ^
-----------------------------------------------------------------------------------------------------------------
Test 1 Test 2 Test 3 Test 4
Answer: the test doesn't explain the order it was taken or dates. So it can be misleading
Step-by-step explanation:
(-4) ⁴ what is the value of this expression
Answers
This is a glucose molecule. How many hydrogen atoms are in a molecule of glucose? A) 10. B) 11. C) 12. D) 13
Answers
Answer:
12 for sure
Step-by-step explanation:
I just know
Quiz
2² =
4² =
use the method, no calculation
Answers
Step-by-step explanation:
2²
= 2 × 2
= 4
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
4²
= 4 × 4
= 16
▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎▪︎
I Hope This HelpIt takes 40 cents worth of meat to make 2 sandwiches. What is the cost of the meat for 20 sandwiches?
Make a Selection:
A. $2.00
B. $3.20
C. $1.60
D. $4.00
Answers
Answer:
D. 4.00
$4.00 will be your cost for meat for 20 sandwiches.
Three business partners, Ren, Jaffary and Abel put money into a business in the ratio 2:3:4. From the profits they shared, Abel got 3400 dollars. How much did ren and Jaffary receive?
HELP GUYS PLS I HAVE 3 MIN TO GO
Answers
Answer:
Ren has 755.4
Jaffray has 1,133.1
Abel has 1,510.8
Solve each equation for the specified variable.
a. a-q=a+sx for x
b. kx-bf=fy/m for y
c. a-q=a+sx for q
d. kx-bf=fy/m for m
PLEASE HELP I WILL GIVE GREATEST ANSWER TO WHOEVER SOLVES ALL OF THEM THE BEST. THANK YOU SO MUCH
Answers
Answer:
a.
a - q = a + sx
a - a - q = a - a + sx
-q = sx
[tex]\frac{-q}{s} = \frac{sx}{s}[/tex]
x = [tex]\frac{-q}{s}[/tex]
b.
kx - bf = [tex]\frac{fy}{m}[/tex]
m(kx - bf) = m([tex]\frac{fy}{m}[/tex])
mkx - mbf = fy
[tex]\frac{mkx - mbf}{f}[/tex] = [tex]\frac{fy}{f}[/tex]
y = [tex]\frac{mkx - mbf}{f}[/tex]
y = [tex]\frac{mkx}{f}[/tex] - [tex]\frac{mbf}{f}[/tex]
y = [tex]\frac{mkx}{f}[/tex] - mb
c.
a - q = a + sx
a - a - q = a - a + sx
-q = sx
-q × (-1) = sx × (-1)
q = -sx
d.
kx - bf = [tex]\frac{fy}{m}[/tex]
m(kx - bf) = m([tex]\frac{fy}{m}[/tex])
m(kx - bf) = fy
[tex]\frac{m(kx - bf)}{kx - bf}[/tex] = [tex]\frac{fy}{kx - bf}[/tex]
m = [tex]\frac{fy}{kx - bf}[/tex]
Which of these situations can be represented by this graph?
Answers
Answer:
Step-by-step explanation:
. Bobignment In what year was the LAWMA Established-
Answers
Evaluate. 2 (14–32 +1) 1:3.-
Answers
Answer:
432
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
Need help with this geometry question
Answers
Answer:
The first option:yellow shirt, white trouseryellow shirt, black trousergreen shirt, white trousergreen shirt, black trouserStep-by-step explanation:
To find the possibilities, you would see that you would have two yellow shirts and two green shirts with different trousers, so you can eliminate the bottom two. And because there will be two of each shirt with defferent trousers, it will be the same for trousers: two of each trouser will be in the possibilities. The only one that fits this description, is the first one.
yellow shirt, white trouser
yellow shirt, black trouser
green shirt, white trouser
green shirt, black trouser
Pls Help! Worth 8 Points Will Give Brainlest
Answers
Answer:
D. x - 5
Step-by-step explanation:
The text said that Sienna's hight is LESS than her brothers hight and less = minus
Answer:D
Step-by-step explanation:hope i helped i love helping people like you. :)
39. The area of a triangle A varies jointly as b and h. If A = 225 in- when b = 18 in. and h = 25
in., find A when b = 35 in. and h = 40 in.
37
Answers
Answer: B
Step-by-step explanation:
Answer:
700 in^2
Step-by-step explanation:
If A = 225 in- when b = 18 in. and h = 25
225 = 18 * 25 / 2
a = 35 * 40 / 2
a = 700
y varies directly as x and x=20 when y=15. Find y when x=68
Answers
change the following numbers to decimals and round to the nearest hundredth 3÷4 and ✔10
Answers
Answer:
0.75 and 10.00
Step-by-step explanation:
Evaluate 4c - 3
When c = -2
Answers
Answer:
-11
Step-by-step explanation:
Answer: -5
Step-by-step explanation:
4*-2=-8
-8 -3=-5
share £650 in the ratio of 4:9
Answers
Answer:
200:450 that would be the answer i believe
We are flying at 30 000 feet.
Our speed is 500 miles per hour.
Our total flight time will be 10 hours and 20 minutes.
Mark knows the distance from London to Cancun is 4944 miles. He asks his daughter to check the information given by the pilot. She knows this formula for speed.
s = dt
s = speed (miles per hour) d = distance (miles)
t = time (hours)
Evaluate the information given by the pilot.
Show calculations to support your answer.
Answers
Answer:
Step-by-step explanation:
500 mph with a flight time of 10 hours and 20 minutes [(20 min)*(1 h/60 min) = 0.333 hr]
Distance = Speed * Time
Time = 10.333 hours
Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles
The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles. That is a 4.3% reduction from the pilot's numbers. Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.
My preference would be to trust the pilot's data. I don't know where Mark got his math education.
The table gives the temperature (in °F) in five citiesſat 6 a.m. on the same day. Use the table to answer the questions.
City
Temperature
(°F)
Toronto
-16
Fairbanks
:-24
Dayton
43
San Antonio
74
Buffalo
-3
5
?
(a) By noon, the temperature in Buffalo had risen by 10 °F.
What was the temperature there
at noon
How much higher was the 6 am temperature in Toronto than in Fairbanks
Answers
Answer:
a) buffalo will be at 7
b) it will be -8
Step-by-step explanation:
a) because if u add - 3 + 10 it will equal 7
b) reason why is because if u substract -24 from - 16 it will be - 8
I took a test on the same thing thats why i kno it
Name x1, x2, y1, and y2. Then, find the distance between the points.
Answers
Answer:
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