Answers
Answer:
k = 0, k = 4
Step-by-step explanation:
Given equation:
[tex]y=x^2+kx+3k+4x+4[/tex]
Rearrange into standard form [tex]ax^2+bx+c[/tex]:
[tex]\implies y=x^2+kx+4x+3k+4[/tex]
[tex]\implies y=x^2+(k+4)x+(3k+4)[/tex]
Therefore:
[tex]a=1, \quad b=(k+4), \quad c=(3k+4)[/tex]
If the vertex lies in the x-axis, then the quadratic has one (repeating) root at (x, 0). Therefore, we can use the discriminant to find the values of k.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
Therefore, set the discriminant to zero and solve for k:
[tex]\implies (k+4)^2-4(1)(3k+4)=0[/tex]
[tex]\implies k^2+8k+16-12k-16=0[/tex]
[tex]\implies k^2-4k=0[/tex]
[tex]\implies k(k-4)=0[/tex]
[tex]\implies k=0, k=4[/tex]
So the vertex lies in the x-axis when k = 0 or k = 4
Related Questions
what is approximate distance between (-1, 3) and (2, -4)
Answers
Answer:
d= 7.62
Step-by-step explanation:
(-1,3)(2,-4)
the formula of distance is-
[tex]d=\sqrt{((x_{2}-x_{1})^2 + (y_{2}-y_{1})^2)} \\\\d=\sqrt{(2+1)^2+(-4-3)^2}\\ d=7.62[/tex]
Ben takes 3 hours to wash 273 dishes, and Frank takes 4 hours to wash 444 dishes. How long will
they take, working together, to wash 3200 dishes?
It will take Ben and Frank
hour(s) and
minute(s) to wash 3200 dishes together.
If needed, round answer to 1 decimal places.
Answers
Select the expression that is equivalent to
(m2-16)
A. (m-4)2
B. (m+4)(m-4)
C. (m2-8m+16)
D. (m2+8m+16)
Answers
Answer:
if it's m^2-16, than it's B, (m+4)(m-4)
Step-by-step explanation:
remember (a+b)(a-b)=a^2-b^2, or m^2-4^2=m^2-16
Write an eqaution in slope-intercwpt form for the line with slope -5 and y-intercept 9
Answers
Answer:
y = -5x + 9
Step-by-step explanation:
Slope-intercept form of an equation is:
y = mx + b
Since they gave you the slope and y-intercept, it is kind of a fill-in-the-blank problem. Nothing to calculate!
Fill in the slope for the m. Fill in the y-intercept for the b.
y = -5x + 9
is planetarium showing programs about the night sky has a shape of a hemisphere. The diameter of the planetarium is 50 ft what is the volume to the nearest cubic foot of the planetarium use 3.14 for pi
Answers
Answer:
32,708.3 cu. ft
Step-by-step explanation:
First we find the volume of a sphere with the same dimensions
is the formula for the volume of a sphere
substitute the radius with 25 because radius is half the diameter and use 3.14 for pie. The answer to that formula is 65,416.6
Since you're finding the volume of a hemisphere, divide the volume of the sphere in half
65,416.6/2= 32,708.3
Find the slope of the line passing through the points , 2−6 and , −9−6
Answers
I will assume that we are trying to find the slope between (2,-6) and (-9,-6)
The slope's equation ⇒ [tex]\frac{y2-y1}{x2-x1}[/tex]
Let's set the variables:
(x1, y1) --> (2, -6)
(x2, y2) --> (-9, -6)
Now let's plug them in:
[tex]Slope = \frac{-6--6}{-9-2} =\frac{0}{-11} =0[/tex]
Thus the slope of the line is 0.
Hope that helps!
Which
interval
function?
contains a local
minimum
for the
graphed
Answers
Answer:
D
Step-by-step explanation:
a local minimum is a low point in the graph, but it isn't the lowest. and If u look at the given interval choices, the only one that has a local minimum Is D.
The main sail of a sailboat has the dimensions shown in the figure at the right. What is the height of the main sail?
Answers
Answer:
[tex]h = 16.1[/tex]
Step-by-step explanation:
[tex]sin A /a = sin B / b = sin C/c[/tex] where A is angle and a is side opposite of angle
[tex]sin (49) / h = sin(41)/ 14[/tex] cross-multiply
[tex]h*sin(41) = 14 * sin(49)[/tex]
[tex]h = (14*sin(49))/ sin(41)[/tex]
[tex]h = 16.1[/tex]
I need help but not urgent but urgent!!
Answers
Answer:
8.6 mile
Explanation:
[tex]\sf equation \ follows : \ \ \ d = 1.2116\sqrt{h}[/tex]
d represents the distance a person can see.h represents the height above the ocean.what the captain sees:
[tex]\hookrightarrow \sf d_c = 1.2116\sqrt{15}[/tex]
what the sailor sees:
[tex]\hookrightarrow \sf d_s = 1.2116\sqrt{120}[/tex]
Difference between them:
[tex]\sf \rightarrow 1.2116\sqrt{120} \ - \ 1.2116\sqrt{15}[/tex]
[tex]\sf \rightarrow 8.58[/tex]
[tex]\sf \rightarrow 8.6[/tex] (rounded to nearest tenth)
Answer:
8.6 miles (nearest tenth)
Step-by-step explanation:
[tex]d=1.2116\sqrt{h}[/tex]
where:
d = approximate distance a person can see (in miles)h = person's height above the ocean (in feet)Captain
Given the Captain is 15 ft above the ocean:
[tex]\implies h = 15[/tex]
Substituting this into the equation:
[tex]\implies d_1=1.2116\sqrt{15}[/tex]
Lookout
Given the lookout is 120ft above the ocean:
[tex]\implies h = 120[/tex]
Substituting this into the equation:
[tex]\implies d_2=1.2116\sqrt{120}[/tex]
Solution
To find how much farther the lookout can see than the captain, subtract the distance the captain can see from the distance the lookout can see:
[tex]\implies d_2-d_1[/tex]
[tex]\implies 1.2116\sqrt{120}-1.2116\sqrt{15}[/tex]
[tex]\implies 1.2116(\sqrt{120}-\sqrt{15})[/tex]
[tex]\implies 8.579906391...[/tex]
[tex]\implies 8.6\: \sf miles\:(nearest\:tenth)[/tex]
I will give Brainliest!!! :D
Match each situation to an equation.
(You can just write the color of the equation card and the fraction in the situation, ex. Green card to 2/5) :)
Answers
Answer:
Going left to right:
2/5
1/5
1/4
13/10
Step-by-step explanation:
A bag contains 15 beads that are either red or yellow.
The probability of randomly removing a red bead is 20%.
What is the probability of randomly removing a yellow bead?
Answers
The probability of randomly removing a yellow bead is 0.8 or 80% if the bag contains 15 beads that are either red or yellow the probability of randomly removing a red bead is 20%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have the probability P(R) of randomly removing a red bead is 20%.
Let's suppose the number of red beads is n(R)
[tex]\rm P(R) = 20\% \Rightarrow 0.20\\\\\rm \frac{n(R)}{15} = 0.20[/tex]
n(R) = 15×0.20
n(R) = 3
Number of yellow beads = 15 -3 = 12
The probability randomly removing a yellow bead:
[tex]=\rm \frac{12}{15}[/tex]
= 0.8 or 80%
Thus, the probability of randomly removing a yellow bead is 0.8 or 80% if the bag contains 15 beads that are either red or yellow the probability of randomly removing a red bead is 20%.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
Katie has these 2 boxes shaped likerectangular prísms. How do the volumes of the two bones compare?
A. Box 2 and Box 1 have the same volume.
B. Box 2 has 3 times the volume of Box1
C. Box2 has 9 times the volume of Box 1.
cm
D. Box 2 has 27 times the volume of Box1.
2 cm
1.5 cm
1.5cm
25
25 am
Box1
Box 2
Answers
Answer:
Box 2 has 3 times the volume of Box 1....
What is the distance between points A and B on the coordinate plane?
a ) 12
b) 10
c) 14.5
d) 100
Answers
Answer:
Step-by-step explanation:
use pythagorean theorem a^2 + b^2 = c^2
a = 6, b = 8
6^2 + 8^2 = c^2
100 = c^2
c = -10
since it cant really be negative, the distance becomes 10.
The school cafeteria has 16 round tables that each fit-8 students and..
12 rectangular tables that each fit 12 students. How many students can
fit in the cafeteria at once?
A 128
- B 256
C 144
D 272
Answers
Answer:
The answer is D. 272
Step-by-step explanation:
All you need to do is find out how many people can be seated at each table, then add them together.
16 x 8 = 128
12 x 12 = 144
128 + 144 = 272
272 students can fit in the cafeteria at once.
What is x in this equation?
Answers
Answer:
x = 6.08 units
Step-by-step explanation:
For a right triangle
sin = opp leg / hyp
for this triangle sin 34 = 3.4 / x re-arrange to
x = 3.4 / sin34 = 3.4 / .5591 = 6.08
NO LINKS!!
The Odd Man Out
For each set of figures below, three are similar (meaning that they are related through a sequence through a sequence of transformations including dilations), and one is an exception. Find the exception in each set of figures and answer the questions. PART 1
Answers
Answer:
Step-by-step explanation:
Elizabeth bought a cheese pizza. It was served on a metal tray with a diameter of 22 centimeters. What is the tray's area?
Answers
The Area of the tray ≈380 cm
Solution:We are given the diameter of the tray, which is equivalent to 22 cm.We are asked to find the area of the tray.Remember the formula:Area of a circle = πr²Whereπ -> pi (3.14...)r -> radiusNotice that we aren't given the radius. We're given the diameter only.No reason to panic. We can easily find the radius by dividing the diameter by 2.The radius is equal to 11 cm.Now, plug the values into the formula:A=π(11)²A=121πA≈380 cmHope it helps.
Do comment if you have any query.
Paul has a car that is 8 years old and has 126,000 miles on it. Even though he couldn't get more than $2,000 if he sold it, he still pays $350 per year for collision insurance to pay him up to the value of his car if it were damaged. If Paul decides to drop his collision insurance coverage, how is he handling that risk? A. Reducing it B. Transferring it C. Assuming it D. Avoiding it
Answers
Answer:
Assuming
Step-by-step explanation:
If he has a wreck he will ASSUME the risk....his loss
What is the ratio of the radius to the circumference of any circle, using 3.14 for pi?
Answers
Answer:
1 : 6.28Step-by-step explanation:
The circumference formula is
C = 2πr orC = 2(3.14)r = 6.28rThe ratio of the radius to the circumference is
r/C = 1/6.28or
r : C = 1 : 6.28r : C = 1 : 6.28
Formula's:
circumference of any circle: 2πr
radius: r
Their ratio:
radius : circumference
r : 2πr
r : 2(3.14)r
1 : 6.28
HELP
Brainleist
and 15 points
Answers
Answer: x=20
Step-by-step explanation:
The two angles provided are vertical angles.
Vertical angles are equal in measurement.
This means we can set (3x+50) and (6x-10) equal to each other and solve for x
[tex]3x+50=6x-10[/tex]
Add 10 to both sides
[tex]3x+50=6x-10\\3x+50+10=6x-10+10\\3x+60=6x[/tex]
Subtract 3x from both sides
[tex]3x-3x+60=6x-3x\\60=3x[/tex]
Divide both sides by 3
[tex]\frac{60}{3} =\frac{3x}{3} \\20=x[/tex]
Answer:
Step-by-step explanation:
(3x + 50)° = (6x - 10)°
3x - 6x = -50 - 10
3x = -60
[tex]\frac{-3x}{-3}[/tex] = [tex]\frac{-60}{3}[/tex]
x=20°
Camilo uses 32 ounces of filling to make empanadas de quest. He puts 0 empanadas on each of the 3 trays. write a fraction to show how many ounces of filling Camilo uses in each empanadas
Answers
The fraction that shows the number of ounces of filling camilo uses in each empanadas is,
↪32 ounces
☆...hope this helps...☆
_♡_mashi_♡_
[tex] \bold{ \underline{SOLUTION }}[/tex]
Required Answer
32Camilo uses ounce = 32
he put emandas = 0
each tray = 3
find how many ounce of filling camilo uses in each empandas
[tex] \bold {\underline{ \underline{Let's Begin -: }}}[/tex]0 × 3 = 0
{and any number is cant divided by zero.}
Thus ,,
32 empanadas fill on each ounce
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
During this year, the budget has increased by 3 %. This increased budget is $ 16,068 . How much was the budget in the past, before the increase?
Answers
Answer:
Step-by-step explanation:
Find the area of an equilateral triangle with a side length of 14.
Answers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
Given - An equilateral triangle with side 14 cm To find - Area of that equilateral triangleSolution -
[tex]Area\: of \:equilateral \:triangle\: = \: \frac{ \sqrt{3} }{4} a {}^{2} \\ \\ \implies \frac{ \sqrt{3}}{4} \times 14^{2} \\ \\ \implies \: \frac{ \sqrt{3} }{\cancel4} \times \cancel{196} \\ \\ \implies \: \sqrt{3} \times 49 \\ \\ \implies \: \bold\blue{49 \sqrt{3} \:units {}^{2}} [/tex]
Further ,
value of [tex]\bold\orange{\sqrt{3} = 1.732}[/tex]
therefore ,
[tex]Area = 49 \times 1.732 \\ \\ \implies \: \bold\red{84.69 \: units {}^{2} \: (approx.)}[/tex]
hope helpful :D
a department store has a jacket on sale for 114 which is 60% of the original price what is the difference between the original price and sale price
Answers
Answer:
$76
Step-by-step explanation:
Let the original price be ‘P’114 = 0.6PDivide both sides by 0.6190 = PTo find difference, subtract sale price from original price190 - 114 = $76What is the probability that someone doesn’t eat breakfast?
Answers
1/2
hope it helps..!!!!!
If a circle is divided into 12 angles, what is the measure of each angle in the circle? 36° 60° 90° 30°
Answers
the angle when a circle is divided into 12 angles.
solution:angle at a point is:
=360°
so to find the angle you'll have to divide 360 by 12.
360 ÷ 12
= 30°
hence, the measure of each angle is 30°.
Answer:
30
Step-by-step explanation:
to find:
the angle when a circle is divided into 12 angles.
solution:
the angle at a point is:
=360°
so to find the angle you'll have to divide 360 by 12.
360 ÷ 12
= 30°
hence, the measure of each angle is 30°.
Give an example of an equation that crosses the x-axis at x=3 and x=-8.
This is a problem on my math homework that I’ve been stuck on. Does anyone know how to help?
Answers
The *graph of a function* (and not an equation) f(x) crosses the x-axis for any value of x such that f(x) = 0. We call x a root of f(x) in that case.
The simplest function with roots at both x = 3 and x = -8 is
f(x) = (x - 3) (x + 8)
since
f(3) = (3 - 3) (3 + 8) = 0 • 11 = 0
and
f(-8) = (-8 - 3) (-8 + 8) = -11 • 0 = 0
Joel is selling a motorcycle for $2,535. He bought the
motorcycle two years ago and paid $4,721 for it. It depreciated
35% during the two years. Is he losing money or making money
on this sale
Answers
Answer:
Making money
Step-by-step explanation:
selling motorcycle for 2,535
After 2 years the motorcycle is worth:
y = 4721(0.65)^2
= 1994.6
2535> 1994.6
Answer:
Joel is selling a motorcycle for $2,535. He bought the
motorcycle two years ago and paid $4,721 for it. It depreciated
35% during the two years. Is he losing money or making money
on this sale
Question 4(Multiple Choice Worth 3 points)
(04.04 MC)
Which is the equation of a parabola with a directrix at y = -3 and a focus at (5, 3)?
a
a
a
HELPPOO
Answers
Answer:
B
Step-by-step explanation:
Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground.
Projectile motion formula:
h = -16t2 + vt + h0
t = time, in seconds, since the ball was thrown
h = height, in feet, above the ground
Which system models the height of the tennis ball and the height of the dog's mouth over time?
h = 4.5t + 18 and h = -16t2 + 1.5t + 21
h = 18t + 4.5 and h =-16t2 + 21t + 1.5
h = -16t2 + 4.5t + 18 and h = -16t2 + 1.5t + 14
h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5
Answers
Using quadratic function concepts, it is found that the system that models the height of the tennis ball and the height of the dog's mouth over time is given by:
h(t) = -16t² + 18t + 4.5 and h(t) = -16t² + 21t + 1.5.
What is the quadratic function for the height of a projectile?It is given by:
h(t) = -16t² + v(0)t + h(0)
In which:
v(0) is the initial velocity.h(0) is the initial height.For the tennis ball, we have that v(0) = 18, h(0) = 4.5, hence the equation is:
h(t) = -16t² + 18t + 4.5.
For the dog jump, we have that v(0) = 21, h(0) = 1.5, hence:
h(t) = -16t² + 21t + 1.5.
Hence, the system is given by:
h(t) = -16t² + 18t + 4.5 and h(t) = -16t² + 21t + 1.5.
More can be learned about quadratic function concepts at https://brainly.com/question/24737967
Answer:
D) h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5
Step-by-step explanation:
The next answer is, "the time at which the ball and the dog's mouth are at the same height"