Answer:
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]
Given equation: [tex]kx^2+2x+(1-k)=0[/tex]
[tex]\implies a=k,\:b=2,\:c=(1-k)[/tex]
[tex]\begin{aligned}\implies b^2-4ac & =(2)^2-4(k)(1-k)\\ & =4-4k(1-k)\\ & =4-4k+4k^2\\ & = 4k^2-4k+4 \end{aligned}[/tex]
Complete the square:
[tex]\begin{aligned}\implies 4k^2-4k+4 & =4(k^2-k+1)\\ & = 4\left[k^2-k+\left(\dfrac{-1}{2}\right)^2+1-\left(\dfrac{-1}{2}\right)^2\right]\\ & = 4\left[\left(k-\dfrac12\right)^2+\dfrac34\right]\\ & = 4\left(k-\dfrac12\right)^2+3\end{aligned}[/tex]
[tex]\textsf{As }\left(k-\dfrac12 \right)^2 \geq 0 \implies 4\left(k-\dfrac12 \right)^2+3\geq 3[/tex]
Therefore, the roots are always real.
What is the distance between points A and B on the coordinate plane?
a ) 12
b) 10
c) 14.5
d) 100
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.
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
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 = $76joe saved up 25 his mother gave him an additional 20 he boua movie that cost 15 how much money dose joe have left
Answer: 30
Step-by-step explanation: Before Joe had $45 in total, He then spent it on a movie which is $15. So $45-$15=30
Answer:
25+20-15=30
Step-by-step explanation:
Here You Go Bud
Which
interval
function?
contains a local
minimum
for the
graphed
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?
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]
What is the difference?
StartFraction x Over x squared + 3 x + 2 EndFraction minus StartFraction 1 Over (x + 2) (x + 1) EndFraction
Answer:
see image
Step-by-step explanation:
You are subtracting fractions. To do this you must have a common denominator. Then subtract the numerators.
In your question, the denominators (expressions on the bottom) are ALREADY THE SAME, because (x+2)(x+1) is the same as x^2+3x+2.
So to subtract, keep the denominator and subtract the tops:
x - 1
The result can be written in either factored form or standard form. The answers are equivalent. See image.
HELP
Brainleist
and 15 points
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°
I need help but not urgent but urgent!!
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]
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
Answer:
Step-by-step explanation:
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
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
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
A hotel has 27 conference rooms. Each room has a capacity of 420 people. What is the total capacity of the 27 conference rooms?
Answer:
11340
Step-by-step explanation:
You would just multiple 27 by 420, since each room has a capacity:
27 x 420 = 11340
Please ASAP I NEED UNDER 5 MINUTES
58. SIMPLIFYING AND SOLVING Compare and contrast the two problems.
Also need help with 3 problems on top
Answer:
55. 16 56. 48 57.27
Step-by-step explanation:
You add all the sides that you are given together and then you subtract that from the perimeter given. EX. In question 55 you would do 20+12=32 so 48-32=16.
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
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
$1,700 is deposited in an account that pays 6.5% annual interest, compounded annually. What is the balance after 3 years?
Answer: $2053.51
Step-by-step explanation:
The formula for compound interest is [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where
A = final amount
P = initial principal balance (1700 for this)
r = interest rate (0.065 for this)
n = number of times interest applied per time period (1 for this)
t = number of time periods elapsed (3 for this)
[tex]A=1700(1+\frac{0.065}{1})^{(3)(1)} \\A=1700(1.065})^{3} \\A=2053.51435[/tex]
Rounded that is 2053.51
Which ordered pair is a solution to the system of inequalties?
y > –x
y ≤ x + 1
Answer:
B) (4, -1)
Step-by-step explanation:
A violates the rule of y <= x + 1, because 3 > 1 + 1
C violates the rule of y <= x + 1, because 5 > 0 + 1
D violates the rule of y > -x, because 0 < -(-4) = 4
B conforms to both rules: -1 > -4 and -1 <= 4 + 1.
Answer:
B) (4,–1)
Step-by-step explanation:
A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.
bedmas 10+45/9-(14/2)=
Answer:
8.
Step-by-step explanation:
1. In PEMDAS, parenthesis always comes first. In this equation, 14 divided by 2 is in parenthesis. this equals 7. Now the equation looks like the following: 10+45/9-(7).
3. In this equation, there are no exponents, nor is there multiplication, so we move on to division. The only division left in this equation is 45 divided by 9, which is equal to 5. Now the equation looks like the following:
10+5-(7)
4. Next in PEMDAS comes addition, which in this case is 10 plus 5, which is equal to 15. Equation presently: 15-(7)
5. Lastly, subtraction. 15 minus 7= 8, therefore the overall answer is 8.
You deposit $2000 in an account earning 3% interest compounded monthly. How much will you have in the account in 20 years
Write a fraction the equivalent of 3/10 that has a denominator of 100
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
Answer:
B
Step-by-step explanation:
a
Suppose a person is standing on the top of a building and that she has an instrument that allows her to
measure angles of depression. There are two points that are 100 feet apart and lie on a straight line that is
perpendicular to the base of the building. Now suppose that she measures the angle of depression from the
top of the building to the closest point to be 33.5º and the angle of depression from the top of the
building to the furthest point to be 28.3º. Determine the height of the building. (Round your answer to the
nearest tenth of a foot.)
The building and the person on it are illustrations of elevation and depression
The height of the building is 76.9 feet
How to determine the height of the building?To calculate the building height, we make use of the attached illustration
Considering the triangle DCB in the figure, we have:
tan(B) = DC/BD
Substitute known values
tan(28.3) = DC/(DA + 100)
Cross multiply
(DA + 100) * tan(28.3) = DC
Divide both sides by tan(28.3)
DA + 100 = DC/tan(28.3)
Subtract 100 from both sides
DA = -100 + DC/tan(28.3)
Considering the triangle DCA in the figure, we have:
tan(A) = DC/DA
Substitute known values
tan(33.5) = DC/DA
Make DA the subject
DA = DC/tan(33.5)
Substitute DA = DC/tan(33.5) in DA = -100 + DC/tan(28.3)
DC/tan(33.5) = -100 + DC/tan(28.3)
Evaluate the tangent ratios
0.56DC = -100 + 1.86DC
Collect like terms
-1.86DC + 0.56DC = -100
Evaluate
-1.3DC = -100
Divide both sides by -1.3
DC = 76.9 feet
Hence, the height of the building is 76.9 feet
Read more about elevation and depression at:
https://brainly.com/question/15580615
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?
Answer:
Step-by-step explanation:
Rename 5/6 and 14/15 using the least common denominator.
Answer:
[tex]\frac{25}{30}~and~\frac{28}{30}[/tex]
Multiply 5 by 5 to get your first parameter.[tex]5 * 5 = 25[/tex]
Multiply 6 by 5 to get the denominator, or your second parameter.[tex]5 * 6 = 30[/tex]
For the second fraction, [tex]\frac{14}{15}[/tex], you need to multiply both parameters by 2, similar to before, but we now must use a different number, otherwise, the denominators will not be the same.[tex]14 * 2 = 28[/tex]
Now, multiply 15 by 2[tex]15 * 2 = 30[/tex]
The last step is to put these numbers you gathered into fractions. The bigger number always goes on the bottom, referred to as the denominator, while the smaller number, referred to as the numerator, always goes on the top.[tex]25~and~30 -- > \frac{25}{30}[/tex]
[tex]28~and~30-- > \frac{28}{30}[/tex]
________________________________________________________
Finally, the problem is solved. Now that the problem is solved, we review what we just learned not through more problems, though.
________________________________________________________
What have we learned?We learned how to efficiently make fractions' deominators match.
Questions related to this topic? Ask me in the comments box, please!
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)
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
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?
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
What is the value of y in the following system of equation? 3x-4y= -20 -× + 2y = 10
Answer:
y=5
Step-by-step explanation:
Let me know if you need an explanation
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.
Sweet tea put a new batch of cupcakes in the oven at 4:15 cupcakehave to break for 20 minutes what time should sweet tea take cupcakes out of the oven
If a circle is divided into 12 angles, what is the measure of each angle in the circle? 36° 60° 90° 30°
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°.
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
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.
Find the area of an equilateral triangle with a side length of 14.
[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