Answer:
C.7, -2
Step-by-step explanation:
A quadratic equation is a polynomial of degree two. A quadratic equation is in the form:
ax² + bx + c = 0; where a, b, c are constants.
Quadratic equation can be solved using different methods, such as completing the square method, quadratic formula.
Solving the equation 2x² - 10x - 20 = 8 using completing the square:
2x² - 10x - 20 = 8
2x² - 10x = 28
Divide through by 2, to make the coefficient of x² to be 1:
x² - 5x = 14
Add to both sides, the square of half of the coefficient of x [i.e. (-5/2)² = 6.25]
x² - 5x + 6.25 = 14 + 6.25
(x - 2.5)² = 20.25
taking square root of both sides:
x - 2.5 = √20.25
x - 2.5 = ±4.5
x = 2.5 ± 4.5
x = 2.5 + 4.5; or x = 2.5 - 4.5
x = 7 or x = -2
explanation would be appreciated. i don’t understand
Answer:
[tex]28\sqrt{3}[/tex]
Step-by-step explanation:
The area of the big triangle is 1/2 b h = 1/2*6*(12^2 = 6^2 + x^2)
that ends up being [tex]\sqrt{108} = 36\sqrt{3}[/tex]
the small triangle are needs to be subtracted....
[tex]\frac{\left(4\cdot \:sin\left(90\right)\right)}{sin\left(30\right)}[/tex] that is the length of the unknown side...
1/2 B * h of that triangle get you to [tex]8\sqrt{3}[/tex]
just subtract the two areas
Answer:
(B) 28√3
Step-by-step explanation:
The area of quadrilateral ABED is equal to the area of triangle CDE subtracted from the area of triangle ABC.
Area of triangle CDE:
Triangle ABC is equilateral. All sides have length 12.
AB = BC = AC = 12
BE = 8
BE + EC = BC
8 + EC = 12
EC = 4
In an equilateral triangle, all angles measure 60°.
m<C = 60°
m<CDE = 30°
Triangle CDE is a 30-60-90 triangle.
DE = EC√3
DE = 4√3
area of triangle CDE = bh/2
area of triangle CDE = (EC)(DE)/2
area of triangle CDE = (4)(4√3)/2
area of triangle CDE = 8√3
Area of triangle ABC:
Side AC is a base of triangle ABC.
AC = 12
(1/2)AC = 6
The altitude of triangle ABC from side AC to vertex B measures
h = 6√3
area of triangle ABC = bh/2
area of triangle ABC = (AC)(h)/2
area of triangle ABC = (12)(6√3)/2
area of triangle ABC = 36√3
area of quadrilateral ABED = area of triangle ABC - area of triangle CDE
area of quadrilateral ABED = 36√3 - 8√3
area of quadrilateral ABED = 28√3
Ethan sells e candy bars for $2.50 apiece and Chloe sells c candy bars for $2.00 apiece to raise
money for a school trip. Ethan sold 15 fewer candy bars than Chloe, but he also got a $6.00
donation. If Chloe and Ethan raised the same amount of money, which of the following systems
could be used to find how many candy bars each sold?
The system that could be used to find how many candy bars each sold is given is option B.
What is the candy bar about?Since Ethan sold 15 fewer candy bars than Chloe, as portrayed in the question, so:
e = C - 15
Based on the fact that Chloe and Ethan raised the same amount of money, the equation will be:
2C: 2.5e + 6
Therefore, The system that could be used to find how many candy bars each sold is given is option B.
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use the prime factors of 3136 and 2744 to evaluate:✓3136/3✓2744
Answer:
3136 = 2^6 × 7^2
2744 = 2^3 x 7^3
✓3136/3✓2744 = ✓(2^6 × 7^2)/3✓(2^3 x 7^3) = (2^3 x 7)/3 x 14(✓14) = 56/42✓14 =4/3✓14
how many subsets can be formed of a set A={a,b}
Answer:
4
Step-by-step explanation:
(a,a),(a,b),(b,a),(b,b)
Which equation below has a slope greater than the slope of the line shown above?
A. y = 2 x + 2
B.y = 3x - 1
C. y = - 3
D. y = 4 + 1.75 x
Answer:
B.y = 3x - 1
Step-by-step explanation:
Pick two points on the line
(0,1) and (2,5)
The slope using the slope formula
m = (y2-y1)/(x2-x1)
= ( 5-1)/(2-0)
= 4/2
= 2
We want a slope that is greater than 2
The slope intercept form of the equation is
y = mx+b where m is the slope
y = 3x - 1 has a slope of 3 which is greater than 2
the ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1, 60), (2, 240), (3, 960), (4, 3840)}
what is the function equation in sequence notation?
wt = ____
Answer:
w = 15 (4^t)
Step-by-step explanation:
Let w be what the function is equal to
Let t be the input variable
equation :
w = k a^t
Plug in any two of the points to solve for k and a
for example, let's take (1, 60) and (2, 240):
60 = k * a^1
k = 60 / a
240 = k a^2
Substituting:
240 = 60/a (a^2)
a = 4
k = 15
The function is
w = 15 (4^t)
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
What is the conditional relative frequency that a participant has red hair, given that he/she has green eyes.
0.5
0.13
5
0.38
Answer:
let R represent red hair
let G represent green eyes
from Baye's theorem:
[tex]P( \frac{R}{G} ) = \frac{P(RnG)}{P(G)} [/tex]
P(RnG) = 5
[tex]P(G) = { \sum}(green \: hair) \\ = (3 + 5 + 5) \\ = 13[/tex]
Therefore:
[tex]P( \frac{R}{G} ) = \frac{5}{13} \\ = 0.385[/tex]
The conditional relative frequency = 0.385
The conditional relative frequency will be 0.385
What is Baye's theorem?It is a theorem showing how to compute the conditional probability of each of a set of possible causes for a given observed outcome using knowledge about the probability of each cause and the conditional probability of each cause's outcome.
let R represent red hair
let G represent green eyes
from Baye's theorem:
[tex]P=\dfrac{R}{G}=\dfrac{P(R\cap G)}{P(G)}[/tex]
P(RnG) = 5
P(G) = ∑(Green hairs)
P(G)= 13+5+5 = 13
Therefore:
[tex]P(\dfrac{R}{G})= \dfrac{5}{13}=0.385[/tex]
The conditional relative frequency = 0.385
Hence the conditional relative frequency will be 0.385
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SEE QUESTION IN IMAGE
Answer:
(b)
Total frequencies:
25 - 4 = 21Multiples of 3 or 5:
6, 9, 10, 12, 15, 18, 20, 21, 24, 25 - total of 10Required probability:
P(3x or 5x) = 10/21(c)
Limes = 10 + 6 = 16Apples = 8 + 6 = 14Total = 16 + 14 = 30(i) Good limes = GL = 10
P(GL, GL) = 10/30*9/29 = 3/29(ii) Good fruits = GF = 10 + 8 = 18
P(GF, GF) = 18/30*17/29 = 51/145(iii) Good apple = GA = 8, Bad lime = BL = 6
P(GA&BL or BL&GA)) = 8/30*6/29 + 6/30*8/29 = 16/1455.
Krishna got on an elevator on the 12" floor and went up 3 floors. If he then went down 8 floors,
what floor is krishna now on?
Answer:
Krishna is at the 7th floor
Step-by-step explanation:
Given
[tex]Start = 12[/tex]
[tex]Up = 3[/tex]
[tex]Down = 8[/tex]
Required
The current floor
This is calculated as:
[tex]Floor = Start + Up - Down[/tex]
[tex]Floor = 12 + 3 - 8[/tex]
[tex]Floor = 7[/tex]
Find the length of UC? Please help
Answer:
The choose C. 18
Step-by-step explanation:
UC —> 105+82=187 —> 96+22+51=169 —> 187–169=18
I hope I helped you^_^
What is the range of f(x)?
{xl-2
{x|-2
{yl-5
{yl-5 sy<-1}
Answer:
-5≤y≤-1
Step-by-step explanation:
The range is the values that y takes
The smallest value of y is -5 and the largest value of y is -1
-5≤y≤-1
assume abc=def. if ab=5, ac=9 and ef=7, what is the length of bc?
Answer:
bc= 7
Step-by-step explanation:
which has a steeper slope y-1/2x or y=2/3x?
Answer:
y=2/3x
Step-by-step explanation:
2/3 is greater than 1/2. It doesn't matter if one of the slopes are negative.
A random walk process for a single stock consists of the toss of a fair coin at the end of each day. If the outcome is heads, the stock price increases by 1.25 percent. If the outcome is tails, the stock price decreases by 0.75 percent. What is the drift of such a process
Answer:
+0.25
Step-by-step explanation:
Calculation to determine the drift of such a process
Using this formula
Drift=(Increases in stock price*50%)- (Decreases in stock price *50%)
Let plug in the formula
Drift = (0.5)(1.25) + (0.5)(-0.75)
Drift =0.625+ (0.375)
Drift = +0.25%
Therefore the drift of such a process is +0.25
0.135 written as a fraction is _____.
27/200
5/37
27/100
Answer:
27/200
Step-by-step explanation:
To write 0.135 as a fraction you have to write 0.135 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 0.135 = 0.135/1 = 1.35/10 = 13.5/100 = 135/1000
Answer:
27/200
Step-by-step explanation:
your teacher tried to be tricky.
0.135 is simply 135/1000.
that is how you can express any finite decimal number.
anyway, now, we need to transform that fraction into one of the provided fractions. so, which one fits ?
with experience you see it right away. otherwise by simply trying.
in any case, the first option is the right one.
proof :
27/200 = 135/1000 ?
the denominator is our driver : what factor do I need to turn 200 into 1000 ? right, 5 ! 200×5 = 1000
so, we multiply numerator and denominator by 5 (it is important to do that for both, so that the value of the fraction does not change).
27/200 × 5/5 = (27×5) / (200×5) = 135/1000
and that is the proof. 27/200 is indeed 0.135
The distance AB rounded to the nearest tenth = [?]
Answer:
4.5 units
Step-by-step explanation:
Use the distance formula
[tex]\sqrt{(-1-3)^{2}+(-1-1)^{2} }[/tex]
[tex]\sqrt{16+4}=\sqrt{20}[/tex]
The distance AB on the diagram rounded to the nearest tenth is: 4.5 units
Meaning of DistanceDistance can me defined as a measure that tells us how far apart two objects or individual are to each other.
Distance is very important as it helps us know where exactly things are located and whether they are close or far apart
In conclusion, The distance AB on the diagram rounded to the nearest tenth is: 4.5 units
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Given that E=MC find E when M=20 and C =2.5
Answer:
50 or 125
Step-by-step explanation:
if u want E=MC then it would be 20 ×2.5=50
OR
if u what to find E=MC² then it would be 20×2.5×2.5 =125
ACCORDING TO ME THIS SHOULD BE THE ANSWER, BUT NOT QUITE SURE ABOUT THIS.
Answer:
E = 50
Step-by-step explanation:
If M=20 and C=2.5, replace the letters in the equation with their numerical values so E=20*2.5
20*2.5 = 50
thus E=50
type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar
HELP HELP
Answer:
Hello,
Step-by-step explanation:
f(x)=x+3 if -3≤x≤-1
(the line is passing trough (-3,0) and (-1,2) ==> y-0=(x+3)((2-0)/(-1+3) ==> y=x+3
f(x)=5 if -1≤x≤1
equation of the line which passes through point (0,5) at gradient of - 1
Answer:
y = - x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here gradient (slope) = - 1 and (0, 5) ⇒ c = 5
y = - x + 5 ← equation of line
HELP!!!
I need to know if this is Function or not a function.
Answer:
Not a function
Step-by-step explanation:
Since x = 1 produces y = 3 and y = 4 , the relation is not a function.
( − 2 , − 5) , ( − 1 , − 3 ) , ( 0 , 0 ) , ( 1 , 3 ) , ( 1 , 4 )
The domain cannot be the same value.
(PLEASE HELP ASAP I REALLY DON’T UNDERSTAND THIS PLEASE EXPLAIN)
Answer:
Intergers
Step-by-step explanation:
A subset is a part of a whole math concept, idea, or sample space.
We need to find what math concept -5 is apart of.
-5 is part of the All Real Numbers section.
-5 is also part of integers as well.
Penny attended a four year state college. She took out a student loan to pay for her tuition and room & board for the four years she was attending the college. Her tuition fees were $6,970 per year, and the cost of her room and board was $11,320 per year. Now that she has graduated, she will have to start paying back her loan. Fortunately, Penny has a grace period of one year before she has to start paying back the loan. Her loan details are as follows: there is a fixed-rate interest of 4.5% and the interest compounds each month. During her one year grace period, interest will accrue on the loan, so that when she has to start paying the loan back she will owe more than what she owes now. Her goal is to be able to payoff the loan in 10 years.
Given all of this information, answer the following questions:
1. What is the original loan amount, i.e. how much were the total costs for tuition plus room & board for the four years that Penny attended the college?
2. What is the new loan amount after the one-year grace period (remember that interest will accrue on the loan during this initial 12-month period that she is not paying anything back on the loan)? This is the amount that she will be responsible for paying back. (Round your answer to the nearest whole dollar)
3. Given that she can pay back the loan in full after 10 years of payments, what is the total amount she will end up paying back (both principal and interest that has accrued over the 10 years)? And how much will her monthly payments on the loan be for those 10 years? (Round your answers to the nearest whole dollar)
Answer:
27,880 for tutitions + 45,280 for room and board= 73,160 total
Let vector a = 3i + j - k.
Find the vector b in the direction of vector a such that |b| = 5
Answer:
5i +(5/3)j - (5/3)k
Step-by-step explanation:
Vector b is in the same direction as vector a, so it is a scalar multiple of a.
b = ca for some positive real number c.
b = c(3i + j - k) = 3ci + cj - ck
|b| = sqrt[(3c)^2 + c^2 - c^2] = sqrt(9c^2) = 3c
If |b| = 5, then 3c = 5 and c = 5/3
That makes b = (5/3)(3i + j - k) = 5i +(5/3)j - (5/3)k
Question 7 of 10
A construction worker needs to put a rectangular window in the side of a
building. He knows from measuring that the top and bottom of the window
have a width of 5 feet and the sides have a length of 12 feet. He also
measured one diagonal to be 13 feet. What is the length of the other
diagonal?
O A. 12 feet
B. 13 feet
O C. 5 feet
O D. 17 feet
Answer:
13
Step-by-step explanation:
The diagonals of rectangle are equal in length.
help me please it's important!!
Answer:
Does the answer help you?
Answer:
102 cm³
Step-by-step explanation:
Volume of R1:
length = 7 cm
Width = 3 cm
Height = 2 cm
Volume = 7* 3 * 2 = 42 cm³
Volume of R2:
length = 5 cm
Width = 4 cm
Height = 3 cm
Volume = 5 * 4 * 3= 60 cm³
Volume of the figure = 42 + 60 = 102 cm³
Please help! Thank you.
Answer:
B
Step-by-step explanation:
x((7/2)-(7/3))=y+x
x(7/6)=y+x
7x=6y+6x, x=6y. y/x=1/6
(52)-1 + 5÷1
Answer please..
Answer:
I believe this might be the answer 52 − 1 + 5/1= 56
Answer:
56
Step-by-step explanation:
hope it helps ^^.
Fill in the blanks to write a verbal description
Answer:
Step-by-step explanation:
17.
The expression 4(x-7) is the product of 4 and the difference of x and 7.
18.
The expression 2+8/c is the sum of 2 and the quotient of 8 and c.
HELP PLEASE 100 POINTS
Answer:
Step-by-step explanation:
That's an awful lot of points. You don't have to give that many. 10 or 15 points would be more than enough.
The graph touches the x axis at 1 point. That means its basic formula is y = (x - a)^2
Since it upside down, the formula is y = -(x - a)^2. A couple of other things are true.
a = 1 because that's where the graph touches the x axis. y = - x^2 has shifted 1 unit to the right.
Finally the y intercept is -4 which means that the final equation is y = -4(x-1)^2
That's all preliminary. The actual question is, what does the discriminate look like?
y = -4(x^2 - 2x + 1)
y = -4x^2 + 8x - 4
a = - 4
b = 8
c = - 4
sqrt(b^2 - 4ac)
sqrt(8^2 - 4(-4)(-4) )
sqrt(64 - 64) = 0
The answer is the third one. The answer will always be 0 when the graph touches the x axis and does not go through it.
Help me please Will give brainlist
Answer:
Step-by-step explanation:
These are geometric means problems. In the top one, a is the geometric mean as the height for both the smaller triangles inside the big one. Therefore,
[tex]\frac{4}{a} =\frac{a}{25\\}\\a^2=100\\a=10[/tex]
The next one has the geometric mean of b, being a part of the smaller triangle on the left and the big triangle as a whole:
[tex]\frac{4}{b} =\frac{b}{29}\\b^2=116\\b=10.77[/tex]
