The vertex of f(x)=x²+10x+1 is found to be (-5,-24).
The Vertex of the quadratic equation f(x)=ax²+bx+c is (h,k) where
h=-b/2a and k=f(h).
In the given question
f(x)=x²+10x+1
On comparing with ax²+bx+c
we get a=1 , b=10 , c=1
So , h=-b/2a
h=-10/2(1)
h=-5 ...(i)
k=f(h)
Substituting the value of x=h in f(x) we get
k=(-5)²+10(-5)+1
k=25-50+1
k=-25+1
k=-24
Therefore , the vertex of f(x)=x²+10x+1 is (-5,-24).
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How much should Roman invest today in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly?
Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.65/100
r = 0.0565 per year,
Then, solve the equation for P
P = A / (1 + r/n)^(nt)
P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}
P = 22,450.15 / (1 + 0.0047)(44.4)
P = $18,223.97
The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.
Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.
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Which lists all the factors of 78?
Answer:
1, 2, 3, 6, 13, 26, 39, and 78
Step-by-step explanation:
:)
what is the answer to 17^2-286
The answer for the given expression, 17²-286 will be 3.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,the expression is,
17²-286
The expression is solved by the arrthmetic operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
=17²-286
=289-286
=3
Thus, the answer for the given expression, 17²-286 will be 3.
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put these numbers in order least to greatest 56,209 5,609 55,209 562,009
Answer:
5,609
55,209
56,209
562,009
What is the sum of 2 3/4 and −2 3/4 ?
A. 0
B. 3/4
C. 5 1/2
D. I don't know.
Answer:
A. 0
Step-by-step explanation:
[tex]2 \frac{3}{4} + ( - 2 \frac{3}{4}) \\ = \frac{11}{4} - \frac{11}{4} \\ = \frac{11 - 11}{4} \\ = \frac{0}{4} = 0 \\ hope \: this \: would \: help[/tex]
Answer:
A. 0
Explanation:
Given:
[tex]2\dfrac{3}{4} +(-2\dfrac{3}{4} )[/tex]
In improper fractions:
[tex]\dfrac{11}{4} +(\dfrac{-11}{4} )[/tex]
Simplify:
[tex]\dfrac{11}{4} -\dfrac{11}{4}[/tex]
Evaluate:
[tex]0[/tex]
Tip:
As the integers are alike, when subtracted they simplify to zero as a result.
Select the correct answer. What is the solution for x in the equation? -x + 3/7=2x-25/7
Answer:
x + 3/7=2x-25/7
X=4
show that the roots of the quadratic equation given by(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are rea land they can not be equal unless a=b=c.
Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
The company made a partial payment of $600 cash on the equipment purchased in transaction d.
Answer: can u finish the question
Step-by-step explanation:
Write an inequality that represents the graph. An inequality that represents the graph is -1 on a number line
a .
The inequality of the number line is x > -1
What is a number line?A number line is a vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval
From the number line in the question, we can see that:
How to determine the inequality?From the question, we have
Point = -1
Assume the following
The endpoint of the circle on the number line is an open circleThe arrow points to the rightAs a general rule, open circles implies that the number at that endpoint is not included part of the solution set.
This means that the inequality of the number line is x > -1
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A sum of money is shared in the ratio 3:4:7.
The smallest share is £210.
What is the total amount of money shared?
Answer:
£980
Step-by-step explanation:
3 portions = 210
1 portion = 70
so 70
70 × 4 = would be 280
70 × 7 = 490
490 + 280 + 210 = 980
hope this works : )
Can someone explain this pls
Answer:
Step-by-step explanation:
( g ° f )(x) = ( x + 7 )² = x² + 14x + 49
20 + 3(x² + 14x + 49) = - 34
20 + 3x² + 42x + 147 = - 34
3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0
D = 196 - 268 = - 72 < 0
There is no any roots in set of real numbers.
The values of x in set of complex numbers are:
[tex]x_{12}[/tex] = [tex]\frac{- 14 }{2}[/tex] ± [tex]\frac{6\sqrt{2}i }{2}[/tex]
[tex]x_{12}[/tex] = - 7 ± 3√2 i
adam has $800 invested in two accounts. one pays 6% annual interest and the other pays 10% interest. the amount of annual interest is the same as he would earn if the entire $800 was invested at 8.25%. How much does he have invested at each rate?
Adam invested $350 at 6% and $450 at 10%
Amount invested by Adam = $800
Interest paid by one account = 6%
Interest paid by another account = 10%
Let the amount invested in one account be x and the other be y
The formula for simple interest is given by:
Simple interest = (P*R*T)/100
where P = Principal
R = rate of interest
T = number of years amount is invested
Substituting the value in the formula we get:
Simple interest in one account = (x*6*1)/100-------(1)
Simple interest in another account = (y*10*1)/100--------(2)
The question states that interest earned would be the same when $800 is invested at 8.25%, therefore
Simple interest = (800*8.25*1)/100
= 66----(3)
Equating (1), (2) and (3) we get:
x + y = 800-----(4)
6x/100 + 10y/100 = 66
6x + 10y = 6600-----(5)
Multiplying (4) with 6 and equating it with (5)
6x + 6y = 4800
6x + 10y = 6600
4y= 1800
y = 450
x = 350
So, Adam invested $350 at 6% and $450 at 10%
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A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?
Answer:
Answer would be 22 km at southward direction.
Answer = 22km
Step-by-step explanation:
As it started from the point O.
* Goes 50 to East direction
* Goes 22 to North direction
* Goes 50 to West direction
* And the it travels back to the starting point when it turn to south direction. It traveled 22 km to southward direction.
> Total kilometers the train traveled is 144 kilometers.
I hope you get this right.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 9x+6y=42
Answer:
4
Step-by-step explanation:
9x+6y=42
solution
Balancing Method :
subtract both sides by 6
9x-6y+6y=42-6=
9x=42-6=36
divide both by 6
9 ÷9=36÷9=4
I got one final question... What is -1/3x + 1 = -7
Answer Formula: x =
Answer: x=24
Step-by-step explanation:
-1/3x+1= -7
you move the negative one to the other side of the equation to get x by itself and get -1/3x= -8
then you divide both sides by -1/3 and get 24
a line skew to AT (in image attatched)
The line skewed to AT is HB
How to determine the line skewed to AT?As a general rule, skew lines are nonparallel lines that do not intersect
This means that the lines are in different planes
From the given figure, we can see that lines HB and AT do not intersect and they are not parallel
Hence, the line skewed to AT is HB
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HELP PLEASE!!!!!!! A zookeeper wrote down the number of fish each of the ten dolphins in the aquarium ate per day. His results were as follows: 18, 15, 25, 17, 13, 15, 23, 27, 30, and 27. Find the mean absolute deviation of this data set. What does the mean absolute deviation tell you about the dolphins at the aquarium?
The mean absolute deviation is 5.4.
The mean absolute deviation tells us that the variance of each data set is 5.4.
What is the mean absolute deviation?The mean absolute deviation is a measure of variance that determines the average distance between each data point in the dataset and its mean.
The mean absolute deviation = 1/n ∑ l x - m(x) l
The first step is to determine the mean of the data set: (18 + 15 + 25 + 17 + 13 + 15 + 23 + 27 + 30 + 27) / 10
= 210 / 10
= 21
The second step is to determine the absolute difference between the mean and each data point. Then add the result together.
|(18 - 21) + (15 - 21)+ (25- 21) + (17- 21) + (13- 21) + (15- 21) + (23- 21) + (27- 21) + (30- 21) + (27- 21)| = 54
Now, divide the sum by the total numbers in the data set : 54 / 10 = 5.4
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The coordinate point (-5, 18) is a point on the graph of f. Write this point in function notation.
f(-5) = 13
f(-5) = 18
f(18) = -3.6
f(18) = -5
The function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18
What are coordinate points?Coordinate points are mathematical statements that are used to represent the location of points on a coordinate plane
How to rewrite the function notation of the coordinate point?The coordinate point is given as
(-5, 18)
The above coordinate point can be represented as
(x, y) = (-5, 18)
The above coordinate point can further be rewritten as
(x, f(x)) = (-5, 18)
So, we have
x = -5
f(x) = 18
Substitute x = -5 in the equation f(x) = 18
f(-5) = 18
Hence, the function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18
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write the equation y=-6+5 in function notation using f (x) to denote the function
The equation y = -6x + 5 when rewritten is f(x) = -6x + 5
How to denote the equation as a function?The equation is given as
y = -6 + 5
Rewrite the above equation properly
So, we have
y = -6x + 5
Express y as a function
So, we have
f (x) = -6x + 5
Hence, the equation y = -6x + 5 when rewritten is f(x) = -6x + 5
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The point G(-5, -1) is reflected over the line y= -3. What are the coordinates of the resulting point, G’
The coordinates of the resulting point after the reflection are (-5, -5)
What are the coordinates of the resulting point?
When we do a reflection over a given line, the perpendicular distancee between the line and the point is invariant.
In this case, we want to reflect the point (-5, -1) over the line y = -3
The distance between the y-value of the point and the line is:
D = |-1 - (-3)| = | -1 + 3| = 2
The point is at 2 units (above) from the line, then after the reflection, the point will be 2 units below the line.
So the new y-value is:
y = -3 - D = -3 - 2 = -5
The coordinates of the resulting point are (-5, -5).
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What are two different names for the plane shown
in the diagram below?
Answer:
Plane Y and CDB
Step-by-step explanation:
Plane Y and CDB
Given:
p: x-5= 10
q: 4x+1 = 60
Which is the inverse of p→q?
If x-5 ≠ 10, then 4x+1≠61.
If 4x+1 ≠61, then x-5≠10.
If x-5=10, then 4x+1=61.
If 4x+1=61, then x-5=10
Answer:
Step-by-step explanation:
Choose the measurement closest to 180 cm: 6 ft, 180 in. or 450 in
Answer:
6ft
Step-by-step explanation:
180cm=5ft10in=70in
So it's closer to 6ft
Directions: For the following problems....
(a) determine the correct conclusion or further conclusion based on the given information and diagram. Your
conclusions should only be based on the given information, not what you believe the diagram may imply.
(b) fill in the appropriate statement/reason chart to organize your work. REMINDER: A reason can only be a
definition or definition reversed.
1. Given: LFHEZKHE
HINT: Your conclusion should NOT be the m2FHE =
m2KHE! There is a better conclusion to draw here...
Conclusion: FHE = KHE
ΔFHE = ΔKHE, as the ∠FHE = ∠KHE. When two triangles contain the same two sides and include the same Angle, the remaining sides, Angle, and area are likewise identical, which means they're congruent.
∠FHE ≅ ∠KHE is an Identical part.
L(FE) = L(KE), as two Congruent angles have equal sides
L( FH) = L(KH)
L(EH)=L(EH), Common part in a figure.
Congruent angles are two or more angles that are exactly the same. As a result, the lengths of these angles are identical.
hence, ΔFHE = ΔKHE, as the ∠FHE = ∠KHE. When two triangles contain the same two sides and include the same Angle, the remaining sides, Angle, and area are likewise identical, which means they're congruent.
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Maya is using a coordinate plane to create a map of her yard drawn to scale. Each unit
on the coordinate plane represents 1 meter. Her yard forms a quadrilateral with vertices
A(5, -3), B(10, -3), C(12, -11), and D(7, -11). Maya would like to fence in her entire
yard. Fencing costs $200 per meter. How much will it cost Maya to fence in her yard?
Answer:
$5,298.48
Step-by-step explanation:
Given vertices:
A = (5, -3)B = (10, -3)C = (12, -11)D = (7, -11)As points A and B, and points C and D, have the same y-coordinates, AB is parallel to CD.
As there is a difference of 5 units between points A and B, and C and D, AB = CD.
As AB is parallel to CD and AB = CD ⇒ AD = BD and AD is parallel to BD.
Therefore, the quadrilateral ABCD is a parallelogram (see attachment).
To find the perimeter of ABCD, calculate the side lengths of AB and AD using the Distance Formula.
[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(10-5)^2+(-3-(-3))^2}\\& =\sqrt{(5)^2+(0)^2}\\& =\sqrt{25}\\& =5\:\:\sf units\end{aligned}[/tex]
[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(7-5)^2+(-11-(-3))^2}\\& =\sqrt{(2)^2+(-8)^2}\\& =\sqrt{4+64}\\& =\sqrt{68}\:\:\sf units\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $ABCD$} & = AB + CD + AD + BC\\& = 2\:AB + 2\:AD\\& = 2 \cdot 5+2 \cdot \sqrt{68}\\& = 10+2 \sqrt{68}\\& = 10+2\sqrt{4 \cdot 17}\\& = 10+2\sqrt{4}\sqrt{17}\\& = 10+2 \cdot2\sqrt{17}\\& = 10+4\sqrt{17}\:\:\sf units\end{aligned}[/tex]
As 1 unit = 1 meter, the perimeter of the fence is (10 + 4√17) m.
If fencing costs $200 per meter:
[tex]\begin{aligned}\sf \implies Cost \:of\:fencing& = 200(10 + 4 \sqrt{17})\\& = 2000+800 \sqrt{17}\\& = 5298.4845\\ & = \$5298.48\end{aligned}[/tex]
Therefore, it will cost Maya $5,298.48 to fence her yard.
Best answer is ready to give gift prize?
Step-by-step explanation:
but please where is the question I'm eager to answer and win the pizza
Ileana wants to know the mean number of pets owned by students in her
grade. She conducts a survey of 20 of her classmates to see how many pets
they own. The results are shown in the dot plot.
Number of Pets In the Home
::::::
0
1 2 3 4 5 6
●●
7
H
8 9 10
Which is the best estimate of the mean number of pets owned by students in
her grade?
Based on the results shown in the dot plot on the number of pets owned by students in Ileana's grade, the mean number of pets owned by students is 2.5 pets
What is the mean number?The number of pets owned per student home according to the dot plot is:
= 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 8
The total number of pets owned is:
= 0 + 0 + 0 +1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 +8
= 50 pets
The mean number of pets owned is:
= 50 / 20 students
= 2.5 pets
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For the month of December, a checking account has a balance of $500 for 12 days, $1250 for 12 days, $1150 for 3 days, and $600 for 4 days. What is the average balance for December?
Answer:
$866.13
Step-by-step explanation:
to get an average, you add up all the factors then divide them by how many there are. I added 500 12 times to 1250 12 times to 1150 3 times and 600 4 times.
aka (500*12)+(1250*12)+1150+1150+1150+600+600+600
then i divided by 31 because 12+12+3+4=31. giving the average $866.13.
Will y=3x+5 pass throught the (0,5) or will it not pass the (0,5) ?
(0,5) is that equations y intercept so it WILL pad through that point.
[tex]Answer:\ y=3x+5\ pass\ throught\ the\ (0,5)[/tex]
Step-by-step explanation:
[tex]y=3x+5\ \ \ \ \ (0,5)\\5=3*0+5\\5=0+5\\5\equiv5\\Hence,\\y=3x+5\ pass\ throught\ the\ (0,5)[/tex]
Solving quadratics factoring G CF, solving equations by factoring
Answer: k=0,-5
Step-by-step explanation:
Your GCF is 5k, as you're able to take it out of both terms.
Once you've taken out a 5k, this will leave you with an equation that looks like this;5k(k+5)=0.
Set your 5k equal to 0 and divide to get k=0
Set your k+5 equal to 0 and subtract on both sides to get k=-5
Hope this helps you, dawg.