vertex at
(
−
1
,
−
4
)
Explanation:
Given:
y
=
2
x
2
+
4
x
−
2
Convert the given form into "vertex form"
y
=
m
(
x
−
a
)
2
+
b
with vertex at
(
a
,
b
)
XXX
y
=
2
(
x
2
+
2
x
)
−
2
complete the square
XXX
y
=
2
(
x
2
+
2
x
+
1
)
−
2
−
2
XXX
y
=
2
(
x
+
1
)
2
−
4
XXX
y
=
2
(
x
−
(
−
1
)
)
2
+
(
−
4
)
which is the vertex form with vertex at
(
−
1
,
−
4
)
graph{2x^2+4x-2 [-5.455, 7.034, -5.54, 0
Question 5
5 pts
Let f(x)
40e^.06t. What is the average rate of change of f over the
interval [0,3]? Give your answer as a decimal with one place of
accuracy to the right of the decimal point.
Answer:
[tex]R= 2.6[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 40e^{.06t[/tex]
[tex][a,b] = [0,3][/tex]
Required
Determine the average rate of change (R)
This is calculated as follows:
[tex]R = \frac{f(b) - f(a)}{b - a}[/tex]
Where
[tex]a = 0[/tex] and [tex]b = 3[/tex]
Substitute 0 for a and 3 for b
[tex]R = \frac{f(3) - f(0)}{3 - 0}[/tex]
[tex]R = \frac{f(3) - f(0)}{3}[/tex]
[tex]R = \frac{1}{3}[f(3) - f(0)][/tex]
Calculate f(3)
[tex]f(x) = 40e^{.06t[/tex]
[tex]f(3) = 40e^{.06*3}[/tex]
[tex]f(3) = 40e^{0.18}[/tex]
[tex]f(3) = 40 * 1.197[/tex]
[tex]f(3) = 47.88[/tex]
Calculate f(0)
[tex]f(x) = 40e^{.06t[/tex]
[tex]f(0) = 40e^{.06*0}[/tex]
[tex]f(0) = 40e^{0}[/tex]
[tex]f(0) = 40*1[/tex]
[tex]f(0) = 40[/tex]
So, the expression:
[tex]R = \frac{1}{3}[f(3) - f(0)][/tex]
[tex]R= \frac{1}{3}[47.88 - 40][/tex]
[tex]R= \frac{1}{3}[7.88][/tex]
[tex]R= 2.62666666667[/tex]
[tex]R= 2.6[/tex]
Hence, the average rate of change is approximately 2.6
Write an expression that represents the area of
the figure in square centimeters.
HELP ASAP
Answer:
its either 98 cm or 28 cm
Step-by-step explanation:
7 x 7 = 49 x 2 = 98 cm
14 x 2 = 28
Evaluate the given expression for x=-14. -3x-5
Answer:
The answer is: 37
Step-by-step explanation:
The reason its this answer because first thing you have to do is the order operations Please Excuse My Dear Aunt Sally, since there is no parenthesis, or exponents we cross those out. Since, there is multiply we put in -14 where is x.
-3x-5=-3(-14)=5
Next, we multiply -3 and -14 and we get:
42, there reason its not a negative because two negatives equal to a positive.
There is Division or Addition, those are out. The only thing that is left Subtraction... So we are going to subtract 42-5 which equals;
37
I hope my answer helps!!
A store is having a sale with a 19% discount on all merchandise. Write an
equation representing between the regular cost of merchandise (r) and
the discount received (d).
Your answer
Answer:
3
Step-by-step explanation:
PLEASE HELP ME!!!!!! Write the information in the table as ordered pairs. Graph the relationship from the table.
Answer:
(3, 60) (5, 100) (8, 160) (9, 180) (12, 240)
Step-by-step explanation:
3. Simplify the following inequalities.
Answer:
7x+7 > 23-x
group like terms
7x+ x > 23-7
8x > 16
we divide both side by
8x > 16
8 8
so 8 cancelled out 8 living
x > 16
8
x > 2
8
we
1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.
2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.
3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency
9514 1404 393
Explanation:
1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.
If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)
__
2. The general form of the equation of a circle is ...
Ax² +Ay² +Dx +Ey +F = 0
Any equation of a circle can be put in this form. If we divide by A, this can be written as ...
x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A
and the equation can be further transformed to the standard form ...
(x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c
The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.
__
3. Again refer to the attached diagram.
a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.
b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.
c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.
d) A secant is a line containing two points of the circle. Lines CG and CE are secants.
e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.
f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).
marie wants to know the most popular car for parents. She plans to survey the people shopping at the used car lot from 10:00 a.m. to 11:00 p.m. Which statement below best reflects Marie's plan?
A. Marie's sample is valid.
B. Marie should also survey people entering the grocery stores.
C. Marie's sample is biased.
D. Marie should make sure she surveys both men and women.
Answer:
C Marie's sample is biased.
Step-by-step explanation:
It is biased because she doesn't know. It is just 1 hour so like there could be like a lot of people at 4-5 and not a lot at 10-11
Hope this helps!
Merry Christmas
Answer:
Give the other person brainliest.
Step-by-step explanation:
The other person is correct.
answer the following questions please
Answer: 11. D 12.d 13. A
Step-by-step explanation:
Answer:
Evern though this isn’t a math question, I’ll still help you :)
11. Option D
12. Option D
13. Option B
Hope this helps! :)
(1 point) A pond contains 100 fish, of which 40 are carp. If 20 fish are caught from the lake, what are the mean and variance of the number of carp among those 20
Answer:
E(X) = 6
Var(X) = 3.394
Step-by-step explanation:
Let X represent the number of carp caught out of the 20 fishes caught. Now, if we are to assume that each
of the (100, 20) ways to catch the 20 fishes will be equally likely.
Thus, we can say that X fulfills a hypergeometric
distribution with parameters as follows;
n = 20, N = 100, k = 30
Formula for expected mean value in hypergeometric distribution is;
E(X) = nk/N
E(X) = (20 × 30)/100
E(X) = 6
Formula for variance is;
Var(X) = (nk/N) × [((n - 1)(k - 1)/(N-1))) + (1 - nk/N)]
Var(X) = ((20 × 30)/100) × [((20 - 1)(30 - 1)/(100 - 1)) + (1 - (20 × 30/100)]
Var(X) = 6 × 0.5657
Var(X) = 3.394
Given the points P(2, –6) and R(8, 3), what is the component form of Vector PR?
- ⟨6, -3⟩
- ⟨10, -3⟩
- ⟨6, 9⟩
- ⟨10, 9⟩
Answer:
the third one
Step-by-step explanation:
jsut took it
Answer:
It’s C
Step-by-step explanation:
Mac uses 3.5 liters of water with 4
lemons to make lemonade. How many
lemons are needed if Mac uses 7 liters of
water to make lemonade?
Answer:
if I'm correct, it should be 6.125. I'm sorry if I'm wrong,
Step-by-step explanation:
take 3.5 and divide it by 4, which gives you the amount for 1 lemon. times that by 7, and you get 6.125
Answer:
8 lemons
Step-by-step explanation:
7- 3.5= 3.5
Therefore we multiple 3.5 by 2.
We always do the same on the other side.
4 times 2 equals 8
7 liters of water: 8 lemons
a square and rectangle are shown below the width of the rectangle is the same length at a side of the square both represented by x the length of the rectangle is one foot more than twice its width the perimeter of the rectangle is 26 feet more than that of the square write an expression for the length of the rectangle in terms of x label of the drawing
Answer:
The answer for the length of the rectangle in terms of x is 2x+1=26
Step-by-step explanation:
What is the value of the function at x = 22 Enter your answer in the box .please help.
Answer:
its gonna be whatever the y value is when x is 22
Step-by-step explanation:
What’s the common factor for 72 and 84
Answer:
Step-by-step explanation:
This is the general method for doing this problem. First factor these numbers into primes.
72: 2 * 2 * 2 * 3 * 3
84: 2*2 * 3 * 7
Now each number has at least two 2s
Each number has at least one 3
The highest common factor is 2 * 2 * 3 = 12
Part B
Line m has a slope of -3. Another line n is parallel to line m. What is the slope of line n?
Slope of linen is
Answer:
Step-by-step explanation:
the slope of line n is also -3 as it is parallel to m
The answer is A
You have $500, sale price is $435. How much change will you get
Answer:
go to sleep its 11:23 also u will get
$65 dollars pls mark me brainleist
Step-by-step explanation:
x-10x+1< 20+ 5x for x = -2
Help me please
Answer:
As the x=-2 does not satisfy the inequality.
Therefore, the solution is False!
Step-by-step explanation:
Given the expression
[tex]x-10x+1<\:20+\:5x\:[/tex]
substituting the value x = -2
[tex]\left(-2\right)-10\left(-2\right)+1<20+5\left(-2\right)[/tex]
[tex]-2+20+1 < 20-10[/tex]
[tex]19 < 10[/tex]
As the x=-2 does not satisfy the inequality.
Therefore, the solution is False!
I'm not understanding
Answer:
D. x = 3
Step-by-step explanation:
We would like to find out for what value of x does f(x) = g(x). This is essentially the same as asking us to find the x-value for which f(x) = k, where k is some number, and g(x) = k, as well.
Looking at the two tables provided, we notice that when x = 3, both f(x) and g(x) equal -2. So, the answer is D.
the solution of 3x+5=x+9 is ____
Answer:
x=2
Step-by-step explanation:
move x to the 3x side and move 5 to 9 side.
you get 2x=4
then you divide 2 from both sides and get 2
Answer:
x=2
Step-by-step explanation:
•Original Expression;
3x+5=x+9
•Group like terms;
3x-x=9-5
•Simplify
3x-x
=2x
Then
9-5
=4
Which is going to be;
2x=4
•Divide both sides by 2 to find x
4 can be divided by 2 two times so;
x=2
Solve the inequality. 2(4x – 3)-3(3x) + + 5x?
Answer:
2 (2 x - 3)
Step-by-step explanation:
Simplify the following:
2 (4 x - 3) - 3×3 x + 5 x
-3×3 = -9:
2 (4 x - 3) + -9 x + 5 x
Grouping like terms, 2 (4 x - 3) - 9 x + 5 x = 2 (4 x - 3) + (5 x - 9 x):
2 (4 x - 3) + (5 x - 9 x)
5 x - 9 x = -4 x:
2 (4 x - 3) + -4 x
2 (4 x - 3) = 8 x - 6:
8 x - 6 - 4 x
Grouping like terms, 8 x - 4 x - 6 = (8 x - 4 x) - 6:
(8 x - 4 x) - 6
8 x - 4 x = 4 x:
4 x - 6
Factor 2 out of 4 x - 6:
Answer: 2 (2 x - 3)
Ms. cooper goes to Panera Bread for dinner and orders the Green Goddess salad. Her total was $8.79. Ms. cooper gave the cashier $10, how much change did she receive?
I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS!!!!
2. Darwin believes that x + b is a factor of (x + b)3 + (x + c)2 – (b - c), while Eunju
believes it is not. Who is correct? Justify your response.
3. How can you prove that x2 + 5x + 6 is a factor of x* + 5x3 + 2x2 – 20x – 24, without
using long or synthetic division?
Answer:
2. Eunju is right
3. [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].
Step-by-step explanation:
Polynomial Remainder Theorem
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).
As a consequence, if a polynomial is divisible by x-a, f(a)=0.
Part 1:
Let's make:
[tex]f(x)=(x+b)^3+(x+c)^2-(b-c)[/tex]
To find out if x+b is a factor of f(x), we find f(-b):
[tex]f(-b)=(-b+b)^3+(-b+c)^2-(b-c)[/tex]
Operating:
[tex]f(-b)=(-b+c)^2-(b-c)[/tex]
The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).
Part 2:
We must find out if [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex] without using long division or synthetic division.
We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:
[tex]x^2+5x+6 =(x+2)(x+3)[/tex]
Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.
Let's make:
[tex]f(x)=x^4+5x^3+2x^2-20x-24[/tex]
Find f(-2):
[tex]f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24[/tex]
[tex]f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0[/tex]
Find f(-3):
[tex]f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24[/tex]
[tex]f(-3)=81-5*27+2*9+60-24[/tex]
[tex]f(-3)=81-135+18+60-24 =0[/tex]
Since both f(-2) and f(-3) are zero, [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].
Write an Equivalent Expression by combining like terms for 2x+3x+y+2y
Answer:
5x+3y
Step-by-step explanation:
2x+3x=5x since they have the same variable.
y+2y
1y+2y u can put a 1 so that would be 3y
5x+3y
Abbey receives a $40 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $2.89 a. Let m represents the number of songs downloaded. Write an inequality that represents this given situation? b. What is the maximum number of songs Abbey can download?
Answer:
A. $2.89(m)=$40
B. 13 songs
Step-by-step explanation:
$2.89(m)=$40
m=$40/$2.89
m=13.84
She can download a maximum of 13 songs
Check:
$2.89 (13 songs)=$37.57
$40-$37.57=$2.43 left on her gift card
m=13.84, check that 0.84 of the cost of a song is left over 0.84*$2.89=$2.43
Answer:
13 songs
Step-by-step explanation:
40 divided by 2.89 is 13.84. DO NOT ROUND TO 14
So its a maximum of 13 songs, otherwise it will cost 40.46 for 14 songs
In the sixth grade, 54% of the students are boys. There are 189 boys in the sixth grade. What is the total number of students in sixth grade? A. 54 B. 161 C. 189 D. 350. (explain what did u do to get you're answer )
Answer:
D
Step-by-step explanation:
189 boys is 54%
x is 46%(100-54)
Cross multiply:
189*46%=54%*x
86.94=0.54x
x=161
189 boys 161 girls
350 altogether
So D
Hope this helps plz hit the crown :D
Here is an expression: 4 ∙ 3ˢ Evaluate the expression when s is 1.
Help 25 points !!!!!!!!!!!
Answer:
1 -> 12s
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Please answer this ASAP
9514 1404 393
Explanation:
1. ∠BAC ≅ ∠BCA, BD ≅ BE, ∆BDA and ∆BEC are right triangles . . . . given
2. ∆ABC is isosceles . . . . definition of isosceles triangle
3. BA ≅ BC . . . . definition of isosceles triangle
4. ∆BDA ≅ ∆BEC . . . . HL theorem
5. AC ≅ CE . . . . CPCTC
Rob is setting up a model train track that is 3 and 3 over 8 feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 3 over 8 foot apart. How many telephone poles does he need? (Input number values only.
Answer:
9?
Step-by-step explanation:
Answer:
sorry dont understaand
Step-by-step explanation:
What is the constant rate???
Answer:
The constant rate is 4
Step-by-step explanation:
40 ÷ 10 = 4
80 ÷ 20 = 4
120 ÷ 30 = 4
160 ÷ 40 = 4
They all equal 4 so that is the constant rate.
Brainliest???
