Answers
Answer:
y + 16 = -1(x + 3)²
Step-by-step explanation:
Looking at the graph, parabola vertex opens upwards with x intercepts as -5 and -1.
Thus, the line of symmetry will be;
x = (-5 + (-1))/2 = -3
Looking at the graph we can see that the vertex when traced to the x - coordinate will be 3 which is same with what we got.
Now, the general form of the equation will be;
y - h = a(x - k)²
where (k,h) is the vertex coordinate
Thus, k = -3
So;
y - h = a(x - (-3))²
>> y - h = a(x² + 6x + 9) =
>> y = ax² + 6ax + 9a + h
When, x = 0
y = 9a + h
From the graph, we can see that the y-intercept is y = -25
Thus;
9a + h = -25
From the graph, h which is the y-coordinate of the vertex = -16
Thus;
9a - 16 = - 25
9a = -25 + 16
9a = -9
a = -9/9
a = -1
Thus, the equation is;
y - (-16) = -1(x - (-3))²
>> y + 16 = -1(x + 3)²
Related Questions
How many solutions does y+x=5 5x+5y=25 have?
A) One
B) Infinitely Many
C) None
D) Two
Answers
Answer:
B is the answer.
Step-by-step explanation:
Given equations y + x = 5 and 5x + 5y = 25.
These equations have infinetely many solutions because they are equivalent.
This can be proven by the multiplicative property of equality and the commutative property of addition.
y + x = 5 → y × 5 + x × 5 = 5 × 5 [multiplicative property of equality] → 5y + 5x = 25 → [commutative property of addition] 5x + 5y = 25.
this is a trignometry question
hope u will do for me
i will mark brainliest..:)
Answers
Step-by-step explanation:
[tex]\cos^{4} x - \sin^{4} x[/tex]
[tex]= ( \cos^{2} x + \sin^{2} x)( \cos^{2} x - \sin^{2} x)[/tex]
[tex] = (1 - \sin^{2} x + \sin^{2} x)( 1 - \sin^{2} x - \sin^{2} x)[/tex]
[tex] = 1 - 2\sin^{2} x[/tex]
Note: I replaced all cos^2x terms using the identity
[tex]\cos^{2} x = 1 - \sin^{2} x[/tex]
Write the equation of the line which contains all images of point C.
(12.1)
С
(8,0)
B
2
10
12
(a,b)
(Α)
2
B
y = 4.3 – 2
C
y = 4.2
4.
Answers
Answer:
A
Step-by-step explanation:
y = 1/4 × x - 2
x=8 => y=0. correct for B
x=12 => y= 1. correct for C
all other answer options fail for these 2 points.
make the letter in the bracket the subject of the A=
[tex]v = u + at \: (a)[/tex]
Answers
Answer:
a=acceleration due to gravity=9.8m/s²
v=final velocity
u=initial velocity
t=time taken
interpretation of the vertical line
Answers
What is the solution to the system of equations?
Solve using the substitution method.
-5x – y=6
-8x + y = 20
A) (-2,4)
B) (1, -2)
D) (2, 1)
C) (1,2)
Answers
Answer:
-8x+y=20
y=20+8x
-5x-y=6
-5x-(20+8x)=6
-5x-20-8x=6
-13x=6+20
-13x=26
-13x÷ -13=26÷ -13
x= -2
-8x+y=20
-8×(-2)+y=20
16+y=20
y=20-16
y=4
A) (-2,4)
Solve the equation 28 + 24p = 36 for p.
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\textsf{28 + 24p = 36}[/tex]
[tex]\textsf{24p + 28 = 36}[/tex]
[tex]\large\textsf{SUBTRACT 28 to BOTH SIDES}[/tex]
[tex]\textsf{24p + 28 - 28 = 36 - 28}[/tex]
[tex]\large\textsf{CANCEL out: 28 - 28 because that gives you 0}[/tex]
[tex]\large\textsf{KEEP: 36 - 28 because that helps solve for the p-value}[/tex]
[tex]\textsf{36 - 28 = \bf 8}[/tex]
[tex]\large\textsf{NEW EQUATION: 24p = 8}[/tex]
[tex]\large\textsf{DIVIDE 24 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{24p}{24}=\dfrac{8}{24}}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{\dfrac{24}{24}}\large\textsf{ because that gives you 1}[/tex]
[tex]\large\textsf{KEEP: }\mathsf{\dfrac{8}{24}}\large\textsf{ because that helps you solve for the p-value any}\\\\\large\textsf{gives you the value of it}[/tex]
[tex]\mathsf{p= \dfrac{8}{24}}\\\\\\\mathsf{p = \dfrac{8\div8}{24\div8}}\\\\\\\mathsf{8\div8=\bf 1}\\\\\mathsf{24\div8=\bf 3}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf p = \dfrac{1}{3}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
1/3
Step-by-step explanation:
Got a 100 on T4L
3x^2 – 8x + 5 = 5x^2
Answers
Answer:
Step-by-step explanation:
[tex]3x^2 -8x +5 = 5x^2\\\\5x^2 - 3x^2 + 8x -5 =0\\\\2x^2 +8x -5 = 0\\\\[/tex]
a = 2, b = 8, c = -5
[tex]x = \frac{-b \pm \sqrt{b^2 -4ac} }{2a}\\\\x = \frac{-8 \pm \sqrt{8^2 - ( 4 \times 2 \times (-5))} }{2 \times 2}\\\\x = \frac{-8 \pm \sqrt{64 +40} }{4}\\\\x = \frac{-8 + \sqrt{64 +40} }{4} \ , \ x = \frac{-8 - \sqrt{64 +40} }{4}\\\\x = \frac{-8 + \sqrt{104} }{4} \ , \ x = \frac{-8 - \sqrt{104} }{4}\\\\x = \frac{-8 + \sqrt{4 \times 26} }{4} \ , \ x = \frac{-8 - \sqrt{4 \times 26} }{4}\\\\x = \frac{-8 +2 \sqrt{26} }{4} \ , \ x = \frac{-8 - 2\sqrt{26} }{4}\\\\[/tex]
[tex]x = \frac{-4 + \sqrt{26} }{2} \ , \ x = \frac{-4 - \sqrt{26} }{2}[/tex]
Select all the numbers that are irrational
Answers
A) [tex]-\sqrt{5}[/tex]
D) [tex]\pi[/tex]
===========================================
Explanation:
Choices B and C are rational because we can simplify them to form a fraction of integers.
[tex]-\sqrt{49} = -7 = -\frac{7}{1}[/tex]
[tex]\sqrt{0} = 0 = \frac{0}{1}[/tex]
Any rational number is of the form P/Q where P,Q are integers and Q is nonzero.
So we can rule out choices B and C.
---------------
Choice A on the other hand cannot be written as a fraction of integers. The 5 isn't a perfect square, which makes [tex]-\sqrt{5}[/tex] irrational.
The same can be said about [tex]\pi[/tex] which is roughly equal to 3.14; the decimal digits go on forever without a known pattern.
Choice A and choice D are the two answers.
----------------
If we know the pattern of the decimal digits, then we can turn the decimal number into a fraction of integers
The number -0.777, where the 7s go on forever, converts to the fraction -7/9
That means we rule out choice E.
Which of the following represents the factorization of the polynomial function
graphed below? (Assume it has no constant factor.)
O A. y = (x+3)(x+5)
B. y = (x-3)(x +5)
C. y = (x-3)(x-5)
O D. y = (x+3)(x-5)
Answers
Answer:
need this anyone got it?
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hii! Does anyone know the answer to this? I’m bad at geometry and need help! Thank you
Answers
Answer:
Length of AC = 23.75 unit
Step-by-step explanation:
Give that BD II CE
Length of AB = 10 unit
Length of AD = 16 unit
Length of DE = 22 unit
Find:
Length of AC
Computation:
Give that BD II CE
So,
AB / BC = AD / DE
AB / [AC - 10] = AD / DE
10 / [AC - 10] = 16 / 22
[10][22] = [AC - 10][16]
220 = 16AC - 160
16AC = 220 + 160
16AC = 380
AC = 23.75
Length of AC = 23.75 unit
Find the length of the arc. Use 3.14 for T.
PLEASE HURRY
Answers
Answer:
Solution given;
angle =270°
radius [r]=8cm
we have
length of arc =270°/360°×2×π*r
=270°/360°×2×3.14*8=37.68cm
length of the arc is 37.68cm.
What is the area of the trapezoid showroelow?
7
25
4.
Answers
Answer:
180
Step-by-step explanation:
what is the value of 3/2 + 4/2?
Answers
Answer:
7/2 or 3 1/2
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
7/2
Step-by-step explanation:
3/2 + 4/2 = 7/2
Hope this helps!!
which of the following is a solid consisting of a disc, a point not in the same plane as the disc, and all the points between them
Answers
Answer:
the answer is cone.
Step-by-step explanation:
a p ex
Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover the exact distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
Answers
Answer:
Then 1/2 or 30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.
Two hours after Tom began Tom would cover 12 miles and three hours after Linda started Linda would be 6 miles far away from the starting point
Step-by-step explanation:
Linda walks in a straight line at 2 miles/hour
then after t ( hours time) she is 2 (m/h) * t = d (L)
for Tom running at 6 m/h starting one hour later to cover the same distance d(L)
d(L) = 6 m/h * ( t - 1 ) then:
2 (m/h) * t = 6 m/h * ( t - 1 )
2*t = 6*t - 6
4*t = 6
t = 6/4
t = 1,5 h
Checking that result.
we see that in 1,5 hours Linda has covered 2* 1,5 = 3 miles
and in 0.5 hours Tom covered the same distance 0,5 * 6 = 3 miles
NOTE: Remember that tom started one hour later.
Then 1/2 or 30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.
b) In this case
d(T) = 6* ( t - 1 ) must be equal to twice of the Linda distance
d(L) = 2 * 2 * t
6*t - 6 = 4*t
2*t = 6
t = 3
To check it
in 3 hours Linda had covered 3 * 2 = 6 miles
in 2 hours Tom had covered 2 * 6 = 12 miles
which function is a translation of the parent absolute value function?
shift 5 units to the right
shifts 4 units down
Answers
Answer:
[tex]g(x) = |x-5|-4[/tex]
Step-by-step explanation:
[tex]f(x) = |x|\\\\g(x) = f(x-5)-4\\\\g(x) = |x-5|-4[/tex]
2
Select the correct answer.
Simplify the expression 53x55
Answers
Answer:
2915
Step-by-step explanation:
What is the surface area of a cylinder with a radius of 5 and a height of 8? round to the nearest 10th
Answers
Answer:
408.4
Step-by-step explanation:
The math question is in the picture thank you
Answers
Answer:
2+2=4 and 4*4=16 16+2 = 18 so WOOSH your answer is now a legal adult
Step-by-step explanation:
d nuts
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a
a
a
a
a
a
a
a
a
a
a
a
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: Show that the solution of the differential equation: = − − − − − is of the form: + + ( − ) = + , When = and =
Answers
Answer:
[tex]y = \tan(x + \frac{x^2}{2})[/tex]
Step-by-step explanation:
Poorly formatted question; The complete question requires that we prove that [tex]y=\tan(x+\frac{x\²}{2})[/tex]
When
[tex]\frac{dy}{dx} =1+xy\²+x+y\²[/tex] and [tex]y(0)=0[/tex]
We have:
[tex]\frac{dy}{dx} =1+xy\²+x+y\²[/tex]
Rewrite as:
[tex]\frac{dy}{dx} =1+x+xy\²+y\²[/tex]
Factorize
[tex]\frac{dy}{dx} = (1+x)+y\²(x+1)[/tex]
Rewrite as:
[tex]\frac{dy}{dx} = (1+x)+y\²(1+x)[/tex]
Factor out 1 + x
[tex]\frac{dy}{dx} = (1+y\²)(1+x)[/tex]
Multiply both sides by [tex]\frac{dx}{1 + y^2}[/tex]
[tex]\frac{dy}{1+y\²} = (1+x)dx[/tex]
Integrate both sides
[tex]\int \frac{dy}{1+y\²} = \int (1+x)dx[/tex]
Rewrite as:
[tex]\int \frac{1}{1+y\²} dy = \int (1+x)dx[/tex]
Integrate the left-hand side
[tex]\int \frac{1}{1+y\²} dy = \tan^{-1}y[/tex]
Integrate the right-hand side
[tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex]
[tex]y(0)=0[/tex] implies that: [tex](x,y) = (0,0)[/tex]
So:
[tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex] becomes
[tex]\tan^{-1}(0) = 0 + \frac{0^2}{2} + c[/tex]
This gives:
[tex]0 = 0 +0 + c[/tex]
[tex]0 =c[/tex]
[tex]c = 0[/tex]
The equation [tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex] becomes
[tex]\tan^{-1}y = x + \frac{x^2}{2} + 0[/tex]
[tex]\tan^{-1}y = x + \frac{x^2}{2}[/tex]
Take tan of both sides
[tex]y = \tan(x + \frac{x^2}{2})[/tex] --- Proved
The midpoint of AB is M(6, 3) . If the coordinates of A are (7, 4) , what are the coordinates of B?
Answers
Answer:
5,2
Step-by-step explanation:
the difference between a and m is 1,1 so 1,1 subtracted from the mid point(M) would be 5,2
Mahak is measuring the maximum space inside a watering can. This is a measure of A weight. B capacity.
Answers
Answer:
B. capacity.
Step-by-step explanation:
In this scenario, Mahak is measuring the maximum space inside a watering can. Thus, this is a measure of capacity because it gives the exact information as to the quantity of water the watering can hold at any given time.
Basically, the capacity of a container is a measure of the volume of fluid or any other substance that it is able to hold, which is typically measured in litres or cubic centimeters.
For example, if the shape of the watering can is cylindrical; its capacity (volume) would be measured using a mathematical expression.
Mathematically, the volume of a cylinder is given by the formula;
V = πr²h
Where;
V is the volume of a right circular cylinder.r represents the radius of the cylinder.h represents the height of the cylinder.David cooks a turkey in the oven at 450° for 30 minutes. Then he lowers the heat to 300° and cooks the Turkey for 2 more hours. How many minutes does David cook the turkey in all
Answers
Answer:
150 mins
Step-by-step explanation:
Answer:
150 minutes
Step-by-step explanation:
Use three-unit multipliers to convert 97 cubic feet to cubic inches
Answers
wuch equation represents O AB OB. re
Answers
Answer:
The answer that is C
Step-by-step explanation:
The equation would be y=1/2x + 8 because the line touches the y-intercept at +8. The others would be incorrect as the line does not increase by a slop of 8/1 and/or is the y-intercept at -8.
A teacher is making a history test composed of the same number of multiple-choice questions as short-answer questions. She estimates it will take students an average of 2 minutes to complete each multiple-choice question and an average of 3.5 minutes to complete each short-answer question.
Write an inequality to determine how many questions, n, the teacher can include if the test must take students less than 45 minutes to complete.
Answers
Answer:
8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.
A total of 16 questions.
Step-by-step explanation:
The number of multiple-choice questions and the number of short answer type questions are the same.
Let it be equal to [tex]x[/tex]
→Average time it takes to attempt multiple choice question = 2 minutes
→Total time it takes to attempt multiple choice question = [tex]2 * x[/tex] minutes
→Average time it takes to attempt short answer type question = 3.5 minutes
→Total Time it takes to attempt short answer type question = [tex]3.5 * x[/tex] minutes
Total time for the test should be less than 45 minutes.
Now finally, we can make an equation out of the information listed above:
[tex]2x +3.5x <45[/tex]
[tex]\\ 5.5x <45[/tex]
[tex]x < 8.18[/tex]
Hence the value of [tex]x = 8[/tex]
Image attached down bellow
Answers
Answer:
C
Step-by-step explanation:
x ≤ 4
answer??? please answer
Answers
Answer:
∠ 1 = 94°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
130° is an exterior angle of the triangle, then
∠ 1 + 36° = 130° ( subtract 36° from both sides )
∠ 1 = 94°
A.)23
B.)30
C.)53
D.)60
Answers
Answer:
m∠ABC = 150°
Step-by-step explanation:
180° - 90° = 90°
[tex](2x+14)+(x+7)=90[/tex]
[tex](2(23)+14)+(23+7)=90[/tex]
[tex]((46)+14)+(30)=90[/tex]
[tex](60)+(30)=90[/tex]
[tex]x=23[/tex]
90° + 60° = 150°