Answers
Answer:
vertex = (0, -4)
equation of the parabola: [tex]y=3x^2-4[/tex]
Step-by-step explanation:
Given:
y-intercept of parabola: -4parabola passes through points: (-2, 8) and (1, -1)Vertex form of a parabola: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex and [tex]a[/tex] is some constant)
Substitute point (0, -4) into the equation:
[tex]\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}[/tex]
Substitute point (-2, 8) and [tex]ah^2+k=-4[/tex] into the equation:
[tex]\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}[/tex]
Substitute point (1, -1) and [tex]ah^2+k=-4[/tex] into the equation:
[tex]\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}[/tex]
Equate to find h:
[tex]\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}[/tex]
Substitute found value of h into one of the equations to find a:
[tex]\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}[/tex]
Substitute found values of h and a to find k:
[tex]\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\implies y=3(x-0)^2-4=3x^2-4[/tex]
So the vertex of the parabola is (0, -4)
It can be solved through some shortcut tricks of parabola
y intercept= (0,-4)It passes through (-2,8) and (1,-1)
The minimum equation of the parabola (as it's quadratic) for vertex at (0,0)
y=ax²whatever our required parabola be it's translated from the above one
So
ax²=yLet a be 0
current equation is y=x²So it has vertex as well as y inetrcept at (0,0)
For x=-2
y=(-2)²=4 (but its 8 in our translated one )For x=1
y=1It wasn't negative but in translation it's negative so something is subtracted
Take a =2 and subtract (-2)² i.e 4 as it's minimal value of y=x² where x≠y
For
(-2,8)
-2=2(4)-4=8-4=4No try a=3
-2=3(4)-4=12-4=8Yes satisfied
Take (1,-1)
-1=3(1)-4=3-4=-1Verified
The required equation is
y=3x²-4Related Questions
Please answer asap!!! i need help w these
2. A display window consists of a stacked pyramid of books for sale. The bottom row has 57
books. Each row has three fewer books than the row below it. The display has 13 rows.
a.) Write the formula you learned in this unit needed to determine how many books are in
the top row of the display. (2 pts)
b.) What is the common difference of the sequence? d =
Show how you found this value. (1 pt)
c.) Use the formula you listed in step (a) to determine how many books are in the top row
of the display. Show all steps needed to solve and provide the final answer. (2 pts)
YTYY
d.) Write the formula leared in this unit needed to determine the number of books in the
entire display. (1 pt)
a.) What is the value of n? (1 pt)
(1 pt)
b.) Use the formula you listed in step (d) to determine the total number of books. Show all
steps needed to solve and provide the final answer. (2 pts)
Answers
The common difference on the sequence is -3 and the number of books will be 21.
How to illustrate the sequence?The formula that can be used to calculate the number of books will be:
= a + (n - 1)d
= 57 + (13 - 1)-
= 57 + (12 × -3)
= 57 - 36
= 21
Also, from the information given, each row has three fewer books than the row below it. Therefore, the common difference is -3.
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PLEASE HELP!!!
i under stand how bioconditional statements work but i don’t understand what this means. Please help me!!!
Answers
Work out the sheet below
Answers
Answer:
188 meters cubed
Step-by-step explanation:
radius = 1/2d d=6 radius =3 height 20formula for thia equation is 1/3 (3.14)(3^2)(20)(3.14)(9)(20)3.14 x 9 = 28.2628.26 x 20 = 565.2565.2/3 = 188.40188.4 round to 3sf is 188Brittany graphs the point (6,3) on a coordinate grid. Which describes where she
should plot the point if she starts at the origin?
Answers
Answer:
Six units to the right and 3 units up.
Step-by-step explanation:
Answer:
Six units to the right and 3 units up
Choose the best answer for the question below
*
5 points
Captionless Image
A
B
C
D
Answers
Answer:
The answer would be D.
Step-by-step explanation:
Hope this Helps! Have a good day!
Answer:
D is the answer
Step-by-step explanation:
is the answer to the question.
To understand these questions, first look at the way the answers are written out.
Alia questions three students from her class, that might be an answer, but she didn't randomly pick them.
Miles randomly surveys a group of customers at a coffee shop, that might be one, but he might have surveyed a 25 year old instead of a 24 year old, so thats not one.
Carson interviews students working part-time to gather data, he didn't select random students, he interviewed all of them, so that is not a valid option.
Lea speaks with the managers at half of the town's 10 supermarkets, which stock similar items, to find out which breakfast cereal is most popular among the town's residents, that one is not stating that she interviewed, but she interviewed half of the 10, which is five, which can be selected randomly.
So the correct answer is D.
I’m confused. Please help!!!
Answers
The values of r and w will be 50 and 140 degrees.
What is the Exterior Angle of a Triangle Property?An exterior angle of a triangle is equal to the sum of the opposite interior angles.
From the Exterior Angle of a Triangle Property;
38° + 103° = w
w = 140°
Let x be the exterior angle so that
x = r + 90°
Similarly,
By vertically opposite angle;
w = x
So, x = r + 90°
140 = r + 90°
r = 140 - 90
r = 50
Hence, the values of r and w will be 50 and 140 degrees.
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(Brainliest will be given as soon as possible!) Pierre wants to know how many people he can count on to vote for him as the school newspaper editor. He takes a poll of 34 random students and finds that 5 said they would vote for him.
If there are 272 students who will vote at the school, what would be Pierre’s best prediction for how many votes he can expect to receive?
Answers
The best prediction for the number votes Pierre should expect to receive is 40 votes
Calculating the number of vote
From the question, we are determine the best prediction for the number of votes Pierre should expect to receive
From the given information,
He takes a poll of 34 random students and finds that 5 said they would vote for him
Then, we can assume that,
Out of every 34 random students, 5 would vote for him
The total number of students that will vote = 272
There are eight 34s in 272
NOTE: 272 ÷ 34 = 8
Then, he should expect 8 × 5 votes
8 × 5 votes = 40 votes
Hence, the best prediction for the number votes Pierre should expect to receive is 40 votes
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please answer its due soon and ill make brainlist and rate 5 stars and like please answer correctly I really need it.
Answers
Answer:
The given quadratic has two solutions.
Step-by-step explanation:
The discriminant of a quadratic equation is [(b^2) - (4 * a * c)]
We're given the quadratic x^2 - 8x - 84 = 0
We can find a, b, and c by analyzing the quadratic.
So,
a = 1 because x^2 has no coeffiecient
b = -8 ( coefficient of 8 * the - )
c = -84 the raw y-intercept value of this function
Now we can plug these numbers into the discriminant expression:
(-8)^2 - ( 4 * 1 * -84 ) =
64 - ( - 336 ) =
64 + 336 =
400
Now that we know the value of the discriminant, we have to anazlyze it.
If the discriminant of a quadratic is positive, the quadratic has 2 solutions.
If the discriminant is negative, the quadratic has no solutions.
If the discriminant is equal to zero, the quadratic only has 1 solution.
In conclusion, because the discriminant = 400, and 400 > 0, the given quadratic equation has two solutions.
Steps:
Factor the expression.
Apply the AC Method
Look at the coefficients, A=1,B=-8,C=-84
Find factors of AC.
{1,2,3,4,6,7,12,14,21,28,42,84}
Find pairs of the above factors, which, when multiplied equal 84.
{1*84,2*42,3*28,4*21,6*14,7*12}
Which pairs of these factors have a difference of B = -8?
6-14=-8
Split the middle term to use above pair.
x^2+(6×-14x)-84
Factor x out of the first pair.
x*(x+6)+(-14x-84)
Factor-14 out of the second pair.
x*(x+6)-14*(x+6)
Group the common factor.
(x-14)*(x+6)
Set 1 st factor x-14 to 0 to solve.
x-14=0
Add 14 to both sides
x-14+14=0+14
Simplify
x=14
Set 2nd factor x+6 to 0 to solve.
x+6=0
Subtract 6 from both sides
x*6-6=0-6
Simplify
x=-6
Solution:
x=(-6,14)
The square root of a negative number can be expressed in?
Answers
Step-by-step explanation
No square root can be taken of a negative number within the system of real numbers because squares of all real numbers are non-negative.
Answer:
imaginary form
Step-by-step explanation:
So how we represent?
Let a number be -9
Find square root
√-9√9(-1)3√-13iSo
i stands for iota and has value √-1
What is the difference between the longest and shortest distances the gliders flew?
Answers
100yards equals how many feet
Answers
Answer: 300 ft
Step-by-step explanation:
100*3 = 300
How: 100*3
what id the diameter lenght of
(x-7)^2+(y-2)^2=225
Answers
The diameter length is 30.
What is equation of circle?We know that the general equation for a circle is(x−h)²+(y−k)²=r²,
where ( h, k ) is the center and r is the radius.
As we know form of a circle.
We will use this form to determine the diameter of the circle.
(x−h)²+(y−k)²=r²
Given equation is :
(x-7)²+(y-2)²=225
(x-7)²+(y-2)²=(15)²
On comparing the above equation with the with equation of circle, we have
r²=(15)²
r=15
So, the diameter will be the twice the radius.
diameter= 2r
diameter= 2*15
diameter= 30
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Solve ln (3x + 7) = 1. Round to the nearest thousandth.
Answers
Answer:
x = -2
Step-by-step explanation:
Step 1: Subtract 7 from both sides.
3x+7−7=1−7
3x=−6
Step 2: Divide both sides by 3.
3x/3 = −6/3
x = −2
what is 20.70% of 5,029,196
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20.70\% of 5029196}}{\left( \cfrac{20.70}{100} \right)5029196}\implies 1041043.572[/tex]
Step 2. 0.207x5029196= 1021
Therefore, the answer is 1021.
Help please:
Rewrite the problem in terms of some using the double-angle formula.
Answers
[tex]sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] ~\dotfill\\\\ sin(x)cos(x)=\cfrac{\sqrt{3}}{4}\implies \stackrel{\textit{multiplying both sides by 2}}{2sin(x)cos(x)=2\left( \cfrac{\sqrt{3}}{4} \right)}\implies sin(2x)=\cfrac{\sqrt{3}}{2}[/tex]
Are the ratios 1:4 and 3:10 equivalent?
Answers
[tex]\pmb{AnSwEr\::}[/tex]
these ratios are not equivalent . Please consult "Explanation" for more details
[tex]\bold{ExPlAnAtIoN}\downarrow[/tex]
We can write the ratios 1 : 4 and 3 : 10 as fractions :
[tex]\text{$\displaystyle\frac{1}{4} $}[/tex]
and
[tex]\text{$\displaystyle\frac{3}{10} $}[/tex]
Put the fractions together :
[tex]\text{$\displaystyle\frac{1}{4} \:and\:\frac{3}{10}$}[/tex]
Both fractions are in their simplest form ; the numerator and denominator do not have any common factors , except 1 , and there's no point in dividing by 1.
[tex]\small\text{hope helpful ( : }[/tex]
Which of the
following proves
these triangles
are congruent?
A. ASA
B. AAS
C. Neither, they are not congruent
Answers
By using '' ASA congruency theorem'' these triangles are congruent.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangles are shown in figure.
Now, We have to given in both triangles,
Two angles are equal to each other.
And, One side of both triangles are common.
Hence, By using ''ASA congruency theorem'' these triangles are congruent.
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What is the rational number equivalent to 1.28?
Answers
Answer: 1 28/100 or 1 7/25
Step-by-step explanation:
Find the solutions of the quadratic equation –9x2 + 49 = 0.
Answers
Answer:
x = 7/3
Step-by-step explanation:
Given equation:
–9x² + 49 = 0To determine the value of "x", we need to isolate the x-variable and it's coefficient on one side of the equation. This can be done by subtracting 49 to both sides of the equation.
⇒ –9x² + 49 - 49 = 0 - 49⇒ –9x² = -49We can see that the negative sign in on both sides of the equation. Remove it by dividing -1 to both sides of the equation.
⇒ –9x² = -49⇒ -9x²/-1 = -49/-1⇒ 9x² = 49Clearly, we can see that 9x² and 49 are perfect squares. Therefore,
⇒ 9x² = 49⇒ (3x)² = (7)²Take square root both sides of the equation:
⇒ √(3x)² = √(7)²⇒ 3x = 7To determine the value of "x", we need to isolate it "completely". This can be done by dividing 3 to both sides of the equation
⇒ 3x/3 = 7/3⇒ x = 7/3Therefore, the value of "x" must be 7/3.
Answer:
x = 7∕3, –7∕3
Step-by-step explanation:
To find the solutions of the quadratic equation -9x^2 + 49 = 0, we can solve for x by isolating x^2 first:
-9x^2 + 49 = 0
-9x^2 = -49
Dividing both sides by -9, we get:
x^2 = 49/9
Taking the square root of both sides, we get:
x = ± 7/3
Therefore, the solutions of the quadratic equation -9x^2 + 49 = 0 are x = 7/3 and x = -7/3.
Which graph shows only corresponding x-values and y-values where the value of y is 2 more than the product of x and 0.5?
Answers
IF YOU ARE MULTIPLYING BY 0.5 IT IS THE SAME AS CUTTING THE NUMBER IN HALF SO ALL X VALUES WOULD NEED TO BE EVEN NUMBER
If s(x) = 2x2 + 3x - 4, and t(x) = x + 4 then s(x) · t(x) =
A) 2x3 + 11x2 + 8x - 16
B) 2x3 + 5x2 + 16x - 16
C) 3x3 + 7x2 + 8x + 16
D) 3x3 - 11x2 + 16x + 16
Answers
Answer:
A) 2x3 + 11x2 + 8x - 16.
Step-by-step explanation:
s(x).t(x) = (x + 4)( 2x2 + 3x - 4)
= x(2x2 + 3x - 4) + 4( 2x2 + 3x - 4)
= 2x3 + 3x2 - 4x + 8x2 + 12x - 16
= 2x3 + 11x2 + 8x - 16
If you jog at a rate of 9 kilometers per hour, how long will it take you to
finish a 15-kilometer run?
Answers
Answer:
1.66667
Step-by-step explanation:
9------1
15-----?
We divide 9 by 9 to get 1 so we divide 15 by 9 to get ?
15 / 9 = 1.66667
Answer:
5/3 hours ( answer in fraction )
1.66 hours ( answer in decimal )
Step-by-step explanation:
Given,
Distance ( d ) = 15 kilometer ( 15 km )
Velocity ( v ) = 9 kilometers per hour ( 9 km / h )
To find : Time ( t )
Formula : -
v = d / t
t = d / v
= 15 / 9
t = 5/3 hours
( or )
t = 1.66 hours ( approximately )
Note : -
1. If the sentence " rate of kilometers " is there, then it is velocity.
2. If the sentence " How long will it take " is there, then it is time.
What is square root, extra points for example.
Answers
Answer:
A square root is a factor of a number that, when multiplied by itself, gives the original number. An example is √9 = 3
Hope this helped! I would appreciate a Brainliest!
Answer:
The square root is the answer to an equation with two number multiplied by itself. Say for example, b/a = a, a is the square root of b. Let's say b = 144 and a = 12, 12 would be the square root of 144.
Step-by-step explanation:
Example 1:
144/12 = 12
12 is the square root of 144
Example 2:
64/8 = 8
8 is the square root of 64
Example 3:
81/9 = 9
9 is the square root of 81
The fourth term of an arithmetic sequence is 20, and the 13th term is 65. Find the sum of the first 13 terms
Answers
Answer:
S₁₃ = 455
Step-by-step explanation:
the sum to n terms of an arithmetic is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
We require to find both a₁ and d
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₄ = 20 and a₁₃ = 65 , then
a₁ + 3d = 20 → (1)
a₁ + 12d = 65 → (2)
subtract (1) from (2) term by term to eliminate a₁
9d = 45 ( divide both sides by 9 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 20
a₁ + 15 = 20 ( subtract 15 from both sides )
a₁ = 5
Then
S₁₃ = [tex]\frac{13}{2}[/tex] [ (2 × 5 ) + (12 × 5 ) }
= 6.5 (10 + 60)
= 6.5 × 70
= 455
Isolate w for the literal equation v = lwh
Answers
[tex]\Large\textsf{\textbf{Answer\::}}[/tex]
view explanation please !
[tex]\Large{\textsf{\textbf{Calculations\::}}[/tex]
What are we asked to do ?
We are asked to isolate w (get w by itself) .
To do that , divide by lh on both sides :
[tex]\displaystyle\frac{V}{lh} = w[/tex]
So the right formula is :
[tex]\bigcirc\!\!\!\!\!\!\bigstar[/tex] [tex]\displaystyle\frac{V}{lh} =w[/tex]
[tex]\footnotesize\text{hope\:helpful~}[/tex]
Answer:
w = v/lh
Step-by-step explanation:
v = lwh
Divide both sides by lh
w = v/lh
Please help
Determine whether the situation illustrates a correlation or causation. Explain your reasoning.
Hae notices that the lower the daily temperature is, the less time she spends outside.
The situation illustrates a ______,
because lower temperatures _________,
Hae to stay indoors.
1st options: causation, correlation
2nd options: do not cause, likey cause
Answers
1st-causation i think bc its a cause for thim not to go outside
2nd-likely cause i put likely cause bc it says its low temp. and he said low tempetures cause his to stay inside.
Kami is in charge of creating a five-digit code to lock and unlock a secure chamber. She can use any digit from 0 through 9, and she can use each digit as many times as she wants. She knows she wants to start the code with an even number.
How many possible codes that start with an even number could Kami create?
40,000 codes
50,000 codes
400,000 codes
500,000 codes
Answers
Using the Fundamental Counting Theorem, it is found that Kami could create 40,000 codes that start with an even number.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
The first digit has to be even, that is, 2, 4, 6 or 8, hence [tex]n_1 = 4[/tex].For the remaining digits there are 10 outcomes for each.Hence:
[tex]N = 4 \times 10^4 = 40000[/tex]
Kami could create 40,000 codes that start with an even number.
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Congruent yes or no
Congruent? _______
If so, what property? ________
Answers
Answer: No
Step-by-step explanation:
If we rotate them so they are both facing the same direction, the congruency between sides and angles do not make the two triangles congruent as a whole.
See attached for the pictures I drew of the triangles rotated. They are not to scale, but I kept the markings on.
An irrigation system waters in circular patterns.
Each irrigated section is a circle with a diameter
of 40 feet. It terms of n, what is the area of an
irrigated section?
Answers
Instructions: In the graph below determine how many real solutions the quadratic function has, and state them, if applicable. List solutions in order from left to right on the graph, or least to greatest. If the function has only one solution, type the solution in both of the boxes. If there are no real solutions type “none” in both boxes.
Answers
The quadratic function has two real solutions. The solutions to the function are x= -2 and x= 0
Solutions of a quadratic function
From the question, we are to determine the number of real solutions the quadratic function has.
NOTE:
If the graph of the quadratic function crosses the x-axis at two points then we have two solutions. If the graph touches the x-axis at one point then we have one solution.If the graph does not intersect with the x-axis then the equation has no real solution.From the given diagram, the graph of the quadratic function crosses the x-axis at two distinct points.
∴ The quadratic function has two real solutions
The solutions of a quadratic function are the points where the graph intersects with the x-axis.
In the given graph, the solutions to the function are x = -2 and x = 0
Hence, the quadratic function has two real solutions. The solutions to the function are x= -2 and x= 0.
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