Answer:
x = 2 and (2, 4 )
Step-by-step explanation:
The equation of a parabola in standard form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = 3(x - 2)² + 4 ← is in vertex form
with vertex = (2, 4 )
This is a vertical parabola, opening upwards and is symmetrical about the vertex.
The axis of symmetry is a vertical line with equation x = 2
According to the equation of the parabola, we have that:
The axis of symmetry is x = 2.The vertex is (2, 4).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
The axis of symmetry is x = h.
In this problem, the equation is:
[tex]f(x) = 3(x - 2)^2 + 4[/tex]
Hence h = 2, k = 4, thus:
The axis of symmetry is x = 2.The vertex is (2, 4).More can be learned about the equation of a parabola at https://brainly.com/question/24737967
Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.
Answer:
To prove that 3·4ⁿ + 51 is divisible by 3 and 9, we have;
3·4ⁿ is divisible by 3 and 51 is divisible by 3
Where we have;
[tex]S_{(n)}[/tex] = 3·4ⁿ + 51
[tex]S_{(n+1)}[/tex] = 3·4ⁿ⁺¹ + 51
[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3·4ⁿ⁺¹ + 51 - (3·4ⁿ + 51) = 3·4ⁿ⁺¹ - 3·4ⁿ
[tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] = 3( 4ⁿ⁺¹ - 4ⁿ) = 3×4ⁿ×(4 - 1) = 9×4ⁿ
∴ [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9
Given that we have for S₀ = 3×4⁰ + 51 = 63 = 9×7
∴ S₀ is divisible by 9
Since [tex]S_{(n+1)}[/tex] - [tex]S_{(n)}[/tex] is divisible by 9, we have;
[tex]S_{(0+1)}[/tex] - [tex]S_{(0)}[/tex] = [tex]S_{(1)}[/tex] - [tex]S_{(0)}[/tex] is divisible by 9
Therefore [tex]S_{(1)}[/tex] is divisible by 9 and [tex]S_{(n)}[/tex] is divisible by 9 for all positive integers n
Step-by-step explanation:
Determine the equation for the given line in
slope-intercept form.
Oy=-5/3x-1
Oy= 5/3x+1
Oy= 3/5x+1
Oy=-3/5x+1
Answer:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
From the graph using points ( 5 , - 4) and
( -5 , 2)
Slope = 2+4/ -5 - 5= 6/-10 = - 3/5
Equation of the line using point (5,-4) is
y + 4 = -3/5(x - 5)
y = -3/5x + 3 - 4
y = -3/5x - 1
Hope this helps
Kayla is going on a trip. The mass of everything she is packing is 8.7 kg. She packs everything into a bag that has a mass when empty of 660 g. What is the total mass of the bag and its contents? Give your answer in kg
Answer:
9.36kg
Step-by-step explanation:
Given That:
Mass of her Packages = 8.7 kg
Mass of bag = 660g = 0.66 kg
Total Mass = ?
To find the total mass, add the 2 weight together :"
8.7 + 0.66 = 9.36kg.
Hope this helps.
Good Luck
Answer:
Mass of the things=8.7kg
Mass of the bag=660g=0.66kg
Total mass=mass of the bag+mass of the things
Total mass=8.7kg+0.66kg
Total mass=9.36kg≈9kg
Step-by-step explanation:
i hope this will help you :)
The binomial (a+5) is a factor of a2+7a+10. What is the other factor? (a+2) (a+5) (a−2) (a−5)The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor? (y − 5) (y + 5) (y − 8) (y + 8)
Step-by-step explanation:
a^2 +7a + 10 = a(a+2) +5(a+2) = (a+5)(a+2)
y^2 -10y +16=y(y-2) -8(y-2) =(y-8)(y-2)
Given ∠R ≅ ∠T and ∠E ≅ ∠A, what other information is needed to prove ΔRED ≅ ΔTAN by AAS? a RE=TA b RD=TN c D=N d none
Answer:
hey I'm going to be able to make it to the meeting
Step-by-step explanation:
hi the address is correct but the number is not
Find the value of x.
Round to the nearest tenth.
X
16
30°
30
x = [?]
Law of Cosines: c2 = a2 + b2 - 2ab cos C
Please need answer asap
Answer:
18.0
Step-by-step explanation:
==>Given:
Triangle with sides, 16, 30, and x, and a measure of an angle corresponding to x = 30°
==>Required:
Value of x to the nearest tenth
==>Solution:
Using the Cosine rule: c² = a² + b² - 2abcos(C)
Let c = x,
a = 16
b = 30
C = 30°
Thus,
c² = 16² + 30² - 2*16*30*cos 30°
c² = 256 + 900 - 960 * 0.8660
c² = 1,156 - 831.36
c² = 324.64
c = √324.64
c = 18.017769
x ≈ 18.0 (rounded to nearest tenth)
its for 100 points Solve the chart save the picture and solve it please it going to save my life --- its first difference
The first column is found by plugging in the x values to get corresponding y values. For instance, if x = -5, then y is...
y = x^2+3x-18
y = (-5)^2+3(-5)-18
y = 25-15-18
y = 10-18
y = -8
So that explains how they got -8 in the second column, next to x = -5.
--------------
The column of first differences is found by subtracting the adjacent terms in the y column. The distance from y = -8 to y = -14 is 6 units, so we'll write 6 in the first row of the "first differences" column. The rest of the values of this column are filled out in a similar fashion. This means that you'll need to completely fill out the y column before you can move onto the "first differences" column.
--------------
The second differences is found by subtracting the adjacent first differences. You should find the results of this column are all the same value. This is true of any quadratic function.
Express in the form of p/q :
(i) 0.12▁3 (ii) 0. ▁621 (iii) 2.2▁18
Answer:
1)0.123( bar on 3)
Let X = 0.123 ( bar on 3)
Then X = 0.1233 --------(1)
Multiply equation (1) by 100 we get,
100X = 12.33 --------(2)
Again multiply equation (2) by 10 we get,
1000X = 123.33 -------(3)
Subtract equation (2) from equation (3) we get,
1000X = 123.33
100X = 12.33
____________
900X = 111
X = 111/900
Hence,
0.123 ( bar on 3) is in the form of 111/900 which is in the form of P/Q.
WILL MARK BRAINLIEST!!!! 40 POINTS ACTUAL ANSWERS PLZ!!! LAST QUESTION!!!!
Answer:
Step-by-step explanation:
the x-intercepts represent that the profit is $0
maximum value represents the highest profit which is $270
increasing intervals: (0, 4)
decreasing intervals: (4, 8)
in order to find the average rate of change, find the x and y coordinates for when x = 1 and x =4. The coordinates are (1, 120) and (4, 270). The average rate of change is basically the slope, which is (270-120)/(4-1) = 160/3= approximately 53.3333. The rate represents the change in profit in $ over the increase of cost of erasers.
As you can see, this a parabola, which consists of going up and down. The constraints of the domain represent that 4 is the best price for eraser because it yields the highest profit. The domain (x values) that are above and below 4 do not yield the best profit.
A local theater company is presenting a musical for kids at the community center. Each adult ticket costs $8, and each child ticket
costs $4. On the opening night, the theater company needs to earn at least $1,280 from ticket sales to cover its costs. The communi
center has a capacity of 240 people.
If the solution region represents the number of adult and child tickets that needs to be sold for the theater company to cover its cost
determine which graph represents the solution set to the system of inequalities representing this situation.
Answer:
Option (1)
Step-by-step explanation:
Let the number of adult tickets sold = x
And the number of child tickets sold = y
Cost of adult tickets sold = $8x
And the cost of child tickets sold = $4y
If the theater company needs to earn at least $1280,
8x + 4y ≥ 1280
2x + y ≥ 320 ---------(1)
Since community center has a capacity of 240 people,
x + y ≤ 240 ----------(2)
By graphing these inequalities with the help of a graphing tool,
Shaded area above the solid line will be represented by inequality (1) (red line)
And the shaded area below the line will be the represented by inequality (2) (blue line)
Common area of both the shaded regions will represent the solution area .
Option (1) will be the answer.
The double number line below shows the number of basketball cards that represent 60% of Juan's basketball card collection. How many basketball cards are in Juan's whole basketball card collection?
Answer:
Check Explanation
Step-by-step explanation:
The number line required to answer this question is missing.
But I'll explain how to get the total number of basketball cards Juan has, given the number that corresponds to 60% of the total number of cards.
Let the total number of basketball cards be x.
The first step is to check the number line presented. We furst require the number that corresponds to 60% of all of Juan's basketball cards..
Let us assume that the number of basketball cards according to the number line is 45.
This means that
60% of the total number of basketball cards = 45
60% × x = 45
0.6x = 45
x = (45/0.6) = 75 basketball cards.
So, the way to go is just to divide the number that the number line gives (which represents 60% of the total number of basketball cards) by 0.6 to obtain the total number of basketball cards.
Hope this Helps!!!
Plz help me and send a picture of what u wrote❤️
【>> https://brainly.com/question/17076084 <<】
, .
Factor the polynomials, show your work. -3x^4 - 9x³ + 15x²; 3x² - 18x + 24; 2x² + 17x + 21; 3x² - 17x + 10; x² - 81; 4x² - 25b²; x² + 14x + 49; x² - 16x + 64 Thank you so much, I know its kind of a lot!
Answer:
hello : here is an solution
Step-by-step explanation:
Simplify the midpoint of QS.
Q (2b, 2c)
R (2a+2b, 2c)
Pl(0,0)
S (2a, 0)
Enter the value that
belongs in the green box. (a + [?], []).
Answer:
[(a + b), c]
Step-by-step explanation:
Midpoint of a segment with extreme ends represented by ordered pairs [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex],
Midpoint = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
It is given that extreme ends of the segment QS are Q(2b, 2c) and S(2a, 0)
Coordinates of the midpoint of QS will be,
= [tex](\frac{2a+2b}{2},\frac{2c+0}{2} )[/tex]
= [(a + b), c]
Therefore, ordered pair representing the midpoint of QS will be [(a + b), c].
Answer:
(a+b, c)
Step-by-step explanation:
CORRECT FOR ACELLUS
Help Plz. My times is limited so I have around 20 mins
Answer:
40 students.
Step-by-step explanation:
There are 60 12th graders that voted for Nick and only 20 12th graders that voted for Garett. 60 - 20 = 40.
Hope this helps!
Pls can someone help it’s due tmrz
Answer:
Step-by-step explanation:
In a quadrilateral all the angles equal to 360 degrees
ADC= 136+90+62=288.
360-288=72
A straight line is equal to 180 degrees
CDE= 180-72=108
x=108
Answer:
the value of x is 62 degrees.
Step-by-step explanation:
we know that corresponding angles are equal, so the value of x is 62 degrees as x is an corresponding angle of 62°
Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4) A' (–1, –1) B' (–1, 1) C' (–4, 1) Which best describes the transformation?
Answer:
The transformation was a 90° rotation about the origin.
Step-by-step explanation:
Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4) A' (–1, –1) B' (–1, 1) C' (–4, 1) Which best describes the transformation? The transformation was a 90° rotation about the origin. The transformation was a 180° rotation about the origin. The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.
Answer: Transformation is the process of moving a point in a graph to another point. The new point formed is the image of the old point. When an object is transformed each point of the object is moved to another point. There are three types of transformation: Reflection, Rotation, Translation and dilation.
If a point O(x, y) is rotated 90° rotation about the origin., the new point is at O'(-y, x). That is the x coordinates becomes negative of the y coordinate and the y coordinate becomes the x coordinate.
The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1, 4), If a transformation of 90° rotation about the origin is done, the new points are A' (–1, –1) B' (–1, 1) C' (–4, 1)
Answer:
The answer is a
Step-by-step explanation:
Polygon ABCD is rotated 90 degrees counter loll about the origin to create polygon A' B' C' D'. Match set of coordinates to vertices of polygon A' B' C' D'
Answer:
A (3, 1)
B (2, 2)
C (1, 2)
D (1, 1)
Step-by-step explanation:
When a point is rotated 90° (90 degrees) counterclockwise about its origin, the coordinate B (x, y) transforms into B' (-y, x).
A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)
Using the formula above B (x, y) ⇒ B' (-y, x), we have the coordinates for the polygon as:
A′ (-1, 3) ⇒ A (3, 1)
B′ (-2, 2) ⇒ B (2, 2)
C′ (-2, 1) ⇒ C (1, 2)
D′ (-1, 1) ⇒ D (1, 1)
∴ coordinates of the original polygon is given by the vertices:
A (3, 1), B (2, 2), C (1, 2), D (1, 1)
One side of a square is 3x + 2. Which expression represents the perimeter?
2(3x + 2)
(3x + 2)²
4(3x + 2)
Answer:
4(3x+2)
Step-by-step explanation:
Since all four sides of a square are the same length, the perimeter can be expressed as four times one of the side lengths. In this case, that is 4(3x+2). Hope this helps!
Step-by-step explanation: since there are 4 sides on a square that will be the answer.
Answer: 4(3x + 2)
Can someone please help me I really need help please help me
Answer:
≈ 18.87 cm²
Step-by-step explanation:
The shaded area is the difference between the area of the trapezium and the semicircle.
The area (A) of the trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h( a + b)
where h is the height and a, b the parallel bases
Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus
A = [tex]\frac{1}{2}[/tex] × 4 × (14 + 8) = 2 × 22 = 44 cm²
area of semicircle = [tex]\frac{1}{2}[/tex]πr² = [tex]\frac{1}{2}[/tex]π × 4² = 8π cm²
Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places )
Answer:≈ 18.87 cm²
Step-by-step explanation:
Answer:
≈ 18.87 cm²
Step-by-step explanation:
The shaded area is the difference between the area of the trapezium and the semicircle.
The area (A) of the trapezium is calculated as
A = h( a + b)
where h is the height and a, b the parallel bases
Here h = 4 ( radius of circle), a = 14 and b = 4 + 4 = 8, thus
A = × 4 × (14 + 8) = 2 × 22 = 44 cm²
area of semicircle = πr² = π × 4² = 8π cm²
Shaded area = 44 - 8π ≈ 18.87 cm² ( to 2 dec. places
What is the difference of (Negative 3.4 x + 4.7) minus (3 + 2.9 x)
Answer:
The answer is
1.7 - 6.3xStep-by-step explanation:
- 3.4x + 4.7 - ( 3 + 2.9x)
Remove the bracket
That's
- 3.4x + 4.7 - 3 - 2.9x
Simplify
Group like terms
- 3.4x - 2.9x + 4.7 + 3
- 6.3x + 1.7
We have the final answer as
1.7 - 6.3xHope this helps you
Answer:
The answer is
1.7 - 6.3x
Step-by-step explanation:
kjihugyfvbjhiuyghnjkiohuygt7o89hub
Find the area of the shaded segment. Round your answer to the nearest tenth. Please include units in your answer.
Answer: 56
Step-by-step explanation:
Let's organise our information :
the radius of the circle is r=14 cm we can get the area of the shaded by substracting the area of that triangle from that quarterThe area of the cercle's quarter area is :
A= 14²×π*(1/4) = 49π cm²The area of the triangle is :
A=14²*(1/2)=98NOw the area of the shaded segment :
A=49π-98= 55.98 ≈ 56A shop has an offer on jumpers as shown below.
Buy 4 jumpers and get 1 free!
Kara gets 5 jumpers
After applying the offer, each one ends up costing £4 80 per jumper
What is the regular cost of one jumper when not in this offer?
Answer: £6.80
Step-by-step explanation:
Kara bought 5 jumpers for the price of 4. Thus, multiply 4.8*5 = 24. Then divide 24/4 to get 6.
Hope it helps <3
Answer:
222222:#&&&#+17265262
I need an asnwer Tutor and the answer to this question
Answer:
[tex] \dfrac{1}{a^6} [/tex]
Step-by-step explanation:
[tex] a^{-6}x^0 = [/tex]
[tex] = \dfrac{1}{a^6} \times 1 [/tex]
[tex] = \dfrac{1}{a^6} [/tex]
Anita plans to cover a solid cone with construction paper for a science project. The cone has a diameter of 11 inches and
a slant height of 28.5 inches. How many square inches of paper will she need to cover the entire cone?
492.20 in.
587.18 in.
982.82 in.
984.39 in.
Answer:
587.18 square inches
Step-by-step explanation:
We would find the Total surface area of the cone
Diameter of the cone = 11 inches
Radius = Diameter ÷ 2 = 11 / 2 = 5.5 inches
Slant height ( l ) = 28.5 inches
Let's take π = 3.14
Total Surface Area of a cone = πrl + πr²
= πr(l + r)
= 3.14 × 5.5( 28.5 + 5.5)
= π × 5.5(34)
= 587.18 square inches
There the square inches of paper will she need to cover the entire cone is 587.18 square inches
Given: DB= DB and EB & CB
Prove: D=A
We have proven that ∠D ≅ ∠A as shown below
Proof of anglesFrom the question, we are to complete the proof
Statements Reasons
AB ≅ DB 1. Given
1. EB ≅ CB
2. ∠ ABC ≅ ∠DBE 2. Congruent postulate
3. ΔABC ~ ΔDBE 3. Side-angle-side postulate
4. ∠D ≅ ∠A 4. CPCTC (Corresponding parts of
congruent triangles are congruent.)
Hence, we have proven that ∠D ≅ ∠A
Learn more on Proof of angles here: https://brainly.com/question/11673033
#SPJ1
Please please help me!!
Answer:
The submarine is 307.8 yards below sea level.
Step-by-step explanation:
Since the 500 yards are the hypotenuse of the right angle triangle, the acute angle opposite the side of the triangle we need to find is known ([tex]38^o[/tex]), we can use the sine function to solve the problem:
[tex]sin(\theta)=\frac{opposite}{hypotenuse} \\sin(38^o)=\frac{x}{500} \\500\,*\,sin(38^o)=x\\x = 307.8307\,\,yards[/tex]
which rounded to the nearest tenth is : 307.8 yards
Match the question with the answer (e.G. 1 + C) 26 x 5 161 2. 25 x 6 130 3. 22 x 6 168 4. 21 x 8 150 5. 23 x 7 132 Answers: 1 + 2 + 3 + 4 + 5 +
Answer:
1+B,2+D,3+E,4+C and 5+A
Step-by-step explanation:
(A)161 (B)130 (C)168 (D)150 (E)132
1. 26 x 5=130
This is Option B, therefore we have the match:1+B
2. 25 x 6=150
This is Option D, therefore we have the match:2+D
3. 22 x 6=132
This is Option E, therefore we have the match: 3+E
4. 21 x 8=168
This is Option C, therefore we have the match: 4+C
5. 23 x 7=161
This is Option A, therefore we have the match:5+A
Find the sum or difference.
81-3
3
Answer:
48
Step-by-step explanation:
81 - 33 = 48
Answer:
48
Step-by-step explanation:
81 - 33 = 48
Do 81 - 30 first = 51
Then do 51 - 3 = 48
04
Apples cost £a and bananas cost £b. Which is a correct expression for how 1 point
much 4 apples and 5 bananas cost? *
4a + 5b
4a 5b
9ab
4 + 5
Simplify fully
Answer:
4a+5b
Step-by-step explanation:
Given:
Apple=£a
Banana=£b
Quantity of Apple=4
Quantity of banana=5
Find the cost of 4 apples and 5 bananas
Total cost=PaQa+PbQb
Where,
Pa=price of Apple
Qa=quantity of Apple
Pb=price of banana
Qb=quantity of banana
Total cost=PaQa+PbQb
=4*a+5*b
=4a+5b