The equation is written as 3(x+12)²+20.The formula for ax² + bx + c is (Ax + B)² + C.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
3x^2+12x+20
The equation is compared the equation with,ax²+bx+c
After comparing the equation we get;
a=3
b=12
c=20
The equation is written in the form as;
⇒a(x+b)^2+c
⇒3(x+12)²+20
The formula for ax² + bx + c is (Ax + B)² + C.
Hence the equation is written as 3(x+12)²+20.
To learn more, about equations, refer;
https://brainly.com/question/10413253
#SPJ1
need help asap willing to give a lot of points!
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
Question 1
Part (a) :
⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ
⇒ 6⁷ = 6ˣ
⇒ x = 7
Part (b) :
⇒ y² = 169
⇒ √y² = √169
⇒ y = ± 13
⇒ y = 13, y = -13
Question 2
Part (a) :
⇒ (√5)² × (√3)²
⇒ 5 × 3
⇒ 15
Part (b) :
⇒ (∛9)³ × (√30)²
⇒ 9 × 30
⇒ 270
D is the midpoint of AB and E is the midpoint of BC. If AC=48, what is the length of DE ?
Answer:
24 is the answer for the following
Step-by-step explanation:
please mark me as brainlest
which greek geometer founded a philosophical society that devoted itself to study of mathematics
Answer:
Pythagoras was the Greek geometer .
Please mark me as the brainliest.
How many solutions for x does the following equation have?
3(x + 8) − 1 = 3x + 4
A.
4
B.
1
C.
0
D.
infinite
Answer:
c. 0
Step-by-step explanation:
3(x+8) - 1 = 3x+4
3x+24-1 = 3x+4
3x+23 = 3x+4
There are no solutions since both equations have the same slope meaning they are parallel and they will never intersect since they have different y-intercepts.
Jerry plans to keep up this saving pattern until he can no longer afford it. At that time he hopes to have enough in his account for his trip. How much will be in the account, after making the down payment, if the most he will be able to contribute in a month is $1,200?
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2
The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2
How to compare the areas?The coordinates are given as:
Parallelogram 1: (0, 2), (2, 6), (6, 4), and (4, 0).
Parallelogram 2: (2, 0), (4, -6), (2, -8), and (0, -2)
Next, calculate the base and the height
For parallelogram 1, we have:
Base = (0, 2) and (2, 6)
Height = (6, 4), and (4, 0).
So, we have:
[tex]Base = \sqrt{(0 - 2)^2 + (2 -6)^2} = \sqrt{20}[/tex]
[tex]Height = \sqrt{(6 - 4)^2 + (4 -0)^2} = \sqrt{20}[/tex]
The area is:
Area = Base * Height
Area = √20 * √20
Area = 20
For parallelogram 2, we have:
Base = (0, -2) and (4, -6)
Height = (4, -6) and (2, -8)
So, we have:
[tex]Base = \sqrt{(0 -4)^2 + (-2 +6)^2} = \sqrt{32}[/tex]
[tex]Height = \sqrt{(4 - 2)^2 + (-6 +8)^2} = \sqrt{8}[/tex]
The area is:
Area = Base * Height
Area = √32 * √8
Area = 16
By comparing both areas, we have:
20 is greater than 16 by 4
This means that the area of parallelogram 1 is greater by 4 units
Read more about parallelogram at:
https://brainly.com/question/3050890
#SPJ1
A laptop costs £600
Students get a 5% discount.
How much discount will a student get?
Answer:
cost price = £ 600
discount = 5%
selling price =
5/100 * 600.
5 * 6
30 £
price = 600 - 30
= 570
can someone please help and explain its due in a littleee
Answer:
slope = 3
y-intercept: -4
explanation on how to graph given in step-by-step explanation
Step-by-step explanation:
y=3x-4 is given in slope-intercept form which is y=mx+b where m is the slope and b is the y-intercept (when x = 0)
So the first coordinate that is easy to graph is the y-intercept since it's just (0, b) or in this case (0, -4). So that's the first point you graph. Now from here you can use the slope to graph all the other points. The slope is 3, which essentially means every time x increases by 1, the y-value increases by 3. So from the y-intercept (0, -4) you're going to go one unit to the right and three units up which should give you the coordinates (1, -1). Then from that coordinate go one unit to the right and three units up which should get you (2, 2) then from that coordinate go one unit to the right and three units up which should get you to (3, 5). Now go back the y-intercept (0, -4) and instead of going to the right 1 and up 3 you're going to do the inverse and instead go left 1 and down 3. So from (0, -4) go to the left one unit and down 3 units which should get you to (-1, -7). And now with all these points plotted draw a line through all of them
Ann cleans 9 vessels in 10 minutes and her friend Kathy cleans 12 vessels in 14 minutes. Who cleans less number of vessels?
Answer:
Kathy
Step-by-step explanation:
Which of them factored 12x^7 correctly?
By rounding to 1 significant figure, estimate the answers to these questions:
a)346 × 904
b) 2451 × 988
c)3204 × 7756
Answer:
a) 270000
b) 2000000
c) 24000000
Step-by-step explanation:
For a)
346 to 1 s.f is 300
904 to 1 s.f is 900
300 × 900 = 270000
For b)
2451 to 1 s.f is 2000
988 to 1 s.f is 1000
2000 × 1000 = 2000000
For c)
3204 to 1 s.f is 3000
7756 to 1 s.f is 8000
3000 × 8000 = 24000000
Hope this helped and have a good day
2. On the snow day, 8 kids from the neighbor-
hood gathered to build snowmen. The kids
used two buttons as the eyes on each snowman.
7 more kids joined to make snowmen and used
buttons for the eyes, too. How many buttons
were used to make the snowmen?
Answer: 30 buttons
Step-by-step explanation:
If there were 8 kids, and 7 more joined, then there were 15 kids making snowmen (8+7 = 15). Each child used 2 buttons for the eyes, so 30 buttons were used (15 x2 = 30). This is assuming no other buttons were used on the snowmen for anything else
You just looked at the graph of this system of equations. Why will the lines never intersect? y = –x + 5 y = –x – 3
Answer: same slope, y int are different
Step-by-step explanation:
Both these lines never intersect because they have the same slope.
they both go down 1 over 1, and also their y interecepts are different
Which point is on the graph of f(x) = 3.4x
Answer:
D(1,12)
Step-by-step explanation:
See attached graph.
A basketball coach recorded how many shots each of the 30 players at tryouts made in a set of 6 attempts.
Answer:
Step-by-step explanation:
what is the question?
Answer:
Median = A
Mean = B
Step-by-step explanation:
Khan Academy
120 is the product of 8 and Julie's score.
Answer:
Julie's score is 15.
Step-by-step explanation:
This can be solved in two ways:
⇒ 120 ÷ 8
⇒ Experimentation on what × 8 = 120 (adding random numbers until you get 120 as a product).
Let's use the first method.
⇒ 120 ÷ 8
1 5
__________
8 | 1 2 0
- 8
____
4 0
- 4 0
____
0
Therefore, Julie's score is 15.
he given line passes through the points and (4, 1).
On a coordinate plane, a line goes through (negative 4, negative 3) and (4, 1).
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (, 3)?
The equation of the line that passes through the point (-4 , 3) with slope ₋2 is:
y = ₋2x ₋ 5
Given the points are (₋4 , ₋3) and (4 , 1)
The gradient of the line through the points' locations (x₁ , y₁) and (x₂ , y₂) is: y₂ ₋ y₁/x₂ ₋ x₁
Substitute the given points in the above formula:
=1 ₋(₋3)/4 ₋ (₋4)
=4/8
=1/2
If the product of the slopes of two perpendicular lines is -1, then the slope of the perpendicular line is ₋1/1/2 = ₋2
Therefore the line that passes through the point (-4 , 3) with slope ₋2 has equation:
y ₋ 3 = ₋2(x ₊ 4)
y = ₋2x ₋ 8 ₊ 3
y = ₋2x ₋ 5
Hence we get the expression as y = ₋2x ₋ 5
Learn more about "intercept forms" here-
brainly.com/question/6202710
#SPJ10
If the means of 5,11,6,4,7,p and 10 is 8,find the value of p.
Answer:
p = 13
Step-by-step explanation:
The mean of 5, 11, 6, 4, 7, 10, p is 8
So 8 = 5+11+6+4+7+10+p divided by 7.
So 56 = 43+p
Therefore p = 56-43
= 13
Hope I helped
⇒ 5 + 11 + 6 + 4 + 7 + p + 10 / 7 = 8
⇒ 43 + p = 56
⇒ p = 13
The value of p is 13.
The graph of g(x), shown below in red, has the same shape as the graph of
f(x) = 2x, shown in blue. Which of the following is the equation for g(x)?
A. g(x) = 2(x-1) - 3
B. g(x) = 2(x+3) - 1
C. g(x) = 2(x-3) -1
D. g(x) = 2(x+1) - 3
How many positive odd integers less than 10,000 can be written using the digits
3, 4, 8, 9 and 0?
In a market survey, 100 traders sell fruits, 40 sell apples, 46 oranges, 50 mangoes. 14 apples and oranges. 15 apples and mangoes, and 10 sell the three fruits. Each of the 100 traders sells at least one of the three fruits. Find the number that sell oranges and mangoes only.
The number of traders that sell oranges and mangoes only are 17.
How to determine the common differenceSince there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
- O∩M = 100 -117
O∩M = 17 traders
Therefore, the number of traders that sell oranges and mangoes only are 17.
Learn more about Venn diagram here:
https://brainly.com/question/24713052
#SPJ1
Please I need help with this question asap
For the matrix given , the element a₂₃ is the number at 2nd row and 3 column ,which is 6 , Option B is the correct answer.
What is a Matrix ?It is a table or a rectangular array of numbers or expressions arranged in rows and columns ,
For a Matrix of m x n , m is the no. of rows and n is the no. of column
For the matrix given the element a₂₃ is the number at 2nd row and 3 column ,
which is 6 ,
Therefore Option B is the correct answer.
To know more about Matrix
https://brainly.com/question/9967572
#SPJ1
What is true about △ABC? Select three options
AB ⊥ AC
The triangle is a right triangle.
The triangle is an isosceles triangle.
The triangle is an equilateral triangle.
BC ∥ AC
Answer: Isosceles triangle
Step-by-step explanation: Two of the base sides are equal distance away. (Sides AB and AC)
Given: ∠T ≅ ∠V; ST || UV
Prove: TU || VW
4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.
Complete the two-column proof.
edge 2022 pls helpppppp
We have proven that line TU is parallel to line VW as shown below. That is, TU || VW
Proof of anglesFrom the question, we are to prove that TU || VW
In the given image,
Statements Reasons
1. ST || UV Given
2. ∠T ≅ ∠U Alternate angles
3. ∠T ≅ ∠V Given
4. ∠U≅ ∠V Substitution property
5. TU || VW Alternate interior angles theorem
NOTE: If the alternate interior angles formed by a transversal of two lines are equal, then the lines are parallel
Hence, we have proven that line TU is parallel to line VW. That is, TU || VW
Learn more on Proof of angles here: https://brainly.com/question/2141319
#SPJ1
Answer:
a c c
Step-by-step explanation:
A shop sells the same type of nails in 3
different sized packets.
Calculate the price per 10 nails for each
size of pack.
Write down which sized packet is the
best value for money in the comment
box.
Answer:
52, 53, 54, pack 1.
Step-by-step explanation:
1)
1.56 = 30
10 = 1.56 / 3
10 = 52 pence
2)
2.12 = 40
10 = 2.12 / 4
10 = 53 pence
3)
3.78 = 70
10 = 3.78 / 7
10 = 54 pence
The cheapest one is the small pack
use the graph below to answer this question: find the average rate of change for the given function from x=1 to x=2.
Answer: D. 2
Step-by-step explanation:
The question is asking for the rate of change from x=1 to x=2. Remember that the rate of change is also the slope, which can be seen as [tex]\frac{rise}{run} or \frac{y}{x}[/tex]. The rise would be going up/down the graph and the run would go left/right of the graph. Let's look at where x=1 and x=2 on the graph.
First, look at where the line falls between x=1 and x=2. Then, on where x=1, go up, then right on the graph, until you find the point where x=2. In this case, the rise over run is [tex]\frac{2}{1}[/tex]. This can be simplified to 2.
Therefore, the answer is 2.
I hope this helps!! Pls mark brainliest :))
Consider the circle represented by this equation.
x² + 4x + y2 - 2y - 4 = 0
Which features are features of the circle?
Answer:
See below
Step-by-step explanation:
arrange to standard form (x-h)^2 + (y-k)^2 = r^2 h,k = center r = radius
x^2 - 4x + y^2 + 2y = 4 complete the square for 'x' and 'y'
(x-2)^2 - 4 + (y-1)^2 -1 = 4
(x-2)^2 + ( y-1)^2 = 4 + 4 + 1 = 9 '9' is equal to r^2 so r = 3
center = 2,1 radius = 3
Answer:
you're welcome!!!
Step-by-step explanation:
Which if the following rules best describes the matrix below?
a.
dilation of scale factor 2
c. reflection over the line y = x
b. reflection over the y-axis
d. translation 1 unit left and 1 unit up
Answer:
D
Step-by-step explanation:
i just know i guess
area = ft
help me please ty:)
find the length using the Pythagorean theorem.
Length = sqrt(20^2 - 12^2)
Length = 16 feet
area = 12 x 16 = 192 square feet
Jaime adds equations A and B to solve this system of equations. Why is this method
generally valid for solving a system of equations?
The elimination method is valid for the system of equation because the y term cancels.
How to solve a system of equation using elimination method?The system of equation can be solved using elimination methods.
Therefore,
x - 2y = 3
3x + 2y = 17
Hence,
x + 3x = 4x
-2y + 2y = 0
3 + 17 = 20
Therefore,
4x = 20
The y term cancels. Therefore, we can solve for x and later solve for y.
learn more on equation here: https://brainly.com/question/17746153
#SPJ1
Answer:
Adding a quantity like x – 2y to one side of an equation and another quantity like 3 to the other side maintains the equality if the two quantities are equal.
