Answer:
value of
a = 1
b = 2
c =1
and equation is
y = x² + 2x + 1
Step-by-step explanation:
Given quadratic equation y = ax² + bx + c
It has y-intercept of (0, 1)
thus, point (0,1) will satisfy equation y = ax² + bx + c.
putting 1 in place of y and 0 in place of x in equation y = ax² + bx + c we have
1 = a*0² + b*0 + c
c = 1
Thus, equation until now is y = ax² + bx + 1
____________________________________________________
The parabola also goes through the points (2, 9) and (-5, 16)
point (2, 9) will satisfy equation y = ax² + bx + 1.
putting 9 in place of y and 0 in place of 2 in equation y = ax² + bx + 1 we have
9 = a*2² + b*2 + 1
9 = 4a+2b+1
=>4a+2b = 9-1 = 8
dividing both side by 2 we have
4a/2+2b/2 = 8/2
=> 2a + b = 4
b = 4-2a
____________________________________________________
The parabola also goes through the points (2, 9) and (-5, 16)
point (-5, 16) will satisfy equation y = ax² + bx + 1.
putting 9 in place of y and 0 in place of 2 in equation y = ax² + bx + 1 we have
16 = a*(-5)² + b*(-5) + 1
16 = 25a-5b+1
=>25a-5b = 16-1 = 15
dividing both side by 5 we have
25a/5-5b/5 = 15/5
=> 5a - b = 3
second equation is 5a - b = 3
substituting value of b as 4-2a from first equation we have
5a - (4-2a) = 3
=> 5a - 4+2a = 3
=> 7a = 3+4 = 7
=> a = 7/7 = 1
value of b is 4-2a
substituting value of a as 1 in 4 - 2a we have
b = 4 - 2*1 = 4-2 = 2
Thus,
value of
a = 1
b = 2
c =1
and equation is
y = x² + 2x + 1
Simplify √63x10y15 to the form a√b.
Answer:
49
Step-by-step explanation:
Add then subtract
Which graph represents a proportional relationship?
The vertical line graph shows how often each number on a standard dice comes up. What percentage of rolls were a 6?
Answer:
21%
Step-by-step explanation:
Out of the 25 + 9 + 12 + 21 + 12 + 21 = 100 total rolls, 6 came up 21 times so the percentage is 21/100 = 21%.
[tex] \frac{200}{l - 12} = \frac{300}{l - 9} [/tex]
Step-by-step explanation:
Hope the Answer is helpful
quadratic function and equation
Answer:
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
Step-by-step explanation:
hope this helps you :)
The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.
Answer:
dimensions are 2.19 inches by 9.14 inches
Step-by-step explanation:
Here, we are interested in knowing the dimensions of the rectangle
Now, let the width of the rectangle be x, from the question, we can write;
6x-4 as the length
Area of rectangle = l * b
x(6x-4) = 20
6x^2 - 4x = 20
divide through by 2
3x^2-2x = 10
3x^2 -2x -10 = 0
using quadratic formula;
x = -b ± √(b^2 - 4ac)/2a
From the quadratic equation, a = 3, b = -2 and c = -10
substituting these values, we have
x = 2 ± √(-2)^2 -4(3)(-10))/6
x = 2 ± √(124)/6
x = 2 + √(124)/6 or 2 - √(124)/6
x = (2+11.14)/6 or (2-11.14)/6
x = 2.19 or -1.52
Since width cannot be negative, we choose 2.19 alone
So the length is 6(2.19) -4 = 9.14
2x - y - 4-0
3x + y - 9=0
What is the solution set of the given system?
Of(5,5)
[(5, 6)) [/13/5, 6/5) [[6/5, 13/5))
Answer:
([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )
Step-by-step explanation:
Given the 2 equations
2x - y - 4 = 0 → (1)
3x + y - 9 = 0 → (2)
Adding the 2 equations term by term will eliminate the term in y, thus
5x - 13 = 0 ( add 13 to both sides )
5x = 13 ( divide both sides by 5 )
x = [tex]\frac{13}{5}[/tex]
Substitute this value into either of the 2 equations and evaluate for y
Substituting into (2)
[tex]\frac{39}{5}[/tex] + y - 9 = 0
- [tex]\frac{6}{5}[/tex] + y = 0 ( add [tex]\frac{6}{5}[/tex] to both sides )
y = [tex]\frac{6}{5}[/tex]
Solution is
([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )
What is the square root of -1?
a. -i
b. i
c. -1
d. 1
The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation 5 x plus 10 y equals 800, where x represents the number of small vehicles and y represents the number of larger vehicles. If the number of larger vehicles washed was 50, how many small vehicles were washed in total? 55 60 130 150
Answer:
150
Step-by-step explanation:
Step 1: Plug in what we know
5x + 10(5) = 800
Step 2: Solve for x (smaller cars)
5x + 50 = 800
5x = 750
x = 150
Answer:
150
Step-by-step explanation:
:)
Mark a cross at (6,8)
Answer
Go 6 across to the right and 8 up from there
Step-by-step explanation:
Answer:
This is a coordinate, and it tells you where to plot a point on a set of axis. The first number in the coordinate tells you the x-value and the second one tells you the y-value. X-values go across the horizontal axis, known as the x-axis. Y-values go up and down the vertical axis, known as the y-axis.
In this case, to plot the point, you would start at the very center of the axis, where y and x both equal 0. You'd go 6 to the right, because they gave you a positive x-value. The you'd go up 8, because they gave you a positive y-value.
If they give you a negative x-value, you'd go to the left, and if they give you a negative y-value, you'd go down.
Hope that helped : )
Carrie had $60. as an allowance for the week. She spent 2/5 of it on snacks, and 1/4 on stickets and saved the remainder. How much money did she save?
Answer:
$ 21
Step-by-step explanation:
Money spent = (2/5) * 60 + (1/4) * 60
= 2*12 + 1*15
= 24 + 15
= $ 39
Money save = 60 - 39 = $ 21
A grocer bought 15 dozen oranges at $1.00 a dozen. She threw away 20 rotten oranges, and then sold the rest at 8 oranges for 85 cents. How much profit did the grocer make, in dollars and cents?
Answer:
$2.00
Step-by-step explanation:
The grocer bought the oranges for $15.00
15x12= 180 To find the number of oranges he bought
180-20=160 To find the rest of the remaining oranges
160/8= 20 To find how many packs he has
20x.85= 17 To find how much he made from selling the remaining oranges
17-15=2 To find the profit
(10 points) Joe’s parents bought him a new car for his birthday. They paid $6990 for a car that was originally priced at $7599. What percent of the original price did they pay?
[A] Set up a proportion that can be used to solve this problem.
[B] Show all steps to solve the problem.
HELP: Please and thank you!
Answer:
91.99%
Step-by-step explanation:
To find what percentage of $7599 is $6990, we simply need to divide $7599 by $6990 and multiply by 100:
6990 / 7599 * 100 = 91.99%
Therefore, they paid 91.99% of the original price.
How do you do this? its so easy but i cant word it right apparently
Answer:
apparently just label each part ( a, b, c, d, so on) and tell the order/ switch em around
Step-by-step explanation:
Answer:
area = 4cm2
Step-by-step explanation:
the area of triangle is gotten by 1/2bh
1/2 × 2 × 4 = 4.
base is 2cm because it has covered 2 grids while the height is the measure from the base to the tip of the triangle, which is 4cm.
area of square is L × L
2 by 2 = 4.
so, the two shapes have same area.
What number and 12 have an average of 27?
Answer:
[tex] \boxed{Number \: that \: give \: average \: of \: 27 \: with \: 12 \: is \: 42} [/tex]
Step-by-step explanation:
Let the number be 'x'
[tex] = > \frac{x + 12}{2} = 27 \\ \\ = > x + 12 = 27 \times 2 \\ \\ = > x + 12 = 54 \\ \\ = > x = 54 - 12 \\ \\ = > x = 42[/tex]
pls answer. i will mark u as branliest
Answer:
60
Step-by-step explanation:
All angles = 180
All sides are equal
Therefore, 180/3 = angle degrees = 60
x is an opposite angle of bottom right angle therfore x = 60
Answer:
(a) x = 60°
(b) Angle x is alternate to the right base angle of the equilateral triangle.
Step-by-step explanation:
(a) The triangle in the figure above is an equilateral triangle in which all sides and angles are equal. The sum of angles in a triangle is 180°. Each angle in the equilateral triangle is 60° (180°/3 = 60°)
Therefore, angle x is 60°.
(b) Alternate angles are equal. Angle x and the right base angle of the equilateral triangle are alternate angles. Therefore, angle x is 60°.
Find the 7th term of the geometric sequence -2, 6, -18, 54, -162, ...
Answer:
-1458
Step-by-step explanation:
Let's find the rule of the sequence. It seems that each term is -3 times the previous term.
Let's continue the sequence.
486, -1458
-1458 is the 7th term
can someone help I need an inequality that shows how much I can spend on brochures I have $1900 to spend and brochures cost $0.40 each
Answer:
0.40x=1900
Step-by-step explanation:
1. A MAP SCALE READS 1CM:5KM. IF A DISTANCE ON THE MAP MEASURES 7CM, THE ACTUAL DISTANCE WILL BE?. 2. A SCHOOL DINING HALL IS 35M LONG. IF ON A PLAN, THIS LENGTH IS REPRESENTED BY 7CM, WHAT IS THE SCALE?. 3. THE LENGTH OF A BUILDING IS 30 METRES. A SCALE DIAGRAM OF THE BUILDING IS BEING DRAWN TO A SCALE OF 1CM TO 5 METRES. THE LENGTH OF THE BUILDING ON THE SCALE DIAGRAM IS?. 4. IF THE ANGLE OF ELEVATION OF A FROM B IS 42°, WHAT IS THE ANGLE OF DEPRESSION OF B FROM A?. 5. A BOY IS FLYING A KITE, THE STRING IS 25M LONG AND IS AT AN ANGLE OF 42° WITH THE HORIZONTAL, USING A SCALE DIAGRAM, FIND HOW HIGH THE KITE IS ABOVE THE BOY’S HEAD?
Answer:
1. 35 km
2. 1 cm to 5m
3. 6 cm
4. [tex]42^\circ[/tex]
5. 16.73 m
Step-by-step explanation:
Solution 1.
Reading of map scale = 1cm:5km
i.e. 1 cm is equivalent to 5 km
Measurement of map = 7 cm
Actual distance = Measurement of map [tex]\times 5[/tex]
Actual distance = 7 [tex]\times 5[/tex] = 35 km
-------------------
Solution 2.
Length of dining hall = 35 m
Measurement of map = 7 cm
Scale = Measurement of map : Length of dining hall (i.e. ratio)
Scale = 7 cm :35 m = 1 cm : 5 m
-------------------
Solution 3.
Length of building = 30 m
Scale = 1 cm to 5m
5 m is equivalent to 1 cm on scale
1 m is equivalent to [tex]\frac{1}{5}[/tex] cm on scale
30m is equivalent to [tex]\frac{1}{5} \times 30[/tex] = 6 cm on scale
-------------------
Solution 4.
Angle of elevation of A from B = [tex]42^\circ[/tex]
Angle of depression of B from A = ?
Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.
Angle of depression of B from A = [tex]42^\circ[/tex]
-------------------
Solution 5.
Given that:
String length, or hypotenuse of triangle BC= 25 m
Angle of string with horizontal, [tex]\angle B = 42^\circ[/tex]
Please refer to the attached image for the clear understanding of the situation.
To find:
Height, AC = ?
We can use trigonometric identity:
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
OR
[tex]sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m[/tex]
============
So, the answers are:
1. 35 km
2. 1 cm to 5m
3. 6 cm
4. [tex]42^\circ[/tex]
5. 16.73 m
What is the solution to the system of equations graphed below?
y = x+2 y=3x-2
Answer:
(2, 4)
x = 2
y = 4.
Step-by-step explanation:
To find the solution to the system of equations, we can simply set the two equations equal to each other as shown:
x + 2 = 3x - 2
Subtract 'x' from both sides:
2 = 2x - 2
Add '2' to both sides:
4 = 2x
x = 2.
Plug this value for 'x' into an equation to solve for 'y':
y = (2) + 2
y = 4.
Therefore, the solution to the system is (2, 4).
Answer:
Y=4
Step-by-step explanation:
How I did this.
y=x+2 y=3x-2
Moved around (you can do this)
y=2+2 y= 3x-x
y=4 y=2x
y=4.
Not sure if this is right. please check other answers
Explain how to determine the zeros of f(x)=(x+3)(x-1)
Answer:
x= -3, x = 1
Step-by-step explanation:
Zeros are values of x, when f(x) = 0.
0=(x+3)(x-1)
x+3 = 0, x - 1=0
x= -3, x = 1
Answer:
x = -3, x = 1
Step-by-step explanation:
To determine the zeroes of the factored quadratic equation, we need to look back at its definition. The zeroes are a function are specific x-values that result in a y-value of 0.
In this case, we want the numbers inside of the parantheses to equal 0. If we substitute in x = -3, we get (0)(x - 1), and we know that is just 0. Similarly, if we substitute in x = 1, we get (x + 3)(0), and we know that is just 0.
As such, these are your solutions.
A circular garden has a circumference of 113 yards. Lars is digging a straight line along a diameter of the garden at a rate of 9 yards per hour. How many hours will it take him to dig across the garden? Use 3.14 for π and round the diameter to the nearest whole number, if necessary.
Answer:3hrs 59min
Step-by-step explanation:
πd=perimeter
(113÷3.14)
=35.99
9yards=1hr
35.99yards=?
35.99÷9=3hrs 59min
don’t even have to write an explaination I need this ASAP
Answer:
The answer is C, 60 degrees.
Step-by-step explanation:
What is the length of the side AC in the triangle above
ROUND THESE TO THE NEAREST THOUSANDTH 48.1754 19.9259 5.5722
Step-by-step explanation:
Nearest thousandth is the third digit after the decimal point.
Or in other words :writing this number till reaching the third digit after the point (3rd digit in decimal part)
48.175
19.926
5.572
Hope this helps you.. Good Luck!
Answer for this...increasing percentages
Answer:
Since it's increasing add 3.5% to 100%
= 103.5% of £16470.45
= 103.5/100 × 16470.45
= 17046.92
= £17046.92
Hope this helps.
Brainliest question please help me answer my question please
Answer:
A) inside the circle
Step-by-step explanation:
equation of the circle is:
[tex](x-a)^{2} + (y-b)^{2} = r^{2}[/tex]
where (a,b) is center of the circle and r is radius so
[tex]x^{2} + y^{2} = r^{2}[/tex] now plug in given point to find the radius
[tex](6)^{2} + (-4)^{2} = r^{2}[/tex]
36 +16 = 52 so
r = [tex]\sqrt{52}[/tex] ≈ 7.2 or [tex]r^{2} =52[/tex]
when you plug point (√2 , -7) into equation of the circle
(√2)^2 + (-7)^2 = 2 +49 =51
51 is less than 52 so this is inside of the circle
Factor out gcf of 4-2n
Answer:
2
Factored out:
2 ( 2 − n )
Answer:
2
Step-by-step explanation:
The GCF (greatest common factor), is 2 because 2 can go into both numbers.
original: 4-2n
with GCF factored out: 2(2-n)
At which value in the domain does f(x) = 0?
Answer:-infinity,infinity
Step-by-step explanation:
None
I NEED HELP 50 POINTS PLZZZ I NEED HELP AND BEST ANSWER GETS BRAINLEST!!
Answer:
(6, 3)
Step-by-step explanation:
Since, the triangle PQR is rotated 360° around the origin so, Q' will coincide with Q, and in this way their coordinates would be same.
Therefore, Q' (6, 3)
The correct answer is (6,3)
Because if you rotate any coordinate points 360 degrees around the origin, it will always remain the same.
Hope this helps :D
Don't forget to mark the other guy brainliest ;)