Answers
Answer:
(i) [tex]y = 2x(x-5)[/tex]
(ii) zeros: x = 0 and x = 5
axis of symmetry: x = 2.5
(iii) vertex: (2.5, -12.5)
(iv) see attached
Step-by-step explanation:
Part (i)
Factor: [tex]y=2x^2-10x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies y=2x(x-5)[/tex]
Part (ii)
Zeros occur when [tex]y=0[/tex]
[tex]\implies 2x(x-5)=0[/tex]
Therefore:
[tex]\implies 2x=0 \implies x=0[/tex]
[tex]\implies (x-5)=0 \implies x=5[/tex]
So the zeros are x = 0 and x = 5
The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.
[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]
Therefore, the axis of symmetry is [tex]x=2.5[/tex]
Part (iii)
The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.
[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]
So the vertex is (2.5, -12.5)
Part (iv)
Plot the zeros and the vertex.
As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.
Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.
*see attached*
Related Questions
At a concession stand, five hot dog(s) and four hamburger(s) cost $15.25, four hot dog(s) and five hamburger(s) cost $16.25. Find the cost of one hot dog and the cost of one hamburger
Answers
Answer:
0.45
3.25
Step-by-step explanation:
16.25 ÷ 5 = 3.25
15.25 - 3.25 × 4 = 2.25
2.25 ÷ 5 = 0.45
Check Answer:
3.25 × 5 = 16.25
0.45 × 4 = 2.25
3.25 - 2.25 = 1
16.25 - 1 = 15.25
~lenvy~
how do you simplify (y+z)^3
Answers
Answer: y3+3y2z+3yz2+z3
Step-by-step explanation:
(y+z)3
=(y+z)*(y+z)*(y+z)
=(y+z)(y2+2yz+z2)
=(y)(y2)+(y)(2yz)+(y)(z2)+(z)(y2)+(z)(2yz)+(z)(z2)
=y3+2y2z+yz2+y2z+2yz2+z3
=y3+3y2z+3yz2+z3
How many different ways can the letters of grade be arranged?
( I have to use permutation to solve please and thank you )
Answers
Explanation:
Assuming you want to arrange the letters of "grade", then we have 5 unique letters. That gives 5! = 5*4*3*2*1 = 120 different permutations. Order matters. The exclamation mark means factorial. It means we start at 5 and count our way down to 1, multiplying along the way.
In other words, we have 5 choices for the first slot, then 4 choices for the next slot, and so on. We count down because we cannot reuse any previously selected letter.
Alternatively, you can use the nPr permutation formula
[tex]_nP_r = \frac{n!}{(n-r)!}[/tex]
where n = 5 and r = 5 since we have 5 letters to pick from and 5 slots to fill.
Answer:
120 ways
Step-by-step explanation:
The given word is :
GRADEIt has five letters⇒ Any of the 5 letters can be in each place
⇒ 5! ways is the number
⇒ 5 x 4 x 3 x 2 x 1
⇒ 20 x 6
⇒ 120 ways
The floor of Taylor's bathroom is covered with tiles in the shape of triangles. Each triangle has a
height of Zin and a base of 12 in. If the floor of her bathroom has 40 tiles, what is the area of the
bathroom floor?
Answers
Answer: 1680
Step-by-step explanation: first we have to find the area of each triangle so we do 7 times 12 then divide by 2 which equals 42. then since there are 40 tiles we multiply by 40 which will equa 1680.
Tori made a scale drawing of an Italian
restaurant. The restaurant's kitchen is 2
millimeters long in the drawing. The actual
kitchen is 16 meters long. What scale did Tori
use for the drawing?
1 millimeter :
meters
Answers
Step-by-step explanation:
2mm : 16m
so to get 1mm you need to divide 16 by 2
16/2 is 8 therefore
1mm : 8m
1 millimeter represents 8 meters in real life
hope that helps :)
a) Write an expression to represent the amount of money you
should have in the following situation.
Angela has $29 in her wallet. She gets paid $19 per hour and she
worked 8 hours last week and 6 hours this week. Then her friend
friend Tom borrowed $58.
b) How much money does Angela have left ?
PLEASE ANSWER THIS. I have an assignment due soon :((
Answers
Answer: $237
Step-by-step explanation:
Angela: 29 + 19(6 + 8) - 58
= -29 + 19(14) = -29 + 266 = $237
find out 6c+4dc when c=4.5 and d=6.6
show how to do it step by step
Answers
Answer:
145.8
Step-by-step explanation:
6c+4dc, where c=4.5 d=6.6
6(4.5) + 4(6.6) (4.5)
27 + 118.8
=145.8
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER. What is the value of X in simplest radical form?
X=_____
Answers
Answer:
X=97
Step-by-step explanation:
The formula for the Pythagorean Theorem is:
[tex]\sqrt{a^2+b^2}=c[/tex]
Now,
A=65
B=72
72x72=5184
65x65=4225
4225+5184=9409
Last,
Take the square root of 9409.
The square root is 97.
Therefore, the hypotenuse is 97.
To check, use the equation:
[tex]a^2+b^2=c^2[/tex]
A=65
B=72
C=97
72x72=5184
65x65=4225
97x97=9409
5184+4225=9409
9409=9409
Therefore, the missing side, which is the hypotenuse, is 97.
Answer:
97
Step-by-step explanation:
Given:
Opposite = 65Adjacent = 72Hypotenuse = xDefinition:
Opposite is a perpendicular/vertical side.Adjacent is a horizontal side, by adding opposite and adjacent together, you have formed a right angle.Hypotenuse is the longest side of all which is the side that’s opposite of the right angle.To find:
Value of xPythagorean Theorem:
[tex]\displaystyle \large{a^2+b^2=c^2}[/tex]
Determine:
a = oppositeb = adjacentc = hypotenuseNote:
a and b can swap each other so you can determine a = adjacent and b = opposite instead of a = opposite and b = adjacent. This is because of addition property.The exception is value of c - ‘c’ cannot be changed and must be hypotenuse.Therefore, substitute given information in:
[tex]\displaystyle \large{65^2+72^2=x^2}[/tex]
Evaluate:
[tex]\displaystyle \large{4225+5184=x^2}\\\displaystyle \large{9409=x^2}[/tex]
Square Root both sides:
[tex]\displaystyle \large{\sqrt{9409} = \sqrt{x^2}}[/tex]
Cancel the squared x, add plus-minus:
[tex]\displaystyle \large{\pm \sqrt{9409} = x}[/tex]
Simplify the surd:
[tex]\displaystyle \large{\pm 97 = x}[/tex]
However, side length is a scalar value so it cannot be negative nor have negative values. Therefore:
[tex]\displaystyle \large{x=97}[/tex]
Hence, the value of x is 97
Please factorise 14cd – 7c
Answers
Answer:
7c (2d - 1)
Step-by-step explanation:
Common factorization
Answer:
[tex]\bold{ 7c(2d - 1)}[/tex]
Step-by-step explanation:
[tex]\sf \rightarrow 14cd - 7(c)[/tex]
take 7(c) as common factor
[tex]\sf \rightarrow 7c(2d - 1)[/tex]
factorised
[tex]\sf 7 c(2d - 1)[/tex]
Multiply and divide rational expressions and simplify the answer
Answers
Answer:
1. 32x/15
2. 2/x-4
3. 1/10x+10
4. 3x^6/5x^9
5. (x-3)(x-9)/6
6. x^2/3
Step-by-step explanation:
multiply the Numerator with the Numerator of other number and multiply the denominator of the first with the denominator of the second. Find a common factor in both the Numerator and denominator to be able to cross out the identical factors.
FIND THE VALUES OF X AND Z FOR BRAINLIEST! :)))
Answers
Answer:
x = 20
z = 87
Step-by-step explanation:
Suplementary angles:
9x - 87 + 87 = 180
9x = 180
x = 20
Vertical angles:
z = 87
Answer:
z=87 x=20
Step-by-step explanation:
z=87 because vertical angles are congruent
87x2=174
360-84 =186
186/2=93 (the other 2 vertical angles are 93 each)
9x-87 =93
9x=180
x=20
A rectangle has a width of 3.5 inches and a length of x inches. If the diagonal of the rectangle is 12.5 inches, what is the value of x?
Answers
Answer:
12.0
Step-by-step explanation:
we solve using the pythagorean theorem.
sqrt of (12.5^2 - 3.5^2)
answer is 12
rounded of to the nearest tenth is 12.0
John's water bill this month was $19.67 . Looking at the water bill, it says he used exactly 10,000 gallons of water. How much does he pay per gallon of water used?
Answers
Answer:
0.001967 per gallon
Step-by-step explanation:
19.67/10000 = 0.001967
What is the answer?
Answers
[tex]\text{Given that,}\\\\\tan x = \dfrac 3{10}\\\\\text{Now,}\\\\\sin 2x = \dfrac{2\tan x}{1+ \tan^2 x}\\\\\\~~~~~~~~=\dfrac{2 \cdot \tfrac 3{10}}{1+ \left(\tfrac 3{10} \right)^2}\\\\\\~~~~~~~~=\dfrac{\tfrac 35}{1+ \tfrac 9{100}}\\\\\\~~~~~~~~=\dfrac{ \tfrac 35}{\tfrac{109}{100}}\\\\\\~~~~~~~~=\dfrac 35 \times \dfrac{100}{109}\\\\\\~~~~~~~~=\dfrac{60}{109}\\\\\\~~~~~~~~=0.5505[/tex]
(3x10^-4)(5x10^8) in scientific notation
Answers
Answer:
[tex]15 \times {10}^{4} [/tex]
Step-by-step explanation:
[tex](3 \times {10}^{ - 4} )(5 \times {10}^{8} ) \\ \\ = 3 \times 5 \times {10}^{8 - 4} \\ \\ = 15 \times {10}^{4} [/tex]
Write an equation in point-slope form for the line that passes through the points (f, g) and (h,j).
Answers
Point-slope form is a form of a linear equation: [tex]y-y_1=m(x-x_1)[/tex]
[tex](x_1,y_1)[/tex] is a point that falls on the linem is the slope of the lineTo write an equation in point-slope form:
Calculate the slope of the line by solving for mPlug m into the general equationPlug a point that falls on the line in the general equation as [tex](x_1,y_1)[/tex]Solving the QuestionWe're given:
The line passes through the points (f,g) and (h,j)Solve for the slope (m):
[tex]y-y_1=m(x-x_1)[/tex]
⇒ Plug in the point (f,g) as (x,y):
[tex]g-y_1=m(f-x_1)[/tex]
⇒ Plug in the point (h,j) as (x₁,y₁):
[tex]g-j=m(f-h)[/tex]
⇒ Isolate m by dividing both sides by (f-h):
[tex]\dfrac{g-j}{f-h}=m[/tex]
⇒ Therefore, the slope of the line is [tex]\dfrac{g-j}{f-h}[/tex].
Plug the slope into the general equation:
[tex]y-y_1=\dfrac{g-j}{f-h}(x-x_1)[/tex]
Plug one of the points, (f,g) or (h,j) into the equation as (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
AnswerThere can be multiple answers for this question, depending on what we consider to be (x,y) and what we consider to be (x₁,y₁). This is one of the possible answers, for (f,g) is (x,y) and (h,j) is (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Answers
Answer:
1 pound of peanuts cost 3 dollars
1 pound of wallnuts costs 2 dollars
Step-by-step explanation:
24/6=4
12/6=2
Nine is 2% of what number?
Answers
Answer:
450
Step-by-step explanation:
9=1/50 times x
x=450
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after seconds is given by the following.
h = 3+44t-16t^2
Find all values of t which the balls height is 23 feet.
Answers
Answer:
See below ↓↓
Step-by-step explanation:
Given function
h = 3 + 44t - 16t²We need to calculate the possible values of t at h = 23 feet.
Subsituting h = 23,
23 = 3 + 44t - 16t²16t² - 44t + 20 = 0Divide throughout by 4 as it is a common factor4t² - 11t + 5 = 0Solving for 't' using quadratic formula
t = 11 ± √121 - 4(4)(5) / 8t = 11 ± √41 / 8Solutions
t = 11 + 6.4 / 8 = 17.4/8 = 2.175 secondst = 11 - 6.4 / 8 = 4.6/8 = 0.575 secondsAnswer:
t = 2.175 s (3 dp)
t = 0.575 s (3 dp)
Step-by-step explanation:
Given equation: [tex]h=3+44t-16t^2[/tex]
To find all values of t for which the ball's height is 23 ft, substitute h = 20 into the equation and solve for t:
[tex]\implies h=23[/tex]
[tex]\implies 3+44t-16t^2=23[/tex]
[tex]\implies 16t^2-44t-3+23=0[/tex]
[tex]\implies 16t^2-44t+20=0[/tex]
Factor out common term 4:
[tex]\implies 4(4t^2-11t+5)=0[/tex]
Divide both sides by 4:
[tex]\implies 4t^2-11t+5=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-(-11) \pm \sqrt{(-11)^2-4(4)(5)} }{2(4)}[/tex]
[tex]\implies t=\dfrac{11 \pm \sqrt{41}}{8}[/tex]
Therefore,
t = 2.175 s (3 dp)t = 0.575 s (3 dp)which statement about the transformation is true? A. the unshaded octagon is a reflection because it is a flip over a diagonal line B. the unshaded octagon is a dilation because it is smaller than the shaded octagon C. the unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon D. the unshaded octagon is a vertical translation because it is directly under the shaded octagon
Answers
If you draw a diagonal line going down and crossing the origin, you can see that the figure reflects over that line. It’s like a mirror.
It is not the case for horizontal reflection because then it had to be reflected to the left of y-axis and it is not vertical reflection because then it would reflect below the x-axis
Question 11
1 pts
A baby was 6 lb 8 oz at birth. At one month old, she weighed 9 lb 2 oz. How much weight did the
baby gain in the first month?
Answers
Answer:
2 lb and 4oz
Step-by-step explanation:
because if you do 9lb 2oz minus 6lb 8oz you get 2 lb 4oz
A straight boardwalk is being built over a
circular wetlands area, so that it divides
the area in half. A hiking path goes around
the outside. The boardwalk is 50 m long.
How long is the hiking path that goes
around the wetlands?
Answers
Answer:
157 if youre going by 3.14
157.08 if youre going by π
Step-by-step explanation:
you want to find the circumference
circumference is 2πr
the radius id 50/2=25, because radius is half of the diameter (the diameter is the length across a circle
2 * 3.141 * 25 = 157
The length of the path that goes around the outside of the circle stands at 157.08 meters.
What is a circle?A circle stands as a curve traced out by a point moving in a plane so that its distance from a given point exists constant; alternatively, it stands for the shape created by all points in a plane that exists at a set distance from a given point, the center.
Given that the boardwalk divides the circle area into two halves, and exists straight with a length of 50 meters. Thus, the straight Boardwalk exists within the length of the diameter of the circle.
Now, the perimeter of the circle exists the length of the path that goes around the outside.
Thus, the perimeter of the circle stands,
Perimeter = π × Diameter
= π × 50 meters
= 157.07963 meters ≈ 157.08 meters
Thus, the length of the path that goes around the outside of the circle exists 157.08 meters.
To learn more about the circle
https://brainly.com/question/23580895
#SPJ2
Write an equation in slope-intercept form of the line shown.
An equation is
Answers
Answer:
Slope-intercept Form: y = 3/4*x -2
Step-by-step explanation:
From looking at the graph we can get out slopes which is rise/run and y-intercept.
m = 3/4 and b = -2
Slope-intercept Form: y = 3/4*x -2
If the teacher wants to show work you would have to use a point-slope form using those two points to solve m. Then using a point and slope plug that into the point-slope form and make it into slope-intercept form.
Find the area of the shape.
Answers
Select the two values of x that are roots of this equation.
x² + 34-3=0
. A. X=
-3+2/3
2
B. X=
-3-3
N
I X =
C. x.-3+27
=
1/21
2
O
D. *= -3-V21
=
2
Answers
Answer:
A. x=3 2.3
B . x=8
C. x=i do not know.
D. x=26
Step-by-step explanation:
A. -3+2/3=2
-3+2/3=-2 1/3
-2 1/3+3 2/3.=2
B. -3-3n=1
-3-3=-6n
-6n+8=1
C i do not understand.
D. -3-v21=2
21√5
Decimal Form:
1.0796532
or -24=2
-24+26=2
5. Solve the following differential equations
(a) dy/dx = 3y sin x (general solution)
(b) dy/dx = (given that x=0 when y=0)
Answers
Answer:
Step-by-step explanation:
hello :
dy/dx = 3y sin x means : (1/3) dy/y =sinx dx.....continu integ
A store sold 200 cell phone covers in April. The circle graph shows the
percent of each color sold in that month. How many more black covers
were sold than blue covers?
Answers
Answer:
24
Step-by-step explanation:
Given
Total is 200
From the attachment, we have:
Required
Black- 35%
Blue-23%
How many more of black than blue were sold
First, calculate the difference in percentage sold
Multiply by the total phones sold;
Hence, 24 more blacks were sold than blue
Hope this helps
Brainliest appreciated :)
Answer:
The answer is 24
Step-by-step explanation:
The total amount of phone covers were 200.
35% of those were black. So, 200 x 35% (or 200 x .35) = 70.
70 of the phone covers sold were black.
23% of the covers were blue. So, 200 x 23% (or 200 x .23) = 46
46 of the phone covers sold were blue.
How many more black covers sold than blue covers means we subtract.
70 black covers - 46 blue covers = 24 more black covers sold.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).
a = and b =
Answers
The value of a is equal to 3 and the value of b is equal to 4.
Complex Number
A Complex Number is represented by z=a+bi, where:
a= real part
bi= imaginary number
b= imaginary part
i= [tex]\sqrt{-1}[/tex], therefore i²= -1
For solving this question, you should solve the product (-11 + 5i) * (1 – i). After that, you should compare the previous results with the result for expression ( (a + bi)* (2 + 3i) )-i. From this comparison, using the linear system you will find the variables a and b.
Step 1 - Solve the product (-11 + 5i) * (1 – i)(-11 + 5i) * (1 – i)=
-11 +11i +5i -5i²
-11 +16i -5i², as i²= -1 you can rewrite
-11 +16i -5(-1)
-11 +16i +5
-6+16i
Then,
(-11 + 5i) * (1 – i)= -6+16i
Step 2 - Simplify the expression ( (a + bi)* (2 + 3i) )-i( (a + bi)* (2 + 3i) )-i
(2a+3ai +2bi +3bi²) -i, as i²= -1 you can rewrite
(2a+3ai +2bi +3b(-1)) -i
(2a+3ai +2bi -3b) -i
( (2a-3b) + i(3a +2b) ) -i ,
For adding complex numbers, you must add or subtract the corresponding real and imaginary parts. Thus, you will have:
(2a-3b) + i(3a +2b-1)
Then,
( (a + bi)* (2 + 3i) )-i= (2a-3b) + i(3a +2b-1)
Step 3 - Identify real and imaginary parts for previous results
For (-11 + 5i) * (1 – i)= -6+16i
real part = -6
imaginary part = 16
For ( (a + bi)* (2 + 3i) )-i= (2a-3b) + i(3a +2b-1)
real part = 2a-3b
imaginary part = 3a +2b-1
Step 4 - Construct a linear system from real and imaginary parts2a-3b= -6
3a +2b-1=16, you can rewrite as 3a +2b=17.
Thus the system will be:
[tex]\begin{bmatrix}2a-3b=-6\\ 3a+2b=17\end{bmatrix}[/tex]
Step 5 - Solving the linear system
2a-3b=-6 (1)
3a+2b=17 (2)
Multiplying equation 1 by 2 and equation 2 by 3, you can rewrite as:
4a-6b= -12
9a+6b=51
Sum the equations
4a-6b+9a+6b= -12 +51
13a= 39
a=39/13=3
Replacing the value of a=3 in equation 1, you can find b.
2a-3b=-6 (1)
2*3-3b= -6
6 -3b = -6
-3b = -6 -6
-3b= -12
b= -12/-3 = 4
Read more about complex numbers here:
https://brainly.com/question/5564133
Find the unit vector in the direction of (6, 7).
Write your answer in component form.
Do not approximate any numbers in your answer.
Answers
Answer:
<(6/√85),(7/√85>
Step-by-step explanation:
Let vector o = 6i + 7j,
The magnitude, | o | = √(6²+7²) = √85
Unit vector, ô = (6i + 7j)/√85
= (6/√85)i + (7/√85)j
In component form, ô = <(6/√85),(7/√85>
Help my 9 year old sister please
Answers
Answer:
He multiplied 28 by 7 instead of dividing it.
28 times 7 equals 196.
Step-by-step explanation:
I hope this helps! Have a lovely day!!! :)
