Answer:
See below.
Step-by-step explanation:
(a)
To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.
[tex] (\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) = [/tex]
[tex] = \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6 [/tex]
[tex]= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}[/tex]
[tex] = \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2} [/tex]
(b)
No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.
The height of the sail on a boat is 7 feet less than 3 times the length of its base. If the The area of the sail is 68 square feet, find its height and the length of the base.
Step-by-step explanation:
It is given that,
The height of the sail on a boat is 7 feet less than 3 times the length of its base.
Let the length of the base is x.
ATQ,
Height = (3x-7)
Area of the sail is 68 square feet.
Formula for area is given by :
[tex]A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0[/tex]
x = 8 feet and x = -3.73 feet
So, length is 8 feet
Height is 3(8)-7 = 17 feet.
So, its height and the length of the base is 17 feet and 8 feet respectively.
PLEASE HELP! 20 POINTS 1) A ball is thrown starting at a time of 0 and a height of 2 meters. The height of the ball follows the function H(t)=−4.9t2+25t+2. What is the height of the ball at each second from 0 to 5? (I'll put a picture of the graph.) 2) Which expression could represent the height of a soccer ball as it is in the air after being kicked? (This is part 2 to question 1) A. −16t+9 B. −16t2+4t3 C. 9t2+25t D. −16t2+25t+1
Answer:
a or b
Step-by-step explanation:
it just looks like b or a
H(t) = -4.9t^2 + 25t + 2
Height is a function of time
plug in 0, 1,2,3,4, and 5 to find the height at 0, 1,2,3,4, and 5 seconds.
at t = 0
H(0) = -4.9(0)^2+25(0) + 2 = 2 meters
Repeat for T=1,2,3,4 and 5
Notice the ball peaks around t = 3 seconds and starts to descend.
H(1) = (-4.9)(1^2) + 25(1) + 2 = 22.1 meters
H(2) = (-4.9)(2^2)+25(2)+2=32.4 meters
H(3) = 32.9 meters
H(4) = 23.6 meters
H(5) = 4.5 meters
find the five rational number lying between square of 5/6 and 6/7
Answer:
71/84
Step-by-step explanation:
Answer:
1229/1764, 1231/1764, 179/252, 1255/1754 and 185/252.
Step-by-step explanation:
(5/6)^2 = 25/36
(6/7)^2 = 36/49
LCM of 36 and 49 is 1764
So 25/36 = 25 * 49 / 1764 = 1225/1764
and 36/49 = 36 * 36 / 1764 = 1296/1764
So the 5 rational numbers could be:
1229/1764, 1231/1764, 1253/1764 ( = 179/252), 1255/1764 and 1295/1764 (= 185/ 252).
Thomas had 19 problems correct of the 25 problems on a recent math quiz. What percent of the
problems on the quiz did he answer correctly?
A.
24%
B. 36%
C. 76%
D.95%
Hey There!!
Your best choice is 76%
Because, 19/25 = x/100
25x = 1900
x = 76
°He got 76% correct!!°
By °Itsbrazts°
Answer:
76%
Step-by-step explanation:
Thomas got 19/25 marks.
** Note: Percents are always out of 100.
We don't know how many marks he got out of 100.
=> 19/25 = x/100
There are two ways to solve it from now.
=> Multiply 19 and 100; 25 and x
=> 25x = 1900
Next, Divide 25 on each side.
=> 25x/25 = 1900/25
=> x = 76
He got 76% on the quiz.
Another way is:
=> 19/25 = x/100
=> We need to divide 25 from 100.
=> We get 4.
So, 25 x 4 = 100
=> 19 x 4 = x
=> x = 76
He got 76% on the quiz.
Both ways are correct.
Help with this find the image of (1 ,2) after a reflection about y=x followed by a reflection about y=-x
Answer: (-1, -2)
Step-by-step explanation:
so at first you have (1, 2)
then you were asked to reflect about y=x which is (x, y) = (y, -x)
(1, 2) = (2, -1)
then followed by y=-x which is (x, y) = (-y, -x)
(2, -1) = (-1, -2)
I hope this helps!
Which graph solves the following system? x+2y=4 5x−2y=8
Answer:
elimination method
x+2y=4 1
5x-2y=8 2
1+2
6x=12
x=2
plug into x+2y=4
2+2y=4
2y=4-2
2y=2
y=1
(2,1)
so graph 1
is y=3x^3+4x^2+15x+7 a function and if it is, explain
========================================================
Explanation:
It is a function because any x input leads to exactly one y output. The graph visually passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the cubic curve, so that's why the graph passes the test, and visually confirms we have a function.
------------------
Extra info:
Something that isn't a function is [tex]y^2 = x[/tex] because it graphs a sideways parabola in which it is possible to draw a vertical line through more than one point on the curve. Two points on this parabola are (9, 3) and (9, -3). The input x = 9 corresponds to more than one output y = 3 and y = -3 simultaneously.
make u the subject of the formula
u-x/v-x=u/v²
Answer:
See below.
Step-by-step explanation:
[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]
Cross multiply and distribute.
[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]
Move all the u to the left side:
[tex]uv-ux-uv^2=-xv^2[/tex]
Factor out a u:
[tex]u(v-x-v^2)=-xv^2[/tex]
Divide:
[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]
(I factored out a negative in the second term.)
Will someone please help me with this problem!! **It's multiple choice!
A = (-7,-6)
B = (8,-9)
Find the slope of line AB
m = (y2-y1)/(x2-x1)
m = (-9-(-6))/(8-(-7))
m = (-9+6)/(8+7)
m = -3/15
m = -1/5
The slope of line AB is -1/5.
Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.
Let m = 5.
Use the coordinates of point C (2,12) along with the perpendicular slope to get
y - y1 = m(x - x1)
y - 12 = 5(x - 2)
y - 12 = 5x - 10
y = 5x - 10+12
y = 5x + 2
Lastly, convert this to standard form
y = 5x + 2
5x+2 = y
5x+2-y = 0
5x-y = -2
Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.
Answer:
5x - y = -2.
Step-by-step explanation:
The equation of this altitude line has a slope = -1/m where m is the slope of line AB . It will also pass through the point C.
The slope of line AB = (-9 - (-6)) / (8 - (-7))
= -3/15
= -1/5
So the slope of the required line = -1 / -1/5 = 5.
Using the point C and the point-slope form of a line:
y - y1 = m(x - x1)
y - 12 = 5(x - 2)
y - 5x = -10 + 12
y - 5x = 2
5x - y = -2.
The points shown on the graph represent the numbers in a geometric sequence.What is the initial value of the sequence? 1 2 3 8
Answer:
1
Step-by-step explanation:
It starts with number one, so one must be the initial value of the sequence.
1
Step-by-step explanation:
Kapil deposited Rs. 1600 in a bank on 1st January 2005. Find the amount in his bank account on 1st January 2006, if the bank pays interest at 8% per annum and the interest is calculated every year on 30th June and 31st December.
Answer:
SI=PRT/100
=10000*5*42/12*100
=1750
SI=1750
TOTAL AMOUNT=PRINCIPLE+SI
=10000+1750
=101750
Help me please! I’ll give brainliest
Answer:
200-150 equals 50
Answer:
50 N
Step-by-step explanation:
It is 50 N because person A is pushing with 200 N, and person B is pushing with 150 N. But they are both pushing at the same time. But since person A is pushing with more force with 200 N than person B with 150 N, that only leaves 50 N. So basically person A is pushing with 50 N.
The number of polynomials having zeros as -2 and 5 is a)1 b)2 c)3 d)more than 3
Answer:
d) More than 3.
Step-by-step explanation:
The polynomial (x - 5)(x + 2) ( = x^2 - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:
- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.
The cosst of 4 1 /4 kg of sugar is £68 .find the coast o 1 kg
Step-by-step explanation:
Hi, there!!
Here according to the question we must find the cost of 1 kg sugar.
Given that:
17/4 kg of sugar cost £68.
then 1 kg sugar costs,
=[tex] \frac{68}{ \frac{17}{4} } [/tex]
after reciprocal we get,
= £68×4/17
=£16
The answer would come £16.
Therefore, The cost of 1 kg sugar is £. 16.
Hope it helps....
Answer:
£ 16
Step-by-step explanation:
Cost of 4 1/4 kg sugar = £ 68
4 1/4 = 17/4
Cost of 17/4 kg of sugar = 68
Cost of 1 kg of sugar =68 ÷ (17/4)
[tex]= 68* \frac{4}{17}\\\\=4*4\\[/tex]
= £ 16
70 POINTS! PLEASE HELP! Explain the difference between the following equation formats: Slope-Intercept, Point-Slope and Standard
Answer and Step-by-step explanation:
1. slope intercept
2. point-slope form
3. standard
Explanation:
1. A slope intercept form equation is when it's set up as y = m x + b
m = slope
b = y-intercept
2. A point-slope form is when a line passes through a point
and the equation is set up as y −b = m ( x−a)
m = slope
(a, b) A point that the line passes through
3. standard lope form is when the equation is set up as
Ax + By = C
PLEASE HELP ASAP!!
The image above shows two dilated figures with lines IJ and JK drawn. If the smaller figure was dilated by a scale factor of 2, what relationship do lines IJ and KL have?
Answer:
[tex] IJ = 2(KL) [/tex]
Step-by-step explanation:
From the information given, the smaller figure was dilated on a scale factor of 2, to produce the bigger figure. In essence, the bigger figure is times 2 of the smaller figure.
Therefore, line IJ would be twice the length of KL.
The relationship that both lines have can be represented as: [tex] IJ = 2(KL) [/tex]
Given: m∠V=103°, m∠VRT=71°, RS ∥ VU Find: m∠TRS, m∠U
Answer:
m∠U = 103° and m∠TRS = 6°
Step-by-step explanation:
In the given circle O,
Since, RS║VU, and VR is a transverse,
Therefor, m∠V + m∠R = 180° [Consecutive interior angles]
m∠R + 103° = 180° [m∠R = 103° given]
m∠R = 180° - 103°
m∠R = 77°
Since m∠R = m∠VRT + m∠TRS
77° = 71° + m∠TRS
m∠TRS = 77° - 71° = 6°
Quadrilateral RTUV is a cyclic quadrilateral.
Therefore, m∠U + m∠R = 180°
m∠U + 77° = 180°
m∠U = 180° - 77° = 103°
I need the answers for my bro
Answer:
1)He will use 144 squares in his design
2)He will use 36 squares in his design
Step-by-step explanation:
1) There is 12 squares going horizontally and 12 squares going vertically meaning the total amount of squares needed is:
12 x 12 = 144 inch squares
2) If he wants to cover a smaller box that is 1/2 feet big than he would take the square of 1/2 which is 1/4 and multiple it to the original answer to get the answer of the new question
144 x (1/4) = 36 inch squares
an equation uses the symbol
Answer:
The '=' sign.
Step-by-step explanation:
The equals sign ( = ). for example:
3x + 1 = 8.
The equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.
Change histul
bols
A store pays two fees when a customer uses a credit card to make a purchase. These fees include:
A flat fee of $0.15
A processing fee equal to 1.75% of the dollar amount of the purchase
There is no sales tax on the purchase.
What is the amount, in dollars and cents, the store pays in fees for a $60.00 purchase by a customer using a credit
card?**
Answer:
So the amount to pay is $1 and 20 cents ( or a total of 120 cents)
Step-by-step explanation:
Here, we want to know the amount paid as fees for a $60 purchase given that the store has to pay a flat fee of $0.15 and a processing fee of 1.75% of the amount of purchase.
Firstly, we establish that there are two fees to be paid.
We already have a fee of $0.15
The other fee to pay is 1.75% of $60
Mathematically that would be;
1.75/100 * 60 = $1.05
Thus, the fees to be paid on the $60 purchase is $1.05 + $0.15 = $1.20
Find the missing probability. P(A)=720,P(B)=35,P(A∩B)=21100 ,P(A∪B)=?
The missing probability P(A∪B) will be 37/50.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given information;
P(A)= 7/20,
P(B)=3/5,
P(A∩B) =21/100 ,
We need to find the missing probability P(A∪B).
We know that
P(A∪B)= P(A) + P(B) + P(A∩B)
P(A∪B) = 7/20 + 3/5 + 21/100
P (A U B) = 37/50
Therefore, the missing probability P(A∪B) will be 37/50.
Learn more about probability here;
https://brainly.com/question/11234923
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Triangle Q M N is shown. The length of Q M is 18, the length of M N is 17, and the length of Q N is 20. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the measure of AngleQ to the nearest whole degree? 43° 49° 53° 58°
The measure of angle Q in the triangle QMN is 52.83°
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
For a triangle with sides a, b, c and respective opposite angles A, B, C, cosine rule is:
a² = b² + c² - 2bc * cos(A)
In triangle QMN, QM = 18, MN = 17, QN = 20, hence:
17² = 18² + 20² - 2(18)(20) * cos(Q)
Q = 52.83°
The measure of angle Q in the triangle QMN is 52.83°
Find out more on equation at: https://brainly.com/question/2972832
#SPJ2
Answer:
53
Step-by-step explanation:
its rounded
A. X>0
B. xis all real numbers.
C. O sxs 5
D. -5 sxs 5
Answer:
B
Step-by-step explanation:
The domain of a function is all of the x values of a function. Since there seem to be no constraints on the values of x (we know this because the function is continuous and it goes on forever in both sides), the answer is B.
Answer:
B. All real numbers
Step-by-step explanation:
Hey there!
Well the domain is all the x-values in the graph and by looking at where the lines are going we can tell that the graph domain is all real numbers.
Hope this helps :)
what is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?
Answer:
-16, 0 real solutions. (Complex Roots)
Step-by-step explanation:
[tex]5x^2-2x=-1\\5x^2-2x+1\\A=5\\B=-2\\C=1\\(-b±√(b^2-4ac))/2a\\=\\=-2^2-4(5)(1)\\=4-20\\=-16[/tex]
The sum of the ages of Noi's and Noy's is 26 years. The different between four times Noi's age and two times Noy's age is 28 years. Find the age of Noi and Noy.
WRITE AS AN EQUATION
Answer:
The age of Noi is 13.333 Years and the age of Noy is 12.67 years
Step-by-step explanation:
The given information are;
The sum of the ages of Noi and Noy = 26 years
Four times Noi's age - Two times Noy's age = 28
Let the age of Noi = X and let the age of Noy = Y
We have;
X + Y = 26 years.................(1)
4X - 2Y = 28 years.............(2)
Divide equation (2) by 2 to get;
(4X - 2Y)/2 = (28 years)/2 which gives;
2X - Y = 14 years.................(3)
Add equation (3) to equation (1), to get;
X + Y + 2X - Y = 26 years + 14 years
3X = 40 years
X = 40/3 = 13.333 Years
From equation (1), X + Y = 26 years, therefore;
Y = 26 - X = 26 - 13.33 = 12.67 years
Therefore, the age of Noi = 13.333 Years and the age of Noy = 12.67 years.
Which of the following statements is true about odd
and/or even numbers?
F. The sum of any 2 even numbers is odd.
G. The sum of any 2 odd numbers is ood.
H. The quotient of any 2 even numbers is odd.
J. The quotient of any 2 even numbers is even.
K. The product of any 2 odd numbers is odd.
Answer:
k) the product of ant 2 odd numbers is odd
I don't know.
Let's check um out.
For each choice, I'll try to find an example to show that it's false.
F. The sum of any 2 even numbers is odd.
2+2=4. 4 is even. This one is false.
G. The sum of any 2 odd numbers is ood.
3+3=6. 6 is even. This one is false.
H. The quotient of any 2 even numbers is odd.
8÷4=2. 2 is even. 10÷4=2.5. 2.5 is neither odd nor even. This one is false.
J. The quotient of any 2 even numbers is even.
10÷2=5. 5 is odd. This one is false.
K. The product of any 2 odd numbers is odd.
I can't find an example where this is false.
So I'm gonna say that this is the true one.
Give the values of a, b, and c needed to write the equation's general form.
1/4x^2+5=0
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]\frac{1}{4} x^2+5=0[/tex]
For this equation: [tex]a=0.25, b=0, c=5[/tex]
[tex]0.25x^2 + 0x + 5 = 0[/tex]
Step 1: Use quadratic formula with [tex]a=0.25, b=0, c=5.[/tex]
[tex]x = \frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex]
[tex]x = \frac{-(0) ± \sqrt{(0)^2 -4 (0.25) (5) } }{2(0.25)}[/tex]
[tex]x = \frac{0 ± \sqrt{-5} }{0.5}[/tex]
Answer : No Real Solutions.
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
Which type(s) of symmetry does the following object have?
Select all that apply.
Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.
We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.
We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.
Answer:
Theres more than one answer so b and a
Step-by-step explanation:
On Wednesday at camp, Samuel went for a hike at 6:30 A.M. The hike took 2 hours and 15 minutes. As soon as he got back from the hike, Samuel played volleyball for 1 hour. What time did Samuel finish playing volleyball?
Answer:
9:45 A.M.
Step-by-step explanation:
First, add the time that took him to hike:
6:30 + 2 hours and 15 minutes = 8:45 A.M.
Next, add the 1 hour that he played volleyball for:
8:45 + 1 hour = 9:45 A.M.
So, he finished playing volleyball at 9:45 A.M.
Answer:
9:45 am
Step-by-step explanation:
He went at 6:30 am to a hike.
It took him 2 hours 15 minutes
=> 6 : 30
+ 2 15
=> 8 : 45
He came back from the Hike at 8:45 am
He played volleyball for 1 hour.
=> 8 : 45
+ 1
=> 9 : 45
He finished playing volleyball at 9:45 am
-
What is the product?
(-3s +2)(4s-1)
Answer: -12s + -2
Step-by-step explanation: You need to combine the like terms so -3sx4s = -12s and 2+-1 = -2 so it’s -12s + -2 or -12s - 2
Answer:
-12s²+11s-2
Step-by-step explanation:
(-3s+2)(4s-1)
First you have to FOIL (First, inner, outter, last)
First: -3s × 4s
Inner: -3s × -1
Outter: 2 × 4s
Last: 2 × -1
Now you should have -12s² + 3s + 8s -2
----------------------
Next you combine your like terms
Finally you have your answer, -12s²+11s-2 .