v₁·v₂ is -18 which is correct option(D)
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculations
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation : Divides left hand operand by right hand operand
For example 4/2 = 2
Given that,
v1 = (3,-4) and v2 = (2,6)
To determine v₁·v₂
v₁·v₂ = 3·(2) - 4·(6)
v₁·v₂ = 6 - 24
v₁·v₂ = -18
Hence, the v₁·v₂ is -18.
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Graph the line that passes through (5, 5), and is perpendicular to a line whose slope is –2.
Answer:
y = 1/2x + 5/2
Step-by-step explanation:
y = 1/2x + b
5 = 1/2(5) + b
5 = 5/2 + b
5/2 = b
make a the subject of the relation p=2(a+b)
Answer:
a = (p - 2b)/2Step-by-step explanation:
Solve for a:
p = 2(a + b)p = 2a + 2b2a = p - 2ba = (p - 2b)/2Which term of the AP. 8 , -4 , -16 , -28 ,......... is -880 ?
Answer: 75th term
Step-by-step explanation:
If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.
Please solve these radical equations and show the steps so that I can understand them. In my notes, it says the steps are to Isolate the radical, square both sides, solve for the variable, and check for the extraneous solutions so if this is what you are supposed to do please show these steps in action. Thank you for your time.
Answer:
1) X = 0
2) X = 0 or X = 1
Step-by-step explanation:
1)
[tex] \sqrt{6x} + 9 + 2 = 11 [/tex]
6x = 0 since root can only be = 0 if radicand is 0
X = 0
2)
[tex] \sqrt{x} - 3 + 3 = x[/tex]
[tex] \sqrt{x} = x[/tex]
X = x^2 ( We are squaring both sides to simplify)
x-x^2 = 0
x (1-x) = 0 (Factor the expression)
X = 0 or
1 -x = 0
X = 1
Answered by Gauthmath
Find the measure of b.
Answer:
b = 55°
Step-by-step explanation:
The angle at the centre is twice the angle on the circle subtended by the same arc, then
a = 0.5 × 110° = 55°
Angles on the circumference subtended by the same arc are congruent, so
b = a = 55°
Cos 600 degrees solved by double angle formula (20 points)
show work please :)))
Answer:
[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]
Step-by-step explanation:
we would like to solve the following using double-angle formula:
[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]
there're 4 double Angle formulas of cos function which are given by:
[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]
since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore
step-1: assign variables
to do so rewrite the given function:
[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]
so,
[tex] \theta = {300}^{ \circ} [/tex]Step-2: substitute:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]
recall unit circle thus cos300 is ½:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]
simplify square:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]
reduce fraction:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]
simplify substraction and hence,
[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]
Help plz Algebra 1
Simplify numbers 10 and 13 <3
Answer:
10t+2
Step-by-step explanation:
2-5t+8+5t-8
10t+2
Moly completes 3/10 of her science project in 4/5 hour
Answer:
1.5 per hour
Step-by-step explanation:
I need help ASAP!!Please explain how you got the answer
Answer:
348 km³
Does the answer help you?
As gamers progress through a video game, they earn a higher rank. In an online gaming network, gamers can see what fraction of the way they
are to the next rank. The line plot displays the fraction of the way to the next rank for all the gamers in the network. What fraction of gamers
have bof the way to go to the next rank?
Gamers Progress to Next Rank
Number
of
Gamers
Fraction of Progress to Next Level
A
A.
c.)
Question isn't well formatted, a picture if the question is attached below.
Answer:
1 / 4
Step-by-step explanation:
From the plot, each dot represent a gamer ; therefore, the total number of gamers will be counting all the dots ;
Total number of gamers = 24
Fraction of gamers that have 7 / 8 of the way to go ;
This means that they have 7/8 of the way left to proceed to next level ;
The fraction is : 1 - 7/8 = 1 /8
This means the number of of people whose progress are on 1/8 ; this is 6
Hence, fraction of gamers that have 7/8 of the way to go :
6 / 24 = 1 / 4
HELPP
3. Divide the following polynomials using the long division model: (4x^4 - 5x^2 + 2x^2 - X+5) = (x^2 + x+1).
Part I: Express this problem using the standard format for a problem of dividend - divisor divisor) dividend (2 points)
Part II: Use this checklist to proceed through this problem: (8 points)
• How many times does x2 go into the largest term in the problem?
* write the value on top of the problem and multiply that value by x^+x+1
*write the product below the lowest line on your work and subtract if from what reminds in the problem
*continue this process until you fab no longer divide x^2 into what reminds in the problem
*include your remainder in the final answer
Answer:
[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1} = 2 \cdot x^2 - 9 \cdot x + 7 \ Remainder \ (x - 2)[/tex]
Step-by-step explanation:
Part I
The problem can be expressed as follows;
The dividend is 4·x⁴ - 5·x³ + 2·x² - x + 5
The divisor is x² + x + 1
[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1}[/tex]
Part II
The number of times x² goes into the larest term, 4·x⁴ = 4·x² times
2·x² - 9·x + 7
[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1}[/tex]
4·x⁴ + 4·x³ + 4·x²
-9·x³ - 2·x² - x + 5
-9·x³ - 9·x² - 9·x
7·x² + 8·x + 5
7·x² + 7·x + 7
x - 2
Therefore, we have;
[tex]\dfrac{4 \cdot x^4 - 5\cdot x^3 + 2 \cdot x^2 - x + 5}{x^2 + x + 1} = 2 \cdot x^2 - 9 \cdot x + 7 \ Remainder \ (x - 2)[/tex]
The area of a square of side X is 8. What's the area of a square of side 3x
Answer:
Step-by-step explanation:
We know, for square
[tex](side)^2=(Area)\\=>X^2=8\\[/tex]
∴[tex]X=2\sqrt{2}[/tex] unit
[tex]Now, Side=3X[/tex]
[tex]Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit[/tex]
hope you have understood this...
pls mark my answer as the brainliest
The area of square of side 3X is 72 square unit.
What is square?The square is a 4 sided figure, each side of the square is equal and make a right angle.
The area of square having sided a unit can be given by a² square unit.
Given that,
Area of square having side X is 8.
Since, formula for area of square having side X is X².
Implies that,
X² = 8
X = 2√2
The area of square having side 3X
side =3 × 2√2
side = 6√2
The area of square = (6√2)²
= 36 x 2
= 72
The area of square is 72 square unit.
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What is the solution of ?
Answer:
The answer to your question would be x=12. Equation is worked out below
Step-by-step explanation:
5 /2 x−7= 3 /4 x+14
5 /2 x-3/4x − 7 = 3 /4 x-3/4x +14
7/ 4 x−7=14
7 /4 x−7+7=14+7
7/ 4 x=21
do the opposite of 7/4x (division)
7/4 / 7/4x = 21 / 7/4
4/7 / 7/4x (cross each other out) = 21 / 4/7
x=12
Answer:
[tex] \frac{5}{2}x - 7 = \frac{3}{4} x + 14 \\ \frac{5}{2} x - \frac{3}{4} x = 14 + 7 \\ \frac{7}{4} x = 21 \\ x = \frac{21 \times 4}{7} \\ x = 12[/tex]
I hope I helped you^_^
HEEEEEEEEEEEEEEEEEEELP
Answer:
2 miles per hour
Step-by-step explanation:
To find her walking pace in 'miles per hour' we need to divide the distance (in miles) by the time (in hours).
Speed = Distance/ Time
The time is given in minutes , but 50 minutes = 50/60 hours
=5/6 hours
1 2/3 ÷ 5/6
=5/3 × 6/5 miles per hour
Now cut it
= 2 miles per hour
ASAP HELP PLS NO WRONG ANSWERS------------
Answer:
d=2
Step-by-step explanation:
We are given equation:
sqrt(4y-3)=d-y
Squaring both sides gives:
4y-3=(d-y)^2
Applying the identity (x+y)^2=x^2+2xy+y^2 on right:
4y-3=d^2-2dy+y^2
Now let's y=7:
4(7)-3=d^2-2d(7)+(7)^2
Simplify:
25=d^2-14d+49
Subtract 25 on both sides:
0=d^2-14d+24
Factor left:
0=(d-12)(d-2) since -2+-12=-14 and -2(-12)=24
This gives d=12 or d=2.
The d that makes d-y or I mean d-7 negative will give us y=7 as extraneous
Since 2-7 is -5, then d=2 is what we are looking for.
Check:
sqrt(4y-3)=d-y
Set d=2: sqrt(4y-3)=2-y
Now solve for y:
Square both sides: 4y-3=4-4y+y^2
Subtract 4y and 3 on both sides: 0=7-8y+y^2
Reorder right side: 0=y^2-8y+7
Factor: 0=(y-7)(y-1) since -7+-1=-8 and -7(-1)=7
This gives y=7 or y=1.
Plugging in y=7 for a check to this equation gives:
sqrt(4×7-3)=2-7
Sqrt(25)=-5
5=-5 which is not true which is what we wanted
9. Find the zero of the polynomial in each of the following
i)f(x) = 3x- 5
Answer:
[tex]f(x) = 3x - 5[/tex]
For a zero, f(x) = 0:
[tex]{ \tt{0 = 3x - 5}} \\ { \tt{x = \frac{5}{3} }}[/tex]
Jack painted 5 8 part of a wall and Sam painted 7 12 part of another wall of the same size. Who painted a larger part of the wall?
Answer:
Jack
Step-by-step explanation:
convert the fractions to decimals to determine the person that painted the larger part of the wall
5/8 = 0.625
7/12 = 0.583
the fraction Jack painted is larger.
Need some help! I don’t get it at all!
Answer:
Min = -16; max = 0
Step-by-step explanation:
I plotted the inequalities for the constraints (see pic).
Sub in the coordinates of the vertices into the optimisation equation.
z = -(-4) + 5(-4) = -16
z = 0
z = -3 + 5(-1) = -8
Therefore, the max value of z is 0, and the min value is -16
What is the degree of this polynomial?
5 + 2s
=====================================================
Explanation:
We can rewrite 5 as 5s^0, since s^0 = 1 where s is nonzero.
Think of 2s as 2s^1
With those ideas in mind, the original polynomial turns into 5s^0 + 2s^1
Sorting the terms so that the largest exponent is first gets us the standard form 2s^1 + 5s^0
The largest exponent is the degree, so the degree is 1.
Side note: This trick only works for single variable polynomials.
How do you do this TwT
Answer:
Step-by-step explanation:
First step plug the numbers into the equation.
-10/(5+2) = (-10/5) + (-10/2)
Solve both sides of the equation separately.
-10/(5+2) Use distributive property, multiply both 5 and 2 by -10.
= -50 + (-20) = -70
-10/5 + -10/2 Multiply the fractions so they can be added together.
-10/5*2 = -20/10 -10/2*5 = -50/10
-20/10 + -50/10 = -70
Now you have solved both equations and they are both equal to -70, so you have verified that the equations are equal to each other because they both equal -70.
Find the length of the arc. Use 3.14 for the value of . Round your answer to the nearest tenth. Enter your answer and also show your work to demonstrate how you determined your
answer.
Answer:
ARC= 15.7
ARC= 2(3.14)10(90/36)
Step-by-step explanation:
Multiply using the FOIL method:
(x + y) (x + 2)
Answer:
x^2 +2x+xy +2y
Step-by-step explanation:
(x + y) (x + 2)
FOIL
first x*x = x^2
outer x*2 =2x
inner y*x= xy
last = y*2 =2y
Add together
x^2 +2x+xy +2y
Answer:
Step-by-step explanation:
F - First ; O - Outside ; I - inside ; L -last
(x + y)(x + 2) = x*x + x*2 +y*x +y*2
= x² + 2x + xy +2y
A pair of parallel lines is cut by a transversal: 15 degrees and 80 degrees are the lines What is the measure of angle x?
60 degrees
65 degrees
70 degrees
80 degrees
Step-by-step explanation:
=80°-15°=65°please mark this answer as brainlist
12 identical coins are placed in the cells on a chess board with 4 rows and 4 columns. If coins are not
allowed to be placed in the same cell, how many ways are there so that there are 3 coins in every rows
and columns?
Answer:
24 waysStep-by-step explanation:
If the coins are identical and not numbered, we need to find the number of patterns.
There are 4 rows and 4 columns. One cell remains empty in each row.
There are 4 options for the first row, 3 options for the second row, 2 options for the third row and 1 option for the fourth row.
The number of options reduces to avoid more than 1 empty cell in each row or column.
Number of options is:
4*3*2*1 = 24_________
[tex] \: [/tex]
4rows, and 4columns.
Soo :
= 4!
= 4 × (4 - 1) × (4 - 2) × (4 - 3)
= 4 × 3 × 2 × 1
= 24
Please answer this!!!
Answer:
12/13
Step-by-step explanation:
we know this is a right triangle, and we know that the hypotenuse is the longest side. so we can already say that the hypotenuse of the triangle is DF or 78.
when you draw it out, you find that the shortest leg is 30 and the second is 72 and the hypotenuse is 78. we also know that cosine is adjacent/hypotenuse. once you draw the triangle and notice which side is adjacent to angle F, just fit it into the formula and you get:
cos F = 72/78
cos F = 12/13
Answer: Choice C. [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
It helps to draw a right triangle with hypotenuse DF=78, and adjacent EF=72.Plug in cosine adjacent over hypotenuse and simplify.plz help quick
Find the area of the circle.
Use 3.14 for n. Do not round your answer.
Hint: A = hr2
Area = [?] inches
6 inches
Enter the number that
belongs in the green box.
Answer:
28.26 in ^2
Step-by-step explanation:
The diameter is 6 inches
The radius is 1/2 of the diameter
r = 1/d = 1/2(6) = 3 inches
A = pi r^2 = 3.14( 3)^2 = 3.14 (9) =28.26 in ^2
what would the equation, slope, and point be for this graph?
Answer:
slope is Δy/Δx =
-5/1 = -5
the B intercept is 4
y = -5x + 4
Step-by-step explanation:
Four friends equally divided a whole pizza for lunch. Binli ate 1 of his 3
share and took the rest of his share home. What fraction of the whole pizza did he eat for lunch?
Please help! Will give brainiest!!!
Answer:
He ate 1/12 of the pizza
Step-by-step explanation:
Divide the pizza by 4 to get the share each friend got
1/4
Then Binli ate 1/3 of his share
1/4 * 1/3 = 1/12
He ate 1/12 of the pizza
In this drawing, line p is parallel to line j and line t is perpendicular to ray ab
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Which of the following equations has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
D. 3x + 5 = 2x - 6
The equation with exactly one solution is 3x + 5 = 2x - 6. Option D is correct.
To determine which equation has exactly one solution, we need to solve each equation and see if we end up with a unique value for 'x'.
4x – 4 + 2x = 6x - 4
Combine the x terms on the left side: 6x - 4 = 6x - 4
This equation is an identity and holds true for all values of x. It doesn't have a unique solution.
B. 2(4x + 5) = 8x + 10
Distribute the 2 on the left side: 8x + 10 = 8x + 10
Similar to the previous equation, this equation is also an identity and holds true for all values of x.
It doesn't have a unique solution.
4x - 8 = 4(x - 4)
Distribute the 4 on the right side: 4x - 8 = 4x - 16
Subtract 4x from both sides: -8 = -16
This equation is contradictory and has no solution.
3x + 5 = 2x - 6
Subtract 2x from both sides: x + 5 = -6
Subtract 5 from both sides: x = -11
This equation has a unique solution, x = -11.
So, the equation with exactly one solution is 3x + 5 = 2x - 6. Option D is correct.
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