The equation can have no solution or as many solutions as possible
Terrence's conclusion that the equation has infinitely many solutions is false
How to determine the number of solutions?The equation is given as:
101 - 6+ 2 = 4(3x - 1) - 2
Open the bracket
101 - 6+ 2 = 12x - 4 - 2
Collect the like terms
12x = 101 - 6+ 2 + 4 + 2
Evaluate the like terms
12x = 103
Divide both sides by 12
x =103/12
The above shows that the equation has one solution
Hence, Terrence's conclusion that the equation has infinitely many solutions is false
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Find the Area of the Trapezoid
Area:-
1/2(Sum of parallel sides) (Height)1/2(2+5)(3)1/2(21)10.5units°2Answer:
[tex]A=\boxed{10.5}\; \;\rm sq. \; un.[/tex]
Step-by-step explanation:
Area of a Trapezoid
[tex]\boxed{A=\dfrac{1}{2}(a+b)h}[/tex]
where:
a and b are the bases of the trapezoid (the parallel sides).h is the height of the trapezoid (perpendicular to the bases).From inspection of the given diagram:
a = SK = 2 unitsb = OC = 5 unitsh = OS = 3 unitsSubstitute the found values into the formula and solve for A:
[tex]\implies A=\dfrac{1}{2}(2+5)(3)[/tex]
[tex]\implies A=\dfrac{1}{2}(7)(3)[/tex]
[tex]\implies A=\dfrac{7}{2}(3)[/tex]
[tex]\implies A=\dfrac{21}{2}[/tex]
[tex]\implies A=10.5\; \;\rm sq. \; un.[/tex]
much appriciated if helping
Please solve this question.
Answer: see proof below
Step-by-step explanation:
Given: A + B + C = π → A + B = π - C
A + C = π - B
B + C = π - A
Cofunction Identities: sin [(π/2) - A] = cos A
cos [(π/2) - A] = sin A
Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]
Pythagorean Identity: cos²A + sin²A = 1 → cos²A = 1 - sin²A
Even/Odd Identity: cos (-A) = -cos(A)
Double Angle Identity: cos (2A) = 2 cos²A - 1
Proof LHS → RHS:
LHS: cos [(B + C) - A] - cos [(A + C) - B] + cos [(A + B) + C]
Given: cos [(π - A) - A] - cos [(π - B) - B] + cos [(π - C) - C]
= cos (π -2A) - cos (π -2B) + cos (π -2C)
Cofunction: cos (-2A) - cos (-2B) + cos (-2C)
Even/Odd: -cos (2A) + cos (2B) - cos (2C)
Double Angle: -(2cos²A - 1) + cos (2B) - cos (2C)
= 1 - 2cos²A + cos (2B) - cos (2C)
Sum to Product: 1 - 2cos²A - 2sin(B+C) · sin (B-C)
Given: 1 - 2cos²A - 2sin (π - A) · sin (B - C)
Cofunction: 1 - 2cos²A - 2sin A · sin (B - C)
Pythagorean: 1 - 2(1 - sin²A) - 2sin A · sin (B - C)
= 1 - 2 + 2sin²A - 2sin A · sin (B - C)
= -1 + 2sin²A - 2sin A · sin (B - C)
Factor: -1 + 2sin A (sin A - sin (B - C))
Given: -1 + 2sin A [sin (π - (B + C)) - sin (B - C)]
Cofunction: -1 + 2sin A [sin (B + C) - sin (B - C)]
Sum to Product: -1 + 2sin A [2 cos B · sin C]
= -1 + 4sin A · cos B · sin C
LHS = RHS [tex]\checkmark[/tex]
Karen is trying to decide which home phone company to use. PhoneHome was a monthly charge of
$45 and charges $0.01 per minute. CallMeMaybe has a monthly charge of $10 and charges $0.05 per
minute. Write an inequality to represent the number of minutes used in order for PhoneHome to
have the better deal.
Answer:
0.01x+45>0.05x+10
HELP HAVING BAD DAY Find the ratio a:b if it is given that:
3a=8b
Answer:
..
Step-by-step explanation:
Answer:
3;8
Step-by-step explanation:
= In circle V, VW = 8 and m<WVX = 20°. Find the length of arch W X. Express your answer as a fraction times pi.
The length of the arc WX is the number of units on the arc
The length of the arc WX is [tex]\frac{8}{9} \pi[/tex]
How to determine the length of the arc WX?The given parameters are:
Central angle, m<WVX = 20 degrees
Radius, VW = 8
The length (L) of the arc is calculated as:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
Substitute known values
[tex]L = \frac{20}{360} * 2\pi *8[/tex]
Evaluate the product
[tex]L = \frac{320}{360} \pi[/tex]
Simplify the fraction
[tex]L =\frac{8}{9} \pi[/tex]
Hence, the length of the arc is [tex]\frac{8}{9} \pi[/tex]
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HELP PLS!!!
Solve the inequality $x^3 + 4x > 5x^2$.
Answer:
de fk?
Step-by-step explanation:
wth is that
What is the x-coordinate of the midpoint of line segment AB with points A(62, 5) and B(-46, -13).
Answer: 5
Step-by-step explanation:
The x-coordinate of the midpoint of the segment is the average of the x-coordinates of the two endpoints.
Therefore, the x-coordinate of the midpoint of AB is the average of the x-coordinate of A and the x-coordinate of B.
We are given that the x-coordinate of A is 62 and of B is -42.
The average of 62 and -42 = (62-42)/2 = 10/2 = 5
if you bought 845.67 mL of dish soap and have already used 242.36 mL, how much do u have left
Answer:
I believe you just subtract 845.67ml - 243.36 which is equal to 602.31
Step-by-step explanation:
Bill wants to purchase some gloves and hats. The gloves cost $12 and a hat costs $8. Bill can spend no more than $56. Let g represent the number of gloves purchased and h represent the number of hats purchased. Which inequality represents this situation?
Step-by-step explanation:
Let g represent the number of gloves purchased and h represent the number of hats purchased.
The gloves cost $12 and a hat costs $8
We need to write an inequality that represents this situation.
Cost of gloves = $12g
Cost of hats = $8h
No more than $56 means [tex]\le 56[/tex].
We can write the inequality as follows :
[tex]12g+8h\le 56[/tex]
Hence, this is the required solution.
Matthew's dad hired him to paint 6 wooden patio chairs for $125. It takes him 9 hours to paint all of the chairs. If it takes the same amount of time to paint each chair, what fraction of an hour does it take Matthew to paint one chair? Justify your thinking with a model.
Given:
Matthew's dad hired him to paint 6 wooden patio chairs for $125.
Time taken by him to paint all of the chairs = 9 hours.
It takes the same amount of time to paint each chair.
To find:
The fraction of an hour does it take Matthew to paint one chair
Solution:
Total time = 9 hours
Total number of chairs = 6
Now, time taken by Matthew to paint one chair is
[tex]\dfrac{\text{Total time}}{\text{Total number of chairs}}=\dfrac{9}{6}[/tex]
[tex]\dfrac{\text{Total time}}{\text{Total number of chairs}}=\dfrac{3}{2}[/tex]
Therefore, Mattew takes [tex]\dfrac{3}{2}[/tex] of an hour to paint one chair.
Thinking with a model: On dividing the total time by total number of chairs we get time taken by Mattew (in hours) to paint one chair. So, the result represents the fraction of an hour taken by Matthew to paint one chair.
Which table represents a linear function? ill give you brainliest if you’re right
There are 900 students
at Acute Middle
School. The ratio of
boys to girls is 2 to 3.
What percent of the
students are girls?
I need work to be shown.
Which equation can you create with the given information? m = 6, b = -2
a
y=6x-2
y=6x+2
y=2x+6
y=-2x-6
Answer:
y = 6x - 2
Step-by-step explanation:
y = mx + b
y = 6x + (-2)
What is the unit circle for sin60
Draw a number line and show the following numbers.
one-digit primes
-----------------------------------------------------
answer: 2, 3, 5, 7
Which statement could be used in step 2 when proving x =
30?
Statements
1. mZORP - 80°; mZORN-(3x+10)°
Reasons
1. given
no
- N در دل
O ZORP and ZORN are a linear pair
O ZORP and ZORN are vertical angles
O 80 = 3x +10
O x = 30
(a) ∠ORP and ∠ORN are a linear pair .
Let us prove that option a , is the correct option by finding the value of x .
Angle ORP and angle ORN are a linear , which means their sum will be equal to 180° .
So :-
[tex]80 + 3x + 10 = 180[/tex]
[tex]3x + 80 + 10 = 180[/tex]
[tex]3x + 90 = 180[/tex]
[tex]3x = 180 - 90[/tex]
[tex]3x = 90[/tex]
[tex]x = \frac{90}{3} [/tex]
[tex]x = 30°[/tex]
As we were able to find put the value of x only after we cam to know that ∠ORP and ∠ORN are a linear pair , we say that option a is the correct statement .
Therefore , the correct answer is :-
(a) ∠ORP and ∠ORN are a linear pair .
The value of x is equal to 30°. Hence, proved.
What are angles at a point on a straight line?Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line add to 180°.
Given that, m∠ORP=80° and m∠ORN=(3x+10)°.
Here, m∠ORP+m∠ORN=180° (Angles on straight line adds upto 180°)
80°+(3x+10)°=180°
90°+3x=180°
3x=90°
x=90°/3
x=30°
Hence, proved.
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How do I solve 5/30 * 100
Answer:
16.67
Step-by-step explanation:
5/30 = 1/6
1/6 x 100 = 100/6
100/6 simplified is 16.67
Answer:
Use PEMDAS
Step-by-step explanation:
P-parenthesis ( )
E-Exponent
M-Multiplication *
D-Division /
A- Addition+
S-Subtraction -
so, first you would do 30 * 100= 3000
Then, you would do 5/3000=???
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7.50 and each adult ticket sells for $11. The drama club must make no less than $990 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, ss, and the number of adult tickets sold, aa, that would satisfy the constraint.
Answer: ss*$7.50 + aa*$11 ≥ $990.
Step-by-step explanation:
We have two variables:
aa = # of adult tickets sold.
ss = # of student tickets sold.
The total profit is:
P = ss*$7.50 + aa*$11
And we want P ≥ $990.
Then we can write the inequality:
ss*$7.50 + aa*$11 ≥ $990.
Now, we have only one equation and two variables, so there are a lot of possible solutions for this system.
helppppppp pleaseeeeeee
Graph the solution of this inequality
å (x+8) > 2 (2.0 + 10)
-5
-4
-3
-2
-1
0
1
2
3
4
5
Drag a point to the number line.
Show Example
The required solution to the given inequality is x > 16, as shown in the graph.
What is inequality?In mathematics, an inequality is a statement that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to). For example, "x + 3 < 10" is an inequality that states that the value of x plus 3 is less than 10.
Here,
As mentioned in the question,
To graph, the solution of the inequality (x+8) > 2 (2.0 + 10).
Simplifying the given inequality:
(x+8) > 2 (2.0 + 10)
x+ 8 > 2(12)
x > 24 - 8
x > 16
Thus, the required solution to the given inequality is x > 16.
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Please help!! If f (x) = e^x sin x, then f’ (x) =
Answer:
[tex] f'(x) = {e}^{x}( \sin x + \cos x ) [/tex]
Step-by-step explanation:
[tex]f(x) = {e}^{x} \sin x \\ \\ f'(x) = \sin x \frac{d}{dx} {e}^{x} + {e}^{x} \frac{d}{dx} \sin x \\ \\ f'(x) = \sin x \: {e}^{x} +{e}^{x} \cos x \\ \\ f'(x) = {e}^{x}( \sin x + \cos x ) [/tex]
How do you do a 180 rotation around the point (2, 0)??
Answer: (x,y)→(−x,−y)
Step-by-step explanation: The rule for a rotation by 180° about the origin is (x,y)→(−x,−y)
HELPPP FOR BRAINLEST PLEASE
Answer:
4th is correct
Step-by-step explanation:
As the object moves in forword direction
so F2 must have great magnitude.
HOPE THIS HELP YOU FOR ANY QUESTION PLEASE ASK ME
what value of n makes this equation true?
Answer:
c
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
When converting radical expressions to rational exponents the exponent on the radicand (1) becomes the numerator of the rational exponent, and the index/root of the radical (4) becomes the denominator of the rational exponent. (1/4)
HELP ASAP I GIVE 60 points total and big brain!!!! Solve the system of equations by substitution. If there is one solution, express it as an ordered pair. If there is no solution, write no solution. If there is an infinite number of solutions, write infinite number of solutions.
x−y=−5x
x−y=1/3
Solution:
Given:
x - y = -5xx - y = 1/3Substitute the value of "x - y" into equation 1.
x - y = -5x1/3 = -5xDivide -5 both sides.
1/3 ÷ -5 = -5x/-51/3 x 1/-5 = xx = 1/-15 = -1/15Substitute the value of x into equation 2.
x - y = 1/3-1/15 - y = 1/3-1/15 - y = 5/15-y = 5/15 + 1/15y = -6/15 = -2/5Putting the solutions in (x,y) form.
⇒ (x,y) ⇒ (-1/15, -2/5)Answer:
(x, y) = (-1/15, -2/5)
Step-by-step explanation:
You want to solve the system of equations by substitution:
x -y = -5xx -y = 1/3SubstitutionWe can use the second equation to substitute for (x-y) in the first equation:
1/3 = -5x
-1/15 = x . . . . . . . . divide by -5
Substituting this value into the second equation, we have ...
-1/15 -y = 1/3
-1/15 -1/3 = y = -6/15 = -2/5
The solution is (x, y) = (-1/15, -2/5).
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Please do your thing smart people.
HELP ME PLEASE
Answer:
C. Natural Numbers
Step-by-step explanation:
Before we determine what groups [tex]\sqrt{100}[/tex] fits into, we must simplify it. We get the number 10, which is much easier to categorize. Out of the four options, the natural numbers are the smallest group, containing only the numbers we use to count (i.e. 1, 2, 3, 4 ...). We know that 10 fits into this category because 10 is a non-zero whole number. Since the natural numbers contain 10 and are the smallest subset, the answer is C.
As a note: 10 will also fit into the whole numbers and rational numbers since all natural numbers are parts of these two groups as well. These groups contain more numbers, however, making them larger than the natural number set so we can eliminate them. 10 is also not an irrational number since we can accurately define it with a fraction.
Members of the ninth grade class at Pine Ridge High School are organizing into service groups. What is
the minimum number of students who must participate for all students to be divided into groups of 4, 6, or 9 students
with no one left out?
Answer:
8
Step-by-step explanation:
There are several groups so there can't be just one. And the lowest number needed for a group is 4. So the minimum amount of people to participate would have to be 8.
what is the area of this circle
Answer:
4,500
Step-by-step explanation:
Can someone help me with this? please and thanks <3
Answer:
80.56%
Step-by-step explanation:
So to solve we have the new value over the original value. the new value being the day the 29 workers showed up, and the original value is the full labor force there, so 36.
we get the equation 29/36 which gives us 80.56%
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