Answer:
Step-by-step explanation:
(xm , ym ) = x1 + x2 / 2 and y1 + y2 / 2
= 9 +3 / 2 = 10 -10 / 2
= 12/2 = 0/2
= 6 = 0
So midpoints are (6 , 0)
Answer:
midpoint = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Step-by-step explanation:
To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.
• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]
= [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]
= [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]
= [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = x^2 - 12, and CE = 4x What is AC?
The length of the AC is x^2 + 4x - 12.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given :
In Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
AE = x^2 - 12,
CE = 4x
We know that the diagonal of a parallelogram bisect each other.
x^2 - 12 = 4x
x^2 - 4x - 12= 0
(x-6)(x-2) = 0
Hence, the value of x = 6, 2.
AC = AE + CE = x^2 + 4x - 12.
The length of the AC is x^2 + 4x - 12.
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can someone find the value of x?
Answer:
[tex]\boxed{\sf x=12}[/tex]
Step-by-step explanation:
By applying Similar Triangles Theorem:-
[tex]\sf \cfrac{x}{6} =\cfrac{6}{3}[/tex]
We'll multiply both sides of the equation by 6, the LCM of 6,3.
[tex]\sf x=2 \times 6[/tex]
[tex]\sf x=12[/tex]
solve for x -
[tex]\bold{x {}^{2} + 5x + 6 = 0}\\\\[/tex]
ty! ~
The solution of the given quadratic equation is x=-2 or x=-3.
The given quadratic equation is x²+5x+6=0.
What are different methods to solve a quadratic equation?The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.
By using the splitting middle term method we can solve x²+5x+6=0.
That is, x²+2x+3x+6=0
⇒x(x+2)+3(x+2)=0
⇒(x+2)(x+3)=0
⇒(x+2)=0, (x+3)=0
⇒x=-2 or x=-3.
Therefore, the solution of the given quadratic equation is x=-2 or x=-3.
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an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude
Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:
A(t) = 30000 - 1000t.H(t) = 500t.They will be equal when:
A(t) = H(t).
Hence:
30000 - 1000t = 500t
1500t = 30000
t = 30000/1500
t = 20 minutes.
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Another day, another math problem
Answer:
4x+2h+5
Step-by-step explanation:
[tex]\frac{(2(x+h)^{2}+5(x+h)) - (2x^{2} +5x) }{h} \\[/tex]
For now I'm just going to ignore the denominator for simplicity
[tex](2(x^{2}+2xh+h^{2})+5x+5h) - (2x^{2} +5x)\\(2x^{2}+4xh+2h^{2}+5x+5h) - (2x^{2} +5x)\\(4xh+2h^{2}+5h)\\\\\frac{(4xh+2h^{2}+5h)}{h}\\ 4x+2h+5[/tex]
Final step just distributes the division
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 10 or 11? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
P(Event) = N(Favorable Outcomes) / N (Total Outcomes)
P(sum of 10 or 11) = 5/36
Step-by-step explanation:
Probability states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.
The higher or lessen the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.
So,
P(Event) = N(Favorable Outcomes) / N (Total Outcomes)
Sample Space:
All the possible outcomes of an event are called Sample spaces.
Examples-
• If two dice are rolled together then total outcomes will be 36 and
Sample space will be
[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]
Probability of rolling a sum of 10 or 11 with two dice:
When two dice are rolled together then total outcomes are 36 and
Sample space is
[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]
So, pairs with sum 10 or 11 are (4, 6) (5, 5) (6, 4) (5,6) (6,5) i.e. total 5 pairs
Total outcomes = 36
Favorable outcomes = 5
Probability of getting the sum of 10 or 11 = Favorable outcomes / Total outcomes
= 5 / 36
So, P(sum of 10 or 11) = 5/36
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g(x)=f(x)-3 which statement best describes the graph of g(x) with the graph of f(x)
Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.
what is the missing pattern 7, 11, 2, 18, -7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
What is the missing element in a sequence?
A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:
[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex] (1)
Now we prove that given expression contains the pattern:
n = 0
7
n = 1
7 + (- 1)² · 2² = 7 + 4 = 11
n = 2
7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2
n = 3
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18
n = 4
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
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What is 1/3 of 26 2/3. Please help me
Answer:
8.888(8)
Step-by-step explanation:
(26 +2/3)/ 1/3 =8.8888888889
PLEASE HELP ASAP I WILL GIVE BRAINLYEST!!!
Answer:
Step-by-step explanation:
the numerator goes in side of the radical
my sis needs help asap
Answer:
3/4 - 5/12
Step-by-step explanation:
first you make the demoninators the same so 3*4=12
and if you *3 you do it to the numerator
so its 9/12-5/12
the unsimplified fraction is 4/12
if wanted simplified version its 1/3
[tex]\frac{3}{4}-\frac{5}{12}\\[/tex]
First make the denominators equal so you can easily add the numerators
Common Factor of 4 and 12: 12
So multiply [tex]\frac{3}{4}[/tex] with 3 for both numerator and denominator (4*3=12, to make denominator equal)
[tex]\frac{9}{12} - \frac{5}{12} =\frac{4}{12}[/tex]
Simplify further
[tex]\frac{4}{12} =\frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] is the answer
Hope it helps!
Will mark brainliest if you can help!
Answer:
ln(20) = 2.9957
Here given:
ln(4) = 1.3863
ln(5) = 1.6094
Evaluating with that:
[tex]\rm \Rightarrow ln\left(20\right)=ln\left(5\right)+ln\left(4\right)\\[/tex]
[tex]\rm \Rightarrow ln\left(20\right)=1.3863 \ + \ 1.6094[/tex]
[tex]\rm \Rightarrow ln\left(20\right)=2.9957[/tex]
3. Omar chooses a marble at random from the bag shown below. Without putting
the first marble back, he chooses another marble.
What is the probability that Omar chooses two blue
marbles? Express your answer as a fraction in lowest terms.
Answer:
Theres no bag we cant solve it without you showing a picture or describing it
Step-by-step explanation:
Two forces, F1 and F2, are acting on a body, as shown in the figure. The resultant force, R, is
newtons.
Answer:
R ,is the Resultant of two forces,
∠ACB +50°=180°
∠ACB=180° -50°
∠ACB=130°
→Cos(130°)=Cos (180°-50°)= -cos 50°= -0.6427
Magnitude of resultant force =70.70 Newtons(Approx)
the height of a toy rocket
How many units were started into production in a period if there were zero units of beginning work in process inventory, 4,714 units in ending work in process inventory, and 20,661 completed and transferred out units?
The number of the units were started into production in a period will be 25,375.
What is inventory?A industry's fully prepared kinds of goods, as well as the primary materials needed to make them, are considered to as inventory.
If there were zero units of beginning work in process inventory, 4,714 units of ending work in process inventory, and 20,661 completed and transferred out units.
Completed and transferred out = 20,661
Ending Inventory = 4,714
Units accounted for = 25,375
Beginning Inventory = 0
Units started into production = [Units accounted for – Beginning work in progress Inventory] = 25,375
Units accounted for = 25,375
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A person buys a used car with a down payment of $1,200 and makes monthly payments of $275 for 3 years.What is the total amount of the person pays for the car?PLEASE EXPLAIN
A.$2,025
B.$9,900
C.11,100
D.13,500
Answer:
2025 $
Step-by-step explanation:
275 multiply 3 +1200
Answer:
A.$2,025
Step-by-step explanation:
$275 x 3 years + $1,200
= $2,025
Please answer this question!! <3 <4 <5 <6 <9
The correct answer is option C which is the angle LMO is 50°
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Given that:-
∠O = 70°
∠L = 60°
∠LMO =?
As we know that the sum of the three angles are 180 degree applying this relation:-
∠LOM + ∠OLM + ∠LMO = 180
70 + 60 + ∠LMO = 180
∠LMO = 180 - 70 - 60 = 50
Therefore the correct answer is option C which is the angle LMO is 50°
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Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. u2+65u
Answer:
(u + [tex]\frac{65}{2}[/tex] )²
Step-by-step explanation:
u² + 65u
to complete the square
add ( half the coefficient of the u- term )²
= u² + 2([tex]\frac{65}{2}[/tex] )u + [tex]\frac{4225}{4}[/tex]
= (u + [tex]\frac{65}{2}[/tex] )²
How much acetic acid is in a 5 - liter container of acetic acid and water that is marked 80% acetic acid ? How much is water ?
Which of the following is the given function's
average rate of change on the interval
Sx≤1?
Answer: 2
Step-by-step explanation:
[tex]g(-2)=-2\\\\g(1)=4\\\\\frac{g(-2)-g(1)}{-2-1}=\frac{-2-4}{-3}=\boxed{2}[/tex]
What is the slope-intercept equation for the line below?
10
(0, 2)
(5, 4)
Answer:slope is 0.4
Step-by-step explanation:
y2-y1 divided by x2-x1
2-4/0-5=0.4
Please help my question is in the attachment!
Answer:
a = -9
b = -3
c = 11
d = 19
Step-by-step explanation:
a. x = -2
y= x² + 3x + 1
y= -2²+ 3(-2)+1
y= -4-6+1
y = -9
b. x= -1
y= x² + 3x+ 1
y= -1² + 3(-1) +1
y= -1 -3 + 1
y = -3
c. x =2
y = x² + 3x +1
y= 2²+ 3(2) +1
y= 4 +6 +1
y = 11
d. x= 3
y = x² +3x +1
y = 3² +3(3) +1
y= 9 +9 +1
y = 19
twice a number increased by 8 is 20. find the number
Answer:
Answer is 6
Step-by-step explanation:
Let the number be ×
Twice a number is 2×
Twice a number increase by 8 is 2×+8
hence the equivalent will be
2×+8=20
2×=12
×6
Answer:
6
Step-by-step explanation:
Let n be the unknown number.
"Twice a number" means to multiply the number by 2:
⇒ 2n
"Increase by 8" means to add 8:
⇒ 2n + 8
"Is 20" means equals 20:
⇒ 2n + 8 = 20
Therefore, the equation is: 2n + 8 = 20
To solve, subtract 8 from both sides:
⇒ 2n + 8 - 8 = 20 - 8
⇒ 2n = 12
Divide both sides by 2:
⇒ 2n ÷ 2 = 12 ÷ 2
⇒ n = 6
Therefore, the unknown number is 6.
2/5x - 1/2 = 1/3 + 5/6x
Answer:
[tex]x = \frac{25}{13} [/tex]
Step-by-step explanation:
Given:
[tex] \frac{2}{5} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x[/tex]
Combine like terms:
[tex] \frac{2}{5} x - \frac{5}{6} x = \frac{1}{3} + \frac{1}{2} [/tex]
Find GCF :
[tex] \frac{12}{30} x - \frac{25}{30} = \frac{2}{6} + \frac{3}{6} [/tex]
Subtraction and Addition :
[tex] \frac{13}{30} x = \frac{5}{6} [/tex]
Divide both sides by 13/30 :
[tex] \frac{ \frac{13}{30} }{ \frac{13}{30} } x = \frac{ \frac{5}{6} }{ \frac{13}{30} } [/tex]
Simplify :
Multiplication (Reciprocal) :
[tex]x = \frac{5}{6} \times \frac{30}{13} [/tex]
[tex]x = \frac{150}{78} [/tex]
[tex]x = \frac{25}{13} [/tex]
Answer :
[tex]x = \frac{25}{13} [/tex]
Hope it helps
Ryan also found that he could model the height of his plant with the equation h = 0.5d + 4, where d is the number of days and h is the height in centimeters. part b question 2
The domain is {0, 1, 2, 3, 4, 5, 6} and range is {4, 4.5, 5, 5.5, 6, 6.5, 7}.
What is Domain and Range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
The complete question is
Ryan also found that he could model the height of his plan with the equation H = 0.5D + 4 where D is the number of days and H is the height in centimeters. Determine the domain and the range for this relationship.
Given:
h = 0.5d + 4
The Domain of the function is: {0, 1, 2, 3, 4, 5, 6}
and the Range is: {4, 4.5, 5, 5.5, 6, 6.5, 7}
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If 80% of a number is 288 and 95% of the same number is 342, find 15% of that
number.
Answer:54
Step-by-step explanation:
There are quicker ways to solve this but a simple and easy way to do this would be by dividing your number by the percent so 288/80 and with this, you would get your number for 1 percent or 3.6. Now you can multiply that number by the percent your need to find so 15. And 15 x 3.6 is = 54.
P, Q and R are points in the same
horizontal plane. The bearing of
Q from P is 150° and the bearing
of R from Q is 060°.
If |PQ| = 5m and QR = 3m,
Find the bearing of R from P.
correct to the nearest degree./
Answer: 119°
Step-by-step explanation:
From the positive y-axis, all angles are measured clockwise
PR = PQ + QR = 5[150°] + 3[60°]
X = 5*sin150 + 3*sin60 = 5.1
Y = 5*Cos150 + 3*Cos60 = -2.83
TanA = X/Y
A = -61° = 61° East of South = 119° Clockwise
Therefore, the bearing of R from P is 119°
Question 7 of 10
Classify the following triangle. Check all that apply.
Answer:
A,C,E
(if you find a better answer choose that.)
Step-by-step explanation:
This one has two acute angles and one obtuse.
This one is a scalene.
So, tick A,C,E
Work out (4 x 3)² ÷ 6
An expression is defined as a set of numbers, variables, and mathematical operations. The solution of (4 x 3)² ÷ 6 is 24.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The solution of the expression (4 x 3)² ÷ 6 is,
(4 x 3)² ÷ 6
= (12)² ÷ 6
= 144 ÷ 6
= 24
Hence, the solution of (4 x 3)² ÷ 6 is 24.
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