Yes, the square of any number like X² is always positive.
Define the term positive numbers?Positive numbers are those above zero or to the right of zero on the number line. Be aware that positive numbers can be either integers or fractions, irrational numbers, or both. For instance, the square root of 2 has an infinite number of non-repeating digits.A number can be multiplied by itself to find its square.Example:
The result of two negative numbers is always positive, as explained.When two negative numbers are added together, the result is always positive.If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².
Here, x² > 0.
Hence, the square of any number like X² is always positive.
To know more about the positive numbers, here
https://brainly.com/question/29711621
#SPJ4
Simplify 4/9 + 1/3
A 5/12
B 7/9
C 1 1/9
D 15/9
Answer:
B) 7/9
Step-by-step explanation:
Fraction addition: If the denominators are not same, find the LCM of the denominators.LCM of 3 and 9 is 9.
Now, find equivalent fractions with denominator as 9.[tex]\sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\[/tex]
[tex]\sf =\dfrac{3}{9}[/tex]
Now add.[tex]\sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\[/tex]
[tex]\sf =\dfrac{7}{9}[/tex]
What is the solution to this system of equations x-2 y=15 2x+4y=-18
Answer:
(3, - 6 )
Step-by-step explanation:
x - 2y = 15 ( add 2y to both sides )
x = 2y + 15 → (1)
2x + 4y = - 18 → (2)
substitute x = 2y + 15 into (2)
2(2y + 15) + 4y = - 18 ← distribute parenthesis and simplify left side
4y + 30 + 4y = - 18
8y + 30 = - 18 ( subtract 30 from both sides )
8y = - 48 ( divide both sides by 8 )
y = - 6
substitute y = - 6 into (1)
x = 2(- 6) + 15 = - 12 + 15 = 3
solution is (3, - 6 )
Answer:
x is 3 y is -6 I really hope this helps
If A and B are independent events and P(A)=0.25 and P(B)=0.333, what is the probability P(ANB)?
a) 1.33200
b) 0.75075
c) 0.08325
d) -0.0830
The probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.
For any two events A and B, the probability of event A and B, that is, P(A ∩ B) is given as:-
When the events are dependent, P(A ∩ B) = P(A).P(B|A).When the events are independent, P(A ∩ B) = P(A).P(B).In the question, we asked the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333.
We know that when the events are independent, P(A ∩ B) = P(A).P(B).
Thus, P(A ∩ B) = (0.25)*(0.333),
or, P(A ∩ B) = 0.08325.
Thus, the probability P(ANB), that is, P(A ∩ B), given that A and B are independent events and P(A) = 0.25 and P(B) = 0.333 is 0.08325. Hence, option C is the right choice.
Learn more about the probability of independent events at
https://brainly.com/question/12783373
#SPJ4
B.) what fraction of the cost is spent on food and entertainment? food- 17% entertainment- 24% they have 3000 dollars
The quantity spent on amusement = 720
quantity spent on food = 510
they have got 3000 for vacation.
amount spent on food = 17% of 3000
⇒ 17/one hundred*3000
17*30= 510
amount spent on amusement = 24% of 3000
⇒ 24/100*3000
24*30= 720
A person would possibly account for a terrible temper or general rude conduct by explaining that bad site visitors affected the morning travel, for example. someone who is exceeded over for a promotion would possibly rationalize the frustration by means of claiming to not have desired so much responsibility in the end.
To carry into accord with cause or reason something to appear reasonable especially: to characteristic (one's actions) to rational and creditable motives without evaluation of proper and especially unconscious motives he attempted to rationalize his merciless behavior. intransitive verb.
Ego protection wherein apparently logical motives are given to justify unacceptable behavior that is influenced by subconscious instinctual impulses. In the psychoanalytic concept, such conduct is considered to be a defense mechanism.
Learn more about rationalization here https://brainly.com/question/14261303
#SPJ4
Gavin has nickles, dimes, and quarters in the ratio of 1:3:6 if 57 of Gavin's coins are dimes how many nickels and quarters does Gavin have?
Answer:
Gavin has 19 nickels & 114 quarters
Step-by-step explanation:
N : D : Q
1 : 3 : 6 = 57
x : 57 : y
57 / 3 = 19
1 x 19 : 3 x 19 : 6 x 19
19 : 57 : 114
On a piece of paper, graph y ≤ -2x. Then determine which answer matches
the graph you drew.
Answer: Graph provided below.
Step-by-step explanation:
Draw the graph of y = -2x and then shade the region below it because y is less than and equal to -2x. To draw the graph of y = -2x, plug in x values into the equation and plot the corresponding coordinates. See this video on how to graph linear equations:
https://www.khanacademy.org/math/in-in-grade-9-ncert/xfd53e0255cd302f8:linear-equations-in-two-variables/xfd53e0255cd302f8:graph-of-a-linear-equation-in-two-variables/v/graphs-of-linear-equations
Based on the estimated cost of college from step 1, determine how you are going to pay for college. You will need to do some research to learn about the various methods used to pay for college costs.
Complete the table below to document your financial needs.
Source Estimated Need
grants
loans
scholarships
work-study
other
This is a budgeting exercise. Based on the estimated cost of college which was set at $58,000, the following steps indicate how I intend to pay for college:
Scholarship - 70% = $40,600Work Study - 17.2% = $10,000Loan - 12.76% = $7, 400$58,000
What is budgeting?Budgeting is simply the process of outlining the total expense requirements of an individual person or a corporate entity and how those expenses will be satisfied and efficiently allocated.
From the above, the total sum of $58,000 will be satisfied from three sources:
ScholarshipsWork-Study; andLoan.Learn more about budgeting at;
https://brainly.com/question/24940564
#SPJ1
Which
expression is equivalent to
(x^6y^8)^3/x^2y^2
Answer: [tex]x^{16}y^{22}[/tex]
Step-by-step explanation:
[tex]\frac{(x^6 y^8)^3}{x^2 y^2}=\frac{x^{18}y^{24}}{x^2 y^2}=x^{16}y^{22}[/tex]
If RT = 90, find the length of RO. (SU = 25)(SO is perpendicular to RT)
In the given figure of circle, if RT = 90, SU = 25, and SO is perpendicular to RT, the length of the radius RO is 53.
In the given figure,
RT = 90
SU = 25
SO is perpendicular to RT.
Here, SO and RO are the radii of the circle and RT is a chord.
The length of the chord, RT is given as,
RT = 2 √(r² - d²)
Here, r is the radius and d is the distance of the chord RT from the center O.
Radius, r = RO and distance, d = OU
∴ RT = 2 √(RO² - OU²)
Substituting RT = 90 in the above equation, we get,
90 = 2 √[(RO)² - (OU)²]
√[RO)² - (OU)²] = 45
(RO)² - (OU)² = 45²
(RO)² - (OU)² = 2025 ........... (1)
Now, OU = SO - SU [From the figure]
⇒ OU = SO - 25
Substituting OU = SO - 25 in equation (1), we obtain,
(RO)² - (SO - 25)² = 2025
(RO)²- [(SO)² + (25)² - 2(SO)(25)] = 2025 [ ∵ (a-b)² = a²+b²-2ab ]
(RO)²- (SO)² - (25)² + 50(SO) = 2025 ........... (2)
Since, RO and SO both are the radii of the same circle, we have,
SO = RO
Thus, we can write equation (2), as follows,
⇒ (RO)² - (RO)² - (25)² + 50(RO) = 2025
⇒ -625 + 50RO = 2025
⇒ 50RO = 2025 + 625
⇒ RO = 2650/50
⇒ RO = 53
Hence, the length of the radius RO of the given circle is 53.
Learn more about a circle here:
https://brainly.com/question/11833983
#SPJ1
Use cylindrical coordinates to find the volume of the region in the first octant bounded by the cylinder r and the plane z.
The volume of the region in first octant is 9.
Given that the region in the first octant bounded by the cylinder r=3 and the plane z=y.
The graph is shown below.
we are given that first octant is bound by r=3 and z=y
We will use the conversion formula, i.e.
x²+y²=r² where x=rcos∅ and y=rsin∅
Firstly, we will find bound octant
0≤∅≤π/2
0≤r≤3
0≤z≤r sin∅
Now, we can set up integral
[tex]V=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}\int_{0}^{rsin(\theta)}rdzdrd\theta[/tex]
Further, we can solve it.
Firstly, we solve integral for z then we solve for r and after that we will solve for ∅, we get
[tex]\begin{aligned}V&=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}r^2 \sin (\theta)dr d\theta\\&=\int_{0}^{\frac{\pi}{2}}\frac{1}{3}r^3\sin \theta d\theta\left|_{0}^{3}\\ &=\int_{0}^{\frac{\pi}{2}}\left(\frac{1}{3}\sin\theta d\theta(27-0)\right)\\ &=\int_{0}^{\frac{\pi}{2}}9\sin \theta d\theta\\ &=0-(-9)\\ &=9\end[/tex]
Hence, the volume of the region in the first octant is bounded by the cylinder r=3 and the plane z=y is 9.
Learn more about volume from here brainly.com/question/4036200
#SPJ4
Someone help me out on these 2 geometry questions, ASAP!!!
“Complete the proofs”
Question 11
1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)
2) [tex]\angle A \cong \angle A[/tex] (reflexive property)
3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)
4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)
Question 12
1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)
2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)
3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)
4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)
5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)
6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)
7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)
Note: I changed the names of the segments in Question 11 because of the word filter.
id love some help!!!
Answer:
Circle:circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
[tex] \sf{formula \: to \: find \: the \: area \: is}[/tex][tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]
[tex] \sf{formula \: to \: find \: perimeter \: of \: circle \: is}[/tex][tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]
Continue to Question.If the radius is 2 inches and
Use 3,14 for π So:
[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]
[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]
[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]
So, The Area of circle is 12.56inches²Geometric series
2 + 6 + 18 + 54 + ... , find tn
The function that gives the value of tn for the geometric series is presented as follows;
[tex]t_n = 2 \times 3^{(n - 1)} [/tex]
How can the expression that represents the geometric series be found?
The given geometric series is presented as follows;
2 + 6 + 18 + 54 +...
From the above series, we have;
First term, a = 2Common ratio, r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3The nth term of the geometric series is therefore;
[tex]t_n = a \cdot r^{(n - 1)} [/tex]
Which gives;
[tex]t_n = 2 \times 3^{(n - 1)} [/tex]
Where, tn is the nth term
Learn more about geometric series here:
https://brainly.com/question/2289626
#SPJ1
WILL MAKE BRAINLIEST
5. If m2ABC= 180°, is the angle right, straight, obtuse, or acute?
obtuse
acute
straight
right
please help!
A) A top-class tennis player can serve the ball, of mass 57 g, at an initial horizontal speed of 50 m/s. The ball remains in contact with the racket for 0.05 s. Calculate the average force exerted on the ball during the serve.
B) A motor car of mass 3000 kg moving with 72 km h-1 made to reduce its speed to 18 km h^-1, in 40 s, by applying brakes. Find the resistive force.
The average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.
Forcea. Average force
Using this formula
Force (F) = Mass ×Acceleration
Where:
Mass (m) = 57 g = 57 / 1000= 0.057 Kg
Acceleration (a) = u / t = 50 / 0.05 = 1000 m/s²
Let plug in the formula
Force (F) = 0.057 × 1000
Force (F) = 57 N
b. Resistive force
F = m(v – u) / t
Where:
Force (F) = ?
Mass (m) = 3000 Kg
Initial velocity (u) = 72 Km/h = 72 / 3.6 = 20 m/s
Final velocity (v) = 18 Km/h = 18 / 3.6 = 5 m/s
Time (t) = 40s
Let plug in the formula
Force = 3000(5 – 20) / 40
Force = 3000(-15) / 40
Force=-45,000/40
Force = -1125 N
Therefore the average force exerted on the ball during the serve is 57 N the resistive force is -1125 N.
Learn more about Force here:https://brainly.com/question/25239010
#SPJ1
Please help
The area of a circle is 354 cm². Find in degrees and minutes, the angle subtended at the centre of the circle by a 2.9cm arc.
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
What is the measure of the central angle of a circular section?
In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:
r = √ (A / π) (1)
r = √ (354 / π)
r ≈ 10.615 cm
Then, the measure of the central angle in radians is found by the equation of circular arc:
θ = s/r
θ = 2.9 cm / 10.615 cm
θ = 0.273 radians
Finally, we convert the angle into DMS system:
θ = 0.273 rad × 180°/π
θ = 15.641°
Degrees: 15°
Minutes and seconds: 0.641° (38.46')
Minutes: 38'
Seconds: (0.46' = 27.6'')
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
To learn more on subtended angles: https://brainly.com/question/17158173
#SPJ1
1/5n+3/5n=7/9
Can you help?
The value of n in 1/5n+3/5n=7/9 is 35/36
How to solve the equation?The equation is given as:
1/5n+3/5n=7/9
Multiply through by 5
n + 3n = 35/9
Evaluate the sum
4n = 35/9
Divide both sides by 4
n = 35/36
Hence, the value of n in 1/5n+3/5n=7/9 is 35/36
Read more about equations at:
https://brainly.com/question/723406
#SPJ1
1/5n+3/5n=7/9
Can you help?
The value of n from the given expression is 35/36
Solving linear equationGiven the equation below expressed as:
1/5n+3/5n=7/9
Find the LCM
(n+3n)/5 = 7/9
4n/5 = 7/9
Cross multiply
4n * 9 = 5* 7
36n = 35
n = 35/36
Hence the value of n from the given expression is 35/36
Learn more on equation here; https://brainly.com/question/2972832
#SPJ1
Transformation example
Answer:
Rotation, Reflection, Dilation.
Step-by-step explanation:
Georgie buys a pack of chocolate which has 18 small chocolate bars. She ate three bars in the morning, Later in the
day, Georgie's brother ate three fifth of the chocolates bar that were left, what fraction of the chocolate bars is left in
the packet?
PLRASE HELPPP PLS IM STUCK
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
5th grade algebra. Pls help with these am offering brainliest + bonus points! :D
Answer:
3. 6 5. 3
Step-by-step explanation:
PEMDAS
3. 0.5 x (24) / 3 + 2
12/3 +2
4 + 2
6
5. (4 + 6/3) x 0.5
(4 + 2) x 0.5
6 x 0.5
3
Answer: number 3. is 6 and number 5. is 3
hope it helped
The sum of all but one interior angle of a heptagon is 776°. What is the measure of the final interior angle? 42º 56º 124º 304º
The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)
What is the measure of the missing interior angle in a heptagon?
Heptagons are polygons with seven sides, seven vertices, seven interior angles and seven central angles. Herein we know the value of the sum of six interior angles and we need to know the measure of the seventh interior angle. We can determine the measure of the seven interior angles by using the following expression:
θ = (n - 2) · 180°, where n is the number of sides of the polygon. (1)
If we know that n = 7, then sum of the internal angles in the heptagon is:
θ = (7 - 2) · 180°
θ = 900°
And the measure of the final interior angle is found by subtraction:
θ₇ = 900° - 776°
θ₇ = 124°
The measure of the seventh interior angle of the heptagon is 124°. (Correct choice: C)
To learn more on polygons: https://brainly.com/question/17756657
#SPJ1
Area=
Help me please thanks so much :)
Answer:
48π
Step-by-step explanation:
To find the area of the shaded region, find the area of the large circle and the small circle then subtract.
Large circle:
8²π=64π
Small circle:
4²π=16π
Now subtract 16 from 64.
64-16=48
The area of the shaded region is 48π.
Hope this helps!
Find the vertex and axis of symmetry
Answer:
Below in bold.
Step-by-step explanation:
f(x) = 2x^2 - 12x + 24
Convert to vertex form:
f(x) = 2(x^2 - 6x) + 24
= 2[(x - 3)^2 - 9] + 24
= 2(x - 3)^2 - 18 + 24
= 2(x - 3)^2 + 6
So the vertex is at (3, 6) and the axis of symmetry is x = 3.
Solve:
-5/2 a + 5 = 25
a =
Answer:
A = -8
You're welcome! :)
Answer: a = -8
Step-by-step explanation:
Combine multiplied terms into a single fraction
then find a Find common denominator for the fraction
then Combine fractions with common denominator,
Multiply the numbers, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator,
Multiply the numbers making your equation like this -5a+10=50
subtract 10 by both sides and then you will need to simplify making it
-5a + 40 then you divide them both by the same factor which is -5 then you simplify again making the answer to your question -8
Figure TUVS is a parallelogram.
Parallelogram T U V S is shown. Angle U is (4 x + 9) degrees and angle V is (6 x minus 29) degrees.
Which angles equal 91°?
angles T and V
angles S and U
angles U and V
angles S and T
Angles T and V of the parallelogram are equal to 91°.
Calculating the Value of x
In the parallelogram TUVS, adjacent angles U and V are given as,
U = 4x+9
V = 6x-29
Since U and V are adjacent angles, and as per the properties of a parallelogram, sum of adjacent angles is equal to 180°.
4x+9 + 6x-29 = 180
10x - 20 =180
10x = 200
x = 20
Calculating the Angles of the Parallelogram
∠U = 4x + 9
∠U = 4(20) + 9
∠U = 80 + 9
∠U = 89°
∠V = 6x - 29
∠V = 6(20) - 29
∠V = 120 - 29
∠V = 91°
According to the properties of a parallelogram, opposite angles are of equal measure.
∴ ∠T = ∠V and ∠S = ∠U
⇒ ∠T = 91° and ∠S = 89°
Learn more about a parallelogram here:
https://brainly.com/question/1563728
#SPJ1
Answer:
angles t and v
Step-by-step explanation:
edge
Find the missing side length of the triangle.
SOLUTION :
c² = 5² + 5²
c² = 25 + 25
c² = 50
c = √50 ft
________________________________
HOPE IT HELPS
join
_____________
518 231 1565
33bi8R
_____________
*Big Boy*
ヮ00m ✧
How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
Learn more about Sequences on:
https://brainly.com/question/12246947
#SPJ4
What is the coordinate point of the linear function 5x+3y=15
Answer: Y-intercept: (0,5) X-intercept: (3,0)
Step-by-step explanation: Set x and y equal to 0.