[tex]\left( \dfrac 49 \right) \div \left( \dfrac{18} 3 \right)\\\\\\=\dfrac 49 \div6\\\\\\=\dfrac 49 \times \dfrac 16\\\\\\=\dfrac{2}{9\times 3}\\\\\\=\dfrac{2}{27}[/tex]
Factor 27a^{3}b^{9} + 8c^{18}.Which of the following is one of the factors
Answer:
Second option is the correct answer
[tex]\bigodot (9a^2b^6-6ab^3c^6+4c^{12})[/tex]
Step-by-step explanation:
[tex]27a^{3}b^{9} + 8c^{18}[/tex][tex]=(3ab^{3} )^3+ (2c^{6})^3[/tex][tex]=(3ab^{3} +2c^{6})[(3ab^3)^2-(3ab^3)(2c^6)+(2c^6)^2][/tex][tex]=(3ab^{3} +2c^{6})\orange{\bold{(9a^2b^6-6ab^3c^6+4c^{12})}}[/tex]Which of the following transformations will result in an image that maps onto itself?
A. rotate 180 degrees counterclockwise and then reflect across the y-axis
B. reflect across the y-axis and then reflect again across the y-axis
C. rotate 90 degrees counterclockwise and then rotate 270 clockwise
D. reflect across the y-axis and then reflect across the x-axis
If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.
What are the rules of Transformations ?The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)
The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)
The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)
The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)
Therefore on application of these rules
For Case A
The point will be (-y , x)
For Case B
The point will be (x,y)
Therefore Option B is the answer.
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Pls Help :(((
If a^x=b^y=c^z is a system of exponential expression where b^2=ac
Prove that 1/x + 1/z = 2/y
[tex]\text{Let,}\\\\~~~~~~~a^x =b^y = c^z = k\\\\\text{So,}\\ \\a = k^{\dfrac 1x}\\\\b=k^{\tfrac 1y}\\\\\ c = k^{\tfrac1z}\\\\\text{Now, given that,}\\\\~~~~~~~~~b^2 = ac\\\\\implies \left( k^\tfrac 1y \right)^2 = k^{\tfrac 1x} \cdot k^{\tfrac 1z}\\\\\implies k^{\tfrac 2y} = k^{\tfrac 1x + \tfrac 1z} ~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies \dfrac 2y = \dfrac 1x + \dfrac 1z\\\\\implies \dfrac 1x + \dfrac 1z = \dfrac 2y \\\\\text{Proved.}[/tex]
Which statement about the angles in the figure is true?
m/3+m/5= 180°
m/7+m/10 = 180°
m/8+m/9 = 90°
m/1+m/8= 90°
The true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°
Determining the measures of anglesFrom the question, we are to determine the statement that is true about the angles in the given figure
In the given diagram, we can observe that
m∠3 + m∠8 + m∠9 + m∠10 = 180° (Sum of angles in a triangle)
Also,
m∠3 = m∠1 (Vertically opposite angles)
m∠9 + m∠10 = 90° (Vertically opposite angles)
∴ m∠1 + m∠8 + 90° = 180°
m∠1 + m∠8 = 90°
Hence, the true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°
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What is the solution for x in the equation?
x-3/7=2x-25/7
Step-by-step explanation:
please mark me as brainlest
Answer: x = 4/3
Step-by-step explanation: I just answered the answer
Need help with math asap
[tex]~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan \theta = \dfrac{LN}{LM}\\\\\\\implies \theta = \tan^{-1} \left( \dfrac{LN}{LM} \right)\\\\\\\implies \theta = \tan^{-1} \left(\dfrac{12.81}{7.72} \right)\\\\\\\implies \theta =58.92^{\circ}[/tex]
Guys help me with a) and b) tasks
ANSWER:
a) 40
b) 25
Thanks<3
Step-by-step explanation:
there are 2 similar triangles : ABE and DCE
that means they have the same angles, and the scaling factor from one triangle to the other is the same for every side.
and that means that
DE/AE = EC/BE (= DC/AB)
we know that
AE = AD + DE
BE = BC + EC
a.
so, we have actually
DE/(AD+DE) = EC/(BC+EC)
DE/(10+DE) = 8/(2+8) = 8/10 = 4/5
DE = 4(10+DE)/5
5DE = 4(10+DE) = 40 + 4DE
DE = 40 cm
b.
AD/DE = 3/5
BC/EC must be 3/5 too.
15/EC = 3/5
15 = 3EC/5
75 = 3EC
EC = 25 cm
Please help me with this
Answer:
42
Step-by-step explanation:
6 times 7 is 42
Which answer shows 0.00897 written in scientific notation?
0.897 times 10 Superscript negative 2
8.97 times 10 Superscript negative 3
8.97 times 10 Superscript negative 2
8.97 times 10 Superscript 3
Answer:
8.97 × 10-3
Step-by-step explanation:
you move the decimal so its a number between 1 and less than 10 so we moved the decimal three spaces.
Answer:
its B
Step-by-step explanation:
Find the values of x and y in the parallelogram.
The one-to-one functions g and h are defined as follows.
g = {(-4, 0), (-1, 1), (0, -5), (3,-1)}
h(x) = 2x-13
If 8n = 128, n equals:
Answer:
8n is the same as 8 times a number.
That means...
Continuation:
[tex]8 * n = 128[/tex]
[tex]128 \div 8 = n[/tex]
[tex]128 \div 8 = 16[/tex]
Therefore, n is 16.
A certain population of bacteria has an initial population of 225. the bacteria triples every hour. determine the multiplier that would allow you to predict the population of bacteria after 2 hours.
Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the growth rate.In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:
[tex]y = a(3)^x[/tex]
Hence, after 2 hours:
[tex]y = a(3)^2 = 9a[/tex]
Which means that the multiplier is of 9.
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what is the value of u ?
Step-by-step explanation:
you do know that the sum of all angles in a triangle is always 180° ?
so,
3u + 6u - 18 + u + 18 = 180
10u = 180
u = 18
The measures of the angles of △ABC are given by the expressions in the table.
Angle Measure
A 48°
B (6x−28)°
C (2x)°
Find the value of x. Then find the measures of angles B and C.
Enter your answers in the boxes.
x =
m∠B=
º
m∠C=
º
Answer:
x = 20 ∠B = 92° ∠C = 40°
Step-by-step explanation:
The sum of angles of a triangle is 180°.
48 +(6x -28) +2x = 180
8x +20 = 180
8x = 160
x = 20
∠B = (6x -28)° = (6*20 -28)° = 92°
∠C = 2x° = 40°
Answer
X= 20
m<B = 92°
m <C = 40°
Step-by-step explanation:
The sum of angles in a triangle = 180°
So, 48 + 6x-28 +2x = 180
8x+20= 180
8x = 160
So x= 160/8 = 20
Substitute x in the equations:
m<B= 6×20-28= 92°
m<C = 2×20 = 40°
Which pairs of events describe independent events? Select all that apply.
O Rolling a six-sided die and having it land on a 4, and then choosing a blue marble from a jar of marbles.
O Rolling a six-sided die and having it land on a 3,
and then rolling a six-sided die and having it land on a 2.
O Choosing a blue marble from a jar of marbles, not replacing it, and then drawing a red marble.
O Entering a raffle 3 times and winning one prize, and then winning another prize in the same raffle.
O Drawing a 3 from a deck of cards, not replacing it, and then drawing a 4 from the same deck of cards.
When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct options are A and B.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent iff we have:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Comparing it with chain rule will give
[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]
Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).
Two events are known to be independent even if the result of one event does not affect the result of the second event.
Rolling a dice in an independent event and choosing a blue marble is another independent event. The two events are independent and the result of one does not affect the other.
Thus, A is correct.
Rolling a dice in an independent event, and rolling it again won't affect the result of the second roll. Therefore, rolling a dice twice or for n number of times is an independent event.
Thus, B is correct.
Hence, the correct options are A and B.
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Using the net below, find the surface area
of the triangular prism.
3cm
6 cm
9 cm
5 cm
9 cm
4 cm
Surface area= [?] cm²
The surface area of the triangular prism is 153 cm².
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The area of the triangular prism is the sum of the area of the rectangle and the area of the triangle, therefore, the area of the prism will be,
Area = A + B + C
=(9 × 15) + (0.5×6×3) + (0.5×6×3)
= 135 + 9 + 9
= 153 cm²
Hence, the surface area of the triangular prism is 153 cm².
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Answer:
9*5 + 6*9 + 9*4 + 1/2*6*3 + 1/2*6*3
=1872+1/2*6*3+1/2*6*3
=1872+18
=1890cm²
Surface area= 1890cm²
liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.
Answer:
Random sampling
Step-by-step explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.
The perimeter of a rectangle is 50 inches. Its width
measures 11 inches. What is its length?
Let x = the length of the rectangle. Choose the equation that represents this
problem.
A. 2x + 22 = 50
B. 2x + 11 = 50
C. x + 11 = 50
D. 2x11 = 50 * don’t try and be funny I need help bad*
Answer:
50-20 or perimeter-2length
Step-by-step explanation:
15 inches is the width
quadratic equation y= (x+4)^2 -2
I need to know if it’s Max or min
Domain
Range
Increasing interval
Decreasing interval
Whoever the first correct answer belongs to gets a crown :) tysmmm
Answer:
Max or Min: min
Domain: (−∞, ∞)
Range: (−2, ∞)
Increasing interval: (−4, ∞)
Decreasing interval: (−∞, -4)
Step-by-step explanation:
Max or Min: You determined that the curve opens upwards meaning that the vertex is at the min. If it opened down then it would be at the max.
In mathematical terms: if a > 0, the parabola opens upward and the vertex is a minimum. If a < 0, the parabola opens downward, and the vertex is a maximum.
Domain: This is all possible x values, since the parabola is upwards its going to have any possible x values
Range: this is all possible y values. we know that the vertex point (min) doesn't go less than the value of -2 for y but anything above is possible hence -2 is the lowest possible y value and anything beyond above
Increasing interval: The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I.
Decreasing interval: The derivative, then set it equal to 0, and then find between which zero values the function is negative.
visual representation attached as well
Hope it helps :)
If you have any questions or anymore help lmk, happy to help with any school work!!
Have a nice day, you got this !!
math quarterly
8th grade
Answer:
the answer is 49
Step-by-step explanation:
which of the following number lines shows the correct sum of the number above and 4?
Answer:
c.
Step-by-step explanation:
because on you have to add 4 to the number above. so 3+4 equals 7 so you move 4 spaces to the right on the number line to get you 7. so C is the correct answer
How many solutions does the system of equations have?
y=-2x+3
y = x² - 6x +3
Answer:
2 solutions
Step-by-step explanation:
y = - 2x + 3 → (1)
y = x² - 6x + 3 → (2)
substitute y = x² - 6x + 3 into (1)
x² - 6x + 3 = - 2x + 3 ( subtract - 2x + 3 from both sides )
x² - 4x = 0 ← factor out x from each term on the left side
x(x - 4) = 0
equate each factor to zero and solve for x
x = 0
x - 4 = 0 ⇒ x = 4
substitute these values into (1)
x = 0 : y = - 2(0) + 3 = 0 + 3 = 3 ⇒ (0, 3 )
x = 4 : y = - 2(4) + 3 = - 8 + 3 = - 5 ⇒ (4, - 5 )
the 2 solutions are (0, 3 ) and (4, - 5 )
Find CD.
A) 5
B) 28
C) 56
D) 96
Answer:
C) 56
Step-by-step explanation:
. What is the length of BC¯¯?
2. What is the length of AC¯¯?
3. What is the length of AD
1.) Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?
O (-4, 11 1/3)
O (3, -2 1/3)
O (6, -2)
O (12, -14)
2.) Line segment AB has endpoints B (-3, 0) and A(5, 4). What are the coordinates of the point located 1/4 of the way from B to A?
O (1, -1)
O (1, 2)
O (3, 3)
O (-1, 1)
3.) Line segment AB has endpoints A(1, 8) and B(7, -4). What are the coordinates of the point located 1/6 of the way from A to B?
O (0, 8 2/3
O (2, 6)
O (8 2/3, -3 1/3)
O (6, -3 1/3)
^Please help, ASAP. These were due yesterday, however I am trying to get this done.
BRAINLIEST AND 5 STARS TO CORRECT RESPONSES ONLY! LOTS OF PTS AVAILABLE TO THOSE WHO PARTICIPATE HOWEVER.
The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)
How to find the length of Line Segment?1) The coordinates of the point located 5/6 of the way from A to B is;
x = ⁵/₆(7 - 1) + 1
x = 6
y = ⁵/₆(-4 - 8) + 8
y = -2
x, y = (6, -2)
2) The coordinates of the point located ¹/₄ of the way from A to B is;
x = -3 + ¹/₄(5 - (-3))
x = -1
y = 0 + ¹/₄(4 - 0)
y = 1
x, y = (-1, 1)
3) The coordinates of the point located ¹/₆ of the way from A to B is;
x = ¹/₆(7 - 1) + 1
x = 2
y = ¹/₆(-4 - 8) + 8
y = 6
x, y = (2, 6)
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28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2
Quadrilateral RUST has a vertex at R (1,5).
T
S
What are the coordinates of R'after the translation (x, y) → (x+1, y-1),
Answer:
R'(2,4)
Step-by-step explanation:
When doing translations you subtract or add within the coordinates like a normal problem.
If it helps you, write it as seperate equations like:
1-1 and 5-1
Hope that helps ✓
Students working at a refreshment stand mixed cranberry juice at $0.50 per liter and apple juice at $0.35 per liter to make 120 L of a fruit drink worth $0.40 per liter. How many liters of each did they mix?
Answer:
40 L cranberry juice; 80 L apple juice
Step-by-step explanation:
Let x = number of liters of cranberry juice.
The total volume is 120 L, so the volume of apple juice is
120 - x.
The value of the cranberry juice is 0.5x.
The value of the apple juice is 0.35(120 - x).
The value of the mixture is 0.4(120) = 48
The value of the cranberry juice plus the value of the apple juice equals the value of the mixture.
0.5x + 0.35(120 - x) = 48
0.5x + 42 - 0.35x = 48
0.15x = 6
x = 6/0.15
x = 40
120 - x = 120 - 40 = 80
Answer: 40 L cranberry juice; 80 L apple juice
A Circular pie with a diameter of 10” Is cut into six equal pieces. What is the surface area of two slices of pie?
To solve this question, let's find the surface area of the entire pie and then divide it by 6 for each slice.
The area of a circle is pi*r^2. We are given the diameter, so divide that by 2 to get the radius.
Now that you have the area, divide by 6. That is the area of each slice. The problem asks for the area of 2 slices though, so multiply that by 2.
Janine sketched a quick graph. "Looks like the solution is (-30, -91)." Is she right? How do you know? Be
clear and complete.
Answer:
- -=+ we should just add it to make the
please help with all of question 4.
Answer:
Step-by-step explanation:
Combine like terms: Like terms have same variable with same power and to combine the like terms, add/subtract the co efficient of the variables.
Perimeter:Perimeter = sum of all sides
a) Perimeter of ΔABC = AB + BC + CA
= x + 14 + x + 14 + x + 14
= x + x + x + 14 + 14 + 14 {Combine like terms}
= 3x + 42
b) EF = DI - GH
= 2x + 3 - x
= 2x - x + 3
= x + 3
c) FG = HI - ED
= 12 + 2x - (x + 5)
= 12 + 2x - x - 5 {To open the brackets, (-1) is distributed to x and 5}
= 12 - 5 + 2x - x
= 7 + x
d) Perimeter of DEFGHI = DE + EF + FG + GH + HI + ID
= x + 5 + x + 3 + 7 +x + x + 12 +2x + 2x + 3
= x +x + x + x + 2x + 2x + 5 + 3 + 7 + 3 + 12
= 8x + 30