Answer: 4
Step-by-step explanation:
We know that a plane is 2 dimensional surface that extends infinitely far.
The number of points required to define a plane = 3
Here , we have 4 points A, B, C, and D.
So, the number of possible combinations of 3 points to make a plane from 4 points = [tex]C(4,3)[/tex]
[tex]=4[/tex] [ [tex]C(n,n-1)=n[/tex] ]
Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.
If(a-b) =4 and ab=2,find the value of a^2+b^2
Answer:
a² + b² = 20
Step-by-step explanation:
Given
(a - b) = 4 ← square both sides
(a - b)² = 4²
a² - 2ab + b² = 16 ← substitute ab = 2
a² - 2(2) + b² = 16
a² - 4 + b² = 16 ( add 4 to both sides )
a² + b² = 20
Solve for x in the equation 2/5x = 12
A: -30
B: -4 4/5
C: 4 4/5
D: 30
Convert -100 grades to a radian measure
A=5pi
18
B=5pi
9
C=-5pi
18
D=-5pi
9
Answer:
-5pi/9
Step-by-step explanation:
The conversion factor is pi/180
-100 degrees * pi/180 = -100/180 *pi =-10pi/18 = -5pi/9
Find the distance between the pair of points.
(7, 3) and (-6, -4)
A. 2.4
B. 11
C. 1.4
D. 14.8
Find the reciprocal of 4/5
Answer:
its 5/4! haha i used to be good at this when i was in 6th grade:)
What is the sign of y = £?
y
Choose 1 answer:
A
Positive
B
Negative
Zero
Answer:
I'm pretty sure is
Positive b
what is the product of 5 1/2 and 1 2/7
Answer:
[tex]\frac{99}{14}[/tex] or [tex]7\frac{1}{14}[/tex]
Step-by-step explanation:
[tex]5\frac{1}{2}[/tex] × [tex]1\frac{2}{7}[/tex]
Step 1. Convert the mixed fractions into an improper fraction (by multiplying the denominator by the whole number and adding the numerator with de denominator to the result)
Answer:
[tex]5\frac{1}{2}=[/tex] [tex]2[/tex] × [tex]5+1=[/tex] [tex]\frac{11}{2}[/tex]
[tex]1\frac{2}{7}=[/tex] [tex]7[/tex] × [tex]1+2=\frac{9}{7}[/tex]
Step 2. Multiply (by multiplying numerator by numerator and denominator by denominator)
Answer:
[tex]\frac{11}{2}[/tex] × [tex]\frac{9}{7}=\frac{99}{14}[/tex] or [tex]7\frac{1}{14}[/tex]
Answer:
The product of 5 1/2 and 1 2/7 is 7 1/14
Step-by-step explanation:
Turn the mixed numbers into improper fractions.
11/2 * 9/7
Multiply.
11/2 * 9/7 = 99/14
Turn into a mixed number.
99/14 = 7 1/14
Hope this helps!
The volume of air in a balloon is represented by the function v(n) = ne?, where r is the radius of the balloon, in
inches. The radius increases with time, in seconds, by the function -1) = 4,2. Which statements are true? Check all
that apply
When V is composed with r, the composite function is
mt
48
When V is composed with r, the composite function is
is u216.
V(r(6)) shows that the volume is 9724 in. when the radius increases to 6 inches
V[r(8)) shows that the volume is 16384 7 in.) when the radius increases to 16 inches.
3
The domain of V(t) is all real numbers.
Answer:
When V is composed with r, the composite function is StartFraction 1 Over 48 EndFraction pi t Superscript 6
V(r(6)) shows that the volume is 972π inches cubed when the radius increases to 6 inches.
Step-by-step explanation:
Answer:
1 and 3 on edge
Step-by-step explanation:
The area of a trapezium is 31.5 cm². If the parallel sides are of length 7.5 cm and 5.3 cm, calculate the perpendicular distance between them
Answer:
The answer is 4.9cmStep-by-step explanation:
To find the perpendicular distance between them that's the height we use the formula
[tex]Area \: \: of \: \: a \: \: trapezium = \frac{1}{2} (a + b) \times h[/tex]
where
a and b are the parallel sides of the trapezium
h is the perpendicular distance
From the question
Area = 31.5cm²
a = 7.5 cm
b = 5.3 cm
Substituting the values into the above formula we have
[tex]31 .5 = \frac{1}{2} (7.5 + 5.3) \times h[/tex]
[tex]31.5 = \frac{1}{2} \times 12.8h[/tex]
[tex]31.5 = 6.4h[/tex]
Divide both sides by 6.4
[tex]h = \frac{31.5}{6.4} [/tex]
h = 4.921875
We have the final answer
h = 4.9cmHope this helps you
You store square notepaper in a cube shape box with an inside edge length of 3 inches. What is the volume of the box
A cube has sides that are all equal lengths .
Volume of a cube is S^3, where S is the length of the side.
Volume = 3^3 = 3 x 3 x 3 = 27 cubic inches.
The volume of box will be 27 inch³.
A square notepaper is stored in a cube shape box with an inside edge length of 3 inches.
We have to calculate the volume of the box.
What is the volume of a cube ?
The volume of a cube is the multiplication of the edge length (a) for three times i.e., a × a × a = a³ .
As per the question ,
Inside edge length of cube = 3 inches
So ,
the volume of box will be ;
= a × a × a
= 3 × 3 × 3
= 27 inch³
Thus , the volume of box will be 27 inch³.
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Make the biggest possible number using the digits below only once 3 , 1 , 3 answer
Answer:
331
Step-by-step explanation:
A number with 3 digits: using only
3, 1, 3
then:
3>1
the biggest possible number is:
331
Answer:
331
Step-by-step explanation:
Possible Combinations:
133
313
331
Out of these combinations, using process of elimination, we can determine that 331 is the greatest value out of the three numbers provided.
Two solid spheres have surface areas of 1441 cm? and 2567 cm² respectively. They are melted and recast to form a larger sphere. Find the surface area of the larger sphere in square centimetres.
Surface area of small sphere = 1441cm^2
Surface area of bigger sphere = 2567cm^2
Surface area of largest sphere = 1441 + 2567
= 4008cm²
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Question 12
1 pts
Whitney recently created a new smartphone app. As a result of the initial costs and
fees of producing the app, she did not make any money, or profit, selling the app during
the first two months of the app's release. For the first month, Whitney had a loss of
$324. During the second month of sales, she had a loss of $97. She hopes that in the
third month, she will sell enough apps to break even-that is, she hopes to earn enough
money to cover her losses. What is the amount of money Whitney needs to make in the
third month in order to break even with app sales so far?
Answer:
The amount (revenue) she makes in the third month to break even is $97
Step-by-step explanation:
The given parameters are;
The cost of the app = Initial cost + fees for producing the app
The amount she loss in the first month = Cost of the app - revenue = $324
The amount she loss in the second month = Loss from first month - revenue in second month = $324 - revenue in second month = $97
The amount Whitney has to make in the third month to break even is therefore;
The amount she makes in the third month to break even is given by the equation;
Revenue from third month - Loss from second month = 0
Which gives;
The amount she makes in the third month to break even is given by Revenue from third month - $97 = 0
∴ Revenue from third month = $97
The amount (revenue) she makes in the third month to break even = $97
Identify the glide reflection rule in the given figure.
Question 8 options:
Translation: (x,y) → (x – 5,y); Reflection across y-axis
Translation: (x,y) → (x,y – 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across x-axis
Answer:
B
Step-by-step explanation:
The shape clearly is reflected across y axis and the x coordinates remain the same. We can see a change in the y coordinates and the shape has shifted 5 units down. Hence (x, y) -> (x, y-5) and then reflection across y axis is the answer
Answer:
B
Step-by-step explanation:
A chef mix his salt and pepper. If he put 2/3 cup of salt and 1/2 cup of pepper in his shaker, what is the ratio of salt to pepper ?
Answer:
salt: pepper
4 : 3
Step-by-step explanation:
salt: pepper
2/3 : 1/2
Multiply each by 6
2/3 *6 : 1/2 *6
4 : 3
The polygons in each pair are similar. find the scale factor of the smallest figure to larger figure.
Greetings from Brasil...
It is said that polygons are similar, so we can use the expression of similarity.
BIG/small = BIG/small
35/14 = 25/X
X = 10
But the scale factor is questioned. Just use one of the expressions. We conclude that the largest is 2.5 times the value of the smallest
35/14 OR 40/16 OR 25/10
We get 2.5x-----------------------------------------------------------
BIG/small = BIG/small
25/5 = 40/Y
Y = 8
25/5 OR 25/5 OR 40/8
We get 5xtimes the value of the smallest
The graph shows the wolf population in
Yellowstone National Park aince 2000 A
student drew a line of beat fit to model the
Wolf Population
180
160
150
Number of Wolves
5 130
120
110
100
.
0
2 4 6 8 10 12 14
Years Since 2000
Which statement best describes the line of
best fit that the student drew?
A. The line of best fit is not a strong model
for the data, because the points are not
close to the line.
B. The line of best fit is not a strong model
for the data, because it does not pass
through any of the data points.
C. The line of best fit is a strong model for
the data, because both the line and the
data show a negative trend.
D. The line of best fit is a strong model for
the data, because about half the data
points are on each side of the line.
Answer:
I think D but im not sure
Step-by-step explanation:
Topic: Simultaneous equations Class 9 ICSE
Denote the number by 10a + b, where both a and b are integers picked from {1, 2, 3, …, 9}.
"the difference of whose digits is 3" ==> |a - b| = 3
"4 times the number is equal to 7 times the number obtained by reversing the digits" ==> 4 (10a + b) = 7 (10b + a)
Simplifying the second equation, you get
40a + 4b = 70b + 7a
33a - 66b = 0
a - 2b = 0
Assume a > b, in which case we would have |a - b| = a - b, so
a - b = 3
Eliminate a to solve for b, then for a :
(a - b) - (a - 2b) = 3 - 0
b = 3 ==> a = 6
Then the original number is 63.
If instead we had assumed a < b, we would have had |a - b| = b - a = 3. Then
2 (b - a) + (a - 2b) = 2×3 + 0
-a = 6
But neither a nor b can be negative, so this case is moot.
Which of the following are true statements about the expression 5 + (-5)
1. the expression equals 0.
2. The expression equals 10.
3. The expression describes the number that is 5 to the left of 5 on the number line.
4. The expression describes the number that is 5 to the right of 5 on the number line.
Answer:
[tex]\huge\boxed{\sf The \ expression\ equals \ zero}[/tex]
Step-by-step explanation:
=> 5 + (-5) [ + (-) = - ]
=> 5 - 5
=> Zero
Answer:
The answer is option A-The expression equals 0.
Step-by-step explanation:
Identify the value of x and the length of each secant segment.
Answer:
x=7; NL=12; NP+20
Step-by-step explanation:
What is the slope of the line containing (-2, 5) and (4,-4)?
O A. 3/2
O B. -2
O C -3/2
O D. 2
Answer:
Option C is correct.
Step-by-step explanation:
[tex]slope \: = \: \frac{y2 - y1}{x2 - x1} [/tex][tex] = \frac{ - 4 - (5)}{4 - (2)} [/tex][tex] = \frac{ - 9}{4 + 2} [/tex][tex] = \frac{ - 9}{6} [/tex][tex] = \frac{3( - 3)}{3 - 2} [/tex][tex] = - \frac{3}{2} [/tex]Hope it is helpful....in right triangle abc below where ac=2 and angle BAC is theta find y in terms of theta
please ignore my work!
Answer:
2tanθ -2 = y
Step-by-step explanation:
First, to make things a little simpler, we can say that the point between C and B is D, so BD = y
We are given that ∠ADC = 45° , and ∠ACD = 90°. Because the angles of a triangle add up to 180 degrees, we can say
∠CAD + ∠ACD + ∠ADC = 180°
∠CAD + 90 + 45 = 180
∠CAD = 45°
In a 45/45/90 degree triangle, we can say that the two non-hypotenuse sides are the same. The hypotenuse is opposite of the right angle, so in this triangle, it would be AD. Therefore, we can say that AC = CD = 2
Because BC = CD + DB , we can say that
BC = CD + DB
BC = 2 + y
y = BC -2
Therefore, if we know BC, we can solve for y.
We want to solve for BC given
- the angle opposite of it (θ)
- the side adjacent to the angle (AC).
One equation that fits this is
tanθ = opposite/adjacent
tanθ = BC/AC
tanθ = (2+y)/2
multiply both sides by 2 to remove a denominator
2 tanθ=2+y
subtract 2 from both sides to isolate th y
2tanθ -2 = y
The graph below shows Roy's distance from his office (y), in miles, after a certain amount of time (x), in minutes: Graph titled Roys Distance Vs Time shows 0 to 10 on x and y axes at increments of 1.The label on x axis is time in minutes and that on y axis is Distance from Office in miles. Lines are joined at the ordered pairs 0, 0 and 1, 1 and 2, 2 and 3, 3 and 4, 4 and 5, 4 and 6, 4 and 7, 4.5 and 7.5, 5 and 8, 6. Four students described Roy's motion, as shown in the table below: Student Description Peter He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 2 minutes. Shane He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 8 minutes. Jamie He drives a car at a constant speed for 4 minutes, then stops at a crossing for 6 minutes, and finally drives at a variable speed for the next 8 minutes. Felix He drives a car at a constant speed for 4 minutes, then stops at a crossing for 2 minutes, and finally drives at a variable speed for the next 2 minutes. Which student most accurately described Roy's motion? Peter Shane Jamie Felix
Answer:
Felix
Step-by-step explanation:
The graph contains 3 segments,
first one is for the first 4minutes,
second one is for the next 2 minutes (standing still)
third one is for the last 2 minutes.
Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end. (e.g., from 4 to 6 is 2 minutes).
The student that most accurately described Roy's motion is Felix.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
We need to find the student that most accurately described Roy's motion.
Here we can see that the graph contains 3 segments, first one is for the first 4 minutes, Second one is for the next 2 minutes (standing still) and the third one is for the last 2 minutes.
Now, Only Felix has it right, the other students use absolute time in their statements, in stead of the difference between start and end.
Therefore, the student that most accurately described Roy's motion is Felix.
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If the curved surface area of a cylinder with height 15cm is 1320cm², find total surface area
Answer:
2552cm^2
Step-by-step explanation:
C.S.A=1320cm^2 ;r=?
h=15cm.
[C.S.A. = 2πrh]
(r=1320×7/660=14cm)
Now,
TSA of cylinder = 2πr (h + r) sq
TSA=2×22/7(15+14)=2552cm^2
You flip a coin and roll a six-sided die. What is the
probability of flipping heads and rolling a number greater
than or equal to 5?
Answer:
The probability of flipping heads is 1/2
The probability of rolling 5 or more is 1/3.
So the total probability is 1/2 x 1/3 , which is 1/6.
Let me know if this helps!
Answer:
1/6
Step-by-step explanation:
The probability of flipping heads is 1/2
The probability of rolling 5 or more is 1/3.
So the total probability is 1/2 x 1/3 , which is 1/6.
multiply the monomials :
a) a³ , -6 a² b and 2 b³
b) 16 x⁶ , -10 xy² and 3/5 x² y²
c) -4 p² q² and 3/8 pq²
here we want to multiply different monomials, the particular important thing about this problem is learning how to simplify these multiplications.
Here we need to remember the property:
[tex]a^n*a^m = a^{n + m}[/tex]
Now we want to directly multiply the monomials:
a) a³ , -6 a² b and 2 b³
Here we just have:
[tex]a^3*(-6*a^2*b)*(2*b^3)[/tex]
Let's reorder that, so we can separate the variables and the coefficients, so then we can use the above property to solve this:
[tex]a^3*(-6*a^2*b)*(2*b^3) = (-6*2)*(a^3*a^2)*(b*b^3) = -12*a^5*b^4[/tex]
b) 16 x⁶ , -10 xy² and 3/5 x² y²
Like before, we want to simplify:
[tex](16*x^6)*(-10*x*y^2)*(\frac{3}{5}*x^2*y^2)[/tex]
Again, reordering that we get:
[tex](16*\frac{3}{5}*-10)*(x^6*x*x^2)*(y^2*y^2)[/tex]
Now solving each parenthesis:
[tex](16*\frac{3}{5}*-10)*(x^6*x*x^2)*(y^2*y^2) = -96*x^{6 +1 + 2}*y^{2 + 2}[/tex]
Simplifying the last expression we get:
[tex]-96*x^{6 +1 + 2}*y^{2 + 2} = -96*x^9*y^4[/tex]
c) -4 p² q² and 3/8 pq²
Here we want to simplify:
[tex](-4*p^2*q^2)*(\frac{3}{8}*p*q^2)[/tex]
Using the same approach as before, we will get:
[tex](-4*p^2*q^2)*(\frac{3}{8}*p*q^2) = (-4*\frac{3}{8})*(p^2*p)*(q^2*q^2) = \frac{-3}{2}*p^3*q^4[/tex]
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Can I name my Angle VTS as STV? And use it interchangeably in proving?
Answer:
both angles are the same, so you can use it interchangeably in proving.
But i suggest you to mantain only one, because it's easier to understand and it looks better.
In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=6.00, b=7.56, y = 54°
Answer:
c=6.31, a=50.28 degrees, B=75.72 degrees
Step-by-step explanation:
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.
Now, Using the law of cosine, we can write,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]
[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]
c = √39.8297
c = 6.311
Now, using the sine law the ratio of the sides and angles can be written as,
[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]
[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]
α = 50.2775°
[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]
β = 75.726°
Hence, the remaining parts of the triangle can be found as shown.
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Factorize: 4m^2-y^2+4m+1
Answer:
(2m + 1 + y) (2m + 1 - y)
Step-by-step explanation:
steps are done in the above photo and i have also written the identifies
Solve D = ABC for C.
Answer:C=d/ab
Step-by-step explanation:
D=abc
D/ab=abc/ab (both side divided by ab)
Ab cancel by ab and c= d/ab remains
The solution of the given equation D = ABC for C will be D/(AB).
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given equation,
D = ABC
The value of the above equation for C will be as,
D = (AB)C
C = D/(AB)
Hence "The solution of the given equation D = ABC for C will be D/(AB)".
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