1. In a group of 500 students, 280 like bananas, 310 like apples, and 55 dislike both the fruits.
i) Find the number of students who like both the fruits.
ii) Find the number of students who like only one fruits.
iii) Show the result in venn-diagram
Answer:
Please see the attached images
Step-by-step explanation:
please solve this please
Answer:
C) [tex]\frac{2z+15}{6x-12y}[/tex]
E) [tex]\frac{7d+5}{15d^2+14d+3}[/tex]
F) [tex]\frac{-7a-b}{6b-4a}[/tex]
Step-by-step explanation:
C)
One is given the following equation
[tex]\frac{z+1}{x-2y}-\frac{2z-3}{2x-4y}+\frac{z}{3x-6y}[/tex]
In order to simplify fractions, one must convert the fractions to a common denominator. The common denominator is the least common multiple between the given denominators. Please note that the denominator is the number under the fraction bar of a fraction. In this case, the least common multiple of the denominators is ([tex]6x-12y[/tex]). Multiply the numerator and denominator of each fraction by the respective value in order to convert the fraction's denominator to the least common multiple,
[tex]\frac{z+1}{x-2y}-\frac{2z-3}{2x-4y}+\frac{z}{3x-6y}[/tex]
[tex]\frac{z+1}{x-2y}*\frac{6}{6}-\frac{2z-3}{2x-4y}*\frac{3}{3}+\frac{z}{3x-6y}*\frac{2}{2}[/tex]
Simplify,
[tex]\frac{z+1}{x-2y}*\frac{6}{6}-\frac{2z-3}{2x-4y}*\frac{3}{3}+\frac{z}{3x-6y}*\frac{2}{2}[/tex]
[tex]\frac{6z+6}{6x-12y}-\frac{6z-9}{6x-12y}+\frac{2z}{6x-12y}[/tex]
[tex]\frac{(6z+6)-(6z-9)+(2z)}{6x-12y}[/tex]
[tex]\frac{6z+6-6z+9+2z}{6x-12y}[/tex]
[tex]\frac{2z+15}{6x-12y}[/tex]
E)
In this case, one is given the problem that is as follows:
[tex]\frac{2}{3d+1}-\frac{1}{5d+3}[/tex]
Use a similar strategy to solve this problem as used in part (c). Please note that in this case, the least common multiple of the two denominators is the product of the two denominators. In other words, the following value: ([tex](3d+1)(5d+3)[/tex])
[tex]\frac{2}{3d+1}-\frac{1}{5d+3}[/tex]
[tex]\frac{2}{3d+1}*\frac{5d+3}{5d+3}-\frac{1}{5d+3}*\frac{3d+1}{3d+1}[/tex]
Simplify,
[tex]\frac{2}{3d+1}*\frac{5d+3}{5d+3}-\frac{1}{5d+3}*\frac{3d+1}{3d+1}[/tex]
[tex]\frac{2(5d+3)}{(3d+1)(5d+3)}-\frac{1(3d+1)}{(5d+3)(3d+1)}[/tex]
[tex]\frac{10d+6}{(3d+1)(5d+3)}-\frac{3d+1}{(5d+3)(3d+1)}[/tex]
[tex]\frac{(10d+6)-(3d+1)}{(3d+1)(5d+3)}[/tex]
[tex]\frac{10d+6-3d-1}{(3d+1)(5d+3)}[/tex]
[tex]\frac{7d+5}{(3d+1)(5d+3)}[/tex]
[tex]\frac{7d+5}{15d^2+14d+3}[/tex]
F)
The final problem one is given is the following:
[tex]\frac{3a}{2a-3b}-\frac{a+b}{6b-4a}[/tex]
For this problem, one can use the same strategy to solve it as used in parts (c) and (e). The least common multiple of the two denominators is ([tex]6b-4a[/tex]). Multiply the first fraction by a certain value to attain this denomaintor,
[tex]\frac{3a}{2a-3b}-\frac{a+b}{6b-4a}[/tex]
[tex]\frac{3a}{2a-3b}*\frac{-2}{-2}-\frac{a+b}{6b-4a}[/tex]
Simplify,
[tex]\frac{3a}{2a-3b}*\frac{-2}{-2}-\frac{a+b}{6b-4a}[/tex]
[tex]\frac{-6a}{6b-4a}-\frac{a+b}{6b-4a}[/tex]
[tex]\frac{(-6a)-(a+b)}{6b-4a}[/tex]
[tex]\frac{-6a-a-b}{6b-4a}[/tex]
[tex]\frac{-7a-b}{6b-4a}[/tex]
x>0, y>0, 2x+3y=8, smallest value of xy? pls help me
Answer:
where there is x in the equation we put 0
For y
=2(0)+3y=8
=0+3y=8 Group likely terms
=3y=8-0
=3y=8 Divide both sides by 3
=3y/3=8/3
Therefore y=2.6
For x
=2x+3y=8
=2x+3(0)=8
=2x+0=8 Group likely terms
=2x=8-0
=2x=8 Divide both sides by 2
=2x/2=8/2
Therefore x=4
The smallest numbers for x and y is 4 and 2.6 respectively
Please help me solve this!
Answer:
Step-by-step explanation:
Reference angle = 27
height = 2
Sin(27) = opposite / hypotenuse
hypotenuse = opposite / sin(27)
opposite = 2
hypotenuse = 2 / sin(27)
hypotenuse = 4.405
The ramp has to be 4.41 feet long.
Could anyone please help me with this question, this is my last one?
#iamarookie
Giving away 15 points this time and I just need help on QUESTION B!
Answer:
28 = 2² x 7
Step-by-step explanation:
Factors of 28: 1, 2, 4, 7, 14, 28.
Prime factorization: 28 = 2 x 2 x 7, which can also be written 28 = 2² x 7.
HELP PLS HELP MEEEEE IM FAILING PYTHAGOREAN THEOREM
7^2 + 6^2 = h^2
49 + 36 = h^2
85 = h^2
√85 = h
h = 9.21m
Answered by Gauthmath must click thanks and mark brainliest
am thinking of a number multiplying it by 4 then subtracting 6 the answer is greater than 14. Write the inequality
18-3×5+32÷4
USE BODMAS RULE
the answer should come 11
Answer:
B-bracket
O-of
D-division
M-multiplication
A-addition
S-subtraction
Step-by-step explanation:
18-3×5+32÷4
18-3×5+8 (by dividing 32 by 4 = 8)
18-15+8(by multiplying 3×5=15)
18-7( by -15 +8= 7 )
11
hence proved
11 is the answer by BODMAS rule .
hope this helps you
mrk me braniliest
Complete the statement with always, sometimes, or never. Explain your reasoning.
An altitude is _____ the same line segment as an angle bisector.
Step-by-step explanation:
it's ur answers I hope it's helpful
Write the equation of the line with a slope of 4 that contains the point (5, 8).
Answer:
y = 4x - 12
Step-by-step explanation:
y = 4x + b
8 = 4(5) + b
8 = 20 + b
-12 = b
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: \: \: we \: know \: that \: \\ \sf \: if \: any \: equation\:of \: line \: which \: slope (m) \\ \sf \: and \: passes \: through \: (x_1,y _1) \: \: then \: its \\ \sf equation \: is \: : \\ \\ \red{ \boxed{ \bf y - y_1 = m(x - x_1)}}\bf\end{array}}}}[/tex]
Given that,
A equation of the line with a slope of m = 4 and that contains / passes through the point (5, 8).
So,
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: x_1 = 5 \: \: \: \\ \bf y_1 = 8 \\ \bf \: m \: = 4 \: \: \end{array}}}}[/tex]
NOW,
The equation is :
[tex] \green{ \boxed{\boxed{\begin{array}{cc} \bf \: y - 8 = 4(x - 5) \\ \\ = > \bf \: y - 8 = 4x - 20 \\ \\ = > \pink{ \boxed{\bf\:4x - y - 12 = 0}} \end{array}}}}[/tex]
find the missing side.
Answer:
I htink x ≈ 8
Step-by-step explanation:
Answer:
X is approximately 7.8.
Step-by-step explanation:
You can use SOH-CAH-TOA to help figure out what function (sin, cos, tan) you need to use in order to figure out the missing side.
For this one, we can see the angle is pointing to the opposite side (x length), and we have been given the hypotenuse (18). So we want to use the sin function.
[tex]sin\ (angle)=\frac{opposite}{hypotenouse}[/tex]
[tex]sin (26)=\frac{x}{18}[/tex]
[tex]0.438=\frac{x}{18}[/tex]
[tex]7.890... = x[/tex]
Using Pythagorean theorm, you can figure out the other side if need be :)
For reference:
[tex]sin (angle)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(angle)=\frac{opposite}{adjacent}[/tex]
can a triangle have two right angles ?explain
Answer:
a triangle is a closed polygon that consists of three sides and three angles,and it's one of the basic shape that we basic shape that we knowing geometry.
Which best describes the relationship between the lines with equations −6x+8y=−1 and −4x−3y=2?
Answer:
it is linear
Step-by-step explanation:
Both of these both lines are perpendicular to each other.
We have the two equations of straight lines :
− 6x + 8y = −1 and −4x − 3y = 2.
We have to identify the relation between these two lines.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question, we have -
−6x + 8y = −1 ...(1)
−4x − 3y = 2 ...(2)
Rearranging the terms of the equations we get -
y = [tex]\frac{3}{4} x - \frac{1}{8}[/tex] ...(3)
and
y = [tex]\frac{-4}{3}x - \frac{2}{3}[/tex] ...(4)
When compared -
The slope of line −6x + 8y = −1 is m(1) = [tex]\frac{3}{4}[/tex].
The slope of line −4x − 3y = 2 is m(2) = [tex]\frac{-4}{3}[/tex].
We can see that -
m(1) x m(2) = - 1
The product of the slopes of two perpendicular lines is -1.
Hence, these both lines are perpendicular to each other.
To solve more questions on relation between straight lines, visit the link below -
brainly.com/question/13792781
#SPJ2
Please answer this!!
Answer:
C, 5/12
Step-by-step explanation:
The tangent of an angle is defined as the side opposite to that angle divided by the side adjacent to that angle. The tangent of angle A would be equal to the value of side BC divided by side AB. The value of side BC is 5, and the value of side AB is 12. The answer is 5/12.
Answer: ∠A=[tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Tangent is opposite over adjacent.
Guys please help me solve this problem, yes I will mark brainliest
Given that the vertex is at (50, 1000), the max profit is $1000 when 50 items are produced
Find the standarddeviation of 125, 136, 150, 119, 150, and 143.
Answer:
S.D=46.04
Step-by-step explanation:
steps are in the picture.
If you have question about it you can ask.Thanks
If the graph of f(x) = x^2, how will the graph be affected if it is changed to f(x) = 3r^2?
Answer:
the graph curve will goes above f(x)=x^2.f(x)=3*x^2 curve will also give higher value same value of x .
Step-by-step explanation:
In the picture below, which lines are lines of symmetry for the figure?
(PICTURE) Can someone please help me out Im reporting trolls. Marking brainliest
Answer:
smart dot company would be c=.50t+12
communication plus would be c=2.50t
Step-by-step explanation:
smart dot starts with $12 a month and adds $0.50 for each hour of internet use. communication plus has no starting fee so it just adds $2.50 for each hour of internet use.
So then for the table you would put the number given for time in for the letter t and find what c would be. This would then find your cost for that amount of hours. To get you started smart dot company starts off with 0 hours so put that in for t being c=0.50(0)+12 and c=12. Communication plus also starts with 0 so it would be c=2.50(0) and c=0
Then you graph once you have both values you can graph having x=time and y=cost
Let me know if this helps!
A student states that Figure JKLM is congruent to Figure PQRS. Determine if the student is correct or has made an error. ;D
Answer:
Student has made an error
Step-by-step explanation:
If two figures are said to be congruent, this implies that area of both is same and both as exactly same or copy or each other.
But from the graph, it can be stated that height of figure JKLM is 4 units whereas that of other is 6 unit.
Hence explained !
Line A is represented by the following equation: X + y = 2
What is most likely the equation for line B so the set of equations has no solution?
Answer:
x+y=3
Step-by-step explanation:
For an equation to have no solution, their slope needs to be same and y intercept needs to be different,
so in this case where x+y=2
doing simply, x+y=3 makes a set of equation which has no solution, you can take any real value which is not 2
See pic below! Need help solving
Answer:
383.54 m
Step-by-step explanation:
The length of the training track running around the field = circumference of the circle formed by the two semicircles + 2(length of the rectangle)
The two semicircles forms a fill circle with diameter (d) = width of rectangle = 61 m
Length of rectangle (L) = 96 m
π = 3.14
The length of the training track running around the field = πd + 2(L)
Substitute the values
The length of the training track running around the field = 3.14*61 + 2(96)
= 191.54 + 192
= 383.54 m
How would the expression x^2 -9 be rewritten using Difference of Squares?
O A. (x+3)(x - 3)
O B. (X-9)^2
O C. (x +9)(x-9)
O D. (x+3)^2
Answer:
A. (x+3)(x - 3)
Step-by-step explanation:
x^2 -9
Rewriting
x^2 - 3^2
We know that a^2 - b^2 = (a-b)(a+b)
(x-3)(x+3)
Answer:
[tex]\left(x+3\right)\left(x-3\right)[/tex]
Step-by-step explanation:
[tex]x^2 -9[/tex]
To factor an integer, we need to divide it by the ascending sequence of primes (2, 3, 5). The number of times each prime divides the original integer becomes its exponent. [tex]3^{2} =9[/tex]
Now, we need to factor this expression by applying the difference of two squares rule:
[tex]A^{2} -B^{2} =(A+B)(A-B)[/tex]
A= x and B= 3
[tex](x+3)(x-3)[/tex]
OAmalOHopeO
Michelle gets10rewards points for each of her purchases at Starbucks. With 500 rewards points, she can get a free smoothie. If she has 370 points saved, how many purchases will it take her to get her free smoothie?
she needs 130 points saved up
Answer:
13
Step-by-step explanation:
plss answer hihihihihihihihiihihihihihihihihihihih
Answer:
C - 60
Step-by-step explanation:
4x^2 = 144
x = 6
p=10*6
P=60
Answer:
hi, thanks for asking! the answer to this question is, 108.
Step-by-step explanation:
first, you must think how much it adds up to if u add the numbers toghether. then, boom!
hope this helps<3
please anyone give me a answer i need it rn
Answer:
The first option is the right one.
Step-by-step explanation:
7/2. Rate is rise/run
7 is your rise
and 2 is your run
therefore, the answer is 7/2
I need help for this question 3 so can anyone help me please
Given: m∠V=103°, m∠VRT=71°, RS ∥ VU Find: m∠TRS, m∠U
Answer:
m∠TRS = 6°
m∠U = 103°
Step-by-step explanation:
In the given figure,
O is the center
RS ∥ VU
m∠V = 103° &
m∠VRT = 71°
So,
m∠V + m∠R = 180° (∵ sum of co-interior angles)
⇒ m∠R = 180° - 103° (m∠V = 103° is given)
∵ m∠R = 77° ...(i)
Now,
m∠R = m∠TRS + m∠VRT
by putting the values given
⇒ m∠TRS = 77° - 71°
∵ m∠TRS = 6°
As we know that,
VURT is a cyclic quadrilateral. So,
m∠U + m∠R = 180°
⇒ m∠U + 77° = 180° (from equation (i)
∵ m∠U = 180° - 77° = 103°
Please help me solve this quickly!
Answer:
33.80
Step-by-step explanation:
AB = BC = AD√2
AB = BC = 7√2
AD = DC
AC = 2AD
perimeter = AC + AB + BC
= 2AD + 2AB
= 2(7) + 2(7√2)
= 14 + 14√2
≈ 33.80
Answer:
33.8
Step-by-step explanation:
45-45-90 degree triangle rules states that the sides that are opposite the angles measure 45 degrees have the same value. That means that BD has the same value as AD, which is 7. Since triangle BDC is also a 45-45-90 degree triangle, DC is equal to BD, which is 7. We have the value of AC, which is 7+7=14. Now, we can use the Pythagorean theorem to figure out BC and AB. We know that [tex]DC^2+BD^2=BC^2[/tex]. We know that DC and BD is equal to 7, so we can simplify that to [tex]49+49=BC^2[/tex], and we can further simplify that to [tex]BC=\sqrt{98}[/tex]. This is also equal to [tex]7\sqrt{2}[/tex]. Since BC is also equal to AB because of 45-45-90 degree triangle rules, we have the perimeter of the triangle as
[tex]7\sqrt{2} + 7\sqrt{2}+14[/tex], which is equal to [tex]14\sqrt{2} + 14[/tex]. We can simplify 14 times the square root of 2 as 19.8 (rounded to 2 decimal places). We have the answer as 19.8 + 14, which is 33.8.
a triangle has a base measuring 6 feet and a height measuring 8.3 feet. How many triangles of this area would fit inside a rectangle with a width 12 feet and a length of 33.2 feet?
Area of the triangle = 1/2 x base x height
Area of triangle = 1/2 x 6 x 8.3 = 24.9 square feet.
Area of rectangle = length x width
Area of rectangle = 33.2 x 12 = 398.4 square feet.
To find the number of triangles that can fit in the rectangle divide the area of the rectangle by the area of the triangle:
398.4 / 24.9 = 16
Answer: 16 triangles