Answer:
5/3
Step-by-step explanation:
5×(10×1/3)
=10×5/3
=since 5×(10×1/3) gives 50/3 so thus 10×5/3.
The fraction is therefore 5/3
1. ABCD is a quadrilateral in which angle A = angle C and angle B = angle D
Prove that, if the opposite angles of a quadrilateral are equal, then the quadrilateral is a
parallelogram.
Answer:
Quadrilateral ABCD is a parallelogram, quadrilateral with opposite sides parallel
Step-by-step explanation:
Statement, Reason
∠A = ∠C, Given
∠B = ∠D, Given
Therefore, we have
∠A + ∠B + ∠C + ∠D = 360°, Sum of interior angles of a quadrilateral
2×∠A + 2×∠B = 360°, Substitution property of equality
∴ ∠A + ∠B = 360°/2 = 180°
∠A + ∠B, are supplementary angles, Angles that sum up to 180°
Similarly,
∠C + ∠D, are supplementary angles, Angles that sum up to 180°
Therefore, segment DA is parallel to segment BC, (Lines with supplementary angles on the same side of the transversal)
Similarly, given ∠A = ∠C and ∠B = ∠D, we have;
∠A + ∠D and ∠C + ∠B are supplementary angles, Angles that sum up to 180°
Therefore, segment AB is parallel to segment DC, (Lines with supplementary angles on the same side of the transversal)
Therefore;
Quadrilateral ABCD is a parallelogram, quadrilateral with parallel opposite sides.
Select the correct answer.
Solve the system of equations.
y = x + 3
y = x^2 - 2x - 1
A. (1,4) and (-4,1)
B. (-1,4) and (4,1)
C. (-1,7 and (4,2)
D. (-1,2) and (4,7)
Answer:
( 4,7) ( -1,2)
Step-by-step explanation:
y = x + 3
y = x^2 - 2x - 1
Set the equations equal to each other
x + 3 = x^2 - 2x - 1
Subtract x from each side
3 = x^2 -3x -1
Subtract 3 from each side
0 = x^2 -3x -4
Factor
0 = ( x-4) ( x+1)
Using the zero product property
x-4 =0 x+1 =0
x = 4 x=-1
Find y for each x
x=4 y =x+3 y = 4+2 y=7
x = -1 y = x+3 y = -1+3 y = 2
( 4,7) ( -1,2)
Answer:
D. (-1, 2) and (4, 7).
Step-by-step explanation:
Eliminating y:
x^2 - 2x - 1 = x + 3
x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = -1, 4.
When x = -1, y = -1 + 3 = 2.
When x = 4, y = 4 + 3 = 7.
So the answer is (-1, 2) and (4, 7).
2. At a local restaurant, 55% of people order an appetizer to start while 25%
order a salad to start. Also, 18% choose both an appetizer and a salad to start.
What percentage of people order a salad or an appetizer to start?
Answer:
Probability of people order a salad or an appetizer P(A∪B) = 62%
Step-by-step explanation:
Given:
Probability of appetizer P(A) = 55%
Probability of salad P(B) = 25%
Probability of choose both P(A∩B) = 18%
Find:
Probability of people order a salad or an appetizer P(A∪B)
Computation:
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∪B) = 55% + 25% - 18%
P(A∪B) = 62%
Probability of people order a salad or an appetizer P(A∪B) = 62%
Find the perimeter of the following rectilinear figure.
Answer:
54
Step-by-step explanation
You can't find the other sides, it may seem impossible, but you have to look at this problem in a different way. To find the perimeter of any figure you just need to know the top base, bottom base, right side, and left side.
We see that the top base equals to the bottom base as it is a rectilinear figure. You have to treat the side with 8 and side with 5 as one base. So they equal 13. Now do the same for the bottom.
So, 13 + 13 = 26
The right side is equal to the left side as it is a rectilinear figure, so the right side is 4 + 10 = 14. The left side is also 14.
So 14 + 14 = 28
26 + 28 = 54 units
Sorry, if I couldn't explain properly. I tried my best. As it is hard for me to explain in words. If I could draw it out, I could do better.
Answer:
45
Step-by-step explanation:
I broke the sections apart and then added:
14+14=28
13+13=26
26+28=54
Please answer ASAP. The question is down below
Answer: 1) D 2) B
Step-by-step explanation:
1) The denominator cannot equal zero, Factor the denominator to find the zeros. n³ - 4n² + 3n = 0
n(n - 3)(n - 1) = 0
n=0 n-3=0 n-1=0
n=0 n=3 n=1
2) In order to be a rational expression, it must be in the form [tex]\dfrac{a}{b}[/tex] where both a and b are integers.
Since [tex]\sqrtb[/tex][tex]\sqrt b[/tex] is irrational and not an integer, then the expressions containing an irrational term after simplified cannot result in an integer.
Therefore, options (i) and (iv) are not rational expressions.
Option (iii) contains b as an exponent. Since there is no information about b, it could be a fraction, which means it could be an irrational number.
How to do this question plz answer me step by step plzz plz
Answer:
196
Step-by-step explanation:
Surface area of a cuboid:
2 ( lw + wh + hl)
L = Length
W = Width
H = Height
Area of the base = 30 = lw; So we could take the length as 15 cm and width as 2 cm.
Volume = lwh; 15 x 2 x (4); So 4 is the height
So, 2 ( lw + wh + hl)
= 2 (15 x 2 + 2 x 4 + 4 x 15)
= 2 (30 + 8 + 60)
= 2 (98)
= 196 is the surface area of cuboid
What is the decimal equivalent of 16/3 ?
A. 5.3
B. 0.1875
C. 53333...
D. 16.3
Answer:
c. 5.333...
Step-by-step explanation:
When converting fractions into decimals, all you have to do is that you have to divide the numerator by the denominator. In this case, we will get 16 divided by 3. If we do this, we will get 5 and 1/3. One third in decimals is 0.3333... so the answer is 5.333...
The decimal 5.33 will be equivalent to 16/3 so option (A) will be correct.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given the fraction of 16/3
So divide 16 by 3
16/3 = (15 + 1 )3
⇒ 15/3 + 1/3
⇒ 5 + 0.333
⇒5.3
Hence "The decimal 5.33 will be equivalent to 16/3".
To learn more about the arithmetic operators,
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evaluate 5!+2!. Thank you!
Answer:
122
Step-by-step explanation:
5!=5 x 4 x 3 x 2 x 1 = 120
2!=2 x 1 = 2
120+2=122
the the diameter of a circular Garden is 140 metre . On its outside there is a road of 7 metre wide find out the outer circumference of the road
Answer:
484 meters
Step-by-step explanation:
diameter of a circular Garden = 140 metre
we know diameter = 2*radius
140 = 2*radius
radius = 140/2 = 70 meter
thus, radius of garden is 70 meter
Given that
On its outside there is a road of 7 metre wide
Thus, radius of garden along-with road will increase by 7 meters
Total radius of garden and road = 70 meter + 7 meter = 77 meter
outer circumference of the road can be calculated using radius 77 meter.
we know that circumference = [tex]2\pi r[/tex]
we will use value of [tex]\pi = 22/7[/tex]
Thus, outer circumference of the road with radius 77 m
= [tex]2\pi r \\=>2*22/7 *77\\=> 44*11 = 484[/tex]
Thus,
The outer circumference of the road is 484 meters.
URGENT PLEASE ANSWER !!
Answer:
(C) [tex]y = 2x+5[/tex]
Step-by-step explanation:
Looking at this graph, we can see that the slope of it is 2. We know this because for every time x increases by 1, y increases by 2.
We also know that the y-intercept of this graph is 5, since it intercepts the y-axis at the value 5.
We can easily create an equation with this info.
[tex]y = 2x + 5[/tex].
Hope this helped!
Answer:
C. y= 2x+5
Step-by-step explanation:
y=mx+b
(+b) is y- intercept
(mx) is the slope.
plot the y- intercept first which the line starts at (0,5)
since the slope isn't a fraction you turn it into one which would be
[tex] \frac{2}{1} [/tex]
Please help...Will give brainiest
Answer:
19.45
Step-by-step explanation:
The median is the middle number. Put the data in order from smallest to largest
16.3, 17.8,17.8 ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4
There are 12 pieces of data,
16.3, 17.8,17.8 ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4
The median lies between the 6th and 7th piece
Add the 6th and 7th together and divide by 2
(19.3+19.6)/2 =19.45
Answer:
[tex]\large \boxed{\mathrm{19.45}}[/tex]
Step-by-step explanation:
Median of a data set is the middle value.
The data is to be arranged from smallest to largest.
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Find the middle value.
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Average the two middle numbers.
(19.3+19.6)/2 = 19.45
The median of the data set is 19.45.
If a^b= b^a and a = 2b then find the value of a^2+b^2
a) 20
b) 30
c) 28
d) 24
Answer:
[tex]\large \boxed{\sf \bf \ \ a^2+b^2=20 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]a^b=b^a\\\\\text{ We can replace a by 2b.}\\\\(2b)^b=2^b\cdot b^b=b^{2a}=b^2\cdot b^b\\\\\text{ Let's assume that b is different from 0 and we can divide by }b^b \\ \\ \text{ both sides of the equation, and it come.}\\\\2^b=b^2\\\\\text{ We find b = 2 and then a = 4, So}\\\\a^2+b^2=4^2+2^2=16+4=20[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which line is parallel to line r? line p line q line s line t
Answer:
Line S
Step-by-step explanation:
Answer:
line s
Step-by-step explanation:
coz if you extend both the line (line r and line s )
they will not intersect at any point...
plz let me know if it was helpful to you dude!
Marissa drew the triangle shown below.
Answer:
13.6
Step-by-step explanation:
tan(45)=x÷8.5
1.6=x/8.5
x=13.6
Use the law of sines
x/sin(45) = 8.4/sin(85)
x = sin(45)*8.4/sin(85)
x = 5.96238563941842
x = 6.0
solve -3.5 = 0.5x +0.5x+x
Answer:
x= 7/4 =1.750
Step-by-step explanation:
Which of the following equations have exactly one solution? Choose all answers that apply: Choose all answers that apply: (Choice A) A 2x-31=2x-31 (Choice B) B 2x-31=-2x-31 (Choice C) C 2x+31=2x-31 (Choice D) D 2x-2=2x-31
Answer:
B 2x - 31 = -2x - 31 have exactly one solution
Step-by-step explanation:
Which of the following equations have exactly one solution?
Choose all answers that apply:
A 2x - 31 = 2x - 31
B 2x - 31 = -2x - 31
C 2x + 31 = 2x - 31
D 2x - 2 = 2x - 31
A. 2x - 31 = 2x - 31
2x-31=2x-31
Collect like terms
2x-2x= -31+31
0=0
Infinite number of solutions
B 2x - 31 = -2x - 31
2x - 31 = -2x - 31
Collect like terms
2x+2x=-31+31
4x=0
x=0
One solution
C 2x + 31 = 2x - 31
2x + 31 = 2x - 31
Collect like terms
2x-2x= -31-31
0= -62
No solution
D 2x - 2 = 2x - 31
2x - 2 = 2x - 31
Collect like terms
2x-2x= -31+2
0= -29
No solution
x + y = 0
y = 2x + 6
8
Now graph y = 2x + 6 What are the graphing points (there needs to be 3 pairs)
Answer:
(-3,6) (1,8) (2,10) and so on.
Find the perimeter of rectangle whose length is 40 and the diagonal is 41 cm
Answer:
P = 98 cmStep-by-step explanation:
Given one side and diagonal of rectangle we can use Pythagorean theorem to calculate the other side of it.
[tex]L=40\, cm\\D=41\,cm\\W=\ ?\\\\W^2+L^2=D^2\\\\W^2+40^2=41^2\\\\W^2+1600=1681\\\\W^2=81\\\\W=9[/tex]
Perimeter:
P = 2W + 2L = 2•40 + 2•9 = 80 + 18 = 98
PLS HURRY!!! Charlie made a table to show how much time he spent on activities last week . Activity Time spent (hours ) Swimming Reading Cooking Soccer On which activities did Charlie spend more than hour? PLS HURRY
Answer:
None
Step-by-step explanation:
All of the fractions listed are not a whole or more than a whole. They are all parts of a whole, therefore she did not spend more than an hour on any of them
Answer:
cooking and swimming
Step-by-step explanation:
What were Malcolm's and Ravi's maximum speeds?
Answer:
Malcom's maximum speed = 200 km/h
Ravi's maximum speed = 320 km/h
Step-by-step explanation:
Let m = Malcom's maximum speed
Let r = Ravi's maximum speed
Average of their maximum speed would be represented as [tex] \frac{m + r}{2} = 260 [/tex]
[tex] m + r = 520 [/tex].
Make m the subject of the formula by subtracting r from both sides:
[tex] m = 520 - r [/tex]. Let this be equation 1.
Given that Malcom's speed (m), when doubled is 80 km/h more than that of Ravi (r). This can be expressed as: [tex] 2m = r + 80 [/tex]. This is equation 2.
Plug in (520 - r) into equation 2 to replace m:
[tex] 2(520 - r) = r + 80 [/tex]
[tex] 1040 - 2r = r + 80 [/tex]
Solve for r. Subtract 1040 from both sides:
[tex] 1040 - 2r - 1040 = r + 80 - 1040 [/tex]
[tex] - 2r = r - 960 [/tex]
Subtract r from both sides
[tex] - 2r - r = r - 960 - r [/tex]
[tex] - 3r = - 960 [/tex]
Divide both sides by -3
[tex] \frac{-3r}{-3} = \frac{-960}{-3} [/tex]
[tex] r = 320 [/tex]
To find m, plug in the value of r into equation 1.
[tex] m = 520 - r [/tex]. =>Equation 1
[tex] m = 520 - 320 [/tex]
[tex] m = 200 [/tex].
Malcom's maximum speed = m = 200 km/h
Ravi's maximum speed = r = 320 km/h
PLEASE HELP QUICK A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids. The volume of the prism is 234 cubic units. What is the height of the prism? 3 units 4 units 6 units 8 units
==========================================================
Explanation:
Let's find the area of the hexagon. It's composed of two identical (aka congruent) trapezoids.
Each trapezoid has two parallel bases of 4+4 = 8 and 5 units. The height is 3. The area of one trapezoid is
area = height(base1+base2)/2
area = 3*(8+5)/2
area = 19.5
which doubles to 2*19.5 = 39 to represent the area of the entire hexagon
--------------------------------
The volume of any prism is found through this formula
volume = (area of base)*(height of prism)
We just found the area of the base to be 39. The height is unknown, so we'll call it h. The volume is given to be 234.
We end up with this equation
234 = 39h
which solves to h = 6 after dividing both sides by 39. This prism has a height of 6 units.
The height of the prism is 6 units
What is Hexagonal prism?The hexagonal prism is a prism with hexagonal base.
What is isosceles trapezoid?An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
What is Volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Given,
Each hexagon is made from two congruent isosceles trapezoids
Therefore
Area of one isosceles trapezoids = [tex](a+b).(\frac{h}{2} )[/tex]
where,
a =4+4 = 8 units
b = 5 units
h = 3 units
Area of one isosceles trapezoids =[tex](8+5)(\frac{3}{2} )[/tex] =19.5 unit square
Area of the hexagon = Area of two isosceles trapezoids
Area of hexagon = 2× 19.5 = 39 unit square
We know that,
Volume = Base area × Height
Volume = 234 cubic units
234 = 39 × h
h = [tex]\frac{234}{39}[/tex] = 6 units
Hence, the height of the prism is 6 units
Learn more about Hexagonal prism, Isosceles trapezoids and Volume here
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Use the difference of squares identity to write this polynomial expression in factored form : 9x^2-49
Answer:
The expression in factored form is (3x - 7)(3x + 7)
Step-by-step explanation:
Here in this question, we are interested in using the difference of two squares to factor the given expression.
Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.
By using the difference of two squares;
a^2-b^2 can thus be written as;
(a-b)(a + b)
Now, we can apply same approach to the problem at hand.
9x^2 - 49
kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2
So applying what we have said earlier about difference of two squares;
9x^2 - 49 will be ;
(3x-7)(3x + 7)
Answer:
The answer is (3x - 7) (3x +7)
Step-by-step explanation:
Which expressions are factors of the quadratic function represented by this graph?
A. x and (x+6)
B. (x-6) and (x+6)
C. x and (x-6)
D. x and -6x
Answer:
C. [tex]x[/tex] and $(x-6)$
Step-by-step explanation:
The roots of the quadratic equation are $0$ and $6$.
Hence the equation is $(x-0)(x-6)=x(x-6)$
Answer:
See below
Step-by-step explanation:
PLEASE HELP!!! Jim made a table to show the length of his walking sticks.
Which walking sticks measured less than 3/5 meters? Choose 2 answers
Answer:
Stick 2: [tex] \frac{1}{2} [/tex]
Stick 3: [tex] \frac{4}{10} [/tex]
Step-by-step explanation:
To determine which of the lengths are less than ⅗ meters, you would compare each given length with ⅗ meters.
Stick 1: Comparing ⁹/10 and ⅗
Find The common denominator of both fractions. 10 is the common denominator. Multiply the numerator and denominator of ⅗ by 2 to create a fraction equivalent to ⁹/10.
Thus,
[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]
Compare the numerator of [tex] \frac{9}{10} [/tex] and [tex] \frac{6}{10} [/tex].
9 is greater than 6. This means [tex] \frac{9}{10} [/tex] > [tex] \frac{6}{10} [/tex].
Therefore, [tex] \frac{9}{10} [/tex] > [tex] \frac{3}{5} [/tex]
Stick 2: comparing ½ and ⅗
Common denominator = 10
Make both fractions equivalent to each other as follows,
[tex] \frac{1*5}{2*5} = \frac{5}{10} [/tex]
[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]
5 < 6. This means, [tex] \frac{5}{10} [/tex] < [tex] \frac{6}{10} [/tex].
Therefore, [tex] \frac{1}{2} [/tex] < [tex] \frac{3}{5} [/tex]
Stick 3: comparing ⁴/10 and ⅗
Common denominator = 10
Make the fractions equivalent as follows,
[tex] \frac{4*1}{10*1} = \frac{4}{10} [/tex]
[tex] \frac{3*2}{5*2} = \frac{6}{10} [/tex]
4 < 6. This means, [tex] \frac{4}{10} [/tex] < [tex] \frac{6}{10} [/tex].
Therefore, [tex] \frac{4}{10} [/tex] < [tex] \frac{3}{5} [/tex]
Stick 4: comparing ⅘ and ⅗
Common denominator = 5
Since both denominators are already the same, both fractions are equivalent. Comparing their numerator, 4 > 3. Therefore, ⅘ > ⅗.
Please answer this question now
Answer:
1001.66 in²
Step-by-step explanation:
radius=r=diameter/2
r=22/2=11
l is the slant =18
surface area of a cone= area of circle + area of the curved part of cone
SA=πr²+πrl
SA=3.14(11)²+3.14(11)(18)=1001.66 in²
If f(x) is a linear function, f(3)=1 and f(2)=5, what is the y-intercept? A) -4 B) 1 C) 3 D) 11 E) 13
Step-by-step explanation:
let the function be $y=mx+c$ since it is linear.
1=3m+c
and
5=2m+c
solve c to get the y intercept
David is buying a cheese wheel priced at 650 before tax. The store charges 8%, percent sales tax.
What is the total price, including tax, David pays for the cheese wheel?
Answer:
....the answer is 682.5
Answer:
The answer is 702. Hope it helped! :D
Step-by-step explanation:
6
1 point
Label the steps in order to solve the following equation:
-11 - 5z = 6 (5z + 4)
&
1
-11 - 5z = 30z + 24
2
-35 = 352
3
-11 = 352 + 24
4
-1=2
Answer:
swap the middle two steps to put them in order
Step-by-step explanation:
The steps in order would be ...
-11 -5z = 30z +24 . . . . . eliminate parentheses-11 = 35z +24 . . . . . . . . add 5z-35 = 35z . . . . . . . . . . . . subtract 24-1 = z . . . . . . . . . . . . . . . . divide by 2what is the diameter of a circle with 28.26 as the area
Answer:
6
Step-by-step explanation:
are=A=πr2
28.26/3.14=9
√9=3
3•2=6
Answer:
6
Step-by-step explanation:
Area = πr^2
r = √(area/π)
r = √(28.26/3.14)
r = 3
and we know that,
d = 2r,
d = 2 x 3 = 6
The town of Madison has a population of 25000. The population is increasing by a factor of 1.12 each year. Write a function that gives the population P(t) in Madison t years from now. Do not use commas in your answer. P(t)=
Answer:
P(t)=25000(1.12)^t
Step-by-step explanation:
only answering so i can go back to not watching ads :/ but hope u dont get it wrong even tho i gave right answer
Answer:
P(t) = 25000 x 1.12^t
Step-by-step explanation:
25000 times 1.12 because it is increasing by a factor of 1.12.