(i) The product of the two expressions is equal to the product of their factors. (ii) The product of the two expressions is equal to the product of their H.C.F. and L.C.M. 2.
Answer:
12 × 15
15×12
9 ×20
Ans=180
A gym has yoga classes. Each class has students. If there are classes, write an equation to represent the total number of students taking yoga.
Answer:
s = 14c
Step-by-step explanation:
Hi can someone please help me.
The bases of a right triangle measure x-3 and x+4. If the hypotenuse of the triangle is 2x-3, what is the length of the hypotenuse?
Answer:
13 units.
Step-by-step explanation:
By Pythagoras:
(x -3)^2 + (x + 4)^2 = (2x - 3)^2
x^2 - 6x + 9 + x^2 + 8x + 16 = 4x^2 -12x + 9
4x^2 - x^2 - x^2 + 6x - 8x - 12x + 9 - 9 - 16 = 0
2x^2 -14x - 16 = 0
2(x^2 - 7x - 8) = 0
2(x -8)(x + 1) =0
x = 8, -1.
As x must be positive we take x = 8
So the hypotenuse is 2(8) - 3 = 13 units long.
What are the values of sin α and tan α, if α is an acute angle in a right triangle: cosα= 5/13
Answer:
sin = 12/13 and tan = 12/5
The value of sin α will be 12/13 and tan α will be 12/5 for the given triangle such that cosα= 5/13.
What is a trigonometric function?Trigonometric functions are functions for right angle triangle which gives the relation between the angle and sides of the triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
The trigonometric functions are found in the four quadrants, as well as their graphs, domains, and differentiation and integration.
We know that
sin²α + cos²α =1 ⇒ sin²α = 1 - cos²α
Given that cosα = 5/13 so by putting it
sin²α = 1 - (5/13)²
sin²α = 144/169 ⇒ sinα = 12/13.
Now since tanα = sinα /cosα
tanα = (12/13) ÷ ( 5/13)
tanα = 12/5.
Hence the value of sinα will be 12/13 and tanα will be 12/5.
For more information about the trigonometric function
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Jo paints some tennis balls and puts them in a bag. She picks a ball at random from the bag and replaces it. She repeats this 60 times, and gets a ball not painted 50 times. Find the experimental probability of getting a painted ball from Jo's bag.
Answer:
1/6
Step-by-step explanation:
An experimental probability is the number of times an event occurred when actually attempted.
So, if Jo does the experiment 60 times and receives 50 unpainted balls, then calculate how many painted balls she got:
60-50 = 10.
So, the probability of picking a painted ball = 10/60 = 1/6
Hope this helps
Joe had 21 pennies, but then he lost 11 pennies. His friend gave him 5 more pennies. How many pennies does Joe have now?
Answer:
15 pennies
Step-by-step explanation:
lost means subtract and gave him means add
21 -11 +5
15
Answer:
15 pennies
Step-by-step explanation:
You can start by saying that after losing 11 pennies from his original amount it is 21-11, which equals to 10.
THen the question says that his friend gives him an additional 5 pennies, which is shown by 10+5=15
THerefore, all you had to do was use the information given and add or subtract the number of pennies from the original.
Answer: 15 pennies
Hope this helped
evaluate 2x squared -1 when x=3
Hey there! :)
Answer:
17.
Step-by-step explanation:
Given:
f(x) = 2x² - 1
Substitute in 3 for x:
f(3) = 2(3)² - 1
f(3) = 2(9) - 1
Simplify:
f(3) = 18 - 1
f(3) = 17.
between which to whole numbers does the square root of 37 lie?
Between 6 and 7
6×6=36
7×7=49
hopefully this helped
The number √37 is lies between whole numbers 6 and 7.
We have to given,
A number is, √37
By the definition of square root, we get;
⇒ √37 = 6.08
And, We know that,
Number 6.08 is lies between whole number 6 and 7.
Hence, We get;
⇒ 6 < √37 < 7
Therefore, The number √37 is lies between whole numbers 6 and 7.
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Simplify the radical /81d^6.
O 9d2
81d3
O 9d3
O 906
Answer:
The answer is option C.
Step-by-step explanation:
[tex] \sqrt{ {81d}^{6} } = \sqrt{81} \times \sqrt{ {d}^{6} } \\ = 9 {d}^{3} [/tex]
Hope this helps you
Answer:c
Step-by-step explanation:
ayuda porfa se ruego :b
Answer:
b) 5u.
Step-by-step explanation:
El triangulo es 45-45-90, entonces los dos lados son iguales. Si un lado es 8u, el otro lado tambien es 8u.
Entonces, 8u + x = 13u.
x = 13u - 8u
x = 5u
Espero que esto te ayude!
Write the rule for finding the coordinates of a point that has undergone a dilation (with the origin as the point of dilation). Use this rule to find the coordinates of this point's dilation from the origin, with a scale factor of 3: (4, 10).
Answer:
(12, 40)
Step-by-step explanation:
The first thing is to assume that we have a point with the following coordinates (x, y).
Now, we can have two different cases since the meaning of the expansion of a point is moving to a new point that is a greater distance from the origin if we are expanding by a value, that is, an integer in the system of coordinates and the other case is that if we are dilating by a fraction that is between 0 <x <1, then the distance from the origin decreases.
Now, the point (x, y) goes through an expansion by a scale factor f (with the origin as the expansion point), then the new coordinate of the point = [f * x, f * y], that scale factor has the value of 3, so if we replace we have:
(3 * 4, 4 * 10) = (12, 40)
solve with ans : the compound interest of a sum of money in 1 years and 2 years are Rs 450 and Rs 945 respectively. find the rate of interest compounded yearly and the sum .
Answer:
The rate of interest compounded yearly =10%The sum compounded is Rs4,500Step-by-step explanation:
Compound Interest Formula, Amount, [tex]A(n)=P(1+r)^n[/tex]
Interest=Amount - Principal
[tex]I=P(1+r)^n-P[/tex]
At the end of 1 year, interest =Rs450, therefore:
[tex]450=P(1+r)-P\\450=P+Pr-P\\450=Pr[/tex]
At the end of 2 years, interest =Rs945, therefore:
[tex]945=P(1+r)^2-P\\945=P(1+r)(1+r)-P\\945=P(1+r+r+r^2)-P\\945=P(1+2r+r^2)-P\\945=P+2Pr+Pr^2-P\\945=2Pr+Pr^2[/tex]
Recall: Pr=450
Therefore:
[tex]945=2(450)+Pr^2\\945-900=Pr^2\\Pr^2=45[/tex]
Comparing Pr=450 and [tex]Pr^2=45[/tex]
[tex]\dfrac{Pr^2}{Pr}= \dfrac{45}{450}\\r=0.1[/tex]
Substitute r=0.1 to obtain P
0.1P=450
P=Rs4500
Therefore:
The rate of interest compounded yearly =0.1=10%The sum compounded is Rs4,500What’s the value of 9 percent
Answer:
Hey!
Well because you havent really specified the question...
I have given you 9% of different numbers!
Step-by-step explanation:
9% of 1 = 0.09
9% of 10 = 0.9
9% of 100 = 9
9% of 1,000 = 90
9% of 10,000 = 900
________________
If you need more values...just let me know!
Hope this helps!
Three angles fits exactly around a point. Two of the angles are equal.The diffrence between the largest and the smallest angle is 30.Find the size ofthe three angles
Answer:
The angles are 110, 110 and 140
Step-by-step explanation:
Let the equal angles be x.
So we have angles x, x and another third one
Now, the other third angle is 30 degrees larger than x, this means that the other third angle is 30 + x
Since they are angles at a point, adding the three together will make or give 360.
Thus,
x + x + x + 30 = 360
3x + 30 = 360
3x = 360-30
3x = 330
x = 330/3
x = 110
So the other third angle is 110 + 30 = 140
So the angles are 110, 110 and 140
explain me step by step plz
Answer:
28
Step-by-step explanation:
We know that the heights and bases of all of the parallelograms will be the same because they are equal, therefore, since the height of 2 parallelograms is 14, the height of one parallelogram is 14 / 2 = 7. Since the areas of all of the parallelograms are congruent, the area of one parallelogram is 308 / 4 = 77. The parallelogram area formula is A = bh where A, b and h are area, base and height respectively and we know both the area and height so we need to solve for b. Doing so we get 77 = b * 7 so that means b = 11. The length of y is two bases + 6 and since we know the base is 11, y = 11 * 2 + 6 = 22 + 6 = 28.
Answer:
28 cm
Step-by-step explanation:
The 4 parallelograms are congruent.
The height and base of each parallelogram are equal.
[tex]h=\frac{14}{2}[/tex]
[tex]h=7[/tex]
Area of each parallelogram:
[tex]A=\frac{308}{4}[/tex]
[tex]A=77[/tex]
Apply the formula for the area of a parallelogram.
[tex]A=bh[/tex]
[tex]b=base\\h=height[/tex]
Solve for base.
[tex]77=b(7)[/tex]
[tex]\frac{77}{7} = b[/tex]
[tex]11=b[/tex]
The sum of 2 bases of the 2 parallelograms and 6 centimeters is the value of y.
[tex]y=11+6+11[/tex]
[tex]y=28[/tex]
Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer:
answer a is correct
Step-by-step explanation:
Answer: A. 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
Step-by-step explanation: On Edge!!!!!!!!!!!
Which is the graph of f(x)=sqrt x?
Answer:
B
Step-by-step explanation:
a parabola would be x2 since it is square rooted it would be a curved so the answer would be the second graph
Three solid shapes A,B and C The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of shape B to the volume of shape C is 27 : 125 Work out the ratio of the height of shape A to the height of shape C
Answer:
9:20
Step-by-step explanation:
Given:
Surface area of shape A = 9 cm²
Surface Area of shape B = 16 cm²
Ratio of volume of shape A to B = 27:125
Required:
Find the ratio of the height of shape A to the height of shape C.
Ratio of surface area (A:B)² = ratio of linear measures (A:B)
Thus,
(A:B)² = (A:B)
(A/B)² = (A/B)
[tex] (\frac{A}{B})^2= (\frac{9}{16}) [/tex]
Take the square root of both sides:
[tex] (\sqrt{\frac{A}{B}})^2 = (\sqrt{\frac{9}{16}}) [/tex]
[tex] \frac{A}{B} = \frac{3}{4}[/tex]
Ratio of volume of shape B to C = 27:125
Thus,
(B:C)³ = 27:125
[tex] (\frac{B}{C})^3= (\frac{27}{125}) [/tex]
Take the cube root of both sides:
[tex](3\sqrt{\frac{B}{C}})^3 = (3\sqrt{\frac{27}{125}})[/tex]
[tex] \frac{B}{C} = \frac{3}{5}[/tex]
Therefore, ratio of lengths A:B:C =
3:4:C
A:3:5
To make them equivalent, we have:
9:12:C
A:4:20
Therefore, the ratio of the height of shape A to the height of shape C =
9:20
Point AAA is at {(-6,-5)}(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and point CCC is at {(4,0)}(4,0)left parenthesis, 4, comma, 0, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that the ratio of ABABA, B to BCBCB, C is 2:32:32, colon, 3.
Answer:
B(-2,-3).
Step-by-step explanation:
The given points are A(-6,-5) and C(4,0).
We need to find the coordinates of point B on segment AC such that AB:BC=2:3.
It means point B divides the line segment AC in the ratio of 2:3.
Section formula: If a point divide a line segment in m:n, then
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Using section formula, the coordinates of point B are
[tex]B=\left(\dfrac{2(4)+3(-6)}{2+3},\dfrac{2(0)+3(-5)}{2+3}\right)[/tex]
[tex]B=\left(\dfrac{8-18}{5},\dfrac{0-15}{5}\right)[/tex]
[tex]B=\left(\dfrac{-10}{5},\dfrac{-15}{5}\right)[/tex]
[tex]B=\left(-2,-3\right)[/tex]
Therefore, the coordinates of point B are (-2,-3).
Answer:
Therefore, the coordinates of point B are (-2,-3).
Step-by-step explanation:
Simple and easy question
please help
Answer:
Volume = πr²h
= 3.14 * 5² * 4
= 314 cubic yards
Answer:
[tex]314 yd^3[/tex]
Step-by-step explanation:
Hey there!
Volume = π r^2 h
Plug in,
(3.14)(5^2)(4)
5•5 = 25
25 • 4 = 100
3.14 • 100
= 314
Hope this helps :)
3/4, 1, 4/3, 16/9,... which of the following are recursive formulas for the nth term of the following geometric sequence?
Answer:
nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]
Step-by-step explanation:
nth term of geometric sequence = a(n)
nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]
Where,
a = first term
r = common ratio
n = number of term
So,
GP: 3/4, 1, 4/3, 16/9
a = 3/4
r = 1 / [3/4] = 4/3
n = n
nth term of geometric sequence = a(n) = [tex]ar^{n-1}[/tex]
nth term of geometric sequence = a(n) = [tex](3/4)(4/3)^{n-1}[/tex]
PLEASE help me with this question!!!!!!
Answer:
270[tex]\sqrt{3}[/tex] cm³
Step-by-step explanation:
A regular hexagon can be cut into 6 equilateral triangles.
The area (A) of an equilateral triangle can be calculated as
A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ← where s is the side length, here s = 6
A = [tex]\frac{6^2\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] cm² ← multiply by 6
area of base = 6 × 9[tex]\sqrt{3}[/tex] = 54[tex]\sqrt{3}[/tex] cm²
The volume (V) of the prism is calculated as
V = area of base × height = 54[tex]\sqrt{3}[/tex] × 5 = 270[tex]\sqrt{3}[/tex] cm³
The company recently reduced its production to 1 million bicycles, but maintained its profit of 30 million dollars. What greater number of bicycles had the company previously produced to make the same profit? Round your answer to the nearest tenth.
Answer:
1.3 million bicycles!
Step-by-step explanation:
Answer:
1.3 million bicycles
Step-by-step explanation:
got it right on edge 2020
The parallelogram is rotated 90° anticlockwise about point G
Which of the points A , B , C and D is the image of point R ?
Answer:
C
Step-by-step explanation:
Let's say that point G is the origin, (0,0). Then, the coordinates of point R would be (-3, -5). Rotating the point 90° counter-clockwise would result in the final coordinates being (5, -3), therefore the answer is C.
Which explains how to find the radius of a circle whose equation is in the form x2 + y2 = z? The radius is the constant term, z. The radius is the constant term, z, divided by 2. The radius is the square root of the constant term, z. The radius is the square of the constant term, z.
Answer:
The radius is the square root of the constant term, z
Step-by-step explanation:
makes sense, also took the test :)
Answer:
C. The radius is the square root of the constant term, z.
Step-by-step explanation:
Hope this helps :)
PLEASEEE HELPPP IT DUE TODAYYY
Answer:
All angles in a rectangle are congruent, because in a rectangle, all angles are 90 degrees.
$15.30 for 3 small pizzas
Answer:
$5.1
Step-by-step explanation:
If it costs $15.30 for 3 pizzas, then we can divide 15.30 by 3 to get $5.1. This concludes that the cost for one pizza is $5.1.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
solve for x -48=6(x-3)
Answer:
[tex]\boxed{x = -6}[/tex]
Step-by-step explanation:
[tex]x-48 = 6(x-3)[/tex]
Resolving parenthesis
[tex]x - 48 = 6x-18[/tex]
Adding 18 to both sides
[tex]x-48+18 = 6x\\x-30 = 6x[/tex]
Subtracting x from both sides
[tex]-30 = 6x-x\\-30 = 5x[/tex]
Dividing both sides by 5
[tex]-30/5 = x[/tex]
[tex]-6 = x\\[/tex]
OR
x = -6
Answer:
x = - 6Step-by-step explanation:
x - 48 = 6(x - 3)
Expand the terms in the bracket
That's
x - 48 = 6x - 18
Group the constants at the right side of the equation and the ones with variables at the left side
x - 6x = 48 - 18
- 5x = 30
Divide both sides by - 5
x = - 6Hope this helps you
.Write the following number in the standard form. a) 0.000000012
Answer:
[tex]1.2 * 10 ^{-8}[/tex]
Step-by-step explanation:
=> 0.000000012
Moving the decimal point after 1st non-zero digit:
=> [tex]1.2 * 10 ^{-8}[/tex]
Answer:
Scientific Notation: 1.2x10^-8, or 1.2e-8
Step-by-step explanation:
fractorise the following (a-b)²+(a-b)
Step-by-step explanation:
taking common (a-b)
so we get the answer
ok I need help with this cylinder volume thing
ok so the volume is 20litres and the diameter is 13.5 but I need to find the length value. Length value needs to be in metres
Answer:
h = 0.139725
Step-by-step explanation:
Volume of a Cylinder Formula: V = πr²h
You are given V = 20 and r = 6.75.
20 = π(6.75)²h
20/45.5625π = h
h = 0.139725
I'm not sure if this is correct or not.
Answer:
≈1.4 m
Step-by-step explanation:
V= 20 l= 20 000 cm³
d= 13.5 cm ⇒ r= 13.5 cm / 2= 6.75 cm (assume it is cm)
V= πr²h
h= V/πr²= 20000/3.14*6.75² ≈ 140 cm= 1.4 m