The concept of greatest common factor is used to solve this question. Then, we use it to find the number of crackers and slices of cheese, and the answer is:
The greatest number of plates you can prepare is 6.Each plate will have 3 crackers.Each plate will have 2 slices of cheese.--------------------------------
To find the greatest number of plates, you need to find the greatest common factor between 12 and 18.
Thus, factoring them, always by the same number:
12 - 18|2
6 - 9|3
2 - 3
The greatest common factor is 2x3 = 6, which means that the greatest number of plates you can prepare is 6.
--------------------------------
18 crackers, so each plate has 18/6 = 3 crackers.
12 slices of cheese, so each plate has 12/6 = 2 slices of cheese.
A similar question is given at https://brainly.com/question/18454593
Select the equivalent expression.
(x^-3*y^3)^-7=?
Choose 1 answer:
Answer:
The equivalent expression for this equation is x²¹ × y⁻²¹
Step-by-step explanation:
When you are multiplying exponents that are in parentheses, you multiply the exponential numbers together. So, for this problem, we will multiply the exponents together so we can get our final equivalent expression.
(x⁻³ × y³)⁻⁷
So, we will multiply -3 by -7 and we will also multiply 3 by -7 because those are our exponential numbers.
x²¹ × y⁻²¹
So, this is the final expression that is equivalent to our equation.
The expression (x⁻³.y³)⁻⁷ is equivalent to x ²¹ . y ⁻²¹.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given expression is,
(x⁻³.y³)⁻⁷
To find the solution for the expression,
Simplify the power terms,
x⁽⁻³ˣ⁻⁷⁾ . y ³ˣ⁻⁷
x ²¹ . y ⁻²¹
The simplified form of the expression (x⁻³.y³)⁻⁷ is x ²¹ . y ⁻²¹.
Hence, option (A) is correct.
To know more about Algebra on:
https://brainly.com/question/24875240
#SPJ2
The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per hour. When the base is 9 meters and the height is 22 meters, then how fast is the HYPOTENUSE changing
Answer:
dL/dt = - 2,019 m/h
Step-by-step explanation:
L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse
If the base of the triangle, let´s call x is increasing at the rate of 2 m/h
then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h
If we take differentials on both sides of the equation (1)
2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt
L*dL/dt = x*dx/dt + y*dy/dt (2)
When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:
L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77
Therefore we got all the information to get dL/dt .
L*dL/dt = x*dx/dt + y*dy/dt
23,77 * dL/dt = 9*2 + 22* ( - 3)
dL/dt = ( 18 - 66 ) / 23,77
dL/dt = - 2,019 m/h
Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.
The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:
[tex]h^2 = x^2 + y^2[/tex]
In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:
[tex]h^2 = 9^2 + 22^2[/tex]
[tex]h = \sqrt{9^2 + 22^2}[/tex]
[tex]h = 23.77[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Simplifying by 2:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].
We want to find [tex]\frac{dh}{dt}[/tex], hence:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]
[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]
[tex]\frac{dh}{dt} = -2.02[/tex]
The hypotenuse is changing at a rate of -2.02 meters per hour.
A similar problem is given at https://brainly.com/question/19954153
helphelphelphelphelphelp
Answer:
see image
Step-by-step explanation:
If 1 angle is four time of another angle in linear pair find the angles. Please do it fast as you can
Answer:
let the angle be x then other angle is 4x
so,
x + 4x = 180
5x = 180
x = 36
so other angle I.e 4x = 4 × 36 = 144
Let one angle be x
Other angle=4xBoth are linear pair hence their sum will be 180
[tex]\\ \sf \longmapsto x+4x=180[/tex]
[tex]\\ \sf \longmapsto 5x=180[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{180}{5}[/tex]
[tex]\\ \sf \longmapsto x=30[/tex]
[tex]\\ \sf \longmapsto 5x=5(30)=150[/tex]
Two trees are leaning on each other in the forest. One tree is 19 feet long and makes a 32° angle with the ground. The second tree is 16 feet long. What is the approximate angle, x, that the second tree makes with the ground? A 0.6° B 35.0° C 39.0° D 58.0°
Answer:
C 39.0
Step-by-step explanation:
To find the approximate angle, x, that the second tree makes with the ground, we can use the concept of similar triangles Therefore the correct option is B.
Let's calculate the height of the first tree using the given information. We can use the formula for the opposite side in a right triangle: opposite = adjacent * tan(angle). Therefore, the height of the first tree is approximately [tex]19 * tan(32°) = 19 * 0.6249 ≈ 11.873[/tex] feet. Now, we can set up a proportion between the two trees based on their heights. Let x be the angle the second tree makes with the ground.
We have the following proportion: (height of first tree)/(height of second tree) = (length of first tree)/(length of second tree). Substituting the known values, we have [tex]11.873/16 = 19/x[/tex]. Cross-multiplying gives us [tex]11.873x = 304,[/tex] and dividing both sides by 11.873 yields[tex]x ≈ 25.63°.[/tex] The approximate angle, x, that the second tree makes with the ground is closest to 35.0°.
Hence the correct option is B
To know more about triangle visit:
https://brainly.com/question/30966657
#SPJ2
Find the square root of 7250 by prime factorisation.
Answer:
The square root of 7250 is 85.15
Step-by-step explanation:
[tex]{ \boxed{ \sf{7250}}} \\ ↓ \div 2 \\ { \boxed{ \sf{3625}}} \\ ↓ \div 5 \\ { \boxed{ \sf{725}}} \\ ↓ \div 5 \\ { \boxed{ \sf{145}}} \\ ↓ \div 5 \\ { \boxed{ \sf{29}}}[/tex]
Find square roots of divisors:
[tex]{ \sf{ = \sqrt{2} \times \sqrt{5 \times 5 \times 5} \times \sqrt{29} }} \\ = { \sf{ \sqrt{2} \times \sqrt{125} \times \sqrt{29} }} \\ = { \sf{85.15}}[/tex]
[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]
Which system of equations is represented by the graph?
Answer:
[tex]y=x\\\\y=\dfrac{-x+10}{x-4}[/tex]
Step-by-step explanation:
Red line is increasing and for any x goes the same y, so it's y = x
The blue graph is [tex]y=\dfrac a{x-h}+k[/tex], where h=4 and k =-1 and for x=5 also y=5
It gives:
[tex]5=\dfrac a{5-4}+(-1)\\5=a-1\\a=6[/tex]
So:
[tex]y=\dfrac6{x-4}-1 =\dfrac6{x-4}-\dfrac{x-4}{x-4} =\dfrac{6-x+4}{x-4}=\dfrac{-x+10}{x-4}[/tex]
2√63 what is the radical
Answer:
7.94
Step-by-step explanation:
Answer:
[tex]\Large \boxed{\sqrt{63}}[/tex]
Step-by-step explanation:
A radical is the root of a number.
[tex]2\sqrt{63}[/tex]
The radical in this expression is [tex]\sqrt{63}[/tex].
2x squared minus 1 equals 21
Answer:
x = √11
Step-by-step explanation:
2x² - 1 = 21
add 1 to both sides
2x² - 1 + 1 = 21 + 1
simplify
2x² = 22
x² = 22 / 2
x = √11
Answer:
x = √11
Step-by-step explanation
2x² - 1 = 21
negative sign crossing an equal to sign becomes a positive sign
2x² - 1 = 21 + 1
2x² = 22
x² = 22 / 2
x = √11
What is a negative rational number times a positive integer?
A) A negative integer
B) A positive rational number
C) A negative rational number
D) An irrational number
Answer:
C
Step-by-step explanation:
The product of a negative rational number and a positive integer is a negative rational number
Answer: C (A Negative Rational Number)
Step-by-step explanation
A Negative number mutiplied by a positive number is a negative number.
Please click thanks and mark brainliest if you like
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 4 comma negative 3 up to the right through the point 5 comma 0
R colon open bracket y is an element of all real numbers close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to 5 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 4 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
Answer:
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
a 6 foot tall man casts a shadow that is 9 ft long. At the same time, a tree nearby casts a 48 ft shadow. how tall is the tree
Answer:
32 ft tall
Step-by-step explanation:
Since a 6 ft man casts a shadow 9 ft long, the shadow is 3/2 of the actual object/person.
SINCE THE TREE'S SHADOW IS AT THE SAME TIME, THE HEIGHT IS THE SAME RULE.
We know the tree's shadow is 48 ft.
--> 48/3 = 16
16 x 2 = 32
32 ft tall
Hope this helps!
Answer: 32ft tall
Step-by-step explanation:
Please solve, -37-2v= -6(2v-3)-5
Answer:
[tex]\huge\boxed{v=5}[/tex]
Step-by-step explanation:
[tex]-37-2v=-6(2v-3)-5\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\-37-2v=(-6)(2v)+(-6)(-3)-5\\\\-37-2v=-12v+18-5\\\\-37-2v=-12v+(18-5)\\\\-37-2v=-12v+13\qquad\text{add 37 to both sides}\\\\-37+37-2v=-12v+13+37\\\\-2v=-12v+50\qquad\text{add}\ 12v\ \text{to both sides}\\\\-2v+12v=50\\\\(-2+12)v=50\\\\10v=50\qquad\text{divide both sides by 10}\\\\\dfrac{10v}{10}=\dfrac{50}{10}\\\\v=5[/tex]
Answer:
v = 5
Step-by-step explanation:
-37 -2v = -6 (2v - 3) - 5
-2v - 37 = -6 (6*2v - 6*3) - 5
-2v - 37 = - (12v - 18) - 5 combine like terms
-37 - 18 + 5 = -12v + 2v
-50 = -10v
v = -50 / -10
v = 5
One day, 45 frogs were captured from a pond, marked and then returned to the pond. The next day, 40 frogs were observed in the pond, of which 10 had been marked the previous day. Assuming the marked frogs are equally distributed among all the frogs in the pond, what is the best estimate of how many frogs live in the pond
Answer:
45
Step-by-step explanation:
estimate
find the missing part of the proportion 12/x = 3/7 x= _
Answer:
x = 28
Step-by-step explanation:
12/x = 3/7
Using cross products
3x = 12*7
3x = 84
Divide by 3
x = 28
how does translation affect the properties of a two-dimensional figure? please i need help
Answer:
It affects the location of the shape and how the shape looks. It doesn't affect the area or perimeter though.
Step-by-step explanation:
how many are 3 raised to 2 ???
Answer:
[tex]\huge \boxed{9}[/tex]
Step-by-step explanation:
3 raised to 2 is 3 to the power of 2.
[tex]3^2 =3 \times 3 = 9[/tex]
3 is multiplied by itself.
Cylinder A has a radius x and height y. Cylinder B has radius y and height x. What is the ratio of the volume of Cylinder A to the volume of cylinder B
Answer:
Step-by-step explanation:
Draco is a daddy’s boy
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.
Make up an expression of your own that satisfies the following:
Must have at least: 4 terms, 1 constant, 2 variables with coefficients and appropriate
operation signs.
There are infinitely many ways to answer this as there is no one single answer to pick from.
Here is one possible answer: x^3 + 5x^2 + 7x + 12The four terms are x^3, 5x^2, 7x and 12. They are separated by the plus signs.
The constant is 12. It does not have any variable attached to it.
Terms 5x^2 and 7x have coefficients of 5 and 7 respectively.
The leading term x^3 has a coefficient of 1, but 1*x^3 = x^3, meaning it's convention to leave the 1 out. So technically x^3 does not have a coefficient directly written/shown. Instead, its more implied.
Find all positive integers less than 100 whose 762nd power ends in the digits "41"
Answer:
21, 29, 71, 79
Step-by-step explanation:
Only integers ending in 1, 3, 7, or 9 have powers that end in 1. For the numbers so ending, their sequences of powers mod 100 have a repeat length that is a divisor of 20. That is, raising any of these numbers to the 762nd power mod 100 is equivalent to squaring them, mod 100.
For example, the powers of 29 mod 100 are, beginning with the first power, ...
{29, 41, 89, 81, 49, 21, 9, 61, 69, 1}
This sequence is of length 10, typical of many of the numbers ending in 1, 3, 7, or 9.
The only positive integers less than 100 whose squares end in 41 are ...
21, 29, 71, 79 . . . . . positive integers < 100 satisfying n^762 mod 100 = 41
A. 4
B.-1/4
C. 4
D. 1/4
45 laboures can repair a road in 24 days .how many labourers should be added to repair the road in 20 days
Answer:
here's your answer .Hope you will understand it.
Answer:
9
Step-by-step explanation:
hope it will help good day.
find the product of the first 3 positive integers and then the first 5 negative integers.
Answer:
6 and -120
Step-by-step explanation:
The first 3 positive integers are 1, 2 and 3 and their product is 6, the first 5 negative integers are -1, -2, -3, -4 and -5 and their product is -120.
What is the difference between {2,3} and {{2,3}}
[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3
[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]
#1 why is it B？
No idea someone help plz
Answer:
Option (B)
Step-by-step explanation:
1). Given function is,
[tex]f(x)=\frac{1}{x-1}+3[/tex]
It the given function 'f' is transformed by a translation of 2 units to the right, the new function will be,
h(x) = f(x - 2)
h(x) = [tex]\frac{1}{(x-2)-1}+3[/tex]
= [tex]\frac{1}{x-3}+3[/tex]
Further the new function is translated by 6 units down,
g(x) = h(x) - 6
g(x) = [tex]\frac{1}{x-3}+3-6[/tex]
= [tex]\frac{1}{x-3}-3[/tex]
Since, transformed function 'g' passes through a point (x, -2),
g(x) = [tex]\frac{1}{x-3}-3[/tex]
-2 = [tex]\frac{1}{x-3}-3[/tex]
3 - 2 = [tex]\frac{1}{x-3}[/tex]
x - 3 = 1
x = 4
Therefore, Option (B) will be the answer.
if ABCD is a square where A(-4;2) B(-2;-1) C(1;1) , determine the coordinates of of D
Answer:
(4;-1)
Step-by-step explanation:
A cartoon has a length of 1 2/3 feet, width of 1 1/6 feet, and height of 1 1/5 feet what is the volume of the cartoon?
A: 2 cubic feet
B: 2 1/3
C: 4 cubic feet
D: 4 2/3
(I'm so confused please help)
Suppose M is the midpoint of XY. If XM = 2x + 11 and MY = 5x - 16, find the value of X.
A) x = -4
B) x = 4
C) x = -9
D) x = 9
E) x = 2
My math:
2x + 11 = 5x + 16
(-5x and -11 from both sides)
-3x=5
(divide -3 on each side)
x=-5/3
But it isn't an option, so I don't know.
Answer:
D
Step-by-step explanation:
Instead of 2x + 11 = 5x + 16, you should have put 2x+11 = 5x - 16. There is a sign change right before the 16, and you may have accidentally written down +16 instead of -16. I think that's where the problem is.
2x + 11 = 5x - 16
subtract 5x from both sides to make all variables on one side
-3x + 11 = -16
subtract 11 from both sides to isolate the x and its coefficient
-3x = -27
divide both sides by -3 to isolate x
x = 9
I DON'T WANT TO BE HOMESCHOOL I WANT REAL SCHOOL SO OPEN BACK UP
Answer:
I agree.
Step-by-step explanation:
Where I am, our parents had a choice, to chose whether they wanted us to go back to school or to do it online, and my grandma has me down for online, and I hate it so much.