13000 divided by 3000 = 4.33 repeating meaning the 33 keps going like 4.33333333333333333333333333333333333333333333333333
what did the mathematization do to practice over winter break
What is the second term in the binomial expansion of (2r – 3s)12?
–73,728r11s
73,728r11s
608,256r10s2
–608,256r10s2
The second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
(2r - 3s)¹²
Using nth term of the binomial expansion is:
= C (12, 2-1) (2r)¹²⁻²⁺¹ (-3s)²⁻¹
After solving
= -73728 r¹¹ s
Thus, the second term in the binomial expansion of (2r - 3s)¹² is -73728 r¹¹ s option (A) is correct.
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help me pleaseee pleaseee pleaseee for a lot of points
Answer:
53 5/7
Step-by-step explanation:
2 + 5/21 = (42 +5)/21 = 47/21
47/21 : 1/12 = x : 2
x = 2 * 47/21 / 1/12
x = 2 * 47/21 * 12
x = 2 * 47/7 * 4
x = 8 * 47/7
x = 376/7
x = 371/7 + 5/7
x = 53 5/7
Which expression is equivalent to (7x3)?(x8)2?
A
14x10
B
49x10
C
14x'
D 49x’
The expression equivalent to 7x³ × (x⁸) × 2 is 14x¹¹.
How to find an equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are the same.
Therefore,
7x³ × (x⁸) × 2
Using the law of indices,
[tex](x^{a}) (x^{b} ) = x^{a+b}[/tex]
Hence,
7x³ × (x⁸) × 2 = 7x³ × 2x⁸
7x³ × 2x⁸ = 14x¹¹
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Find two positive numbers whose difference is 23
23
and whose product is 3408
3408
The two positive numbers are 71 and 48
How to calculate for the two positive numbersWe shall apply algebra in finding the unknown numbers as follows;
Let us represent the two numbers with the letters x and y
so that;
x - y = 23...(1)
xy = 3408...(2)
from equation (1),
x = 23 + y {adding y to both sides}
putting the value 23 + y for x in equation (2) we get;
(23 + y)y = 3408 {by expansion}
23y + y² = 3408
y² + 23y - 3408 = 0 {we rearrange to get a quadratic equation}
we factorize as follows;
y² + 48y - 71y - 3408 = 0
y(y + 48) - 71(y + 48) = 0
(y + 48)(y - 71) = 0
so by factorization; y = -48 or y = 71
the numbers are positive hence we take y = 71
putting the value 71 for y in equation (2) we get;
x71 = 3408 {divide through by 71}
x = 3408/71
x = 48
Thus; 71 - 48 = 23 and 71 × 48 = 3408, and we can say that the two positive numbers are 71 and 23.
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Work
Find the radius of a square with perimeter 32cm
Answer: 5.66
Step-by-step explanation:
The perimeter of the square being 32, the sides are 8 units. The diameter of the circumscribing circle is the diagonal of the square which is 8 sec 45 = 11.3 units. Hence, the radius of the circle = 5.66 units.
Given that m_G = 81°, what is m
Answer:
180-81=
Step-by-step explanation:
A video streaming company offers two monthly plans. Plan A charges $3 per video viewed plus a flat rate of $8 per month. Plant B charges $5 per video viewed and no additional flat rate.
A write and solve an inequality to determine when the cost of viewing n videos using plan A is less that the cost of viewing n video using plan B _________________
Plan A is less expensive when ____________________
The inequality is 8 + 3 n < 5 n. Plane A is less expensive when n > 4
What is inequality ?
Inequality of wealth in major cities Economic inequality comes in many forms, but two stand out above the rest: wealth inequality as measured by the distribution of wealth and income inequality as measured by the distribution of income.
The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are universal.
Plan A: flat rate $8 per month and $3 per video viewed
Plan B: $5 per video viewed
The number of viewing videos is n
∵ The number of viewing videos is n
→ Plan A
∵ The cost per viewing is $3
∵ Cost per month is $8
∴ The cost = 8 + 3 n
→ Plan B
∵ The cost per viewing is $5
∴ The cost = 5 n
We need the cost of viewing n videos using Plan A is less than the
cost of viewing n videos using Plan B
→ Cost Plan A < Cost Plan B
∵ Cost Plan A is 8 + 3 n
∵ Cost Plan B is 5 n
∴ 8 + 3 n < 5 n
* The inequality is 8 + 3 n < 5 n
∵ 8 + 3 n < 5 n
Subtract 3 n from both sides
∴ 8 < 2 n
Divide both sides by 2
∴ 4 < n
∴ n > 4
* Plane A is less expensive when n > 4
The inequality is 8 + 3 n < 5 n. Plane A is less expensive when n > 4
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
b = 40 , c = 70
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 5x² + bx + c ← is in standard form
with a = 5 and b = b , then
x = - [tex]\frac{b}{10}[/tex]
equating to the given x- coordinate of the vertex , that is - 4
- [tex]\frac{b}{10}[/tex] = - 4 ( multiply both sides by - 10 )
b = 40
then
y = 5x² + 40x + c
substitute (- 4, - 10 ) into the equation and solve for c
- 10 = 5(- 4)² + 40(- 4) + c
- 10 = 5(16) - 160 + c
- 10 = 80 - 160 + c
- 10 = - 80+ c ( add 80 to both sides )
70 = c
then b = 40 and c = 70
What is the image of the point (-6, 2) after a rotation of 180° counterclockwise
about the origin?
Answer:
[tex](6,2)[/tex]
Step-by-step explanation:
When rotating 180° about the origin, [tex](x,y) \longrightarrow (-x, -y)[/tex].
(3×10³) (2× 10²)
Write your answer in scientific notation
pleaseeee help lol, will mark brainliest
Transforming the function f(x) = 2x by compression of a factor of 1/4 gives g(x) = 1/2x
Transformation of a FunctionTransformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f(x) = x2 + 3 is obtained by just moving the graph of g(x) = x2 by 3 units up. Function transformations are very helpful in graphing the functions just by moving/expanding/compressing/reflecting the curve without actually needing to graph it from scratch.
In the given function;
f(x)= 2x;
After a compression by a factor of 1/4, the function becomes
g(x) = 2x * 1/4 = 1/2x
The compressed function g(x) is 1/2x
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The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y=3.9x+441 , and for women, the equation is y=14.3x+312, where x is the number of years after 1970
The point (12,489) will be the solution of our given equations.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
number of men given by y=3.9x+441 ,
and for women equation is y=14.3x+312,
Now, Let us find the coordinates of the point of intersection of both lines by equating our both equations as:
3.9x+ 441 = 14.3x + 312
14.3x - 3.9x = 441 - 312
10.4x= 129
x= 129/10.4
x = 12.40
and, y= 3.9(12.4)+ 441
y= 489.36
Hence, the point (12,489) will be the solution of our given equations.
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find the slope of the line passing through the points (-6,2) and (-7, 7).
Answer:
y-2=7(x+6)
Step-by-step explanation:
You got it there bro
Find an expression which represents the sum of (7x-y) and (5x+3y) in simplest terms.
An expression that represent the sum of (7x-y) and (5x+3y) in simplest terms is 12x + 2y
How to find the sum of the expressionsThe given expressions are (7x-y) and (5x+3y)
The applying the addition property of equality we have
= (7x - y) + (5x + 3y)
= 7x - y + 5x + 3y
collecting like terms
= 7x + 5x - y + 3y
= 12x + 2y (in simplest terms)
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After reading a book for English class,100 students were asked whether or not they enjoyed it.
The number of students who like the book is 64 students.
How many students like the book?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
Given: Total students in English class = 100
Nine twenty-fifths of the class did not like the book.
Thus, the number of students did not like the book = 9/25 × 100
= 36
Therefore, the number of students like the book =Total students- students did not like the book will be:
= 100-36
= 64 students.
The number of students is 64.
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Complete question
After reading a book for English class, 100 students were asked whether or not they enjoyed it. Nine twenty-fifths of the class did not like the book. How many students liked the book?
[tex]5^{2x+1} =25[/tex]
Answer:x=1/2
Step-by-step explanation:
[tex]5^{2x+1} =5^{2}[/tex]
2x+1=2
2x=1
x=1/2
Can someone help pls it’s due in about 2 hour
Answer:
see below
Step-by-step explanation:
A
The hypotenuse is ALWAYS the longest side of a right triangle, and located Directly Across from the Right Angle: c = √79
Pythagorean Theorem: a² + b² = c²
a = 2√5
b = ?
c = √79
(2√5)² + b² = (√79)²
20 + b² = 79
b² = 59
√b² = √59
b = √59 = KJ
B
tan=opposite side / adjacent side
From I, KJ is opposite; and IK is adjacent
tan(I) = √59/(2√5) ≈ 1.72
C
cos=adjacent side / hypotenuse
From J, KJ is adjacent; and IJ is the hypotenuse
cos(J) = √59/√79 ≈ 0.86
Given f(x)=2x-2, find f(-3)
PLEASE HELP!!!!
Answer:4
Step-by-step explanation:
replace x with -3
f(x) = 2x-2
find f(-3)
f(-3) = 2(-3) - 2
f(-3) = -6 -2
f(-3) = -8
The length of a rectangle is 4 inches longer than it is wide. If the area is 32 square inches, what are the dimensions of the rectangle?
Answer:
width = 4in
length = 8in
Step-by-step explanation:
A = LxW = 32
L = W + 4
W(W+4) = 32
W² + 4W - 32 = 0
(W + 8)(W - 4) = 0
W ≠ -8 (dimensions cannot be negative)
W = 4in
L = W+4 = 4+4 = 8in
Aiden runs a farm stand that sells apples and strawberries. Each pound of apples sells
for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a
total of 35 pounds of apples and strawberries. Write a system of equations that could
be used to determine the number of pounds of apples sold and the number of pounds
of strawberries sold. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
Two friends are renting a property with a monthly rent of $975.00. The total square footage is 1,225 square feet, the first bedroom is 150 square feet, and the second bedroom is 130 square feet. Determine how much the friend with the smaller bedroom will pay for rent if they split the cost based on the square footage of each bedroom. (2 points)
$479.50
$481.35
$495.50
$501.35
Answer:
(a) $479.50
Step-by-step explanation:
You want to know how much the friend with the smaller bedroom will pay for rent if they split the $975 cost based on the square footage of each bedroom. The two bedrooms in the 1225 square foot property are 130 and 150 square feet.
SplitApparently, the cost of the non-bedroom area is to be split evenly. That common area is ...
1225 ft² -(150 +130) ft² = 945 ft²
Then the proportion due from the occupant of the smaller bedroom is ...
(945/2 +130)/1225 = 241/490 ≈ 0.49184
RentThat fraction of the rent is ...
0.49184 · $975 = $479.54
The nearest answer choice is $479.50.
__
Additional comment
If we were to assume the split is based only on bedroom size, then the rent paid for the 130 ft² space would be (13/28)($975) ≈ $452.68. This would be equivalent to splitting the rent for the common area in the same proportion as for the bedrooms.
We note that half the rent is $487.50, a number less than either of the last two answer choices. Those can be rejected for that reason. (The smaller bedroom is expected to pay less than half of the rent.)
What number makes the expressions equivalent? Enter your answer in the box.
12 (–1.4m + 0.4) =
m + 0.2
The number makes the expression equivalent is m = 0.2584.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 12(- 1.4m + 0.4) = m + 0.2.
- 16.8m + 4.8 = m + 0.2.
- 16.8m - m = 0.2 - 4.8
- 17.8m = - 4.6.
m = (-4.6/-17.8).
m = 0.2584.
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pls answerrrr correctly
The rate of change from the hour 4 to hour 7 is equal to the slope of 0 miles per hour.
How to determine the rate of change of a segment of a graph
The rate of change of a segment of a graph is represented by its slope, the slope that can be determined by the secant line formula:
m = Δd / Δt
Where:
Δd - Change in distance, in miles.Δt - Time, in hours.First, determine the coordinates of the initial and final points of the graph:
(t₁, d₁) = (4, 120), (t₂, d₂) = (7, 120)
Second, find the rate of change of the segment:
m = (120 - 120) / (7 - 4)
m = 0 mi / h
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Question
What is the value of x?
Enter your answer in the box.
x =
The value of x is 4/3
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangles be ΔRST and ΔQRT
Now , from the figure
∠S = 90° in the triangle ΔRST
And RS = 2/√3
∠T = 60° in the triangle ΔRST
Now ,
sin 60° = opposite / hypotenuse
= RS / RT
= ( 2/√3 ) / RT
We know , sin 60° = √3 / 2
Substituting the value of sin 60° in the equation , we get
√3 / 2 = ( 2 / √3 ) / RT
Multiply by RT on both sides , we get
RT x ( √3 / 2 ) = ( 2 / √3 )
Divide by ( √3 / 2 ) on both sides , we get
RT = ( 2 / √3 ) x ( 2 / √3 )
RT = 4 / 3
Therefore , the value of RT = 4/3
Now , from the figure
∠R = 90° in the triangle ΔQRT
and ∠T = 45° in the triangle ΔQRT
So ,
tan 45° = opposite / adjacent
We know tan 45° = 1
Substituting the value for tan 45° = 1 in the equation , we get
1 = opposite / adjacent
1 = x / RT
Multiply by RT on both sides , we get
x = RT
So , x = 4/3
Hence , The value of x is 4/3
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Answer:
x = 3
Step-by-step explanation:
we are here given a figure in which we have to calculate the value of x . The given figure is made up of two right angled triangles , ∆RST and ∆QRT . So , firstly in ∆RST, we have ,
sinθ = p/h = RT/RS
sinθ = RT/2√3
and here θ = 60° , so that,
sin60° = RT/2√3
√3/2 = RT/2√3
RT = 2√3 * √3/2
RT = 3 . . . . . . . (1)
again in ∆RTQ , we have;
tanθ = p/b = RQ/RT
tanθ = x/3 ( from equation 1 )
and here , θ = 45° , so that ;
tan45° = x/3
1 = x/3
x = 3
and we are done!
Equation with one solution 8x-3x+2-x=
[tex]\fbox{4x+2}[/tex]
Simplify:
[tex]8x-3x+2[/tex]
[tex]8x+-3x+2+-x[/tex]
Combine Like Terms:
[tex](8x+-3x+-x)+(2)[/tex]
[tex]4x+2[/tex]
30 Points! Tell me everything you know about congruent polygons. How can we prove that triangles are congruent?
The polygons that are congruent are those whose vertices and sides line up perfectly. The 4 triangle congruence theorems that help in finding if the triangles are congruent or not are SSS, SAS, ASA, AAS, and RHS.
Define congruent polygons.The polygons that are congruent are those whose vertices and sides line up perfectly. Congruent polygons are polygons having the same size and shape, even if they can be rotations, translations, or mirror reflections of one another. This is another way to conceive of the idea.
A triangle's congruence can be established using the triangle congruence theorem or triangle congruence criterion. The definition of congruent is "absolutely equivalent in shape and size regardless of rotation, flipping, or turning." Congruent figures are described in geometry as shapes that are superimposed on one another, such as triangles and quadrilaterals.
The following are the triangle congruence criteria that aid in demonstrating triangle congruence.
SSS (Side, Side, Side)SAS (Side, Angle, Side)ASA (Angle, Side, Angle)AAS (Angle, Angle, Side)RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)To know more about congruency, visit:
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If Karla has 3 more nickels than quarters and they have a combined value of 135 cents, how many of each coin does she have?
Answer:
Step-by-step explanation:
n=3+d
n -d = 3
5n -5d = 15
5n +10d = 135
5n - 5d = 15
15d = 120
d= 8 dimes
n = 11 nickels
5x11 + 8x10 = 55 + 80= 135
The scatter plot shows the daily oil production in
the United States in the years since 1994. The
equation y=-168x+6,750 is the trend line for the
data. According to the equation of the trend line,
how many thousands of barrels of oil will be
produced daily in the United States 6 years from
1994?
168
5.406
5.742
(3 Points)
6.750
5700
$100
$100
0
5/00
Answer:
Step-by-step explanation:
168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
The scatter plot shows the daily oil production in the United States in the years since 1994.
The equation y=-168x+6,750 is the trend line for the data.
According to the equation of the trend line, we need to find how many thousands of barrels of oil will be produced daily in the United States 6 years from 1994
In the equation y=-168x+6,750
The 168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994
Hence, 168 represents the thousands of barrels of oil will be produced daily in the United States 6 years from 1994
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Dan went for a drive in his new car. He drove at a speed of 64 miles per hour for 102.4 miles. For how many hours did he drive?
___ hours
Answer:
Step-by-step explanation:
Dan drove for 1.6 hours.
64 miles per hour (mph) is the unit rate so divide by 102.4 by 64 and you get 1.6