Expansion of x(3.25y - 4.86) is 3.25xy - 4.86x and expansion of
x(-1.75y + 5y - 3.86) + x is 3.25xy - 2.86x. The expressions are not equivalent as the coefficient of x is different in the expanded form.
What are equivalent expressions?
In expanded form, the expression combines all its like terms.
Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other.
According to the given question:
The given expressions are
1. x (3.25y - 4.86)
2. x (-1.75y + 5y - 3.86) + x
Expanding each expression
1. x (3.25y - 4.86)
= 3.25*x*y - 4.86*x
= 3.25xy - 4.86x
2. x (-1.75y + 5y - 3.86) + x
= -1.75*x*y + 5*x*y - 3.86*x + x
= 3.25xy - 2.86x
Clearly coefficient of x variable is different after expansion of expressions. Therefore, the expressions are not equivalent.
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What is 70% of 45???????
Answer: 31.5
Step-by-step explanation:
Answer:
31.5
Step-by-step explanation:
[tex]45 \times .7 = 31.5[/tex]
Baker barrowed $7,400 at 10.5% for 1/4 years. How much interest will he pay
back?
Answer: $194.25
Step-by-step explanation:
Given data
Principal= $7400
Rate= 10.5%
time= 1/4 years
The simple interest formula is given as
SI= PRT/100
substitute
SI= 7400*10.5* 0.25/100
SI= 19425/100
SI= $194.25
Hence Mark will pay $194.25
What is the total perimeter of this figure?
The compound figure formed by a square and four circular sections has an approximate perimeter of 308.496 centimeters.
How to calculate the perimeter of a compound figure
In this question we find a compound figure formed by a square with a side length of 30 centimeters and four circular sections with central angle of 270° and a radius of 10 centimeters. The perimeter of the compound figure (p), in centimeters, is the sum of the perimeter of the square and the perimeter of the four circular sections:
p = p' + 4 · p''
Where:
p' - Perimeter of the square, in centimeters.p'' - Perimeter of the circular section, in centimeters.p = 4 · (30 cm) + 4 · (3π / 2) · (10 cm)
p = 120 cm + 60π cm
p ≈ 308.496 cm
The perimeter is approximately equal to 308.496 centimeters.
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HELP ME PLEASE SOMEONE
Answer:
x = 3
Step-by-step explanation:
15x + 8 and 9x + 26 are corresponding angles and are congruent , then
15x + 8 = 9x + 26 ( subtract 9x from both sides )
6x + 8 = 26 ( subtract 8 from both sides )
6x = 18 ( divide both sides by 6 )
x = 3
Mean=3, find the probability that X is at most 3
Answer: honestly the only thing i know is that mean is another way of saying expected value
Step-by-step explanation:
Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon.
The sum of interior angles of a tray that is of pentagon shape is 540°
Given,
There is a tray which is of pentagon shape.
We have to find the sum of interior angles of the tray.
We have to find the sum of interior angles of pentagon.
That is,
Sum of interior angle of polygon formula = (n - 2) × 180°
Where, n is the number of sides in a polygon.
Here,
Pentagon has 5 sides.
Then,
Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°
That is,
The sum of interior angles of a tray that is of pentagon shape is 540°
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The question is incomplete. Completed question is given below;
Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon. The sum of the interior angles of the tray will be
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
X = 67, Y = 113
Step-by-step explanation:
To find y: 180-62-51=67
To find x: 180-67 = 113
Total angle in a triangle sums to 180 degrees
Total angle in a straight line is also 180 degrees
If a bus is charged $122, how many people do you think it contains?
Answer:
38 people
Step-by-step explanation:
In this case, we can see that, being two people, the cost is 14 and when it is double, that is, 4 people, the value is not 28 but 20.
Which means that there is an additional value that is being charged for the vehicle, that is:
let "c" be the value of the vehicle and "x" be the value per person
c + 2 * x = 14
c + 4 * x = 20 => c = 20 - 4 * x
replacing:
20 - 4 * x + 2 * x = 14
-2 * x = 14-20
-2 * x = -6
x = 6/2
x = 3
for C:
c = 20 - 4 * 3
c = 8
Which means that the formula for the value of the input would then be:
e = 8 + 3 * n
where "n" is the number of people.
Now, we are told that for e = 122
122 = 8 * + 3 * n
3 * n = 122 -8
n = 114/3
n = 38
which means that for that bus there are a total of 38 people
What is the value of x?
C 5
C42
(+6)
(3-16)
22
38
Find the exact solution(s) to the equation 2 sin²x-cosx + 1 = 0
Answer: x=2πn (n=0, 1, 2, 3,...)
Step-by-step explanation:
2sin²x-cosx+1=0
2(1-cos²x)-cosx+1=0
2(1)-2(cos²x)-cosx+1=0
2-2cos²x-cosx+1=0
-2cos²x-cosx+3=0
Multiply both parts of the equation by -1:
2cos²x+cosx-3=0
Let cosx=t
Domain:
-1≤cosx≤1
Hence, -1≤t≤1
2t²+t-3=0
D=b²-4ac
a=2 b=1 c=-3
D=1²-4(2)(-3)
D=1+24
D=25
√D=√25
√D=5
[tex]\displaystyle\\t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-1б5}{2(2)}\\\\t=\frac{-1б5}{4}\\\\t=-1.5\notin domain\\\\t=1\in domain\\\\cosx=1\\\\x=2\pi n\ where\ n=0, \ 1,\ 2,\ 3,\ ...[/tex]
Evaluate the following permutations and combination
a) N = ( 3P4 ) ( 5P2 ) b) N = (3C2) / (4C2)
By using the definitions of combinations and permutations:
a) The first permutation is not defined.
b) N = (³C₂) / (⁴C₂) = 1/2.
How to evaluate the permutations and combinations?A permutation:
ⁿPk is written as:
ⁿPk= n!/(n - k)!
(the denominator only appears if nk)
And a combination is written as:
ⁿCk = n!/(n - k)ka)
We have the product of two permutations, but there is a problem:3P4 The first number is the size of the set, and the second is the number of elements we take from that set.
In that permutation we have a set of 3 elements and we need to select 4, so that permutation is not defined.
b) (³C₂) = 3!/(3 - 2)!*2! = (3*2*1)/(2*1) = 3
(⁴C₂) = 4!/(4 - 2)!*2! = (4*3*2*1)/[(2*1)*(2*1)]
= 3*2 = 6
Then the quotient can be written as:
(³C₂) (⁴C₂) = 3/6 = 1/2.
Note that A quotient is seen as the outcome of dividing two numbers by each other.
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please help me with these questions there not answered by the way
The equivalent expression of 6⁵ is 6² × 6³.
The equivalent expression of 5⁻² × 5⁵ × 5 is 5⁴.
How to find equivalent expression?Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.
Equivalent expressions are expressions that work the same even though they look different.
Therefore, let's find the expression, equivalent to 6⁵,
Using law of indices,
[tex]A^{x} X A^{y} = A^{x +y }[/tex]
Hence,
6² × 6³ = 6²⁺³ = 6⁵
5⁻² × 5⁵ × 5 = 5⁻²⁺⁵⁺¹ = 5⁴
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A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef wants to make 320 milliliters of a dressing that is 8% vinegar. How much of each brand should she use?
The total mixture to contain 8% vinegar so: .06F plus .11S equal to .08(320).Now, we can solve the system of equations using substitution.F + S is 310
How much of each brand should she use?.06F + .11S = .08(310)
F = 310 - S [solve 1st equation for F]
.06(310 - S) + .11S = .08(320) [substitute into 2nd equation]
18.6 -.06S +.11S = 24.8
.05S = 6.2
S = 124
F + 124 = 310
F = 186
make a 320mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.
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solve 3x + 5 = 2x + 7
Answer:
x = 2
Step-by-step explanation:
3x + 5= 2x + 7
Subtract 2x from both sides
3x + 5 −2x = 7
Combine 3x and −2x to get x
x + 5 = 7
Subtract 5 from both sides
x = 7 − 5
Subtract 5 from 7 to get 2
x = 2
What is the equation in slope-intercept form of the line that passes through the point (2,-5) and is perpendicular to the line represented by y=2x+6
Answer:
y = (-1/2)x - 4
Step-by-step explanation:
y = 2x + 6
Perpendicular: y = (-1/2)x + 6
m = (-1/2); (2, -5)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - (-5) = (-1/2)(x - 2)
y + 5 = (-1/2)x + 1
-5 -5
----------------------------
y = (-1/2)x - 4
I hope this helps!
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y- value when x = 0).
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
a perpendicular slope simply turns the original slope upside-down with x and y, and it flips the sign.
the slope of the origins line is 2 = 2/1.
the perpendicular slope is -1/2.
so, the equation looks like
y = -1/2 x + b
to get b we use the point coordinates :
-5 = -1/2 × 2 + b = -1 + b
-4 = b
so, the full equation is
y = -1/2 x - 4
What is the domain of the relation? {(3,4),(2,3),(2,0),(4,2),(3,6)} Responses {0,2,3,4,6} {0,2,3,4,6} {0,3,6} {0,3,6} {0,2,3,4} {0,2,3,4} {2,3,4}
The domain of the given relation is: {2, 3, 4].
What is the Domain of a Relation?A relation has ordered pairs of values that are given as x and y coordinates, (x, y) In a relation, the values of the x coordinates are the domain of the relation while the values of the y coordinates are the range of the relation.
Given the relation, {(3,4),(2,3),(2,0),(4,2),(3,6)}, the set of x-values is: {2,3,4}. the set of y-values is: {0, 2, 3, 4, 6}.
{2,3,4} represents the domain while {0, 2, 3, 4, 6}. represents the range.
Therefore, the domain of {(3,4),(2,3),(2,0),(4,2),(3,6)} is given as: {2, 3, 4].
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Angel spends $29 to order binders online.
They buy 8 binders and pay a flat fee of $5 for shipping.
What is x, the cost of each binder?
The cost of each binder is $3.
Given,
In the question:
Angel spends $29 to order binders online.
They buy 8 binders and pay a flat fee of $5 for shipping.
To find the what is x, the cost of each binder?
Now, According to the question;
Based on the given conditions:
Formulate:
Angel spends = $29 to order binders online.
Buy the = 8 binders
Paying = $5 for shipping .
5 + 8 × x = 29
Solve the equation:
5 + 8x = 29
Rearrange the terms;
8x = 29 - 5
8x = 24
x = 24/8
x = 3
Hence, The cost of each binder is $3.
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PLEASE HELP THIS IS OVER DO
Answer:
its the third one
oh this is easy
Help me please!!!!!!
Answer:5 35/36
Step-by-step explanation:
63 13/18 − 57 3/4 =?
Solving the whole number parts
63−57=6
Solving the fraction parts
13/18−3/4 is equal to 26/36 − 27/36
Combining the whole and fraction parts
6−1/36 = 5 35/36
{Question 14} Please help! Need this by tonight! Thanks so much :)
The slope of equation is 3x + y = 3 is -3
The standard from of Slope - intercept form of equation is y = mx +b
where , m is slope of line
b is y-intercept
and x and y are the variables
Slope of line represents steepness of a line and also termed as gradient .
Y- intercept represents the y- coordinate of the point where the line intersect the y-axis.
In the given question ,
The equation of the line is given as : 3x + 1y = 3
bring 3x to right side,
y = -3x + 3
comparing the equation to standard from
slope of line : m = -3
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help me please (asap)
(C) represents a function with the same rate of change at the function [tex]y = \frac{7}{4}x+3[/tex].
Given equation,
[tex]y = \frac{7}{4}x+3[/tex]
Slope = m = 7/4
Slope = (x2-x1)/(y2-y1)
Now we will check every option and find slope which we be 7/4.
(A) A(1,0) and B(5,-4)
Slope = (-4-0)/(5-1)
= -4/4
= -1
≠ m
(B) A(-1,1) and B(0,4)
Slope = (4-1)/(0+1)
= 3/1
= 3
≠ m
(C) A(-4,-6) and (0,1)
Slope = (1+6)/(0+4)
= 7/4
= m
(D) A(0,-2) and B(-4,5)
Slope = (5+2)/(-4-0)
= 7/-4
= -7/4
≠ m
Hence, only (C) satisfies the situation.
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PLEASE HELP!!!! (geometry)
A line passes through the points (6,0) and (9,1). What is its equation in slope-intercept form?
Equation of line will be y = x/3 - 2
A line's equation can be written in many forms in which one is slope-intercept form.
Equation in slope-intercept form is written as y = mx + c where
m = slope
c = y intercept
Slope shows the steepness of the line. It can be given by change in y axis by change in x axis.
y intercept is the point where the line cuts the y axis that is x = 0 at this point.
Points given to us are (6 , 0) and (9 , 1)
slope = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
m = (1 - 0) / (9-6)
m = 1/3
For c put values of either point in the equation as they both are on the line so they both will satisfy the equation.
y = mx + c
0 = (1/3)*6 + c
0 = 2 + c
c = -2
now put values of m and c in the equation and get a general equation.
Therefore of equation of line will be y = x/3 - 2
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Write an equation in standard form on the line shown in the graph. (-4,3) (-5,2)
The equation to line is x-y+7=0.
What is a line?
A line is an indefinitely long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.
Main Body:
We know that equation of line in two point form =
y-y₁ =( y₂-y₁)/(x₂-x₁)(x-x₁)
points given are (-5,2) and (-4,3).
Therefore
y-2 =( 3-2)/(-4+5) *( x+5)
y-2 = x+5
x-y+7=0
Hence the equation is x-y+7=0.
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"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket by evaluation is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Ultimately, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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HELP ME PLEASEEE FREE 15 POINTS
The transformation of the graphs is
1st graph is (x,y)→(x-4,y+2)
2nd graph is (x,y)→(x+6,y+0)
Given that,
There are two graphs with 2 triangles in each graph.
We have to find the transformation of the graphs.
Take the 1st graph,
We have 2 triangles ABC and A'B'C'.
The points are,
A=(0,0), B=(3,-4) and C=(-1,-2)
A'=(-4,2), B'=(1,-2) and C'=(-5,0)
We get the transformation as
(x,y)→(x-4,y+2)
Check the A and A' points
The A terms goes left for 4 times to A' so we take x-4 and the A terms goes up for 2 times to A' so we take y+2.
Similarly,
The B terms goes left for 4 times to B' so we take x-4 and the B terms goes up for 2 times to B' so we take y+2.
Similarly,
The C terms goes left for 4 times to C' so we take x-4 and the C terms goes up for 2 times to C' so we take y+2.
Now the 2nd graph,
We have triangle FCP and F'C'P'
The points are,
F=(-5,5), C=(-2,5) and P=(-3,0)
F'=(1,5), C'=(4,5) and P'=(3,0)
We get the transformation as
(x,y)→(x+6,y+0)
Check the F and F' points
The F terms goes right for 6 times to F' so we take x+6 and the F terms remain same so we take y+0
Similarly,
The C terms goes right for 6 times to C' so we take x+6 and the C terms remain same so we take y+0
Similarly,
The P terms goes right for 6 times to P' so we take x+6 and the P terms remain same so we take y+0
Therefore, The transformation of the graphs is
1st graph is (x,y)→(x-4,y+2)
2nd graph is (x,y)→(x+6,y+0)
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Answer:1 is (x,y)>(x-4,y+2)
2nd is (x,y)>(x+6,y+0)
Step-by-step explanation:
(> = an arrow)
I talked to my professional tutor about this, she didn’t happen to explain the answer though. She’s been working as a teacher for 20 years.
How does the US tax policy encourage long-term investments?
A.
by making long-term investments tax exempt
B.
by making Treasury bonds tax exempt
C.
by making it illegal to earn short-term gains
D.
by providing a lower tax rate for long-term gains
Answer: its D
Step-by-step explanation
Long Term Capital Gains Taxes tend to be lower than short term
Answer: D by providing a lower tax rate for long-term gains
simplify (4^7/5^2) ^3
1. 4^10/5^5
2. 4^4/5
3. 4^21/5^6
4. 12^7/15^2
Answer: 3: 4^21/5^6
Step-by-step explanation:
Remember when you are raising you need to multiple the powers.
Which values are in the solution set of the compound inequality? Select two options. 4(x + 3) ≤ 0 or x+1>3 –6 –3 0 3 8
The values -3 , -6 , 3 , 8 are in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3
Given, a compound inequality
4(x + 3) ≤ 0 and x + 1 > 3
Now, on solving the first inequality, we get
4(x + 3) ≤ 0
4x + 12 ≤ 0
On subtracting both the sides by 12, we get
4x + 12 - 12 ≤ 0 - 12
4x ≤ -12
On dividing both the sides by 4, we get
4x/4 ≤ -12/4
x ≤ -3
So, the solution set of the 4(x + 3) ≤ 0 inequality be, x ≤ -3 i.e. all the real numbers less than -3.
Now, on solving the second inequality, we get
x + 1 > 3
On subtracting both the sides by 1, we get
x + 1 - 1 > 3 - 1
x > 2
So, the solution set of the x + 1 > 3 inequality be, x > 2 i.e. all the real number greater than 2.
Now, the values in the solution set of the compound inequality
4(x + 3) ≤ 0 and x + 1 > 3 be,
x ≤ -3 and x > 2.
As, we can see -3 , -6 , 3 , 8 are satisfying the condition.
Hence, -3 , -6 , 3 , 8 are the values in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3.
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If you have 6 eggs and 2 bananas for 4 people how many eggs and bananas would you need for 10 people?