Answers
Note that equation means " that two mathematical expressions are equal each other"
2. Solution: A value or values that make a mathematical sentence true.
Another word for Solution can be "answer", or the 'final product' of an expression (now turned into equation)
hope this helps
Related Questions
Which sequence is modeled by the graph below? Coordinates are 1,1 2,2 3,4 4,8
Answers
1,1
2,2
3,4
4,8
The first point indicates the number of term and second points indicate the value of the term in the sequence.
So, the sequence we get is:
1, 2, 4, 8, ...
Notice that each term of the sequence is obtained by multiplying the previous term by 2. A sequence with such a relation is known as Geometric Sequence or a Geometric Progression (G.P)
Then the sequence is:
For the x-coordinate:1,2,3,4,5,6,7...
For the y-coordinate:1,2,4,8, which is 2^0,2^1,2^2,2^3... so there for the next y-coordinates are 16,32,64,128, ...
So the sequence is: 1,2,4,8,16,32,... 2^x.
The endpoints of one diagonal of a rhombus are (-5,2) and (1,6). If the coordinates of the 3rd vertexare (-6,10), what arethe coordinates of the 4th vertex?
A.(2,-2)
B.(-8,0)
C.(4,8)
D.(-9,8)
Answers
[tex]E\left(\dfrac{-5+1}{2};\ \dfrac{2+6}{2}\right)\to E\left(\dfrac{-4}{2};\ \dfrac{8}{2}\right)\to E(-2;\ 4)[/tex]
[tex]\vec{BE}=[-2-(-6);\ 4-10]=[4;\ -6][/tex]
[tex]D(x;\ y)\\\\\vec{ED}=[x-(-2);\ y-4]=[x+2;\ y-4]\\\\\vec{ED}=\vec{BE}\ therefore\\\\ \ [x+2;\ y-4]=[4;\ -6]\to x+2=4\ and\ y-4=-6\\\\x=2\ and\ y=-2\\\\Answer:\ \boxed{A.\ (2;\ -2)}[/tex]
Answer:
A. (2,-2)
Step-by-step explanation:
That is the right answer. Hope this helps!!!
a garden patio is covered with grey slabs and yellow slabs. 1/5 is grey. 1/4 is yellow. there’s 55 slabs in total. what is the number of yellow slabs
Answers
Answer:
44
Step-by-step explanation:
1:4
4+1=5
55/5=11
11*4=44
the answer is 44
Find the price per ounce rounded to the nearest cent: 1 lb 10 oz for $10.98.
A.) 0.5
B.) 1.98
C.) 0.42
D.) 0.9
Answers
What is the square root of 325 rounded to two decimal places?
Answers
A pet store is selling a new dog collar for $12.00. If there is a sales tax of 10 percent, what is the actual cost of the collar
Answers
Sales Tax = 10% x $12 = 0.1 x 12 = $1.20
Total Cost = $12.00 + $1.20 = $13.20
Answer: $13.20
An item that originally cost $100 is decreased by 8%. The reduced price is then increased by 8%.
The resulting price is _____.
Answers
100 x 0.08 = 8
100-8 = 92 ( reduced price )
now multiply reduced price by 8% and add:
92 x 0.08 = 7.36
92 + 7.36 = $99.36
Answer:
The resulting price is $99.36.
Step-by-step explanation:
Original cost of the item = $100
The decrease percentage is 8% or 0.08
So, the reduced price becomes :
[tex]100-(0.08\times100)=92[/tex] dollars
Now again the reduced price is increased by 8%.
So, multiplying the reduced price by 8% and adding it again we get;
[tex]92+(0.08\times92)[/tex] =$99.36
So, the resulting price is $99.36.
3 problems, 50 points
Answers
2.vertical: x=4, horizontal y=1
3.So if y = 3 and x = 5 then we have
3= y(1/6)
Solve for y
y= 24
Therefore the equation should be
y = 24/x
So when x = 3
y = 24/3
y = 8
hope this helps and sorry if I'm wrong
Suppose two fair six-sided dice are rolled. what is the probability that they will both come up with the same number?
Answers
If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?
4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC
Answers
The ratio of similar sides to triangles should be equal AC/XC=BC/YC BC=BY+YC BC=4+7=11
AC/10=11/7 or 7/11=10/AC the ratio above should be used for calculation of AC
Answer:
The correct option is 4.
Step-by-step explanation:
In triangle ABC and XYC,
[tex]\angle BAC=\angle YXC=60^{\circ}[/tex] (Given)
[tex]\angle BCA=\angle YCX[/tex] (Reflexive Property)
By AA rule of similarity,
[tex]\triangle ABC\sim \triangle XYC[/tex]
The corresponding sides of similar triangles are proportional.
Since triangle ABC and XYC, therefore
[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]
[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]
[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]
[tex]\frac{10}{AC}=\frac{7}{11}[/tex]
Therefore option 4 is correct.
What is the equation of this circle in general form? x² + y² + 2x + 6y + 4 = 0 x2+y2−2x−6y−26=0 x2+y2−2x−6y+4=0 x2+y2+2x+6y−26=0 a circle on a coordinate plane centered at begin ordered pair 1 comma 3 end ordered pair. the horizontal x-axis ranges from negative 10 to 10 increments of 1. the vertical y-axis ranges from negative 10 to 10 in increments of 1. the circle passes through begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair 1 comma 9 end ordered pair, begin ordered pair 7 comma 3 end ordered pair, and begin ordered pair 1 comma negative 3 end ordered pair?
Answers
A circle on a coordinate plane is centered at the beginning ordered (1, 3). The equation of the circle is x²+y²-2x-6y-26=0
What is the equation of the circle with radius r units, centered at (x,y)?If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
A circle on a coordinate plane is centered at the beginning ordered (1, 3).
The horizontal x-axis ranges from negative 10 to 10 increments of 1. and the vertical y-axis ranges from negative 10 to 10 in increments of 1.
The equation of the circle is
[tex]x^2+y^2-2x-6y-26=0[/tex]
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(need help!) A dart is thrown at the board shown. It hits the board at a random point. Find the probability that it will land in the unshaded region. Round to the nearest percent.
20%
33%
17%
25%
Answers
[tex] |\Omega|=360\\
|A|=120\\\\
P(A)=\dfrac{120}{360}=\dfrac{1}{3}\approx33\% [/tex]
How to find all values of x where the tangent line is horizontal?
Answers
To find x-values where a function's tangent line is horizontal, find the derivative, set it to zero, and solve for x considering any function's restriction.
Explanation:To find all the values of x where the tangent line is horizontal, we need to understand that these are the points where the derivative of the function is zero. This is because the derivative of a function at a point gives us the slope of the tangent line at that point. And, for a line to be horizontal, its slope needs to be zero.
So, to find these values:
Find the derivative of the given function. Set this derivative equal to zero.Solve the equation for x.The solutions will give you the x-values where the tangent line is horizontal. Do note that you need to be aware of the domain and any restrictions of the original function to have valid solutions.
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Which expression is equivalent to 3(4m − 5)?
Answers
your answer is:
using the distributive property of multiplication, the equivalent expression is:
12m-15
I hope this helps, and have a nice day!
The equivalent expression for the given expression is 12m-15.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 3(4m-5).
Using distributive property A(B+C)=AB+AC, we get
3×4m-3×5
= 12m-15
Therefore, the equivalent expression for the given expression is 12m-15.
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There is an expression some people use that says, “What you put into it is what you get out of it.” People might use this expression to describe your skills at a sport or activity and how that relates to the amount of time and effort you spend practicing that activity. Does this expression apply to functions? How? Give an example to support your answer.
Answers
The phrase 'What you put into it is what you get out of it' applies to functions in mathematics, where given an value x (input) into a function, you get an output y. It also applies to real life examples, like sports practice, where your input of time and effort has a corresponding output of skill level.
Explanation:Yes, the expression “What you put into it is what you get out of it” can be applied in mathematics, particularly to functions. In mathematical context, this statement represents the fundamental concept of a function, where an input (what you put into it) mapped to an output (what you get out of it). For example, consider a linear function y = 2x + 3. The value of y (output) depends on the value chosen for x (input). Thus, if x = 2 (input), y = 7 (output). The output here is a result of the input 'fed' into the function.
The same idea can be extrapolated to functions in everyday life, such as practicing a sport. The input to the 'function' is the time and effort you put in, and the output is the proficiency you achieve. As with mathematical functions, each 'input' in life tends to have a corresponding 'output', reinforcing the idea of causes having effects.
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The expression 'What you put into it is what you get out of it' applies to functions such that what you put into the function (input) directly influences what you get out of the function (output).
Explanation:Yes, the expression 'What you put into it is what you get out of it' can indeed be applied to the concept of functions in mathematics. A function is a special relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. The input you 'put into' a function is the independent variable and the output or 'what you get out of' the function is the dependent variable.
As an example, consider an equation of a function like y = 2x. Here, 'x' represents the inputs and 'y' the outputs. If you 'put into' this function x = 3 (input), you 'get out of' the function y = 6 (output). Thus, what you 'put into' the function (input) directly influences what you 'get out of' the function (output), demonstrating the principle of 'What you put into it is what you get out of it'
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Techechtium-99m has a half-life of 6 hours. If 1000mg is in use, in how many hours will 62.5mg remain?
Answers
One half life 500 mg to 500/2 = 250 mg
One half life 250 mg to 250/2 = 125 mg
Etc .......
Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
Explanation:To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.
Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.
So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:
1000mg / 62.5mg = 16.
Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:
16 x 6 = 96.
Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.
The dot product of u with itself is 12. what is the magnitude of u?
Answers
we know it's dot product is 12, thus
[tex]\bf \ \textless \ a,b\ \textgreater \ \cdot \ \textless \ a,b\ \textgreater \ \implies (a\cdot a)+(b\cdot b)\implies \boxed{a^2+b^2=12}\\\\ -------------------------------\\\\ ||\ \textless \ a,b\ \textgreater \ ||=\sqrt{a^2+b^2}\implies \sqrt{\boxed{12}}[/tex]
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
Help please? what is the length of side x?
Triangle AAS use sine rule
Answers
make sure your calculator is in Degree mode.
What is the slope-intercept form equation of the line that passes through (3, 4) and (5, 16)?
Answers
y = 6x - 14
Explanation:
The general formula of the linear line is:
y = mx + c
where:
m is the slope and c is the y-intercept
1- getting the slope:
slope is calculated as follows:
m = [tex] \frac{y2-y1}{x2-x1} [/tex] = [tex] \frac{16-4}{5-3} = 6[/tex]
The equation of the line now is:
y = 6x + c
2- getting the y-intercept:
To get the y-intercept, we will use any of the given points, substitute in the equation and solve for c.
I will use the point (3,4) as follows:
y = 6x + c
4 = 6(3) + c
4 = 18 + c
c = -14
Based on the above calculations, the equation of the line is:
y = 6x - 14
Hope this helps :)
Find the area of the rectangle below (3x-2) (4x-7)
Answers
-> 12x^2-21x-8x+14
= 12x^2 - 29x + 14
So the area of the rectangle would be 12x^2 - 29x + 14.
Hope this helps. If you have any questions, place it in the comment section below.
If and only if this assumption is correct, then the area is L * W, or
(3x-2)(4x-7) = 12x^2 -13x + 14.
The measure of an angle is two times the measure of a supplementary angle. what is the measure of each angle
Answers
Let 2x = 180-x.
Then 3x = 180, and x = 60. One angle is 60 degrees and the other is 180-60, or 120, degrees.
Answer:
60 and 120 have a good day!
Step-by-step explanation:
A museum charges a school $200 to hold a trip + $2 entrance fee per person. The students must share the total cost of the trip equally include the entrance feee for 8 teachers. What is the function Y(x) that gives that gives the cost per X person attending the trip?
Answers
This is because 16 needs to be added to the base amount since the teachers cost is automatically added in.
jen is thinking of a number. the product of this number and 3.4 is 176.8. find jens number.
Answers
The product of the number and 3.4 is 176.8, so we can write the equation as:
3.4x = 176.8
Dividing by 3.4 on both sides, we get:
x = 52
Thus, Jen is thinking of 52 as his number
Let the unknown number equal X. We are given that the product of X and 3.4 is equal to 176.8. The term "product" implies the use of multiplication. With this knowledge, we can represent the problem using the following formula:
3.4x = 176.8
Now divide both sides of the equation by 3.4:
x = 52
We have now proven that Jen is thinking of the number 52.
I hope this helps!
Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/2x y <1/2 x + 1
Answers
Look at the picture.
[tex]y=-\dfrac{1}{2}x\\\\for\ x=0\to y=-\dfrac{1}{2}\cdot0=0\to(0;\ 0)\\\\for\ x=2\to y=-\dfrac{1}{2}\cdot2=-1\to(2;\ -1)\\\\\\y=\dfrac{1}{2}x+1\\\\for\ x=-2\to y=\dfrac{1}{2}\cdot(-2)+1=-1+1=0\to(-2;\ 0)\\\\for\ x=0\to y=\dfrac{1}{2}\cdot0+1=1\to(0;\ 1)[/tex]
Answer: Every points on orange area.
Answer: is c on edge (5,-2) , (3,1) ,(4,2)
Help me please.
Luke Skywalker's height is 68 inches. The mean height for all Jedi is 66.5 inches and the standard deviation of the Jedi heights is 2.4 inches. What is the z score for Luke Skywalker's height?
Round to the nearest thousandth
Answers
[tex]z=\frac{x-\mu }{\sigma }=\frac{68-66.5}{2.4}=0.625[/tex].
The z-score is 0.625.
The z-score for Luke Skywalker's height is 0.625, indicating that his height is 0.625 standard deviations above the mean.
Z-score Formula: The z-score for Luke Skywalker's height can be calculated using the formula: z = (x - μ) / σ, where x is the individual's height, μ is the mean height, and σ is the standard deviation.
Plugging in the values, we get z = (68 - 66.5) / 2.4 = 0.625 (rounded to the nearest thousandth).
Find the dot product, a • b. a = 6i + 5j, b = -5i + 4j
Answers
a.b = (6i + 5j).(-5i+4j)
a.b = 6(-5)+5(4)
a.b = -30 + 20
a.b = -10
The dot product results in a scalar quantity, so you only get a magnitude not a vector.
Answer:
-10
Step-by-step explanation:
took the test
Solve the inequality. Graph the solution set.
2r−9≤−6
Answers
2r−9≤−6------> 2r ≤ -6+9-------> 2r ≤ 3-----> r ≤ 1.5
the solution is the interval (-∞, 1.5]
using a graph tool
see the attached figure
The first step to solving this inequality is to change the equation. We'll change the equation by adding plus nine to both sides of the equation. This will help us get 2r on its own.
Original Equation :
2r - 9 ≤ -6
New Equation {Added Plus 9 to Both Sides} :
2r - 9 + 9 ≤ -6 + 9
Now we'll simplify the equation by solving -9 + 9 and -6 + 9.
Old Equation :
2r - 9 + 9 ≤ -6 + 9
New Equation {Old Equation Simplified} :
2r ≤ 3
Once again we'll have to change the equation. We'll do this by adding divide both sides by two. This will give us the variable ( r ) on its own.
Old Equation :
2r ≤ 3
New Equation {Added Divide 2 to Both Sides} :
[tex] \frac{2r}{2} [/tex] ≤ [tex] \frac{3}{2} [/tex]
Now we simplify.
Old Equation :
[tex]\frac{2r}{2}[/tex] ≤ [tex]\frac{3}{2}[/tex]
New Equation {Old Equation Simplified} :
r ≤ [tex] \frac{3}{2} [/tex]
Now, that is, in fact, the solution but since I'm not sure which form you need, I've written it in other forms as well.
Solution → r ≤ [tex] \frac{3}{2} [/tex]
Decimal → 1.5
Interval Notation → [tex](-[/tex] ∞[tex], \frac{3}{2} )[/tex]
Below, I have also attached a graph that shows how this inequality should be graphed.
Hope this helps!
- Lindsey Frazier ♥
Q: what is the complete factorization of the polynomial below x^3+4x^2-x-4?
A. (x+1)(x-1)(x+4)
B. (x-1)(x-1)(x-4)
C. (x+1)(x-1)(x-4)
D. (x-1)(x-1)(x+4)
Answers
The solution is Option A.
The factorized form of the polynomial equation A = x³ + 4x² - x - 4 is given by B = ( x + 1 ) ( x - 1 ) ( x + 4 )
What is an 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.
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 data ,
Let the factorized equation be represented as = B
Now , let the equation be A
The value of A is given by A = x³ + 4x² - x - 4
On simplifying the equation , we get
A = x³ + 4x² - x - 4
Taking x² as the common term in the first two terms of the equation ,
A = x² ( x + 4 ) - x - 4
The equation can be further simplified as
A = x² ( x + 4 ) - ( x + 4 )
Taking ( x + 4 ) as the common term in the first two terms of the equation ,
A = ( x² - 1 ) ( x + 4 )
Now , ( x² - 1 ) can be simplified as ( x + 1 ) ( x - 1 )
So , the value of B is
B = ( x + 1 ) ( x - 1 ) ( x + 4 )
Therefore , the value of B is ( x + 1 ) ( x - 1 ) ( x + 4 )
Hence , the factorized equation is ( x + 1 ) ( x - 1 ) ( x + 4 )
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PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of x and y.
Answers
[tex]\left\{\begin{array}{ccc}2x+3y=68&|\cdot(-15)\\30x+11y=112\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-30x-45y=-1020\\30x+11y=112\end{array}\right}\\.\ \ \ \ \ \ \ -34y=-908\ \ \ |:(-34)\\\\.\ \ \ \ \ \ \ \ \ \ \ y=\dfrac{908}{34}\to y=\dfrac{454}{17}\\\\2x+3\cdot\dfrac{454}{17}=68\ \ \ \ |\cdot17\\\\34x+1362=1156\ \ \ \ |-1362\\34x=-206\ \ \ \ |:34\\\\x=-\dfrac{206}{34}\to x=-\dfrac{103}{17}\\\\ \left\{\begin{array}{ccc}x=-\dfrac{103}{17}\\\\y=\dfrac{454}{17}\end{array}\right[/tex]
Haley measured the distances between her house and two of her friends' houses. ellen's house is 1.41 miles away from haley's, and dirk's house is 6,547 feet away from haley's. whose house is farther away from haley's, and how many feet farther away is it, to the nearest whole foot?
Answers
H = Haley's house
E= Ellen's house
D = Dirk's house
In the figure below we can see the representation of this problem.
Given that there are two measurements with different units, namely, the distance between Haley and Ellen's houses is in miles and the distance between Haley and Dirk's houses is in feet, we need to convert one of these units.
As the final question demands which house is farther away from Haley's, we will convert the distance between Haley and Ellen's houses from miles to feet, so:
[tex]1mi = 5280ft[/tex]
[tex]1.41mi(\frac{5280ft}{1mi}) = 7444.8ft[/tex]
So:
The distance between Haley and Ellen's houses = [tex]7444.8ft[/tex]
The distance between Haley and Dirk's houses = [tex]6547ft[/tex]
Then Ellen's house is farther away from haley's, and the nearest whole foot is:
[tex]7444ft[/tex]
Answer: Ellen's house is farther away by 898 feet.
Step-by-step explanation:
Given: The distance between Haley's house and Ellen's house = 1.41 miles
We know that 1 mile = 5,280 feet
Then, [tex]1.41\text{ miles}=1.41\times5,280\text{ feet}=7,444.8\text{ feet}[/tex]
The distance between Haley's house and Dirk's house = 6,547 feet
Clearly, 6,547<7,444.8
And [tex]7444.8-6547= 897.8\approx898[/tex]
Therefore, Ellen's house is farther away by 898 feet.