So the x-coordinates of the points where the proton crosses the x-axis are x = ±√(5).
What is function?In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain or range) with the property that each input is related to exactly one output. In other words, a function is a rule or a mapping that assigns a unique output value to each input value. Functions can be represented in various ways, such as equations, tables, graphs, or diagrams. They are used to describe and model a wide range of phenomena in mathematics and other fields, such as physics, engineering, economics, and social sciences. Functions are often denoted by symbols such as "f(x)", "g(x)", or "h(t)" and can be composed or combined to form new functions. They can also be classified according to various properties, such as whether they are continuous, differentiable, invertible, or periodic. In summary, in mathematics, a function is a relation between a set of inputs and a set of possible outputs that assigns a unique output value to each input value.
Here,
To find the x-coordinates of the points where the proton crosses the x-axis, we need to find the roots of the function f(x) = x⁴ - 2x² - 15. These are the values of x that make the function equal to zero, which correspond to the points where the proton crosses the x-axis.
To find the roots, we can use the factoring method or the quadratic formula. In this case, we can factor the function as follows:
f(x) = x⁴ - 2x² - 15
= (x² - 5)(x² + 3)
Setting each factor equal to zero and solving for x, we get:
x² - 5 = 0 or x² + 3 = 0
Solving for x in each equation, we get:
x = ±√(5) or x = ±i*√(3)
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Estelle has $300 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year?
$15 is the interest on the amount saved in a year
Calculating the simple interest on a sum of moneyThe formula for calculating simple interest is expressed according to the equation below:
I = PRT
where:
P is the principal = $300
R is the rate = 5% = 0.05
T is the time = 1 year
Substitute to have:
I = 300 * 0.05 * 1
I = $15
Hence the interest that she will earn in a year is $15
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What is 0.25 as an improper fraction?
Answer:
1/4
Step-by-step explanation:
0.25 * 4 = 1
so, 1/4 = 0.25
What is the equation of the line with slope -5 and y-intercept 6 in slope-intercept form?
Answer:y=-5x+6
Step-by-step explanation:
HURRY PLEASE LIKE TODAY
What could you multiply the second (purple) equation by to make the y-values additive inverses?
-2 is to be multiplied in the second equation to make the y-values additive inverses.
What are additive inverses?Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
Given are two equations,
3x-4y = -5.....(i)
5x-2y = -6.....(ii)
We need to find the additive inverse of y variable,
The coefficients of y variables in the both equations are ;-
-4 and -2
The additive inverse of -4 is 4,
If we multiply -2 by -2 it becomes 4,
Hence, -2 is to be multiplied in the second equation to make the y-values additive inverses.
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[tex]456.232 ÷ 4[/tex]pls help me
Answer:
Step-by-step explanation:
$\frac{456.232}{4}$
What is 5.3 as a fraction?
Answer:
Step-by-step explanation:53/10
Need help ASAP please!!!!!
Answer:
122
Step-by-step explanation:
the question is asking for the area of the whole shape
however, it's split into a trapezoid and rectangle, so all you have to do is find the area of the respective shapes and then add them
the formula for area of a rectangle is [tex]A = L(W)[/tex]
if you substitue, A = 15(6)
so the area of the rectangle is 90
then, you have the trapezoid
area of a trapezoid = [tex]\frac{1}{2} (h)(b_{1} +b_{2})[/tex]
you might assume that you don't have the second base, but it's in the rectangle - 6
A = 1/2(4)(6+10)
A=32
90+32 = 122
6(2x²-5) = [?]
x = -3
Answer:
Below
Step-by-step explanation:
Put ' - 3' into the equation where 'x' is and compute
6 ( 2(-3)^2 -5) =
6 ( 2*9 -5)
6 ( 18-5)
6(13) = 78
Sean painted 1/3 of a fence. Sandra painted 1/4 of the fence. How much
of the fence remains to be painted?
Answer:7/12
Step-by-step explanation:
1/3 = 4/12
1/4=3/12
3/12+4/12 = 7/12
7/12 is the answer
(x + 3)^2 Write your answer as a list of values separated by commas.
The values are written in commas as x², 6x and 9
How to determine the valuesIt is important to note that algebraic expressions are expressions that are made of terms, variables, coefficients, factors and constants.
From the information given, we have the quadratic expression as:
(x + 3)^2
Now, take the following steps to determine the values
(x + 3)(x +3)
expand the bracket, we get;
x² + 3x + 3x + 9
Now, collect the like terms and add the values
x² + 6x + 9
Hence, the value is x² + 6x + 9
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2x _ 2 +9x _−5 . factor trinomials (a>1) level 2
The factored form of the given trinomial as required in the task content is; (2x - 1) (x + 5).
What is the factored form of the given trinomial?It follows from the task content that the factored form of the trinomial 2x² + 9x - 5 is to be determined.
Therefore, the factorisation is as follows;
2x² + 10x - x - 5
2x (x + 5) -1 (x + 5)
(2x - 1) (x + 5)
Ultimately, the factored form of the trinomial is; (2x - 1) (x + 5).
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An art teacher enlarged the area of a copy of a painting by 49%. Let d represent the
area of the original painting. The expression d+ 0.49d is one way to represent the area of the new painting. Write two additional expressions that will give the area of the new
painting.
The required two other expression are d + 49d/100 and 149d/100.
What is percentage?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
According to question:We have;
An art teacher enlarged the area of a copy of a painting by 49%. and d represent the area of the original painting.
Given expression is d+ 0.49d
New expressions are
1) d+ 0.49d
= d + 49d/100
2) d+ 0.49d
= d + 49d/100
= 149d/100
Thus, required two other expression are d + 49d/100 and 149d/100.
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1. 3x3 2x2 y 4x2 y is equivalent to:
a. 9x7 y 2 b. 9x12 y 2 c. 24x7 y 2 d. 24x12 y e. 24x12 y
Option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 3x³. 2x²y. 4x²y.
We need to find the equivalent expression of the given expression.
Equivalent expressions are expressions that work the same even though they look different.
(3×2×4)x³. x²y. x²y.
24x³. x²y. x²y.
When bases are same then the powers will be added.
24x⁷y²
Hence, option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.
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If aΔb=a² + ab + b², then what is the value of -3Δ5?
A. 4
B. -14
C. -7
D. 1
E. 19
Answer:
E) 19
Step-by-step explanation:
To find the value of -3Δ5, we need to substitute -3 and 5 into the equation: aΔb = a² + ab + b².
So, we have:
-3Δ5 = (-3)² + (-3)(5) + (5)²
= 9 - 15 + 25
= 19
Therefore, the answer is E) 19.
Which expression can be used to find the value of the expression shown below?
1,284 ÷ 4
A (1,200 ÷ 4) × (84 ÷ 4)
B (1,200 ÷ 4) ÷ (84 ÷ 4)
C (1,200 ÷ 4) + (84 ÷ 4)
D (1,200 ÷ 4) - (84 ÷ 4)
The square footage and monthly rental of 10 rental of 10 similar one-bedroom apartments yield the linear regression y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. Grace can afford $1,500 per month rent. Using the equation, what size apartment should she expect to be able to rent for that price? Explain work in a sentence. :)
Answer:
Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.
Step-by-step explanation:
The given linear regression equation is y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. To find the size of the apartment Grace can expect to rent for $1,500 per month, we can substitute y with 1,500 in the equation and solve for x:
1,500 = 0.775x + 950.25
0.775x = 1,500 - 950.25
0.775x = 549.75
x = 710.32
Therefore, Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.
Estimate the following difference by replacing each fraction with 0, 12
, or 1.
7/8−6/11
If we substitute so every tiny proportion with 0, 1, or 12, the approximate distinction among 7/8 and 6/11 is then equal to 0.
What is a difference example?the end result of subtracting two numbers. the difference between two numbers. Example: Subtract five to get the difference between eight and three.
We can substitute each percentage with either a 0, 1, or 12 to calculate the difference between 7/8 and 6/11.
We can round up to one because we know that 7/8 is larger than 1/2 but much less over 1.
For 6/11, we can round up to 1 since we know it is larger than 1/2 but a little less than 1.
As a result, we can calculate the difference as follows:
7/8 - 6/11
= 1 - 1
= 0
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Reeta has spent 2/7 of her salary on car repair work. She has 15,000 rupees left with her. what is her salary?
Answer 15489 Rupees
Step-by-step explanation:
Total parts= 7+2=9 parts
total salary= 9x
taken salary for car repair= 2x/7
remaining salary= 15000 rupees
9x-2x/7= 15000
(63x-2x)/7=15000
61x/7=15000
61x=105000
x= 105000/61
x= 1721(approx)
Total salary= 9x
= 9*1721
=15489 rupees
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3x + 6 = 8x - 11, what is the value of 10x + 2
Answer:
36
Step-by-step explanation:
3x+6= 8x-11
3x-8x= -11-6
-5x= -17x
x= 3 2/5
10x+2= 10(3 2/5)+2
= 34+2
= 36
Consider the equation
2x + 3y - 6 - 3z + 4y - 6x = 4x + 2y = 4z + 10
a. How many terms are there in this equation?
b.
What are the variables in this equation?
c.
What are the constants in this equation? (hint: constants are the numbers that
are "unattached" to variables)
d. Combine the like terms on the left side of the equation. What are the coefficients
of the variables? (hint: the coefficients are the numbers that multiply the
variable-for example, in 6x, 6 is the coefficient)
There are 10 terms in the equation
The variables are x, y, z
The constants in this equation are -6, 10
The coefficients of the variables of the equation are; 8, 7 and -3
How many terms are there in this equation?2x + 3y - 6 - 3z + 4y - 6x = 4x + 2y - 4z + 10
The left side of the equation is;
2x + 3y - 6 - 3z + 4y - 6x
= 2x - 6x + 3y + 4y - 3z - 6
= 8x + 7y - 3z - 6
Therefore, the coefficients of the variables on the left side of the equation are; 8, 7 and -3
Variables are unknown numbers usually represented by letters or symbols.
The constant are numbers that cannot change its value
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what's the domain and range of the function f(x) = 5(4)^x + 2
The required domain and range of the function are (-∞, ∞) and (2, ∞).
How to find the domain and range of the function?The domain of a function is the set of all possible values of the input variable (x) for which the function is defined. In this case, the function is an exponential function with base 4, which means it is defined for all real numbers.
Therefore, the domain of f(x) is all real numbers, or (-∞, ∞).
The range of a function is the set of all possible values of the output variable (f(x)) for all possible values of the input variable (x).
Since 4^x is always positive (for all x), the value of the function f(x) will always be greater than 2 (the constant added to 5(4)^x), no matter what the value of x is.
As x approaches negative infinity, 5(4)^x approaches zero, so the minimum value of f(x) is 2.
As x approaches positive infinity, 5(4)^x increases without bound, so the range of f(x) is (2, ∞).
Thus, required domain and range of the function are (-∞, ∞) and (2, ∞).
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C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?
It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle.
It is given that C is the circumcenter of triangle ABD, making segment BE a median.
By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles.
Triangles ABE and DEB share side BE making it congruent to itself by the reflexive property.
Triangles ABE and DBE are congruent by HL.
Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD, segment BC is extended past C with dashed lines so that it intersects with side AD at point E.
There is an error in line 1; segments AB and BD are given to be congruent.
There is an error in line 2; segment BE should be a perpendicular bisector.
There is an error in line 4; segment BE is not a shared side.
The proof is correct.
The proof is not correct.
How did we arrive at this assertion?The given information that segments AB and BD are congruent does not imply that triangles ABE and DBE are congruent. Congruency of triangles requires more information, such as additional side lengths or angle measures.
While it is true that point C is the circumcenter of triangle ABD and that segment BE is a median, it is not necessarily true that BE is also a perpendicular bisector. In fact, this would only be true if triangle ABD were also an equilateral triangle.
The statement that triangles ABE and DEB share side BE is incorrect. Triangles ABE and DEB do not share any sides, but rather have segment BE as a common hypotenuse.
Therefore, the conclusion that triangles ABE and DBE are congruent by HL (hypotenuse-leg) is not valid since the previous steps in the proof are flawed.
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In AVWX, the measure of ZX=90°, XW = 3, WV = 5, and VX = 4. What is the value of
the tangent of ZW to the nearest hundredth?
the value of y varies directly with x. if y = 20 and x = 30, what is the value of y if x = 1?
A. 200
B. 2/3
C. 110/3
D. 9/2
Answer:
B. 2/3
Step-by-step explanation:
If y directly varies with x, then y = kx where k is a constant
Given that when y = 20 when x = 30 we get the equation: 20 = k x 30
or
20 = 30k
Dividing by 30 both sides and switching sides gives
k = 20/30 = 2/3
The equation becomes
y = 2/3 x
Therefore if x = 1 we get
y = 2/3 x 1 = 2/3
Choice B
The names of the months of the year are cut from a calendar and put into a bag. A month with more than 5 letters in its name is drawn. What is the probability of the complement of the event? Express your answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
There are 12 months in a year, and 7 of them have more than 5 letters in their names (July, August, September, October, November, December, and January).
The complement of the event is drawing a month with 5 or fewer letters in its name. There are 5 months with 5 letters in their names (May, March, April, June, and August), and 2 months with 4 letters in their names (July and June). Therefore, there are 7 months with 5 or fewer letters in their names.
The probability of drawing a month with 5 or fewer letters in its name is 7/12. The probability of the complement of the event (drawing a month with more than 5 letters in its name) is 1 - 7/12 = 5/12.
Therefore, the probability of the complement of the event is 5/12.
If yall ain't gotta show work just put 5/12 that's the answer the person with the long paragraph
pls help i don’t understand how to graph
Answer:
Slope: [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]
y-intercept: [tex]\boxed{-1}[/tex]
Equation: [tex]\boxed{\bf{y=-\dfrac{1}{3}x - 1}}[/tex]
The two boxes at the bottom are asking you to repeat the above information:
the slope is [tex]\bf \boxed{-\dfrac{1}{3}}[/tex] the y-intercept is [tex]\boxed{-1}[/tex]
Step-by-step explanation:
Actually, you don't have to graph the equation since the graph is already provided
You have to answer the questions based on the provided graph
To find slope
1. Take any two well=defined points on the graph:
We can see that point (0, -1) which has x value at 0 and y-value 1 unit down is a distinguishable point. Let's call this point P1Another point is (3, -2). Let's call this point P22. Find the difference in y-values between P2 - P1. This called rise
rise = P2 v-value - P1 y-value = -2 - (-1) = -2 + 1 = - 1
3. Find the corresponding difference in x-values: P2 - P. This is called run
4. The slope is computed as rise/run = - 1/3
To find y-intercept
Just note where the line crosses the y-axis and the y-value corresponding to that would be the y-intercept
This is also the y-value at which x = 0
Looking at the graph we see that the line crosses(intercepts) the y-axis at y = - 1
So y-intercept = - 1
To write the equation
The equation of the line is
y = mx + b
where
m = slope
b = y-intercept
So the equation of this particular line is
[tex]\bf{-\dfrac{1}{3}x - 1}[/tex]
A cylinder is full at 471 cubic centimeters and has a radius of 5 centimeters. What is the height of the cylinder?
Use 3.14 for pi.
Dont forget to track your thinking on paper. You will need this answer for the next problem.
Question 7 options:
A 94.2 cm
B 18.84 cm
C 30 cm
D 6 cm
The height of the cylinder having a volume of 471 cubic centimetres will be 6 cm. The correct option is D.
The volume of the cylinder is defined as the three-dimensional space occupied by the cylinder.
We can use the formula for the volume of a cylinder, which is given:
V = πr²h
Where V is the volume, r is the radius, and h is the height of the cylinder.
We are given that the cylinder is full at 471 cubic centimetres and that the radius is 5 centimetres. Therefore, we can plug in these values into the formula and solve for h:
471 = π(5²)h
471 = 25πh
h = 471 / (25π)
h ≈ 6 centimeters
Therefore, the height of the cylinder is approximately 6 centimetres.
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What is a monomial example?
A monomial is an algebraic expression that consists of a single term. A monomial can contain constants and/or variables, which are multiplied together.
The expression 3x²y is a monomial. It contains the constant 3, the variable x squared, and the variable y. The variables can be raised to an exponent, as in this example; however, the exponent must be a whole number.A monomial can also contain coefficients, which are the numbers that are multiplied with a variable. In the example above, the coefficient is 3. If there is no coefficient stated, then the coefficient is assumed to be 1. Therefore, the expression x²y is also a monomial, with the coefficient being 1.Additionally, a monomial can contain a product of numbers and variables, such as the expression 2xyz. This is also considered a single term, since all of the numbers and variables are multiplied together.
Monomials can be used to calculate polynomials, which are algebraic expressions consisting of multiple terms. By adding, subtracting, and multiplying monomials together, you can create a polynomial. For example, the expression (3x²y) + (2xyz) is a polynomial, since it consists of two terms. The first term is the monomial 3x²y, and the second term is the monomial 2xyz.
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Drag and drop numbers into the boxes to complete the expanded form of 916.408
The expanded form of 916.408 can be written as:
(9 x 100) + (1 x 10) + (6 x 1) + (4 x 0.1) + (8 x 0.01)
What is expanded form?Expanded form is a way of writing a number that shows the place value of each digit in the number. In expanded form, a number is expressed as the sum of individual terms, each representing a digit in the number multiplied by its place value.
For example, the number 356 can be written in expanded form as:
3 x 100 + 5 x 10 + 6 x 1
Expanded form can be used to better understand the structure of numbers and how place value works.
So, the numbers should be placed as follows:
(9 x 1,000) + (1 x 100) + (6 x 10) + (4 x 1) + (8 x 0.1)
Therefore, the correct order is:
1000, 100, 10, 1, 0.1
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y=x-6 and y=-x-2 graph the system then right a solution if there is one
Answer: To graph the system of linear equations, you can plot the two lines on the same coordinate plane and look for the point where they intersect. If they intersect, that point represents the solution to the system.
The equation y = x - 6 can be written in slope-intercept form, y = mx + b, where m = 1 and b = -6. The equation of the line will be y = x - 6.
The equation y = -x - 2 can be written in slope-intercept form, y = mx + b, where m = -1 and b = -2. The equation of the line will be y = -x - 2.
Plotting these two lines on the same coordinate plane, we can see that they intersect at the point (2, -4). This means that there is one solution to the system of equations: (2, -4).
Step-by-step explanation: