Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.
Answers
The statement which is true about the y-values of the graph of the function as required is; Choice B; The y-values are all greater than or equal to 2.
Which statement is true regarding the y-values?It follows from the task content that the statement which is true regarding the y-values of the graph defined by; f(x) = lx-5l +2 is to be determined.
Therefore, we must recall that expressions enclosed in the absolute value sign upon evaluation are always greater than or equal to zero.
Hence, it can be concluded that we the y-values of the resulting graph to be greater than or equal to 2 (on the occasion that; lx-5l = 0).
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Related Questions
The sets A and I are defined as follows: A = { − 2 , − 1 , 0 , 1 , 7 } I = { − 2 , − 1 , 1 , 2 , 8 } Find the intersection of A and I .
Answers
The intersection of A and I, A ∩ I = {-2, -1, 1}
What is intersection and union of sets?The intersection of two sets A and B is the set of all common elements, it is denoted with A ∩ B.
Whereas the union of those two sets is the set of all elements that are either in A or in B, it is denoted by A ∪ B.
The given sets are,
A = {-2, -1, 0, 1, 7}
And I = {-2, -1, 1, 2, 8}
Intersection of A and I,
A ∩ I = {-2, -1, 1}
The intersection of A and I is {-2, -1, 1}.
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Leg A of a right triangle is 12 inches long, and the hypotenuse, C, is 13 inches long. How long is the other leg, B?
Answers
We get:
12^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 25
b = 5
Leg B is 5 inches long.
Find the measure of EACH numbered angle. m
Answers
The value of x in the given triangle is x = -8 .
Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .
In the question ,
a triangular figure is given
in which , the measure of first angle is 51°
the measure of second angle is 83°
the measure of third angle is (x + 54)°
So , By Angle sum property ,
we get
first angle [tex]+[/tex] second angle [tex]+[/tex] third angle [tex]=[/tex] 180°
substituting the values of angles
we get
51° + 83° + (x + 54)° = 180°
134 + x + 54 = 180
188 + x = 180
x = 180 - 188
x = -8
Therefore , the value of x in the triangle is -8 .
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The production of a gold mine decreases by 5% per year.
What is the approximate half-life for the production decline?
Based on this approximate half-life and assuming that the
mine's current annual production is 5000 kilograms, about
what will its production be in 10 years?
Answers
Answer:d
Step-by-step explanation:d
Jessica and her family bought five tickets to a music concert tickets for adults cost $5.10 and tickets for children cost $3.60 Jessica and her family spent a total of $21 how many tickets for adults and how many tickets for children did they buy
Answers
Answer: 2 Adult 3 Kid
Step-by-step explanation:
5.10 x 2 = 10.2
3.60 x 3 = 10.8
10.8 + 10.2 = 21
Yu is considering two different banks for
his $3,000 savings account:
OPTION B
2% FOR 10 YEARS
COMPOUND
INTEREST
a. What is the interest earned on option A?
OPTION A
4% FOR 10 YEARS
SIMPLE INTEREST
b. What is the total value on option A?
c. What is the interest earned on option B?
d. What is the total value on option B?
e. Which is the better option?
Answers
The simple or compound interest will be
a. $120
b. $12,000
c. $15,000
d. $18,000
e. Option B is better as it is giving us more interest.
Formula of total simple interest is
SI = (P * R * T) /100 where
P = initial principal balance
r = annual interest rate
t = time (in years)
Formula of compound interest is
C.I.= P × [tex](1 + r/n)^{nt}[/tex] - P where
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
a. By applying the formula given above we will get
SI = (3000 * 0.4 * 10) / 100
SI = $120
b. Formula to find total value is P * R * T. By applying this we will get
I = 3000 * 0.4 * 10
I = $12,000
c. By putting values in the formula we will get
CI = 3000 * [tex](1 + 0.2)^{10}[/tex] - 3000
CI = 18000 - 3000
CI = $15,000
d. formula to find total compound value is P * [tex](1 + r/n)^{nt}[/tex]. By applying this in the formula we get
A = 3000 [tex]( 1 + 0.2 )^{10}[/tex]
A = $18,000
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The side length of a square is √8, find the perimeter.
is the number rational or irrational?
Answers
Step-by-step explanation:
Square has perimeter 4a because every side is equal,
so :
if a=√8 , then 4a = 4*√8 or 11.313708499
and the number is rational
Use Figure 1 to evaluate each trigonometric function of angle A . The side adjacent to angle A has length 4 and the side opposite angle A has length 10.
Answers
The trigonometric ratios for angle A are measured below.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a right angled triangle as shown in the image attached.
The six trigonometric ratios are -
sin (A) = 10/√116
cos (A) = 4/√116
tan (A) = 10/4
cosec (A) = √116/10
sec (A) = √116/4
cot (A) = 4/10
Therefore, the trigonometric ratios for angle A are measured above.
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Select the correct answer.
Use a graphing tool to solve the equation for x.
-4x-1= 5x + 4
Answers
As per the system of linear equations concept, the solution of x is -1.282
Linear equations:
Linear equation is referred as the algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.
Given,
Here we have the equations -4x - 1 = 5ˣ + 4
Now, we need to find the value of x by using the graph.
In order to plot the graph for the given linear equation,
First, we have to split the equation into two,
Like the following:
y = -4x - 1
y = 5ˣ + 4
Now, we plot the graph of both equations
Then we get the graph like the following.
Where the red line represents the equation y = -4x - 1 and the green line represents the equation y = 5ˣ + 4.
While we looking into the graph, we have identified the solution is,
x = -1.282
Therefore, the solution of x is -1.282
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Given: 5(2x-4)=10
Prove: x=3
Drag the correct reason to the box.
Answers
After simplifying an equation the value of x is x = 3.
What is solving an equation?
Unifying Principle for Equation Solving
By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.
The variable term on one side of the equation can be separated using addition or subtraction.
To find the variable, use multiplication or division.
Consider, the given equation
5(2x - 4) = 10
10x - 20 = 10 Removing parenthesis
10x -20 + 20 = 10 + 20 Adding 20 on both sides
10x = 30 Simplifying
x = 3 Dividing both sides by 10
Hence, the value of x is, x = 3.
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Find the equation of the line
Answers
Answer:
y=4x+1
Step-by-step explanation:
Our slope is 4/1 or 4, so we know 4x is our slope. Then our y intercept is at (0,1), so we know our b=1. So we know our equation is y=4x+1.
-Hope this helped.
Ted invests in an annuity which earns 6.2% annual interest and he contributes $250 per month for 30 years. If Ted wants to perform some calculations to determine his future value, what formula would Ted use?
Answers
The future value of the annuity investment is expressed in option A
Future ValueThe future value formula is used to calculate the future value (FV) of an investment with given inputs of compounding periods (N), interest/yield rate (I/Y), starting amount, and periodic deposit/annuity payment per period (PMT).
The formula can be expressed as
FV = [MP(1 + r/n)^nt - 1] / [r/n]
FV = future valuemp = monthly paymentr = rate n = number of times compoundedWe can substitute the values into the equation;
FV = 250[(1 + 0.062/12)^12 * 30] / 0.062 /12
The answer to this question is option A
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To determine the size of the county's moose population, naturalists catch 65 moose, tag them and
then set them free. Months later, 48 moose are caught, of which 14 have tags.
The estimated size of the moose population is___?
. (Round to nearest whole moose.)
Answers
The size of the moose population, 65 + (48-14)=99.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
naturalists have = 65 moosetheycatch and tag = 48set them free and catch them later,= 14now total moose= 65 + (48-14)99learn more about unitary method click here:
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Simplify quantity 15 x squared minus 18 end quantity over 6. 15x + 3 x + 3 quantity 5 x squared minus 18 end quantity over 2 quantity 5 x squared minus 6 end quantity over 2
Answers
The expressions are:
(5x² - 6)/ 2 5x² - 18/2 5x² -6 /2What is expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
15 x squared minus 18 end quantity over 6.
= 15x² - 18 / 6
= 3(5x² - 6)/ 6
= (5x² - 6)/ 2
and, 5 x squared minus 18 end quantity over 2
= 5x² - 18/2
and, 5 x squared minus 6 end quantity over 2
= 5x² -6 /2
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Ben is one Year younger than Amara.Write an equation that can be user ti find isabelle’s age i.How old is isabelle
Answers
The Linear equation used is x -y = 1; to find the age of Isabelle's age.
What is Linear Equation?
An equation is said to be linear if the maximum power of the variable is consistent Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.
Let the age of Ben be x;
Let the age of Amara be y;
According to the question:
It is given that:
Ben is one year younger than Amara. That means we have to form a linear equation such that Amara is one year older than Ben.
So,
We have assumed the Age of Ben is x;
we have assumed the Age of Amara is y;
So, According to the question,
Framing the linear equation,
x -1 =y;
⇒x -y = 1;
Hence, We can find the age of Isabelle using the linear equation: x -y = 1;
where x is ben's age;
where y is Amara's age.
Therefore, The Linear equation used is x -y = 1; to find the age of Isabelle's age.
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Which is the equation of a line that has a slope of 4 and passes through point (1, 6)?
Oy=4x-2
Oy = 4x+6
Oy = 4x + 2
y=4x-3
Mark this and return
Save and Exit
Next
Submit
Answers
Equation of a line that has a slope of 4 and passes through point (1, 6) is y = 4x + 2 . Hence, C is the correct option.
What is equation of the line?To represent the standard form of equation of a line are:
Slope-intercept form:
y = mx + c
Here m represent the slope of the given line and c is the y intercept.
Intercept form:
x/a + y/b = 1
Generic way of representing the straight line, i.e. Ax+By+C = 0
x/(-C/A) + y/(-C/B) = 1
Hence a = -C / A and b = – C / B
Normal form:
The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:
x cos α+y sin α = p
General equation of the line is represented in the form:-
y - y1 = m (x-x1) ,
Where x1, y1 represents a point on the line whereas,
m represents the slope of the line.
= (1 , 6) point on the line
= Slope (m) = 4
Putting all the required values in general equation:-
y - 6 = 4 ( x-1 )
Hence, we get y = 4x + 2
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help please and thanks math..................
Answers
The value of f after solving the expression, 2-f/4 = f-3f/4+3, is -2.
According to the question,
We have the following expression:
2-f/4 = f-3f/4+3
We know that to find the value of f we will have to move the terms with the same variable on one side. Now, moving f and 3f/4 from the right hand side to the left hand side will result in the change of their signs.
3f/4-f/4-f +2 = 3
Moving 2 from the left hand side to the right hand side:
3f/4-f/4-f = 3-2
Taking the least common factor as 4:
(3f-f-4f)/4 = 1
(-2f)/4 = 1
Using the cross multiplication method:
-2f = 4
f = -4/2
f = -2
Hence, the value of f for the given expression is -2.
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Solve using substitution.
x = –6
x − y = –5
Answers
-6 - y = -5
Move -6 to the right
-y = 6 - 5
-y = 1
Divide y by negative and 1 by negative
Answer: y = -1
do we have to find x using quadratic formula or what?
Answers
Step-by-step explanation:
The base of the separated triangle is (x+5) - (2x - 4) = x + 5 - 2x + 4 = 9 - x
So, area of the separated triangle would be:-
1/2 * b* h
or, 1/2 * (9-x)* (x+3)
or, (6x + 27 - x² )/2
Total area of trapezium = (6x + 27 - x²)/2 + (2x-4)(x + 3)
or, 60 = (6x + 27 - x²)/2 + 2x² + 2x - 12
or, 60 = (6x + 27 - x² + 4x² + 4x - 24)/2
or, 120 = 10x + 3x² + 3
or, 0 = 3x² + 10x + 3 - 120
hence, 3x² + 10x - 117 = 0 (proved)
Again,
Use quadratic formula to figure out value of x.
(It woun't be a natural number)
Write the value of x with only one digit after it's decimal.
mathematical shapes
Answers
Answer:
A square is an sqaure.
Step-by-step explanation:
circle is a circle. :) happy to help
The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000. How much will the price decrease in dollars? What
will be the price of the next model?
Decrease in price:
Price of next model:
Answers
The decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.
According to the question,
We have the following information:
The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000.
We will find the 13.6% of 42,000 to find the decrease in the price of the next model:
(13.6*42000)/100
$5712
Now, the price of next model will be:
42000-5712
$36288
Hence, the decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.
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The triangle and the square shown have the same perimeter. Solve the equation 3x+4x+5x=4(x+2)
Answers
The solution of the linear equation:
3x+4x+5x=4(x+2)
is x = 1
How to solve the linear equation?Here we need to solve the following linear equation:
3x + 4x + 5x = 4*(x + 2)
First, we should expand the right side to get:
3x + 4x + 5x = 4x + 8
Now we group like terms:
3x + 4x + 5x - 4x = 8
Taking x as a common factor in the left side:
(3 + 4 + 5 - 4)*x = 8
(3 + 5)*x = 8
8x = 8
x = 8/8
x = 1
The solution is x = 1.
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looooooooooooooooootttttttsss offffffffffffffffffff pointtttttttttttttttttttssssssssssssssssssssssssss
Answers
Line AD and line EG are parallel line, Transversal CH < ABC and EFH are same side exterior angles
What are same side exterior angles?The presence of two parallel lines and a transversal line leads to some important theorem used in geometry
Some of the theorems include
alternate interior anglesalternate exterior anglescorresponding angles same side exterior anglesThe exterior angles refers to angles above line AD and below line EG, which are the parallel lines. These angles according to the figure are 4 and they include
< ABC< CBD< EFH< GFHThe exterior angles to the left of the transversal line forms a pair of same side exterior, similarly, to the right of the transversal line forms another pair of same side exterior angles.
The question is asking of same side exterior angles to < ABC, which is to the left of the transversal line. The pair that are same side exterior angles to the left of the transversal line are
< ABC< EFHHence < EFH and < ABC are same side exterior angles
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Given f(x) = −2x^2 + 5, evaluate f(4)
Responses
Answers
The composition f(4) has a value of -27
How to evaluate the function composition?The definition of the functions is given as
f(x) = -2x^2 + 5
Rewrite the above function properly
So, we have the following representation
f(x) = -2x² + 5
To find the function f(4), we set the value of x in the equation f(x) = -2x² + 5
This is represented by
Calculate f(x), when x = 4
Substitute 4 for x in the equation f(x) = -2x² + 5
So, we have the following equation
f(4) = -2(4)² + 5
Evaluate the exponents
This gives
f(4) = -2 * 16 + 5
Evaluate the products
This gives
f(4) = -32 + 5
Evaluate the sum
f(4) = -27
Hence, the value of the function is -27
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PLEASE HELP ASAP 30 POINTS PLUS BRAINLEST Simplify (3.2 x 10^−9) − (6.4 x 10^−8). Write the final answer in scientific notation.
−6.08 x 10^−9
−6.08 x 10^−8
−3.2 x 10^−1
−3.2 x 10^1
Answers
Answer:
B. -6.08 x 10^-8
To find 12 / 3/5 we rewrite 12 as
A. 12/1
B.1/12
Answers
wa can rewrite it as 12/1 which is A
Write an expression that is equivalent to 3(7+ x).
3(7+ x)= ? + ?x
Answers
Answer:
21 + 3x
Step-by-step explanation:
Its simple really. Just expanding the brackets by bringing the 3 inside the bracket :
3 × 7 = 21
3 × x = 3x
So our answer will 21 + 3x
Hope this helped and have a good day
Mid point of AB is M (1,-4). If the coordinates of A are (-3,-6) what are the coordinates of B?
Answers
The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2).
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
The coordinate of midpoint between two points (x₁, y₁) and (x₂, y₂) is given by,
( (x₁ + x₂)/2 ,(y₁+ y₂)/2)
Given that, M is the midpoint of A and B.
Let's say the coordinate of point B is B(x,y).
Then,
1 = (-3 + x)/2
x = 2 + 3 = 5
And,
(-6 + y)/2 = -4
y = -8 + 6 = -2
Hence "The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2)".
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proof that (x-1/x)(x^4/3+x^2/3) = x⅓(x²-1/x²)
Answers
The given polynomial solved as same as RHS is x^3/3(x^2- 1/x^2)
What is polynomial?Polynomial is defined as the sum of variable terms in the form of k×x^n, where k is constant and x variable and n is an integer.
According to give data:we have given a polynomial,
(x-1/x)(x^4/3+x^2/3) = (x^3/3)(x²-1/x²)
Take LHS
⇒ (x-1/x)(x^4/3+x^2/3)
⇒ (x^2-1/x)×(x^4 + x^2/3)
⇒ (x^2-1/x) x^2(x^2+1/3)
⇒ x^2/3x (x^2-1)(x^2+1)
⇒x^2/3x(x^4-1) ∴(a^2-b^2 = (a+b)(a-b))
multiply numerator and denominator by x
⇒x^3/3 (x^4-1/x^2)
⇒x^3/3(x^2- 1/x^2) = RHS
Hence, given problem has solved.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
The valid equations are written below. Then the correct options are C, D, and E.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The sum of the two interior angles is equal to the exterior angle of the third angle.
The sum of the supplementary angle will be 180°.
From the diagram, the equations are written as,
m∠5 + m∠6 = 180° (Supplementary angle)
m∠2 + m∠3 = m∠6 (Exterior angle)
m∠2 + m∠3 + m∠5 = 180° (Angle sum of triangle)
Then the correct options are C, D, and E.
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The complete question is attached below.