The quadrilaterals ABCD and JKLM are similar. Find the length x of JK.
The length of x in the similar quadrilateral is 1.5 units.
How to find the sides of similar quadrilateral?Quadrilaterals are polygons with 4 sides. The sum of the interior angles of a quadrilateral is 360 degrees.
Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same and two adjacent sides have equal ratios.
Therefore, quadrilaterals ABCD and JKLM are similar.
Hence, let's find the side x of the quadrilaterals.
Therefore,
CD / LM = BC / KL
CD = 5
LM = 2.5
BC = 3
KL = x
Hence,
5 / 2.5 = 3 / x
cross multiply
5x = 2.5 × 3
5x = 7.5
x = 7.5 / 5
x = 1.5
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Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f() = 6sec + 3tan , 0 < < 2
The critical numbers of the function are; θ = π/6, 5π/6
How to find the critical value of a trigonometric function?
We are given the trigonometric function as;
f(θ) = 6secθ + 3tanθ ; 0 < θ < 2π
The critical points of a function are defined as those points of the domain where the function is not differentiable or those points for which the derivative is equal to zero.
Let us find the first derivative;
f'(θ) = 6(-sin θ/cos² θ) + 3(1/cos² θ)
f'(θ) = (3 - 6sin θ)/cos² θ
At f'(θ) = 0, we have;
3 - 6sin θ = 0
θ = sin⁻¹(3/6)
Since sin is positive, then;
θ = π/6, 5π/6
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Which inequality has the graph shown below?
The inequality is y > 2x-3
option C is correct
What is inequality in math?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
The line intersects the y- axis at point (0,-3)
i.e., The y-intercept =-3
We know that,
Equation of lime, y= mx + b
b: y-intercept
m: Slope of the line
Slope of the line,
m = 0-(-3)/3/2 = 2
m ⇒ 2
∴ Equation of line, y = 2x - 3
The shaded are is above the line, and line is represented with dotted lines,
hence the inequality is,
y > 2x - 3
Hence, option C is correct
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If you have 3 cups of half ( 2/6) filled cups how much do you have for one cup?
I will have the fraction of 1/6 cups of one cup, if 3 cups of half 2/6 fill is what I have.
Fractions in word problemWe can solve word problems in mathematics using the 4 basic operations (addition, subtraction, multiplication and division) on fractions.
From the question, we are have 3 cups of half 2/6 filled cups, this implies that;
2/6 filled cups = 1/3
half 2/6 filled cups = (1/3)/2
half 2/6 filled cups = 1/3 × 1/2 {changing the division to multiplication}
half 2/6 filled cups = 1/6
Therefore, I have 1/6 for one cup and for 3 cups of half 2/6 filled cups, I will have 1/2.
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Question
The price of a pair of shoes is reduced by $5.19. The price is now $22.50
What was the original price of the shoes?
SOMEONE HELP PLEASE!
Answer:
$27.69
Step-by-step explanation:
Chaz has an account with $ 9 , 200 . He transferred this amount into an account paying 4.9 % annual interest compounded quarterly. How much money will be in the account after 5 years? Round to the nearest cent if necessary.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9200\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=9200\left(1+\frac{0.049}{4}\right)^{4\cdot 5}\implies A=9200(1.01225)^{20} \implies A \approx 11736.63[/tex]
Dos cuadrados de lado
10 cm se sobreponen formando un
rectángulo de 17 cm de largo, como se
muestra en la figura. ¿Cuál es el área
de la franja amarilla en centímetros
cuadrados?
La franja amarilla del rectángulo tiene un área de 30 centímetros cuadrados.
¿Cuál es el área de la franja amarilla del rectángulo?
En este problema tenemos un rectángulo formado por dos cuadrados que se traslapan uno al otro. La franja amarilla es el área en la que los cuadrados se traslapan. La anchura del rectángulo es descrita por la siguiente ecuación:
(10 - x) + 2 · x = 17
Donde x se mide en centímetros.
A continuación, despejamos x en la ecuación descrita:
10 + x = 17
x = 7
Ahora, el área de la franja amarilla se determina mediante la fórmula de area de un rectángulo:
A = b · h
Donde:
b - Base del rectángulo, en centímetros. h - Altura del rectángulo, en centímetros. A - Área del rectángulo, en centímetros cuadrados.A = (10 - 7) · 10
A = 3 · 10
A = 30
El área de la franja amarilla del rectángulo es igual a 30 centímetros cuadrados.
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2. If AJKL AQRS, find each missing value.
R
J
3x-1
58°
32
(4z + 3)°
K
L
27
Q
y + 10
87⁰
14
S
X=
Y=
Z=
4
Answer:gat big
Step-by-step explanation:
Struggling on factoring quadratics. Could someone help me out with this worksheet, any examples of how to do the different types of problems would be great as well as finished problems
Answer:
When factoring, you want to get all of the terms on one side first and set all of it equal to 0. Many of the problems here are already in this format =0, but there are some where you'll have to move the terms around.
In these examples, it also looks like the highest power you have is x^2. This makes things easier to work with.
Let's just start with the first one, x^2 - 9x + 18 = 0.
We need to find two numbers that multiply to give us 18, and add together to give us -9. That would be -6 and -3.
-6 + -3 = -9
- 6 * -3 = 18
We can rewrite it now. This is the factored form.
(x - 6) * (x - 3) = 0
If you want to, you can go back to expanded form using the acronym 'FOIL'. First, Outside, Inside, Last. This refers to the order of multiplying the terms.
(x - 6) * (x - 3)
x * x = x^2
x * -3 = -3x
-6 * x = -6x
-6 * -3 = 18
Simplify
x^2 - 3x - 6x + 18 = 0
And we're back to where we started.
x^2 - 9x + 18 = 0
Hope this helps.
Find the slope: (-1,1) and (-2,-3)
Thank you!
slope formula can be illustrated as , (y₂ - y₁) / (x₂ - x₁)
It is given in question that-
x₁ = -1 and y₁ = 1
x₂ = -2and y₂ = -3
so by using given formula for slope
slope= (y₂ - y₁) / (x₂ - x₁)
slope = (-3- (1) / (-2 - (-1) = (-3 - 1) / (-2 + 1) = -4/-1 = 4
final answer , slope =4
What is slope ?
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
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Answer:
[tex] \sf \: slope(m) = 4[/tex]
Step-by-step explanation:
Now we have to,
→ find the required slope.
Formula we use,
→ Slope(m) = (y2 - y1)/(x2 - x1)
Then the slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (-3 - 1)/(-2 -(-1))
→ m = (-4)/(-2 + 1)
→ m = (-4)/(-1)
→ m = 4/1
→ [ m = 4 ]
Hence, the slope is 4.
Graph this line y+4=1/4(x+10)
Answer:
See below
Step-by-step explanation:
I would start off writing the equation in the slope intercept form of a line
y + 4 = 1/4(x + 10) Distribute the 1/4
y + 4 = 1/4x + 10/4 Simplify 10/4
y + 4 = 1/4 x + 5/2 Subtract 4 from both sides
y = 1/4 x + 5/2 -4
y = 1/4 x + 5/2 - 8/2
y = 1/4 x - 3/2
Then I used the free graphing calculator Desmos to graph.
Which statement about Shawn’s line is true?
The slope of the line is 1/3
The y-intersect of the line is (4,0)
The y-interpect means Shawn ran 4 laps at week 0
The slope represents the average number of weeks it is Shawn to run laps
The slope represents the average number of weeks it is Shawn to run laps is true about Shawn's line.
Define slope.The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
Given,
Graph to show number of taps he is scheduled to run a week.
True statement is,
The slope represents the average number of weeks it is Shawn to run laps.
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Phil and Matt made cookies for a fundraiser at their high school. The cookies sold for $0.25 each. Phil and matt made a total of $72.00 selling the cookies. How many cookies did they sell. Show your work
By solving a linear equation, we will see that they sold a total of 288 cookies.
How many cookies did they sell?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
We know that Phil and Matt sell cookies for $0.25 each, so, if they sell x cookies, the total revenue is: R(x) = $0.25*x
Now, we know that they made a total of $72.00, so now we need to solve the linear equation:
$0.25*x = $72.00x
= $72.00/$0.25 = 288
They sold 288 cookies.
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Simplify. Show your work. Circle your answer.
2√10·5√12
Simplify the [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] we will get 20 · √30.
What do you mean by exponent and radicals?
Exponents are a convenient way of describing repeated multiplication of the same number. Radicals include the use of radical characters √
These are sometimes called surdos. The exponent is the power p of an expression of the form [tex]a^{p}[/tex]
The process of raising a base number to a given power is called exponentiation. (where a ≠ 0)
Given:
[tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex]
= (2 × 5)· [tex](\sqrt{10}\times \sqrt{12)}[/tex]
= 10 · [tex]\sqrt{120}[/tex]
= 10 · 2 · [tex]\sqrt{30}[/tex]
= 20 · √30
Therefore, [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] = 20 · √30
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Help me please
dont even need a full explanation just answer
The correct option C: -4 ≤ x ≤ -2, are the intervals in which the graph is constant.
Explain the term constant function?An algebraic expression known as a linear expression has terms that are either constants or variables raised to first power. Alternatively put, no of the exponents could be greater than 1.A linear function with a slope of 0 is known as a constant function. The function's value will remain constant regardless of the value you select for "x." A constant function has a graph that is a horizontal line and through y-intercept, "b." Example A's graph is indeed a horizontal line that passes through y = 4 since b is equal to 4.So, from the shown graph, the horizontal line have the constant function which lies in the intervals -4 ≤ x ≤ -2.
Thus, in the intervals -4 ≤ x ≤ -2, the function is constant.
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if f(a)=a²-1 find f(5)
Answer: 24
Step-by-step explanation:
A=5 so F(x)=5^2-1
F(x)=24
please help im really bad at this
two friends share 76 blueberries. to count the blueberries, they put them into small bowls of 10 blueberries. draw a picture to show how the blueberries can be shared equally. will they have to split apart any of the bowls of 10 berries when they share them?
So each friend will get by dividing 3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.
What is Division ?One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation may be used to quickly and simply fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will thus be 6 groups with 5 students each. The initial number, 30, which is obtained by multiplying 6 by 5 may be used to confirm this figure.
The names of the phrases connected with the division process are referred to as division parts. The division is made up of the following four components: dividend, divisor, quotient, and remainder.
Two friends can divide 76 blueberries by dividing 76 divided by 10 .
The value we get is Divisor is 10 , Dividend is 76
So, The Quotient is 7 and Remainder is 6
So there will be 7 box of 10 blueberries and 1 box with 6 berries.
Pictorial Representation is :
(10), (10), (10), (10), (10), (10), (10), (06).
Now since there are 7 bowls of 10 berries so 7 divide by 2 is 3 as quotient and 1 as remainder so 1 box will be split apart into 10 divided by 2 is 5 berries each.
So each friend will get 3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.
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So each friend will get by dividing 3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.
What is Division ?
One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation may be used to quickly and simply fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will thus be 6 groups with 5 students each. The initial number, 30, which is obtained by multiplying 6 by 5 may be used to confirm this figure.
The names of the phrases connected with the division process are referred to as division parts. The division is made up of the following four components: dividend, divisor, quotient, and remainder.
Two friends can divide 76 blueberries by dividing 76 divided by 10 .
The value we get is Divisor is 10 , Dividend is 76
So, The Quotient is 7 and Remainder is 6
So there will be 7 box of 10 blueberries and 1 box with 6 berries.
Pictorial Representation is :
(10), (10), (10), (10), (10), (10), (10), (06).
Now since there are 7 bowls of 10 berries so 7 divide by 2 is 3 as quotient and 1 as remainder so 1 box will be split apart into 10 divided by 2 is 5 berries each.
So each friend will get 3*10 + 5 + 6/2 = 30 + 5 + 3 =38 blueberries.
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Solve the problems.
Write the complete proof in your paper homework and for online to questions or statements (if any) that are parts of your proof
Given m ∠A=m ∠C=90°
AB ║ DC
Prove Δ ABD ≅ Δ CDB
Answer= m ∠ABD= m ∠CDB by reason ____
By AAS congruence theorem, ΔABD is congruent ΔCDB.
Quadrilateral ABCD is given in the figure.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given, AB║DC
Consider ΔABD and ΔCDB
m∠A=m∠C=90° (Given)
m∠ABD=m∠BDC (Alternate interior angles)
BD = BD (Common)
Using AAS congruence theorem, ΔABD ≅ ΔCDB
Hence, by AAS congruence theorem, ΔABD is congruent ΔCDB.
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A store sells two competitive products, A and B. A model for the revenue from selling qA units of product A and qB units of product B is R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB. What values of qA and qB maximize the revenue? (Fractional amounts of the products are permitted)
In differentiation , qA = 13/5 , qB = 11/5 are values of qA and qB maximize the revenue .
What does mathematics differentiation serve?
In mathematics, differentiation is used to compute rates of change. For instance, in mechanics, velocity is the amount at which a displacement changes over time.
The acceleration is the speed at which velocity is changing with respect to time.
R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB
Let aA = x , qB = y
so,
R= 40x + 50y - 6x² - 9y² - xy
Partially differentiate above equation with respect to x and y .
Rx = 40 - 12x - 4y
Ry = 50 - 18y - 4y
Set Rx = 0 and Ry = 0 solve x and y .
40 - 12x - 4y = 0
50 - 18y - 4x = 0
Solving above questions
x = 13/5 , y = 11/5
therefore,
qA = 13/5 , qB = 11/5
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How many boards 6 5/6 will it take to cover 205 in wide
By using fraction, it can be calculated that
30 boards are required to cover a floor of width 205 inches wide
What is fraction?
Suppose there is a collection and a part of collection has to be taken.
The part which is taken is called fraction. In other words part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
This is a word problem on fraction
Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches
Total width of floor = 205 inches
Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30
30 boards are required
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Suppose the average yearly salary of an individual whose final degree is a master's is $49 thousand less than twice that of an individual whose final degree is a
bachelor's. Combined, two people with each of these educational attainments earn $116 thousand. Find the average yearly salary of an individual with each of
these final degrees.
Answer:
Bachelor's Degree: $55,000
Master's Degree: $61,000
Step-by-step explanation:
First start defining variables for each of the salaries
Let M be the salary of the master's individual
Let B be the salary of the bachelor's individual
Given:
Average yearly salary of an individual whose final degree is a master's is $49 thousand less than twice that of an individual whose final degree is a bachelor's
can be translated into the equation
M = 2B - 49,000
Subtract M from both sides and add 49,000 to both sides:
49,000 = 2B - M
Switch sides:
2B - M = 49,000 [1]
Together they earned 116,000 becomes
B + M = 116,000 [2]
Add equations [1] and [2] to eliminate M
2B - M + B + M = 49,000 +116000
3B = 165000
B = 165000/3 = 55,000
Using equation 2, B + M = 116000 we get
55000 + M = 116000
M = 116000 - 55000 = 61,000
Solution
Bachelor's Degree: $55,000
Master's Degree: $61,000
FIND THE TWO POINTS HAVING AN X-COORDNATE OF 3 WHOSE DISTANCE FROM THE POINT(-2,-1) IS 13.
POINT 1: (3, ?)
POINT 2: (3, ?)
To find the two points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13, you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the coordinates of the first point, and (x2, y2) is the coordinates of the second point.
In this case, you can use the distance formula to find the y-coordinates of the two points having an x-coordinate of 3:
Distance = √((3 - (-2))^2 + (y - (-1))^2)
= √(5^2 + (y + 1)^2)
= √(25 + y^2 + 2y + 1)
= √(26 + y^2 + 2y)
= 13
If you set the distance equal to 13 and simplify the equation, you get:
y^2 + 2y + 12 = 0
This is a quadratic equation, which means it can be solved using the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation.
Substituting the values into the quadratic formula, you get:
y = (-2 ± √(-2^2 - 4 * 1 * 12)) / (2 * 1)
= (-2 ± √(-4 - 48)) / 2
= (-2 ± √(-52)) / 2
Since the square root of a negative number is not a real number.
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Fall 2018 FT Enrollment numbers for Lee Business School by Department and Level of Instruction.Accounting: Undergrad 390 Master 83 Doctoral 0, Total 473Economics Undergrad 467, Master 20, Doctoral 0, Total 487Finance Undergrad: 215, Master 7, Doctoral 0, Total 222Management, Entrenp & Tech: Undergrad 590, Master 75, Doctoral 1, Total: 666Marketing and Int; Business: Undergrad 259, Master 10, Doctoral 1, Total: 270MBA: Undergrad 0, Masters 63, Doctoral 2: 65Data #2:Create a visual from the data above that compares the total percentage of students in each department, to the whole of Lee Business School.
Total percentage of students in each department, to the whole of Lee Business School is 85.5298308 11.48709 0 2.983081 100.
What is percentage ?
A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The sign "%" is frequently put after the number to indicate percentages.
Department Undergrad Master Doctoral Total
Total % Total % Total % Numbers %
Accounting 390 17.364203 83 3.695459 0 0 473 21.05966
Economics 467 20.79252 20 0.890472 0 0 487 21.68299
Finance 215 9.5725735 7 0.311665 0 0 222 9.884239
Management, E&T 590 26.268923 75 3.33927 1 0.044524 666 29.65272
Marketing and I.B. 259 11.531612 10 0.445236 1 0.044524 270 12.02137
MBA 0 0 63 2.804987 65 2.894034 128 5.69902
Total 1921 258 67 2246
Percentage of total students 85.5298308 11.48709 0 2.983081 100
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triangle abc is shown below.
It is rotated to result in A” B” C”. Which triangle contains enough information to prove that it could be the result of this transformation?
Answer choices in the picture.
Answer:
C
Step-by-step explanation:
it is still C, as the angle-angle-angle information of D is not enough. the sides could all grow or shrink (in the same relation, but still) and the angles would still be the same.
so, D is not enough (although we have 3 pieces of information, but this is the special case, where even that is not enough - we need at least one side in the mix).
A movie complex is open from 10:00 A.M. to
2:00 A.M. daily. It contains 8 theaters, each of which
has 225 seats. The number of viewers in the theaters
is a function of the number of hours after 10:00 A.M.
each day. Describe a reasonable domain and range
of the function. Then determine whether the function
must be linear. Explain.
The collection of all logical values for each independent variable under consideration.
What is the difference between reasonable domain and range?The set of all independent variable values that are logical in the particular circumstance. the collection of every possible value for the dependent variable the collection of all feasible dependent variable values that are appropriate in the situation.
Let y = f(x) represent a function where x and y are independent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of successfully producing a single value y while using a value for x to that end.
The set of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The set of potential output values that make up the range is represented by the y-axis.
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an object travels 4/5 miles in 1/2 hour. what is her speed?
Answer:
[tex]\huge\boxed{\sf v = 0.4\ mph}[/tex]
Step-by-step explanation:
Given data:Distance = S = 4/5 miles = 0.2 miles
Time = t = 1/2 hour = 0.5 hours
Required:Speed = v = ?
Formula:v = S/t
Solution:v = 0.2/0.5
v = 0.4 mph[tex]\rule[225]{225}{2}[/tex]
Answer: 8/5 mph
Step-by-step explanation:
According to definition, an object's speed is determined by:
s=d/t where,
d is the object's travel distance, and t is the amount of time it takes.
We can replace these values with:
Since, s= (4/5) / (1/2) mph
=> s= 8/5 mph
The object's speed to cover 4/5 miles in 30 minutes is: 8/5 mph
Dr. Arman has 1,000
vitamin samples to give his
patients. The number of
samples remaining
decreases by 18% each
week. Which equation
represents the remaining
number of samples after x
weeks?
1000 - 180x represents the remaining number of samples after x weeks.
What is exponents?
Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".
Main body:
Consider what is actually happening in the question.
You begin with 1000 samples, after it decreases to
=1000-18% of 1000
= 820
You can see the pattern shows that the number of samples decreases 18% every week ,1000-18% of 1000 - 18% 0f 1000.
= 1000 - 180x where x denotes number of weeks.
Hence 1000 - 180x represents the remaining number of samples after x weeks.
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You find yourself in a strange undulating landscape given by the function z = f (x, y) = cos y − cos x, where z is the elevation.
1. Find all maxima, minima, and saddle points. What are the level curves for z = 0?
Graph this function.
You are now at the origin and wish to hike to the point (4π, 0, 0). You contemplate two rather different routes.
2. Your first route always keeps you at the same elevation. Determine such a route of minimal length. What is the length?
3. Your second route always moves along the gradient. Determine such a route of minimal length, assuming you start hiking in the positive x-direction. What is its length? If you cannot find an exact answer, determine an upper bound and a lower bound between which the actual length must lie.
4. Which route is the shorter—that of part (b), or (c)?
Appropriate pictures should be supplied throughout. Justify your answers.
Answer:
24-3-32233'2]/2
Step-by-step explanation:
Which of the following could be an example of a function with a range (-∞, α) and a domain [b, ∞) where a > 0 and b>0?
Explanation:
Choices A and B are ruled out because they are cube root functions, which have a domain and range of "all real numbers".
Choice C is ruled out because the domain is [tex][a, \infty)[/tex]
To determine this domain, we set the radicand (aka stuff under the square root) to be greater than or equal to zero.
[tex]x-a \ge 0 \ \ \text{ solves to } \ \ x \ge a[/tex]
[tex]x \ge a \ \ \text{ turns into the interval notation } \ \ [a, \infty)[/tex]
The square bracket is used to include the value 'a' as part of the interval. This is the interval from x = a to positive infinity.
The domain of choice D is [tex][b, \infty)[/tex] found using similar steps as shown above.
The range is [tex](-\infty, a][/tex] since this square root function is decreasing, due to the negative out front, which means y = a the largest output possible. I recommend graphing it out using a tool like desmos or geogebra. These tools offer a way to use parameters.