Answer:
1) No,2) Yes, x ≈ 5.32-----------------------------
Part 1Given sequence:
t(n) = 5 · 2ⁿIf t(n) = 200, we can try to find the value of n:
5 · 2ⁿ = 2002ⁿ = 40There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.
The sequence should include integer numbers, so there is no solution.
Part 2Given function:
f(x) = 5 · 2ˣSolve for x if f(x) is 200:
5 · 2ˣ = 2002ˣ = 40log 2ˣ = log 40x log 2 = log 40x = log 40 / log 2x = 5.32 (rounded)Answer:
1. No
[tex]\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)[/tex]
Step-by-step explanation:
Question 1Given sequence:
[tex]t(n)=5 \cdot 2^n[/tex]
To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:
[tex]\implies 5 \cdot 2^n=200[/tex]
[tex]\implies 2^n=40[/tex]
[tex]\implies \ln 2^n=\ln 40[/tex]
[tex]\implies n\ln 2=\ln 40[/tex]
[tex]\implies n=\dfrac{\ln 40}{\ln 2}[/tex]
[tex]\implies n=5.3219280...[/tex]
In a sequence, n is a positive integer. Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.
Question 2Given function:
[tex]f(x)=5 \cdot 2^x[/tex]
To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:
[tex]\implies 5 \cdot 2^x=200[/tex]
[tex]\implies 2^x=40[/tex]
[tex]\implies \ln 2^x=\ln 40[/tex]
[tex]\implies x=\dfrac{\ln 40}{\ln 2}[/tex]
[tex]\implies x=5.3219280...[/tex]
Therefore, it is possible for the function to have an output of 200 when:
[tex]x=\dfrac{\ln 40}{\ln 2}[/tex]
Please help me with this...
Answer:
[tex]\boxed{x = 8 \;m}[/tex]
Step-by-step explanation:
Nice drawing! :)
From the figure we see that the rectangle has a length of 30 m and a width of 20 m
The total area of the rectangle PQRS = 20 x 30 = 600 m²
The square footage of the planted area = area of figure MNSR = 388 m²
Therefore the rest of the area (the unshaded portion) is:
600 - 388 = 212 m²
This is the combined area of the two triangles ΔPNM and ΔMRG
Let's find the area of each of these triangles. Each of them is a right triangle which makes calculations easier
Area of a right triangle = (1/2) x base x height
ΔPNM has base = 30 - x and height = 20 -x
Area of ΔPNM
= (1/2) (30-x)(2-x)
We can use the FOIL method to evaluate (30-x)(2-x)
(30-x)(20-x)
= 30·20 + (30)(-x) + x(20) + (-x)(-x)
= 600 - 30x + 20x + x²
= 600 -50x + x³
We usually rewrite with coefficients in decreasing magnitude of x degree
Area of ΔPNM
[tex]=\dfrac{x^2 - 50x + 600}{2}[/tex]
Let's now find the area of ΔMRQ with a base of x and a height of 20
Area of ΔMRQ
[tex]=\dfrac{1}{2}\cdot 20 = \dfrac{20x}{2}[/tex]
Adding both terms together we get
[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} \\[/tex]
We have computed the area of the unshaded region as 212
So the above sum must be equal to 212
[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} = 212[/tex]
Multiply throughout by 2 to get rid of the denominator:
[tex]\rightarrow \;\;x^2 - 50x + 600 + 20x = 212\times 2 = 424\\\\\rightarrow \;\;x^2 -30x + 600 =424\\[/tex]
Move 424 to the left:
[tex]x^2-30x+600-424=424-424\\\\x^2-30x+176=0[/tex][tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]
This is a quadratic equation which can be solved using the quadratic formula or by factoring
[tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]
So
[tex]x^2-30x+176=0 \rightarrow (x -8)(x-22) = 0\\\\[/tex]
So x = 8 or x = 22 are two possible solutions to this quadratic
If x = 22, it will be greater than the width of 20 and also 20-x = -2 so it is not a valid solution for this situation
Therefore we get the final answer as [tex]\boxed{x = 8 \;m}[/tex]
Calculate the degrees of freedom associated with a small-sample test of hypothesis for (H H2 assuming o12 o22 and n n2 16. O A. 15 O B. 31 O C. 32 O D. 30
Option A, The degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex], and [tex]n_1[/tex], [tex]n_2[/tex] is 15.
To calculate the degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex] and [tex]n_1[/tex], [tex]n_2[/tex], you would use the following formula:
df = ([tex]o_{12}^2[/tex]/n_1) + ([tex]o_{22}^2[/tex]/n_2)
In this case, the degrees of freedom would be:
df = ([tex]o_{12}^2[/tex]/16) + ([tex]o_{22}^2[/tex]/16) = 15 and represents the number of values that are free to vary in the sample.
So, the answer would be A. 15
It's important to note that this formula is only used for small sample sizes. For large sample sizes, the degrees of freedom are approximated using the Welch-Satterthwaite approximation.
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calculate the molar solubility of cui (ksp= 1.27×10−12).
CuI's molar solubility is determined to be 1.27 x 10⁻¹².
The quantity of ions dissolved per litre of solution is measured by molar solubility. The quantity of ions that are dissolved in this situation's amount of solvent is represented as solubility.
Think about the equation.
Cu+(aq) CuI.(s) + I- (aq)
Let's assume that CuI (s) has a molar solubility of "S" mol/L.
Thus,
Product of solubility = [Cu+(aq)] + [ I-(aq)] → [Cu+(aq)] Ksp
[ I-(aq)] ———(1)
We are aware of
For CuI, the solubility product Ksp is 1.27 x 10⁻¹².
Consequently, from equation (1)
1.27 × 10⁻¹² = S.S
S² =1.27 × 10⁻¹²
= (1.27 × 10⁻¹² )½ = 1.127 x 10⁻⁶ M
Therefore, CuI has a molar solubility of 1.127 x 10-6 M.
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A $659,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by
y = 659,000 − 1800x dollars.
After how many months will the value of the building be $450,200?
Answer:
116 months
Step-by-step explanation:
A $659,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by:
y = 659,000 − 1800x
After how many months will the value of the building be $450,200?
y = 659,000 − 1800x
450,200 = 659,000 − 1800x
subtract 659,000 from both sides:
450,200 - 659,000 = 659,000 − 1800x - 659,000
-208,800 = − 1800x
divide both sides by -1800:
-208,800/1800 = − 1800x/1800
116= x
so:
x = 116
Help me solve please y-9 terms,variables, coefficient s,constants
The terms in given expression like variables, coefficient, constant are respectively, y, 1, -9
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression,
⇒ y-9
In given expression, y is term which is variable
And coefficient of y is 1
constant term is -9
Therefore, we can write our terms are, y, 1, -9
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435% of 6.6 Is what?
Answer:
28.71
I looked it up.
Answer:
28.71
Step-by-step explanation:
To be honest with you, I looked it up
For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
36,13
Answer:
9 and 4
Step-by-step explanation:
xy = 36
x+y = 13 or 13 - x = y <====sub this into the first equation
x ( 13-x) = 36
-x^2 + 13x - 36 = 0 multiply the entire equation by -1 to make it easier solve
x^2 -13x+36 = 0 this factors to
(x -9)(x-4) = 0 showing x = 9 or 4 with y being 4 or 9
Decimals to the tenths?
The first digit to the right of the decimal point indicates the number of tenths. For example, the decimal 0.3 is the same as the fraction 3/10.
Examine the triangle below, solve for x, rounded to two decimal places.
45°
I’m stuck on this question
a) The polygon has 11 sides
b) The Sum of the Interior Angles of the 11 sided Polygon = 1620 degrees
What is a polygon ?
The definition of a polygon is a closed, two-dimensional, plane shape created by connecting three or more line segments. During our study of geometry, polygons are a common sight.
A polygon's sides are constructed from segments of straight lines joined end to end. The sides or edges of a polygon are the line segments that make up its shape. The vertex or corners formed by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon.
There are 11 sides, So, n=11
Sum of the Interior Angles of a Polygon = 180 (n-2) degrees
So,
The Sum of the Interior Angles of the 11 sided Polygon
= 180 (11-2) degrees
= 180 ( 9)
= 1620 degrees
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Mrs. Jones needs new fencing for her backyard the dimensions of the rectangular yard are 3.4 M by 2.7 M how many centimeters of fencing will she need?
The Fencing Mrs. Jones will need in centimeters is 1220 cm
How to find the fencing Mrs. Jones will needThe fencing is a measure of the perimeter of the region to be covered
With the dimensions in meters deduced form the problem as 3.4 m by 2.7 m. the perimeter is calculated using the formula
= 2( length * width)
= 2(3.4 + 2.7)
= 2(6.1)
= 12.2 m
To convert 12.2 m to cm we use the factor, 1 m i= 100 cm, therefore
= 12.2 * 100
= 1220 cm
the perimeter is 1220 cm
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12. Suppose U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} is the universal set and G = \{1, 2, 3, 4, 5, 6, 7\} . What (1 point)
O \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
O cannot be determined
O \{1, 2, 3, 4, 5, 6, 7\}
O \{8, 9, 10\}
is G'?
The complement of A∪B is A′∩B ′.
In sets, what does complement mean?A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.
Given, universal set, U={1,2,3,4,5,6,7}
A={1,2,5,7}
B={3,4,5,6}
(A∪B) ′=U−(A∪B)
={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ
A′∩B′=(U−A)n(U−B)
={3,4,6}n{1,2,7}=ϕ
Hence ( A∪B)′=A′∩B ′.
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Felipe, Jill, and Cindy are neighbors. Jill is 7 years older than Cindy and Felipe is two-
thirds the age of Jill. The sum of their three ages is 137.
a. If a represents Jill's age, write an equation in terms of that can be used to
determine each person's age.
b. How old is Felipe?
On solving the provided question, we can say that vertex form of the equation is in the form of y = a(x-h)^2 + k.
In mathematics, what is the vertex?A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedral, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.
Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.
a = -1/4 * (4 - 12) = -1
h = -b/(2a) = 12/(2(-1)) = -6
k = f(h) = -(-6)^2 + 12(-6) - 4 = 36
Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.
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can someone please solve this
The <HDI of the circle is 70 degree. A circle is divides into 360 equal degrees.
How to find <HDI?A circle is divides into 360 equal degrees.
In relation to a circle, angles are measured in degrees or radians, with one full rotation being equal to 360 degrees or 2 Pi radians.
so, <EDI = 140 degree.
so
A circle is 360 equal degrees.
360 - 140 = 220
< IDH = <EDF = 2x
<FDG = <GDH = 2y
so
2x + 2y = 220
2 * 70 + 2 * 40 = 220 degree
so,
<HDI = 70 degree.
so
The <HDI of the circle is 70 degree.A circle is divided into 360 equal degrees.
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(x'2-3x+5) dived (x-1)
The quotient of the division (x^2-3x+5) divided (x-1) is x - 2 with a remainder of 3
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
(x^2-3x+5) divided (x-1)
Using the long division method of quotient, we have
x - 1 | x^2 - 3x + 5
The division steps are as follows
x - 2
x - 1 | x^2 - 3x + 5
x^2 - x
------------------------------------------------
-2x + 5
-2x + 2
------------------------------------------------
3
Hence, the quotient is x - 2
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john wants to buy a bicycle worth R750 . how many hours should he work to earn R750
Answer: To determine how many hours John needs to work to earn R750, you would need to know his hourly wage. If John earns R50 per hour, he would need to work 15 hours to earn R750 (R750 / R50/hour = 15 hours). If his hourly wage is different, the number of hours he needs to work will be different.
Step-by-step explanation:
A family eats at a restaurant. The bill is $42. The family leaves a tip and spends $49.77. a.) How much was the tip in dollars?
b.) How much was the tip as a percentage of the bill?
The tip was $7.77 in total, and it is a 18.5% of the bill cost.
How much was the tip in dollars?Here we know that the bill was $42, while the family spend a total of $49.77
Then the amount for the tip is equal to the difference between the bill and the amount that the family spends.
Tip = $49.77 - $42 = $7.77
Now we want to see which percentage of the bill this is, to check that, we need to take the quotient between the tip and the bill, and multiply that by 100%, we will get:
percentage = ($7.77/$42)*100%
percentage = (0.185)*100% = 18.5%
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A house on the market was valued at $289,00 . After several years, the value increased by 17% . By how much did the house's value increase in dollars? What is the current value of the house?
Answer:
the answer is 338.13
Step-by-step explanation:
289,00×.17=49.23
49.13+289.00
hope this helps:)
Which ordered pairs lie on graph of the exponential function f(x) = 5(4)^x
Answer:
(0,5) and (3,320)
Step-by-step explanation:
Plug in the ordered pair into the function and see if it makes sense.
Plug in 5 for y and 0 for x:
5= 5(4)^0
4^0 = 1 (anything to the power of 0 except 0 is one)
5x1 = 5
5=5
(0,5) works
320 = 5(4)^3
4^3 = 64
64x5 = 320
320=320
320=320 (3,320) works
(0,5) and (3,320) both work.
QS bisects PQR and m/PQR = 119°.
Find m/PQS and m/RQS.
Q
m/PQS = ?
m/RQS =
Therefore , the solution to the given problem of angles comes out to be
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
Define angles.
An angled structure in geometry is composed of two rays that converge at the vertex, or core, of the angle. These rays are referred to as the angle's faces. Depending upon where they are situated, two beams may be able to form any angle within a plane. The intersection of two planes also produces an angle. Diahedral angles are the name for them. Light beams or lines that share the same endpoint in plane geometry can have a wide variety of shapes or angles. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of the two rays is known as the vertex, or vertex of the angle.
Here,
QS cuts an angle. PQR, followed by ∠SQR = ∠ PQS and
∠PQS + ∠RQS = ∠PQR.
The equation then changes to
∠PQR = ∠PQS + ∠PQS
∠PQR = 2∠PQS
∠PQS equals ∠PQR/2
assuming∠ PQR = 119°
Replace in the resulting expression from the above;
∠PQS equals ∠PQR/2
∠PQS = 119/2
∠PQS = 59.5°
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
Therefore , the solution to the given problem of angle comes out to be
∠RQS is 59.5 degrees as ∠RQS = ∠PQR.
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Amelia used 6 liters of gasoline to drive 48 kilometers. How many kilometers did Amelia drive per liter?
PLEASE HELP SERIOUSLY NEED IT
Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.
Describe the circle.Every point in the plane of a circle is equally separated from the center and is a closed, two-dimensional object. Each line tracing the circle contributes to the formation of the line of reflection symmetry. Additionally, each angle has rotational symmetry around the center.
Here,
calculation
The formula for arc length is (/2) 2r.
because of length of an arc equals r.
16 = 4θ
=> θ = 4
4r is the length of an arc.
Four times the radius, the subtended arc is longer.
Angle A is subtended by an arc if its length and radius are equal.
=> θ = 16 /4
=>4 rad
Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.
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What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?
In a linear graph line diagram, A line passes through (minus 4, minus 6) and (8, 3) which intersects the x-axis at 4 units and the y-axis at minus 3 units.
A.
y
=
−
4
3
x
−
47
3
B.
y
=
3
4
x
−
11
C.
y
=
3
4
x
+
1
D.
Answer:
Step-by-step explanation: The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.
What is Algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
Variables and constants can both be used in an algebraic expression.
A coefficient is any quantity that is added before a variable and then multiplied by it.
The Algebraic expression in this case is:
x + y = 8
which traverses points (8,-5)
Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.
y = mx + c →(1)
x + y = 8
y = -x + 8
Comparing the aforementioned Algebraic expression to equation (1), we obtain
m = -1
The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.
Let's use the point-slope equations of line to determine the linear equation now:
(y-y₁) = m(x-x₁)
Changing every value in the equation above to obtain the Algebraic expression for a line
(y-(-5)) = -1(x-8) (x-8)
(y+5) = -x+8
y + 5 = -x +8
y = -x +3
The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3
Write an expression to represent emaily number
On solving the provided question we can say that the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
here,
the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]
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write the equation of the line given the following information in
point-slope form then re-write in slope-intercept form.
20. through the points (1, 3) and (-4, 5)
21. Through the point (4, -7) and is parallel to y = -2x-5
22. Through the point (3, 5) and is perpendicular to y = -3/2x + 1
We can use the formula:
[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]
Describe a slope.In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
20) The point-slope form of a line is[tex]y - y1 = m(x - x1)[/tex], where [tex](x1, y1)[/tex] is a point on the line and m is the slope. The slope of the line can be found by using the coordinates of two points on the line. To find the slope between the points [tex](1, 3)[/tex] and [tex](-4, 5)[/tex], we can use the formula:
[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]
The point-slope form of the line is then:
[tex]y - 3 = (2/5)(x - 1)[/tex]
To convert this to slope-intercept form (y = mx + b), we can solve for y:
[tex]y = (2/5)x + (3 - (2/5)) = (2/5)x + (12/5)[/tex]
21) The line is parallel to [tex]y = -2x - 5[/tex], so we know that the slope of the line is -2. We can use the point [tex](4, -7)[/tex]and the slope -2 to write the equation in point-slope form:
[tex]y - (-7) = -2(x - 4)[/tex]
or
[tex]y + 7 = -2x + 8[/tex]
To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:
[tex]y = -2x + 1[/tex]
22) The line is perpendicular to [tex]y = -3/2x + 1[/tex], so we know that the slope of the line is the negative reciprocal of [tex]-3/2[/tex]. The slope of the line is [tex]2/3[/tex]. We can use the point [tex](3, 5)[/tex] and the slope [tex]2/3[/tex] to write the equation in point-slope form:
[tex]y - 5 = (2/3)(x - 3)[/tex]
or
[tex]y = (2/3)x + (5 - (2/3)3) = (2/3)x + (5 - 2) = (2/3)x + 3[/tex]
To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:
[tex]y = (2/3)x + 3[/tex]
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sometimes a change of variable can be used to convert a differential equation into a separable equation. one common change of variable technique is as follows. consider a differential equation of the form , where , and are constants. use the change of variable to rewrite the differential equation as a separable equation of the form . solve the initial value problem (a) help (formulas) (b) help (formulas)
The differential equation is [tex]y=\frac{-7t^2+22t-7}{7t-22}[/tex]
We are given the Initial value problem:
y'=(t=y)²-1, y(3)=4
Substitute the value z=t+y
When t=3 and y=4 then z=3+4=7
y'=z²+1
Differentiate z w.r.t t
[tex]\frac{dz}{dt} =1+y'[/tex]
Then, we get [tex]z'=1+z'-1=z^2[/tex]
z⁻²dz=dt
Integrate on both sides:
-1/zdz=t+c
z=-1/t=c
Substitute t=3 and z=7
Then, we get
7=-1/3+c
21+7c=-1
7c=-1-21=-22
c=-22/7
Substitute the value of C then we get:
z=-1/t-22/7
z=-7/7t-22
y=z-t
y=-7/7t-22-t
y=-7-7t²+22t/7t-22
y=-7t²+22t-7/7t-22.
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A manager of a clothing store always orders 2 small T-shirt and 3 small T-shirts for every 4 medium T-shirt. The manager plans to order 24 medium T-shirts. How many small T-shirts should the manager order
The manager of the clothing store always orders 2 small T-shirts and 3 small T-shirts for every 4 medium T-shirts.
What in mathematics is a linear equation?
According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The manager plans to order 24 medium T-shirts and we want to find out how many small T-shirts the manager should order.
We can use the information given to set up an equation to represent the relationship between the number of small T-shirts and medium T-shirts. Let S be the number of small T-shirts and M be the number of medium T-shirts.
We know that:
S = 2 + (3/4)M
We are given that the manager plans to order 24 medium T-shirts, so we can substitute this value into the equation:
S = 2 + (3/4) * 24
We can simplify and solve for S:
S = 2 + (3/4) * 24
S = 2 + 18
S = 20
Therefore, the manager should order 20 small T-shirts.
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ANYONE GOOD AT MATH COME ON OVER AND HELP A FELLOW SLOW PERSON PLEASE WILL GIVE 30 POINTS!!!
The completed table with the values for composite functions in column 3, f(g(x)) and column 4, g(f(x)) included is presented as follows;
[tex]\begin{array}{|c|c|c|c|}f(x) & g(x) & f(g(x)) &g(f(x)) \\&&&\\x^2+1 &-2\cdot x + 5 &4\cdot x^2 -20\cdot x +26 & -2\cdot x^2+3 \\&&&\\2\cdot x^2 - 2\cdot x + 4 & x+3 & 2\cdot x^2 + 10\cdot x + 16& 2\cdot x^2 - 2\cdot x + 7 \\&&&\\ \sqrt{x-4} &2\cdot x^2+ 4 &x\cdot \sqrt{2} & 2\cdot x - 4 \\\end{matrix}[/tex]
f(g(x)) ≠ g(f(x)), because the operations and the order of operations in the functions are different
What are composite functions?Composite functions are functions in which the input or argument are also functions.
The values of the composite functions based on the defined functions are found as follows;
f(x) = x² + 1, g(x) = -2·x + 5
Therefore; f(g(x)) is obtained by plugging in x = g(x) in f(x) as follows;
f(x) = x² + 1
f(g(x)) = (-2·x + 5)² + 1 = -2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1
-2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1 = 4·x² - 10·x - 10·x + 25 + 1
4·x² - 10·x - 10·x + 25 + 1 = 4·x² - 20·x + 26
When f(x) = x² + 1, and g(x) = -2·x + 5, f(g(x)) = 4·x² - 20·x + 26
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = -2·x + 5
f(x) = x² + 1
g(f(x)) = -2 × (x² + 1) + 5 = -2·x² - 2 + 5
g(f(x)) = -2·x² + 3
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, we get;
f(g(x)) = 2×(x + 3)² - 2×(x + 3) + 4 = 2×(x² + 6·x + 9) - 2·x - 6 + 4
2×(x² + 6·x + 9) + 2·x + 6 + 4 = 2·x² + 10·x + 16
f(g(x)) = 2·x² + 10·x + 16
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, f(g(x)) = 2·x² + 10·x + 16
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = x + 3
f(x) = 2·x² - 2·x + 4
g(f(x)) = 2·x² - 2·x + 4 + 3 = 2·x² - 2·x + 7
g(f(x)) = 2·x² - 2·x + 7
When f(x) = [tex]\sqrt{x - 4}[/tex], and g(x) = 2·x² + 4, we get;
f(g(x)) = [tex]\sqrt{2\cdot x^2 + 4 - 4} = x\cdot \sqrt{2}[/tex]
g(f(x)) = 2 × ([tex]\sqrt{x - 4}[/tex])² + 4 = 2 × (x - 4) + 4 = 2·x - 4
g(f(x)) = 2·x - 4
The values of the composite functions in column 3 and column 4 are included in the table in the first section of the response.
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To the nearest hundredth, find the value of x.
220
292
17.09
14.83
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo. Do note that since this is a right-angled triangle, Pythagoras' Theorem can be used to find the length of one side：
[tex]c^{2} = a^{2} + b^{2}[/tex]
Jim is talking out a $135,000 mortgage. His bank offers him an APR of 3.32%. He wants to compare monthly payments on a 20- and a 30-year mortgage. Find, to the nearest dollar, the difference in the monthly payments for these two loans?
The difference in the monthly payments for a 20-year mortgage and a 30-year mortgage on a $135,000 loan at 3.32% APR is $430.
Find, to the nearest dollar, the difference in the monthly payments for these two loans?The monthly payment on the 20-year mortgage is $902 and the monthly payment on the 30-year mortgage is $1,332.For Jim to compare the monthly payments on a 20-year mortgage and a 30-year mortgage, he needs to calculate the principal and interest for each loan. The principal and interest for a 20-year mortgage at 3.32% APR for $135,000 is $715.09 per month. The principal and interest for a 30-year mortgage at 3.32% APR for $135,000 is $572.72 per month. The difference in the monthly payments for these two loans is $142.37 per month.To calculate the difference in the monthly payments for a 20-year mortgage and a 30-year mortgage, you must first calculate the principal and interest for each loan. To do this, multiply the loan amount by the monthly interest rate, which is the APR divided by 12. Then subtract the principal from the total amount.This will give you the monthly principal and interest payment. The difference in the monthly payments for the two loans is the difference between the monthly principal and interest payments.To learn more about the difference in the monthly payments refer to:
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