The two-step exchange process is an illustration of composite functions
The function that converts dollars to Euro is [tex]\mathbf{g(d) = 0.897d - 3.3 }[/tex]You would receive 400.35 Euros, when you exchange 450 dollarsYou would receive 70.6 dollars, when you exchange 60 EurosConverting from dollars to British pounds, we have:
[tex]\mathbf{f(d) = 0.69d - 1}[/tex]
Converting from British pounds to Euro, we have:
[tex]\mathbf{g(p) = 1.3p - 2}[/tex]
(a) Function that converts dollars to Euro
To do this, we simply calculate gf(d)
So, we have:
[tex]\mathbf{g(f(d)) = 1.3f(d) - 2}[/tex]
Substitute [tex]\mathbf{f(d) = 0.69d - 1}[/tex]
[tex]\mathbf{g(f(d)) = 1.3 \times (0.69d - 1) - 2}[/tex]
Expand
[tex]\mathbf{g(f(d)) = 0.897d - 1.3 - 2}[/tex]
[tex]\mathbf{g(f(d)) = 0.897d - 3.3 }[/tex]
Rewrite as:
[tex]\mathbf{g(d) = 0.897d - 3.3 }[/tex]
Hence, the function that converts dollars to Euro is [tex]\mathbf{g(d) = 0.897d - 3.3 }[/tex]
(b) Euro equivalent of $450
In (a), we have [tex]\mathbf{g(d) = 0.897d - 3.3 }[/tex]
Substitute 450 for d
[tex]\mathbf{g(450) = 0.897 \times 450 - 3.3 }[/tex]
[tex]\mathbf{g(450) = 403.65 - 3.3 }[/tex]
[tex]\mathbf{g(450) = 400.35}[/tex]
Hence, you would receive 400.35 Euros, when you exchange 450 dollars
(c) Dollar equivalent of 60 Euros
In (a), we have [tex]\mathbf{g(d) = 0.897d - 3.3 }[/tex]
Substitute 60 for g(d)
[tex]\mathbf{60 = 0.897d - 3.3 }[/tex]
Add 3.3 to both sides
[tex]\mathbf{0.897d = 63.3 }[/tex]
Divide both sides by 0.897
[tex]\mathbf{d = 70.6}[/tex]
Hence, you would receive 70.6 dollars, when you exchange 60 Euros
Read more about composite functions at:
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The volume of one serving of fruit punch
is 3.5 fluid Ounces. How many servings
are there in 29.75 fluid Ounces of
fruit punch?
A. 8.25 Servings
B. 8.5 Servings
C. 9.25 Servings
D. 9.5 Servings
In a population of 128 people, 45 have curly hair, 66 have straight hair, and 17 have no hair. What is the probability of randomly choosing someone with curly hair or no hair?
Write a rule to describe each transformation.
- A
- B
- C
- D
Answer:
A, a dilation of 2
Step-by-step explanation:
The answer is, A dilation of 2 because the image is getting dilated to a bigger form. If it was a decimal or a fraction; the image would be smaller and than the pre-image.
(Pre-image is a shape before a transformation, image is after a ransformation.)
Have a great day friend! :D
PLEASE HELPP!! What is the slope and Y intercept of this equation?
Answer:
The slope is 10
The y - intercept is 20
Step-by-step explanation:
The equations are written as:
y = ?x + ?
The first ? is the slope of the equation, every time y increases by that amount, x increases by one, the slope here is 10
The second ? is the y-intercept, or the place where x is 0. Here, when x is 0, y is 20, so it is the y-intercept
Use the Distributive Property to solve the equation.
3(x−6)+8=5x−2
Answer:
x = -4
Step-by-step explanation:
2x=-2+10
-2=8
x=-4
Answer:
3x-18+8=5x-2
3x-10=5x-2
3x-5x=-2+10
-2x=8
X=-4
Step-by-step explanation:
Have a great day
Make x the subject of the formula x + t = q
Answer:
x = t - q
Step-by-step explanation:
because to make q, you need to add x and t
so to make x the subject, you should subtract q
Example
x + t = q
t = 7
q = 36
x = t - q
36 -7 = 29
x = 29
!!!WILL MARK BRAINLIEST IF ALL ARE ANWSERED!!! please provide short explanations
Answer:
20= 20
21. 10
22. 1.8
23. 4.4
24. 32
25. 7/9
If a=6, b=12,and c=4, then what does 2ab-c^2 equal?
Answer: 2(6)(12)-4^2 = 128
What is the prime factorization of 100,000?
Answer: 2^5× 5^5
Solve for x. 5.8 = 4x+0.2
Answer: x= 1.4
Find the area of this shape.
Answer: Area = 1.21
What is the lateral surface area of this rectangular prism?
Answer: 208 in^2
5/9 + 1/3 × 1/3 = 0.66666666666 = 2/3
Step-by-step explanation:
The prime factorization of 100,000 is 2^5 × 5^5. Since it has a total of 10 prime factors, 100,000 is a composite number.
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5.8-0.2=4+0.2−0.2
5.6 = 4x
5.6/4 = 4x/4
x= 1.4
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Square sides are equal..
A=a^2=1.1^2≈1.21
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The lateral surface area of a rectangular prism can be calculated by finding the sum of all the lateral faces of the prism, i.e. the total area excluding the area of the bases. The formula to find the surface area of a rectangular prism is given as, Lateral surface area of a rectangular prism = 2(l + b) h square units.
When a prism has its bases facing up and down, the lateral area is the area of the vertical faces. (For a rectangular prism, any pair of opposite faces can be bases.) The lateral area of a right prism can be calculated by multiplying the perimeter of the base by the height of the prism.
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How do you solve for x?
2(x - 3)^2 - 32 = 0
[tex] \: \: \: \: \: \: \: \: [/tex]
[tex]x = - 1 \\ x = \: 7[/tex]
Step-by-step explanation:
[tex]2(x - 3 {)}^{2} - 32 = 0[/tex]
divide both sides[tex](x - 3 {)}^{2} - 16 = 0[/tex]
use a²- b² =(a - b ) (a + b) to factor the expression[tex](x - 3 - 4) \times (x - 3 + 4) = 0[/tex]
calculate the difference and the sum[tex](x - 7) \times (x + 1) = 0[/tex]
when the product of factors equals 0 ,at least one factor is 0[tex]x - 7 = 0 \\ x + 1 = 0[/tex]
solve the equation for x[tex]x = 7 \\ x + 1 = 0[/tex]
the equation has 2 solutions[tex]x = - 1 \\ x = 7[/tex]
hope it helps[tex] \: \: \: \: \: \: \: [/tex]
When a child is more than two standard deviations underweight for his or her age, the child is suffering from a condition called _____.
Urgent…. I need help
You don’t gotta explain
I will mark brainiest asp
Which one is a function?
A.
Step-by-step explanation:
To find out the answer, there is a method that can be used to find out if a line is a function. It is called the vertical line method. And it also has to be per x, One y value has to be there. Analyzing the graphs, the answer should be option A.
V^2=u^2 + 2as rearrange to s subject
[tex]v^2 = u^2 + 2as \\\\\implies 2as = v^2 -u^2 \\\\\implies s = \dfrac{v^2 - u^2}{2a}[/tex]
HELP ME PLEASE AAAAAAAAAAA
Answer:
180°consecutive interior angles are supplementary∠620°, 160°Step-by-step explanation:
The blanks get filled in like this:
Statement 3: m∠6 +m∠4 = 180°
Reason 3: Consecutive interior angles are supplementary
Statement 4: m∠6 +8·m∠6 = 180°
Statement 5: m∠6 = 20°, m∠4 = 160°
_____
You can see from the diagram that angles 4 and 6 are consecutive interior angles. You know the relation between those angles is that they are supplementary. The problem is asking you to state that relationship as Reason 3.
The given relation between the angles, m∠6 = 1/8·m∠4, can be recast as ...
8·m∠6 = m∠4
This is the substitution that is used in statement 4.
Simplifying that statement gives 9·m∠6 = 180° ⇒ m∠6 = 180°/9 = 20°. Then m∠4 = 8·m∠6 = 8·20° = 160°.
help me
[tex] \: [/tex]
if mCE =100° ,mCA =110° and CR is a diameter find
mAR
mER
ANSWER 6-10 PLSS
see the attachment plss
need properly answer
right answer get brainlist
nonsense answer will be reported
[tex] \: [/tex]
Step-by-step explanation:
#6mAR = mCR - mCA = 180° - 110° = 70°#7mER = mCR - mCE = 180° - 100° = 80°#8m∠CAR = 90° as CR is diameter#9m∠CRA = 1/2(mCA) = 1/2(110°) = 55°#10m∠ROE = m∠COR - m∠COE = 180° - 100° = 80°Given loga (m) = 10 and loga (n) = 25 , find loga (m * n ^ 2)
The result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
According to the law of logarithm if [tex]log_ab=y[/tex] then [tex]b=a^y[/tex]
Given the following expressions
[tex]log_am=10\\log_an=25[/tex]
This can be expressed as
[tex]m =a^{10} \ and \ n = a^{25}[/tex]
Substitute the value of m and n into the expression [tex]log_a (m * n ^ 2)[/tex] to have:
[tex]log_a (m * n ^ 2) = log_a(a^{10}\times a^{50})\\=log_aa^{60}\\=60log_aa\\=60(1) \\= 60[/tex]
This shows that the result of the log function [tex]log_a (m * n ^ 2)[/tex] is 60
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Both Alex and Chris left their homes at 7:00 a.m. and walked to school. The graph shows the distances that each boy was from school as they walked.
A graph titled Distance from school has minutes since leaving home on the x-axis, and miles from school on the y-axis. A line labeled Chris goes through points (0, 4) and (15, 3). A line labeled Alex goes through points (0, 2) and (25, 1).
Which statement is best supported by the graph?
Alex lives farther from the school than Chris lives, and Alex walked to school at a faster rate than Chris walked.
Alex lives closer to the school than Chris lives, and Alex walked to school at a faster rate than Chris walked.
Chris lives farther from the school than Alex lives, and Chris walked to school at a faster rate than Alex walked.
Chris lives closer to the school than Alex lives, and Chris walked to school at a faster rate than Alex walked.
Answer:
Chris lives farther from school than Alex lives, and Chris walks to school at a faster rate than Alex
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Since it was 7 years ago, Mr. Ly's age was 28 years old.
Can someone please tell me what is his age at present (In now)?
Answer:
28+7=35. 35 is your answer.
Answer:
35
Step-by-step explanation:
35 because 7+28 is 35 7
28
The following machine doubles each input, subtracts 3, and then squares the result. (check photo) For example, if we input 5, then double 5 to get 10, subtract 3 to get 7, and finally square 7 to get 49.
-Write the expression that comes out of the machine if the input is 4.
Use ^ to express exponents. For example. 3² = 3^2
-If 121 is the output, what was the input?
Answer:
Step-by-step explanation:
Somebody, please help me with this MATH question.
the answer is abffj uynjy uymn mhk um
Phil has a three-year contract for his cell phone service. He pays $572.60 each year to cover everyone and his family. How much will the cell phone service cost over the three-year period
Answer:
$1717.80
Step-by-step explanation:
We are given one clue: He pays $572.60 each year to cover everyone and his family.
We are asked to find how much does Phil have to pay after 3 years. So, we must multiply 572.60 by 3 to find the total cost Phil has to pay after 3 years.
572.60 x 3 = Total cost to pay after 3 years.
=> $1717.80 = Total cost to pay after 3 years.
We can conclude that Phil will have to pay $1717.80 after 3 years.
what is (−
2
1
)
5
Step-by-step explanation:
i don't understand your question
Someone plz help me I’m begging
Answer:
answer is D
pls I don't confirm sorry
Write the slope-intercept form of the equation
Answer:
y= [tex]\frac{1}{3}[/tex]x-1
Step-by-step explanation:
Slope intercept form= y=mx+b
m=slope
b=y-intercept
b=-1
m= [tex]\frac{1}{3}[/tex]
y= [tex]\frac{1}{3}[/tex]x-1
Find the area of the polygon below. ( and please show work)
Answer:
89.6875
Step-by-step explanation:
you need to find out area of rectangle (length x width) and add area of the triangle (length x width divided by 2)
Mike has $84 less than three times as much as Dave. Together they have $132. How much money does Mike have? I have to use either the strategy of elimination or substitution to solve this. I realize that the first equation is m + d = 132. But I don’t get what the second equation should be!
Answer:
D+M=132?
Sorry if this is not helpful. I tried my best
Find the 32nd term of this sequence.
9, 4, -1, -6, -11, ...
Answer:
-146
Step-by-step explanation:
so it seems that the sequence is moving down by 5, so therefore the sequnce would be as follows
9, 4, -1, -6, -11, -16, -21, -26, -31, -36, -41, -46, -51, -56, -61, -66, -71, -76, -81, -86, -91, -96, -101, -106, -111, -116, -121, -126, -131, -136, -141, -146
the 32nd term would be -146
choose the correct description of the system of equations. 3x-y=5 6x=2y+5 A.Consistent and independent B.Consistent and dependent C.Inconsistent D.Inconsistent and dependent
Answer:
C. inconsistent
Step-by-step explanation:
3x - y = 5 6x = 2y + 5 Solve for y
3x - 5 = y 6x - 5 = 2y
3x - 5 = y [tex]\frac{6x}{2} - \frac{5}{2} = \frac{2y}{2}[/tex]
3x - 5 = y 3x - 2.5 = y
Slope = 3 Slope = 3 Same slope
y-intercept: -5 y-intercept: 2.5 Different intercepts
not solution set
Who knows what is 2 x 5 ?
If you earn both hourly wages and a commission at your job, your gross wages, w, can be calculated with the following equation:
cs + rh = w
where c is your commission rate, s is your total sales in dollars, r is your hourly rate, and h is your hours worked.
Solve for s to rewrite the equation for total sales.
The equation that is used to represent (s) the total sales is s = (w - rh)/c
An equations is used to show the relationship between two or more variables.
Given the equation:
cs + rh = w
To solve for s, we have to make s the subject of the equation:
cs + rh = w
subtract rh from both sides:
cs + rh - rh = w - rh
cs = w - rh
Divide both sides by c:
cs/c = (w - rh)/c
s = (w - rh)/c
The equation that is used to represent (s) the total sales is s = (w - rh)/c
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Solve for x using
multiplication.
Cross
-
3x - 3
5
=
2x - 2
4.
x = [?]
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{3x-3}{5}[/tex] = [tex]\frac{2x-2}{4}[/tex] ( cross- multiply )
4(3x - 3) = 5(2x - 2) ← distribute parenthesis on both sides
12x - 12 = 10x - 10 ( subtract 10x from both sides )
2x - 12 = - 10 ( add 12 to both sides )
2x = 2 ( divide both sides by 2 )
x = 1