Given a function f(x) we translate the function:
• a units horizontally (a > 0 to the right, a < 0 to the left),
,• b units vertically (b > 0 up, b < 0 down),
by the transformation:
\(f(x)\rightarrow g(x)=f(x-a)+b.\)In this case, we have:
\(\begin{gathered} f(x)=|x|, \\ g(x)=|x-2|+4=f(x-2)+4. \end{gathered}\)Comparing f(x) and g(x) with the general transformation above, we see that the graph of g(x) is the graph of f(x) translated:
• a = 2 units to the right,
,• b = 4 units up.
Translating the graph of f(x), we get:
AnswerThe translated graph is the graph in red:
Petra wants to buy a skateboard. The skateboard deck usually costs $37.50, but it is on sale for 20% off.
Part A
If the sales tax rate is 5.2%, how much will Petra pay for the skateboard deck in all?
$30.00
$31.56
$31.95
$39.45
Part B
If the selling price of $37.50 represents a 20% markup, will the store still make a profit after the 20% markdown? Explain.
Yes, they added 20% and then subtracted 20%.
No, the store will lose $1.25.
Yes, the store will earn $1.25.
No, the store will lose 40% of the cost.
answer the number 3 only
The values of the variables in number 3, in simplest radical form, are:
f = 6; o = 3.
How to Find the Values of the Variables in the Simplest Radical Form?The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.
Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:
sin 60 = opp/hyp
sin 60 = 9√3 / f
f = 9√3 / sin 60
f = 9√3 / √3/2 [sin 60 = √3/2]
f = 9√3 * 2/√3
f = 18/3
f = 6
tan 60 = opp/adj
tan 60 = 9√3 / o
o = 9√3 / tan 60
o = 9√3 / √3 [sin 60 = √3]
o = 9√3 * 1 / √3
o = 9/3
o = 3
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Answer:
o = 9
f = 18
Step-by-step explanation:
Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.
The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.
Side a is opposite the 30° angle (shortest leg).Side a√3 is opposite the 60° angle (longest leg).Side 2a is the hypotenuse (longest side).In triangle #3, the longest leg is 9√3 units.
As "a√3" is the shortest leg, the scale factor "a" is 9.
The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:
\(o = a=9\)
The side labelled "f" is the hypotenuse of the triangle. Therefore:
\(f= 2a = 2 \cdot 9=18\)
Therefore:
o = 9f = 18Jill’s new outfit originally cost $94. she received 25% off. How much did Jill’s new outfit cost?
Answer:2,335
Step-by-step explanation: Because you have to multiply 94x25. Then once you’ve done that you would have gotten 2,335!
pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee answer
Answer:
no its not a function
Step-by-step explanation:
i hope i help ;)
Find (fog)(2).
f(x) = 3x + 2
g(x) = x²
(fog)(2)=
Answer:
(f·g)(2) = 14----------------------------
Find the composition of the functions f(x) and g(x), which is written as f(g(x)).
Given functions:
f(x) = 3x + 2,g(x) = x² .Find f(g(x)):
f(g(x)) = f(x²) = 3(x²) + 2Evaluate f(g(2)):
f(g(2)) = 3(2²) + 2 = 3(4) + 2 = 12 + 2 = 14So, (f·g)(2) = 14.
Solve each equation by completing the square.
d² - 24d + c
Answer:
d² - 24d + c = (d - 12)² - 144 + c
Answer this correctly I’ll give brainalist + 10 points
Answer: 118
Step-by-step explanation:
These angles are a linear pair. They sum to 180 degrees.
62 + x = 180
-62 -62
X= 118
The P(A)= 0.03 and the P(B) = 0.34. Events A and B are mutually exclusive. What is the P(A or B).
Answer:
Step-by-step explanation:
The probability of A or B occurring is the sum of the probabilities of A and B occurring, since they are mutually exclusive events.
Mutually exclusive events are events that cannot occur at the same time. In other words, if one event occurs, the other event cannot occur.
Therefore, the probability of A or B is:
P(A or B) = P(A) + P(B)
P(A or B) = 0.03 + 0.34
P(A or B) = 0.37
So, the probability of A or B is 0.37.
Write an ordered pair for the point in Quadrant III that is 3 units away from point Q (1.5, -1.5) on the coordinate plane.
The point Q'(x, y) = (- 1.5, - 1.5) is located in quadrant III and 3 units away from point Q(x, y) = (1.5, - 1.5).
What is the possible ordered pair related to another one on the coordinate plane?
In this question we find the location of an ordered pair on the coordinate plane and we are asked to find a possible solution that is in quadrant III and three units away from the original point.
A point (x, y) is in the quadrant III if x < 0 and y < 0 and we can determine a resulting point by using the following translation formula:
(x, y) → (x - 3, y)
If we know that (x, y) = (1.5, - 1.5), then the resulting point is:
Q'(x, y) = (1.5, - 1.5) + (- 3, 0)
Q'(x, y) = (- 1.5, - 1.5)
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Find the value of x .. assume that segments that appear to be tangent are tangent .
We got x = 16.54 by using Pythagorean theorem .
What is the Pythagorean theorem in plain English?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90° .
18² = 7.1² + x²
324 = 50.41 + x²
x² = 324 - 50.41
= 273.59
x = √ 273.59
x = 16.54
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find the common solution for each system of equations
1. y=4x-2 y=2x+3
2. 4y+4x=8 y+2x=4
3. 2y+4x=12 3x+y=5
4. 5x+6=y 4x-7=y
Answer:
elimination method
Step-by-step explanation:
2) 4y+4x=8;y+2x=4
4y+4x=8. ------(1)
y+2x=4 -------(2)
multiply equation (1) by 2 and (2) by 4 to eliminate x
8y+8x=16
4y+8x=4
What is the surface area of the rectangular prism?
Answer:
250m² drawing a model or visualizing it would help
Ryan is a runner. He can run 100 meters in 13 seconds. He
frequently races against Juan, who can run at a speed of 15
miles per hour. Which runner is faster? (1 mile = 1609.34
meters)
Answer:
Ryan: (100/13)(1/1,609.34)(3,600) =
17.21 miles per hour
Ryan is faster than Juan, by about 2.21 miles per hour
Find the missing lengths
Answer:
x = 13 cm
Step-by-step explanation:
The figure given is a square.
Area of the given square (A) = 169 cm²
Formula for area of a square is:
A = s²
Where,
s = x
Thus:
169 = x²
Take the square root of both sides
√169 = √x²
13 = x
x = 13 cm
A triangle has an area of 900m2 . If a parallelogram has the same height and base as the triangle, what is the area of the parallelogram?
Answer:
1800 \(m^{2}\) is the area of parallelogram.
Step-by-step explanation:
Given that:
Area of a triangle = 900 \(m^{2}\)
To find:
Area of a parallelogram which has same height and base as that of the given triangle.
Solution:
First of all, let us have a look at the formula for Area of a parallelogram:
\(Area_{Par} = Base \times Height\) ...... (1)
So as to find the area of a parallelogram, we need to have the product of Base and Height of Parallelogram.
Now, let us have a look at the formula for area of a triangle:
\(Area_{Tri} = \dfrac{1}{2} \times Base \times Height\)
Given that height and base of triangle and parallelogram are equal to each other.
So,the product of base and height will also be equal to each other.
\(900 = \dfrac{1}{2} \times Base \times Height\\\Rightarrow Base \times Height = 2 \times 900\\\Rightarrow Base \times Height = 1800\ m^2\)
By equation (1):
Area of parallelogram = 1800 \(m^{2}\)
Jenna and Benito each marked 1/4 on a number line the length of the part from 0 to 1/4 on Jenna number line is shorter than on Benito’s did someone make a mistake?
Yes, one of them made a mistake either Jenna did or Benito did or else both made the mistake.
Given that,
Jenna and Benito each marked 1/4 on a number line the length of the part from 0 to 1/4 on Jenna's number line is shorter than on Benito’s did someone make a mistake is to be justify.
A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
If both of them marked same measure on the number line,
Possibilities
1) one them made a mistake
(2) both of them made a mistake
Thus, Yes, one of them made a mistake either Jenna did or Benito did or else both made the mistake.
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what is the estimate square root of 63
What is the measure of missing angle F?
Answer:
84 (:
Step-by-step explanation:
7th grade math help me pleaseee
Answer:
Hope this helped C:
Step-by-step explanation:
a) 149
b) 112
c) 18
d) -8 you subtract -14 from -22
e) -3.3 you subtract -2.8 from -6.1
f) -0.16
convert the fractions to decimals and then add 0.3(3/10) and -0.46(7/15)
is 4.702 greater than 47.02
You want to buy some rice. A 7-ounce package costs $2.59. A 16-ounce package costs $5.60. A 24-ounce package costs$9.36. Which package is the best buy?
Answer:
Thanks
Step-by-step explanation:
Thanks
The gasoline tax is a ______ tax
Answer:
Excise tax
Step-by-step explanation:
Correct me if I'm wrong <3
sin (a/2) = + or - sqrt 1-cos a / 2
for all values of a.
A. True
B. False
Answer:
True is the answer of this
How man terms are there in 4n-2y+7
I think 2, but I could be wrong
Simplify the product using the distributive property
(3h - 5)(5h + 4)
Step-by-step explanation:
(3h - 5)(5h + 4) = 3h * 5h + 3h * 4 - 5*5h - 5 *4
= 15h^2 - 13h -20
\((3h-5)(5h+4)\)
\(=(3h+-5)(5h+4)\)
\(=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)\)
\(=15h^2+12h-25h-20\)
Answer:
\(\bold{=15h^2-13h-20}\)How much would you need to deposit in an account now in order to have $2000 in the account in 5 years? Assume the account earns 5% interest compounded monthly.
I need to deposit $1558.41 to have $2000 in the account in 5 years.
What is compound interest?
The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.
∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ (∵ for monthly interest)
P = Principal
r = rate of interest per month
n = number of months
Given:
r = 5% per month
n = 5 years = 5*12 = 60 months
CI = P (1+5/(12 * 100))⁶⁰
2000 = P(1.0041)⁶⁰
2000 = P(1.2834)
P = 1558.41
Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.
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Simplify (a÷b)³×(b÷c)×(c÷a)³ when a=3,b=a²,c=a³
Answer:
To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.
Substituting the values of a, b, and c:
a = 3
b = a² = 3² = 9
c = a³ = 3³ = 27
Now let's simplify the expression:
(a÷b)³×(b÷c)×(c÷a)³
(3÷9)³×(9÷27)×(27÷3)³
Simplifying each term:
(3÷9) = 1/3
(9÷27) = 1/3
(27÷3) = 9
Now we can substitute the simplified values back into the expression:
(1/3)³×(1/3)×9
Simplifying further:
(1/27)×(1/3)×9
1/9
Therefore, the simplified expression is 1/9.
The phone company Splint has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 380 minutes, the monthly cost will be $173. If the customer uses 570 minutes, the monthly cost will be $249.
A) Find an equation in the form
y
=
m
x
+
b
,
where
x
is the number of monthly minutes used and
y
is the total monthly cost of the Splint plan.
Answer:
y
=
B) Use your equation to find the total monthly cost if 942 minutes are used.
Answer: If 942 minutes are used, the total cost will be
dollars.
The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.
What is an equation?The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.
Part A:
Given:
customer uses 380 minutes, the monthly cost will be $173.customer uses 570 minutes, the monthly cost will be $249.To find an equation,
Where x is number of monthly minutes.
and y is total monthly of splint plan.
So, equation is:
\(\rightarrow \text{y} =\text{mx} +\text{b}\)
For the first case:
\(\rightarrow\bold{173 = 380x + b}\)
Second case:
\(\rightarrow\bold{249= 570x + b}\)
Solve for x:
\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)
\(\rightarrow{-207=-321\)
\(\rightarrow \text{x} =\dfrac{321}{207}\)
\(\rightarrow \text{x} =\dfrac{107}{69}\)
\(\rightarrow \text{x} \thickapprox1.55\)
For value of b
\(\rightarrow 173 = 380(1.55) + \text{b}\)
\(\rightarrow 173 - 589 = \text{b}\)
\(\rightarrow -416 = \text{b}\)
Part B:
\(\rightarrow \text{y} = 942(1.55) - 416\)
\(\rightarrow \text{y} = 1460.1 - 416\)
\(\rightarrow \text{y} \thickapprox1044\)
Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.
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The conservation club has 32 members. There are 18 girls in the club.
What is the ratio of girls to boys in simplest form?
a.7/9
b.9/7
c.9/16
d.7/16
The requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
The conservation club has 32 members. There are 18 girls in the club.
Number of boys = 32 - 18 = 14
Ratio of boys to girls = number of boys / number of girls
= 14 / 18 = 7/9
Thus, the requried ratio of boys in the club to girls is given as 7/9 or 7:9. Option A is correct.
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the parent function of the function g(x)