Answer: Translation up 5 units means g(x)=f(x)+5g(x)=f(x)+5. Reflecting this across the x-axis means g(x)=-(f(x)+5)g(x)=−(f(x)+5).
-(4x+5)=-4x-5
−(4x+5)=−4x−5
Step-by-step explanation:
Answer:
g(x) = -|x + 12|
Step-by-step explanation:
Translation to left ≡ f(x + 12)
f(x + 12) = | x + 12 |
Reflection of a function f(x) about the x - axis is keeping the x value same but negating the y values
Reflected f'(x) = -y = -f(x)
Taken together
g(x) = -(|x + 12|)
Solve: 1/4 (36x – 16) = 5x – 18
We must solve for x the following equation:
[tex]\frac{1}{4}(36x-16)=5x-18.[/tex]1) We multiply both sides by 4, and we get:
[tex]\begin{gathered} 36x-16=4\cdot(5x-18), \\ 36x-16=20x-72. \end{gathered}[/tex]2) We pass the -16 at the left side as +16 at the right side:
[tex]\begin{gathered} 36x=20x-72+16, \\ 36x=20x-56. \end{gathered}[/tex]3) We pass the -56 at the right side as +56 at the left side:
[tex]\begin{gathered} 36x-20x=-56, \\ 16x=-56. \end{gathered}[/tex]4) Finally, dividing both sides by 16, we get:
[tex]x=-\frac{56}{16}=-3.5.[/tex]Answerx = -3.5
Determine whether the given numbers represent the lengths of sides of a right triangle.9,40,41Do the given numbers represent the lengths of the sides of a right triangle?YesNo
To prove that these numbers form the sides of a right triangle we should do these steps
1. Square the longest side
2. Find the sum of the squares of the other 2 sides
3. If the sum equals the square of the longest side, then the numbers can form a right triangle
Since the longest side is 41, then
[tex](41)^2=1681[/tex]Since the other 2 numbers are 40 and 9, then
[tex](40)^2+(9)^2=1600+81=1681[/tex]From both steps, we can say
[tex](41)^2=(40)^2+(9)^2[/tex]Then the answer is
YES, 9, 40, 41 can form the sides of a right triangle
I know how to do everything except the #1 step
Answer:
[tex]A^{\doubleprime}(-6,-21),B^{\doubleprime}(6,-15)\text{ and C}^{\doubleprime}(-3,-12)[/tex]Explanation:
Given the coordinates A, B and C as follows:
[tex]A(-3,4),B(1,2)\text{ and C(-2,1)}[/tex]If a point is reflected across the x-axis, we have the transformation rule:
[tex](x,y)\to(x,-y)[/tex]Thus, the image of A are:
[tex]A(-3,-4),B(1,-2)\text{ and C(-2,-1)}[/tex]Next, a translation by <1,-3>:
[tex]\begin{gathered} A(-3+1,-4-3),B(1+1,-2-3)\text{ and C(-2+1,-1-3)} \\ A(-2,-7),B(2,-5)\text{ and C}(-1,-4) \end{gathered}[/tex]Finally, a dilation by K=3 gives the final image required:
[tex]A^{\doubleprime}(-6,-21),B^{\doubleprime}(6,-15)\text{ and C}^{\doubleprime}(-3,-12)[/tex]Find the value of x.
Answer:
x = 82
Step-by-step explanation:
The sum of the interior angles of a polygon with n sides = (n-2) x 180°
This polygon has 7 sides so the sum of its interior angles
= (7-2) x 180°
= 5 x 180°
= 900°
Adding up the given angles we get
x + 160 + 2x + 125 + 110 + 112 + 147 = 900
3x + 654 = 900
3x = 900 - 654
3x = 246
x = 246/3 = 82
Answer:
x = 82
Step-by-step explanation:
Sum of interior angles of a polygon
[tex]S=(n-2) \times 180^{\circ}[/tex]
where n is the number of sides.
The given polygon has 7 sides:
n = 7To find the value of x, substitute the sum of the interior angles and the found value of n into the formula and solve for x:
[tex]\implies x+160+2x+125+110+112+145=(7-2)\times 180[/tex]
[tex]\implies x+2x+160+125+110+112+145=5\times 180[/tex]
[tex]\implies 3x+654=900[/tex]
[tex]\implies 3x+654-654=900-654[/tex]
[tex]\implies 3x=246[/tex]
[tex]\implies \dfrac{3x}{3}=\dfrac{246}{3}[/tex]
[tex]\implies x=82[/tex]
Therefore, the value of x is 82.
Compare 8º and 8 ^-2. Which is greater? Explain
Note that any number raised to the power of zero is 1.
Therefore:
[tex]8^0=\text{ 1}[/tex][tex]8^{-2}=\text{ }\frac{1}{8^2}=\text{ }\frac{1}{64}=\text{ 0.015625}[/tex]Since 1 > 0.015625:
[tex]8^0>8^{-2}[/tex]
In the past 2 months, your bank account has decreased by $80.00 The account decreased by the same amount each month What was the change
each month?
Answer:
$40.00
Step-by-step explanation:
In the first month your money went down by $40 then the second month another $40, so in total $80 has been lost
A man who weighs 200 lbs goes on a diet and loses 16%of his body weight. How much weight, in ounces, did he loses?
We know that the man loses 16% of his weight, to find how much was that we just have to multiply his total weight by 0.16, like this:
lost weight = 0.16 * total weight, by replacing 200 lbs for total weight, we get:
lost weight = 0.16 * 200 = 32
Now we need to express 32 lbs in ounces, we can do this by multiplying the weight in pounds by 16, since 1 pound is equivalent to 16 ounces, then we get:
lost weight in ounces = 32 * 16 = 512
Then, the man lost 512 ounces
A trade magazine routinely checks to drive-through service times of fast food restaurants and 95% confidence interval that results from examining 501 customers in one fast food chains drive-through has a lower bound of 166.2 seconds in an upper bound of 169.6 seconds what does this mean?
The confidence level of an interval is the probability that the mean of an distribution rest inside this interval.
Then, there is a 95% probability that the mean drive-through service time of this fast-food chain is between 166.2 seconds and 169.6 seconds.
A metallurgist has one alloy containing 29% titanium and another containing 70% titanium. How many pounds of each alloy must he use to make 54 pounds of a third alloy containing 52% titanium? (Round to two decimal places if necessary.)
The weights of the first and second alloys to be used are 23.707 and 30.293 pounds.
The percentage of titanium in the first alloy is 29%.The percentage of titanium in the second alloy is 70%.Let the weight of the first alloy taken be "x".Let the weight of the second alloy taken be "y".The percentage of titanium in the third alloy is 52%.The weight of the third alloy is 54 pounds.The weights of the first and second alloys taken are equal to the weight of the third alloy.x + y = 54We also know that the third alloy is made using the first and second alloys.29x + 70y = 52*5429x + 70y = 2808We have a system of two equations in two variables.Upon solving, we get the values of "x" and "y".The value of "x" is 23.707.The value of "y" is 30.293.To learn more about equations, visit :
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A rectangle has vertices at (0, 0), (3,0), and (0,6). What is the area of the rectangle? у 10- 9- 8 ? square units 7 6 DONE 5- 4 3- 2 1 х o i 2 3 4 5 6 ; 8 9 10
Shawn, this is the solution to the exercise:
Width of the rectangle = 3 units (from 0 to 3)
Length of the rectangle = 6 units (from 0 to 6)
In consequence, the area is:
• Area = Width * Length
,• Area = 3 * 6
,• Area = 18 units²
Which expression is equivalent to 8x3 − 27 when factored completely?
The given expression is
[tex]8x^3-27[/tex]To find the equivalent expression, we use the formula for the difference of perfect cubes.
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]But, we have to express the numbers 8 and 27 as cubic powers.
[tex]\begin{gathered} 8=2\cdot2\cdot2=2^3 \\ 27=3\cdot3\cdot3=3^3 \end{gathered}[/tex]Then, we know that a and b are
[tex]\begin{gathered} a=2x \\ b=3 \end{gathered}[/tex]So, the difference would be
[tex](2x)^3-(3)^3[/tex]Once we have the difference expressed in cubes, we apply the formula using the a and b values we determined before.
[tex](2x)^3-(3)^3=(2x-3)((2x)^2+(2x)(3)+(3)^2)_{}=(2x-3)(4x^2_{}+6x+9)[/tex]Therefore, the factors are
[tex](2x-3)(4x^2+6x+9)_{}[/tex]let f(x) = 4x -8 and g(x) =1/x^2
find (f . g) (x), then choose the correct domain for (f . g) (x).
Multiplication of two real functions, (f . g) (x) is 4/x - 8/x² and the correct domain for (f . g) (x) is (-∞,0) U (0,∞)
Let f(x) and g(x) are two real functions.
f(x)= 4x -8
g(x)= 1/x²
then
(f . g)(x) = (4x -8 ) x (1/x²)
(f . g)(x) = 4/x - 8/x²
The set of all the initial elements in all the ordered pairs in a relation R is known as the domain of R.
domain for (f . g) (x).(f . g)(x) = 4/x - 8/x²we know that f(x) is undefined at x=0
so, domain will be
(-∞,0) U (0,∞)
Multiplication of two real functions, (f . g) (x) is 4/x - 8/x² and the correct domain for (f . g) (x) is (-∞,0) U (0,∞)
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Simplify the expression 6x4÷2+3^3
Answer:12+27= 39.
Step-by-step explanation: You would do 6x4 first due to PEMDAS. Then you would do 24 divided by 2 which is 12. Then, you add it to 3 to the power of 3, which is 39. The simplified equation would be be 12+27.
help me please
thank you
Answer:
Domain: A, [tex][1, \infty)[/tex]
Range: A, [tex][-4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Use the Law of Sines to find the indicated angle 0. (Assume C = 67º. Round your answer to one decimal place.)
Answer
40.3º
Explanation
The Sine rule is used to solve angles and sides of triangle.
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]For this triangle,
Angle A = ? (Isn't given)
Angle B = θ
Angle C = 67º
Side a = ? (Isn't given)
Side b = 56.3
Side c = 80.2
We are then told to find the Angle B, that is, θ
So, using the later parts of the Sine Rule
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]Substituting the known variables, we have
[tex]\begin{gathered} \frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c} \\ \frac{\text{ Sin }\theta}{56.3}=\frac{\text{ Sin }67º}{80.2} \\ \text{ Sin }\theta=\frac{56.3\times\text{ Sin }67º}{80.2}=\frac{56.3\times0.9205}{80.2} \\ \text{ Sin }\theta\text{ = 0.6462} \\ \theta=Sin^{-1}(0.6462)=40.3º \end{gathered}[/tex]Hope this Helps!!!
negative h over 4 equal 15 ?
7=- (1/5)x
[tex]\begin{gathered} 7=-\frac{1}{5}x \\ 7\cdot-5=x \\ -35=x \end{gathered}[/tex]Interpret the decay factor from the exponential function y = 900(0.65)3.
Answer:
0.65
Explanation:
If we have an exponential equation of the form
[tex]y=ab^x[/tex]where
a = inital amount
b = decay factor
Now in our case, the function we have is
[tex]y=900(0.65)^x[/tex]therefore,
the inital amount = 900
the decay factor = 0.65
Hence, the decay factor of the exponential function is 0.65.
Stella bought 4 chicken wings for $7.60. What's the unit cost of one wing?
Answer:
$1.90 for each chicken wing
Step-by-step explanation:
7.6 / 4 = 1.9
Answer: $1.90
Step-by-step explanation:
divide 7.60 by 4. you get 1.9 :)
May I please get help with this for I am confused on were I should put the triangle translation as I have tried multiple times but still could not get it right
Explanation
Labeled the given triangle as shown below:
The coordinates of triangle ABC are:
A(-4, -2)
B(0, -4)
C(2, 2)
The translation of the triangle 4 units to the left and 3 units down will be given as:
A(-4, -2) → A'(-8, -5)
B(0, -4) → B'(-4, -7)
C(2, 2) → C'(-2, -1)
So, the diagram of the triangle after a translation of 4 units to the left and 3 units down is shown below:
Which model represents 3×15?
Need help with homework
We have an original function, this is:
[tex]y=x^2[/tex]In addition, we have a second function that is based on the original function but with a translation.
As you can see in the above image, the function in the red line is moved 6 units to the right.
Let's remember one of the rules of function translation.
y = f(x) Original function
y = f(x-c) Where it is translated horizontally, "c" units to the right.
Since in this case, we have 6 units of translation to the right the equation of the function shown in red is:
[tex]y=(x-6)^2[/tex]
What is the expression in simplest radical form?√432
ANSWER :
12√3
EXPLANATION :
From the problem, we have the radical expression :
[tex]\sqrt{432}[/tex]We need to factor 432 in which one of the factors is a perfect square.
Note that 432 is 3 x 144
and 144 is a perfect square.
Then :
[tex]\sqrt{432}=\sqrt{3\times144}[/tex]Extracting the root of 144 which is 12 since 12 x 12 = 144.
[tex]\sqrt{3\times144}=12\sqrt{3}[/tex](8) Write the equation of the line that passes through the points (12, 4) and 1 (22,9).
Answer:
Step by step solution:
The
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DUE IN 30 MINS!!!!!!
Answer:
x = 11
Step-by-step explanation:
all angles in a triangle will add up to 180.
So we can start with the equation:
(19 + x) + (7 + 8x) + angle str = 180.
we are given the angle stv. This angle equals 125.
the angle of a straight line is 180. In order to find the angle next to another angle like angle stv and str are, all you have to do is subtract the angle from 180.
So to find str:
180 - 125 = 55
we already have one of our angles which is 55
so the equation is now:
(19 + x) + (7 + 8x) + 55 = 180
now do some simple simplification:
(19 + x) + (7 + 8x) + 55 = 180
______________ -55_-55
(19 + x) + (7 + 8x) = 125
26 + 9x = 125
-26_____-26
9x = 99
99/9 = 11
x = 11
Therefore, x = 11
The circumference of a wheel is 150 cm what would be the diameter
With a circumference of 150cm, the diameter of the wheel will be
47.77 cm
by using the formula d = C/π
Explanation:The circumference of a circle is the length of one complete lap around it. It is the outer measurement, Diameter is the length of the line segment that divides a circle in half. while the diameter is the inner measurement.Circumference is calculated as,
C = dπ
is the formula for calculating circumference with diameter.
As a result, to calculate the diameter from the circumference, divide the circumference value by π, where π = 22/7 or 3.142.
⇒ d= C/π
here given C= 150 cm
by substituting the values ,
d = 150/3.14
= 47.77 cm
∴ the value of diameter of the wheel with a circumference of 150cm will be 47.77 cm
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The topic of this problem is "Scale Factors". This is the information: Solid 1 has: * A surface area of 128 cm^2* A volume of 15360 cm^3 Solid 2 has: * An unknown surface area. * A volume of 6480 cm^3 I need to find the surface area of solid 2.
Let the unknown surface area be x
The ratio of the surface area to volume in solid 1 must be equal to the ratio of the surface area to volume in solid 2.
[tex]\begin{gathered} \frac{128}{15360}=\frac{x}{6480} \\ \Rightarrow x=\frac{128}{15360}\times6480=54\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area of solid 2 is 54 cm^2
Sean has $900 in a savings account that earns 5% annually. The interest is notcompounded. How much will he have in 1 year?Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), ris the interest rate expressed as a decimal, and t is the time in years.Submit
Answer:
The interest after one year is $45
Explanation:
Principal = $900
Rate = 5%
Time = 1 year
I = P x R x T / 100
I = 900 x 5 x 1 / 100
I = 4500/100
I = $45
Therefore, the interest after one year is $45
Raios de luz solar estão atingindo a superfície de um lago formando um ângulo x com a sua superfície, conforme indica a figura. Em determinadas condições, pode-se supor que a intensidade luminosa desses raios, na superfície do lago, seja dada aproximadamente por i(x) = k . sen(x) sendo k uma constante, e supondo-se que X está entre 0° e 180°. Quando X = 150°, a intensidade luminosa se reduz a qual percentual de seu valor máximo? A
sua resposta é a letra b eu não sei se a resposta está certa
The following formula is used to calculate the monthly payment on a personal loan.
P= PV.
i
1-(1+i)^-n
In this formula, n represents the
a. number of periods over which interest is calculated on the loan
b.number of applicants for the loan
c.number of years it will take to pay the loan back
d. number of dollars the loan is for
For his long distance phone service, Bill pays an $8 monthly fee plus 6 cents per minute. Last month, Bill's long distance bill was $13.64. For how many minutes was Bill billed?
The long distance bill is
Monthly fixed $8
Monthly variable $0.06 per minute
If the cost is c and minutes m, we can write cost as:
[tex]c=8+0.06m[/tex]Given, last month's cost, c, to be $13.64, we want to find the minutes.
We put 13.64 into 'c' of the formula found and find m.
Shown below:
[tex]\begin{gathered} 13.64=8+0.06m \\ 13.64-8=0.06m \\ 5.64=0.06m \\ m=\frac{5.64}{0.06} \\ m=94 \end{gathered}[/tex]Ansswe
