The domain of a function is the set of input or argument values for which the function is real and defined.
So, for the given function to be defined, we need to find the possible values for which the values of x makes the square root to be positive.
That is;
-9 -5x ≥ 0
Now, let's solve for x
Add 9 to both-side of the equation
-5x ≥ 9
Divide both-side by -5
x ≤ -9/5
Therefore, the domain of the function can be represented in interval notation as: ( - ∞ , -9/5]
Find X.
A. 27.2
B. 12.9
C. 30.3
D. 17.8
Answer: 27.2
Step-by-step explanation:
\(\sin 54^{\circ}=\frac{22}{x}\\\\x \sin 54^{\circ}=22\\\\x=\frac{22}{\sin 54^{\circ}} \approx \boxed{27.2}\)
help me please
dont even need a full explanation
After Thanksgiving, Allie’s family has 1/4 of a pumpkin pie left. If Allie is allowed to eat
1/6 of what is left on Friday, what fraction of the original pie can Allie eat on Friday?
Answer:
1/24
One fourth of 1/6 is 1/24
Find the present value of $25,000 due 20 years later at 7.8%, compounded continuously.
A) $5253.4
B) $118,970.53
C) $4990.73
D) $44,642.86
Question 6(Multiple Choice Worth 5 points)
(Reflections MC)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Please Fast only have 10 minutes.
The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).
What is the image coordinates?To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2 from the y-coordinates of each vertex:
N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)
M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)
O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)
Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)
So the reflected vertices are:
The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have a y-coordinate of -6.
The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so one need to move down 3 units to have a y-coordinate of -5.
The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so one need to move down 5 units to have a y-coordinate of -7.
So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)
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Answer:
D) N′(−5, −6), M′(−2, −5), O′(−3, −7)---------------------
Given triangle MNO with vertices:
N = (-5, 2), M = (-2, 1) and O = (-3, 3)It is reflected in line y = - 2.
This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.
Since y = - 2 is the line of symmetry, it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.
Using midpoint equation, find the y-coordinates.
Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7So the coordinates of the image are:
N′(−5, −6), M′(−2, −5), O′(−3, −7)This is matching the option D.
See attached for visual representation of the problem.
Write the sum of the given geometric series as a rational number.
0.8 + 0.08 + 0.008 + 0.0008 + ...
The rational number is:________.
(Simplify your answer. Type an integer or a fraction.)
Answer:
\(\frac{8}{9}\)
Step-by-step explanation:
Given
Series: 0.8 + 0.08 + 0.008 + 0.0008 + ...
Required
Determine a rational number to represent the series
To do this, we simply get the sum to infinity of the series;
This is done as follows;
\(S = \frac{a}{1 - r}\)
Where a represent the first term
\(a = 0.8\)
r represent the common ratio
\(r = \frac{0.08}{0.8}\)
\(r = 0.1\)
Substitute these values in the above formula
\(S = \frac{0.8}{1 - 0.1}\)
\(S = \frac{0.8}{0.9}\)
Multiply the numerator and denominator by 10
\(S = \frac{8}{9}\)
Hence;
The number is \(\frac{8}{9}\)
19. Annie registra cuánto dinero encuentra en una semana. Encuentra $0.19 el lunes, 0.22 el miércoles y $0.35 el jueves. El resto de los días no encontró dinero.
The amount of money found on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday is $0.19, $0, $0.22, $0.35, $0, $0, and $0, respectively.
Annie finds money on certain days of the week and records the amount. The amount of money she found on Monday is $0.19. The amount of money she found on Wednesday is $0.22. The amount of money she found on Thursday is $0.35.
We know that she does not find any money on rest of the days. There are seven days in a week. So, she found $0 on Tuesday, Friday, Saturday, and Sunday.
Hence, the amount of money found on Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday is $0.19, $0, $0.22, $0.35, $0, $0, and $0, respectively.
The complete question is given below.
Annie records how much money she finds in a week. She finds $0.19 on Monday, $0.22 on Wednesday, and $0.35 on Thursday. The rest of the days he found no money. Write the amount of money found on all the days of the week.
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Patricia visited a friend who lives 120 miles away. On her way there she averaged 60 mph. On the way back, she only averaged 40 mph. What was the total amount of time she spent driving?
Answer:
5 hours
Step-by-step explanation:
120/60= 2
120/40= 3
3+2=5
what is the surface area of the rectangle prism below? HELP ME ASAP PLEASE !!
Answer:
C. 248
Step-by-step explanation:
\(A=2(wl+hl+hw)\\2(4*6+10*6+10*4)\\2(24+60+40)\\48+120+80=248\)
The temperature on Thursday afternoon was 77 °F. A thunderstorm rolled through, and the temperature dropped by 10 °C. What was the temperature after the storm?
Answer:
15 °C
Step-by-step explanation:
°C = (°F - 32) * (5/9)
Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.
Initial temperature: 77 °F
Converting to Celsius:
°C = (77 - 32) * (5/9)
°C ≈ 25
The temperature dropped by 10 °C, so the final temperature is:
Final temperature = Initial temperature - Temperature drop
Final temperature ≈ 25 - 10 = 15 °C
Therefore, the temperature after the storm was approximately 15 °C.
what is 3/8 divided by 2/5
Answer:
15/16
Decimal form: 0.9375
plz mark as brainliest :DD
What is the slope of -x+ 5y = 10?
Answer:
Slope = 1/5
Step-by-step explanation:
Given equation,
→ -x + 5y = 10
The slope-intercept form,
→ y = mx + b
→ slope = m
Now the slope-intercept form is,
→ -x + 5y = 10
→ 5y = x + 10
→ y = (x + 10)/5
→ [ y = (1/5)x + 2 ]
Then the required slope will be,
→ y = (1/5)x + 2
→ Slope = m = 1/5
Hence, the required slope is 1/5.
Answer:
\(\textsf{Slope}=\dfrac{1}{5}\)
Step-by-step explanation:
\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)
Given equation:
\(-x+5y=10\)
To find the slope of the given equation, use algebraic operations to isolate y.
Add x to both sides of the equation:
\(\implies -x+5y+x=10+x\)
\(\implies 5y=x+10\)
Divide both sides of the equation by 5:
\(\implies \dfrac{5y}{5}=\dfrac{x+10}{5}\)
\(\implies y=\dfrac{1}{5}x+\dfrac{10}{5}\)
\(\implies y=\dfrac{1}{5}x+2\)
The coefficient of x is the slope of the equation.
Therefore, the slope of the given equation is ¹/₅.
there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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i need help on these please
The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.
How to calculate the constant rate of gas?From the given table;
The volume of the first gas Layla bought = 3 gallons.
The cost of the 3 gallons = 9.45
Therefore the cost of 1 gallon = ?
That is:
3 gallons = $9.45
1 gallon = X
Make X the subject of formula:
X = 9.45/3 = $3.15
Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.
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what is the unit digits of 3^40
Answer:
1
Step-by-step explanation:
the answer is 1.21576655000000000.
the unit of this no. is 1.
the square root of a negative number is known as an _______ number
Positive number is a square root
If 16x = 1/64, find the value of x
Answer:
\(16^x = 1/64\)
\((2^4)x=64-^1=(2^6)=2-^6\)
\(2^4x=2-^6\)
\(4x=-6\)
\(x = - \frac{6}{4} = - \frac{3}{2} \)
Step-by-step explanation:
\(Thanks!!!\)
johnny was excited to go to his first sci-fi convention. as a souvenir, he bought a deck of 200 sci-fi trading cards. on the way home, he randomly picked some cards from the deck to see what types of cards he got. type number of cards comic book 6 movie 4 video game 5 tv series 7 based on the data, estimate how many movie cards are in the whole deck. if necessary, round your answer to the nearest whole number.
______ movie cards.
We get an estimate of 36 movie cards in the deck.
What is meant by proportional?Twο numerical sequences—οften experimental data—are prοpοrtiοnal οr directly prοpοrtiοnal if the ratiο between their cοrrespοnding elements is cοnstant.
Jοhnny chοse a tοtal οf 22 cards at randοm, which is 6 + 4 + 5 + 7.
The percentage οf each type οf card in the sample, if assumed tο be representative οf the percentage οf each type οf card in the entire deck, can be used tο calculate the apprοximate number οf mοvie cards in the deck.
The prοpοrtiοn οf mοvie cards in the sample is 4/22, which simplifies tο 2/11.
Sο we can estimate the number οf mοvie cards in the deck as:
(2/11) x 200 = 36.36
We estimate there are 36 mοvie cards in the deck by rοunding tο the nearest whοle number.
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Brainliest for correct answer
Answer:
1/2
Step-by-step explanation:
Scale factor = (new figure measurement)/(original figure measurement)
Find IP using pythagorus
IP²=(y\(_{I}\)-y\(_{P}\))²+(x\(_{I}\)-x\(_{P}\))²
IP²=(4-(-4))²+(4-2)²
IP²=8²+2²
IP²=68
IP=\(\sqrt{68}\)
Find I'P' using pythagorus
I'P'²=(y\(_{I'}\)-y\(_{P'}\))²+(x\(_{I'}\)-x\(_{P'}\))²
I'P'²=(2-(-2))²+(2-1)²
I'P'²=4²+1²
I'P'²=17
I'P'=\(\sqrt{17}\)
Scale factor = (new figure measurement)/(original figure measurement)
=\(\sqrt{17}\)/\(\sqrt{68}\)
=1/2
Find the slope of the line that passes through (6, 8) and (10, 9).
Simplify your answer and write it as a proper fraction, improper fraction, or integer
Step-by-step explanation:
Slope is equal to the change in y over the change in x, or rise over run.
\(m = \frac{change \: in \: y}{change \: in \: x} \)
The change in x is equal to the difference in x-coordinates, and the change in y is equal to the difference in y-coordinates.
\(m = \frac{y2 - y1}{x2 - x1} \)
Substitute in the values of x and y into the equation to find the slope.
\(m = \frac{9 - (8)}{10 - (6)} \)
Simplify.
\(m = \frac{1}{4} \)
Therefor, the slope is 1/4.
39 is 40% of what number (please explain)
Answer:
97.50
Step-by-step explanation:
dont have one XD
Answer: 97.50
Step-by-step explanation:
just do 39 divided by 40%
What is the surface area of the rectangle pyramid below 13 13 13
Answer:
Step-by-step explanation:
Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:
First, we need to calculate the area of the rectangular base, which is simply length x width:
Area of rectangular base = 13 x 13 = 169 square units
Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.
To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:
a² + b² = c²
where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.
13² + 13² = c²
338 = c²
c ≈ 18.38
Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:
Area of isosceles triangle = (1/2) x base x height
Area of isosceles triangle = (1/2) x 13 x 18.38
Area of isosceles triangle ≈ 119.14 square units
To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:
Area of right triangle = (1/2) x base x height
Area of right triangle = (1/2) x 13 x 18.38
Area of right triangle ≈ 119.14 square units
Since there are two of each type of triangular face, the total surface area of the pyramid is:
Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle
Surface area = 169 + 2 x 119.14 + 2 x 119.14
Surface area = 546.28 square units
Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.
A salesperson had 50 shirts to sell and must sell a minimum of 20 shirts. The salesperson sells the shirts for $35 each. The amount of money the salesperson makes for selling x shirts is represented by a function.
f(x)=35x
What is the practical range of the function?
All real numbers
all multiple of 35 between 700 and 1750, inclusive
all integers from 20 to 50, inclusive
all multiple of 35 between 0 and 1750, inclusive
Answer:
3x-100
Step-by-step explanation:
Find the exterior of a rectangle in a polygon
The measure of each exterior angles of rectangle is 90°
Finding the exterior of a rectangle in a polygonFrom the question, we have the following parameters that can be used in our computation:
A rectangle
A rectangle is a polygon with 4 sides
So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon
The exterior angles in a polygon are found by using:
Exterior of a rectangle in a polygon = 360°/Number of sides of the polygon
In this case,
The number of sides of the rectangle = 4
So, we have
Exterior of a rectangle = 360°/4
Evaluate
Exterior of a rectangle = 90°
Hence, the value of the measure of each exterior angles of rectangle is 90°
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Complete question
Find the measure of each exterior angles of rectangle?
Step by step
There are 31 students in a class and 61.3% of these students passed their Math Applications test. What number of these students passed their test? Round your answer to the nearest whole number if necessary.
Answer:
19
Step-by-step explanation:
Alr so.
what you have to do is first convert yourpercentage into a decimal and to do that you need to move the decimal 2 places to the left like so-
61.3% ---> .613
Next you need to multiply 31 x .613 which gives you 19.003
or 19 Passed :)
enjoy!!!!
Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person, and the third buyer bought 4/5 of what was left and the last 10 lb. How many pounds of potatoes did farmer Bill sell?
Answer:
Farmer Bill sold 120 lb of potatoes
Step-by-step explanation:
Suppose farmer Bill had x lb of potatoes. He sold a quarter to the first person. A quarter is written as (1/4)x. After that, Bill had x-(1/4)x = (3/4)x.
Then he sold 4/9 of what was left to the second person, thus it was left 1-4/9=5/9 of the remaining potatoes. Multiplying both factors:
\(\frac{5}{9}*\frac{3}{4}x=\frac{5}{12}x\)
This is the remaining portion of the potatoes.
Finally, he sold 4/5 of it and the last 10 lb. This means 1 - 4/5 = 1/5 of the remaining is equivalent to 10 lb:
\(\frac{1}{5}*\frac{5}{12}x=\frac{1}{12}x\)
Thus:
\(\frac{1}{12}x=10\)
x = 120 lb
Farmer Bill sold 120 lb of potatoes
The Farmer will sold 120 lb of potatoes.
Let us consider that farmer have x lb of potatoes.
He sold a quarter to the first person, that is \(\frac{x}{4}\)
Potatoes left,\(=x-\frac{x}{4} =\frac{3x}{4}\)
4/9 of what was left to the second person,
Potatoes sell to second person is, \(\frac{3x}{4} *\frac{4}{9} =\frac{x}{3}\)
the third buyer bought 4/5 of what was left
that is, \(\frac{4}{5}*(\frac{3x}{4} -\frac{x}{3} ) =\frac{x}{3}\)
Potatoes left \(=\frac{5x}{12} -\frac{x}{3} =\frac{x}{12}\)
Since, Potatoes left = 10 lb
So, \(\frac{x}{12} =10\\\\x=12*10=120\)
Thus, The Farmer will sold 120 lb of potatoes.
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Dario spends 3 1/2 hours on the phone with technical support and pays $10. What is his unit rate?
Answer:
20/7 dollars per hour
Step-by-step explanation:
He pays 10 dollars per 3 1/2 hours. To find the unit rate, we divide the two.
10 / (3 1/2) =
10 / (7/2) =
(10/1) x (2/7) =
20/7
What is
equal to? (5 points)
3^3/2
3^√9
2^√9
3^√27
2^√27
The expression 3^(3/2) is equal to ²√27. The 4th option is the answer
How to find what is equal to 3^(3/2)?
Index is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3. The 3 is called the base. The plural form of index is indices.
The expression 3^(3/2) can be written in form of root and power. That is:
3^(3/2) = ²√3³
3^(3/2) = ²√27
Therefore, the expression 3^(3/2) is equal to ²√27
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Number of car sold are 98.
Number of trucks sold are 66.
Given,
Dealer 1 sold 164 cars and trucks and dealer 2 sold 229 cars and trucks .
Let number of cars sold are x.
Let number of cars sold of y .
Now,
For dealership 1 equation will be,
x + y = 164 ......(1)
For dealership 2 equation will be,
As the cars are sold twice and trucks are sold half .
2x + y/2 = 229......(2)
Solving 1 and 2,
y = 66
x = 98
Thus number of car sold are 98.
Thus number of trucks sold are 66.
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At a family reunion, each of Shamar's aunts and uncles is getting photographed once. The aunts are taking
pictures in groups of 5 and the uncles are taking pictures in groups of 10. If Shamar has the same total number
of aunts and uncles, what is the minimum number of aunts that Shamar must have?
The minimum number of aunts that Shamar must have based on the information provided is 10.
What are the possible number of uncles and aunts?It is known that uncles will take a photograph in groups of 10, while aunts will take a photograph in groups of 5. Based on this, the possible number for each are:
Uncles: 10, 20, 30, 40, 50
Aunts: 5, 10, 15, 20, 25
How to find the minimum number of relatives?In this case, the minimum number is the LCM or Least Common Multiple and based on the previous list, this number is 10.
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