what is the domain of the function Y= square root 2x+10 explain and show work ) A. X≥5 B. Y≥5 C. X≥-5 D. Y≤-5
Answers
Solution: x ≥ -5
StepsDomain Definition: The domain of a function is the set of input or argument values for which the function is real and defined
squareroot 2x + 10 ⇒ 2x + 10 ≥ 0
Solve 2x + 10 ≥ 0:
Subtract 10 from both sides
2x + 10 - 10 ≥ 0 - 10
Simplify
2x ≥ -10
Divide both sides by 2
2x / 2 ≥ -10 / 2
Simplify
2x / 2
Divide the numbers: 2 / 2 = 1
= x
Note: x has the same value as 1
Divide the numbers: -10 / 2 = -5
= -5
The function domain is
x ≥ -5
Answer:
[tex]\boxed{\text{C. }x \geq -5}}[/tex]
Step-by-step explanation:
The domain is the set of all possible x-values that will make the function work.
The definition automatically eliminate options B and D.
Your function is
[tex]y = \sqrt{2x + 10}[/tex]
The number under the radical cannot be negative, because the square root of a negative number is imaginary.
Thus, we must have
[tex]\begin{array}{rcr}2x+ 10 & \geq & 0\\2x & \geq & -10\\x & \geq & -5\\\end{array}\\\\\text{The domain is }\boxed{\mathbf{x \geq -5}}[/tex]
The graph of your function shows that the range is x ≥ -5.
Related Questions
Find all solutions for a triangle with A=40 degrees , B=60 degrees and c = 20.
Answers
Answer: 40 +60+20= 120
Step-by-step explanation:
Answer:
A = 40 degrees
B = 60 degrees
C = 80 degrees
a = 13.1
b = 17.6
c = 20
Step-by-step explanation:
They give us A = 40 degrees and B = 60 degrees and in one triangle the sum of the angles should be 180, so you add 40 and 60, and then subtract that value by 180.
40 + 60 = 100
180 - 100 = 80
C = 80 degrees
From here you use the law of sines
20/sin(80) = a/sin(40)
when you cross multiply them you should get this:
20 * sin(40) = sin(80)*a
Simplify them
12.9 = sin(80) * a
Divide them to isolate the variable
12.9/sin(80) = a
a = 13.1
To find side length b you use law of sines again
20/sin(80) = b/sin(60)
Cross multiply
20 * sin(60) = sin(80) * b
Simplify
17.3 = sin(80) * b
Divide to isolate the variable
17.3/sin(80) = b
b = 17.6
B
=
Round your answer to the nearest hundredth.
Answers
The measure of B is 51.06°
From pythagoras;
sinθ = opposite / Hypotenus opposite = 7Hypotenus = 9Substituting into the relation;
Sin(B) = 7/9
Sin(B) = 51.057
To the nearest hundredth , we have ; 51.06
Andy, David and Tim altogether have 180 stamps. Andy has 20 fewer than David, and Tim has 80% of the sum of Andy's and David's stamps.How many stamps does each of them have?
Answers
andy has 40
david has 60
tim has 80
Answer:
Step-by-step explanation:
Alright, lets get started.
Let Andy have A stamps.
Let David have D stamps.
Let Tim have T stamps.
Andy, David and Tim altogether have 180 stamps, means
[tex]A+D+T=180....................... equation 1[/tex]
Andy has 20 fewer than David, means
[tex]A+20=D...............................equation 2[/tex]
Tim has 80% of the sum of Andy's and David's stamps, means
[tex](A+D)*0.8=T........................equation 3[/tex]
Putting the value of D as A+20 in equation 1 and 3
[tex]A+A+20+T=180[/tex]
[tex]2A+T=160[/tex]........................equation 5
[tex](A+A+20)0.8=T[/tex]
[tex](2A+20)0.8=T[/tex]
[tex]1.6A+16=T[/tex] ....... equation 6
Plugging the value of T in equation 5
[tex]2A+1.6A+16=160[/tex]
[tex]3.6A=144[/tex]
[tex]A=40[/tex]
[tex]D = 40+20 = 60[/tex]
[tex]T=1.6*40+16[/tex]
[tex]T=64+16=80[/tex]
It means Andy has 40 stamps.
It means David has 60 stamps.
It means Tim has 80 stamps.
Hope it will help :)
What is the effect on the graph of the parent function f(x)=x when f(x) is replaced with f(x-7)
Answers
Answer:
I think it shifts horizontally by 7 units to the right. Not completely sure though.
Step-by-step explanation:
The point (-2,11) is on the graph of y=4x^2+2x-1
True
False
Answers
Nope, it aint there. False
Find all of the polar coordinates of point P if p=(1,-pi/6)
Answers
Answer:
The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n).
Step-by-step explanation:
The polar coordinates can be written as (r,Ф)= (r,Ф+2nn) or (r,Ф) =(-r,Ф+(2n+1)n) and n is any integer value.
We are given p=(1,-pi/6)
P(r,Ф), then r = 1 and Ф = -pi/6
The polar coordinates will be
P(r,Ф)= (r,Ф+2nn) = (1 , -pi/6 + 2nn) and n is any positive integer and the value of r is positive.
P(r,Ф) =(-r,Ф+(2n+1)n) = (-1, -pi/6+(2n+1)n) and n is any positive integer and the value of r is negative.
The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n)
Every day you travel 4 3/4 miles each way to get to school. How many miles do you travel all together to get to and from school during a typical school week? please include explanation, it would be very helpful
Answers
Answer:
47.5 miles
Step-by-step explanation:
So, every morning, you travel 4.75 miles to get to school... and another 4.75 miles in the afternoon to return.
So, each day, you travel a total of 9.5 miles (4.75 + 4.75) to go school and back.
On a typical school week, you'll go to school 5 times... so you'll need to travel a total of 47.5 miles (5 * 9.5).
Suppose the probability of an event occurring is P(A), and the probability of the event not occurring is P(A'). If P(A) = m and P(A') = n, which of the following equations must be true?
A. m = 1 + n
B. n = 1 - m
C. n = m + 1
D. M =n -1
Answers
Answer:
B
Step-by-step explanation:
P(A)+P(A')=1
m+n=1
B is the only answer equal this if you add m to both sides.
Answer:
I got B! n=1-m
Lizzie has 12 pounds of clay and wants to use all of it. She does not need to make all of the projects, and may make more than one of any project. Describe a plan for Lizzie to use 12 pounds of clay making projects from the chart. Show how you know she will use exactly 12 pounds of clay with this plan, with no clay left over.
Answers
Answer:
many answers,
Step-by-step explanation:
she could make 9 mugs, (3/4 x 9 = 12)
she could make 1 small bowl, 1 small plate, 2 large bowls and 2 mugs. (2.5 + 1.5 = 4, 3.25 x2 = 6.5 .75 x 2 = 1.5; 4+ 6.5= 10.5 10.5 + 1.5 = 12) etc
A toy box has 6 faces.There are square there are 12 edges and 8 vertices.Identify the shape of the toy box.
Answers
Answer:
A cube or a cuboid.
Step-by-step explanation:
A cube or a cuboid is a three dimensional shape that has
12 edges, 8 corners or vertices, and 6 faces.
The difference between a cube and cuboid is that a cube has all edges equal which makes every face a square while a cuboid has two square faces and four rectangular faces.
An ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin. Which is the equation of the ellipse in standard form?
Answers
ANSWER
[tex]\frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]
EXPLANATION
The given ellipse has a vertex at (4,0), a co-vertex at (0,3), and a center at the origin.
The equation of an ellipse with vertices on the x-axis and center at the origin is:
[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
The ellipse has vertex at (4,0) , hence a=4.
Also the co-vertex is at (0,3) , b=3
We substitute the values into the equation to get:
[tex] \frac{ {x}^{2} }{ {4}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{ 16} + \frac{ {y}^{2} }{ 9} = 1[/tex]
The equation of the ellipse centered at the origin with a vertex at (4,0) and a co-vertex at (0,3) is (x/4)² + (y/3)² = 1.
Explanation:The ellipse in question has a vertex at (4,0) and a co-vertex at (0,3), with a center at the origin. The standard form equation for an ellipse with a center at the origin is given by (x/a)² + (y/b)² = 1. In this case, 'a' represents the distance from the center to a vertex, and 'b' represents the distance from the center to a co-vertex. Since our vertex is at (4,0), 'a' equals 4, and since our co-vertex is at (0,3), 'b' equals 3.
So in this case the standard form equation of the ellipse would be (x/4)² + (y/3)² = 1.
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How can the areas of certain shapes be found? What are the meanings of surface area and volume and how can surface area and volume be found
Answers
Answer:
Well, to find the area of a:
square and rectangle you multiply (Length x Width) the formula is (LxW)
triangle you multiply (Base x Height) ÷ 2 the formula is (BxH/2)
The meaning of area is: the number of unit squares that can be contained in an object.
The meaning of volume is: the number of unit cubes that completely fill up a solid figure such as an ice cube.
To find the surface area of an object you:
Multiply the length times the width. (of only one side)
But for a triangle you multiply the base times the height, then divide the answer by 2 ( of only one side)
To find the volume you multiply the length times width times height.
But for a triangle you multiply the base times height.
Hope I helped ; )
Final answer:
The surface area and volume of shapes can be found using specific formulas. Surface area is the total area of the outside surface of a three-dimensional object, while volume is the amount of space occupied by the object.
Explanation:
The surface area and volume of certain shapes can be found using specific formulas. Surface area refers to the total area of the outside surface of a three-dimensional object. It is measured in square units. The formula for surface area depends on the shape of the object. For example, the formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
Volume, on the other hand, refers to the amount of space occupied by a three-dimensional object. It is measured in cubic units. Like surface area, the formula for volume also depends on the shape of the object. For a rectangular prism, the formula is V = lwh.
A flower bed has the shape of a rectangle 27 feet long and 9 feet wide. What is the area in square yards?
Answers
The answer is 243 27×9 is 243 and area is length times width
ANSWER
243 square feet.
EXPLANATION
The rectangular flower bed has length,
l=27 ft
and width, w=9ft.
The area of a rectangle is
Area=length x width
Since the flower bed is rectangular, we use this formula to find its area.
[tex]Area = 27 \times 9 = 243 {ft}^{2} [/tex]
Therefore the area of the flower bed is 243 square feet.
Can anyone help me with the answer for number 4
Answers
Answer:
b
Step-by-step explanation:
Given K is the midpoint of JL, then
JK = KL ← substitute values
6x = 3x + 3 ( subtract 3x from both sides )
3x = 3 ( divide both sides by 3 )
x = 1
Hence
JK = 6x = 6 × 1 = 6
KL = 3x + 3 = (3 × 1) + 3 = 3 + 3 = 6
JL = 6 + 6 = 12
The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. What is the probability that a person chosen at random from this group has brown or green eyes?
Answers
Answer: 13/25
Step-by-step explanation:
The probability that a person chosen at random from this group has brown or green eyes is 0.52.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The table of the number of people and the colour of their eyes colour is given as,
Colour of Eyes Number of People
Brown 20
Green 6
Blue 17
Hazel 7
According to the table, the total number of people who participated in the survey is 50. Therefore, the probability that a person chosen at random from this group has brown or green eyes can be written as,
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
[tex]\rm Probability=\dfrac{\text{Number of people with brown and green eyes}}{\text{Total number of people who participated in the survey}}[/tex]
[tex]\rm Probability=\dfrac{20+6}{50}=\dfrac{26}{50} = 0.52[/tex]
Hence, the probability that a person chosen at random from this group has brown or green eyes is 0.52.
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which of the symbols correctly relates the two numbers below? check all that apply 13?13
Answers
Answer:
Correct symbol is = .
Step-by-step explanation:
Given statement is : 13?13
Now we need to find about which of the symbols correctly relates the two numbers 13?13.
When we compare two numbers then there are only three cases possible.
First number is less than ( < ) second number.
First number is greater than ( > ) second number.
First number is equal to ( = ) the second number.
we see that both numbers 13 and 13 are equal so we will use = symbol.
Hence correct symbol is = .
Final answer:
The correct symbol to relate two identical numbers, such as 13 and 13, is the equals to (=) symbol.
Explanation:
The question asks which symbols correctly relate the two numbers 13 and 13. In mathematics, numbers can be compared using different symbols to show their relationship. These symbols include equals to (=), greater than (>), less than (<), greater than or equal to (>=), and less than or equal to (<=). When two numbers are identical, the correct symbol to relate them is the equals to (=) symbol because they have the same value.
Determine whether y varies directly with x. If so, find the constant of variation and write the equation.
Answers
Answer:
The answer is yes , k = -2 and y = -2x ⇒ first answer
Step-by-step explanation:
* To prove the variation
- Check the constant change in the values of x and y
- Lets check that from the table
# At x = 1 ⇒ y = -2
# At x = 3 ⇒ y = -6
# At x = 5 ⇒ y = -10
* -6 - -2 = -6 + 2 = -4 ⇒ 3 -1 = 2
-10 - -6 = -10 + 6 = -4 ⇒ 5 - 3 = 2
∴ y decreased by 4 when x increased by 2
* This is a constant change
∴ y is varies directly with x
∴ y ∝ x
∴ y = k x ⇒ where k is the constant of the variation
* Lets find the value of k
- You can use one value of x and y from the table
∵ x = 3 and y = -6
∴ -6 = k (3) ⇒ divide two sides by 3
∴ k = -2
∴ The equation of the variation is = y = -2x
* The answer is yes , k = -2 and y = -2x
Answer:
Yes, k=-2 and y=-2x
Step-by-step explanation:
Using (1,-2) and (3,-6)
[tex]k=\frac{-6--2}{3-1}=-2[/tex]
This implies that
y=-2x
check for the 3rd point;
When x=5,
y=-2(5)=-10
Hence y varies directly as x. The constant of variation is k=-2
For the following question, what is the value of x to the nearest tenth?
Answers
Answer:
I believe it is 11.5 but I’m not 100% sure
Step-by-step explanation:
Given the net of the rectangular prism, what is its surface area?
96 m2
144 m2
160 m2
180 m2
Answers
Answer:
[tex]160\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to the area of its six rectangular faces of the net
so
[tex]SA=2(2*4)+2(12*2)+2(12*4)\\ \\SA=16+48+96\\ \\SA=160\ m^{2}[/tex]
Answer:
160 m2
Step-by-step explanation:
A deep-sea exploring ship is pulling up a diver at the rate of 25 ft./min. the driver is 200 feet below sea level how deep it was the diver 10 minutes ago show your thinking
Answers
Answer:
Ten minutes ago, the diver was 450 feet below sea level.
Step-by-step explanation:
Since the diver is being pulled up, measuring his movement for the past 10 minutes requires that we use −25 for the movement over those 10 minutes. So, his depth 10 minutes ago is given by the expression
−200−25(10)
−200
−250
−450
So, 10 minutes ago, the diver was 450 feet below sea level.
Answer:
The diver 450 feet deep into sea 10 minutes ago.
Step-by-step explanation:
At present position ,depth at which diver was = 200 feet
Rate at which diver is pulled up = 25 ft/min
Let the depth of the diver 10 minutes ago be x
The depth of the diver 10 minutes ago will be sum of present position and distance covered by exploring ship by pulling diver in a 10 minutes.
x = 200 + 25ft/min × 10 = 200 ft + 250 ft = 450 ft
The diver 450 feet deep into sea 10 minutes ago.
Convert 150 pounds into kg.
Answers
Answer:
About 68 or 68.03
Step-by-step explanation:
Answer:
it is 68.0388555 Kg when you convert it to Kg.
Step-by-step explanation:
1 pound is 0.45359237 Kg
What is the height of the triangular prism? Where it says C, what's the height?
Answers
Answer:
√7 ≈ 2.646
Step-by-step explanation:
The triangle apparently has two sides of length 4 and a third side of length 6. The altitude of the triangle will divide the long side in half, making that half one leg of the right triangle with hypotenuse 4.
The altitude of interest is then the length of the other leg:
√(4² -3²) = √7 ≈ 2.646
In one study, the daily use of toilet flushes is 9.1 gallons of water per person per day.
In New York City, water costs $7.64 per 100 cubic feet of water. Calculate the annual cost of toilet flushes for a family of four.
Recall that 7.48 gallons = 1 cubic foot, and assume there are 365 days in a year.
Answers
Answer:
$135.70
Step-by-step explanation:
First step is to calculate the daily consumption for this family of four. We'll assume they're all in age to use and flush the toilet themselves (no babies).
So, one person flushes 9.1 gallons a day, a family of 4 would then flush 4 times that:
daily family flushes = 9.1 gal/person * 4 persons/family = 36.4 gal/family
That's for one day... now for a year...
yearly = 36.4 gal/day * 365 days/yr = 13 286 gal/year
Let's convert those gallons into cubic feet:
13 286 gal / 7.48 gal/ft³ = 1,776.2 ft³
Then we multiply the gallons by the price for 100 cubic feet and divide by 100:
1,776.2 ft³ * $7.64 /100 ft³ = $135.70
finding the solutions of inequality
-7x+14>-3x-6
Answers
Answer:
x < 5
Step-by-step explanation:
- 7x + 14 > - 3x - 6
14 > 4x - 6
20 > 4x
x < 5
Answer:
x>5
Step-by-step explanation:
-7x+14>-3x-6
-4x+14>-6
-4x>-20
-x>-5
x>5
Which is the answer
Answers
Answer:
Inverse property
Step-by-step explanation:
The definition of the inverse property is to add to get a result of zero. Since we are adding the inverse of each term to get a result of zero each time, we are using the inverse property.
6r+7=13+7r help me asap
Answers
Answer:
r = - 6
Step-by-step explanation:
Given
6r + 7 = 13 + 7r ( collect terms in r on the left and numbers on the right )
Subtract 7r from both sides
- r + 7 = 13 ( subtract 7 from both sides )
- r = 6 ( multiply both sides by - 1 )
r = - 6
6r+7=13+7r
-6r -6r
------------
7=13+1r
flip the equasin to make it easier
13+1r= 7
-13 -13
---------
1r= -6
If f(x)= 3x^2-4 and g(x)= 2x-6 what is g(f(2))?
Answers
Answer:
10
Step-by-step explanation:
g (3 (2)² - 4)
g (3 (4) - 4)
g (12 - 4)
g (8)
------
2 (8) - 6
16 - 6
10
To find the value of g(f(2)), we first compute f(2) and then substitute this output into the g(x) function. So, f(2)=8, and g(8)=10, which means that g(f(2))=10.
Explanation:The question is related to the concept of functions in mathematics. Specifically, it asks to compute the function g(f(2)), where f(x)= 3x^2-4 and g(x)= 2x-6.
First, we need to find the value of f(2). substitute x=2 in the function f(x). f(2)= 3*(2)^2 - 4 = 3*4 - 4 =12 - 4 = 8.
put this value into the function g(x), so find g(8). By substituting x=8 in g(x): g(8) = 2*8 - 6 = 16 - 6 = 10.
So, g(f(2)) = g(8) = 10.
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heeeeeeeellllllllpppppppppp
Answers
Answer:
False
Step-by-step explanation:
To be a function each x can only go to one y
The number 5 goes to both 2 and 1, which violates the rule
Therefore, this is a relation, not a function
The length and width of a rectangle are consecutive even integers. The area of the rectangle is 80 square units. What are the length and width of the rectangle?
Answers
Answer:
10 and 8
Step-by-step explanation:
consecutive even numbers have a difference of 2 between them.
let the width be n then the length is n + 2
Area = n(n + 2) = 80, thus
n² + 2n = 80 ( subtract 80 from both sides )
n² + 2n - 80 = 0 ← in standard form
(n + 10)(n - 8) = 0 ← in factored form
Equate each factor to zero and solve for n
n + 10 = 0 ⇒ n = - 10
n - 8 = 0 ⇒ n = 8
But n > 0 ⇒ n = 8
width = n = 8 and length = n + 2 = 8 + 2 = 10
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answers
Answer:
y = - 6x - 57
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 6, thus
y = - 6x + c ← is the partial equation
To find c substitute (- 9, - 3) into the partial equation
- 3 = 54 + c ⇒ c = - 3 - 54 = - 57
y = - 6x - 57 ← equation of line
Answer:
y + 3 = –6(x + 9)
Step-by-step explanation: