Simplify the rational expression . x^2+9x+20/x+7The quotient is , and the remainder is .
Final answer:
The rational expression x^2+9x+20/x+7 simplifies to (x+5) with a remainder of (x+4)/(x+7) after factoring the numerator.
Explanation:
To simplify the rational expression x^2+9x+20/x+7, you would factor the numerator and then divide the factors by the denominator if possible.
The factoring of x^2+9x+20 would yield (x+5)(x+4), as these are the factors of 20 that add to 9. Now the expression becomes:
((x+5)(x+4))/(x+7)
Since x+7 doesn't factor with either x+5 or x+4, the expression is already in its simplest form. So the quotient is x+5 with a remainder of (x+4)/(x+7).
Remember to check your answer to ensure it is reasonable.
Can someone answer 14,15 and 16? Thank you!
Which statement describes if there is an extraneous solution to the equation √x-3 = x-5? A. there are no solutions to the equation, B. the extraneous solution is x = 7, C. the valid solutions are x = 7 and x = 4, or D. the extraneous solution is x = 4
Answer:
D. the extraneous solution is x = 4
Step-by-step explanation:
You want to know the statement that describes if there is an extraneous solution to the equation √x-3 = x-5.
SolutionA straightforward (blind) solution to the problem proceeds by squaring both sides and solving the quadratic:
x -3 = x² -10x +25
x² -11x +28 = 0
(x -7)(x -4) = 0 ⇒ x = 4 or x = 7
When you try these solutions in the original equation, you get ...
√(4 -3) = 4 -5 ⇒ 1 = -1 . . . . . x = 4 is an extraneous solution, choice D
√(7 -3) = 7 -5 ⇒ 2 = 2 . . . . . x = 7 is the solution
DomainThe square root function is only defined for non-negative values, so the left side of the equation is only defined for x ≥ 3.
The left side of the equation produces non-negative values. The right side of the equation will have non-negative values only for x ≥ 5.
Considering the domain of the equation is x ≥ 5, we know that x = 4 cannot be a solution. It can be ignored. This value only arises because squaring the radical allows values of x that require the root to be negative.
__
Additional comment
The attached graph shows the only solution is x=7, the value that makes the difference between the sides of the equation be zero. We find it useful to write radical equations in the form f(x) = 0, making the x-intercepts of the graph of f(x) be the solution(s). The graphing calculator does not graph the function where it is undefined, so the domain restrictions are automatically accommodated.
A section in a stained glass window is shaped like a trapezoid. The top base is 1 centimeter and the bottom base is 3.5 centimeters long. If the area of the section of glass is 8.1 square centimeters, how tall is the section?
The height of the trapezoidal section is approximately 3.6 centimeters.
Explanation:To find the height of the trapezoidal section, we can use the formula for the area of a trapezoid: A = 1/2 * (top base + bottom base) * height. In this case, the top base is 1 centimeter and the bottom base is 3.5 centimeters. We are given that the area is 8.1 square centimeters. Plugging these values into the formula:
Therefore, the height of the trapezoidal section is approximately 3.6 centimeters.
The height of the trapezoidal section of stained glass is calculated using the area formula for trapezoids. With the given measurements, the height is found to be 3.6 centimeters.
Explanation:To find the height of a trapezoid section in a stained glass window with a top base of 1 centimeter, a bottom base of 3.5 centimeters, and an area of 8.1 square centimeters, we use the formula for the area of a trapezoid, which is Area = 1/2 × (base1 + base2) × height. In this case, base1 is the top base, base2 is the bottom base, and Area is already given as 8.1 cm2.
Plugging the values into the formula gives us:
8.1 = 1/2 × (1 + 3.5) × height
8.1 = 1/2 × 4.5 × height
8.1 = 2.25 × height
To find the height, we divide both sides by 2.25:
height = 8.1 / 2.25
height = 3.6 centimeters
Thus, the height of the trapezoid section is 3.6 centimeters.
Math please help ( ASAP vv easy )
a. the answer is the first one
If the volume of a sphere is 36 cubic units, what is the radius?
A. 3 units
B. 4√3 units
C. 9 units
The radius of the sphere is 2.048 units .
The volume of a sphere is :
4/3πr³Volume = 36substituting into the formula:
36 = 4/3πr³
36 × 3 = 4 πr³
108 = 4πr³
πr³ = 27
r³ = 27/π
r³ = 8.59436
r = 2.048
Hence, the radius of the sphere is 2.048 units .
Please help I’m stuck.
Find the value of x
Using distributive law find the square of 101 and 72
To find the square of 101, we can use the distributive law as follows: 101^2 = (100 + 1)^2 = 10000 + 200 + 1 = 10201. Similarly, to find the square of 72: 72^2 = (70 + 2)^2 = 4900 + 280 + 4 = 5184.
Explanation:The use of the distributive law allows us to expand expressions by multiplying each term inside the parentheses by the term outside the parentheses. To find the square of 101, we can use the distributive law as follows:
101^2 = (100 + 1)^2 = 100^2 + 2(100)(1) + 1^2 = 10000 + 200 + 1 = 10201
Similarly, to find the square of 72:
72^2 = (70 + 2)^2 = 70^2 + 2(70)(2) + 2^2 = 4900 + 280 + 4 = 5184
What percent of the June budget was for babysitting and movies (to the nearest tenth)?
The scale on a map is 1 cm = 30 km. The map distance between two towns is 3.5 cm. What is the actual distance between the two towns?
Using unitary method, the actual distance between the two towns is 105 km.
What is unitary method?The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
1 cm = 30 km
3.5 cm = 30 * 3.5 = 105 km
Learn more about unitary method here
https://brainly.com/question/22056199
#SPJ2
What is the surface area of the regular pyramid
The center of the inscribed circle of Triangle ABC is point , and the center of the circumscribed circle of Triagnle ABC is point .
Answer:
Part A: The center of The inscribed circle is the point S
Part B: The center of The circumscribed circle is the point P
Step-by-step explanation:
Part A: Find the center of The inscribed circle of ΔABC
The inscribed circle will touch each of the three sides of the triangle in exactly one point,
The center of the inscribed circle is the point of intersection between the angle bisectors of the triangle.
So, According to the previous definition:
A₁A₂ and B₁B₂ are the angle bisectors of ∠A and ∠B
So, the inter section between them is the center of The inscribed circle
So, the center of The inscribed circle is the point S
=====================================================
Part B: Find the center of The circumscribed circle of ΔABC
The circumscribed circle is the circle that passes through all three vertices of the triangle.
The center of the circumscribed circle is the point of intersection between the perpendicular bisectors of the sides.
So, According to the previous definition:
P₁P₂ and Q₁Q₂ are the perpendicular bisectors of AB and BC
So, the inter section between them is the center of The circumscribed circle
So, the center of The circumscribed circle is the point P
HELP!!!!!! THIS IS GEOMETRY!
Find the perimeter of the shape below:
A four sided figure RSTU is shown. R is located at negative 1, 3. S is located at negative 2, 7. T is located at 2, 5. U is located at negative 1, 5
Answer:
13.6 is the correct answer
Step-by-step explanation:
got it right on the test
Final answer:
To find the perimeter of the given quadrilateral, calculate the distance between each pair of consecutive points using the distance formula and sum these distances. The perimeter is the sum of √17 + √20 + 3 + 2 which is 13.59 units.
Explanation:
The question you've asked involves finding the perimeter of a four-sided figure, known as a quadrilateral, with vertices R, S, T, and U located at (-1, 3), (-2, 7), (2, 5), and (-1, 5) respectively. To find the perimeter of this shape, we need to calculate the distance between each pair of consecutive vertices and sum these distances up.
Firstly, use the distance formula – d = √((x2 - x1)² + (y2 - y1)²) – to calculate the length of each side:
RS = √((-2 - (-1))² + (7 - 3)²) = √(1 + 16) = √17=4.12
ST = √((2 - (-2))² + (5 - 7)²) = √(16 + 4) = √20 = 4.47
TU = √((-1 - 2)² + (5 - 5)²) = √(9 + 0) = 3
UR = √((-1 - (-1))² + (3 - 5)²) = √(0 + 4) = 2
Finally, sum these distances to find the perimeter: √17 + √20 + 3 + 2 which comes out to be 13.59 units. The exact perimeter involves square roots since we're dealing with irrational distances.
What are the similarities and differences between these data sets in terms of their centers and their variability?
Data Set A: 1, 2, 4, 1, 9
Data Set B: 2, 7, 8, 12, 1
Select from the drop-down menus to correctly complete the statements.
Comparing the centers of the data sets, the median for Data Set A is the median for Data Set B. Further, based on the range, Data Set is more variable
Answer:
The answer is less than and B
Step-by-step explanation:
took the test
Help..please simplify this
How many sides does a regular polygon have if each exterior angle measures 30?
The number of sides that the polygon with each exterior angle measuring 30° has is 12.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The sum of all the exterior angles of a regular polygon is always equal to 360°. Therefore, the measure of an exterior angle for a regular polygon is given as,
[tex]\theta = \dfrac{360^o}{n}[/tex]
where n is the number of sides.
Given that the measure of the exterior angle is 30°. Therefore, the number of sides will be,
[tex]\theta = \dfrac{360^o}{n}\\\\ 30^o = \dfrac{360^o}{n}\\[/tex]
n = 12
Learn more about Polygon:
https://brainly.com/question/10441863
#SPJ5
A warden meets with 23 prisoners. He tells them the following:
Each prisoner will be placed into a room numbered 1-23. Each will be alone in the room, which will be soundproof, lightproof, etc. In other words, they will NOT be able to communicate with each other.
They will be allowed one planning session before they are taken to their rooms.
There is a special room, room 0. In this room are 2 switches, which can each be either UP or DOWN. They cannot be left in between, they are not linked in any way (so there are 4 possible states), and they are numbered 1 and 2. Their current positions are unknown.
One at a time, a prisoner will be brought into room 0. The prisoner MUST change one and only one switch. The prisoner is then returned to his cell.
At any time t, given some N>0, there exists a finite t_0 by which time every prisoner will have visited room 0 at least N times. (In other words, there is no fixed pattern to the order or frequency with which
prisoners visit room 0, but at any given time, every prisoner is guaranteed to visit room 0 again. If you’re still confused by this statement, ignore it, and you should be ok).
At any time, any prisoner may declare that all 23 of them have been in room 0. If right, the prisoners go free. If wrong, they are all executed.
What initial strategy is 100% guaranteed to let all go free?
Emily used the number sentence 736.82 + 146.89 = to solve this story problem. A small bin held 146.89 pounds of almonds. A large bin held 736.82 pounds of peanuts. What is the total weight of the nuts in the two bins? Which story problem could also be solved by using the number sentence 736.82 + 146.89 = ? A. Ian weighs 146.89 pounds. The elevator's limit is 736.82 pounds. How many more pounds can be put on the elevator? B. A large fish tank had 736.82 liters of water. A worker removed 146.89 liters of water to make room for the pebbles and sculptures. How much water is left in the tank? C. A northern train route has 736.82 miles of track. A southern route has 146.89 miles of track. How many more miles of track does the northern route have than the southern route? D. Harold earned $146.89 delivering flyers. Sheila earned $736.82 mowing lawns. How much money did they earn altogether?
What is the correct meaning of the word guarantor ?
During the new deal of the 1930s the federal government acted as a guarantor of economic security
A) one who provides assurance of something
B) one who is the original source of something
C) one who gradually reduces something
D) one who rebuilds or restores something
The words and their correct definitions are:
Restoration - To return something to its original state
Method - A way of doing something
Annexation - To legally take control of another territory and add it to one's own
Protectorate - A country that is defended or protected by another country
Modernize - To begin to use the newest technology or knowledge
What do the words mean?A protectorate refers to a nation that is protected by another nation such as Bechuanaland before 1966. Modernization allows for people to use newer methods of doing things.
Methods are how people go about doing something and annexing a territory means adding it to a nation's territory like the Russians did with the Crimea.
Hence, The words and their correct definitions are:
Restoration - To return something to its original state
Method - A way of doing something
Annexation - To legally take control of another territory and add it to one's own
Protectorate - A country that is defended or protected by another country
Modernize - To begin to use the newest technology or knowledge
Find out more on the words mean at
brainly.com/question/20617971
#SPJ2
complete question:
Words to know
Match each vocabulary word with the correct definition.
Restoration
A country that is defended or
protected by another country
Method
To legally take control of another
territory and add it to one's own
Annexation
OOOOO
To return something to its original
state
Protectorate
To begin to use the newest
technology or knowledge
Modernize
A way of doing something
How much greater is the median number of pairs of shoes in the inventory at the Golf Pro Shop than the median number of pairs of shoes in the inventory at the Tennis Pro Shop?
Please help, Thanks!
kiara downloaded 264 pictures from her cellphone to her computer. these pictures took up 528 megabytes of space on her computer. each picture took up the same amount of space. how many megabytes do 35 of these picture take up
Answer:
"70, because 528 divides by 264 is 2, which means each picture is 2 megabytes, so therefore 35x2 = 70"
Step-by-step explanation:
this is good
70 megabytes can do 35 of these picture take up.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is given that kiara downloaded 264 pictures from her cellphone to her computer. These pictures took up 528 megabytes of space on her computer.
Each picture took up the same amount of space.
We have to find that how many megabytes do 35 of these picture take up.
therefore, we have to first divide the 528 by 264 then multiply it with 35.
So, we get
= 528/264 x 35
= 35 x 2 = 70
Hence, 70 megabytes can do 35 of these picture take up.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ6
Please help as soon as possible!!!
Sal scored g goals this season. Ben has scored four times as many goals as Sal. Chun has scored three fewer goals than Ben. a. 9g - 3 c. 3g - 9 b. g - 4g d. 3g + 9
complete question:
Write an expression in simplest form that represent the total amount.
Sal scored g goals this season. Ben has scored four times as many goals as Sal. Chun has scored three fewer goals than Ben.
a. 9g - 3
b. 3g - 9
c. g - 4g
d. 3g + 9
Answer:
a. 9g - 3
Step-by-step explanation:
Sal scored g number of goals this season . Ben has scored 4 times as many goals as Sal . Chun has scored 3 fewer goals than Ben. There goals can be expressed as follows
Sal's goal = g
Ben's goal = 4(g) = 4 × g = 4g
Chun's goal = 4g - 3
sum of their goals = g + 4g + (4g - 3)
sum of their goals = g + 4g + 4g - 3
sum of their goals = 9g - 3
a suitcase measures 24 inches long and the diagonal is 30 inches long how much material is needed to cover one side of the suitcase
The material i.e. needed should be 18.
Given that,
a suitcase measures 24 inches long and the diagonal is 30 inchesBased on the above information, the calculation is as follows:
[tex]a^2+b^2=c^2 \\\\ 24^2+b^2=30^2\\\\ 576+b^2=900 \\\\ b^2=324 [/tex]
18=b
Learn more: https://brainly.com/question/10309631?referrer=searchResults
PLEASE HELP !Barry has an ice tray that makes ice cubes shaped like a cone with a diameter of 2 cm and height of 2 cm. To the nearest cubic centimeter, what is the volume of an ice cube from Barry's tray? 2 cm³ 8 cm³ 25 cm³ 101 cm³
#16, can someone please explain it ASAP?
graph x+3<1/2(4x-12)<20
once again super confused
wheat grass is grown in planters that are 3 1/2 inch by 1 3/4 inch. if there is a 6x6 array of these planters with no space between them what is.the area covered by the planter ?
The area covered by the planter is 220¹/₂ in² = 220,5 in²
Further explanationTo solve the above questions, we need to recall some of the formulas as follows:
Area of Square = (Length of Side)²
Perimeter of Square = 4 × (Length of Side)
Area of Rectangle = Length × Width
Perimeter of Rectangle = 2 × ( Length + Width )
Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Rhombus = 4 × ( Length of Side )
Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )
Let us now tackle the problem !
Given:
Length of Rectangle = L = 3¹/₂ inches
Width of Rectangle = W = 1³/₄ inches
Unknown:
Area of Plainter = A = ?
Solution:
This problem is about Area of Rectangle.
[tex]\texttt{Area of Rectangle} = \texttt{Length} \times \texttt{Width}[/tex]
[tex]\texttt{Area of Rectangle} = \texttt{Length} \times \texttt{Width}[/tex]
[tex]\texttt{Area of Rectangle} = 3\frac{1}{2} \times 1\frac{3}{4}[/tex]
[tex]\texttt{Area of Rectangle} = \boxed {6\frac{1}{8} ~ \texttt{in}^2}[/tex]
There is a 6 × 6 array of these planters with no space.
[tex]\texttt{Total Area Covered} = 6 \times 6 \times \texttt{Area of Rectangle}[/tex]
[tex]\texttt{Total Area Covered} = 6 \times 6 \times 6\frac{1}{8}[/tex]
[tex]\texttt{Total Area Covered} = \boxed {220\frac{1}{2} ~ \texttt{in}^2}[/tex]
Learn moreThe perimeter of a polygon : https://brainly.com/question/6361596The perimeter of a rectangle : https://brainly.com/question/7619923The perimeter of a triangle : https://brainly.com/question/2299951Answer detailsGrade: College
Subject: Mathematics
Chapter: Two Dimensional Figures
Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width