The length of the given rectangle is x + 5 meters.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.Given:
Area of rectangle = x² + 8x + 15 sq.metersWidth = x + 3 metersTo find: Length of the rectangle
Finding:
Let 'a' be the length of the rectangle.
We know that area of a rectangle = length * width
On substituting the given values in the above formula, we get:
=> x² + 8x + 15 = a (x + 3)
=> a = [tex]\frac{x^2+8x + 15}{x+3}[/tex]
=> a = [tex]\frac{(x+5)(x+3)}{x+3}[/tex]
=> a = x + 5
Hence, The length of the given rectangle is x + 5 meters.
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Find the 8th term of the geometric sequence shown below. 6x,18x^4,54x^7
please help
The 8th term of the geometric sequence is 13122x^22
Explicit form of a geometric sequenceThe explicit form of a geometric sequence is expressed according to the equation;
Tn = ar^n-1
where
r is the common ratio
a is the first term
n is the number of terms
Given the sequence below;
6x,18x^4,54x^7
r = 18x^4/6x
r = 3x^3
a = 6x
n = 8
Substitute to have:
T8 = 6x(3x^3)^8-1
T8 = 6x (3x^3)^7
T8 = 13122x^22
Hence the 8th term of the geometric sequence is 13122x^22
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Find the sum of the following numbers:
-7, 14, 10, -21
Answer:
-4
Step-by-step explanation:
Let's solve this step by step:
-7 + 14 = 7
7 + 10 = 17
17 - 21 = -4
Your answer would be -4
Maker the subject of this formula.
V = ³√p+r?
Answer:
here's the answer I have in the photo and solution too
If f (x) = 3x^4+5, then what is the remainder when f (x) is divided by x+4?
The remainder when polynomial function is divide by linear function is 773.
Given that the polynomial functon f(x)=3x⁴+5 and the linear function is x+4.
As it is given that we have to find the remainder the polynomial
f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4.
f(x)=3x⁴+5 .......(1)
g(x)=x+4 .......(2)
We know the remainder theorem that when a polynomial f(x) is divided by a linear expression (x−a), the remainder will be f(a).
From equation (2), we have a linear expression.
Now, on simplifying equation (2) to obtain the zero of g(x), we get
g(x)=x+4=0
x+4=0
Now, on comparing (x+4) and (x−a), we get
a=-4 ......(3)
Here, we have to get the value of f(a).
Now, using the remainder theorem, we can say that to get the remainder when the polynomial f(x)=3x⁴+5 is divided by g(x)=x+4, we have to replace x by -4 in the polynomial f(x)=3x⁴+5, we get
f(-4)=3(-4)⁴+5
f(-4)=3(256)+5
f(-4)=768+5
f(-4)=773
Therefore, the remainder when the polynomial f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4 is 773.
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Which weight represents the 65th percentile?
The 65-th percentile is approximately 83.8 ounces.
A number at or below which a particular percentage falls in its frequency distribution, or a score below which a given percentage falls, is known as the k-th percentile in statistics. The 50th percentile, for instance, is the score at or below which 50% of the distribution's scores can be found.
The 50-th percentile is called the median.The 25th and 75th percentile is called the lower and upper percentile respectively.Mean of a data-set is the measure of central tendency which denotes the average of the data.The standard deviation denotes the fluctuations of the data from the central tendency.The percentile can be calculated by using the formula
Percentile Value = μ + zσ where
z is the z-score , μ is the mean and σ is the standard deviation.
Here the percentile that is to be calculated is 65.
So we take the value that is closest to 0.65 from the z-table.
We get the value of the data to be 0.39
Now putting the values in the equation we get:
Percentile Value = μ + zσ
or, Percentile Value = 83 + (0.39 × 2)
or, Percentile Value = 83.78
or, Percentile Value ≈ 83.8
Hence the 65th percentile value of the function is given by 83.8 .
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Rearrange the formula d=rt to solve for time.
im having a lil trouble with this one guys
Answer:
t = d/r
Step-by-step explanation:
d = rt
We are solving for t, so you need t alone on the left side.
Switch sides.
rt = d
t is being multiplied by r, so you need to divide the left side by r to get rid of r. You must do the same operation to both sides of an equation, so divide both sides of the equation by r.
rt/r = d/r
rt/r is simply t, so we get:
t = d/r
determine whether the data are qualitative or quantitative. the colors of automobiles on a used car lot
The data is qualitative one.
Qualitative Data:
Qualitative data consists of Labels, Attributes, Descriptions
This type of data is observed not measured
Examples: Colors, categories, appearances, dogs, etc.
Basically it considers the qualities of the data.
Quantitative Data:
Quantitative data Consists of numbers or counts in the data.
This type is mainly focused on the measurement. Which means it only consider the quantities.
Examples: Length, height, area, speeds, dollar amounts, ages, etc.
Given,
The colors of automobiles on a used car lot.
Here we need to determine the given data is qualitative or quantitative.
Based on the definition of the qualitative or quantitative,
We conclude that the given data is qualitative.
Because it describe the quality of the car.
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4(r-2+y) distribute to creat an equivalent expression with the fewest symbols possible
Answer: 4r-8+4y
Step-by-step explanation: Distribution is when you multiply every term inside the parantheses by the outside term. So 4(r-2+y)=4(r)+4(-2)+4(y). This is the same as 4r-8+4y. Since none of these are like terms we have the fewest symbols possible.
100 points, please help
In 8-11, write a justification for each conclusion.
Answer:
8. Supplementary means that two angles add up to 180 degrees (straight line). For the justification, I would simply write "def. of supplementary angles."
9. Equilateral means that all sides equal. For the justification, I would simply write "def. of equilateral triangle."
10. In a circle, all radiuses equal in length. TC and ZC are both radiuses. For the justification, I would simply write "def. of radius."
11. A midpoint divides a line segment in half. For the justification, I would simply write "def. of midpoint."
PLS HELPP IM LOST
1: Find the missing Statements #3, #7, and #8 in the Algebraic Proof below.
2: What are the missing statements for #4 and #6?
Answer:
#3: -2 = 2y - 8
#7: 3 = y
#8: y = 3
#4: Angle1 + Angle2 = Angle ABC
#6: Angle 1 and Angle 2 are supplementary
Step-by-step explanation:
6y - 2 = 8y - 8
8 - 2 = 8y - 6y
6/2 = 2y/2
3 = y
y = 3
HELP 14 POINTS!!! QUESTION IN PICTURE!!
The value of x is 27
In this question, we have been given a line AB and a point O on the line AB.
From figure we can see that, there are linear angles ∠AOM, ∠MON, and ∠NOB
Also, ∠AOM = 36°,
∠MON = 90°, and
∠NOB = 2x
We need to find the value of x.
We know that the sum of linear angles is 180°
⇒ ∠AOM + ∠MON + ∠NOB = 180°
⇒ 36° + 90° + 2x = 180°
⇒ 126° + 2x = 180°
⇒ 2x = 180 - 126°
⇒ 2x = 54°
⇒ x = 27
Therefore, the value of x is 27
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The equation y = 2.50x determines the total cost, y, of buying x carnival tickets. Use the drop-down menu to complete the sentence.
According to the equation, 15 carnival tickets would cost.
.
The cost of 15 carnival tickets is 37.5 dollars.
How to use the equation to find the cost of 15 ticket ?The equation y = 2.50x determines the total cost, y, of buying x carnival tickets.
where
x = number of carnival tickety = total costTherefore, according to the equation, the cost of 15 carnival ticket can be calculated as follows:
y = 2.50x
where
x = 15
Hence,
y = 2.50 × 15
y = 37.5 dollars
Therefore, the cost of 15 carnival tickets is 37.5 dollars.
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Pablo mixes 3 units of white paint and 1 unit of black oaint to make gray paint. What two equations show the relationship between units of white paint and unites of black paint
Which fractions have the same value as -1/4 please help
(different question and look at picture)
Answer:
-1/4 ,-(-1/-4) and 1/-4 are the answers please
f(x)=x+5
g(x)=\sqrt 3x+1
find f/g and f-g then give their domains using interval notation
[tex] \frac{f(x)}{g(x)} = \frac{x + 5}{ \sqrt{3x + 1} } [/tex]
[tex]x ∈ \: \: ] \frac{ - 1}{3} ,∞[[/tex]
[tex]f(x) - g(x) = x + 5 - \sqrt{3x + 1} [/tex]
[tex]x ∈ \: \: [ \frac{ - 1}{3} ,∞[[/tex]
A fisk tank in the shape of a cube. its volume is 125ft. what is the area of one face of the tank
The area of one face of the fish tank in the shape of a cube is 25 ft²
The formulas and the procedures we will use are:
v = s³A= 6*s²Where:
s= edge lengthv= volumeA = areaInformation about the problem:
v = 125ft³s = ?A = ?Applying the volume formula and isolating the edge length, we have:
v = s³
s = [tex]\sqrt[3]{}[/tex]v
s = [tex]\sqrt[3]{}[/tex](125 ft³)
s = 5 ft
With the edge length, we calculate the area of the cube of one face of the tank:
Total faces of the cube = 6
One face of the cube = 1
A= 1*s²
A= 1*(5ft)²
A= 1*25ft²
A= 25 ft²
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2
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What is the domain and range for first graph
We need to know about domain and range of a graph to solve this problem. The domain is (-∞,5) and the range is (-∞,2).
The domain of a function is the input values that the function can take. The range is the set of values that can be the possible output of the function. The domain of a graph are the values that are on the x-axis and the range is on the y-axis. The arrow means that the graph goes on till infinity, a solid sphere means that the graph ends at that point and the ending point is included in the function, a hollow sphere means the graph ends at that point and the ending point is not included in the function. In the graph in the question, along x-axis the values on left goes on till negative infinity and on right the domain is open at 5. For range along y-axis, the range on the left side goes on till negative infinity and on the right it is open at 2.
Therefore we see that the domain of the graph is (-∞,5) and the range is (-∞,2).
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(7x10^9)(5.3x10^2). Write this in scientific Notation
The required answer would be 3.7×10¹⁰ which is written in the form of scientific notation.
What is the Scientific Notation?Scientific Notation is a way of writing down in the easy form of very large or very small numbers.
We have been given that expression as:
⇒ (7×10⁹)(5.3×10²)
⇒ 7×5.3 ×10⁹×10²
We have to add exponents of tens and apply the multiplication operation between 7 and 5.3,
⇒ 37 ×10⁹⁺²
⇒ 3.7×10⁻¹ ×10¹¹
⇒ 3.7×10¹⁰
Hence, the required answer is 3.7×10¹⁰ which is expressed in scientific notation.
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I need help asap!! (Fractions)
Answer:3 5/7
Step-by-step explanation:
Answer: A ----------------3 5/7
Of the numbers 0.4761, 0.04761, 0.4671, and 0.04671, which is the largest?
Answer:
0.4761
Step-by-step explanation:
It is in the 10ths place making it bigger than 0.04761 and 0.04671
Then in the hundreths place for 0.4761 7 is bigger than the 6 in in the hundreths place of 0.4671, so the answer is
0.4761
PLEASE HELP ME THANK YOU
Answer:
number 2. A
number 3. C
number 4. B
Step-by-step explanation:
if the answer's are correct then comment or like
#35 i
Find the measure of the exterior angle.
to
38°
The measure of the exterior angle is
Answer:
128°
Step-by-step explanation:
The three INTERIOR angles of the triangle are 90 38 and 52° ( they sum to 180 °)
52 ° and 'x' form a straight line = 180 ° so x = 128°
Answer:
128
Step-by-step explanation:
Add the two farthest angles, 90 and 38, so that's 128
brainliest pls
prove that if all of the 2n subsets of a set containing 2n 1 are equal, then all elements of set n are equal
when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).
Take the power set. It has 2^(2n+1) members.
Replace any member which has n+1 or more elements with its complements.
Now the power set has members, which have n or fewer elements, and each such member appears twice.
Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).
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This question is throwing me off track. Help?
Solve 1/3x + 6/5 = 3/5
The slashes means that it is a fraction btw! Thanks so much if you do help me :)
Answer:
x= -9/5
Step-by-step explanation:
I hope this helps!
In an AP the 9th Term is 2 times the 4th Term and the 12th Term is 78. What is the sum of the first twenty terms?
The sum of the first twenty terms of the given AP is 1380.
An arithmetic progression is given in this problem.Let the first term of the AP be "a".Let the common difference between the terms of the AP be "d".Let the term in the "n" position be denoted by t(n).t(n) = a + (n-1)*dIt is given that the 12th term is 78.t(12) = a + 11d78 = a + 11dThis is equation 1.It is given that the 9th term is twice the 4th term.t(9) = 2*t(4)a + 8d = 2(a + 3d)a + 8d = 2a + 6da = 2dThis is equation 2.Solving equations 1 and 2, we get the values of "a" and "d".The value of "a" is 12 and "d" is 6.The sum of the first "n" terms of an AP is given by the formula :S(n) = (n/2)[2a + (n-1)d]We need to find the sum of the first 20 terms.S(20) = (20/2)[2*12 + 19*6]S(20) = 10*(24 + 114)S(20) = 10*138S(20) = 1380To learn more about common difference, visit :
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Given: A is between B and C. if AB =x+2, BC=4x-7 , and AC =2x-1 , find x and AC
If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1, then the x=8 and AC=15 units.
Given,
That A is between B and C.
AB= x+2
BC= 4x-7
AC= 2x-1
Then,
BC = AB+AC
4x-7= x+2+2x-1
4x-7= 3x+1
4x-3x=1+7
x=8
Then the length of the line AC is
AC= 2x-1
AC= 2×8-1 =15 units
Hence, If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1, then the x= 8 and AC= 15 units
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Make c subject of the formula
πc² =A
Answer: c=[tex]\sqrt{A/\pi}[/tex]
Step-by-step explanation:
πc²=A
c²=A/π
c=[tex]\sqrt{A/\pi}[/tex]
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 777 points less than 222 times as many points as Carlos. Fabio scored 313131 points in the game.
Write an equation to determine the number of points (c) Carlos scored in the last game.
Find the number of points Carlos scored in the last game.
Considering the definition of an equation and the way to solve it, the number of points Carlos scored in the last game is 19.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing:
"C" the number of points Carlos scored."F" the number of points Fabio scored.and knowing that in the last game, Fabio had 7 points less than 2 times as many points as Carlos, the equation to determine the number of points Carlos scored in the last game is:
2C - 7= F
Fabio scored 31 points in the game. So you get:
2C - 7= 31
Solving:
2C= 31 + 7
2C= 38
C= 38 ÷ 2
C=19
Finally, the number of points Carlos scored in the last game is 19.
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a rectangular parking lot has a length that is 420 yards greater than the width. the area of the parking lot is 13 square yards. find the length and the width.
The length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Let L be the length and W be the width of the rectangle.
From the question:
L = 420 + W (based on the data given in the question)
LW = 13
(420 + W)W = 13
W² + 420W - 13 = 0
After solving the above quadratic equation:
W = 0.031, W = -420.03 (width cannot be negative)
W = 0.031 yards (which is not practical but from a mathematical point of view it can be considered)
L = 420 + 0.031 = 420.031 yards
Thus, the length and the widths are 420.031 yards and 0.031 yards if a rectangular parking lot has a length that is 420 yards greater than the width.
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What are the solutions to the equation
w squared
=
36
? Select all that apply.
−
18
6
−
9
−
6
18
9
Answer:-4
Step-by-step explanation: