Answers
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be w. Then, the length is w+2.
[tex]w(w+2)=32\\\\w^2 +2w=32\\\\w^2 +2w-32=0\\ \\ w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7\\\\\implies w+2 \approx 6.7[/tex]
Related Questions
Find the quotient of -20x9 and 2x³.
Answers
Answer:
-20x9= -180. 2 to the power of three =8 if you want the quotient it would be -22.5
Step-by-step explanation:
at a butcher shop, hilda bought 7 1/4 lb of beef she left with 18 9/20 lb of meat express the numbers of pounds of pork she bought using a decimal
Answers
Using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the pounds of pork the girl bought:
Beef bought: 7¼Total meat: 18 9/20Calculate pork as:
18 9/20 - 7¼369/20 - 29/4369 - 5(29)/20369 - 145/20224/2011.2Therefore, using mathematical operations, we can conclude that the pound of pork the girl brought was 11.2 pounds.
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What is the remainder when x2 + 15x + 9 is divided by x + 5 ?0 -41O 49O 42O 59
Answers
When a polynomial is dived by x - a, to find the remainder, we can plug is x = a into the equation and find the remainder.
When it is divided by x + a, the remainder is found by plugging in x = -a.
Now, the polynomial here is:
[tex]x^2+15x+9[/tex]It is divided by x + 5, so we need to plug in x = -5 to get the remainder, which is:
[tex]\begin{gathered} x^2+15x+9 \\ (-5)^2+15(-5)_{}+9 \\ =-41 \end{gathered}[/tex]The remainder is - 41, 1st answer choice.
Type the correct answer in the box. Rewrite the quadratic function in the form that best reveals the zeros of the function.
Answers
Answer:
f(x) = (2x + 3)(2x + 1)
Explanation:
The form that best reveals the zeros of the function is:
f(x) = (x - a)(x - b)
Where a and b are the zeros of the function.
So, we need to apply the distributive property as:
[tex]\begin{gathered} f(x)=2(2x^2+4x)+3 \\ f(x)=2\cdot2x^2+2\cdot4x+3 \\ f(x)=4x^2+8x+3 \end{gathered}[/tex]Then, we can factorize the quadratic function as:
[tex]f(x)=(2x+3)(2x+1)[/tex]So, now we can identify the zeros of the function if we solve the following equation:
[tex]\begin{gathered} f(x)=(2x+3)(2x+1)=0 \\ 2x+3=0\rightarrow x=-\frac{3}{2} \\ or \\ 2x+1=0\rightarrow x=-\frac{1}{2} \end{gathered}[/tex]Therefore, the form that best reveals the zeros in the function is:
f(x) = (2x + 3)(2x + 1)
mDE= ?Use O, A to find mDE , given that BF is a diameter of O. A.
Answers
STEP 1: Identify and Set Up
We are required to get the angle subtended by the arc DE.
We first acknowledge that it is part of the angles in a quadrant as this will help us find it.
STEP 2: Execute
First find angle DAE
[tex]\begin{gathered} Angle subtended by DE = 45 degreesWing Ko replaces watch bands. He is paid $24.60 per band How many bands must he replace to eam at least $122.50 per day?
Answers
To earn at least $122.50 per day, Wing Ko must replace 5 watch bands
Here, we want to find the number of bands that Wing Ko must replace to earn at least $122.50 per day
Let the number of watch bands be x
Using mathematical relatio to represent this inequality, we have;
[tex]\begin{gathered} 24.\text{ 6 }\times\text{ x }\ge\text{ 122.50} \\ 24.6x\text{ }\ge\text{ 122.50} \\ \\ x\text{ }\ge\text{ }\frac{122.5}{24.6} \\ \\ x\text{ }\ge\text{ 4.97} \\ \\ x\text{ }\ge\text{ 5} \end{gathered}[/tex]Find the equation of the line that passes through the point (-2, 7) and is parallel to the line y=4x+1. The answer must be written in the form ax+by+c=0, where a, b, c are integers
Answers
The equation of the line 4 · x - y + 15 = 0 is parallel to the line y = 4 · x + 1.
How to find the equation of the line parallel to another line
In this problem we must determine the equation of a line that is parallel to the line y = 4 · x + 1 and that passes through the point (x, y) = (- 2, 7). Lines are represented by algebraic equations of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.Two lines are parallel if both share the same slope.
First, find the slope of the first line:
m = 4
Second, determine the intercept of the parallel line:
b = y - m · x
b = 7 - 4 · (- 2)
b = 7 + 8
b = 15
Third, write the resulting expression and find its standard form:
y = 4 · x + 15
4 · x - y + 15 = 0
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lucy uses 4 round beads and 5 cube head beads to make a special necklace. lucy bought one package of 56 triangular beads, one package of 30 round beads, six bananas, one package of 24 cube bead beads, and three fish sandwiches. she usually makes her necklaces in the living room, but today she plans to make them in her bedroom
Answers
The number of special necklaces that she can produce, using proportions, is obtained as follows:
4.
What is a proportion?A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations to find the desired amounts in whichever context of a problem.
The requirements for each special necklace are listed as follows, from the problem:
4 round beads.5 cube heads.The amounts purchased are given as follows:
30 round beads.24 cube beads.The amount of round beads purchased is enough for:
30/4 = 7.5 special necklaces.
The amount of cube beads purchased is enough for:
24/5 = 4.8 special necklaces.
Hence the number of special necklaces that she can make is of:
4.
Because:
The lower limit of the amounts is of 4.The amount is rounded down, as there would not be enough cube beads for the fifth necklace.Missing InformationThe complete problem is given by the image shown at the end of the answer.
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Two and six-tenths times a number, x, plus 5 is y.
Answers
Answer:
2,6x +5 = y
Step-by-step explanation:
Don’t know if you wanted the equation, but this is how it’s written
Eddie Munson can ship 52 chocolates in a hour so how long will it take for him to ship 65 chocolates
Answers
What is the value of x?
30 points if answered
Answers
Answer: 20
Step-by-step explanation: They are both equal to each other, so 3x+50=6x-10. Then just solve for x by canceling out both sides.
Find the 54th term of the following arithmetic sequence.15, 22, 29, 36,...
Answers
a young entrepreneur purchased a lemonade stand for $30 each cup of lemonade cost $0.25 in materials let x equal the number of lemonade cups sold which functions represents the average cost C, if a cup of lemonade ?
Answers
The cost of the lemonade stand is $ 30.
The number of lemonade cups is x.
The price of each cup of lemonade is $ 0.25.
The cost function can be determined as,
[tex]\begin{gathered} c(x)=average\cos t\text{ of lemonade stand}+\text{price of each cup} \\ =\frac{30}{x}+0.25 \\ =\frac{30+0.25x}{x} \end{gathered}[/tex]Thus, option (A) is the correct option.
Please fill the gaps in!!
Answers
Answer:
[tex]2 {d}^{2} + 5d - 7 [/tex]
[tex](2d + 7)(d - 1)[/tex]
The length of a rectangle is 3 more than twice the width. Which of the following represents the length of the rectangle if the perimeter is 42 inches? 2(x) +2(2x+3)=42
Answers
Answer:
Step-by-step explanation: if the width is x then the length is 2x+3
The perimeter is 2x+2(2x+3)=42
then 6x+6=42
6x=36
x=6
Then the length is 2*6+3=15
What is the center and radius of -10x = -121 - y2 - x2 -22y
Answers
We need to find the center and the radius of
[tex]-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y[/tex]The general circle equation is the following
[tex](x-h)^2+(y-k)^2=r^2[/tex]where
(h,k) is the center and
r is the radius
1. rearrange the equation
[tex](x^2-10x)+(y^2+22y+121)=0[/tex]2. Add 25 on both sides
[tex](x^2-10x+25)+(y^2+22y+121)=25[/tex]3. Factor
[tex](x-5)^2+(y+11)^2=5^2[/tex]Now we have an equation that is very similar to the circle equation, so let's compare them
Center -> (h,k) = (5,-11)
radius -> r = 5
3. Last year in January Nugget Park employed 520 workers. At the end of the
year 195 employees were made redundant. What fraction of the workforce
kept their jobs?
Answers
[tex]\frac{325}{520}[/tex] fraction of the workforce kept their jobs
What is the Percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
What is Percentage change?
The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.
where growth in number equals new number minus initial number.
Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.
decreasing number where original number - new number
In other words, there is a percentage decline if the response is negative.
Here, It is given:
In January 520 workers were employed;
In the end, 195 employees were redundant;
So, The fraction of the workforce who kept their job:-
The fraction of the workforce who kept their job=[tex]\frac{520-195}{520}[/tex]
The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]
Hence,
The fraction of the workforce who kept their job=[tex]\frac{325}{520}[/tex]
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55 POINTS!!!
1. Identify the set of ordered pairs that represents y as a function of x.
Responses
{(−1, 0), (−1, 1), (−2, 2), (0, 3)}
{(−1, 1), (−2, 0), (−3, 4), (−3, 3)}
{(0, 0), (1, 1), (2, 2), (3, 3)}
{(0, 0), (1, 0), (2, 4), (2, 3)}
2. Which table represents y as a function of x?
Responses
x y
0 1
0 2
1 3
2 3
x y
1 0
2 0
3 1
3 2
x y
−1 −1
0 −1
2 0
3 2
x y
−1 −1
−1 0
0 2
2 3
Answers
Answer:
1) B, 2) C
===========
As per definition, functions have only one y-value per x-value.
Let's test it with given sets and tables.
Part 1A) {(−1, 0), (−1, 1), (−2, 2), (0, 3)} - Not a function x = - 1 repeatedB) {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} - Not a function x = - 3 repeatedC) {(0, 0), (1, 1), (2, 2), (3, 3)} - FunctionD) {(0, 0), (1, 0), (2, 4), (2, 3)} - Not a function x = 2 repeatedPart 2A)
x y
0 1
0 2
1 3
2 3
Not a function, x = 0 is repeatedB)
x y
1 0
2 0
3 1
3 2
Not a function, x = 3 is repeatedC)
x y
−1 −1
0 −1
2 0
3 2
FunctionD)
x y
−1 −1
−1 0
0 2
2 3
Not a function, x = - 1 repeated1) The set of ordered pairs that represents y as a function of x is;
B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}
2) The table that represents y as a function of x is; Table 3
How to Interpret Ordered Pairs?An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.
1) The first function given as {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.
The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.
The third function {(0, 0), (1, 1), (2, 2), (3, 3)}; This is a function because each input has unique output values.
The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ; This cannot be regraded as a function because the input x = 2 is repeated with different output values.
2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.
Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.
Table 3 is a Function because each input has unique output values.
Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.
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If
C
=
−
x
+
2
C=−x+2 and
D
=
x
2
+
8
x
−
1
,
D=x
2
+8x−1, find an expression that equals
3
C
+
3
D
3C+3D in standard form.
Answers
The expression that equals 3C+3D in standard form is:
x²+7x+1
Given:
C = -x+2
and D = x²+8x-1
we are asked to find out an expression which equals 3C+3D in standard form.
based on the conditions, formulate:
3C+3D
substitute C and D values.
⇒ 3(-x+2) + 3(x²+8x-1)
Apply multiplicative distribution law:
⇒ open the parenthesis.
⇒ -3x+6+3x²+24x-3
calculate the product or quotient
⇒ arrange the like terms.
⇒ 3x²+21x+3
⇒ Reduce the terms.
⇒ x²+7x+1
Hence we get the equation in standard form.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 +170t+40=10\\\\16t^2 -170t-30=0\\ \\ t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
could you help me out
Answers
we can do a triangle to solve the apothem
the upper angle is equal to 360 divided by 8 since 360 is a complete turn and an octagon is composed of 8 equal triangles, so is 45
now we take a triangle from the triangle to apply trigonometric ratios and solve a
the upper angle of the new triangle is the half of the original so is 45/2
now i will use the trigonometric ratio of tangent
[tex]\tan (\alpha)=\frac{O}{A}[/tex]where alpha is the angle, O the opposite side drom the angle and a the adjacent side from the angle
so replacing
[tex]\tan (\frac{45}{2})=\frac{3.5}{a}[/tex]and solve for a
[tex]\begin{gathered} a=\frac{3.5}{\tan (\frac{45}{2})} \\ \\ a\approx8.4 \end{gathered}[/tex]the aphotem is 8.4
and the formula of the area of the octagon is
[tex]A=4\times a\times l[/tex]where a is the aphotem and l the measure f each side so 7
replacing
[tex]\begin{gathered} A=4\times8.4\times7 \\ A=235.2 \end{gathered}[/tex]the area is 235.2 square units
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: Width = 5.7 feet, Length = 10.5 feet
Step-by-step explanation:
Let the width be w. Then, the length is 2w-0.9.
[tex]w(2w-0.9)=59.85\\\\2w^2 -0.9w-59.85=0\\\\w =\frac{-(-0.9) \pm \sqrt{(-0.9)^2 -4(2)(-59.85)}}{2(2)}\\\\w =5.7\\\\\implies 2w-0.9=10.5[/tex]
Reduce the algebraic fraction. y^3-3y^2+y-3/y^2-9
Answers
The reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]
What is algebraic fraction?Algebraic fraction are simply fractions with algebraic expressions on the top and/or bottom
We follow the step to reduce to algebraic fraction
[tex]\frac{y^3 - 3y^2 -3 }{y^2 - 9}[/tex]
Simplify the numerator
[tex]\frac{ (y - 3) )(y^2 + 1 )}{y^2 -9}[/tex]
Factor out the greatest common factor from each group
[tex]\frac{(y^3 -3y^2 ) = y -3}{y^2 - 9}[/tex]
Find out greatest common factor (GCF) from each group
[tex]\frac{y^2 (y + 3) + 1 (y - 3)}{y^2 - 9}[/tex]
Simplify the denominator and rewrite 9 as [tex]3^{2}[/tex]
[tex]\frac{( y - 3 ) (y^2 + 1 ) }{y^2 - 3^2}[/tex]
Since both terms are perfect squares, factor using the difference of squares formula
[tex]a^{2}- b^2 = (a +b ) (a -b)[/tex] where a = y and b = 3
[tex]\frac{( y - 3) (y^2 + 1 )}{(y + 3 ) (y -3)}[/tex]
Evaluate the equation and rewrite the expression
[tex]\frac{y^2 + 1}{y + 3}[/tex]
Therefore, the reduce algebraic fraction is [tex]\frac{y^2 + 1}{y + 3}[/tex]
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The length of the base of an isosceles triangle is x. The length of a leg is 5x−4. The perimeter of the triangle is 102. Find x.
Answers
In the given isosceles triangle, the value of x is 10 units.
What is a triangle?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the value of 'x' will be:
Given triangle is an isosceles triangle. Then,
x + 5x - 4 + 5x - 4 = 10211x - 8 = 10211x = 102 + 811x = 110x = 110/11x = 10Therefore, in the given isosceles triangle, the value of x is 10 units.
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If 200 copies are made for $6.00, then what is the unit rate price per copy? How much will 150 copies cost?
Answers
To calculate the unit race price per copy, we can divide $6.00 by 200 copies:
[tex]\frac{6}{200}=0.03\text{ usd}[/tex]Each copy cost $0.03, to determine how much will cost 150 copies, we have to multiply the unit rate price by 150:
[tex]0.03\cdot150=4.5\text{ usd}[/tex]150 copies will cost $4.5
A supervisor finds the mean number of miles that the employees in a department live from work. He finds x Overbar = 29 and s = 3.6. Which mileage is within a z-score of -1.5?
Answers
The mean number of miles that the employees in a department live from work is 24.
What is a z-score?
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The z-score is given as
x = 29
s = 3.6
z = -1.5
Then the mean will be
[tex]-1.5 = \frac{29-u}{3.6}[/tex]
μ = 29 - 5.4
μ = 23.6 ≅ 24
Hence the answer is the mean number of miles that the employees in a department live from work is 24.
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Evaluate the expression shown below and write your answer as a fraction in simplest form.
\frac{4}{5}\div\frac{9}{5}\cdot\frac{7}{3}
5
4
÷
5
9
⋅
3
7
Answers
The rules of BODMAS are useful in calulating mathematical expressions involving many operators. The given expression can be simplified as a simple fraction 28 / 27.
What are the rules of BODMAS?The rules of BODMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.
The given expression can be written as,
4 / 5 ÷ 9 / 5 × 7 / 3
In the given expression there are three fractions separated by the sign of multiplication and division.
As per the rule of BODMAS, the division operator has the priority over multiplication operator.
Apply the rule mentioned above in the given expression to get,
4 / 5 ÷ 9 / 5 × 7 / 3
= 4 / 5 × 5 / 9 × 7 / 3
= 4 / 9 × 7 / 3
= 28 / 27.
Hence, the given expression is simplified to get the result as 28 / 27.
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What is the mean daily snowfall 8,3,12,1,1
Answers
Answer:25
Step-by-step explanation:
1. you place the numbers in order from least to greatest so 1,1,3,8,12
2. then you add those all up
3.then you divide how many numbers there are together
1+1+3+8+12=25
then you divide by 5 because that's how many numbers are shown for the daily snow fall
HOPE THIS HELPS
Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet. Which model shows how much money Ilya has all together?
Answers
The model is a linear function that shows $3.25 money that Ilya has all together
What is meant by a linear function?The phrase linear function relates to two distinct but related concepts in mathematics:
Some authors use the term "linear function" only for linear mappings that accept values in the scalar field; these are more frequently known as linear forms.
Calculus' "linear functions" qualify as "linear mappings" when (and only when) f(0,..., 0) = 0, or, equivalently, when the aforementioned constant b equals zero.
A linear function in calculus and related fields is one whose graph is a straight line, that is, a polynomial function of degree zero or one. The word affine function is commonly used to distinguish such a linear function from the other idea.
A linear function is also known as a linear map in linear algebra, mathematical analysis, and functional analysis.
Given,
Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet.
Total money=$1.40+$1.85
=$3.25
The model is a linear function that shows $3.25 money that Ilya has all together.
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I need help please hellp asap now pleas