The number of homes in 2011 is 44,313
Explanation:Given that 57 homes are built each year, in 2002, there were 43,800 homes, then the next years have the number of homes as follows:
2003: 43,800 + 57
2004: 43,800 + 57 + 57
2005: 43,800 + 57 + 57 + 57
This goes on until 43,800 + 57n
where n is the number of years after 2002.
2011 is 9 years after 2002, so the number of homes will be:
43,800 + 57(9)
= 43,800 + 513
= 44,313
Water is drained at constant rate of 2 gallons per minute from a fish tank containing 28 gallons of water which equation represent the number of gallons of water remaining in the tank y based on the number of minutes t since water started draining from the fish tank where 0<_t_<14?
The equation represent the number of gallons of water remaining in the tank is y = 28 - 2t
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The water remaining is illustrated as y.
The time taken is t.
The appropriate equation will be:
y = 28 - (2 × t)
y = 28 - 2t
This illustrates the water remaining in the tank.
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Which of the following shows the values of −0.5, −2.8, 1.9, 0.9, and −1.7 plotted on a number line?
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.7 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 3, negative 1.9, negative 0.7, 0.8, and 1.9 are plotted.
A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.9, negative 2, negative 0.6, 0.9, and 1.9 are plotted.
The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."
Here the values are
-0.5,-2.8,1.9,0.9 and -1.7
The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7
The positive numbers are 1.9 and 0.9
The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions
Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."
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Translate this phrase into an algebraic expression. Seven more than the product of 17 and Julie's savings Use the variable j to represent Julie's savings.
17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.
What is Expression?Expression is a combination of variables, operators and numbers.
The given phrase is
"Seven more than the product of 17 and Julie's savings"
and j is variable to represent Julie's savings.
In the phrase we have Seven more than, it means we are adding 7 to something.
According to problem we are adding 7 to "product of 17 and Julie's savings"
Product means multiplying a number with another factor. Here the factor is julies saving j.
17j+7 is the translated algebraic expression.
Hence 17j+7 is the translation of Seven more than the product of 17 and Julie's savings.
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Determine the rule for translating ABC to A'B'C'
Correct answer is A, the rule for translating ABC to A'B'C' is left 2, up 9.
What does translating a triangle mean?An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. are frequently called slides. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."
A translation in geometry is a type of transformation that shifts a geometric figure in a certain direction without altering its size or orientation. The figures are congruent before and after the transformation since it is a type of stiff transformation.
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The nth term of a sequence is 2n - 6
a) Work out the first three terms of the sequence.
b) Work out the tenth term of the sequence.
Answer:
a) do the first three terms
Answer: a) -4, -2, 0 b) 14
Step-by-step explanation:
To find any term, we plug the number into the equation for n.
a)
1st term => 2(1) - 6 = 2 - 6 = -4
2nd term => 2(2) - 6 = 4 - 6 = -2
3rd term => 2(3) - 6 = 6 - 6 = 0
b)
10th term => 2(10) - 6 = 20 - 6 = 14
What is the slope of the line that passes through the points (-8, -1)(−8,−1) and (-8, -11)(−8,−11)? Write your answer in simplest form.
Answer:
Undefined slope
Step-by-step explanation:
Slope , m is equal to rise/run Or ( y1-y2) / ( x1 -x2)
This line is a vertical line at x = -8 And thus has undefined slope
(Because you cannot divide by zero)
Answer:
Undefined
Step-by-step explanation:
Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.
We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:
[tex]y=mx+b[/tex]
When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, all we have to do is plug in the values as such and solve:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]
From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.
At a butcher shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat. Express the number of pounds of pork he bought using a decimal.
The number of pounds of pork he bought in decimal is 12.21 lb
Decimal:
A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
For example 12.34 is a decimal.
Given,
At a butcher shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.
Here we need to find the number of pounds of pork he bought using a decimal.
First, we have to convert the given fractions into decimal then we get,
Amount of beef = 2 7/20
Which is equal to,
=> 2 + 7/20
=> 2 + 0.35 = 2.35 lb
Similarly, total amount of meat = 14 14/25
=> 14 + 14/25
=> 14 + 0.56 = 14.56
Therefore, the amount of pork is,
=> total amount of meat - the amount of beef
=> 14.56 - 2.35
=> 12.21.
Therefore, the the number pounds of pork in decimal is 12.21 lb.
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A pedestrian is walking at a speed of 3 km/hr. Express the distance in kilometers, d, as a function of time in hours, t.
The question format : d(t) =
This is because
distance = rate*time
Rate is another term for speed.
Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) Q(x) + R(x).
P(x) = 3x³-4x²-3x, D(x) = 3x - 4
P(x) =
The value of Q(x) = x² - 1
R(x) = 4
What is Long Division?
Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.
By long Division method:
x² - 1
_______________________________
(3x - 4) | 3x³ - 4x² - 3x
3x³ - 4x²
_________________
0 - 0 - 3x
- 3x + 4
___________________
0 + 4
Q(x) = x² - 1
R(x) = 4
Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1 ) + 4
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the long division method to find the result when 12x^{3}+5x^{2}-27x+1312x
3
+5x
2
−27x+13 is divided by 3x-13x−1. If there is a remainder, express the result in the form q(x)+\frac{r(x)}{b(x)}q(x)+
b(x)
r(x)
(hope it makes sense)
The solution of the polynomial division 12x³ + 5x² - 27x + 13 is divided by 3x - 1 is; 4x² + 3x - 8 + (5/(3x - 1))
How to carry out Polynomial Long Division?
We want to use long division method to solve the polynomial division when 12x³ + 5x² - 27x + 13 is divided by 3x - 1.
4x² + 3x - 8
-------------------------
3x - 1 | 12x³ + 5x² - 27x + 13
- 12x³ - 4x²
-----------------------------
9x² - 27x
- 9x² - 3x
-----------------------------
-24x + 13
- -2x + 8
-----------------------------
5
-----------------------------
Expressing the solution of the polynomial division in the given quotient and remainder form gives us; 4x² + 3x - 8 + (5/(3x - 1))
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6.0 x 10^4 ÷ 4.0 x 10^8
Scientific Notation Please
Answer:
1.5x10^12
1500000000000
Step-by-step explanation:
Simplify the expression.
X - 11 = -44 solve one step equation.
Answer: x = -33
Explanation:
Given the following question:
x - 11 = -44
Step 1: collect the like terms
x = -44 + 11
x = -33
Therefore, x = -33
The midpoint of GH is M(3, 6). One endpoint is H(6, 5). Find the coordinates of the other endpoint G.
The coordinates of the endpoint G is (0, 7).
The midpoint of the coordinate is the centre point which can be calculated by finding the average. So, the relation representing the endpoints and midpoint is as follows -
Midpoint (x, y) = ([tex] x_{1}[/tex] + [tex] x_{2}[/tex]/2), ([tex] y_{1}[/tex] + [tex] y_{2}[/tex]/2)
Keep the value in mentioned formula to find the endpoint G, represented as [tex] x_{1}[/tex] and [tex] y_{1}[/tex].
(3, 6) = ([tex] x_{1}[/tex] + 6/2) ([tex] y_{1}[/tex] + 5/2)
Relating the x and y values -
x value :
3 = [tex] x_{1}[/tex] + 6/2
[tex] x_{1}[/tex] + 6 = 3×2
[tex] x_{1}[/tex] + 6 = 6
[tex] x_{1}[/tex] = 6 - 6
[tex] x_{1}[/tex] = 0
y value :
6 = [tex] y_{1}[/tex] + 5/2
[tex] y_{1}[/tex] + 5 = 6×2
[tex] y_{1}[/tex] + 5 = 12
[tex] y_{1}[/tex] = 12 - 5
[tex] y_{1}[/tex] = 7
Thus, the coordinates of point G from the line GH is (0, 7).
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Select all the lines that are perpendicular to 3x – y = 10. A. y = 3x + 5 B. y = –13x + 17 C. x + 3y = 27 D. y – 2 = 13(3x + 36) E. y = 13x + 2
From the list given, the line that is perpendicular to 3x – y = 10 is x + 3y = 27. (Option C)
What is a perpendicular line?It is to be noted that lines that intersect at a right angle (90 degrees) are considered perpendicular lines.
To justify the above results, we recall that when two lines are perpendicular then the product of their slope is -1.
The slope is given by y = mx + c where m is the slope.
Hence, the slope of the given equation 3x -y = 10 is arrived at by re-writing the expression as follows:
Y = 3x -10 where
slope m₁ = 3
given Lets attempt to derive the slope of the options given:
1) y = 3x + 5
m₂ = 3
The product of the slopes are:
= m₁ x m₂
= 3 x 3
⇒ 9 ≠ -1
Therefore, this is not a perpendicular line.
2) y = -13x + 17 our new m₂ = -13
m₁ x m₂
⇒ 3 x -13
⇒ -39 ≠ -1
Again, this is not the required line.
3) x + 3y = 27 [divide all sides by 3]
y = -1/3(x) + 9
The new m₂ = -1/3
Compute for slope:
= 3 x - (1/3)
= -3/3
= -1
Hence, x + 3y = 27 is the perpendicular line.
4) y -2 = 13(3x + 36)
y = 39x + 468 +2
y = 39x + 470
New Slope (m₂) = 39
Solving to check the slope, we have:
m₁ x m₂ = 3 x 39
⇒ 117 ≠ -1.
Thus, we have our final answer as option C.
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The required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
What is the slope perpendicular line?
The slope of the perpendicular lines is equal to the inverse and of the opposite sign.
Here,
Standard equation of the line,
y = mx + c
The property of the perpendicular line states that the product of their slopes is equal to -1.
So the slope of the given line is m = 3,
Let the slope of the perpendicular line that we have to determine, be x
According to the property,
The slope of line × slope of perpendicular line = -1
3 × x = -1
x = -1/3
So looking forward to the option, the line that has a slope of -1/3 is x + 3y = 27. because
x + 3y = 23
Transform the above equation to standard form,
y = -1/3x + 23
From the above equation, the slope of the above line is m = -1/3,
Thus, the required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
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Thu has the same amount of money automatically deposited into a new savings account each week. After 2 weeks, she has $14. After 5 weeks, she has $35. The unit rate is measured in dollars per week. What is the constant of proportionality?
For the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
As given in the question,
For the saving account,
Amount deposited is directly proportional to the number of weeks
Let y be the amount deposited and x be the number of weeks
y ∝ x
y = kx
'k' is the constant of proportionality
As per data unit rate is measured in dollars per week
For y = $14 then x = 2 weeks
14 = 2k
⇒ k = $7
For y = $35 then x = 5weeks
35 =5k
⇒ k = $7
Therefore, for the given data of saving account, unit rate is measured in dollars per week then constant of proportionality is equal to $7.
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If what is the length of DF?
Answer:
DF = 13
Step-by-step explanation:
Congruent triangles:
In ΔABC & ΔDEF,
∠A = ∠D
∠C = ∠F
CB = FE
ΔABC ≅ ΔDEF {Angle Angle Side congruency}
DF = AC = 13
need asap pleaseeeeeeee
Answer:
c) f = 28
Step-by-step explanation:
Given problem,
→ f³ = 21952
Now the value of f will be,
→ f³ = 21952
→ f = ³√21952
→ [ f = 28 ]
Let's check the following,
→ 28³
→ (28 × 28) × 28
→ 784 × 28 = 21952
Hence, option (c) is correct.
Fill in the blanks to express the quantities given in ratio language. Ratios must be
expressed in simplest form.
Number of Animals in the Pet Store:
Animal Count
16 cats
8 dogs
For every __ cats in the pet store, there are __dogs.
Find the value of x.
(5x − 17)°
13
132
12
48
Answer:
its 12
Step-by-step explanation:
I need help with this
Answer:
113.85
Step-by-step explanation:
230*55% because 100%-45%=55% is 126.5
Then 126.5*90% because 100%-10%=90% which is 113.85
A scale drawing of a field is shown below.8 in.10 in.6 in.The drawing uses a scale of 1 in. = 14 ft. What is the area of the actual field?
We can multiply each side by 14ft yo find the value on feet and late calculate the area
[tex]\begin{gathered} 8\times14=112ft \\ 10\times14=140ft \\ 6\times14=84ft \end{gathered}[/tex]tha area formula is
[tex]A=\frac{b\times h}{2}[/tex]where b=84ft and h=112ft
[tex]\begin{gathered} A=\frac{84\times112}{2} \\ A=4704 \end{gathered}[/tex]the area is 4,704ft2
Elizabeth is posting 12 flyers for the science club and 20 for the music club. She wants to make all the locations identical, with the same combination of science club flyers and music club flyers. In addition, she wants to make sure that no flyers are left over. What is the greatest number of locations that Elizabeth can post at?
we have the following:
in this case we must find the largest divisor between the numbers 12 and 20, this number is 4:
[tex]\begin{gathered} \frac{12}{4}=3 \\ \frac{20}{4}=5 \end{gathered}[/tex]Therefore 3 flyers for the science club and 5 flyers for the music club. And it would be 4 places
Determine the range of the following graph:
Answer:
The range is the allowed values of y.
Set notation: { y | -9 [tex]\leq[/tex] y [tex]\leq[/tex] 0, y ∈ R}
Interval notation: [-9,0]
Hope that helps
What are the The values of X and why that satisfy this equation (x+yi)+(4+9i)=9-4i
The values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
In the question ,
the equation is given as
(x+yi)+(4+9i)=9-4i
to find the value of x and y , we solve LHS and RHS of the equation separately
So LHS =
(x+yi)+(4+9i)
x+yi+4+9i
Adding the real and imaginary terms , we get
(x+4)+(y+9)i which is equal to RHS that is 9-4i
So , on comparing , we get
x+4 = 9 and y+9 = -4
x= 9-4 and y = -4-9
x = 5 and y = -13
Therefore , the values of x and y that satisfy the equation (x+yi)+(4+9i)=9-4i is x = 5 and y = -13 .
The given question is incomplete , the complete question is
What are the The values of X and Y that satisfy this equation (x+yi)+(4+9i)=9-4i ?
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The average cost of producing x game disks for a computer is given by the function C(x)=2.6+5460/x. Find the number of game disks that must be produced for the average cost to be $4.70.
The number of game disks that must be produced for the average cost to be $4.70 is 2600.
Given:
The average cost of producing x game disks for a computer is given by the function C(x) = 2.6+5460/x
To determine the number of game disks that must be produced for the average cost to be $4.70.
Substitute the average cost in the equation and solve to find the value of x i.e. number of disks,
4.70 = 2.6 + 5460/x
4.70 - 2.6 = 5460/x
2.1x = 5460
x = 5460/2.1
x = 2600
Therefore, the number of game disks that must be produced for the average cost to be $4.70 is 2600.
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Please help!! Name the reciprocals for the equations
In picture
1. 3
_ x = 9
4
4
2. -4 — x
7
If n is a real number, then its reciprocal will be 1/n.
1. If the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex] then the value of x = 12.
2. If the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex] then the value of x = -7.
What is meant by reciprocals?The inverse of a value or a number is the definition of reciprocal in mathematics. If n is a real number, then its reciprocal will be 1/n. Reciprocals are used to convert division to multiplication when dividing fractions, which simplifies the division process.
1. Let the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex]
Multiply both sides by 4
[tex]$4 \cdot \frac{3}{4} x=9 \cdot 4$$[/tex]
Simplifying the above equation, we get
3x = 36
Divide both sides by 3
[tex]$\frac{3 x}{3}=\frac{36}{3}$$[/tex]
Simplify
Therefore, the value of x = 12.
2. Let the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex]
Switch sides
[tex]$\left(\frac{4}{7}\right) x=-4$$[/tex]
Multiply both sides by 7
[tex]$7 \cdot \frac{4}{7} x=7(-4)$[/tex]
Simplifying the above equation, we get
4x = -28
Divide both sides by 4
[tex]$\frac{4 x}{4}=\frac{-28}{4}$$[/tex]
Therefore, the value of x = -7.
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C = dn or C = 2rn
(What is the radius of a circle with a circumference of 25cm?)
Hello!
Let's take this problem step by-step:
What is the formula for the circumference of a circle:
[tex]\text{Circumference} = 2\pi *\text{radius}[/tex]
Since the circumference is 25 cm
[tex]25 = 2\pi *\text{radius}\\\\\text{radius} = \dfrac{25}{2\pi }[/tex]
Answer: [tex]\text{radius} = \dfrac{25}{2\pi }[/tex]
Hope that helps!
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Amy got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 19 cents per yard. If after that purchase there was $16.77 left on the card, how many yards of ribbon did Amy buy? pls answer this!
Answer:
price for one ribbon =19 cents
she got $20
20- 16.77 the rest from the money = 3.23
so she spends 3.23 from buying the ribbon
how much ribbon does she buy
3.23 ÷ 0.19= 17 ribbons
Solve the equation for x. −0.24x − 16.4 = 1.48 x = −62.2 x = 62.2 x = −74.5 x = 74.5
hurry pls
The solution of the given linear equation is x = -9.53
How to solve the equation for x?Here we have the linear equation:
-0.24*x - 16.4 = 1.48*x
To solve this, first we need to move all the terms with x to the left and the terms without x to the right.
-0.24*x - 1.48*x = 16.4
(-0.24 - 1.48)*x = 16.4
-1.72*x = 16.4
Now we can divide both sides by -1.72 to get:
x = 16.4/-1.72 = -9.53
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Answer: c) (is it c?)
Step-by-step explanation: c) x= - 74.5
0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4
0.24x= -17.88 (divide)
x= −74.5
there
i hope this helps!!
Select the pair that could be a reasonable approximation for the diameter and
circumference of a circle.
5 meters and 22 meters
19 inches and 60 inches
33 centimeters and 80 centimeters
Explain your reasoning.
Your answer
We know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.So, let 'D' be the diameter and 'C' be the circumference.
Calculate C as:
C = πD (π = 3.14)(A) D = 5 m and C = 22 m
C = πD C = 3.14 × 5C = 15.7 mSo, C = 15.7 m does not approximate 22 m.
(B) D = 19 in and C = 60 in
C = πD C = 3.14 × 19C = 59.66 inSo, C = 59.66 approximates 60 in.
(C) D = 33 cm and D = 80 cm
C = πD C = 3.14 × 33C = 103.62cmSo, C = 103.62cm does not approximate 80cm.
Therefore, we know that pair (B) (19 inches and 60 inches) can be a fair estimation of a circle's diameter and circumference.
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The correct question is given below:
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. * 1 point A. 5 meters and 22 meters. B. 19 inches and 60 inches. C. 33 centimeters and 80 centimeters.