Answer:
(a) expression: (6 yd)²; area: 36 yd²
(b) expression: (10 yd)²; area: 100 yd²
(c) Jones: 18; Evansbee: 50
(d) Jones: $89.82; Evansbee: $249.50
Step-by-step explanation:
You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.
Area of a squareThe formula for the area of a square of side length s is ...
A = s²
(a) Jones' gardenThe area of a square garden with a side length of 6 yards is ...
A = (6 yd)² . . . . . expression for the area
A = 36 yd² . . . . . the area of the garden
(b) Evansbee's gardenThe area of a square garden with a side length of 10 yards is ...
A = (10 yd)² . . . . . expression for the area
A = 100 yd² . . . . . the area of the garden
(c) Number of plants
The area used by the plants is the product of their number and the area taken by each.
For Jones' garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 36 yd²
n = (36 yd²)/(2 yd²/plant) = 18 plants
Mr. Jones can place 18 plants in his garden.
For Evansbee's garden, the number of plants that can be placed is ...
n(2 yd²/plant) = 100 yd²
n = (100 yd²)/(2 yd²/plant) = 50 plants
Mr. Evansbee can place 50 plants in his garden.
(d) Cost of plantsAt $4.99 each, the cost of plantings will be $4.99 times the number of plants.
Plants for Jones' garden cost 18($4.99) = $89.82.
Pants for Evansbee's garden cost 50($4.99) = $249.50.
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he
has 3 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 13 left over. How many
chairs does Liam have?
Liam has
chairs.
The most appropriate choice for linear equation will be given by-
Liam have 43 chairs
What is linear equation?
At first, we need to know the meaning of algebraic expressions.
Algebraic expressions consists of numbers and variables connected with addition,subtraction, multiplication and division sign.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions with an equal to sign
A one degree equation is known as linear equation.
Let the number of chairs in one row be x
Number of chairs in 8 rows = 8x
3 chairs are left
Total number of chairs = 8x + 3
Number of chairs in 6 rows = 6x
13 chairs are left
Total number of chairs = 6x + 13
By the problem,
[tex]8x+3=6x+13\\8x-6x=13=3\\2x=10\\x=\frac{10}{2}\\x=5[/tex]
Number of chairs Liam has =
[tex]6\times 5 + 13\\30+13\\43[/tex]
Liam has 43 chairs
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You pick a card at random. Without putting the first card back, you pick a second card at random.4567What is the probability of picking an even number and then picking an even number?Simplify your answer and write it as a fraction or whole number.
Given:
4 5 6 7
Given that you picked a card at random, without replacement, you then pick a second card at random.
Let's find the probability of picking an even number and then picking an even number.
Number of possible events = 4
Number of even numbers = 4, 6, ==> 2 even numbers.
Hence, to find the probability, we have:
[tex]\begin{gathered} P=\frac{2}{4}*\frac{1}{3} \\ \\ P=\frac{2*1}{4*3} \\ \\ P=\frac{2}{12}=\frac{1}{6} \end{gathered}[/tex]Therefore, the probability of picking an even number and then picking an even number is 1/6.
ANSWER:
[tex]\frac{1}{6}[/tex]A cylinder shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?
Question: A cylinder-shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?
Explanation:
The cylinder-shaped jelly has a volume of gelatin equal to its cylindrical volume. Therefore, we must find the volume of the given cylinder. The volume V of the cylinder with radius r and height h is given by the following formula:
[tex]V=h\pi r^2[/tex]Applying the data of the problem, we obtain:
[tex]V=h\pi r^2=6\text{ * }\pi\text{ * \lparen2}^\text{\rparen}^2\text{ = 24}\pi\text{ =75.398}[/tex]Answer: we can conclude that the correct answer is:
[tex]\text{ 24}\pi\text{ =75.398}[/tex]Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?
Printer B= 114 pages per 3 minutes. Printer B is the fastest printer. I did scratchwork on paper but I still sent it to you. Sorry my handwriting is sloppy. ; ) I hope it helps.
pls help. this is so confusing on how to find the p=S(t)=r+i part of the word problem.
Using a linear function, it is found that:
a) Sales are increasing at a constant rate of 30 purchases/month.
b) The linear function is: p = S(t) = 30t + 3990.
c) The total purchases will be of 5130 in June 2010.
d) The sales will be of 5400 in March of 2011.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have that:
The reference month is of April 2007, hence the intercept is of b = 3990.In 16 months, from April of 2007 to August of 2008, sales increased to 4470, hence the slope is given by: m = (4470 - 3990)/16 = 30.The slope of 30 is the constant rate of purchases per month, and the linear function is given by:
p = S(t) = 30t + 3990.
June 2010 is 3 x 12 + 2 = 38 months after April 2007, hence the purchases will be of:
S(38) = 30 x 38 + 3990 = 5130.
The sales will be of 5400 in t months after April 2007, for which:
S(t) = 5400
Hence:
30t + 3990 = 5400
t = (5400 - 3990)/30
t = 47 months.
One month shy of four year, hence in March of 2011.
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- Lana had a fixed budget for a party. She spent one third of the
budget on decorations. Of the money that remained, she spent
on refreshments and the rest on door prizes for the guests.
If she spent $60 on door prizes, what was her budget?
Lana's fixed budget for a party is $180.
How to find Lana's fixed budget for a party?Let x be Lana's fixed budget for a party.
Lana spent one-third of the budget on decorations.
x - 1/3x = 2x/3
Remaining money,
2x/3 -x + (2x/3-x)-x =0
Since she spent $60 on door prizes
-x/3 + 60 = 0
-x/3 = -60
x = 180
Lana's fixed budget for a party is $180.
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Larry and his brother wanted to put new carpet down in threerooms in his house. The three rooms measured 10' x 12, 13' x 15,and 12' x 12'. If the carpet Larry wants to use is $25.56 a sq. yd.and the roll of padding is $99 for a 30 sq.yd. roll, answer thefollowing questions. Remember that 1 square yard = 9 square feet.1. Total square footage to be covered with carpeting would besquare feet.2. How many square yards would that be?sq.yd.3. Based on the price of $25.56 a sq.yd., what would the total costbe for the carpeting? $4. To make sure Larry has enough padding, how many rolls wouldhe have to buy?What would that cost? $5. What would the total cost of the carpeting job be includingcarpet and padding? $
Find the area of each room and then add the three areas.
[tex]\begin{gathered} 10\times12=120 \\ 13\times15=195 \\ 12\times12=144 \\ \\ 120+195+144=459 \end{gathered}[/tex]The total square footage to be covered is 459.
Part 2)Since each square yard has 9 square feet, divide the square footage by 9 to find how many yards is that equal to:
[tex]\frac{459}{9}=51[/tex]Then, the area is equal to 51 square yards.
Part 3)The cost for each square yard is $25.56. Multiply that amount by 51 to find the total cost:
[tex]25.56\times51=1303.56[/tex]The total cost for the carpeting is $1303.56.
Part 4)Each roll of padding has 30 square yards. Since 51 yards must be covered, and two rolls would yield 60 square yards, then, the minimum amount of rolls needed is 2.
The cost for 2 rolls would be 2*$99 = $198.
Part 5)Add the cost of the two rolls of padding and the carpeting job to find the total cost:
[tex]\text{ \$}198+\text{ \$}1303.56=\text{ \$}1501.56[/tex]Then, the total cost of the carpeting job including the carpet and padding would be $1501.56.
Therefore, the answers are:
Part 1) 459 square feet.
Part 2) 51 square yards.
Part 3) $1303.56
Part 4) 2 rolls for $198
Part 5) $1501.56
Solve using substitution. y=103x + 4y = 19
We want to find the solutions for the following system
[tex]\begin{cases}y=10 \\ 3x+4y=19\end{cases}[/tex]We already know the value for the y variable, if we substitute this value on the second equation it is possible to find the x value.
[tex]\begin{gathered} 3x+4\cdot(10)=19 \\ 3x+40=19 \\ 3x=19-40 \\ 3x=-21 \\ x=\frac{-21}{3} \\ x=-7 \end{gathered}[/tex]And those are the results for our system
[tex]\begin{cases}x=-7 \\ y=10\end{cases}[/tex]Round 0.4275 to the nearest thousand
we have
0.4275
if we round to the nearest thousand, we look at the third digit of our number
0.4275
do you know the answer now?
0.42 is not correct
and only 2 decimals will be rounded to the nearest hundreth
becuase we have a 5 after 7, the number will be rounded up
0.428
this is the answer
if we would have for example
0.3521
the rounded to the nearest thousand would be 0.352
I will show you the pic
The general form of a linear equation is given by:
y = kx
where k is a constant.
From the given options you can notice that the only equation similar to the previous one is:
y = 1/6 x
Then, the previous equation is the linear equation.
Which graph correctly represents ? 1/5y - 1/2x > 2
A graph which represents the solution to this inequality is shown in the image attached below.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would evaluate and simplify the given inequality in order to determine the graph which represent its solution as follows:
1/5y - 1/2x > 2
Subtracting 2 both sides, we have:
1/5y - 1/2x - 2 > 2 - 2
1/5y - 1/2x - 2 > 0
(2y - 5x - 20)/10 > 0
2y - 5x - 20 > 0
2y > 5x + 20
Dividing both sides by 2, we have:
y > 5x/2 + 10
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parallel linessolve for x
We have two parralel lines with angles 32x + 4 and 34x - 2
From the figure, the angles are corresponding angles
Corresponding angles are equal
That is,
34x - 2 = 32x + 4
Collect the like terms
34x - 32x = 4 + 2
2x = 6
Divide both sides by 2
2x / 2 = 6 / 2
x = 3
The answer is 3
The length of a rectangular room is 12 feet more than 3 times the height of the room. The floor of the room has an area that is represented by the function below, where h is the height of the room in feet. A(R) 9h2 + 45h + 36 Which statement best describes the width of the room? A. The width is 3 feet shorter than the length. B. The width is 9 feet shorter than the length. C. The width is 9 feet longer than the height. D The width is 3 feet longer than the height.ill send a picture of the question
Okay, here we have this:
Considering the provided information, and that the area of a rectangle is the product of its length and width, we obtain the following:
[tex]\begin{gathered} Width=\frac{Area}{Length} \\ Width=\frac{9h^2+45h+36}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3\left(h+4\right)} \\ =3\mleft(h+1\mright) \\ =3h+3 \end{gathered}[/tex]Now, to know if the width is greater or less than the length, we will subtract it, then we have:
[tex]\begin{gathered} (3h+12)-(3h+3) \\ =3h+12-3h-3 \\ =12-3 \\ =9 \end{gathered}[/tex]Finally we obtain that the width is feet 9 shorter than the length, so the correct answer is the option B
Can anyone answer this
Answer:
add the number of sides then divide the number by the number of sides
Find the four terms of the arithmetic sequence given the 13th term (a_{13}=-60) and the thirty third term (a_{33}=-160).Given terms: a_{13}=-60 and a_{33}= -160Find these terms:a_{14}= Answera_{15}= Answera_{16}= Answera_{17}= Answer
Given:
13th term = -60
33rd term = -160
Find:
14th, 15th, 16th, and 17th term
Solution:
For us to determine the 14 - 17th term, we need to identify the common difference in this arithmetic sequence. The formula is:
[tex]\frac{a_{33}-a_{13}}{33-13}[/tex]Let's plug in the values of a₃₃ and a₁₃ in the formula above.
[tex]\frac{-160-(-60)}{33-13}[/tex]Then, solve.
[tex]\frac{-100}{20}=-5[/tex]Hence, the common difference between the terms is -5.
So, the next 4 terms after a₁₃ are shown below:
[tex]\begin{gathered} a_{14}=-65 \\ a_{15}=-70 \\ a_{16}=-75 \\ a_{17}=-80 \end{gathered}[/tex]
if you could give me the answer without explantion i would be happy to leave a good review
The coordinates of the fourth side are (6, -8)
Explanation:Let the coordinate of the fourth side be (x, y)
The diagonals of a parallelogram bisect eachother, so the midpoint of (-3, -2) and (x, y) is equal to the midpoint of (4, -4) and (-1, -6)
[tex]\begin{gathered} (\frac{x-3}{2},\frac{y-2}{2})=(\frac{4-1}{2},\frac{-6-4}{2}) \\ \\ (\frac{x-3}{2},\frac{y-2}{2})=(\frac{3}{2},-5) \\ \\ \frac{x-3}{2}=\frac{3}{2}\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(1) \\ \\ \frac{y-2}{2}=-5\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots.(2) \end{gathered}[/tex]Solving these equations:
x - 3 = 3
x = 3 + 3 = 6
and
y - 2 = -10
y = -10 + 2 = -8
The coordinates are (6, -8)
please answer this using the foil method[tex] {9x}^{2} + 60x + 100[/tex]
Answer
Given expression
[tex]9x^2+60x+100[/tex]By factorization, we have
[tex]\begin{gathered} 9x^2+30x+30x+100 \\ 3x(3x+10)+10(3x+10) \\ (3x+10)(3x+10) \end{gathered}[/tex]Now to check, using FOIL method, we have
F = First, i.e 3x(3x) = 9x²
O = Outer = 3x(+10) = +30x
I = Inner = +10(3x) = +30x
L = Last = +10(+10) = +100
Select the correct inequality and graph for the statement. Samuel gets 25 or more for mowing the lawn. PLSSS HELP!!
The statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
Given is the following statement - "Samuel will get 25 or more for mowing the lawn".
The given statement is -
Samuel will get $25 or more for mowing the lawn.
Assume that Samuel gets $x for mowing the lawn.
Then according to the question, we can write the inequality as -
x ≥ 25
" ≥ " sign to represent either 25 or more.
So, the inequality can be written as x ≥ 25 and the graph number [2] represents the correct graph.
Therefore, the statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
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[Refer to image attached for complete question]
identify the set of numbers that best describes each situation explain your choice. 9. the amount of money in a bank account
The sets of the real numbers are
Whole numbers
Integers
Rational numbers
Irrational numbers
The whole numbers mean positive integers with zero
The integers mean positive , negative whole numbers, and zero
Rational numbers mean
Graph the line y= 3x - 5 using the slope and y-intercept.
Step-by-Step Solution
Step 1: Identify the slope and y-intercept of the line.
y = 3x-5
The slope is m = 1.
(Type an integer or a fraction.)
The required slope m is 3 and the y-intercept is - 5.
What is a y-intercept?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Given : The line y = 3x - 5
This is of the form y = mx + c which is the equation of the line.
On comparing these two equations
Thus the slope is 3 .
And y intercept is :
y = 3x - 5 and when x = 0
y =- 5.
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If g(x)=5x, h(x)=√x, find the composition.
(g . h)(0)
( g . h ) ( 0 ) = _____
The value of the composition (g . h)(0) is 0
What is a function?A function can be defined as a mathematical law, expression of rule that explains the relationship between two variables in an equation.
These variables are;
The independent variableThe dependent variableThe functions are;
g(x) = 5xh(x) = √xThe composite function is gotten by substituting the value of x of the independent variable in the function.
The composite function (g . h)(0) is determined by substituting the value of x as h(x) in the function g(x), we get;
(g . h) = 5√x
Now, substitute the value of x as 0, we have;
(g . h)(0) = 5√0
Find the square root
(g . h)(0) = 5(0)
Find the product
(g . h)(0) = 0
Hence, the value is 0
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18. A student turned in the following incorrect work. - In what line was the mistake made? - What should the correct step be? - What is the correct final answer?
Be sure to describe your answer in 4-5 sentences.
Answer:
4y³/x³
Step-by-step explanation:
Line 1 is completely correct.
Line 2 has an error.
The 4/1 from line 1 should remain as 4/1 in Line 2, but the student wrote it as 1/4 on Line 2.
To fix it, rewrite Line 2, but change the first fraction, 1/4, to 4/1.
The correct final answer is 4y³/x³
Hello, I need some assistance with this homework question please for precalculusHW Q30
EXPLANATION
Since the degree is 6, the polynomial has 6 zeros:
Then, using the Complex Root Theorem, since the polynomial has 2 complex roots, thus the conjugate of 5 + i is 5 - i, and the conjugate of 7 - i is 7 + i:
In conclusion, the remaining zeros are: 5 - i, 7 + i
A triangle is placed in a semicircle with a radius of , as shown below. Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Solution:
Given the figure below:
The area of the shaded region is expressed as
[tex]area\text{ of shaded region = area of semicircle - area of triangle}[/tex]step 1: Evaluate the area of the semicircle.
The area of the semicircle is expressed as
[tex]\begin{gathered} area\text{ of semicircle=}\frac{1}{2}\times\pi r^2 \\ where\text{ r is the radius of the circle} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of semicircle = }\frac{1}{2}\times3.14\times4cm\times4cm \\ \Rightarrow area\text{ of semicircle =25.12 cm}^2 \end{gathered}[/tex]step 2: Evaluate the area of the triangle.
The area of the triangle is expressed as
[tex]\begin{gathered} area\text{ of triangle =}\frac{1}{2}\times base\times height \\ thus,\text{ we have} \\ area\text{ of triangle =}\frac{1}{2}\times8cm\times4cm \\ =16\text{ cm}^2 \end{gathered}[/tex]step 3: Evaluate the area of the shaded region.
Recall that
[tex]\begin{gathered} area\text{ of shaded reg}\imaginaryI\text{on = area of sem}\imaginaryI\text{c}\imaginaryI\text{rcle- area of tr}\imaginaryI\text{angle} \\ \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} area\text{ of shaded region = \lparen25.12 -16\rparen cm}^2 \\ =9.12\text{ cm}^2 \end{gathered}[/tex]Hence, the area of the shaded region is
[tex]9.12\text{ cm}^2[/tex]how much bags of fertilizer will brett need to cover the entire garden.
Area A = ?
Bag area covers = 54 ft2
Square Area S = 18ft X 18 ft
. = 324 ft2
Then now divide S/B
S/B = 324/54
. = 36/6
. = 6
Then answer is
Brett will need 6 bags of fertilizer
Choose two consecutive points on the graph and find the rate of change. Is the slope the same or different?
Choose two consecutive points on the graph and find the rate of change.
We will start with t = 1000 and t = 1500:
[tex]P(1000)=12.643(1.0027)^{1000}=187.4412[/tex][tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex]Remember that the rate of change is found by the difference in y over the difference in x.
[tex]RATEOFCHANGE=\frac{721.7263-187.4412}{1500-1000}[/tex][tex]RATEOFCHANGE=\frac{534.2851}{500}\approx1.0686[/tex]Let's do it now for t = 1500 and t = 2000.
[tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex][tex]P(2000)=12.643(1.0027)^{2000}=2778.9454[/tex]In this case the rate of change would be:
[tex]\text{rateofchange=}\frac{2778.9454-721.7263}{2000-1500}[/tex][tex]\text{rateofchange}=\frac{2057.2191}{500}\approx4.1144[/tex]The slopes are different and due to the type of function they will always increase when taking larger values.
Solve the equation for all complex and real solutions. Use potential zeros and synthetic division[tex]5x^4+7x^3+119x^2+175x-150=0[/tex]
Answer: the complex solutions are:
Step-by-step explanation: x = 5i , -5i , 3/5 ,-2
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function?
The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6].
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given function,
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6
The graph of this function has been plotted below,
The vertex is the point where the function is changing its sign of slope or turning point.
It is clear that at (-4,0) it is changing its slope of sign therefore (-4,0) will be the vertex.
The range is the interval where the function exists since the given function goes from y = 0 to y = 6 so [0,6] will be the range of the function.
Hence "The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6]".
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Here is a vertical algorithm that we can use to find 60.19 – 47.52.Which place value column(s) will require regrouping?Please see image below.
Regrouping happens when we need to "borrow" value from the higher order digits to perform a subtraction properly. This happens on the tenths, because we need to subtract 5 from 1, which we can't do normally. So we need to regroup from the ones and tens, in order to solve the problem. The correct answer is B.
Solve for n in the proportion 7/3 = n/21.